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Calculation of 15N NMR chemical shifts: Recent advances and perspectives
Accepted Manuscript Calculation of 15N NMR chemical shifts: recent advances and perspectives Leonid B. Krivdin PII: DOI: Reference:
S0079-6565(17)30036-5 http://dx.doi.org/10.1016/j.pnmrs.2017.08.001 JPNMRS 1446
To appear in:
Progress in Nuclear Magnetic Resonance Spectroscopy
Received Date: Revised Date: Accepted Date:
20 July 2017 21 August 2017 21 August 2017
Please cite this article as: L.B. Krivdin, Calculation of 15N NMR chemical shifts: recent advances and perspectives, Progress in Nuclear Magnetic Resonance Spectroscopy (2017), doi: http://dx.doi.org/10.1016/j.pnmrs.2017.08.001
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Calculation of 15N NMR chemical shifts: recent advances and perspectives Leonid B. Krivdin A. E. Favorsky Irkutsk Institute of Chemistry, Siberian Branch of the Russian Academy of Sciences, Favorsky St. 1, 664033 Irkutsk, Russia Edited by Geoffrey Bodenhausen and David Neuhaus
ABSTRACT Recent advances in computation of 15N NMR chemical shifts are reviewed, concentrating mainly on practical aspects of computational protocols and accuracy factors. The review includes the discussion of the level of theory, the choice of density functionals and basis sets together with taking into account solvent effects, rovibrational corrections and relativistic effects. Computational aspects of
15
N NMR are illustrated for the series of
neutral and protonated open-chain nitrogen-containing compounds and nitrogen heterocycles, coordination and intermolecular complexes.
© 2018 Elsevier B.V. All rights reserved.
____________ E-mail address: [email protected]
Graphical abstract
Contents 1.
Introduction
2.
Computational protocols and accuracy factors
3.
4.
2.1.
Level of theory
2.2.
Functionals and basis sets
2.3.
Locally dense basis sets
2.4.
Solvent effects
2.5.
Rovibrational corrections
2.6.
Relativistic effects
2.7.
Practical recommendations
Structural applications 3.1.
Open-chain nitrogen-containing compounds
3.2.
Nitrogen heterocycles
3.3.
Protonated nitrogen-containing compounds
3.4.
Coordination complexes
3.5.
Intermolecular complexes and hydrogen bonding
3.6.
Biological applications
Conclusions Acknowledgement References
1. Introduction Recent advances in computational NMR (see reviews [1,2,3,4,5,6,7,8,9,10,11,12] including those on the relativistic level [13,14,15,16,17]) have had a profound impact on calculations of
15
N nuclear magnetic resonance chemical shifts, beyond the early
experimental papers reviewed in four fundamental compilations by Witanowsky, Stefaniak and Webb [18,19,20,21]. In the present compilation we have concentrated mainly on the computational protocols and accuracy factors of the calculation of
15
N
chemical shifts exemplified by a series of nitrogen-containing molecules, without paying too much attention to purely theoretical aspects. The review consists of two parts: the first concentrates mainly on existing computational protocols with special emphasis on the level of theory, the choice of density functionals and basis sets, while taking into account solvent effects, rovibrational corrections and relativistic effects; the second provides some practical examples for different organic and inorganic molecules including open-chain nitrogen-containing compounds, nitrogen heterocycles and their protonated forms, coordination and intermolecular complexes.
2.
Computational protocols and accuracy factors
2.1. Level of theory
Accurate calculations of Nuclear Magnetic Resonance (NMR) shielding constants include the evaluation of electron correlation effects, zero-point vibrational corrections, temperature effects, intermolecular interactions, solvent effects, and finally relativistic effects, as recently reviewed by Antušek and Jaszuńsky [22]. In this connection, the very first question arising before any calculations of molecular properties (including 15N NMR isotropic shielding constants and chemical shifts) can commence is the level of theory that should be applied. Semi-empirical quantum chemistry attempts to address two obstacles, namely slow speed and low accuracy, by omitting or parameterizing certain integrals based on experimental data, such as ionization energies of atoms and dipole moments of molecules, and neglecting electron correlation effects. As a result, semi-empirical methods are very fast, are applicable to large molecules, and may give accurate results
when applied to molecules that are similar to those used for parameterization. However, in this century, almost no one applies "good old" semi-empirical methods like the Moderate Neglect of Differential Overlap (MNDO), the Austin Model 1 (AM1) or the Parameterized Model 3 (PM3) family for the calculation of molecular properties like 15N NMR chemical shifts in organic molecules, probably with the exception of very large molecular systems comprising several hundreds or even thousands of atoms. At present, for the calculation of NMR parameters such as
15
N NMR chemical
shifts, the following levels of theory are generally applied: Density Functional Theory (DFT) and, alternatively, wave-function ab initio methods including uncorrelated Restricted Hartree-Fock (RHF), Møller-Plesset perturbation theory with electron correlation effects taken into account to second order (MP2), Coupled Cluster Singles and Doubles (CCSD), and Coupled Cluster Singles and Doubles with perturbative Triples corrections, CCSD(T). In addition to this, one can use Sauer's second-order polarization propagator family of methods [23,24,25,26,27,28,29], namely the Second-Order Polarization Propagator Approach (SOPPA), the Second-Order Polarization Propagator Approach in combination with second-order approximate Coupled Cluster to second order, SOPPA(CC2), and the Second-Order Polarization Propagator Approach in combination with Coupled Cluster Singles and Doubles, SOPPA(CCSD). Such methods are, however, a subject of more specialized theoretical reviews dealing with computational NMR [1,2,4,5,11,12,22]. With some exceptions, references to particular theoretical methods together with numerous basis sets and DFT functionals are not given in this review and can be found in the more theoretical reviews cited above. In the majority of papers dealing with calculations of
15
N NMR chemical shifts,
the much more economical DFT methods rather than time-consuming wave-function calculations are applied, so that in the present review we will mainly pay attention to the practical aspects of the DFT approach.
2.2.
Functionals and basis sets
Among the factors affecting the accuracy of calculation of
15
N NMR chemical
shifts at the DFT level, the choice of a proper combination of functional and basis set is of key importance. A good number of functionals and basis sets have been tested for the calculation of
15
N NMR chemical shifts, and this is well covered in the early review by
Alkorta and Elguero (dedicated in memoriam to Professor Lech Stefaniak) [30] published in 2003. Accordingly, in the present review we will concentrate mainly on the papers that appeared more recently. In one of the early papers by Kupka et al. [31]
15
N NMR isotropic shielding
constants of ammonia and HCN were calculated at the RHF and B3PW91 levels using correlation-consistent basis sets of Dunning aug-cc-pVXZ, X x = D, T, Q, 5 and 6. The 15
N NMR shielding constants appeared to converge monotonically to their Complete
Basis Set (CBS) values, and these calculations using augmented basis sets converged more rapidly than their non-augmented counterparts. This effect was slightly more pronounced for ammonia than for HCN. Interesting to note is that core-valence basis sets produced a further enhancement of the convergence for the 15N nucleus. In this study, the first detailed complete basis set approach was proposed testing the accuracy of fitting the 15
N NMR parameters using two- and three-parameter functions. In addition, the core-
valence basis sets produced further enhancement of the convergence for the nitrogen nuclei. The Hartree-Fock calculations (not taking into account electronic correlations) of CBS for 15N NMR isotropic shielding constants were closer to experiment than those of B3PW91. At the same time, the MP2-derived CBS values (taking into account electronic correlations), even limited to the smallest basis sets, showed the best agreement with experiment and theoretical benchmark studies. In a subsequent paper Kupka et al. [32] performed a systematic study of a basisset effect on 15N NMR nuclear shielding anisotropy in a set of simple nitrogen-containing molecules studied using the B3PW91 functional. In general, a similar pattern was observed for all compounds under study. The aug-cc-pVXZ correlation-consistent basis set appeared to predict smooth increases and convergeance of
15
N NMR shielding
anisotropy values with increasing cardinal zeta number, x. There was a significant gap observed between the values of the NMR parameters calculated with Pople's basis sets. Not surprisingly, the values and gaps were similar to those obtained with the significantly larger Dunning's aug-cc-pVDZ and aug-cc-pVTZ basis sets for the same set of compounds. In this paper, the convergence of DFT and RHF 15N NMR nuclear shielding anisotropy and tensor components predicted with cc-pVXZ and aug-cc-pVXZ basis sets has been evaluated for a model series of simple nitrogen-containing molecules N2, NH3, HCN and CH3CN. The first detailed CBS approach to computational 15N NMR has tested the possibility and accuracy of obtaining the anisotropy parameters using two- and three-
parameter fitting functions. In addition, an effective CBS approach was proposed for calculating reasonably accurate
15
N NMR anisotropic shielding parameters for larger
molecules, resulting in significant savings in computation time. The next paper in this series by Kupka and Lim [33] was devoted to the study of the basis sets used for calculations of 15N NMR shieldings and chemical shifts. Compared to the correlation-consistent basis sets, it was not known if polarization-consistent Jensen's pc-n basis sets (which were initially developed for HF and DFT calculations) could provide a monotonic and faster convergence toward the basis set limit for results at correlated levels, as well as better accuracy for a similar number of basis set functions. It was also not known whether the pc-n basis sets could efficiently compute second derivatives of energy, such as nuclear magnetic shielding tensors. To address these questions, in this paper the pc-n (n = 1-4), ccpVXZ, and/or aug-cc-pVXZ (X = D, T, Q, 5 and 6) basis sets were used to compute 15N NMR shieldings of the NH3 molecule at the RHF, B3LYP, MP2 and CCSD(T) levels of theory. The results showed that compared to the cc-pVXZ and aug-cc-pVXZ basis sets the pc-n basis sets yield faster convergence toward the basis set limit at the RHF, DFT, MP2 and CCSD(T) levels. Because the pc-n basis sets show faster convergence, fewer basis set functions were needed to reach the accuracy obtained with the aug-cc-pVXZ basis sets, enabling faster and more economical calculations of 15N NMR chemical shifts. The CBS approach at the B3LYP level for the calculation of NMR parameters was further extended [34] by applying Dunning's cc-pVXZ, cc-pCVXZ, cc-pVXZ-sd, ccpVXZ-sd+t (x = D, T, Q, 5 and 6) and Jensen's pcJ-n (n = 0, 1, 2, 3 and 4) basis sets after careful selection of data points used for fitting. To continue these studies, B3LYP calculations of the NMR parameters of the HOH and HOD isotopomers of water in chloroform-d [35] were performed within the CBS limit using Jensen's pcJ-n basis set, resulting in good agreement with experiment. Good performance of segmented contracted basis sets XZP (X = D, T, Q and 5) for obtaining nuclear isotropic shielding constants in the series of classical di- and tri-atomics using the BHandH Kohn–Sham basis set limit was shown [36]. The results of two- and three-parameter complete basis set limit extrapolation schemes obtained in this study were compared with experimental results and benchmark ab initio calculations. Similar convergence patterns of shieldings obtained from the calculations using general purpose XZP basis sets and from polarization-consistent basis sets pcS-n and pcJ-n (n = 0, 1, 2, 3 and 4), designed to
accurately predict magnetic properties, were observed. It was also shown that BHandH density functional markedly outperforms B3LYP method in predicting 15N shieldings and chemical shifts. In two related papers by the same author [37,38], B3LYP and BHandH density functionals were used to estimate nuclear magnetic isotropic shieldings of water and methanol in the complete basis set limit. Polarization-consistent pcS-n and pcJ-n (n = 0, 1, 2, 3 and 4) together with segmented contracted XZP (X = D, T, Q and 5) basis sets were used, and the results fitted well with simple mathematical formulas. The performance of these methods was assessed from the comparison with experiment and higher-level calculations. It is noteworthy that BHandH/pcS-n results approached the accuracy of the advanced CCSD(T) calculations. In two milestone papers by Kupka et al. [39,40] convergence patterns and limiting values of isotropic nuclear magnetic shieldings and nuclear spin-spin coupling constants for several small molecules including "nitrogen-oriented" N2 and NH3, were studied in the Kohn-Sham limit. Individual results of calculations using dedicated families of Jensen’s basis sets (pcS-n and pcJ-n) were fitted in the limit of the complete basis set using a simple two-parameter formula. Several density functionals were used. For comparative purposes, similar calculations were performed using non-empirical RHF, MP2, SOPPA, SOPPA(CCSD) and CCSD(T) methods. Finally, the CBS estimated results were critically compared with earlier reported literature data and experimental results. Among the 42 (!) studied DFT functionals (VXSC, HCTH, HCTH97, HCTH147, THCTH, M06L, B97D, B3LYP, B3P86, B3PW91, B1B95, MPW1PW91, MPW1LYP, MPW1PBE, MPW3PBE, B98, B971, B972, PBE1PBE, B1LYP, O3LYP, BHandH, BHandHLYP, BMK, M06, M06HF, M062X, tHCTHhyb, HSEh1PBE, HSE2PBE, PBEh1PBE, wB97XD, wB97, wB97X, TPSSh, X3LYP, LC-wPBE, CAM-B3LYP, WP04, KT1, KT2 and KT3), the KTn family of functionals produced the most accurate isotropic nuclear shieldings. These data were critically compared with the CBS estimated results together with those obtained at the non-empirical RHF, MP2, SOPPA, SOPPA(CCSD) and CCSD(T)
levels and available experimental results to give
preference to the Keal-Tozer's family of NMR-oriented exchange-correlation generalized gradient approximation functionals KTn. In a later publication [41] it was shown that a linear correlation exists between 15N NMR nuclear shielding constants of N2 and NH3 calculated within the CBS limit using
the family of Jensen's polarization-consistent basis sets pcS-n and those evaluated with different DFT and non-empirical methods (including 42 DFT functionals together with RHF, MP2, SOPPA, SOPPA(CCSD) and CCSD(T) used in combination with aug-ccpVTZ-J basis set). It was shown that the remaining basis set error of the aug-cc-pVTZ-J basis set is very similar in DFT and CCSD(T) calculations. As the aug-cc-pVTZ-J basis set is significantly smaller,
CCSD(T)/aug-cc-pVTZ-J calculations allowed in
combination with affordable DFT/pcS-n complete basis set calculations the prediction of 15
N NMR nuclear shieldings at the CCSD(T) level of nearly similar accuracy as those
obtained by fitting results from computationally demanding pcS-n calculations at the CCSD(T) limit. It was found that significant saving of computational efforts could thus be achieved by scaling inexpensive CCSD(T)/aug-cc-pVTZ-J calculations of
15
N NMR
nuclear isotropic shieldings with affordable DFT complete basis set limit corrections. To continue these studies, a rough estimate of CCSD(T)/CBS and MP2/CBS nuclear isotropic shieldings of non-hydrogen atoms for molecular systems of medium size by combining less demanding DFT/CBS approach and affordable calculations at CCSD(T)/pcS-2 and MP2/pcS-2 levels of approximation was proposed [42]. This scheme was able to decrease the absolute errors by a factor of 3 or more in comparison to CCSD(T)/pcS-2 and MP2/pcS-2 calculations. A number of functionals and basis sets used for the calculation of
15
N NMR
chemical shifts in the key nitrogen-containing heterocycles (azoles, oxazoles, thiazoles, azines) have been recently tested for better agreement of DFT calculations with experiment [43]. In the calculation of 15N NMR chemical shifts, the best result has been achieved with the KT3 functional used in combination with Jensen’s pcS-3 basis set resulting in a value of mean absolute error as small as 5 ppm for the range of more than 270 ppm in a benchmark series of 23 nitrogen-containing heterocycles with an overall number of 41 different
15
N NMR chemical shifts, as illustrated in Fig. 1. Results of this
study [43] are summarized in Figs. 2 and 3, where the mean absolute errors of 15N NMR chemical shifts calculated in the whole series of 23 compounds, as compared to experiment, are arranged by the DFT functionals (Fig. 2) and basis sets (Fig. 3).
Fig. 1. Correlation plot of 15N NMR chemical shifts calculated in a series of 23 key azoles, oxazoles, thiazoles and azines at the DFT-KT3/pcS-3 level versus experiment. Reproduced from ref. [43] with permission of John Wiley and Sons Inc.
Fig. 2. Mean absolute errors of 15N NMR chemical shifts calculated in the same series of 23 key azoles, oxazoles, thiazoles and azines arranged by DFT functionals for different basis sets, as compared to experiment. Reproduced from ref. [43] with permission of John Wiley and Sons Inc.
Fig. 3. Mean absolute errors of 15N NMR chemical shifts calculated in the same series of 23 key azoles, oxazoles, thiazoles and azines arranged by basis sets for different DFT functionals, as compared to experiment. Reproduced from ref. [43] with permission of John Wiley and Sons Inc. The main conclusion drawn from these data is that the best result in the calculation of
15
N NMR chemical shifts of the representative series of the nitrogen-containing
heterocycles at the DFT level was achieved with correlation-exchange Keal-Tozer's KT2 [44] and KT3 [45] functionals and Jensen's pcS-2 and pcS-3 basis sets [46] characterized by a mean absolute error of about 5 ppm across a range of about 300 ppm.
2.3.
Locally dense basis sets
The general idea of the so-called Locally Dense Basis Set (LDBS) [47,48] is very simple: it consists in a dramatic decrease of computational demands by employing a large high-quality basis set on a particular atom or on a particular atom and on its first bonding
sphere and much smaller basis sets elsewhere in the molecule, preserving high accuracy at much lower computational cost. This approach has been shown to be very effective in calculating NMR chemical shifts and spin-spin coupling constants within a general Gauge Including Atomic Orbitals (GIAO) approach, as exemplified in a number of recent publications by Russian authors [49,50,51,52,53,54,55,56,57,58,59,60]. To the best of our knowledge, no such approach has been implemented, at least systematically, to the
15
N NMR chemical shifts, and one of such rare examples is
presented in the paper by Samultsev et al. [43] who have chosen a benchmark set of the most representative five- and six-membered heterocycles - N-methylpyrrole, oxazole, thiazole, pyridine, pyrimidine and 1,3,5-triazine. For this series, they have performed calculations of
15
N NMR chemical shifts at the GIAO-DFT-KT3 level with 6-
311++G(d,p), aug-cc-pVTZ and pcS-3 on nitrogen within different LDBS schemes by using 6-31G, 6-311G, 6-31G(d), 6-311G(d), cc-pVDZ, pc-1 and pc-2 for the rest of the molecules. The 15N NMR chemical shifts calculated within different LDBS schemes for the subject series of heterocycles are compiled in Table 1, while the corresponding values of the Mean Absolute Error (MAE) as compared with the full basis set (FBS) results are given in Table 2.
Table 1. 15
N NMR chemical shifts (ppm) of the representative five- and six-membered nitrogencontaining heterocycles calculated at the GIAO-DFT-KT3 level within the LDBS approximation as compared to FBS results.
Compound
N Me N O
Rest of molecule
Nitrogen basis set (LDBS)
6-31G
6-311G
6-31G(d)
6-311G(d)
cc-pVDZ
FBS
6-311++G(d,p)
-211.6
-209.7
-214.4
-212.0
-211.2
-210.2
aug-cc-pVTZ
-215.3
-212.8
-216.8
-213.8
-213.0
-213.1
pcS-3
-221.8
-220.2
-224.3
-222.4
-220.8
-219.6
6-311++G(d,p)
-119.2
-118.1
-121.9
-120.9
-120.0
-119.1
aug-cc-pVTZ
-125.0
-123.5
-125.5
-123.9
-122.8
-122.9
pcS-3
-127.1
-127.1
-129.5
-128.3
-126.6
-124.5
N S
N N N
N
N N
6-311++G(d,p)
-67.5
-66.8
-65.0
-64.0
-63.3
-61.5
aug-cc-pVTZ
-73.9
-72.0
-68.5
-66.3
-67.7
-60.6
pcS-3
-74.6
-73.6
-70.2
-68.7
-64.8
-62.6
6-311++G(d,p)
-63.1
-60.7
-68.1
-65.4
-64.8
-62.6
aug-cc-pVTZ
-69.8
-66.5
-72.0
-68.7
-67.6
-66.3
pcS-3
-71.5
-69.1
-74.1
-70.9
-69.2
-65.5
6-311++G(d,p)
-77.6
-76.5
-84.6
-83.2
-82.4
-81.5
aug-cc-pVTZ
-84.2
-82.2
-88.0
-86.1
-84.8
-85.7
pcS-3
-86.5
-85.7
-90.2
-88.6
-86.7
-85.7
6-311++G(d,p)
-87.0
-86.5
-95.1
-94.6
-93.8
-93.4
aug-cc-pVTZ
-93.1
-91.8
-97.7
-96.9
-97.7
-97.6
pcS-3
-96.2
-95.5
-100.7
-99.8
-98.0
-98.2
Table 2. Mean absolute errors (ppm) of 15N NMR chemical shifts calculated at the GIAO-DFTKT3 level within different LDBS schemes as compared to FBS results.
Rest of molecule Nitrogen 6-31G
6-311G
6-31G(d)
6-311G(d)
cc-pVDZ
FBS
6-311++G(d,p)
3.1
3.4
3.5
2.0
1.2
0.0
aug-cc-pVTZ
4.1
3.2
3.3
1.4
0.9
0.0
pcS-3
4.6
3.8
5.8
4.1
2.6
0.0
As
follows
from
these
results,
the
GIAO-DFT-KT3/pcS-3//pc-2
recommended as one of the most effective LDBS schemes for the calculation of NMR chemical shifts.
2.4.
Solvent effects
was 15
N
In most cases solvent effects in 15N NMR calculations are taken into account using the Tomasi's Integral Equation Formalism Polarizable Continuum Model scheme (IEFPCM) [61] reviewed in [62], which is often referred to as simply PCM. The idea of PCM is rather simple: the solvent effect is simulated as an apparent charge distribution spread on the cavity surface not taking into account solute-solvent interactions at short distances (the so-called non-electrostatic effects), so that all solvent effects calculated within the PCM scheme are constrained not to take into account any specific solvation effects. This model works quite well when no specific intermolecular solvate-solvent interactions are expected. In contrast, in supermolecular model (SM) solvent molecules are added directly into calculation space to form solvation complexes. Usually this is done in PCM media and denoted as SM+PCM. As an example, a systematic study of solvent effects for 15N NMR chemical shifts of pyrrole, pyridine and related five- and six-membered nitrogen-containing heterocycles has been performed in three essential papers by a group of Russian authors [63,64,65]. In the first paper [63], solvent effects were examined for the
15
N NMR chemical
shifts of pyrrole and N-methylpyrrole, see Table 3. It was shown that considerable deviations were observed for 15N NMR chemical shifts calculated for pyrrole in methanol and water, presumably due to specific interactions of the former with solvent molecules, in particular due to the weak hydrogen bonding between the NH proton of pyrrole and oxygen atom of a solvent. This is obviously due to a considerable contribution of a specific solvation effect which should therefore be considered in an explicit way. On the other hand, the lack of specific interactions resulted in a small difference between calculated and experimental
15
N NMR chemical shifts of N-methylpyrrole. Obviously,
the continuum model may be used to calculate 15N NMR chemical shifts for compounds that do not form intermolecular hydrogen bonds with solvent molecules. It was also found [63] that increase in the solvent polarity on going from carbon tetrachloride to water leads to deshielding of the nitrogen atom in pyrrole and N-methylpyrrole, so that their resonance signals are shifted by as much as 8–12 ppm downfield. Thus it followed that a continuum solvent model was insufficient for an adequate description of solvent effects in
15
N NMR chemical shifts of pyrrole in polar solvents, making it necessary to
include at least one solvent molecule in an explicit way.
Table 3. Calculated
15
N NMR chemical shifts (ppm) of the supermolecules of pyrrole
and N-methylpyrrole with one molecule of solvent in IEF-PCM media using different functionals with TZP basis set.
B3LYP/TZP Compound
PBE0/TZP
B1PW91/TZP
Solvent
Experiment
δ(15N)
Absolute error
δ(15N)
Absolute error
δ(15N)
Absolute error
CCl4
-232.1
5.7
-237.9
0.1
-237.3
0.5
-237.8
CHCl3
-227.4
7.3
-233.3
1.4
-231.5
3.2
-234.7
(CH3)2CO
-228.0
2.3
-233.7
3.4
-232.7
2.4
-230.3
CH3OH
-218.5
11.4
-224.8
5.1
-231.2
1.3
-229.9
(CH3)2SO
-215.1
9.1
-221.6
2.6
-221.0
3.2
-224.2
H2 O
-216.2
10.3
-222.5
4.0
-221.8
4.7
-226.5
CCl4
-225.7
8.4
-232.9
1.2
-232.0
2.1
-234.1
CHCl3
-224.4
6.4
-231.7
0.9
-231.0
0.2
-230.8
(CH3)2CO
-219.8
11.6
-227.1
4.3
-226.4
5.0
-231.4
CH3OH
-218.2
13.2
-225.6
5.8
-224.5
6.9
-231.4
(CH3)2SO
-219.1
10.2
-226.5
2.8
-225.5
3.8
-229.3
H2 O
-217.4
9.5
-224.9
2.0
-224.1
2.8
-226.9
Table 4. Calculated
15
N NMR chemical shifts (ppm) and their absolute errors (ppm) of
the supermolecules of pyridine, pyridazine, pyrimidine, pyrazine and 1,3,5-triazine with one molecule of solvent in IEF-PCM media at the KT2/aug-сс-pVTZ level.
15
Compound
N
N
N
N N
N NMR chemical shift
Solvent Calculated
Experimental
Absolute error
CCl4
-60.7
-60.5
0.2
CHCl3
-67.9
-68.7
0.8
CH3OH
-74.5
-81.1
6.6
H2 O
-75.3
-84.3
9.0
(CH3)2CO
-73.8
-61.8
12.0
(CH3)2SO
-74.9
-63.1
11.8
CCl4
32.4
29.4
3.1
CHCl3
22.6
19.0
3.6
CH3OH
13.4
6.3
7.0
H2 O
12.3
-6.2
18.5
(CH3)2CO
14.4
25.9
11.4
(CH3)2SO
12.8
20.9
8.1
CCl4
-81.5
-81.6
0.1
CHCl3
-87.4
-86.2
1.2
CH3OH
-92.8
-90.8
2.0
H2 O
-93.5
-97.1
3.7
(CH3)2CO
-92.2
-83.4
8.8
(CH3)2SO
-93.2
-83.9
9.3
N N
N
N N
CCl4
-47.2
-43.4
3.9
CHCl3
-52.9
-47.8
5.1
CH3OH
-58.1
-51.7
6.4
H2 O
-58.8
-59.0
0.3
(CH3)2CO
-57.6
-44.9
12.7
(CH3)2SO
-58.5
-45.3
13.2
CCl4
-93.8
-95.9
2.1
CHCl3
-98.9
-98.1
0.8
CH3OH
-103.5
-100.3
3.1
H2 O
-104.0
-106.3
2.3
(CH3)2CO
-102.9
-97.4
5.5
(CH3)2SO
-103.7
-98.1
5.7
In the second paper from this series [64], solvent effects were studied in the
15
N
NMR chemical shifts of a classical series of azines - pyridine, pyridazine, pyrimidine, pyrazine and 1,3,5-triazine in different solvents calculated with the use of Keal-Tozer's KT2 functional in combination with Dunning's aug-cc-pVTZ basis set, see Table 4. It was found that Tomasi's polarizable continuum model provides an appropriate simulation of solvation effects in weak polar aprotic solvents but that this model is clearly insufficient for the description of polar solvent effects, in particular of specific solvation via the formation of intermolecular complexes between solvent and solute. Based on these results, it was found that the most efficient way to take into account solvent effects was using the IEF-PCM model for non-polar solvents and a supermolecular approach (with at least one solvent molecule being included into calculation space in an explicit way) for specific solvation, typical of polar solvents. As an example, Figs. 4 and 5 show the supermolecules of, respectively, pyrrole and pyridine, with different solvents of different polarity studied in [65].
Fig. 4. Equilibrium geometries of supermolecules (1:1) of pyrrole with different solvents optimized at the MP2/6-311++G(d,p) level with taking into account bulk solvent effect within the IEF-PCM scheme. The salient interatomic distances are given in Å. Reproduced from ref. [65] with permission of John Wiley and Sons Inc.
Fig. 5. Equilibrium geometries of supermolecules (1:1) of pyridine with different solvents optimized at the MP2/6-311++G(d,p) level with taking into account bulk solvent effect within the IEF-PCM scheme. The salient interatomic distances are given in Å. Reproduced from ref. [65] with permission of John Wiley and Sons Inc.
As was shown in the same paper [65] (the third in this series), in some cases inclusion of more than one molecule of solvent into the calculation space could result in much improved agreement of calculation with experiment. It was found that the largest absolute error for the IEF-PCM scheme was observed for pyridazine in water (27.9 ppm). Undoubtedly, this is due to a strong specific solvation of pyridazine molecule by water, which is not accounted for in full by adding only one molecule of water into calculation space, resulting in unreasonably large absolute error of 15.5 ppm. Following this idea, calculations of 15N NMR chemical shift of pyridazine in water were performed [65] using the supermolecular scheme (1 : n), that is, adding consequently 1, 2, …, n molecules of water into calculation space of pyridazine, all placed into the IEF-PCM cavity. These results are illustrated in Fig. 6, and it is seen that the absolute error for the gas phase (solvent effect is not taken into account) is unreasonably large (51.8 ppm); that it is somewhat smaller, though still large, when the solvent effect is treated within the IEFPCM scheme (27.9 ppm); and that it sharply decreases with n when the supermolecule (1 : n) solvation model is applied, reaching 15.5 ppm at n = 1, 6.7 ppm at n = 2 and 5.6 ppm at n = 3. It thus appears that further increasing of the number of water molecules placed into calculation space makes no sense because at n > 2 the absolute error becomes less than mean absolute error of the IEF-PCM and supermolecular schemes in the whole series of compounds under study.
Fig. 6. Absolute errors of 15N NMR chemical shift of pyridazine in water calculated at the GIAO-DFT-KT3/pcS-3//pc-2 level using different solvation models to account for solvent effect. The most characteristic interatomic distances in the solvate are given in Å. Reproduced from ref. [65] with permission of John Wiley and Sons Inc. 2.5.
Rovibrational corrections
For a meaningful comparison of theory with experimental data, the so-called rovibrational corrections to the nuclear shieldings are necessary. Rovibrational and temperature effects play an important role in theoretical studies of
15
N NMR chemical
shifts, including vibrational corrections, rotational contributions, temperature averaging and secondary isotope effects [66]. One such study was that of Kupka et al. [39] for the
15
N NMR of the simplest
diatomic - the molecule of N2. In this paper, CBS-predicted theoretical 15N NMR nuclear shieldings calculated at experimental equilibrium geometry were compared to empirical equilibrium values including vibrational correction terms obtained from separate calculations. The contributions of Zero-Point Vibrations (ZPV) were calculated at the DFT (BHandH/pcS-2, BHandH/pcS-3) and MP2 levels with a pcS-3 basis set. In most cases, MP2 provided larger absolute corrections than those obtained at the DFT level. It was found that inclusion of the vibrational corrections leads to smaller shielding tensor values, and does not improve the overall agreement of 15N NMR nuclear shieldings with experimental results. The vibrational corrections calculated in this study seemed to be important, but their contribution might be smaller than the error of the equilibrium values. In a more recent paper [67] vibrational corrections were calculated at the CCSD(T) level for the chemical shifts of the noble gas dimers and the second-row, Ne2 in particular. The ZPV corrections to the values at the optimized geometries were found to be very small (<1 ppm) and did not reflect the large variations in the absolute shieldings. However, although the ZPV corrections were thus negligible for the dimer nuclear shieldings, they were more important for the dimer chemical shifts. Relative to the values at the optimized geometries, the ZPV-averaged chemical shifts were accordingly 43, 11, 5 and 3% smaller for Ne2, Ar2, Kr2 and Xe2. Since all other calculations in this work were carried out at the experimental geometries, it was, however, more relevant to compare with those values at experimental geometries. Compared to these values, the ZPV
averaged chemical shifts for Ne2, Ar2 and Kr2 were reduced by accordingly 38, 18 and 42%, while for Xe2, the chemical shift was actually increased by 3%. A series of further recent publications by the same team (principal authors: Buczek and Kupka) devoted to harmonic and anharmonic vibrational modes in the Kohn-Sham limit for simple molecules has recently appeared [68,69,70,71,72,73,74]. In particular, it was shown [68] that the calculated wavenumber of the anharmonic asymmetric stretching mode is very sensitive to grid size for large basis sets which was not observed for harmonic modes. As a result, BLYP-calculated anharmonic frequencies consistently underestimated observed wavenumbers. It was shown that increasing the Pople's basis set size did not lead to improved agreement between anharmonic frequencies and experimental values. In the next paper in the series [69] it was demonstrated that the anharmonic frequency of the diagnostic amide vibration C=O in gas phase and in solution was significantly closer to experiment than was the case for the corresponding harmonic frequency. Both harmonic and anharmonic calculated frequencies of the C=O stretching mode decreased linearly with solvent polarity. However, an unphysical behavior of solvent dependence of some low frequency anharmonic amide modes of formamide was found, probably due to the presence of strong anharmonicity and Fermi resonance. In the third paper from this series [70] a linear correlation between harmonic and anharmonic frequencies of water calculated at the B3LYP level of theory was observed with a number of basis sets. Similar relationships were found in calculated data for both the gas phase and solution for several small molecules. The proposed approach was tested successfully
on a larger
molecule
of
E
and
Z isomers
of
N-acetyl-α,β-
dehydrophenylalanine-N′,N′-dimethylamide [71]. In this paper, solvent effect was approximated using a simple PCM model, the pc-n basis sets were selected, and the CBS results were estimated with the two-parameter formula for the corresponding B3LYP Kohn–Sham limits, calculated in the gas phase and in solution. However, no unique method was suggested that correctly reproduced fundamental modes in gas phase. In the case of water all studied methods performed very similarly. A singularity was observed for some vibrational modes sensitive to solvent effect. In two recent publications from this series [72,73] the ZPV corrections were examined in cytosine and ethylene. Thus the applicability of the popular and efficient B3LYP hybrid density functional and medium-size Pople type basis set in combination
with a computationally expensive anharmonic model to obtain a more accurate theoretical structure, vibrational frequencies and NMR parameters of cytosine was tested [72]. This paper included prediction of cytosine equilibrium and rovibrationally averaged structures and harmonic and anharmonic vibrational frequencies in the gas phase and DMSO solution. In comparison with initial harmonic data, a significantly better agreement between scaled and anharmonic frequencies versus experiment was observed. On the other hand, the regular convergence patterns of harmonic and anharmonic vibrational parameters towards the Kohn–Sham complete basis set limit in water were demonstrated for the first time [73]. The authors examined the performance of the vibrational perturbation scheme implemented using BLYP and B3LYP in combination with two Pople's basis sets, 6-311++G** and the much larger 6-311++G(3df,2pd), the polarization consistent basis sets pc-n, aug-pc-n and pcseg-n (n = 0, 1, 2, 3, 4) together with correlation-consistent basis sets cc-pVXZ and aug-cc-pVXZ (X = D, T, Q, 5 and 6). The BLYP-calculated harmonic frequencies were found to be markedly closer to the experimental values than were the B3LYP-calculated harmonic frequencies, while the calculated
anharmonic
frequencies
consistently
underestimated
the
observed
wavenumbers. The different basis set families gave very similar estimated values for the CBS parameters. The anharmonic frequencies calculated with B3LYP/aug-pc-3 were significantly higher than those obtained with pc-3 basis set. However, applying the augpcseg-n basis set family alleviated this problem. Utilization of B3LYP/augpcseg-n basis sets instead of B3LYP/aug-cc-pVXZ (the latter being less computationally expensive) was suggested for medium-sized molecules. It was also found [73] that harmonic BLYP/pc-2 calculations produced fairly accurate frequencies as compared to experiment. In the most recent study by Faber et al. [74] the method and basis set dependence of the zero-point vibrational corrections to NMR shielding constants and anisotropies have been investigated. A systematic comparison has been made at the MP2, CCSD and CCSD(T) levels together with Kohn–Sham density functional theory with the B3LYP exchange-correlation functional methods in combination with the second order vibrational perturbation theory approach for the vibrational corrections. The results showed that basis set convergence of the vibrational corrections was not monotonic and that very large basis sets were needed before a reasonable extrapolation to the basis set limit could be performed. Furthermore, the results of this study suggested that coupled cluster methods and a decent basis set were required before the error of the electronic
structure approach was lower than the inherent error of the second order vibrational perturbation theory approach.
2.6.
Relativistic effects
Relativistic effects evaluated from relativistic two- and four-component Hamiltonians play a major role in the calculation of NMR parameters, as derived and exemplified in a number of very recent [75,76,77,78,79,80,81,82,83,84,85,86] as well as earlier [87,88,89,90,91,92,93,94,95,96,97] publications by Aucar and coworkers; see also reviews on relativistic calculations of NMR parameters [13,14,15,16,17]. These cited publications outline some basic concepts of relativistic quantum chemistry and recent developments of relativistic methods for the calculation of NMR shielding constants, indirect nuclear spin-spin coupling and electric field gradients (nuclear quadrupole coupling). Density functional methods have been very successful in calculations of molecular properties, despite a number of problems related to approximations in the functionals. In particular, for heavy-element systems, the large electron contribution and the need for a relativistic treatment often restrain the application of correlated wave function ab initio methods [16]. As a matter of fact, almost nothing is known about relativistic effects in
15
NMR
chemical shifts and it is generally believed that they are next to negligible, which would make it safe not to take them into account in practical calculations. However, for
15
NMR
chemical shifts, such effects may be expected when nitrogen atom is bonded to, or in close proximity to, a heavy element. Examples of the first case are very scarce because chemical compounds containing N-X bonds (where X is a heavy element) are rather uncommon. More examples can be found for N-C-X, N-C-C-X or N-C-C-C-X moieties, however, these long-range relativistic effects are generally believed to be negligible and not worth studying. For these reasons, documentation of relativistic effects in
15
NMR
chemical shifts are very scarce in the literature. Nonetheless, one such rare example is reported in a very recent publication by Samultsev et al. [98], who studied the long‐range β‐ and γ‐relativistic effects of halogens in 15N NMR chemical shifts of 20 halogenated azines (pyridines, pyrimidines, pyrazines, and 1,3,5‐triazines). Relativistic effects were shown to be inessential for fluoro‐, chloro‐,
and bromo‐derivatives (1–2 ppm in average for bromine and much less for chlorine and fluorine). However, for iodo-containing compounds, β‐ and γ‐relativistic effects are important contributors to the accuracy of the
15
N NMR calculation. Indeed, taking into
account long‐range relativistic effects essentially improves the agreement of calculation with experiment. Thus, mean average errors of the 15N NMR chemical shifts of the title compounds calculated at the non‐relativistic and full four‐component relativistic levels in gas phase are accordingly 7.8 and 5.5 ppm for the range of about 150 ppm. Taking into account solvent effects within the PCM scheme marginally improves agreement of computational results with experiment, decreasing MAE from 7.8 to 7.4 ppm and from 5.5 to 5.3 ppm at the non‐relativistic and relativistic levels, respectively (See Fig. 7). The best result (MAE 5.3 ppm) was achieved at the four-component relativistic level using Keal and Tozer's KT3 functional used in combination with Dyall's relativistic basis set dyall.av3z while taking into account solvent effects within the polarizable continuum solvation model. Such long‐range relativistic effects play a major role (of up to dozen of parts per million) in the
15
N NMR chemical shifts of halogenated nitrogen‐containing
heterocycles, and are especially crucial for iodine derivatives. Thus, this effect should apparently be taken into account for practical purposes.
Fig. 7. Mean absolute errors of 15N NMR chemical shifts in the series of 20 halogenated azines (pyridines, pyrimidines, pyrazines, and 1,3,5‐triazines) calculated at the non‐relativistic and four‐component relativistic KT3/dyall.av3z levels. Solvent effects are taken into account within the non‐relativistic IEF‐PCM solvation model. Reproduced from ref. [98] with permission of John Wiley and Sons Inc. More examples can be found in heavy metal complexes with nitrogen-containing ligands such as those reported in the paper by Pazdersky et al. [99], where an attempt was made to take into account relativistic effects at the two-component Zeroth Order Regular Approximation contributions to
15
(ZORA)
level
accounting
for
both
scalar
relativistic
N NMR chemical shifts (Darwin correction and mass-velocity
correction together with spin-orbit contribution) in gold(III), cobalt(III) and rhodium(III) chloride complexes with pyridine, 2,2'-bipyridine and 1,10-phenanthroline. However, ZORA calculations have generally resulted in errors comparable to those obtained by the effective core potential methods that do not take into account relativistic effects. In this paper, the inclusion of spin-orbit relativistic interactions resulted in slightly better agreement with experiment only in the case of the heaviest Au(III) central ion in this series, and resulted in almost no effect in Co(III) and Rh(III) chloride complexes. In the recent paper by Jankowska et al. [67] relativistic corrections were reported for the noble gas dimers. In this paper, relativistic corrections were calculated with the scalar and spin-orbit zeroth-order regular approximation Hamiltonian in combination with the large Slater-type basis set QZ4P as well as with the four-component Dirac– Coulomb Hamiltonian using Dyall’s acv4z basis set. The relativistic corrections to the nuclear magnetic shieldings and chemical shifts were combined with CCSD(T) calculations using a very large polarization consistent basis set, aug-pcSseg-4. The size of the relativistic contribution to nuclear shieldings were essentially the same for the noble gas dimers and free atoms. At the Hartree-Fock level they were <0.1% (He), 0.6% (Ne), 1.7% (Ar), 5.8% (Kr), and 13% (Xe) of the total ZORA values and <0.1%, 1.1%, 2.9%, 9.5%, and 19.6% of the total four-component relativistic values, respectively. This is by far a more important contribution as compared to both electron correlation and vibrational corrections. It followed that relativistic corrections to helium and neon nuclear magnetic shieldings could safely be omitted in nuclear shielding calculations. For the chemical shifts of the noble gas dimers, relativistic corrections almost cancel each other (which is referred to as "mutual compensation of errors"), so that ZPV corrections
become more important than relativistic corrections, and this statement could be safely extended to 15N NMR chemical shifts.
2.7.
Practical recommendations
Level of theory, functionals and basis sets. Based on our experience of calculating 15
N NMR chemical shifts for medium-sized nitrogen-containing compounds, for practical
purposes we recommend using the DFT level with Keal and Tozer's generalized gradient exchange-correlation functional, KT2, and generalized gradient functional with the gradient-corrected exchange and correlation terms, KT3, in combination with Jensen's NMR-oriented pcS-2 and pcS-3 basis sets on nitrogen(s) and pc-2 elsewhere in the molecule within the LDBS scheme. Solvent effects. For all practical calculations of
15
N NMR chemical shifts, we
recommend taking into account solvent effects at the IEF-PCM level when no specific solute-solvent interactions are expected, and at the supermolecular level otherwise. Rovibrational corrections and relativistic effects. Rovibrational corrections play a major role in the calculation of 15N NMR chemical shifts. However, their evaluation even at the uncorrelated level with small basis sets is extremely computationally demanding, so that unfortunately in most cases they can be calculated only for very small molecules. Relativistic effects are also very time consuming and computationally demanding but fortunately they are negligibly small for
15
N NMR chemical shifts provided no heavy
atom is bonded to a nitrogen atom directly, and such cases are very rare in practice. So, in the majority of cases, relativistic effects could safely be neglected in practical calculations. Converting calculated shielding constants to chemical shifts. The term "shielding constant" originates in the concept of the effective nuclear charge, which may be defined as the actual nuclear charge minus the screening effect caused by the electrons intervening between the nucleus and valence electrons. In other words, the actual charge is equal to what is expected from a certain number of protons, but minus a certain amount of charge from the electrons. Shielding constants consist of diamagnetic and paramagnetic parts. The diamagnetic term describes the net electron density around the nucleus, while the paramagnetic shielding term arises from the perturbation of the ground state wave
function due to the coupling between electronic orbital momentum and the external magnetic field. Application of an external magnetic field induces electronic currents that, in turn, generate an additional local magnetic field. In atoms, which are spherically symmetric, these currents are purely diamagnetic in origin and the resulting local magnetic field opposes the external field leading to shielding of the atomic nucleus (lowering of the resonance frequency). However, in molecules, the circulation of electronic currents around the nucleus is hindered due to the presence of other nuclei and electrons revolving about them, and this deviation from spherical symmetry leads to the emergence of an additional contribution to the total nuclear shielding, which is known as the paramagnetic term. Because the paramagnetic contribution opposes the diamagnetic shielding, this results in deshielding (an increase in the resonance frequency) of the target nucleus as compared to an isolated atom [11]. Calculated
15
N absolute shielding constants should be converted into
15
N NMR
chemical shifts as recommended by IUPAC [100] using the equation δ = (σo – σ)/(1 - 10-6 σo), where σ and σo (ppm) are the
15
(1)
N NMR isotropic absolute shielding constants of,
respectively, a compound under consideration and neat nitromethane used as a standard. For this standard, a value of σo = -139.5 ppm was evaluated at the KT3/pcS-3 level [65] for the individual molecule of nitromethane and σo = -140.9 ppm calculated by the same authors at the same level of theory for the optimized cluster of the mostly computationally achievable five molecules of nitromethane in IEF-PCM continuum (averaged over all nitrogens in the intermolecular complex modelling neat liquid phase). It is interesting to note that an absolute 15N NMR shielding scale was proposed long ago by Jameson et al. [101] based on extrapolating
15
N NMR gas phase measurements to a
zero-density limit as well as molecular beam experiments, giving the absolute
15
N
shielding constant of neat nitromethane of -135.8 ppm, which is rather close to both values calculated most recently at the KT3/pcS-3 level. Software. Based on our experience, among dozens of software packages which might be used for the calculation of 15N NMR chemical shifts at the non-relativistic and relativistic levels we recommend the following: Geometry optimization: GAMESS [102], GAUSSIAN [103];
Non-relativistic calculations of 15N NMR chemical shifts: DFT, RHF, RPA levels - DALTON [104], GAUSSIAN [103]; MP2, CCSD, CCSD(T) levels - CFOUR [105]; Rovibrational corrections to 15N NMR chemical shifts: DFT, RHF, RPA levels - DALTON [104]; MP2, CCSD, CCSD(T) levels - CFOUR [105]; Relativistic calculations of 15N NMR chemical shifts: two-component level - ADF [106]; four-component level - DIRAC [107].
3. 3.1.
Structural applications Open-chain nitrogen-containing compounds
This Section covers compounds that contain side-chain nitrogen atoms, i.e. those that are not part of a heterocyclic moiety. In an early publication by Schraml et al. [108],
15
N NMR chemical shifts were
calculated at the GIAO-B3LYP/6–31+G∗ level in an extensive series of para-, meta- and ortho-substituted benzonitriles, X–C6H4–CN, and compared with thorough experimental measurements. The former exhibited the expected positive correlations with Hammett substituent constants, and they fitted well with the dual substituent parameter analysis including field and resonance σ-constants and correlated with the
13
C substituent
chemical shifts of the nitrile carbon. The deviations noted for hydroxyl derivatives were shown to be due to the interaction of the nitrile nitrogen with the OH group. The negative correlations with 13C substituent chemical shifts were explained by the polarization of the C≡N bond. Good correlations between DFT calculated and observed 15N NMR chemical shifts signified that the calculations, at the level used, are useful, provided that sufficient care is taken not to include compounds involving specific interactions. More recently, a theoretical and experimental
15
N NMR study of five
nitrobenzene-1,2-diamines has been carried out [109]. The combination of experimental results together with DFT calculations has resulted in a very coherent picture of
15
N
NMR chemical shifts in a series of nitro-o-phenylenediamines. It was found that calculated
15
N NMR chemical shifts for the nitrogen atoms can be analyzed using an
additive model for substituents, providing the rotational barriers around amino groups are sufficiently low. In a continuation of this study,
15
N NMR chemical shifts of eighteen
aliphatic linear amines, from methylamine to stearylamine, have been experimentally studied and theoretically calculated at the GIAO-B3LYP/6-311**G(d,p) level [110]. An exploration of their conformation has been carried out, mainly to determine the conformational effect on 15N NMR chemical shifts. In solution, 15N NMR chemical shifts indicated the presence of a mixture of two rapidly interconverting conformers. Very recently Semenov et al. [111] investigated the performance of different computational schemes used for calculation of
15
N NMR chemical shifts in a
representative series of sixteen open-chain amides. Among three different functionals, B3LYP, B3PW91 and KT3, used in combination with three different basis sets, 6311++G(2d,2p), aug-cc-pVTZ and pcS-3, the best performance was observed for the combination of KT3 with pcS-3. The most straightforward LDBS approach using pcS-3 on nitrogens and pc-2 on the rest of atoms (KT3/pcS-3//pc-2) results in a dramatic decrease in computational cost (more than an order of magnitude in time scale) with insignificant loss of accuracy as compared to the full basis set scheme. Taking into account solvent effects at either PCM or SM+PCM level (in the latter case, via adding one molecule of a solvent into computational space explicitly in the appropriate IEFPCM medium) generally improved the agreement of calculated 15N NMR chemical shifts of amides with experiment. Fig. 8 shows the mean absolute errors of the
15
N NMR
chemical shifts of sixteen representative amides studied in [111] and calculated using different methods (for details, see caption to figure). It is seen that best result (MAE 5.8 ppm) is achieved with KT3/pcS-3 full basis set scheme with solvent effects taken into account in explicit way using supermolecular (1:1) model.
Fig. 8. Mean absolute errors of calculated 15N NMR chemical shifts in the series of sixteen amides at the KT3/pcS-3 level in gas phase (GP), in solution within the PCM scheme (PCM) and with supermolecular model in PCM medium (SM+PCM) using locally dense basis set (LDBS) and full basis set (FBS) schemes. Reproduced from ref. [111] with permission of John Wiley and Sons Inc. In a very recent publication by the same authors [112] the benchmark calculations of 15N NMR chemical shifts in the series of sixteen open-chain amines were performed at the DFT level using different functionals and basis sets with particular interest concentrated on solvent effects and the so-called "multistandard scheme". Taking all these factors into account resulted in a noticeable improvement of the agreement of the calculated 15N NMR chemical shifts with experiment, decreasing MAE from 13 to 4 ppm for a range of about 60 ppm.
3.2.
Nitrogen heterocycles
In an early paper by Claramunt et al. [113]
15
N NMR chemical shifts were
calculated at the RHF/6-311G** level in a representative series of azolides (Nacylazoles), which are a characteristic and well-studied class of heterocyclic compounds that includes derivatives of pyrrole, imidazole, pyrazole, both triazoles, tetrazole, pentazole, indole and carbazole. In the correlation equation of 15N NMR chemical shifts with nitrogen shielding constants the intercept (-130 ppm) was not far away from the
absolute shielding constant of nitromethane in CDCl3 (-139.2 ppm), the reference substance used in
15
N NMR spectroscopy. The calculated values of
15
N NMR chemical
shifts predicted that based on such values, it would be easy to determine the position of the acetyl group in azole moiety. Extending such studies, molecular structures and tautomeric equilibria and transformations of halogenotriazoles have been investigated [114] by means of X-ray molecular structures and calculation of 15N NMR chemical shifts at the GIAO-B3LYP/631G* level. Based on these results, the tautomeric structures of halo-1,2,4-triazoles have been determined unambiguously. In particular, it was shown that a halogen substituent prefers to occupy the 3-position and that a tautomeric proton at N-1 links, through hydrogen bonds, to the N-4 of another molecule. The structure of N1-hydroxylophine N3-oxide in solid state and liquid phase was determined by means of X-ray powder-diffraction data and 15N NMR calculations at the GIAO-B3LYP/6-31G* level and compared with experiment [115]. Calculated 15N NMR chemical shifts of the title compound together with three model benzotriazoles allowed their unambiguous structural elucidation. These and preceding early papers of this group of authors dealing with structural applications of the calculations of
15
N NMR chemical shifts in nitrogen-containing
heterocycles are discussed in more detail in the early review by Alkorta and Elguero [116]. In more recent publications by Alkorta and coworkers, calculations of
15
N NMR
chemical shifts were exploited to investigate the molecular structure and NMR properties of P-phosphinoylmethyl aminophosphonium salts [117], to study amines and to reveal the potential of
15
15
N shieldings in
N NMR calculations in conformational analysis
[118], to elucidate the structure of 1,1,3-trimethyl-Δ2-pyrazolinium perchlorate [119], Nsubstituted pyrazoles [120], N-substituted pyrazoles and indazoles [121], and a series of Tröger's bases and related compounds [122]. The computation of
15
N NMR chemical
shifts was used to study the structure of pyrazolo[1,5-a]pyrimidines (the products obtained by condensation of 3(5)-amino-4-phenyl-1H-pyrazole and β-dicarbonyl compounds bearing a trifluoromethyl group) [123], a number of open-chain aliphatic, aromatic and heteroaromatic nitrogen-containing compounds [124], the NH and OH tautomers of pyrazolinones [125], three bis(amino acids) linked by the amino groups (namely alanine-alanine, alanine-glycine and glycine-glycine) [126], three targeted azines
(benzalazine, acetophenoneazine and cinnamaldazine) [127], two tautomeric bispyrazolylbenzenes providing a proton-transfer dynamic equilibrium [128], and a series of N-H, N-methyl and N-propyl aziridines and their C-lithium derivatives [129]. More recently, García et al. [130] employed calculation of
15
N NMR chemical
shifts to study the structure of aminobenzimidazoles in solution and in solid state. The tautomerism
of
4(7)-aminobenzimidazoles
and
5(6)-aminobenzimidazoles
was
investigated, and a clear predominance of the 4-amino tautomer over the 6-amino tautomer was established, in line with team included computational
15
15
N NMR calculations. Further papers from this
N NMR studies of five borates (from the borohydride to
tetrakis(pyrazol-1-yl)borate) anions [131], seventeen derivatives of 1H-pyrazoles, 1H1,2,4-triazoles and 1H-1,2,4-diazaphospholes (three of them existing in two tautomeric forms, thus forming 20 families of compounds) [132], NH-benzimidazoles in solution and in the solid state demonstrating proton transfer and tautomerism [133], a series of of 2,2'-, 3,3'- and 4,4'-bipyridines and their conjugated acids [134], together with some novel [1,2,4]-triazolo-[1,5-α]pyrimidine derivatives prepared by oxidative cyclization of suitable N-benzylidene-N'-pyrimidin-2-yl hydrazine precursors [135]. Other nitrogen-containing heterocycles studied via calculation of their
15
N NMR
chemical shifts were 2,4,6-trifluoro-1,3,5-triazine, a highly symmetrical molecule with NMR parameters obtained by reducing its symmetry through the introduction of 14N/15N isotopomers [136], three benzazoles (1H-benzimidazoles, 1H- and 2H-indazoles, 1H- and 2H-benzotriazoles) reviewed in [137], and three azines derived from 2-formylimidazole, 4(5)-formylimidazole and 4(5)-formyl-5(4)-methylimidazole [138]. In the most recent publications by Alkorta and coworkers calculation of 15N NMR chemical shifts at the DFT level was used to study the structure of parent 1-, 2-, and 3pyrazolines and their methylated derivatives [139] together with representative azolo[α]pyrimidines including targeted pyrazolo[1,5-α]pyrimidines [140], a series of 4,5,6,7-tetrafluorobenzazoles with special emphasis on PCM calculations of chemical shifts [141], a representative series of atranes [142], and pyridine-supported bicyclic guanidine superbases [143]. Recently 15N NMR chemical shifts of a sizeable number of azoles and azines have been calculated at the DFT level by a group of Russian authors [43,63,64,65]. It was shown that the most reliable functional was KT2 of Keal and Tozer used in combination with Jensen's pcS-3 on nitrogen and pc-2 elsewhere, as illustrated in Fig. 9 showing
correlation plots of calculated
15
N NMR chemical shifts in IEF-PCM media and for
supermolecular model versus experiment for 27 azoles and azines [65].
Fig. 9. Correlation plots of calculated 15N NMR chemical shifts of a series of 27 targeted azoles and azines (10 solvents for each compound) in IEF-PCM media and in supermolecular (1:1) IEF-PCM media versus experiment (460 points in total). Reproduced from ref. [65] with permission of John Wiley and Sons Inc. Results of this study [65] showed that for nonpolar solvents (cyclohexane, carbon tetrachloride, benzene, chloroform and dichloromethane) taking into account solvent effects within either IEF-PCM or supermolecular schemes resulted in improved agreement of calculated
15
N NMR chemical shifts with experiment by about 2 ppm.
There was almost no difference between those two methods of taking into account solvent effects, implying that no specific solvation effects were occurring in these nonpolar solvents. On the other hand, a difference between results from these methods became visible in calculations for polar and especially polar protic solvents, where the supermolecular scheme improved agreement with experiment as compared with IEFPCM by about 1-2 ppm, reaching almost 6 ppm for water. This result indicated that there was a marked specific solvation of nitrogen-containing heterocycles by water, so that the use of the supermolecular scheme is strongly recommended to account for solvent effects in water solutions.
Experimental and calculated
15
N NMR chemical shifts were used in structural
elucidation of bis[(z)-cyanomethylidene]-diazapentacyclodienedicarboxylates comprising both the tetrahydropyridine rings and highly reactive cyano and carboxylate groups, and regarded as an intermediate stage for further preparation of biologically active amides and acids [144]. A joint application of the DFT calculations of 1Н and 13С and 15N NMR data for a series of the E and Z isomers of 1-styrylpyrroles, 1-(1-propenyl)pyrroles, 1vinylpyrroles and styrene suggested a reduction of conjugation between the unsaturated fragments, which was interpreted [145] as the result of the mutual influence of the donor conjugation. The Z isomer of 1-styrylpyrrole was shown to have an essentially nonplanar structure because of steric hindrance while the E isomer of 1-styrylpyrrole was also shown to have an out-of-plane structure despite the absence of a sterical barrier. Deviation of the E isomer from the planar structure seemed to be caused by the influence of conjugation. The structure of the E isomer of the 2-substituted 1-styrylpyrroles was similar to that of the 2-substituted 1-vinylpyrroles. Based on
15
N NMR calculations,
steric effects in the Z isomer of the 2-substituted 1-styrylpyrroles were interpreted as resulting from an increase of the dihedral angle between the planes of the pyrrole ring and double bond [145]. Another example of structural elucidation based on
15
N NMR
calculations is presented in the paper by Afonin et al. [146], where 1H, 13C, 15N and 77Se shielding constants in the configurational isomers of selenophene-2-carbaldehyde azine were evaluated at the MP2-GIAO level, allowing determination of the energy-favorable conformation of the title compound with syn orientation of both selenophene rings relative to the C=N groups. In the recent paper by Semenov et al. [147] the tautomeric structure of 4trifluoromethyl[b]benzo-1,4-diazepine system in solution has been evaluated by means of the calculation of
15
N NMR chemical shifts of the individual tautomers in comparison
with the averaged experimental shifts to show that the enamine-imine equilibrium is entirely shifted toward the imine form. Indeed, using the remarkable gap of about 250 ppm between amine-type and imine-type nitrogens, one can easily estimate the tautomeric ratio in the enamine–imine equilibrium based on the calculated
15
N NMR
chemical shifts of individual tautomers A, B and C (Fig. 10) in comparison with the averaged experimental shifts.
Fig. 10. Tautomeric forms of 4-trifluoromethyl[b]benzo-1,4-diazepine system. The adequacy of theoretical level used for the computation of 15N NMR chemical shifts in this study [147] has been verified based on the benchmark calculations in a series of the model push-pull and captodative enamines together with related azomethynes, which demonstrated a good to excellent agreement with experiment.
3.3.
Protonated nitrogen-containing compounds
Protonation effects on nitrogen are of prime practical importance for the structural elucidation of the biologically active nitrogen-containing compounds. For instance, there is a practically important and marked upfield protonation shift of about 100 ppm in 15N chemical shifts that is observed, for example, in the series of the Schiff bases of 3hydroxypyridine-4-carboxaldehyde with 1-aminopyrazole and 1-aminobenzimidazole related to pyridoxal-5'-phosphate [148], a natural biologically active form of vitamin B6,. It is well known that both liquid and solid-state 15N NMR chemical shifts of aminoacids, peptides and related biochemical species are extremely sensitive to the protonation state, tautomeric structure, hydrogen bonding and rotameric structures [149]. In addition,
15
N
NMR measurements of nucleoside bases can serve as a direct probe for studies of nitrogen environment in oligomeric fragments of nucleic acids and nucleosides, resulting in a deeper insight in vitally important phenomena such as self-association, molecular recognition and base-pairing, and providing a powerful tool in structural elucidation of nitrogen-containing organic and biological molecules. Noticeable protonation effects (exceeding 100 ppm) in protonated amines, imines, azoles and azines were shown [150] to originate mainly in the changes of paramagnetic terms of the nitrogen shielding constants, with the diamagnetic term remaining fairly
constant. The nature of the upfield (shielding) protonation effect in
15
N NMR of azines
and azoles was explained by the change of the contribution of the sp2-hybridized nitrogen lone pair on protonation that causes a marked shielding of nitrogen by about 100 ppm. In contrast, for amine nitrogen protonation of the nitrogen lone pair results in a deshielding protonation effect of about 25 ppm; thus the total deshielding protonation effect is due to the interplay of the contributions of other adjacent natural bond orbitals. This was rationalized in terms of the Natural Chemical Shielding [151] analysis within a general Natural Bond Orbitals approach of Weingold [152], as illustrated below for pyridine (Fig. 11), representing aromatic nitrogen-containing heterocycles, and trimethylamine (Fig. 12), representing open-chain aliphatic amines [150].
Fig. 11. Isosurfaces of salient natural bond orbitals of pyridine and protonated pyridine accounting for the protonation effect on 15N NMR absolute shielding constants. Reproduced from ref. [150] with permission of John Wiley and Sons Inc.
Fig. 12. Isosurfaces of salient natural bond orbitals of triethylamine and protonated triethylamine accounting for the protonation effect on 15N NMR absolute shielding constants. Reproduced from ref. [150] with permission of John Wiley and Sons Inc. As follows from these results, protonation effects are determined by the change in the shielding contribution of the nitrogen lone pair, noticeably exceeding 100 ppm and serving as a guiding thread in the unambiguous elucidation of the protonated forms of nitrogen-containing compounds [150].
3.4.
Coordination complexes
Examples of
15
N NMR calculations to determine the structure of coordination
complexes are provided in a series of publications by Pazderski et al. [153,154,155] who calculated number
15
of
N NMR coordination shifts of Pd(II) and Pt(II) chloride complexes with a nitrogen-containing
heterocycles
(pyridine,
2,2'-bipyridine,
1,10-
phenanthroline, quinoline, isoquinoline and 2,2'-biquinoline) at the B3LYP/LanL2DZ level (implying LDBS schemes) and found that they are noticeably dependent on the type of a platinide metal and coordination sphere geometry. The formation of the platinide metal-nitrogen bonds results in significant (ca 78–100 ppm) high-field
15
N NMR
coordination shifts. It was also found that this shielding effect is larger for Pt(II) than
Pd(II) complexes (by ca 15 ppm), decreasing upon the change of trans to cis geometry by ca 15 ppm. It was suggested that such a phenomenon, occurring via the decrease of the absolute value of paramagnetic contribution in the relevant
15
N shielding constant, is
probably caused by the replacement of the main n(N)→π* electronic transition by that of n(N-M)→π*, resulting in an increase of the mean electron excitation energy. Generally, these calculations predicted a large
15
N shielding effect upon complexation of nitrogen-
containing compounds. Although the calculated absolute values of the respective highfield
15
N NMR coordination were noticeably smaller than in real experiments, the
phenomenon itself remains the same. The improvement of calculated results relative to experiment after inclusion of solvent effects was rather small, which is consistent with a fact that
15
N NMR chemical shifts of the nitrogen-containing heterocycles together with
their platinide(II) chloride complexes are only slightly dependent on the solvent. In a continuation of this study,
15
N NMR coordination shifts of the related
complexes of nitrogen-containing heterocycles with Au (III), Co(III) and Rh(III) [99], Au(III), Pd(II) and Pt(II) [156,157,158], and Fe(II), Ru(II) and Os(II) [159] were investigated at the same level of theory and in the same manner. For the gold(III), cobalt(III) and rhodium(III) chloride complexes with pyridine, 2,2'-bipyridine and 1,10-phenanthroline it was found [99] that metal coordination generally results in large
15
N NMR high-field shifts (78–107 ppm), with their absolute
magnitudes increasing in the order of Au(III) < Rh(III) < Co(III). For Au(III) complexes, the
15
N NMR coordination shifts range from 78 to 85 ppm, while for the Co(III) and
Rh(III) complexes they are within relatively broad ranges, namely from 88 to 107 ppm, and from 82 to 96 ppm, with their absolute values being always larger (by 6–11 ppm) for the respective cobalt species than for the rhodium ones. The
15
N NMR chemical shift
calculations have been done separately for each type of central ion, and this is why computational results have not reproduced the experimental differences between the metals under study. However, the application of fitting procedures using distinct empirical constants for Au, Co and Rh species has been necessary because without them 15
N NMR chemical shifts did not reflect actual metal-dependent trends. Nevertheless, the
approach used did finally provide qualitatively consistent results within each group of complexes containing the same metal, reproducing well the correlations between the fitted calculated values and structural features of the molecules such as the coordination sphere geometry and the type of ligand, even in the case of methods excluding solvent
effects. The quantitative agreement between calculated and experimental
15
N NMR
chemical shifts was noticeably improved by the use for ligand atoms of the Pople's 6– 31G** and 6–31G* basis sets (containing polarization functions) and the B3LYP functional upon geometry optimization. Taking into account solvent effects yielded a slightly better agreement with experiment for the Au(III) complexes, but not for those of Co(III) or Rh(III). For the Au(III), Pd(II) and Pt(II) chloride complexes with picolines and phenylpyridines [156,157,158], quantum-chemical calculations of
15
N NMR chemical
shifts were performed at the B3LYP/LanL2DZ level (implying the LDBS scheme) in gas phase, and taking into account solvent effects within the PCM model with geometries directly constructed by molecular modelling and then optimized using the B3LYP/LanL2DZ+6-31G* method. These calculations were performed to reproduce the experimentally observed structural trends between Au(III), Pd(II) and Pt(II) complexes, as well as their trans and cis isomers. These calculations qualitatively reproduced the 15N NMR high-field shifts observed upon complexation by platinide(II) ions. However, calculated 15N NMR coordination shifts were found to be generally almost half the size of those found in real experiments. Furthermore, no significant distinction between Pd(II) and Pt(II) complexes could be derived from these data because calculated coordination 15
N NMR chemical shifts were nearly the same. For Fe(II), Ru(II) and Os(II) cationic complexes with 2,2':6',2''-terpyridine [159],
the main result reached from calculations of
15
N NMR chemical shifts at the same level
of theory was that coordination of 2,2':6',2''-terpyridine by Fe(II), Ru(II) and Os(II) ions resulted in a
15
N shielding effect that was more prominent for the outer nitrogen atoms
(ca. 60–90 ppm) than for the inner ones (ca. 10–35 ppm), increasing in the Fe(II)→Ru(II)→Os(II) series and resulting in the reversal of the 15N NMR spectral order. The main conclusions derived from the computational studies of chemical shifts performed by Pazderski et al.
15
N NMR
[99,153,154,155,156,157,158,159],
together with associated experimental papers [160,161,162,163] reviewed in [164], are the substantial highfield
15
N NMR coordination shifts (up to several dozens of ppm) in
Pd(II), Pt(II), Au(III), Co(III), Rh(III), Ir(III), Pd(IV) and Pt(IV) complexes with pyridine, 2,2'-bipyridine, 1,10-phenanthroline, quinoline, isoquinoline, 2,2'-biquinoline, 2,2':6',2'-terpyridine and their alkyl or aryl derivatives, and the practical insignificance of
relativistic and solvent effects in nitrogen chemical shielding in these series of complexes.
3.5.
Intermolecular complexes and hydrogen bonding Calculation of dynamically averaged 15N NMR chemical shifts and intermolecular
spin-spin coupling constants involving 15N nuclei provides a guiding thread to the nature of intermolecular bonding involving nitrogen, as exemplified in a series of recent publications by Del Bene et al. [165,166,167,168,169,170,171] stemming mainly from their earlier papers [172,173,174,175,176,177] reviewed in [178]. Among a wide range of noncovalent interactions, hydrogen bonds together with the so-called pnicogen bonds (the latter including intermolecular bonding of nitrogen and phosphorus with phosphorus, arsenic, antimony and bismuth) are of major significance in view of their particular role in vitally important chemical and biochemical processes. When describing conventional hydrogen bonding, the notation A-H···D is used with A denoting the electron acceptor and D standing for the electron donor. Otherwise, when describing pnicogen bonding, the notation H-A···D is used to indicate that the electron density donated by D transfers into the proximate orbital lobe of the A-H bond. In both cases, a favorable electrostatic interaction energy between the two molecules provides this intermolecular charge transfer from the donating atom (nitrogen or phosphorus) to the accepting atom (phosphorus, arsenic, antimony and bismuth). For more details on the nature of pnicogen bonding, see a comprehensive paper by Scheiner [179] and references given therein. Thus very recently Del Bene et al. [171] performed an ab initio MP2/aug'-ccpVTZ study of the intermolecular binary complexes PH3:N-base together with the corresponding ternary complexes XY:PH3:N-base (N-base = NCH, NH3, NCF, NCCN and N2), to investigate P···N pnicogen bond formation through the lone-pair hole at P in the binary complexes and P···N pnicogen-bond formation assisted by P···Y halogen bond formation through the σ-hole at Y. It was found that calculated intermolecular coupling constants involving nitrogen and phosphorous are larger in ClCl:PH3:N-base complexes compared to those in FCl:PH3:N-base complexes, despite the shorter P−N distances in the latter. This paper is an example of how computational
15
N NMR can
serve for the structural elucidation of intermolecular complexes with N-bases.
In the preceding paper [170] MP2/aug′-cc-pVTZ calculations were performed to investigate the pnicogen-bonded complexes F4−nHnP+:N-base, for n = 0, 1, 2 and 3, each with a linear or nearly linear F−P···N alignment. Coupling constants 1pJ(P−N) across the pnicogen bond were shown to vary with the P−N distance, but different patterns were observed for complexes with F4P+ and complexes of the sp3 bases with F3HP+. For the remaining complexes, 1pJ(P−N) was shown to increase with decreasing P−N distance. MP2/aug′-cc-pVTZ calculations have also been carried out for the pnicogenbonded complexes HnF5−nP:N-base, for n = 0−5 and nitrogen bases NC−, NCLi, NP, NCH, and NCF [168]. It was shown that spin-spin coupling constants 1pJ(P−N) for (PF5, PHF4) complexes with nitrogen bases are negative with the strongest bases NC− and NCLi but positive for the remaining bases while complexes of (PH4F, PH2F3) with these same two strong bases and H4FP:NP have positive
1p
J(P−N) values but negative values
for the remaining bases. On the other hand, (PH5, PH3F2) have negative values of 1p
J(P−N) only for complexes with NC−. The same calculations were performed also for the pnicogen-bonded anionic
complexes with phosphorus instead of nitrogen [169]. It was found that spin-spin coupling constants
1p
J(P−A) differentiate between shorter ion-molecule pnicogen bonds
with partial covalent character and longer P···A ion-molecule pnicogen bonds. Similarly, coupling constants 1J(P−A′) were found to differentiate between longer covalent P−A′ bonds with partial ion-molecule character and shorter P−A′ covalent bonds. The same approach was followed to identify local minima on the (NH2F)2, H2FP:NFH2, and (PH2F)2 potential surfaces, to characterize the types of interactions which stabilize the complexes found at these minima, and to evaluate their binding energies [167]. It was found that (NH2F)2 complexes are stabilized by N−H···N or N−H···F hydrogen bonds. Although net charge transfer occurs in complexes in which the two monomers are inequivalent, charges on N and P did not correlate with N and P absolute chemical shieldings, the latter reflecting charge distributions and overall bonding patterns. Calculated two-bond spin-spin coupling constants
2h
J(X−Y) across
X−H···Y hydrogen bonds were rather small, due to the nonlinearity of many of the hydrogen bonds. In contrast,
1p
J couplings across a given type of pnicogen bond were
relatively large and varied significantly, but did not correlate with corresponding distances.
A bit earlier the influence of F−H···F hydrogen bonds on the P···N pnicogen bond in complexes of general formula nFH:(H2FP:NFH2) for n = 1 and 2, and a selected complex with n = 3 was investigated [166]. It was found that
31
P and
15
N chemical
shieldings did not correlate with charges on P and N, respectively, but 31P shieldings did correlate quadratically with the P−N distance. On the other hand,
1p
J(P−N) coupling
constants did not correlate with the intermolecular P−N distance. However, when hydrogen bonding occurs only at P−F, 1pJ(P−N) decreased in absolute value as the P−N distance decreased, thereby approaching 1J(P−N) for H2P−NH2. However, the P···N bond in the 3FH:(H2FP:NFH2) intermolecular complex had little covalent character, unlike the P···P bond in the corresponding complex 3FH:(PH2F)2. In an earlier paper [165] from this series corresponding calculations were carried out in a systematic investigation of P···N pnicogen complexes H2XP:NXH2 for X = H, CH3, NH2, OH, F, and Cl, as well as for selected complexes with different substituents X bonded to P and N. It was found that complexation increased 31P chemical shieldings in complexes with binding energies larger than 19 kJ/mol. One-bond spin-spin coupling constants
1p
J(N-P) across the pnicogen interaction exhibited a quadratic dependence on
the N-P distance for complexes H2XP:NXH2, similar to the dependence of
2h
J(X-Y) on
the X-Y distance for complexes providing X-H···Y hydrogen bonds. However, when the mixed complexes H2XP:NX'H2 were included, the curvature of the trend was changed and the good correlation between 1pJ(N-P) and the N-P distance was lost. In a related paper by Alkorta et al. [180], calculations of 1JNH,
1h
JNH and
2h
JNN
spin-spin coupling constants of 27 complexes including N–H···N hydrogen bonds allowed an analysis of these through-hydrogen-bond coupling as a function of the hybridization of both nitrogen atoms and the charge of the complex. The main conclusion reached was that the hybridization of the N atom of the hydrogen bond donor was much more important for this type of interaction than that of the hydrogen bond acceptor in determining the value of J. Positive and negative charges in cationic and anionic complexes exerted opposite effects while the effect of the transition states was considerable. In addition, a series of interesting numerical relationships were found in that study that can be useful in structural studies of biomolecules, small molecules at low temperature, and new materials, as also reviewed by Alkorta et al. [181]. Very recently, in continuation of these studies, Sánchez-Sanz et al. [182] performed a computational study of the intramolecular pnicogen bond in 8-
phosphinonaphthalen-1-aminederivatives (1-NX2, 8-PX2 with X = H, F, Cl, Br, CH3, CN and NC), which are proton sponge analogues, with intramolecular P···N pnicogen interactions to determine their structural and geometric parameters, interaction energies and electronic properties. It was shown that substitution of H atoms in the PH2 group by electron withdrawing groups on the Lewis acid moiety strengthened the P···N pnicogen bond, evidenced by the increasing electron density values at the bond critical point and by shorter distances. However, substitutions on the Lewis base moiety (NX2) showed weaker P···N interactions than when the substitution was done on the Lewis acid counterpart. In addition,
15
N NMR spectroscopy proved to be the one of the most efficient
methods for the investigation of hydrogen bonds of the N–H···X and X-H···N types where X is a heteroatom bearing lone pair(s). Thus in a series of publications by Afonin et al. [183,184,185,186,187] calculations of 15N NMR chemical shifts were performed to investigate hydrogen bonding involving nitrogen. According to 15N NMR spectroscopic data and ab initio calculations, a strong N– H···O intramolecular hydrogen bonding in Z-isomers of 2-(2-acylethenyl)pyrroles was established, which causes a decrease of the nitrogen shielding by about 15 ppm together with substantial lengthening of the N–H bond, in line with experimental data [183]. In a subsequent publication by the same group of authors [184], the bifurcated hydrogenbonding effect on the
15
N NMR shielding in trifluoroacetyl pyrroles was studied at the
DFT level in comparison with experiment. 2-Trifluoroacetyl pyrroles have been recognized as possessing an intramolecular N–H···O hydrogen bond between the oxygen of the trifluoroacetyl group and the hydrogen of the N–H covalent bond of the pyrrole ring. Moreover, the hydrogen of the N–H covalent bond of the pyrrole ring in 2trifluoroacetyl-5-(2'-pyridyl)-pyrrole was found to be involved in a bifurcated hydrogen bond with participation of both the oxygen of the trifluoroacetyl group and the nitrogen of the pyridine ring. It was found by means of
15
N NMR calculations [184] that
components of the bifurcated hydrogen bond in 2-trifluoroacetyl-5(2'-pyridyl)pyrrole were predominantly electrostatic in nature, so that their influence on the geometrical and spectral characteristics of the N–H covalent bond were additive. In the next publication from this series [185] the comparative analysis of the hydrogen bonding with participation of nitrogen in 2(2'-heteroaryl)pyrroles and their trifluoroacetyl derivatives was performed based on DFT calculations of
15
N NMR
chemical shifts. N–H···O and N–H···S intramolecular hydrogen bonds in the 2(2'-furyl)and 2(2'-thienyl)pyrrole, as well as the bifurcated N–H···O, N–H···O and N–H···O, N– H···S intramolecular hydrogen bonds in 2-trifluoroacetyl-5-(2'-furyl)- and -5-(2'thienyl)pyrrole, were studied by means of the calculation of 15N NMR chemical shifts at the DFT level. Essentially, these calculations supported the assumption that no fundamental difference exists between the conventional N–H···X hydrogen bond in the 2-(2'-heteroaryl)pyrroles
and
C–H···X
hydrogen
bond
in
the
1-vinyl-2-(2'-
heteroaryl)pyrroles. In continuation of these studies, C–H···N intramolecular hydrogen bonding effects were investigated in the
15
N NMR chemical shifts of configurational isomers of 1-
vinylpyrrole-2-carbaldehyde oxime at the DFT level [186]. It was shown that the Eisomer of 1-vinylpyrrole-2-carbaldehyde adopts a preferred conformation with an antiorientation of the vinyl group relative to the carbaldehyde oxime group and with a synarrangement of the carbaldehyde oxime group relative to the pyrrole ring. It follows from these calculations that an intramolecular C–X···N hydrogen bond is present in the Eisomer of the 1-vinylpyrrole-2-carbaldehyde oxime, whereas an intramolecular C–H···O hydrogen bond occurs in its Z-isomer. Theoretical calculations indicated that intramolecular C–H···N and C–H···O hydrogen bonds caused a pronounced highfrequency shift of the bridge hydrogen. Later, the study of conformations and hydrogen bonding in the configurational isomers of pyrrole-2-carbaldehyde oxime by means of MP2 and DFT calculations of 15N NMR chemical shifts combined with NBO analysis was performed by the same team [187]. It was shown that pyrrole-2-carbaldehyde oxime adopted a preferred conformation with syn orientation of the oxime group with respect to the pyrrole ring, and that the syn conformation of E and Z isomers of pyrrole-2-carbaldehyde oxime was stabilized by the N–H···N and N–H···O intramolecular hydrogen bonds. The N–H···N hydrogen bond in the E isomer of pyrrole-2-carbaldehyde increased the 1J(N,H) coupling by about 3 Hz due to the strengthening of the N–H···O hydrogen bond in its Z isomer. The MP2 calculations indicated that the syn conformation of E and Z isomers was energetically less favorable by ∼3.5 kcal/mol relative to the anti conformation. The calculations of 1J(N, H) couplings in the syn and anti conformations allowed estimation of the contribution of N– H···N and N–H···O hydrogen bonding. The NBO analysis suggested that the N–H···N hydrogen bond in the E isomer was a pure electrostatic interaction, whereas charge
transfer from the oxygen lone pair to the antibonding orbital of the N–H bond through the N–H···O hydrogen bond occurred in the Z isomer only. Claramunt et al. [188] studied protonation and phase effects on the
15
N NMR
chemical shifts of five imidazoles and pyrazoles, including imidazole, 4,5dimethylimidazole,
pyrazole,
3,5-dimethylpyrazole
and 4,5-dihydro-3-methyl-2H-
benz[g]indazole. Based on these results, the existence of multiple N–H⋯N hydrogen bonds was established in the solid phase. A series of nitrogen-containing H-bonded molecules that have (or have not) delocalized bonds were studied, and the values of both NMR spectroscopic parameters, σ and J-couplings, and also the energy stability of such molecules, were analyzed as a function of H-bond strength [189]. It was observed that shieldings of atoms belonging to the donor substructure gave a clear evidence about the presence of the resonance phenomenon
in
the
model
compounds
studied,
namely
malonaldehyde,
nitromalonaldehyde, and nitromalonamide. 15
Recently Afonin et al. [190] employed
N NMR calculations for the
configurational assignment of methylglyoxal bisdimethylhydrazone. The C–H⋯N intramolecular hydrogen bonding in the ZE isomer was established from quantumchemical calculations including Bader’s quantum theory of atoms in molecules analysis. Effects of C–H⋯N hydrogen bonding were found in
15
N chemical shifts for nitrogens
that manifested the twisting out from the plane of the backbone and loss of conjugation. As a result, the degree of charge transfer from the nitrogen lone pairs to the p-framework was found to be different in different isomers, affecting their 15N shieldings. In addition, DFT calculations on the adsorption of several gaseous homo- and hetero-diatomic molecules including N2 and NO on the external surface of an H-capped pristine armchair (5,5) single-walled carbon nanotube were conducted and critically compared with available experimental data [191]. Significant changes of chemical shifts and shielding anisotropies at sites of addition were observed and critically discussed.
3.6.
Biological applications
At present, not very much is known about
15
N NMR calculations in biological
molecules, which is a consequence of their large molecular size and the enormous computational effort that would be needed to perform such calculations at the modern
level of theory. However, a number of promising examples can be found in the comprehensive review by Mulder and Filatov [11], which we recommend to readers interested in 15N NMR calculations for biological species. As they stated, "the use of 13C and 15N chemical shifts as a source of structural information can extend the applicability of NMR as a tool for 3D structure determination of proteins in solution. The range of proteins that can be characterized structurally with NMR spectroscopy can be markedly increased with the use of structural restraints obtained from a comparison of the theoretically calculated chemical shifts for specific spatial conformations of amino acid backbone and side chains, bringing within reach many systems of biological significance" [11].
4. Conclusions Calculations of
15
N NMR chemical shifts play a major role in the structural
elucidation of inorganic, organic and bioorganic molecules. At present, computation of 15
N NMR chemical shifts is performed mainly at the DFT level, however pure non-
empirical correlated methods like MP2, SOPPA, SOPPA(CC2), SOPPA(CCSD), CCSD and CCSD(T) are also used. Among the different DFT functionals used to calculate
15
N
NMR chemical shifts, we recommend correlation-exchange generalized gradient approximation Keal-Tozer's functionals KT2 and KT3 used in combination with Jensen's pcS-2 and pcS-3 basis sets on nitrogens, and pc-2 elsewhere in the molecule within a general LDBS scheme. All practical calculations of
15
N NMR chemical shifts are
recommended to be performed with the inclusion of solvent effects at the IEF-PCM level when no specific solute-solvent interactions are expected, and at the supermolecular level otherwise. In most cases, rovibrational corrections and relativistic effects can safely be neglected in practical calculations of 15N NMR chemical shifts. Calculations of 15N NMR chemical shifts are widely used in the structural elucidation of organic and inorganic species, as exemplified for a range of different organic and inorganic molecules, including open-chain nitrogen-containing compounds, nitrogen heterocycles and their protonated forms, coordination and intermolecular complexes.
Acknowledgement
This work was supported by The Federal Agency for Scientific Organizations, Russia (Project No 0342-2014-0006). I am very much grateful to my former PhD students, colleagues and collaborators, first of all to Dr. Valentin A. Semenov, Dr. Dmitry O. Samultsev and late Dr. Kirill A. Chernyshev, with whom we have started calculations of 15
N NMR chemical shifts.
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bonds, J. Phys. Chem. A 107 (2003) 3121-3125. [174] J.E. Del Bene, S.A. Perera, R.J. Bartlett, M. Yáñez, O. Mó, J. Elguero, I. Alkorta, Two-bond
15
N-19F spin-spin coupling constants (2hJN-F) across N-H+···F hydrogen
bonds, J. Phys. Chem. A 107 (2003) 3126-3131. [175 ] J.E. Del Bene, S.A. Perera, R.J. Bartlett, M. Yáñez, O. Mó, J. Elguero, I. Alkorta, Two-bond
13
C-15N spin-spin coupling constants (2hJC-N) across C-H-N hydrogen
bonds, J. Phys. Chem. A 107 (2003) 3222-3227. [176] I. Alkorta, J. Elguero, J.E. Del Bene, A theoretical investigation of N–H···O=P hydrogen bonds through
15
N–31P and 1H–31P coupling constants, Chem. Phys. Lett.
412 (2005) 97-110. [177] J.E. Del Bene, J. Elguero, I. Alkorta, O. Mó, M. Yáñez, Ab initio study of the influence of trimer formation on one- and two-bond spin-spin coupling constants across an X-H-Y hydrogen bond: AH:XH:YH3 complexes for A, X = 19F, 35Cl and Y = 15N, 31P, J. Phys. Chem. A 109 (2005) 2350-2355. [178] J.E. Del Bene, Characterizing two-bond NMR 13C-15N, 15N-15N, and 19F-15N spin– spin coupling constants across hydrogen bonds using ab initio EOM-CCSD calculations, in: M. Kaupp, M. Bühl, V.G. Malkin (Eds.), Wiley VCH, Weinheim, 2004. [179] S. Scheiner, The pnicogen bond: its relation to hydrogen, halogen, and other noncovalent bonds, Acc. Chem. Res. 46 (2013) 280-288. [180] I. Alkorta, F. Blanko, J. Elguero, A theoretical structural analysis of the factors that affect 1JNH, 1hJNH and 2hJNN in N–H···N hydrogen-bonded complexes, Magn. Reson. Chem. 47 (2009) 249-256. [181] I. Alkorta, J. Elguero, G.S. Denisov, A review with comprehensive data on experimental indirect scalar NMR spin-spin coupling constants across hydrogen bonds, Magn. Reson. Chem. 46 (2008) 599-624. [182] G. Sánchez-Sanz, C. Trujillo, I. Alkorta, J Elguero, Modulating intramolecular P···N pnictogen interactions, Phys. Chem. Chem. Phys. 18 (2016) 9148-9160. [183] A.V. Afonin, I.A. Ushakov, L.N. Sobenina, Z.V. Stepanova, O.V. Petrova, B.A. Trofimov, Different types of hydrogen bonds in 2-substituted pyrroles and 1-vinyl
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13
C and
15
N NMR spectroscopy and ab initio
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13
C,
15
N spectroscopy and DFT calculations, Magn. Reson. Chem.
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15
N shielding constants in the isomers of methylglyoxal bisdimethylhydrazone:
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S0079-6565(17)30036-5 http://dx.doi.org/10.1016/j.pnmrs.2017.08.001 JPNMRS 1446
To appear in:
Progress in Nuclear Magnetic Resonance Spectroscopy
Received Date: Revised Date: Accepted Date:
20 July 2017 21 August 2017 21 August 2017
Please cite this article as: L.B. Krivdin, Calculation of 15N NMR chemical shifts: recent advances and perspectives, Progress in Nuclear Magnetic Resonance Spectroscopy (2017), doi: http://dx.doi.org/10.1016/j.pnmrs.2017.08.001
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Calculation of 15N NMR chemical shifts: recent advances and perspectives Leonid B. Krivdin A. E. Favorsky Irkutsk Institute of Chemistry, Siberian Branch of the Russian Academy of Sciences, Favorsky St. 1, 664033 Irkutsk, Russia Edited by Geoffrey Bodenhausen and David Neuhaus
ABSTRACT Recent advances in computation of 15N NMR chemical shifts are reviewed, concentrating mainly on practical aspects of computational protocols and accuracy factors. The review includes the discussion of the level of theory, the choice of density functionals and basis sets together with taking into account solvent effects, rovibrational corrections and relativistic effects. Computational aspects of
15
N NMR are illustrated for the series of
neutral and protonated open-chain nitrogen-containing compounds and nitrogen heterocycles, coordination and intermolecular complexes.
© 2018 Elsevier B.V. All rights reserved.
____________ E-mail address: [email protected]
Graphical abstract
Contents 1.
Introduction
2.
Computational protocols and accuracy factors
3.
4.
2.1.
Level of theory
2.2.
Functionals and basis sets
2.3.
Locally dense basis sets
2.4.
Solvent effects
2.5.
Rovibrational corrections
2.6.
Relativistic effects
2.7.
Practical recommendations
Structural applications 3.1.
Open-chain nitrogen-containing compounds
3.2.
Nitrogen heterocycles
3.3.
Protonated nitrogen-containing compounds
3.4.
Coordination complexes
3.5.
Intermolecular complexes and hydrogen bonding
3.6.
Biological applications
Conclusions Acknowledgement References
1. Introduction Recent advances in computational NMR (see reviews [1,2,3,4,5,6,7,8,9,10,11,12] including those on the relativistic level [13,14,15,16,17]) have had a profound impact on calculations of
15
N nuclear magnetic resonance chemical shifts, beyond the early
experimental papers reviewed in four fundamental compilations by Witanowsky, Stefaniak and Webb [18,19,20,21]. In the present compilation we have concentrated mainly on the computational protocols and accuracy factors of the calculation of
15
N
chemical shifts exemplified by a series of nitrogen-containing molecules, without paying too much attention to purely theoretical aspects. The review consists of two parts: the first concentrates mainly on existing computational protocols with special emphasis on the level of theory, the choice of density functionals and basis sets, while taking into account solvent effects, rovibrational corrections and relativistic effects; the second provides some practical examples for different organic and inorganic molecules including open-chain nitrogen-containing compounds, nitrogen heterocycles and their protonated forms, coordination and intermolecular complexes.
2.
Computational protocols and accuracy factors
2.1. Level of theory
Accurate calculations of Nuclear Magnetic Resonance (NMR) shielding constants include the evaluation of electron correlation effects, zero-point vibrational corrections, temperature effects, intermolecular interactions, solvent effects, and finally relativistic effects, as recently reviewed by Antušek and Jaszuńsky [22]. In this connection, the very first question arising before any calculations of molecular properties (including 15N NMR isotropic shielding constants and chemical shifts) can commence is the level of theory that should be applied. Semi-empirical quantum chemistry attempts to address two obstacles, namely slow speed and low accuracy, by omitting or parameterizing certain integrals based on experimental data, such as ionization energies of atoms and dipole moments of molecules, and neglecting electron correlation effects. As a result, semi-empirical methods are very fast, are applicable to large molecules, and may give accurate results
when applied to molecules that are similar to those used for parameterization. However, in this century, almost no one applies "good old" semi-empirical methods like the Moderate Neglect of Differential Overlap (MNDO), the Austin Model 1 (AM1) or the Parameterized Model 3 (PM3) family for the calculation of molecular properties like 15N NMR chemical shifts in organic molecules, probably with the exception of very large molecular systems comprising several hundreds or even thousands of atoms. At present, for the calculation of NMR parameters such as
15
N NMR chemical
shifts, the following levels of theory are generally applied: Density Functional Theory (DFT) and, alternatively, wave-function ab initio methods including uncorrelated Restricted Hartree-Fock (RHF), Møller-Plesset perturbation theory with electron correlation effects taken into account to second order (MP2), Coupled Cluster Singles and Doubles (CCSD), and Coupled Cluster Singles and Doubles with perturbative Triples corrections, CCSD(T). In addition to this, one can use Sauer's second-order polarization propagator family of methods [23,24,25,26,27,28,29], namely the Second-Order Polarization Propagator Approach (SOPPA), the Second-Order Polarization Propagator Approach in combination with second-order approximate Coupled Cluster to second order, SOPPA(CC2), and the Second-Order Polarization Propagator Approach in combination with Coupled Cluster Singles and Doubles, SOPPA(CCSD). Such methods are, however, a subject of more specialized theoretical reviews dealing with computational NMR [1,2,4,5,11,12,22]. With some exceptions, references to particular theoretical methods together with numerous basis sets and DFT functionals are not given in this review and can be found in the more theoretical reviews cited above. In the majority of papers dealing with calculations of
15
N NMR chemical shifts,
the much more economical DFT methods rather than time-consuming wave-function calculations are applied, so that in the present review we will mainly pay attention to the practical aspects of the DFT approach.
2.2.
Functionals and basis sets
Among the factors affecting the accuracy of calculation of
15
N NMR chemical
shifts at the DFT level, the choice of a proper combination of functional and basis set is of key importance. A good number of functionals and basis sets have been tested for the calculation of
15
N NMR chemical shifts, and this is well covered in the early review by
Alkorta and Elguero (dedicated in memoriam to Professor Lech Stefaniak) [30] published in 2003. Accordingly, in the present review we will concentrate mainly on the papers that appeared more recently. In one of the early papers by Kupka et al. [31]
15
N NMR isotropic shielding
constants of ammonia and HCN were calculated at the RHF and B3PW91 levels using correlation-consistent basis sets of Dunning aug-cc-pVXZ, X x = D, T, Q, 5 and 6. The 15
N NMR shielding constants appeared to converge monotonically to their Complete
Basis Set (CBS) values, and these calculations using augmented basis sets converged more rapidly than their non-augmented counterparts. This effect was slightly more pronounced for ammonia than for HCN. Interesting to note is that core-valence basis sets produced a further enhancement of the convergence for the 15N nucleus. In this study, the first detailed complete basis set approach was proposed testing the accuracy of fitting the 15
N NMR parameters using two- and three-parameter functions. In addition, the core-
valence basis sets produced further enhancement of the convergence for the nitrogen nuclei. The Hartree-Fock calculations (not taking into account electronic correlations) of CBS for 15N NMR isotropic shielding constants were closer to experiment than those of B3PW91. At the same time, the MP2-derived CBS values (taking into account electronic correlations), even limited to the smallest basis sets, showed the best agreement with experiment and theoretical benchmark studies. In a subsequent paper Kupka et al. [32] performed a systematic study of a basisset effect on 15N NMR nuclear shielding anisotropy in a set of simple nitrogen-containing molecules studied using the B3PW91 functional. In general, a similar pattern was observed for all compounds under study. The aug-cc-pVXZ correlation-consistent basis set appeared to predict smooth increases and convergeance of
15
N NMR shielding
anisotropy values with increasing cardinal zeta number, x. There was a significant gap observed between the values of the NMR parameters calculated with Pople's basis sets. Not surprisingly, the values and gaps were similar to those obtained with the significantly larger Dunning's aug-cc-pVDZ and aug-cc-pVTZ basis sets for the same set of compounds. In this paper, the convergence of DFT and RHF 15N NMR nuclear shielding anisotropy and tensor components predicted with cc-pVXZ and aug-cc-pVXZ basis sets has been evaluated for a model series of simple nitrogen-containing molecules N2, NH3, HCN and CH3CN. The first detailed CBS approach to computational 15N NMR has tested the possibility and accuracy of obtaining the anisotropy parameters using two- and three-
parameter fitting functions. In addition, an effective CBS approach was proposed for calculating reasonably accurate
15
N NMR anisotropic shielding parameters for larger
molecules, resulting in significant savings in computation time. The next paper in this series by Kupka and Lim [33] was devoted to the study of the basis sets used for calculations of 15N NMR shieldings and chemical shifts. Compared to the correlation-consistent basis sets, it was not known if polarization-consistent Jensen's pc-n basis sets (which were initially developed for HF and DFT calculations) could provide a monotonic and faster convergence toward the basis set limit for results at correlated levels, as well as better accuracy for a similar number of basis set functions. It was also not known whether the pc-n basis sets could efficiently compute second derivatives of energy, such as nuclear magnetic shielding tensors. To address these questions, in this paper the pc-n (n = 1-4), ccpVXZ, and/or aug-cc-pVXZ (X = D, T, Q, 5 and 6) basis sets were used to compute 15N NMR shieldings of the NH3 molecule at the RHF, B3LYP, MP2 and CCSD(T) levels of theory. The results showed that compared to the cc-pVXZ and aug-cc-pVXZ basis sets the pc-n basis sets yield faster convergence toward the basis set limit at the RHF, DFT, MP2 and CCSD(T) levels. Because the pc-n basis sets show faster convergence, fewer basis set functions were needed to reach the accuracy obtained with the aug-cc-pVXZ basis sets, enabling faster and more economical calculations of 15N NMR chemical shifts. The CBS approach at the B3LYP level for the calculation of NMR parameters was further extended [34] by applying Dunning's cc-pVXZ, cc-pCVXZ, cc-pVXZ-sd, ccpVXZ-sd+t (x = D, T, Q, 5 and 6) and Jensen's pcJ-n (n = 0, 1, 2, 3 and 4) basis sets after careful selection of data points used for fitting. To continue these studies, B3LYP calculations of the NMR parameters of the HOH and HOD isotopomers of water in chloroform-d [35] were performed within the CBS limit using Jensen's pcJ-n basis set, resulting in good agreement with experiment. Good performance of segmented contracted basis sets XZP (X = D, T, Q and 5) for obtaining nuclear isotropic shielding constants in the series of classical di- and tri-atomics using the BHandH Kohn–Sham basis set limit was shown [36]. The results of two- and three-parameter complete basis set limit extrapolation schemes obtained in this study were compared with experimental results and benchmark ab initio calculations. Similar convergence patterns of shieldings obtained from the calculations using general purpose XZP basis sets and from polarization-consistent basis sets pcS-n and pcJ-n (n = 0, 1, 2, 3 and 4), designed to
accurately predict magnetic properties, were observed. It was also shown that BHandH density functional markedly outperforms B3LYP method in predicting 15N shieldings and chemical shifts. In two related papers by the same author [37,38], B3LYP and BHandH density functionals were used to estimate nuclear magnetic isotropic shieldings of water and methanol in the complete basis set limit. Polarization-consistent pcS-n and pcJ-n (n = 0, 1, 2, 3 and 4) together with segmented contracted XZP (X = D, T, Q and 5) basis sets were used, and the results fitted well with simple mathematical formulas. The performance of these methods was assessed from the comparison with experiment and higher-level calculations. It is noteworthy that BHandH/pcS-n results approached the accuracy of the advanced CCSD(T) calculations. In two milestone papers by Kupka et al. [39,40] convergence patterns and limiting values of isotropic nuclear magnetic shieldings and nuclear spin-spin coupling constants for several small molecules including "nitrogen-oriented" N2 and NH3, were studied in the Kohn-Sham limit. Individual results of calculations using dedicated families of Jensen’s basis sets (pcS-n and pcJ-n) were fitted in the limit of the complete basis set using a simple two-parameter formula. Several density functionals were used. For comparative purposes, similar calculations were performed using non-empirical RHF, MP2, SOPPA, SOPPA(CCSD) and CCSD(T) methods. Finally, the CBS estimated results were critically compared with earlier reported literature data and experimental results. Among the 42 (!) studied DFT functionals (VXSC, HCTH, HCTH97, HCTH147, THCTH, M06L, B97D, B3LYP, B3P86, B3PW91, B1B95, MPW1PW91, MPW1LYP, MPW1PBE, MPW3PBE, B98, B971, B972, PBE1PBE, B1LYP, O3LYP, BHandH, BHandHLYP, BMK, M06, M06HF, M062X, tHCTHhyb, HSEh1PBE, HSE2PBE, PBEh1PBE, wB97XD, wB97, wB97X, TPSSh, X3LYP, LC-wPBE, CAM-B3LYP, WP04, KT1, KT2 and KT3), the KTn family of functionals produced the most accurate isotropic nuclear shieldings. These data were critically compared with the CBS estimated results together with those obtained at the non-empirical RHF, MP2, SOPPA, SOPPA(CCSD) and CCSD(T)
levels and available experimental results to give
preference to the Keal-Tozer's family of NMR-oriented exchange-correlation generalized gradient approximation functionals KTn. In a later publication [41] it was shown that a linear correlation exists between 15N NMR nuclear shielding constants of N2 and NH3 calculated within the CBS limit using
the family of Jensen's polarization-consistent basis sets pcS-n and those evaluated with different DFT and non-empirical methods (including 42 DFT functionals together with RHF, MP2, SOPPA, SOPPA(CCSD) and CCSD(T) used in combination with aug-ccpVTZ-J basis set). It was shown that the remaining basis set error of the aug-cc-pVTZ-J basis set is very similar in DFT and CCSD(T) calculations. As the aug-cc-pVTZ-J basis set is significantly smaller,
CCSD(T)/aug-cc-pVTZ-J calculations allowed in
combination with affordable DFT/pcS-n complete basis set calculations the prediction of 15
N NMR nuclear shieldings at the CCSD(T) level of nearly similar accuracy as those
obtained by fitting results from computationally demanding pcS-n calculations at the CCSD(T) limit. It was found that significant saving of computational efforts could thus be achieved by scaling inexpensive CCSD(T)/aug-cc-pVTZ-J calculations of
15
N NMR
nuclear isotropic shieldings with affordable DFT complete basis set limit corrections. To continue these studies, a rough estimate of CCSD(T)/CBS and MP2/CBS nuclear isotropic shieldings of non-hydrogen atoms for molecular systems of medium size by combining less demanding DFT/CBS approach and affordable calculations at CCSD(T)/pcS-2 and MP2/pcS-2 levels of approximation was proposed [42]. This scheme was able to decrease the absolute errors by a factor of 3 or more in comparison to CCSD(T)/pcS-2 and MP2/pcS-2 calculations. A number of functionals and basis sets used for the calculation of
15
N NMR
chemical shifts in the key nitrogen-containing heterocycles (azoles, oxazoles, thiazoles, azines) have been recently tested for better agreement of DFT calculations with experiment [43]. In the calculation of 15N NMR chemical shifts, the best result has been achieved with the KT3 functional used in combination with Jensen’s pcS-3 basis set resulting in a value of mean absolute error as small as 5 ppm for the range of more than 270 ppm in a benchmark series of 23 nitrogen-containing heterocycles with an overall number of 41 different
15
N NMR chemical shifts, as illustrated in Fig. 1. Results of this
study [43] are summarized in Figs. 2 and 3, where the mean absolute errors of 15N NMR chemical shifts calculated in the whole series of 23 compounds, as compared to experiment, are arranged by the DFT functionals (Fig. 2) and basis sets (Fig. 3).
Fig. 1. Correlation plot of 15N NMR chemical shifts calculated in a series of 23 key azoles, oxazoles, thiazoles and azines at the DFT-KT3/pcS-3 level versus experiment. Reproduced from ref. [43] with permission of John Wiley and Sons Inc.
Fig. 2. Mean absolute errors of 15N NMR chemical shifts calculated in the same series of 23 key azoles, oxazoles, thiazoles and azines arranged by DFT functionals for different basis sets, as compared to experiment. Reproduced from ref. [43] with permission of John Wiley and Sons Inc.
Fig. 3. Mean absolute errors of 15N NMR chemical shifts calculated in the same series of 23 key azoles, oxazoles, thiazoles and azines arranged by basis sets for different DFT functionals, as compared to experiment. Reproduced from ref. [43] with permission of John Wiley and Sons Inc. The main conclusion drawn from these data is that the best result in the calculation of
15
N NMR chemical shifts of the representative series of the nitrogen-containing
heterocycles at the DFT level was achieved with correlation-exchange Keal-Tozer's KT2 [44] and KT3 [45] functionals and Jensen's pcS-2 and pcS-3 basis sets [46] characterized by a mean absolute error of about 5 ppm across a range of about 300 ppm.
2.3.
Locally dense basis sets
The general idea of the so-called Locally Dense Basis Set (LDBS) [47,48] is very simple: it consists in a dramatic decrease of computational demands by employing a large high-quality basis set on a particular atom or on a particular atom and on its first bonding
sphere and much smaller basis sets elsewhere in the molecule, preserving high accuracy at much lower computational cost. This approach has been shown to be very effective in calculating NMR chemical shifts and spin-spin coupling constants within a general Gauge Including Atomic Orbitals (GIAO) approach, as exemplified in a number of recent publications by Russian authors [49,50,51,52,53,54,55,56,57,58,59,60]. To the best of our knowledge, no such approach has been implemented, at least systematically, to the
15
N NMR chemical shifts, and one of such rare examples is
presented in the paper by Samultsev et al. [43] who have chosen a benchmark set of the most representative five- and six-membered heterocycles - N-methylpyrrole, oxazole, thiazole, pyridine, pyrimidine and 1,3,5-triazine. For this series, they have performed calculations of
15
N NMR chemical shifts at the GIAO-DFT-KT3 level with 6-
311++G(d,p), aug-cc-pVTZ and pcS-3 on nitrogen within different LDBS schemes by using 6-31G, 6-311G, 6-31G(d), 6-311G(d), cc-pVDZ, pc-1 and pc-2 for the rest of the molecules. The 15N NMR chemical shifts calculated within different LDBS schemes for the subject series of heterocycles are compiled in Table 1, while the corresponding values of the Mean Absolute Error (MAE) as compared with the full basis set (FBS) results are given in Table 2.
Table 1. 15
N NMR chemical shifts (ppm) of the representative five- and six-membered nitrogencontaining heterocycles calculated at the GIAO-DFT-KT3 level within the LDBS approximation as compared to FBS results.
Compound
N Me N O
Rest of molecule
Nitrogen basis set (LDBS)
6-31G
6-311G
6-31G(d)
6-311G(d)
cc-pVDZ
FBS
6-311++G(d,p)
-211.6
-209.7
-214.4
-212.0
-211.2
-210.2
aug-cc-pVTZ
-215.3
-212.8
-216.8
-213.8
-213.0
-213.1
pcS-3
-221.8
-220.2
-224.3
-222.4
-220.8
-219.6
6-311++G(d,p)
-119.2
-118.1
-121.9
-120.9
-120.0
-119.1
aug-cc-pVTZ
-125.0
-123.5
-125.5
-123.9
-122.8
-122.9
pcS-3
-127.1
-127.1
-129.5
-128.3
-126.6
-124.5
N S
N N N
N
N N
6-311++G(d,p)
-67.5
-66.8
-65.0
-64.0
-63.3
-61.5
aug-cc-pVTZ
-73.9
-72.0
-68.5
-66.3
-67.7
-60.6
pcS-3
-74.6
-73.6
-70.2
-68.7
-64.8
-62.6
6-311++G(d,p)
-63.1
-60.7
-68.1
-65.4
-64.8
-62.6
aug-cc-pVTZ
-69.8
-66.5
-72.0
-68.7
-67.6
-66.3
pcS-3
-71.5
-69.1
-74.1
-70.9
-69.2
-65.5
6-311++G(d,p)
-77.6
-76.5
-84.6
-83.2
-82.4
-81.5
aug-cc-pVTZ
-84.2
-82.2
-88.0
-86.1
-84.8
-85.7
pcS-3
-86.5
-85.7
-90.2
-88.6
-86.7
-85.7
6-311++G(d,p)
-87.0
-86.5
-95.1
-94.6
-93.8
-93.4
aug-cc-pVTZ
-93.1
-91.8
-97.7
-96.9
-97.7
-97.6
pcS-3
-96.2
-95.5
-100.7
-99.8
-98.0
-98.2
Table 2. Mean absolute errors (ppm) of 15N NMR chemical shifts calculated at the GIAO-DFTKT3 level within different LDBS schemes as compared to FBS results.
Rest of molecule Nitrogen 6-31G
6-311G
6-31G(d)
6-311G(d)
cc-pVDZ
FBS
6-311++G(d,p)
3.1
3.4
3.5
2.0
1.2
0.0
aug-cc-pVTZ
4.1
3.2
3.3
1.4
0.9
0.0
pcS-3
4.6
3.8
5.8
4.1
2.6
0.0
As
follows
from
these
results,
the
GIAO-DFT-KT3/pcS-3//pc-2
recommended as one of the most effective LDBS schemes for the calculation of NMR chemical shifts.
2.4.
Solvent effects
was 15
N
In most cases solvent effects in 15N NMR calculations are taken into account using the Tomasi's Integral Equation Formalism Polarizable Continuum Model scheme (IEFPCM) [61] reviewed in [62], which is often referred to as simply PCM. The idea of PCM is rather simple: the solvent effect is simulated as an apparent charge distribution spread on the cavity surface not taking into account solute-solvent interactions at short distances (the so-called non-electrostatic effects), so that all solvent effects calculated within the PCM scheme are constrained not to take into account any specific solvation effects. This model works quite well when no specific intermolecular solvate-solvent interactions are expected. In contrast, in supermolecular model (SM) solvent molecules are added directly into calculation space to form solvation complexes. Usually this is done in PCM media and denoted as SM+PCM. As an example, a systematic study of solvent effects for 15N NMR chemical shifts of pyrrole, pyridine and related five- and six-membered nitrogen-containing heterocycles has been performed in three essential papers by a group of Russian authors [63,64,65]. In the first paper [63], solvent effects were examined for the
15
N NMR chemical
shifts of pyrrole and N-methylpyrrole, see Table 3. It was shown that considerable deviations were observed for 15N NMR chemical shifts calculated for pyrrole in methanol and water, presumably due to specific interactions of the former with solvent molecules, in particular due to the weak hydrogen bonding between the NH proton of pyrrole and oxygen atom of a solvent. This is obviously due to a considerable contribution of a specific solvation effect which should therefore be considered in an explicit way. On the other hand, the lack of specific interactions resulted in a small difference between calculated and experimental
15
N NMR chemical shifts of N-methylpyrrole. Obviously,
the continuum model may be used to calculate 15N NMR chemical shifts for compounds that do not form intermolecular hydrogen bonds with solvent molecules. It was also found [63] that increase in the solvent polarity on going from carbon tetrachloride to water leads to deshielding of the nitrogen atom in pyrrole and N-methylpyrrole, so that their resonance signals are shifted by as much as 8–12 ppm downfield. Thus it followed that a continuum solvent model was insufficient for an adequate description of solvent effects in
15
N NMR chemical shifts of pyrrole in polar solvents, making it necessary to
include at least one solvent molecule in an explicit way.
Table 3. Calculated
15
N NMR chemical shifts (ppm) of the supermolecules of pyrrole
and N-methylpyrrole with one molecule of solvent in IEF-PCM media using different functionals with TZP basis set.
B3LYP/TZP Compound
PBE0/TZP
B1PW91/TZP
Solvent
Experiment
δ(15N)
Absolute error
δ(15N)
Absolute error
δ(15N)
Absolute error
CCl4
-232.1
5.7
-237.9
0.1
-237.3
0.5
-237.8
CHCl3
-227.4
7.3
-233.3
1.4
-231.5
3.2
-234.7
(CH3)2CO
-228.0
2.3
-233.7
3.4
-232.7
2.4
-230.3
CH3OH
-218.5
11.4
-224.8
5.1
-231.2
1.3
-229.9
(CH3)2SO
-215.1
9.1
-221.6
2.6
-221.0
3.2
-224.2
H2 O
-216.2
10.3
-222.5
4.0
-221.8
4.7
-226.5
CCl4
-225.7
8.4
-232.9
1.2
-232.0
2.1
-234.1
CHCl3
-224.4
6.4
-231.7
0.9
-231.0
0.2
-230.8
(CH3)2CO
-219.8
11.6
-227.1
4.3
-226.4
5.0
-231.4
CH3OH
-218.2
13.2
-225.6
5.8
-224.5
6.9
-231.4
(CH3)2SO
-219.1
10.2
-226.5
2.8
-225.5
3.8
-229.3
H2 O
-217.4
9.5
-224.9
2.0
-224.1
2.8
-226.9
Table 4. Calculated
15
N NMR chemical shifts (ppm) and their absolute errors (ppm) of
the supermolecules of pyridine, pyridazine, pyrimidine, pyrazine and 1,3,5-triazine with one molecule of solvent in IEF-PCM media at the KT2/aug-сс-pVTZ level.
15
Compound
N
N
N
N N
N NMR chemical shift
Solvent Calculated
Experimental
Absolute error
CCl4
-60.7
-60.5
0.2
CHCl3
-67.9
-68.7
0.8
CH3OH
-74.5
-81.1
6.6
H2 O
-75.3
-84.3
9.0
(CH3)2CO
-73.8
-61.8
12.0
(CH3)2SO
-74.9
-63.1
11.8
CCl4
32.4
29.4
3.1
CHCl3
22.6
19.0
3.6
CH3OH
13.4
6.3
7.0
H2 O
12.3
-6.2
18.5
(CH3)2CO
14.4
25.9
11.4
(CH3)2SO
12.8
20.9
8.1
CCl4
-81.5
-81.6
0.1
CHCl3
-87.4
-86.2
1.2
CH3OH
-92.8
-90.8
2.0
H2 O
-93.5
-97.1
3.7
(CH3)2CO
-92.2
-83.4
8.8
(CH3)2SO
-93.2
-83.9
9.3
N N
N
N N
CCl4
-47.2
-43.4
3.9
CHCl3
-52.9
-47.8
5.1
CH3OH
-58.1
-51.7
6.4
H2 O
-58.8
-59.0
0.3
(CH3)2CO
-57.6
-44.9
12.7
(CH3)2SO
-58.5
-45.3
13.2
CCl4
-93.8
-95.9
2.1
CHCl3
-98.9
-98.1
0.8
CH3OH
-103.5
-100.3
3.1
H2 O
-104.0
-106.3
2.3
(CH3)2CO
-102.9
-97.4
5.5
(CH3)2SO
-103.7
-98.1
5.7
In the second paper from this series [64], solvent effects were studied in the
15
N
NMR chemical shifts of a classical series of azines - pyridine, pyridazine, pyrimidine, pyrazine and 1,3,5-triazine in different solvents calculated with the use of Keal-Tozer's KT2 functional in combination with Dunning's aug-cc-pVTZ basis set, see Table 4. It was found that Tomasi's polarizable continuum model provides an appropriate simulation of solvation effects in weak polar aprotic solvents but that this model is clearly insufficient for the description of polar solvent effects, in particular of specific solvation via the formation of intermolecular complexes between solvent and solute. Based on these results, it was found that the most efficient way to take into account solvent effects was using the IEF-PCM model for non-polar solvents and a supermolecular approach (with at least one solvent molecule being included into calculation space in an explicit way) for specific solvation, typical of polar solvents. As an example, Figs. 4 and 5 show the supermolecules of, respectively, pyrrole and pyridine, with different solvents of different polarity studied in [65].
Fig. 4. Equilibrium geometries of supermolecules (1:1) of pyrrole with different solvents optimized at the MP2/6-311++G(d,p) level with taking into account bulk solvent effect within the IEF-PCM scheme. The salient interatomic distances are given in Å. Reproduced from ref. [65] with permission of John Wiley and Sons Inc.
Fig. 5. Equilibrium geometries of supermolecules (1:1) of pyridine with different solvents optimized at the MP2/6-311++G(d,p) level with taking into account bulk solvent effect within the IEF-PCM scheme. The salient interatomic distances are given in Å. Reproduced from ref. [65] with permission of John Wiley and Sons Inc.
As was shown in the same paper [65] (the third in this series), in some cases inclusion of more than one molecule of solvent into the calculation space could result in much improved agreement of calculation with experiment. It was found that the largest absolute error for the IEF-PCM scheme was observed for pyridazine in water (27.9 ppm). Undoubtedly, this is due to a strong specific solvation of pyridazine molecule by water, which is not accounted for in full by adding only one molecule of water into calculation space, resulting in unreasonably large absolute error of 15.5 ppm. Following this idea, calculations of 15N NMR chemical shift of pyridazine in water were performed [65] using the supermolecular scheme (1 : n), that is, adding consequently 1, 2, …, n molecules of water into calculation space of pyridazine, all placed into the IEF-PCM cavity. These results are illustrated in Fig. 6, and it is seen that the absolute error for the gas phase (solvent effect is not taken into account) is unreasonably large (51.8 ppm); that it is somewhat smaller, though still large, when the solvent effect is treated within the IEFPCM scheme (27.9 ppm); and that it sharply decreases with n when the supermolecule (1 : n) solvation model is applied, reaching 15.5 ppm at n = 1, 6.7 ppm at n = 2 and 5.6 ppm at n = 3. It thus appears that further increasing of the number of water molecules placed into calculation space makes no sense because at n > 2 the absolute error becomes less than mean absolute error of the IEF-PCM and supermolecular schemes in the whole series of compounds under study.
Fig. 6. Absolute errors of 15N NMR chemical shift of pyridazine in water calculated at the GIAO-DFT-KT3/pcS-3//pc-2 level using different solvation models to account for solvent effect. The most characteristic interatomic distances in the solvate are given in Å. Reproduced from ref. [65] with permission of John Wiley and Sons Inc. 2.5.
Rovibrational corrections
For a meaningful comparison of theory with experimental data, the so-called rovibrational corrections to the nuclear shieldings are necessary. Rovibrational and temperature effects play an important role in theoretical studies of
15
N NMR chemical
shifts, including vibrational corrections, rotational contributions, temperature averaging and secondary isotope effects [66]. One such study was that of Kupka et al. [39] for the
15
N NMR of the simplest
diatomic - the molecule of N2. In this paper, CBS-predicted theoretical 15N NMR nuclear shieldings calculated at experimental equilibrium geometry were compared to empirical equilibrium values including vibrational correction terms obtained from separate calculations. The contributions of Zero-Point Vibrations (ZPV) were calculated at the DFT (BHandH/pcS-2, BHandH/pcS-3) and MP2 levels with a pcS-3 basis set. In most cases, MP2 provided larger absolute corrections than those obtained at the DFT level. It was found that inclusion of the vibrational corrections leads to smaller shielding tensor values, and does not improve the overall agreement of 15N NMR nuclear shieldings with experimental results. The vibrational corrections calculated in this study seemed to be important, but their contribution might be smaller than the error of the equilibrium values. In a more recent paper [67] vibrational corrections were calculated at the CCSD(T) level for the chemical shifts of the noble gas dimers and the second-row, Ne2 in particular. The ZPV corrections to the values at the optimized geometries were found to be very small (<1 ppm) and did not reflect the large variations in the absolute shieldings. However, although the ZPV corrections were thus negligible for the dimer nuclear shieldings, they were more important for the dimer chemical shifts. Relative to the values at the optimized geometries, the ZPV-averaged chemical shifts were accordingly 43, 11, 5 and 3% smaller for Ne2, Ar2, Kr2 and Xe2. Since all other calculations in this work were carried out at the experimental geometries, it was, however, more relevant to compare with those values at experimental geometries. Compared to these values, the ZPV
averaged chemical shifts for Ne2, Ar2 and Kr2 were reduced by accordingly 38, 18 and 42%, while for Xe2, the chemical shift was actually increased by 3%. A series of further recent publications by the same team (principal authors: Buczek and Kupka) devoted to harmonic and anharmonic vibrational modes in the Kohn-Sham limit for simple molecules has recently appeared [68,69,70,71,72,73,74]. In particular, it was shown [68] that the calculated wavenumber of the anharmonic asymmetric stretching mode is very sensitive to grid size for large basis sets which was not observed for harmonic modes. As a result, BLYP-calculated anharmonic frequencies consistently underestimated observed wavenumbers. It was shown that increasing the Pople's basis set size did not lead to improved agreement between anharmonic frequencies and experimental values. In the next paper in the series [69] it was demonstrated that the anharmonic frequency of the diagnostic amide vibration C=O in gas phase and in solution was significantly closer to experiment than was the case for the corresponding harmonic frequency. Both harmonic and anharmonic calculated frequencies of the C=O stretching mode decreased linearly with solvent polarity. However, an unphysical behavior of solvent dependence of some low frequency anharmonic amide modes of formamide was found, probably due to the presence of strong anharmonicity and Fermi resonance. In the third paper from this series [70] a linear correlation between harmonic and anharmonic frequencies of water calculated at the B3LYP level of theory was observed with a number of basis sets. Similar relationships were found in calculated data for both the gas phase and solution for several small molecules. The proposed approach was tested successfully
on a larger
molecule
of
E
and
Z isomers
of
N-acetyl-α,β-
dehydrophenylalanine-N′,N′-dimethylamide [71]. In this paper, solvent effect was approximated using a simple PCM model, the pc-n basis sets were selected, and the CBS results were estimated with the two-parameter formula for the corresponding B3LYP Kohn–Sham limits, calculated in the gas phase and in solution. However, no unique method was suggested that correctly reproduced fundamental modes in gas phase. In the case of water all studied methods performed very similarly. A singularity was observed for some vibrational modes sensitive to solvent effect. In two recent publications from this series [72,73] the ZPV corrections were examined in cytosine and ethylene. Thus the applicability of the popular and efficient B3LYP hybrid density functional and medium-size Pople type basis set in combination
with a computationally expensive anharmonic model to obtain a more accurate theoretical structure, vibrational frequencies and NMR parameters of cytosine was tested [72]. This paper included prediction of cytosine equilibrium and rovibrationally averaged structures and harmonic and anharmonic vibrational frequencies in the gas phase and DMSO solution. In comparison with initial harmonic data, a significantly better agreement between scaled and anharmonic frequencies versus experiment was observed. On the other hand, the regular convergence patterns of harmonic and anharmonic vibrational parameters towards the Kohn–Sham complete basis set limit in water were demonstrated for the first time [73]. The authors examined the performance of the vibrational perturbation scheme implemented using BLYP and B3LYP in combination with two Pople's basis sets, 6-311++G** and the much larger 6-311++G(3df,2pd), the polarization consistent basis sets pc-n, aug-pc-n and pcseg-n (n = 0, 1, 2, 3, 4) together with correlation-consistent basis sets cc-pVXZ and aug-cc-pVXZ (X = D, T, Q, 5 and 6). The BLYP-calculated harmonic frequencies were found to be markedly closer to the experimental values than were the B3LYP-calculated harmonic frequencies, while the calculated
anharmonic
frequencies
consistently
underestimated
the
observed
wavenumbers. The different basis set families gave very similar estimated values for the CBS parameters. The anharmonic frequencies calculated with B3LYP/aug-pc-3 were significantly higher than those obtained with pc-3 basis set. However, applying the augpcseg-n basis set family alleviated this problem. Utilization of B3LYP/augpcseg-n basis sets instead of B3LYP/aug-cc-pVXZ (the latter being less computationally expensive) was suggested for medium-sized molecules. It was also found [73] that harmonic BLYP/pc-2 calculations produced fairly accurate frequencies as compared to experiment. In the most recent study by Faber et al. [74] the method and basis set dependence of the zero-point vibrational corrections to NMR shielding constants and anisotropies have been investigated. A systematic comparison has been made at the MP2, CCSD and CCSD(T) levels together with Kohn–Sham density functional theory with the B3LYP exchange-correlation functional methods in combination with the second order vibrational perturbation theory approach for the vibrational corrections. The results showed that basis set convergence of the vibrational corrections was not monotonic and that very large basis sets were needed before a reasonable extrapolation to the basis set limit could be performed. Furthermore, the results of this study suggested that coupled cluster methods and a decent basis set were required before the error of the electronic
structure approach was lower than the inherent error of the second order vibrational perturbation theory approach.
2.6.
Relativistic effects
Relativistic effects evaluated from relativistic two- and four-component Hamiltonians play a major role in the calculation of NMR parameters, as derived and exemplified in a number of very recent [75,76,77,78,79,80,81,82,83,84,85,86] as well as earlier [87,88,89,90,91,92,93,94,95,96,97] publications by Aucar and coworkers; see also reviews on relativistic calculations of NMR parameters [13,14,15,16,17]. These cited publications outline some basic concepts of relativistic quantum chemistry and recent developments of relativistic methods for the calculation of NMR shielding constants, indirect nuclear spin-spin coupling and electric field gradients (nuclear quadrupole coupling). Density functional methods have been very successful in calculations of molecular properties, despite a number of problems related to approximations in the functionals. In particular, for heavy-element systems, the large electron contribution and the need for a relativistic treatment often restrain the application of correlated wave function ab initio methods [16]. As a matter of fact, almost nothing is known about relativistic effects in
15
NMR
chemical shifts and it is generally believed that they are next to negligible, which would make it safe not to take them into account in practical calculations. However, for
15
NMR
chemical shifts, such effects may be expected when nitrogen atom is bonded to, or in close proximity to, a heavy element. Examples of the first case are very scarce because chemical compounds containing N-X bonds (where X is a heavy element) are rather uncommon. More examples can be found for N-C-X, N-C-C-X or N-C-C-C-X moieties, however, these long-range relativistic effects are generally believed to be negligible and not worth studying. For these reasons, documentation of relativistic effects in
15
NMR
chemical shifts are very scarce in the literature. Nonetheless, one such rare example is reported in a very recent publication by Samultsev et al. [98], who studied the long‐range β‐ and γ‐relativistic effects of halogens in 15N NMR chemical shifts of 20 halogenated azines (pyridines, pyrimidines, pyrazines, and 1,3,5‐triazines). Relativistic effects were shown to be inessential for fluoro‐, chloro‐,
and bromo‐derivatives (1–2 ppm in average for bromine and much less for chlorine and fluorine). However, for iodo-containing compounds, β‐ and γ‐relativistic effects are important contributors to the accuracy of the
15
N NMR calculation. Indeed, taking into
account long‐range relativistic effects essentially improves the agreement of calculation with experiment. Thus, mean average errors of the 15N NMR chemical shifts of the title compounds calculated at the non‐relativistic and full four‐component relativistic levels in gas phase are accordingly 7.8 and 5.5 ppm for the range of about 150 ppm. Taking into account solvent effects within the PCM scheme marginally improves agreement of computational results with experiment, decreasing MAE from 7.8 to 7.4 ppm and from 5.5 to 5.3 ppm at the non‐relativistic and relativistic levels, respectively (See Fig. 7). The best result (MAE 5.3 ppm) was achieved at the four-component relativistic level using Keal and Tozer's KT3 functional used in combination with Dyall's relativistic basis set dyall.av3z while taking into account solvent effects within the polarizable continuum solvation model. Such long‐range relativistic effects play a major role (of up to dozen of parts per million) in the
15
N NMR chemical shifts of halogenated nitrogen‐containing
heterocycles, and are especially crucial for iodine derivatives. Thus, this effect should apparently be taken into account for practical purposes.
Fig. 7. Mean absolute errors of 15N NMR chemical shifts in the series of 20 halogenated azines (pyridines, pyrimidines, pyrazines, and 1,3,5‐triazines) calculated at the non‐relativistic and four‐component relativistic KT3/dyall.av3z levels. Solvent effects are taken into account within the non‐relativistic IEF‐PCM solvation model. Reproduced from ref. [98] with permission of John Wiley and Sons Inc. More examples can be found in heavy metal complexes with nitrogen-containing ligands such as those reported in the paper by Pazdersky et al. [99], where an attempt was made to take into account relativistic effects at the two-component Zeroth Order Regular Approximation contributions to
15
(ZORA)
level
accounting
for
both
scalar
relativistic
N NMR chemical shifts (Darwin correction and mass-velocity
correction together with spin-orbit contribution) in gold(III), cobalt(III) and rhodium(III) chloride complexes with pyridine, 2,2'-bipyridine and 1,10-phenanthroline. However, ZORA calculations have generally resulted in errors comparable to those obtained by the effective core potential methods that do not take into account relativistic effects. In this paper, the inclusion of spin-orbit relativistic interactions resulted in slightly better agreement with experiment only in the case of the heaviest Au(III) central ion in this series, and resulted in almost no effect in Co(III) and Rh(III) chloride complexes. In the recent paper by Jankowska et al. [67] relativistic corrections were reported for the noble gas dimers. In this paper, relativistic corrections were calculated with the scalar and spin-orbit zeroth-order regular approximation Hamiltonian in combination with the large Slater-type basis set QZ4P as well as with the four-component Dirac– Coulomb Hamiltonian using Dyall’s acv4z basis set. The relativistic corrections to the nuclear magnetic shieldings and chemical shifts were combined with CCSD(T) calculations using a very large polarization consistent basis set, aug-pcSseg-4. The size of the relativistic contribution to nuclear shieldings were essentially the same for the noble gas dimers and free atoms. At the Hartree-Fock level they were <0.1% (He), 0.6% (Ne), 1.7% (Ar), 5.8% (Kr), and 13% (Xe) of the total ZORA values and <0.1%, 1.1%, 2.9%, 9.5%, and 19.6% of the total four-component relativistic values, respectively. This is by far a more important contribution as compared to both electron correlation and vibrational corrections. It followed that relativistic corrections to helium and neon nuclear magnetic shieldings could safely be omitted in nuclear shielding calculations. For the chemical shifts of the noble gas dimers, relativistic corrections almost cancel each other (which is referred to as "mutual compensation of errors"), so that ZPV corrections
become more important than relativistic corrections, and this statement could be safely extended to 15N NMR chemical shifts.
2.7.
Practical recommendations
Level of theory, functionals and basis sets. Based on our experience of calculating 15
N NMR chemical shifts for medium-sized nitrogen-containing compounds, for practical
purposes we recommend using the DFT level with Keal and Tozer's generalized gradient exchange-correlation functional, KT2, and generalized gradient functional with the gradient-corrected exchange and correlation terms, KT3, in combination with Jensen's NMR-oriented pcS-2 and pcS-3 basis sets on nitrogen(s) and pc-2 elsewhere in the molecule within the LDBS scheme. Solvent effects. For all practical calculations of
15
N NMR chemical shifts, we
recommend taking into account solvent effects at the IEF-PCM level when no specific solute-solvent interactions are expected, and at the supermolecular level otherwise. Rovibrational corrections and relativistic effects. Rovibrational corrections play a major role in the calculation of 15N NMR chemical shifts. However, their evaluation even at the uncorrelated level with small basis sets is extremely computationally demanding, so that unfortunately in most cases they can be calculated only for very small molecules. Relativistic effects are also very time consuming and computationally demanding but fortunately they are negligibly small for
15
N NMR chemical shifts provided no heavy
atom is bonded to a nitrogen atom directly, and such cases are very rare in practice. So, in the majority of cases, relativistic effects could safely be neglected in practical calculations. Converting calculated shielding constants to chemical shifts. The term "shielding constant" originates in the concept of the effective nuclear charge, which may be defined as the actual nuclear charge minus the screening effect caused by the electrons intervening between the nucleus and valence electrons. In other words, the actual charge is equal to what is expected from a certain number of protons, but minus a certain amount of charge from the electrons. Shielding constants consist of diamagnetic and paramagnetic parts. The diamagnetic term describes the net electron density around the nucleus, while the paramagnetic shielding term arises from the perturbation of the ground state wave
function due to the coupling between electronic orbital momentum and the external magnetic field. Application of an external magnetic field induces electronic currents that, in turn, generate an additional local magnetic field. In atoms, which are spherically symmetric, these currents are purely diamagnetic in origin and the resulting local magnetic field opposes the external field leading to shielding of the atomic nucleus (lowering of the resonance frequency). However, in molecules, the circulation of electronic currents around the nucleus is hindered due to the presence of other nuclei and electrons revolving about them, and this deviation from spherical symmetry leads to the emergence of an additional contribution to the total nuclear shielding, which is known as the paramagnetic term. Because the paramagnetic contribution opposes the diamagnetic shielding, this results in deshielding (an increase in the resonance frequency) of the target nucleus as compared to an isolated atom [11]. Calculated
15
N absolute shielding constants should be converted into
15
N NMR
chemical shifts as recommended by IUPAC [100] using the equation δ = (σo – σ)/(1 - 10-6 σo), where σ and σo (ppm) are the
15
(1)
N NMR isotropic absolute shielding constants of,
respectively, a compound under consideration and neat nitromethane used as a standard. For this standard, a value of σo = -139.5 ppm was evaluated at the KT3/pcS-3 level [65] for the individual molecule of nitromethane and σo = -140.9 ppm calculated by the same authors at the same level of theory for the optimized cluster of the mostly computationally achievable five molecules of nitromethane in IEF-PCM continuum (averaged over all nitrogens in the intermolecular complex modelling neat liquid phase). It is interesting to note that an absolute 15N NMR shielding scale was proposed long ago by Jameson et al. [101] based on extrapolating
15
N NMR gas phase measurements to a
zero-density limit as well as molecular beam experiments, giving the absolute
15
N
shielding constant of neat nitromethane of -135.8 ppm, which is rather close to both values calculated most recently at the KT3/pcS-3 level. Software. Based on our experience, among dozens of software packages which might be used for the calculation of 15N NMR chemical shifts at the non-relativistic and relativistic levels we recommend the following: Geometry optimization: GAMESS [102], GAUSSIAN [103];
Non-relativistic calculations of 15N NMR chemical shifts: DFT, RHF, RPA levels - DALTON [104], GAUSSIAN [103]; MP2, CCSD, CCSD(T) levels - CFOUR [105]; Rovibrational corrections to 15N NMR chemical shifts: DFT, RHF, RPA levels - DALTON [104]; MP2, CCSD, CCSD(T) levels - CFOUR [105]; Relativistic calculations of 15N NMR chemical shifts: two-component level - ADF [106]; four-component level - DIRAC [107].
3. 3.1.
Structural applications Open-chain nitrogen-containing compounds
This Section covers compounds that contain side-chain nitrogen atoms, i.e. those that are not part of a heterocyclic moiety. In an early publication by Schraml et al. [108],
15
N NMR chemical shifts were
calculated at the GIAO-B3LYP/6–31+G∗ level in an extensive series of para-, meta- and ortho-substituted benzonitriles, X–C6H4–CN, and compared with thorough experimental measurements. The former exhibited the expected positive correlations with Hammett substituent constants, and they fitted well with the dual substituent parameter analysis including field and resonance σ-constants and correlated with the
13
C substituent
chemical shifts of the nitrile carbon. The deviations noted for hydroxyl derivatives were shown to be due to the interaction of the nitrile nitrogen with the OH group. The negative correlations with 13C substituent chemical shifts were explained by the polarization of the C≡N bond. Good correlations between DFT calculated and observed 15N NMR chemical shifts signified that the calculations, at the level used, are useful, provided that sufficient care is taken not to include compounds involving specific interactions. More recently, a theoretical and experimental
15
N NMR study of five
nitrobenzene-1,2-diamines has been carried out [109]. The combination of experimental results together with DFT calculations has resulted in a very coherent picture of
15
N
NMR chemical shifts in a series of nitro-o-phenylenediamines. It was found that calculated
15
N NMR chemical shifts for the nitrogen atoms can be analyzed using an
additive model for substituents, providing the rotational barriers around amino groups are sufficiently low. In a continuation of this study,
15
N NMR chemical shifts of eighteen
aliphatic linear amines, from methylamine to stearylamine, have been experimentally studied and theoretically calculated at the GIAO-B3LYP/6-311**G(d,p) level [110]. An exploration of their conformation has been carried out, mainly to determine the conformational effect on 15N NMR chemical shifts. In solution, 15N NMR chemical shifts indicated the presence of a mixture of two rapidly interconverting conformers. Very recently Semenov et al. [111] investigated the performance of different computational schemes used for calculation of
15
N NMR chemical shifts in a
representative series of sixteen open-chain amides. Among three different functionals, B3LYP, B3PW91 and KT3, used in combination with three different basis sets, 6311++G(2d,2p), aug-cc-pVTZ and pcS-3, the best performance was observed for the combination of KT3 with pcS-3. The most straightforward LDBS approach using pcS-3 on nitrogens and pc-2 on the rest of atoms (KT3/pcS-3//pc-2) results in a dramatic decrease in computational cost (more than an order of magnitude in time scale) with insignificant loss of accuracy as compared to the full basis set scheme. Taking into account solvent effects at either PCM or SM+PCM level (in the latter case, via adding one molecule of a solvent into computational space explicitly in the appropriate IEFPCM medium) generally improved the agreement of calculated 15N NMR chemical shifts of amides with experiment. Fig. 8 shows the mean absolute errors of the
15
N NMR
chemical shifts of sixteen representative amides studied in [111] and calculated using different methods (for details, see caption to figure). It is seen that best result (MAE 5.8 ppm) is achieved with KT3/pcS-3 full basis set scheme with solvent effects taken into account in explicit way using supermolecular (1:1) model.
Fig. 8. Mean absolute errors of calculated 15N NMR chemical shifts in the series of sixteen amides at the KT3/pcS-3 level in gas phase (GP), in solution within the PCM scheme (PCM) and with supermolecular model in PCM medium (SM+PCM) using locally dense basis set (LDBS) and full basis set (FBS) schemes. Reproduced from ref. [111] with permission of John Wiley and Sons Inc. In a very recent publication by the same authors [112] the benchmark calculations of 15N NMR chemical shifts in the series of sixteen open-chain amines were performed at the DFT level using different functionals and basis sets with particular interest concentrated on solvent effects and the so-called "multistandard scheme". Taking all these factors into account resulted in a noticeable improvement of the agreement of the calculated 15N NMR chemical shifts with experiment, decreasing MAE from 13 to 4 ppm for a range of about 60 ppm.
3.2.
Nitrogen heterocycles
In an early paper by Claramunt et al. [113]
15
N NMR chemical shifts were
calculated at the RHF/6-311G** level in a representative series of azolides (Nacylazoles), which are a characteristic and well-studied class of heterocyclic compounds that includes derivatives of pyrrole, imidazole, pyrazole, both triazoles, tetrazole, pentazole, indole and carbazole. In the correlation equation of 15N NMR chemical shifts with nitrogen shielding constants the intercept (-130 ppm) was not far away from the
absolute shielding constant of nitromethane in CDCl3 (-139.2 ppm), the reference substance used in
15
N NMR spectroscopy. The calculated values of
15
N NMR chemical
shifts predicted that based on such values, it would be easy to determine the position of the acetyl group in azole moiety. Extending such studies, molecular structures and tautomeric equilibria and transformations of halogenotriazoles have been investigated [114] by means of X-ray molecular structures and calculation of 15N NMR chemical shifts at the GIAO-B3LYP/631G* level. Based on these results, the tautomeric structures of halo-1,2,4-triazoles have been determined unambiguously. In particular, it was shown that a halogen substituent prefers to occupy the 3-position and that a tautomeric proton at N-1 links, through hydrogen bonds, to the N-4 of another molecule. The structure of N1-hydroxylophine N3-oxide in solid state and liquid phase was determined by means of X-ray powder-diffraction data and 15N NMR calculations at the GIAO-B3LYP/6-31G* level and compared with experiment [115]. Calculated 15N NMR chemical shifts of the title compound together with three model benzotriazoles allowed their unambiguous structural elucidation. These and preceding early papers of this group of authors dealing with structural applications of the calculations of
15
N NMR chemical shifts in nitrogen-containing
heterocycles are discussed in more detail in the early review by Alkorta and Elguero [116]. In more recent publications by Alkorta and coworkers, calculations of
15
N NMR
chemical shifts were exploited to investigate the molecular structure and NMR properties of P-phosphinoylmethyl aminophosphonium salts [117], to study amines and to reveal the potential of
15
15
N shieldings in
N NMR calculations in conformational analysis
[118], to elucidate the structure of 1,1,3-trimethyl-Δ2-pyrazolinium perchlorate [119], Nsubstituted pyrazoles [120], N-substituted pyrazoles and indazoles [121], and a series of Tröger's bases and related compounds [122]. The computation of
15
N NMR chemical
shifts was used to study the structure of pyrazolo[1,5-a]pyrimidines (the products obtained by condensation of 3(5)-amino-4-phenyl-1H-pyrazole and β-dicarbonyl compounds bearing a trifluoromethyl group) [123], a number of open-chain aliphatic, aromatic and heteroaromatic nitrogen-containing compounds [124], the NH and OH tautomers of pyrazolinones [125], three bis(amino acids) linked by the amino groups (namely alanine-alanine, alanine-glycine and glycine-glycine) [126], three targeted azines
(benzalazine, acetophenoneazine and cinnamaldazine) [127], two tautomeric bispyrazolylbenzenes providing a proton-transfer dynamic equilibrium [128], and a series of N-H, N-methyl and N-propyl aziridines and their C-lithium derivatives [129]. More recently, García et al. [130] employed calculation of
15
N NMR chemical
shifts to study the structure of aminobenzimidazoles in solution and in solid state. The tautomerism
of
4(7)-aminobenzimidazoles
and
5(6)-aminobenzimidazoles
was
investigated, and a clear predominance of the 4-amino tautomer over the 6-amino tautomer was established, in line with team included computational
15
15
N NMR calculations. Further papers from this
N NMR studies of five borates (from the borohydride to
tetrakis(pyrazol-1-yl)borate) anions [131], seventeen derivatives of 1H-pyrazoles, 1H1,2,4-triazoles and 1H-1,2,4-diazaphospholes (three of them existing in two tautomeric forms, thus forming 20 families of compounds) [132], NH-benzimidazoles in solution and in the solid state demonstrating proton transfer and tautomerism [133], a series of of 2,2'-, 3,3'- and 4,4'-bipyridines and their conjugated acids [134], together with some novel [1,2,4]-triazolo-[1,5-α]pyrimidine derivatives prepared by oxidative cyclization of suitable N-benzylidene-N'-pyrimidin-2-yl hydrazine precursors [135]. Other nitrogen-containing heterocycles studied via calculation of their
15
N NMR
chemical shifts were 2,4,6-trifluoro-1,3,5-triazine, a highly symmetrical molecule with NMR parameters obtained by reducing its symmetry through the introduction of 14N/15N isotopomers [136], three benzazoles (1H-benzimidazoles, 1H- and 2H-indazoles, 1H- and 2H-benzotriazoles) reviewed in [137], and three azines derived from 2-formylimidazole, 4(5)-formylimidazole and 4(5)-formyl-5(4)-methylimidazole [138]. In the most recent publications by Alkorta and coworkers calculation of 15N NMR chemical shifts at the DFT level was used to study the structure of parent 1-, 2-, and 3pyrazolines and their methylated derivatives [139] together with representative azolo[α]pyrimidines including targeted pyrazolo[1,5-α]pyrimidines [140], a series of 4,5,6,7-tetrafluorobenzazoles with special emphasis on PCM calculations of chemical shifts [141], a representative series of atranes [142], and pyridine-supported bicyclic guanidine superbases [143]. Recently 15N NMR chemical shifts of a sizeable number of azoles and azines have been calculated at the DFT level by a group of Russian authors [43,63,64,65]. It was shown that the most reliable functional was KT2 of Keal and Tozer used in combination with Jensen's pcS-3 on nitrogen and pc-2 elsewhere, as illustrated in Fig. 9 showing
correlation plots of calculated
15
N NMR chemical shifts in IEF-PCM media and for
supermolecular model versus experiment for 27 azoles and azines [65].
Fig. 9. Correlation plots of calculated 15N NMR chemical shifts of a series of 27 targeted azoles and azines (10 solvents for each compound) in IEF-PCM media and in supermolecular (1:1) IEF-PCM media versus experiment (460 points in total). Reproduced from ref. [65] with permission of John Wiley and Sons Inc. Results of this study [65] showed that for nonpolar solvents (cyclohexane, carbon tetrachloride, benzene, chloroform and dichloromethane) taking into account solvent effects within either IEF-PCM or supermolecular schemes resulted in improved agreement of calculated
15
N NMR chemical shifts with experiment by about 2 ppm.
There was almost no difference between those two methods of taking into account solvent effects, implying that no specific solvation effects were occurring in these nonpolar solvents. On the other hand, a difference between results from these methods became visible in calculations for polar and especially polar protic solvents, where the supermolecular scheme improved agreement with experiment as compared with IEFPCM by about 1-2 ppm, reaching almost 6 ppm for water. This result indicated that there was a marked specific solvation of nitrogen-containing heterocycles by water, so that the use of the supermolecular scheme is strongly recommended to account for solvent effects in water solutions.
Experimental and calculated
15
N NMR chemical shifts were used in structural
elucidation of bis[(z)-cyanomethylidene]-diazapentacyclodienedicarboxylates comprising both the tetrahydropyridine rings and highly reactive cyano and carboxylate groups, and regarded as an intermediate stage for further preparation of biologically active amides and acids [144]. A joint application of the DFT calculations of 1Н and 13С and 15N NMR data for a series of the E and Z isomers of 1-styrylpyrroles, 1-(1-propenyl)pyrroles, 1vinylpyrroles and styrene suggested a reduction of conjugation between the unsaturated fragments, which was interpreted [145] as the result of the mutual influence of the donor conjugation. The Z isomer of 1-styrylpyrrole was shown to have an essentially nonplanar structure because of steric hindrance while the E isomer of 1-styrylpyrrole was also shown to have an out-of-plane structure despite the absence of a sterical barrier. Deviation of the E isomer from the planar structure seemed to be caused by the influence of conjugation. The structure of the E isomer of the 2-substituted 1-styrylpyrroles was similar to that of the 2-substituted 1-vinylpyrroles. Based on
15
N NMR calculations,
steric effects in the Z isomer of the 2-substituted 1-styrylpyrroles were interpreted as resulting from an increase of the dihedral angle between the planes of the pyrrole ring and double bond [145]. Another example of structural elucidation based on
15
N NMR
calculations is presented in the paper by Afonin et al. [146], where 1H, 13C, 15N and 77Se shielding constants in the configurational isomers of selenophene-2-carbaldehyde azine were evaluated at the MP2-GIAO level, allowing determination of the energy-favorable conformation of the title compound with syn orientation of both selenophene rings relative to the C=N groups. In the recent paper by Semenov et al. [147] the tautomeric structure of 4trifluoromethyl[b]benzo-1,4-diazepine system in solution has been evaluated by means of the calculation of
15
N NMR chemical shifts of the individual tautomers in comparison
with the averaged experimental shifts to show that the enamine-imine equilibrium is entirely shifted toward the imine form. Indeed, using the remarkable gap of about 250 ppm between amine-type and imine-type nitrogens, one can easily estimate the tautomeric ratio in the enamine–imine equilibrium based on the calculated
15
N NMR
chemical shifts of individual tautomers A, B and C (Fig. 10) in comparison with the averaged experimental shifts.
Fig. 10. Tautomeric forms of 4-trifluoromethyl[b]benzo-1,4-diazepine system. The adequacy of theoretical level used for the computation of 15N NMR chemical shifts in this study [147] has been verified based on the benchmark calculations in a series of the model push-pull and captodative enamines together with related azomethynes, which demonstrated a good to excellent agreement with experiment.
3.3.
Protonated nitrogen-containing compounds
Protonation effects on nitrogen are of prime practical importance for the structural elucidation of the biologically active nitrogen-containing compounds. For instance, there is a practically important and marked upfield protonation shift of about 100 ppm in 15N chemical shifts that is observed, for example, in the series of the Schiff bases of 3hydroxypyridine-4-carboxaldehyde with 1-aminopyrazole and 1-aminobenzimidazole related to pyridoxal-5'-phosphate [148], a natural biologically active form of vitamin B6,. It is well known that both liquid and solid-state 15N NMR chemical shifts of aminoacids, peptides and related biochemical species are extremely sensitive to the protonation state, tautomeric structure, hydrogen bonding and rotameric structures [149]. In addition,
15
N
NMR measurements of nucleoside bases can serve as a direct probe for studies of nitrogen environment in oligomeric fragments of nucleic acids and nucleosides, resulting in a deeper insight in vitally important phenomena such as self-association, molecular recognition and base-pairing, and providing a powerful tool in structural elucidation of nitrogen-containing organic and biological molecules. Noticeable protonation effects (exceeding 100 ppm) in protonated amines, imines, azoles and azines were shown [150] to originate mainly in the changes of paramagnetic terms of the nitrogen shielding constants, with the diamagnetic term remaining fairly
constant. The nature of the upfield (shielding) protonation effect in
15
N NMR of azines
and azoles was explained by the change of the contribution of the sp2-hybridized nitrogen lone pair on protonation that causes a marked shielding of nitrogen by about 100 ppm. In contrast, for amine nitrogen protonation of the nitrogen lone pair results in a deshielding protonation effect of about 25 ppm; thus the total deshielding protonation effect is due to the interplay of the contributions of other adjacent natural bond orbitals. This was rationalized in terms of the Natural Chemical Shielding [151] analysis within a general Natural Bond Orbitals approach of Weingold [152], as illustrated below for pyridine (Fig. 11), representing aromatic nitrogen-containing heterocycles, and trimethylamine (Fig. 12), representing open-chain aliphatic amines [150].
Fig. 11. Isosurfaces of salient natural bond orbitals of pyridine and protonated pyridine accounting for the protonation effect on 15N NMR absolute shielding constants. Reproduced from ref. [150] with permission of John Wiley and Sons Inc.
Fig. 12. Isosurfaces of salient natural bond orbitals of triethylamine and protonated triethylamine accounting for the protonation effect on 15N NMR absolute shielding constants. Reproduced from ref. [150] with permission of John Wiley and Sons Inc. As follows from these results, protonation effects are determined by the change in the shielding contribution of the nitrogen lone pair, noticeably exceeding 100 ppm and serving as a guiding thread in the unambiguous elucidation of the protonated forms of nitrogen-containing compounds [150].
3.4.
Coordination complexes
Examples of
15
N NMR calculations to determine the structure of coordination
complexes are provided in a series of publications by Pazderski et al. [153,154,155] who calculated number
15
of
N NMR coordination shifts of Pd(II) and Pt(II) chloride complexes with a nitrogen-containing
heterocycles
(pyridine,
2,2'-bipyridine,
1,10-
phenanthroline, quinoline, isoquinoline and 2,2'-biquinoline) at the B3LYP/LanL2DZ level (implying LDBS schemes) and found that they are noticeably dependent on the type of a platinide metal and coordination sphere geometry. The formation of the platinide metal-nitrogen bonds results in significant (ca 78–100 ppm) high-field
15
N NMR
coordination shifts. It was also found that this shielding effect is larger for Pt(II) than
Pd(II) complexes (by ca 15 ppm), decreasing upon the change of trans to cis geometry by ca 15 ppm. It was suggested that such a phenomenon, occurring via the decrease of the absolute value of paramagnetic contribution in the relevant
15
N shielding constant, is
probably caused by the replacement of the main n(N)→π* electronic transition by that of n(N-M)→π*, resulting in an increase of the mean electron excitation energy. Generally, these calculations predicted a large
15
N shielding effect upon complexation of nitrogen-
containing compounds. Although the calculated absolute values of the respective highfield
15
N NMR coordination were noticeably smaller than in real experiments, the
phenomenon itself remains the same. The improvement of calculated results relative to experiment after inclusion of solvent effects was rather small, which is consistent with a fact that
15
N NMR chemical shifts of the nitrogen-containing heterocycles together with
their platinide(II) chloride complexes are only slightly dependent on the solvent. In a continuation of this study,
15
N NMR coordination shifts of the related
complexes of nitrogen-containing heterocycles with Au (III), Co(III) and Rh(III) [99], Au(III), Pd(II) and Pt(II) [156,157,158], and Fe(II), Ru(II) and Os(II) [159] were investigated at the same level of theory and in the same manner. For the gold(III), cobalt(III) and rhodium(III) chloride complexes with pyridine, 2,2'-bipyridine and 1,10-phenanthroline it was found [99] that metal coordination generally results in large
15
N NMR high-field shifts (78–107 ppm), with their absolute
magnitudes increasing in the order of Au(III) < Rh(III) < Co(III). For Au(III) complexes, the
15
N NMR coordination shifts range from 78 to 85 ppm, while for the Co(III) and
Rh(III) complexes they are within relatively broad ranges, namely from 88 to 107 ppm, and from 82 to 96 ppm, with their absolute values being always larger (by 6–11 ppm) for the respective cobalt species than for the rhodium ones. The
15
N NMR chemical shift
calculations have been done separately for each type of central ion, and this is why computational results have not reproduced the experimental differences between the metals under study. However, the application of fitting procedures using distinct empirical constants for Au, Co and Rh species has been necessary because without them 15
N NMR chemical shifts did not reflect actual metal-dependent trends. Nevertheless, the
approach used did finally provide qualitatively consistent results within each group of complexes containing the same metal, reproducing well the correlations between the fitted calculated values and structural features of the molecules such as the coordination sphere geometry and the type of ligand, even in the case of methods excluding solvent
effects. The quantitative agreement between calculated and experimental
15
N NMR
chemical shifts was noticeably improved by the use for ligand atoms of the Pople's 6– 31G** and 6–31G* basis sets (containing polarization functions) and the B3LYP functional upon geometry optimization. Taking into account solvent effects yielded a slightly better agreement with experiment for the Au(III) complexes, but not for those of Co(III) or Rh(III). For the Au(III), Pd(II) and Pt(II) chloride complexes with picolines and phenylpyridines [156,157,158], quantum-chemical calculations of
15
N NMR chemical
shifts were performed at the B3LYP/LanL2DZ level (implying the LDBS scheme) in gas phase, and taking into account solvent effects within the PCM model with geometries directly constructed by molecular modelling and then optimized using the B3LYP/LanL2DZ+6-31G* method. These calculations were performed to reproduce the experimentally observed structural trends between Au(III), Pd(II) and Pt(II) complexes, as well as their trans and cis isomers. These calculations qualitatively reproduced the 15N NMR high-field shifts observed upon complexation by platinide(II) ions. However, calculated 15N NMR coordination shifts were found to be generally almost half the size of those found in real experiments. Furthermore, no significant distinction between Pd(II) and Pt(II) complexes could be derived from these data because calculated coordination 15
N NMR chemical shifts were nearly the same. For Fe(II), Ru(II) and Os(II) cationic complexes with 2,2':6',2''-terpyridine [159],
the main result reached from calculations of
15
N NMR chemical shifts at the same level
of theory was that coordination of 2,2':6',2''-terpyridine by Fe(II), Ru(II) and Os(II) ions resulted in a
15
N shielding effect that was more prominent for the outer nitrogen atoms
(ca. 60–90 ppm) than for the inner ones (ca. 10–35 ppm), increasing in the Fe(II)→Ru(II)→Os(II) series and resulting in the reversal of the 15N NMR spectral order. The main conclusions derived from the computational studies of chemical shifts performed by Pazderski et al.
15
N NMR
[99,153,154,155,156,157,158,159],
together with associated experimental papers [160,161,162,163] reviewed in [164], are the substantial highfield
15
N NMR coordination shifts (up to several dozens of ppm) in
Pd(II), Pt(II), Au(III), Co(III), Rh(III), Ir(III), Pd(IV) and Pt(IV) complexes with pyridine, 2,2'-bipyridine, 1,10-phenanthroline, quinoline, isoquinoline, 2,2'-biquinoline, 2,2':6',2'-terpyridine and their alkyl or aryl derivatives, and the practical insignificance of
relativistic and solvent effects in nitrogen chemical shielding in these series of complexes.
3.5.
Intermolecular complexes and hydrogen bonding Calculation of dynamically averaged 15N NMR chemical shifts and intermolecular
spin-spin coupling constants involving 15N nuclei provides a guiding thread to the nature of intermolecular bonding involving nitrogen, as exemplified in a series of recent publications by Del Bene et al. [165,166,167,168,169,170,171] stemming mainly from their earlier papers [172,173,174,175,176,177] reviewed in [178]. Among a wide range of noncovalent interactions, hydrogen bonds together with the so-called pnicogen bonds (the latter including intermolecular bonding of nitrogen and phosphorus with phosphorus, arsenic, antimony and bismuth) are of major significance in view of their particular role in vitally important chemical and biochemical processes. When describing conventional hydrogen bonding, the notation A-H···D is used with A denoting the electron acceptor and D standing for the electron donor. Otherwise, when describing pnicogen bonding, the notation H-A···D is used to indicate that the electron density donated by D transfers into the proximate orbital lobe of the A-H bond. In both cases, a favorable electrostatic interaction energy between the two molecules provides this intermolecular charge transfer from the donating atom (nitrogen or phosphorus) to the accepting atom (phosphorus, arsenic, antimony and bismuth). For more details on the nature of pnicogen bonding, see a comprehensive paper by Scheiner [179] and references given therein. Thus very recently Del Bene et al. [171] performed an ab initio MP2/aug'-ccpVTZ study of the intermolecular binary complexes PH3:N-base together with the corresponding ternary complexes XY:PH3:N-base (N-base = NCH, NH3, NCF, NCCN and N2), to investigate P···N pnicogen bond formation through the lone-pair hole at P in the binary complexes and P···N pnicogen-bond formation assisted by P···Y halogen bond formation through the σ-hole at Y. It was found that calculated intermolecular coupling constants involving nitrogen and phosphorous are larger in ClCl:PH3:N-base complexes compared to those in FCl:PH3:N-base complexes, despite the shorter P−N distances in the latter. This paper is an example of how computational
15
N NMR can
serve for the structural elucidation of intermolecular complexes with N-bases.
In the preceding paper [170] MP2/aug′-cc-pVTZ calculations were performed to investigate the pnicogen-bonded complexes F4−nHnP+:N-base, for n = 0, 1, 2 and 3, each with a linear or nearly linear F−P···N alignment. Coupling constants 1pJ(P−N) across the pnicogen bond were shown to vary with the P−N distance, but different patterns were observed for complexes with F4P+ and complexes of the sp3 bases with F3HP+. For the remaining complexes, 1pJ(P−N) was shown to increase with decreasing P−N distance. MP2/aug′-cc-pVTZ calculations have also been carried out for the pnicogenbonded complexes HnF5−nP:N-base, for n = 0−5 and nitrogen bases NC−, NCLi, NP, NCH, and NCF [168]. It was shown that spin-spin coupling constants 1pJ(P−N) for (PF5, PHF4) complexes with nitrogen bases are negative with the strongest bases NC− and NCLi but positive for the remaining bases while complexes of (PH4F, PH2F3) with these same two strong bases and H4FP:NP have positive
1p
J(P−N) values but negative values
for the remaining bases. On the other hand, (PH5, PH3F2) have negative values of 1p
J(P−N) only for complexes with NC−. The same calculations were performed also for the pnicogen-bonded anionic
complexes with phosphorus instead of nitrogen [169]. It was found that spin-spin coupling constants
1p
J(P−A) differentiate between shorter ion-molecule pnicogen bonds
with partial covalent character and longer P···A ion-molecule pnicogen bonds. Similarly, coupling constants 1J(P−A′) were found to differentiate between longer covalent P−A′ bonds with partial ion-molecule character and shorter P−A′ covalent bonds. The same approach was followed to identify local minima on the (NH2F)2, H2FP:NFH2, and (PH2F)2 potential surfaces, to characterize the types of interactions which stabilize the complexes found at these minima, and to evaluate their binding energies [167]. It was found that (NH2F)2 complexes are stabilized by N−H···N or N−H···F hydrogen bonds. Although net charge transfer occurs in complexes in which the two monomers are inequivalent, charges on N and P did not correlate with N and P absolute chemical shieldings, the latter reflecting charge distributions and overall bonding patterns. Calculated two-bond spin-spin coupling constants
2h
J(X−Y) across
X−H···Y hydrogen bonds were rather small, due to the nonlinearity of many of the hydrogen bonds. In contrast,
1p
J couplings across a given type of pnicogen bond were
relatively large and varied significantly, but did not correlate with corresponding distances.
A bit earlier the influence of F−H···F hydrogen bonds on the P···N pnicogen bond in complexes of general formula nFH:(H2FP:NFH2) for n = 1 and 2, and a selected complex with n = 3 was investigated [166]. It was found that
31
P and
15
N chemical
shieldings did not correlate with charges on P and N, respectively, but 31P shieldings did correlate quadratically with the P−N distance. On the other hand,
1p
J(P−N) coupling
constants did not correlate with the intermolecular P−N distance. However, when hydrogen bonding occurs only at P−F, 1pJ(P−N) decreased in absolute value as the P−N distance decreased, thereby approaching 1J(P−N) for H2P−NH2. However, the P···N bond in the 3FH:(H2FP:NFH2) intermolecular complex had little covalent character, unlike the P···P bond in the corresponding complex 3FH:(PH2F)2. In an earlier paper [165] from this series corresponding calculations were carried out in a systematic investigation of P···N pnicogen complexes H2XP:NXH2 for X = H, CH3, NH2, OH, F, and Cl, as well as for selected complexes with different substituents X bonded to P and N. It was found that complexation increased 31P chemical shieldings in complexes with binding energies larger than 19 kJ/mol. One-bond spin-spin coupling constants
1p
J(N-P) across the pnicogen interaction exhibited a quadratic dependence on
the N-P distance for complexes H2XP:NXH2, similar to the dependence of
2h
J(X-Y) on
the X-Y distance for complexes providing X-H···Y hydrogen bonds. However, when the mixed complexes H2XP:NX'H2 were included, the curvature of the trend was changed and the good correlation between 1pJ(N-P) and the N-P distance was lost. In a related paper by Alkorta et al. [180], calculations of 1JNH,
1h
JNH and
2h
JNN
spin-spin coupling constants of 27 complexes including N–H···N hydrogen bonds allowed an analysis of these through-hydrogen-bond coupling as a function of the hybridization of both nitrogen atoms and the charge of the complex. The main conclusion reached was that the hybridization of the N atom of the hydrogen bond donor was much more important for this type of interaction than that of the hydrogen bond acceptor in determining the value of J. Positive and negative charges in cationic and anionic complexes exerted opposite effects while the effect of the transition states was considerable. In addition, a series of interesting numerical relationships were found in that study that can be useful in structural studies of biomolecules, small molecules at low temperature, and new materials, as also reviewed by Alkorta et al. [181]. Very recently, in continuation of these studies, Sánchez-Sanz et al. [182] performed a computational study of the intramolecular pnicogen bond in 8-
phosphinonaphthalen-1-aminederivatives (1-NX2, 8-PX2 with X = H, F, Cl, Br, CH3, CN and NC), which are proton sponge analogues, with intramolecular P···N pnicogen interactions to determine their structural and geometric parameters, interaction energies and electronic properties. It was shown that substitution of H atoms in the PH2 group by electron withdrawing groups on the Lewis acid moiety strengthened the P···N pnicogen bond, evidenced by the increasing electron density values at the bond critical point and by shorter distances. However, substitutions on the Lewis base moiety (NX2) showed weaker P···N interactions than when the substitution was done on the Lewis acid counterpart. In addition,
15
N NMR spectroscopy proved to be the one of the most efficient
methods for the investigation of hydrogen bonds of the N–H···X and X-H···N types where X is a heteroatom bearing lone pair(s). Thus in a series of publications by Afonin et al. [183,184,185,186,187] calculations of 15N NMR chemical shifts were performed to investigate hydrogen bonding involving nitrogen. According to 15N NMR spectroscopic data and ab initio calculations, a strong N– H···O intramolecular hydrogen bonding in Z-isomers of 2-(2-acylethenyl)pyrroles was established, which causes a decrease of the nitrogen shielding by about 15 ppm together with substantial lengthening of the N–H bond, in line with experimental data [183]. In a subsequent publication by the same group of authors [184], the bifurcated hydrogenbonding effect on the
15
N NMR shielding in trifluoroacetyl pyrroles was studied at the
DFT level in comparison with experiment. 2-Trifluoroacetyl pyrroles have been recognized as possessing an intramolecular N–H···O hydrogen bond between the oxygen of the trifluoroacetyl group and the hydrogen of the N–H covalent bond of the pyrrole ring. Moreover, the hydrogen of the N–H covalent bond of the pyrrole ring in 2trifluoroacetyl-5-(2'-pyridyl)-pyrrole was found to be involved in a bifurcated hydrogen bond with participation of both the oxygen of the trifluoroacetyl group and the nitrogen of the pyridine ring. It was found by means of
15
N NMR calculations [184] that
components of the bifurcated hydrogen bond in 2-trifluoroacetyl-5(2'-pyridyl)pyrrole were predominantly electrostatic in nature, so that their influence on the geometrical and spectral characteristics of the N–H covalent bond were additive. In the next publication from this series [185] the comparative analysis of the hydrogen bonding with participation of nitrogen in 2(2'-heteroaryl)pyrroles and their trifluoroacetyl derivatives was performed based on DFT calculations of
15
N NMR
chemical shifts. N–H···O and N–H···S intramolecular hydrogen bonds in the 2(2'-furyl)and 2(2'-thienyl)pyrrole, as well as the bifurcated N–H···O, N–H···O and N–H···O, N– H···S intramolecular hydrogen bonds in 2-trifluoroacetyl-5-(2'-furyl)- and -5-(2'thienyl)pyrrole, were studied by means of the calculation of 15N NMR chemical shifts at the DFT level. Essentially, these calculations supported the assumption that no fundamental difference exists between the conventional N–H···X hydrogen bond in the 2-(2'-heteroaryl)pyrroles
and
C–H···X
hydrogen
bond
in
the
1-vinyl-2-(2'-
heteroaryl)pyrroles. In continuation of these studies, C–H···N intramolecular hydrogen bonding effects were investigated in the
15
N NMR chemical shifts of configurational isomers of 1-
vinylpyrrole-2-carbaldehyde oxime at the DFT level [186]. It was shown that the Eisomer of 1-vinylpyrrole-2-carbaldehyde adopts a preferred conformation with an antiorientation of the vinyl group relative to the carbaldehyde oxime group and with a synarrangement of the carbaldehyde oxime group relative to the pyrrole ring. It follows from these calculations that an intramolecular C–X···N hydrogen bond is present in the Eisomer of the 1-vinylpyrrole-2-carbaldehyde oxime, whereas an intramolecular C–H···O hydrogen bond occurs in its Z-isomer. Theoretical calculations indicated that intramolecular C–H···N and C–H···O hydrogen bonds caused a pronounced highfrequency shift of the bridge hydrogen. Later, the study of conformations and hydrogen bonding in the configurational isomers of pyrrole-2-carbaldehyde oxime by means of MP2 and DFT calculations of 15N NMR chemical shifts combined with NBO analysis was performed by the same team [187]. It was shown that pyrrole-2-carbaldehyde oxime adopted a preferred conformation with syn orientation of the oxime group with respect to the pyrrole ring, and that the syn conformation of E and Z isomers of pyrrole-2-carbaldehyde oxime was stabilized by the N–H···N and N–H···O intramolecular hydrogen bonds. The N–H···N hydrogen bond in the E isomer of pyrrole-2-carbaldehyde increased the 1J(N,H) coupling by about 3 Hz due to the strengthening of the N–H···O hydrogen bond in its Z isomer. The MP2 calculations indicated that the syn conformation of E and Z isomers was energetically less favorable by ∼3.5 kcal/mol relative to the anti conformation. The calculations of 1J(N, H) couplings in the syn and anti conformations allowed estimation of the contribution of N– H···N and N–H···O hydrogen bonding. The NBO analysis suggested that the N–H···N hydrogen bond in the E isomer was a pure electrostatic interaction, whereas charge
transfer from the oxygen lone pair to the antibonding orbital of the N–H bond through the N–H···O hydrogen bond occurred in the Z isomer only. Claramunt et al. [188] studied protonation and phase effects on the
15
N NMR
chemical shifts of five imidazoles and pyrazoles, including imidazole, 4,5dimethylimidazole,
pyrazole,
3,5-dimethylpyrazole
and 4,5-dihydro-3-methyl-2H-
benz[g]indazole. Based on these results, the existence of multiple N–H⋯N hydrogen bonds was established in the solid phase. A series of nitrogen-containing H-bonded molecules that have (or have not) delocalized bonds were studied, and the values of both NMR spectroscopic parameters, σ and J-couplings, and also the energy stability of such molecules, were analyzed as a function of H-bond strength [189]. It was observed that shieldings of atoms belonging to the donor substructure gave a clear evidence about the presence of the resonance phenomenon
in
the
model
compounds
studied,
namely
malonaldehyde,
nitromalonaldehyde, and nitromalonamide. 15
Recently Afonin et al. [190] employed
N NMR calculations for the
configurational assignment of methylglyoxal bisdimethylhydrazone. The C–H⋯N intramolecular hydrogen bonding in the ZE isomer was established from quantumchemical calculations including Bader’s quantum theory of atoms in molecules analysis. Effects of C–H⋯N hydrogen bonding were found in
15
N chemical shifts for nitrogens
that manifested the twisting out from the plane of the backbone and loss of conjugation. As a result, the degree of charge transfer from the nitrogen lone pairs to the p-framework was found to be different in different isomers, affecting their 15N shieldings. In addition, DFT calculations on the adsorption of several gaseous homo- and hetero-diatomic molecules including N2 and NO on the external surface of an H-capped pristine armchair (5,5) single-walled carbon nanotube were conducted and critically compared with available experimental data [191]. Significant changes of chemical shifts and shielding anisotropies at sites of addition were observed and critically discussed.
3.6.
Biological applications
At present, not very much is known about
15
N NMR calculations in biological
molecules, which is a consequence of their large molecular size and the enormous computational effort that would be needed to perform such calculations at the modern
level of theory. However, a number of promising examples can be found in the comprehensive review by Mulder and Filatov [11], which we recommend to readers interested in 15N NMR calculations for biological species. As they stated, "the use of 13C and 15N chemical shifts as a source of structural information can extend the applicability of NMR as a tool for 3D structure determination of proteins in solution. The range of proteins that can be characterized structurally with NMR spectroscopy can be markedly increased with the use of structural restraints obtained from a comparison of the theoretically calculated chemical shifts for specific spatial conformations of amino acid backbone and side chains, bringing within reach many systems of biological significance" [11].
4. Conclusions Calculations of
15
N NMR chemical shifts play a major role in the structural
elucidation of inorganic, organic and bioorganic molecules. At present, computation of 15
N NMR chemical shifts is performed mainly at the DFT level, however pure non-
empirical correlated methods like MP2, SOPPA, SOPPA(CC2), SOPPA(CCSD), CCSD and CCSD(T) are also used. Among the different DFT functionals used to calculate
15
N
NMR chemical shifts, we recommend correlation-exchange generalized gradient approximation Keal-Tozer's functionals KT2 and KT3 used in combination with Jensen's pcS-2 and pcS-3 basis sets on nitrogens, and pc-2 elsewhere in the molecule within a general LDBS scheme. All practical calculations of
15
N NMR chemical shifts are
recommended to be performed with the inclusion of solvent effects at the IEF-PCM level when no specific solute-solvent interactions are expected, and at the supermolecular level otherwise. In most cases, rovibrational corrections and relativistic effects can safely be neglected in practical calculations of 15N NMR chemical shifts. Calculations of 15N NMR chemical shifts are widely used in the structural elucidation of organic and inorganic species, as exemplified for a range of different organic and inorganic molecules, including open-chain nitrogen-containing compounds, nitrogen heterocycles and their protonated forms, coordination and intermolecular complexes.
Acknowledgement
This work was supported by The Federal Agency for Scientific Organizations, Russia (Project No 0342-2014-0006). I am very much grateful to my former PhD students, colleagues and collaborators, first of all to Dr. Valentin A. Semenov, Dr. Dmitry O. Samultsev and late Dr. Kirill A. Chernyshev, with whom we have started calculations of 15
N NMR chemical shifts.
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