Differential ring proton NMR shieldings and cyclic stabilization energies

Chemical Physics 231 Ž1998. 1–11

Differential ring proton NMR shieldings and cyclic stabilization energies D.B. Chesnut P.M. Gross Chemical Laboratory, Duke UniÕersity, Durham, NC 27708, USA Received 27 October 1997

Abstract Ring currents are thought to be responsible for unusual magnetic susceptibility effects in organic ring systems and represent a method of measuring cyclic stabilizationrdestabilization Žaromaticityrantiaromaticity.. They should, in principle, also affect nuclear shieldings in such systems, especially proton shieldings. By studying a variety of four-, five-, and six-membered organic ring systems, we investigate the question here by theoretical means as to whether proton shieldings reflect such cyclic stabilizationrdestabilization effects as measured by homomolecular homodesmotic reaction energies. While absolute shieldings show only a slight hint of correlation, it is found that differences in ring proton shieldings between the fully unsaturated species and its monoene counterpart show a clear correlation with this energy. In particular, mean differential shieldings exhibit a good linear relationship with the homomolecular homodesmotic reaction energy that is quantitatively comparable to other measures of aromaticityrantiaromaticity. q 1998 Elsevier Science B.V. All rights reserved.

1. Introduction The question of how to properly define Žand detect. cyclic stabilizationrdestabilization Žaromaticityrantiaromaticity. is still with us, a question that has been thoroughly reviewed in the recent book by Minkin et al. w1x. Part of the problem has been the variety of ways that cyclic resonance effects are characterized, such as the tendency toward bond length equalization in the methods of Julg and Francois w2x or Bird w3–5x, the use of the large anisotropy of the diamagnetic susceptibility as suggested by Palmer et al. w6,7x, and, of course, energetic criteria involving a variety of reactions relating the conjugated molecule to non-ring-conjugated systems w8–15x.1 Schleyer and coworkers w16x have shown that linear relationships exists among these various criteria of aromaticity and that these relationships even extend to antiaromatic systems. Fleischer et al. w17x carried out an extensive theoretical study on the magnetic susceptibilities of benzene and some of its isomers and were able to construct an increment system that leads to a definition and detection of ‘extra’ cyclic stabilization. Their paper cites some of the early effort in this area dating back to the late 1920s and early 1930s involving names like

1

While George et al. w10x defined this type of reaction as ‘homodesmotic’, the term ‘homodesmic’ has also been used in the literature.

0301-0104r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 3 0 1 - 0 1 0 4 Ž 9 8 . 0 0 0 4 5 - 7

D.B. Chesnutr Chemical Physics 231 (1998) 1–11

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Ehrenfest w18,19x, Raman w20–22x, Pauling w23x, Lonsdale w24x, and London w25x. The magnetic susceptibility is a global property of the molecule wholly unlike NMR chemical shifts which are essentially local in nature. The source of the large anisotropy of the diamagnetic susceptibility in ring systems is thought to be due to what are called diatropic ring currents, movement of the electrons around the conjugated ring that creates an internal magnetic field generally in opposition to the external applied magnetic field. Such ring currents should also affect the nuclear chemical shielding, especially hydrogen atoms in positions to experience either upfield Ždiamagnetic. shifts if internal to the ringŽs. or downfield Žparamagnetic. shifts if in positions external to the ringŽs.. Fleischer et al. w17x point out that it was not long after the large difference in NMR chemical shielding between benzene and non-cyclic olefins was observed w26x that Pople w27x presented a ring current model to rationalize the effect. Fleischer and coworkers also studied NMR shieldings in their theoretical paper but characterize the analysis of ring currents in benzene as being ‘‘far from trivial’’ and state that conclusions on a more rigorous ring current model would be premature. Another group working with Schleyer w28x has made the very interesting observation that absolute magnetic shieldings calculated in the center of rings Žin single or multi-ring species. can be correlated with cyclic stabilization energies and provide yet another way of characterizing aromaticity and antiaromaticity. They provide energy and ‘nucleus-independent chemical shift’ data for five-membered ring systems but, aside from benzene, none is given for other molecules with a single six-membered ring. This approach is very appealing in that one feels that ring current effects should likely best be measured at ring centers. A drawback to the method is that since there Žusually. are no detecting nuclear probes located in such positions it is mainly theoretical in nature. In the present paper, we do not address the ‘ring current question’ directly but rather simply ask whether there is any noticeable effect on proton shieldings in systems where ring currents might be expected to be present. We report an observation relating mean differential proton shieldings obtained by theory Žbut also accessible by experiment. that appear to correlate well with stabilizationrdestabilization energies as calculated by the homomolecular homodesmotic approach w11,15x. While absolute ring shieldings show only a slight tendency to correlate with this energy, mean differential shieldings that compare the conjugated ring system to its monoene counterpart exhibit a clear linear relationship.

2. Theoretical methods Ditchfield’s gauge including atomic orbital ŽGIAO. method w29x was used to calculate absolute nuclear magnetic resonance ŽNMR. isotropic shieldings at the RHFr6-311GŽd,p. level on MP2Žfrozen core.r6-31GŽd. optimized structures. 2 Homomolecular homodesmotic reaction energies w11,15x Ždenoted here as HE. were used to measure ring stabilizationrdestabilization energies; these were taken from previous work w15x with the exception of the deprotonated pyrrole, silole, and phosphole anions, the deprotonated silole cation, the protonated thiophenium cation, and phosphole forced into an all planar form, species whose reaction energies are calculated in the present work at the same level of theory and basis set as before w15x. The hypothetical cyclohexatriene molecule was formed by forcing the six-membered ring to have ethane-like single bonds alternating with ethene-like double bonds obtained from optimizations on ethane and ethene, respectively. The ring molecules studied are indicated in the tables by the ring substituent X for the structures as shown below.

2

For notation, see Ref. w9x.

D.B. Chesnutr Chemical Physics 231 (1998) 1–11

3

All the calculations were carried out with the GAUSSIAN 94 code w30x on the North Carolina Supercomputing Center’s Cray T916.

3. Results and discussion The shielding calculations were carried out at the restricted Hartree–Fock ŽRHF. level since shielding correlation effects for hydrogen are small w31–35x. While programs to determine shieldings at second-order many-body perturbation theory ŽMBPT2 or MP2. such as ACES II w36x are available, such calculations are relatively time-consuming and basically do not provide significant changes to the hydrogen HF results. Furthermore, we believe the small correlation effects that are present will tend to cancel when shielding differences are employed, such as is done here Žvide infra.. It is necessary to use rather large basis sets and to take into account rovibrational effects if one is interested in accurate absolute proton shieldings w35x. The results of our current RHF shieldings are shown in Table 1 for the ring systems studied here and for some other, representative organic systems; readily available experimental shielding data are also given. The agreement between theory and experiment is illustrated in Fig. 1a while in Fig. 1b the calculated shieldings obtained by linear regression are compared with experiment, a comparison that has been presented previously with structures optimized with a slightly different basis set w45x. Table 1 and Fig. 1 do not contain any of the simple mono-heavy-atom hydrides since their shielding is rather sensitive to geometry, and geometries optimized at the 6-31GŽd. level are likely not adequate for them; HF is a particularly sensitive case. Fig. 1a shows a systematic offset of calculated and observed proton shieldings, an offset that can be empirically removed by linear regression. The statistical measures of goodness of agreement between calculated and observed quantities shown in Fig. 1b Žthe root-mean-square error ŽRMSE. and standard deviation ŽSD.. have both been reduced over those shown in Fig. 1a. There are two points to be made here. First, one can empirically adjust proton shieldings to fit experiment if desired, but there remains a fundamental difficulty in the unmodified absolute shieldings. Compared to other elements at the same level of basis, hydrogen is harder to calculate in terms of the RMSE as a percentage of the shielding range w45x. For first and second row elements Žat the RHF level. an error of 3–4% is typical w45,46x while here for hydrogen it is 10–15%. Second, shielding differences Žas measured by the standard deÕiation of calculated versus observed. are reasonably good whether one uses the unmodified ŽSD s 0.31. or linear regression ŽSD s 0.20. approaches. This point is important to make here since ultimately we shall be comparing shielding differences Žchemical shifts. to homomolecular homodesmotic reaction energies rather than absolute shieldings. We want to try and relate the ring proton shieldings to one of the more straightforward indicators of cyclic stabilizationrdestabilization, namely an energy criterion. While there are a number of reactions whose energy differences purport to do this, we choose here the homomolecular homodesmotic approach w10,11,15x. Homodesmotic reactions were first proposed by George et al. w10x and involve reactions in which ring systems are converted to species like butadiene in order to maintain the same number of carbon atoms in their various states of hybridization. George et al. w11x went on to point out what we believe to be a more appropriate type of homodesmotic reaction, namely one in which the ring nature of both reactants and products is maintained, a reaction we have labeled as homomolecular homodesmotic w15x. Such reactions are illustrated below for pyrrole and pyridine where we see that the conjugated ring systems are compared to their monoene counterparts.

D.B. Chesnutr Chemical Physics 231 (1998) 1–11

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Table 1 Proton shielding data from RHFr6-311GŽd,p.rrMP2r6-31GŽd. GIAO perturbed HF calculationsa

A: small molecules C2 H2 C2 H4 C2 H6 C3H6 HCN CH 3 )OH CH 3 )CH 2 OH CH 3 CH 2 )OH ŽCH 3 . 2 CO CH 3 )CHO CH 3 F ŽCH 3 .4 Si B: 4-membered ring cyclobutadiene C: 5-membered rings BH BHy 2 CH 2 CHy CHq NH Ny O AlH AlHy 2 SiH 2 SiHy SiHq PH

Py plPH b S SHq

a b a b a b a b a b a b a b a b a b a b a b a b a b PH a b a b a b a b

Calculated

LR calculated

Observed

Reference

30.43 26.44 31.25 32.04 29.32 28.98 30.99 28.86 30.16 30.08 28.15 32.24

28.94 25.29 29.69 30.41 27.93 27.61 29.45 27.51 28.69 28.62 26.86 30.60

29.27 25.43 29.86 30.54 27.78 27.33 29.37 27.09 28.79 28.82 26.61 30.74

w37x w37x w37x w37x w38x w39x w39x w39x w40x w40x w40x w41x c

26.32

25.18

26.50 25.26 25.16 26.09 25.35 25.42 26.72 27.15 25.07 25.14 25.72 25.44 26.56 24.46 25.59 26.40 24.72 25.86 25.52 25.85 24.79 26.00 25.99 26.14 23.68 25.09 24.86 27.14 25.05 25.69 25.33 25.09 24.63 24.92 24.69 23.74

25.35 24.21 24.12 24.97 24.29 24.36 25.55 25.94 24.04 24.10 24.63 24.38 25.40 23.48 24.51 25.25 23.72 24.76 24.45 24.75 23.78 24.89 24.88 25.02 22.77 24.06 23.85 25.93 24.02 24.61 24.28 24.06 23.64 23.90 23.69 22.82

24.56 24.41

w42x w42x

24.16 24.62

w42x w42x

23.55 24.60

w42x w42x

23.74 23.51 25.65 24.06 24.22

w43x w43x w43x w43x w43x

23.66 23.85

w42x w42x

D.B. Chesnutr Chemical Physics 231 (1998) 1–11

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Table 1 Žcontinued.

D: 6-membered rings B

CH cyclohexatriene N

SiH

P

a b g

a b g a b g a b g

Calculated

LR calculated

26.12 23.62 25.70 24.50 24.71 23.07 24.83 24.09 24.66 23.54 25.28 22.89 23.85 24.28

25.00 22.71 24.61 23.52 23.71 22.21 23.82 23.14 23.66 22.64 24.23 22.04 22.92 23.32

Observed

Reference

23.60

w42x

22.32 23.68 23.29

w42x w42x w42x

22.24 23.12 23.46

w44x w44x w44x

a

Results are given for the calculated shieldings without correction, the fit given by linear regression ŽLR calculateds1.104q 0.9148)calculated., and observed shieldings. References to the observed data are given in the last column. For most of the ring systems only the a , b , and g proton data are given. The absolute values reported here are based on the absolute proton shielding in CH 4 being equal to 30.61 ppm. b Fully planar phosphole. c The absolute value of TMS is determined by its shift relative to CH 4 .

The advantage of using this type of reaction is that, by maintaining the same type of ring structure on both sides of the reaction equation, strain effects tend to cancel out, leaving the desired measure of cyclic stabilization or destabilization. Such reactions are straightforward for the five-membered rings but less so for those involving six-membered rings where one must ‘average’ over the several possible monoenes. We shall take here the theoretically calculated reaction energy differences of such reactions as a measure of aromaticityrantiaromaticity in the ring compounds studied. Most of this data has been presented previously w15x with the exception of the deprotonated pyrrole, silole, and phosphole anions, the deprotonated silole cation, the 1H-thiophenium cation, and phosphole forced into an all planar form, calculations that were done here. The pyrrole anion is isoelectronic to the cyclopentadienyl anion, and the phosphole anion is its second row counterpart. The thiophenium cation and the deprotonated silole anion are isoelectronic with phosphole and have similar Žnon-planar. geometric structures. The fully planar phosphole molecule is not a stable entity but when forced into this geometry has a large resonance stabilization energy. The deprotonated silole anion is slightly aromatic Žpositive HE. while the cation provides another example of an antiaromatic molecule Žnegative HE.. The energy

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D.B. Chesnutr Chemical Physics 231 (1998) 1–11

Fig. 1. Ža. Calculated versus observed absolute isotropic hydrogen chemical shieldings Žppm.. The RMSE and SD of the data are shown. Žb. Calculated absolute isotropic hydrogen chemical shieldings modified by linear regression versus observed shieldings Žppm.. See the footnote in Table 1 for the regression parameters. The RMSE and SD of the data are shown.

calculations were performed at the Žfrozen core. MP2r6-311GŽd,p.rrMP2r6-31GŽd. level Žsee footnote 2., that is, energies calculated at second order many-body theory with a relatively large basis set on structures optimized Žalso second order many-body theory. with a slightly smaller basis. As indicated in Section 1, the question we wish to pose is whether ring proton shieldings in aromaticrantiaromatic systems reflect the cyclic stabilizationrdestabilization involved. We have chosen as the determinator of resonance the homomolecular homodesmotic reaction energy which Schleyer et al. w16x have shown correlates well with other determinators of resonance. Positive values of HE correspond to cyclic stabilization or aromaticity while negative values correspond to cyclic destablization or antiaromaticity. We wish to see if the proton shieldings or shielding differences correlate in a simple manner with this energy or not. Fig. 2a shows the calculated absolute a , b , and g shieldings of a variety of cyclic systems Žsee Tables 1 and 2 for the molecules involved. as a function of HE. It is clear that there is some slight correlation of the shieldings with HE, but the RMSE of a linear regression is 0.88 ppm and the correlation argument is not

D.B. Chesnutr Chemical Physics 231 (1998) 1–11

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Table 2 MP2r6-311GŽd,p.rrMP2r6-31GŽd. homomolecular homodesmotic reaction energies ŽHE, kcalrmol. and RHFr6-311GŽd,p.rrMP2r631GŽd. mean differential ring shieldings ŽMDS, ppm. for a variety of four-, five- and six-membered ring systems. The data are arranged in order of increasing reaction energy Žincreasing HE. within each ring-size category HE A: four-membered ring cyclobutadiene B: five-membered rings CHq SiHq BH AlH SiH 2 AlHy 2 SHq CH 2 BHy 2 PH SiHy O S N: y NH CHy P: y plPH a C: six-membered rings cyclohexatriene B N SiH P CH a

MDS

y33.72

0.52

y56.77 y23.25 y19.08 y6.06 y1.17 1.40 1.96 3.21 5.34 6.99 10.28 19.83 23.18 24.32 25.18 27.71 28.67 34.52

3.87 1.63 1.30 0.73 y0.15 y0.10 y0.73 y0.65 y0.60 y0.69 y0.69 y1.32 y1.33 y1.64 y0.95 y1.17 y0.89 y1.24

21.05 26.88 35.63 36.59 41.27 41.46

y1.51 y1.12 y2.03 y1.48 y1.93 y1.72

Fully planar phosphole.

convincing. The slope of the data is negative as we would expect, namely resonance stabilization Žpositive HE. should lead to lower Ždeshielded. values of the shielding. Note that in each of Fig. 2a,b,c the extent of the shielding axis is 10.0 ppm, essentially the range of chemical shieldings Žor shifts. for hydrogen. It would seem that the absolute isotropic shielding does not provide an adequate description of the resonance energy involved. The problem here likely has as its major source of difficulty the fact that the nature of the heteroatom involved also affects the calculated shielding. This lead us to look at shielding differences between the completely unsaturated system and its monoene counterpart. That is, just as in the homomolecular homodesmotic reaction energy one compares differences involving these two molecules Žand the completely saturated molecule., it would seem appropriate to consider such differences Žchemical shifts. in the shieldings.

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D.B. Chesnutr Chemical Physics 231 (1998) 1–11

D.B. Chesnutr Chemical Physics 231 (1998) 1–11

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So, in the case of pyrrole for example, one calculates the differences of the ethylenic a and b hydrogen shieldings in 1 and 2 and compares these differential shieldings to HE. Whereas there are unique a and b shielding differences for each five-membered ring molecule, the case for six-membered rings is more complicated Žas it is in this case for the homomolecular homodesmotic reaction energy.. As illustrated below for pyridine, there are three monoenes Ž4a, 4b, and 4c. to compare to the fully unsaturated species Ž3..

In such cases we take the aÕerage of the Žethylenic. a , b , and g shielding differences. Fig. 2b shows a plot of these differential shieldings and the correlation between these differences and HE is much more apparent, although the associated linear regression RMSE is essentially the same Ž0.88 ppm. as that of the absolute shieldings. The linear regression slope is now statistically more significant than in the first case, and the intercept of the data fit is close to zero as one might hope for in a physically interpretable relationship between these two quantities. The statistical scatter of the data Žas measured by the linear regression RMSE. in Fig. 2b is contributed to in large degree by the points for the cyclopentadienyl, pyrrole, and phospholide anions, the sets of three rather high Žthe alpha protons. and rather low Žthe beta protons. differential shieldings in the region of HE of about 24–29 kcalrmol; removing these points reduces the RMSE by almost one half. The large split in these values arises from the unusual shieldings seen in their monoenes which contain allyl-like three-atom segments Žexactly allyl-like for the cyclopentene anion., as illustrated below for the dihydropyrrole anion.

For this particular molecule, the Žethylenic. a and b proton shieldings are 25.11 and 30.16 ppm, respectively, the latter being unusually high for an ethylenic type proton. Shieldings similar in magnitude are found for the cyclopentadienyl and phospholide monoene anions and all are very close to the shieldings predicted for the terminal protons in the allyl anion itself Ž30.58 and 31.17 ppm.. This is in sharp contrast to the allyl cation

Fig. 2. Ža. Absolute proton shieldings Žppm. versus the homomolecular homodesmotic reaction energy ŽHE, kcalrmol.. Data are presented for alpha ŽI., beta Žv ., and gamma Ž`. hydrogens. Žb. Differential proton shieldings Žppm. versus the homomolecular homodesmotic reaction energy ŽHE, kcalrmol.. Data are presented for Žthe single. four-membered ring ŽB., five-membered ring alpha ŽI. and beta Žv . hydrogens, and six-membered ring alpha Ž`., beta Ž'., and gamma Ž^. hydrogens. Žc. Mean differential proton shieldings Žppm. versus the homomolecular homodesmotic reaction energy ŽHE, kcalrmol. for four- ŽB., five- ŽI., and six-membered Žv . rings. The straight line is the linear regression fit.

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D.B. Chesnutr Chemical Physics 231 (1998) 1–11

where the terminal protons have calculated shieldings of 21.46 and 21.86 ppm, values very much to the lowfield side; such deshielded values are also seen in the monoene of the cyclopentadienyl cation. Finally, one more average suggests itself, that of averaging the a and b shielding differences for each five-membered ring and the a , b , and g differences in each six-membered ring; cyclobutadiene, the only four-membered ring studied, is unique in this sense, having only an a shielding difference. The mean differential shieldings are given in Table 2 along with the associated values of HE. The plot of this data is shown in Fig. 2c, revealing a rather good linear relation. In this last case the linear regression RMSE has dropped to 0.47 and the linear regression intercept is statistically not different from zero. The slope fit to the data is y0.0501 " 0.0036 ppmrkcal moly1 . While taking the mean differential shielding is in a sense ad hoc, we may feel somewhat more comfortable by looking at cis-butadiene and Ž cis . 1-butene. The protons in these two molecules corresponding to the alpha and beta hydrogens in the conjugated five-membered rings exhibit differential shieldings of y0.24 and 0.28 ppm, respectively, and their mean differential shielding is 0.02, a value well within the theoretical noise limit. That is to say, we expect no contribution Žor only a very small one. from the butadiene portion of the five-membered rings when computing the mean differential shielding. While the mean differential shielding correlates nicely with the homomolecular homodesmotic energy, the linear regression RMSE of 0.47 Ž0.41 without the highly strained cyclobutadiene ring. does not permit perhaps as quantitative a measure of ring stabilizationrdestabilization as one might like. We need to recall, however, that we are comparing theoretically determined shieldings to theoretically determined energies and there are errors in both calculations when compared to experiment. The results of the linear regression of the theoretical calculations predict errors in the shieldings of the order of 0.2–0.3 ppm. errors in accord with the standard deviation of our calculated versus observed shieldings given earlier. The homomolecular homodesmotic energies are also not free of error. In an earlier work w47x we compared isodesmic bond separation reaction energies to experiment using RHF, MP2 and density function theory methods; the RMSE for the MP2 approach was about 4.3 kcalrmol. Such an error in the energy would produce an error in the predicted mean differential shielding of 0.21 ppm. We may also ask how our relationship here compares to those found by Schleyer et al. w16x where they showed that energetic, structural, and magnetic criteria of aromaticity Žand antiaromaticity. were all linearly related. Taking as a measure of the goodness of fit the RMSE divided by the observed range of the quantity considered, the magnetic exaltation, anisotropy in the magnetic susceptibility, and the bond index plotted as a function of the homodesmotic energy show values of 4.4, 7.0, and 7.9%, respectively; the corresponding number for the mean differential shieldings plotted against the same energy is 7.9%, clearly comparable with these other results. All these indicators of cyclic stabilizationrdestabilization taken individually correlate with the energetic criterion but not in a quantitatively definitive manner Ždepending on one’s taste.. Taken together, however, they constitute a reasonable set of criteria to use in judging aromaticrantiaromatic behavior. The isotropic NMR mean differential shielding is certainly an important member of this set. Acknowledgements I am indebted to the North Carolina Supercomputing Center for providing CPU time on the Cray T-916 platform that allowed these calculations to be carried out, and to Professor L.D. Quin for helpful discussions. References w1x V.I. Minkin, M.N. Glukhovtsev, B.Ya. Simkin, Aromaticity and Antiaromaticity ŽJohn Wiley, New York, 1994.. w2x A. Julg, P. Francois, Theor. Chim. Acta 7 Ž1967. 249. w3x C.W. Bird, Tetrahedron 41 Ž1985. 1409.

D.B. Chesnutr Chemical Physics 231 (1998) 1–11 w4x w5x w6x w7x w8x w9x w10x w11x w12x w13x w14x w15x w16x w17x w18x w19x w20x w21x w22x w23x w24x w25x w26x w27x w28x w29x w30x

w31x w32x w33x w34x w35x w36x w37x w38x w39x w40x w41x w42x w43x w44x w45x w46x w47x

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