Vibrational averaging of NMR properties for an N–H–N hydrogen bond

5 October 2001

Chemical Physics Letters 346 (2001) 288±292

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Vibrational averaging of NMR properties for an N±H±N hydrogen bond Meredith J.T. Jordan a, Justin S.-S. Toh a, Janet E. Del Bene b,* a b

School of Chemistry, University of Sydney, Sydney, NSW 2006, Australia Quantum Theory Project, University of Florida, Gainesville, FL 32611, USA Received 16 May 2001; in ®nal form 20 August 2001

Abstract Vibrational e€ects on NMR shielding constants and nuclear spin±spin coupling constants have been investigated in a model hydrogen-bonded complex, CNH:NCH. Expectation values of the spin±spin coupling constant 2h JN±N , obtained from a two-dimensional EOM±CCSD/(qzp,qz2p) surface, and of the isotropic proton shielding constant rH , obtained from a two-dimensional MP2/(qzp,qz2p) surface, are presented as functions of vibrational state. The expectation values have been computed from anharmonic dimer- and proton-stretching vibrational wavefunctions obtained from a twodimensional MP2/aug0 -cc-pVTZ potential surface. Equilibrium values, ground-state expectation values, and thermally averaged values at 298 K of 2h JN±N and rH are compared. Ó 2001 Elsevier Science B.V. All rights reserved.

1. Introduction It is well known that nuclear motion leads to temperature and isotopic e€ects in NMR shielding constants and nuclear spin±spin coupling constants [1]. Calculations of these properties in hydrogen-bonded complexes have focused primarily on equilibrium structures, although the dependence of these properties on the intermolecular distance or hydrogen-bond geometry has been examined in some cases [2±18]. However, hydrogen-bonded complexes usually have a low-frequency dimer-stretching mode, and this vibration as well as the proton-stretching vibration may be

* Corresponding author. Present address: Department of Chemistry, Youngstown State University, Youngstown, OH 44555, USA. E-mail address: [email protected] (J.E. Del Bene).

signi®cantly anharmonic. As a result, vibrational wavefunctions describing ground and excited states may be delocalized over a wide region of the potential energy surface, and property expectation values may di€er signi®cantly from equilibrium values. Therefore, a more reliable calculation of any particular property involves generation of a surface describing the property and averaging over the relevant vibrational, and if possible, ro-vibrational wavefunctions. The CNH:NCH complex has been chosen as a prototype for an N±H±N hydrogen bond. This complex is small and linear, factors that facilitate computation. Furthermore, it has recently been shown that 2h JN±N values appear to be remarkably insensitive to the hybridization of the nitrogens, but strongly dependent on the N±N distance [10,18], so much so that 2h JN±N for CNH:NCH computed at the N±N distance in adenine±uracil and guanine±cytosine base pairs agrees with ex-

0009-2614/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 ( 0 1 ) 0 0 9 7 8 - 2

M.J.T. Jordan et al. / Chemical Physics Letters 346 (2001) 288±292

perimental values [19]. Previous work on the CNH:NCH complex also demonstrated that 2h JN±N is dominated by the Fermi-contact interaction over a wide range of N±N distances, with this term accounting for better than 99% of the total 2h JN±N [11,18]. Therefore, coupling constants presented here have been estimated solely from the Fermi contact term. The distance-dependence of the Fermi-contact term and its dominance in determining the total spin±spin coupling constant are general phenomena that have been observed across N±H±N, N±H±O, O±H±O, and Cl±H±N hydrogen bonds [9,11,16,18]. However, for F±F couplings across F±H±F hydrogen bonds, other terms must also be evaluated [12,20]. 2. Methods To obtain expectation values of the NMR properties, a two-dimensional potential energy surface for CNa H:Nb CH was generated in the Na ±H and Nb ±H distances. 108 ab initio singlepoint energies were calculated at second-order Mùller±Plesset perturbation theory [MBPT(2) ˆ MP2] [21±24] using Dunning's [25±27] correlation consistent valence triple-split basis set augmented with di€use functions on C and N (aug0 -ccpVTZ). For these calculations, the C±N and C±H distances were frozen at their optimized MP2/ aug0 -cc-pVTZ values. At this level the equilibrium structure of CNH:NCH has a traditional hydrogen bond with N±N and Na ±H distances (Re ) of  respectively. The ab initio data 2.946 and 1.012 A, points span the chemically relevant regions of the potential energy surface, with N±N distances  For each N±N disranging from 2.50 to 3.30 A. tance, the Na ±H distance was set initially to  and then increased until the Nb ±H distance 0.90 A  A global potential energy decreased to 0.90 A. surface was constructed using two-dimensional spline interpolation and polynomial extrapolation. A model two-dimensional Schr odinger equation was solved on this surface using methods outlined previously [28], and anharmonic vibrational eigenfunctions and eigenvalues were obtained for the dimer- and proton-stretching modes.

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The N±N spin±spin coupling constant and the shielding constant surfaces were calculated on the same grid as the potential surface. Spin±spin coupling constants were computed using the equationof-motion coupled cluster singles and doubles (EOM±CCSD) method [29,30], a method that gives computed results in good agreement with experimental coupling constants [10±12,20,31,32]. Proton shielding constants were computed at MP2 using the gauge-invariant atomic orbital method [33]. All NMR calculations employed the Ahlrichs (qzp,qz2p) basis set [34]. The single-point energies and NMR properties were calculated using AC E S II [35]. Global property surfaces were constructed from the ab initio data points analogously to the potential surface. The sensitivity of the calculations to the procedures used to generate the potential energy, spin±spin coupling constant, and proton shielding constant surfaces was examined. Uncertainties were estimated as the largest observed variation in a property as the order of the polynomial extrapolation was varied. The uncertainties are 2 cm 1 for the fundamental vibrational frequencies, 0.001 Hz for 2h JN±N , and 0.05 ppm for rH . 3. Results and discussion Table 1 reports the anharmonic vibrational frequencies and expectation values of the N±N and Na ±H distances, 2h JN±N , and rH as functions of vibrational state (i; j) for C15 Na H:15 Nb CH. The notation …i; j† represents i quanta of excitation in the dimer-stretching mode and j in the protonstretching mode. Equilibrium values of these properties are also listed in Table 1. It is apparent from Table 1 that h2h JN±N i changes signi®cantly with vibrational state, whereas hrH i shows a lesser dependence. This di€erence can be understood from Fig. 1, which shows the square of the wavefunctions for the ground (v ˆ 0) and the ®rst excited (v ˆ 1) states of the dimerand proton-stretching modes superimposed on the spin±spin coupling constant and shielding constant surfaces. From Fig. 1 it can be seen that the contours on the shielding constant surface are

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Table 1  the spin±spin Vibrational frequencies …m; cm 1 † and expectation values of the N±N and Na ±H distances (hRN±N i and hRNa±H i, A), coupling constant (h2h JN±N i, Hz) and the proton shielding constant (hrH i, ppm) as a function of vibrational state …i; j† for the C15 NH:15 NCH complexa

a

Vibrational assignment

m

hRN±N i

hRNa±H i

h2h JN±N i

hrH i

(0,0) (1,0) (2,0) (3,0) (4,0) (5,0) (0,1) Equilibrium

±

2.946 2.983 3.020 3.059 3.095 3.131 2.906 2.946

1.030 1.029 1.028 1.028 1.027 1.027 1.066 1.012

7.05 6.70 6.35 6.03 5.78 5.56 9.11 6.37

25.31 25.40 25.49 25.58 25.65 25.73 24.10 25.88

162 319 468 613 754 3232 ±

The notation …i; j† refers to i quanta of excitation in the dimer-stretching vibration and j quanta in the proton-stretching vibration.

nearly parallel to the Nb ±H axis. The dimer stretch changes the Nb ±H and N±N distances but leaves Na ±H essentially unchanged. As a result, excitation of the dimer-stretching mode has little e€ect on rH . In contrast, the contours on the spin±spin coupling constant surface are nearly parallel with the Na ±H axis. Therefore, 2h JN±N is sensitive to the dimer-stretching mode, and h2h JN±N i decreases as hRN±N i increases. Table 1 also shows that hRN±N i is shorter and hRNa±H i slightly longer in the v ˆ 1 state of the

proton-stretching mode relative to the ground state. These changes are opposite to those observed in the excited states of the dimer-stretching mode. Thus, in the v ˆ 1 state of the protonstretching mode, hrH i decreases from its ground state value of 25.31 to 24.10 ppm, and h2h JN±N i increases from 7.05 to 9.11 Hz. The square of the wavefunction for the excited state of the protonstretching mode is shown superimposed on the chemical shielding surface in Fig. 1. The square of this wavefunction extends to shorter and longer

Fig. 1. The square of the vibrational wavefunctions for the ground state and the ®rst dimer- and proton-stretching excited states of CNa H:Nb CH superimposed on the N±N spin±spin coupling constant surface (upper plots) and the shielding constant surface (lower plots). Countours are drawn at increments of 3 Hz for the 2h JN±N surface and 3 ppm for the rH surface, with the value of the lowest contour marked.

M.J.T. Jordan et al. / Chemical Physics Letters 346 (2001) 288±292

Na ±H distances than the square of either the ground state or the dimer excited state wave functions. As a result, hrH i does not change as dramatically as might have been expected. The signi®cant increase in h2h JN±N i in the v ˆ 1 excited state of the proton-stretching mode arises primarily from the decrease in hRN±N i. The C15 NH:15 NCH two-dimensional anharmonic dimer-stretching vibration has a very low frequency of 162 cm 1 . The accurate prediction of room temperature NMR parameters therefore requires averaging over excited dimer vibrational states. The variation of 2h JN±N and rH with the dimer-stretching state can be seen in Table 1. As the dimer stretch is excited, h2h JN±N i decreases and hrH i increases. The thermally averaged values of 2h JN±N and rH at 298 K are 6.75 Hz and 25.39 ppm, respectively. The thermally averaged value of 2h JN±N is intermediate between the equilibrium and ground-state values, while the thermally averaged value of rH is closer to the ground state value than the equilibrium value. The two-dimensional anharmonic protonstretching frequency for C15 NH:15 NCH occurs at 3232 cm 1 . Because the proton-stretching motion leads to a shorter hRN±N i, h2h JN±N i is signi®cantly larger in the v ˆ 1 state of the proton-stretching mode than in the ground state. Although the proton-stretching mode will not be excited at room temperature, if the coupling constant could be measured in this excited state, the predicted increase in 2h JN±N may be experimentally observable. Finally, it should be noted that the e€ect of vibrational averaging on the N±N spin±spin coupling constant in CNH:NCH is quite di€erent from the e€ect on the F±F spin±spin coupling constant in FHF 1 . In this anion, the expectation value of 2h JF F in the ground vibrational state is signi®cantly less than 2h JF±F evaluated at the equilibrium geometry. However, thermal vibrational averaging over the lower-energy excited states of the dimer- and proton-stretching modes has no e€ect on 2h JF±F [20]. Studies are currently underway to further evaluate the e€ects of zeropoint motion and thermal vibrational averaging on spin±spin coupling constants in other hydrogen-bonded complexes.

291

Acknowledgements This work was supported by the National Science Foundation (grant CHE-9873815) and by the Australian Research Council (grant A2543). Computing facilities at the Ohio Supercomputer Center and the University of Sydney were used for these calculations. References [1] See for example T. Helgaker, M. Jaszurski, K. Ruud, Chem. Rev. 99 (1999) 293, and references therein. [2] N.S. Golubev, G.S. Denisov, S.N. Smirnov, D.N. Shchepkin, H.-H. Limbach, Z. f. Phys. Chem. 196 (1996) 73. [3] I.G. Shenderovich, S.N. Smirnov, G.S. Denisov, V.A. Gindin, N.S. Golubev, A. Dunger, R. Reibke, S. Kirpekar, O.L. Malkina, H.-H. Limbach, Ber. Bunsenges Phys. Chem. 102 (1998) 422. [4] H. Benedict, H.-H. Limbach, M. Wehlan, W.-P. Fehlhammer, N.S. Golubev, R. Janoschek, J. Am. Chem. Soc. 120 (1998) 2939. [5] G.A. Kumar, M.A. McAllister, J. Org. Chem. 63 (1998) 6968. [6] J.E. Del Bene, S.A. Perera, R.J. Bartlett, J. Phys. Chem. A. 103 (1999) 8121. [7] A.G. Dingley, J.E. Masse, R.D. Peterson, M. Bar®eld, J. Feigon, S. Grzesiek, J. Am. Chem. Soc. 121 (1999) 6019. [8] C. Scheurer, R. Br uschweiler, J. Am. Chem. Soc. 121 (1999) 8661. [9] J.E. Del Bene, M.J.T. Jordan, J. Am. Chem. Soc. 122 (2000) 4794. [10] J.E. Del Bene, R.J. Bartlett, J. Am. Chem. Soc. 122 (2000) 10480. [11] J.E. Del Bene, S.A. Perera, R.J. Bartlett, J. Am. Chem. Soc. 122 (2000) 3560. [12] S.A. Perera, R.J. Bartlett, J. Am. Chem. Soc. 122 (2000) 1231. [13] H. Benedict, I.G. Shenderovich, O.L. Malkina, V.G. Malkin, G.S. Denisov, N.S. Golubev, H.-H. Limbach, J. Am. Chem. Soc. 122 (2000) 1979. [14] M. Pecul, J. Leszczynski, J. Sadlej, J. Phys. Chem. A. 104 (2000) 8105. [15] M. Bar®eld, A.J. Dingley, J. Feigon, S. Grzesiek, J. Am. Chem. Soc. 123 (2001) 4104. [16] J.E. Del Bene, S.A. Perera, R.J. Bartlett, J. Phys. Chem. A. 105 (2001) 930. [17] K. Chapman, D. Crittenden, J. Bevitt, M.J.T. Jordan, J.E. Del Bene, J. Phys. Chem. A 105 (2001) 5442. [18] J.E. Del Bene, S.A. Perera, R.J. Bartlett, Mag. Reson. Chem. (in press). [19] A.G. Dingley, S. Grzesiek, J. Am. Chem. Soc. 120 (1998) 8293. [20] J.E. Del Bene, M.J.T. Jordan, S.A. Perera, R.J. Bartlett, J. Phys. Chem. A 105 (2001).

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