3056
J . Phys. Chem. 1988, 92, 3056-3059
such comparisons between theory and experiment is noteworthy, and the experimental data are qualitatively in accord with our finding of very large X r / X M mixing for the Co/NH3 case. The comparisons concerning radial extent of the 3d orbitals (relative to those for the neutral atom) are also encouraging and suggest that radial relaxation is not likely to be a significant factor in determining transfer integral magnitudes. As a final comment, we emphasize that the role of hyperconjugation in facilitating electron transfer, exemplified for small transition-metal-ion complexes in the present study, is expected to be important in many other electron-transfer systems. For example, methyl group hyperconjugation has been implicated as a significant contributor to the transfer integral in some photosynthetic electron-transfer processes.34 (34) Fischer, F.; Scherer, P. 0. J. Chem. Phys. 1987, 115, 151-158. (35) The scaling used here for the face-to-face approach supersedes that employed in ref 36.
Acknowledgment. This research was carried out at Brookhaven National Laboratory under Contract DE-AC02-76CH00016 with the U S . Department of Energy and supported by its Division of Chemical Sciences, Office of Basic Energy Sciences. We are grateful to Prof. M. Zerner for making available a copy of the computer program for implementing the modified INDO method developed by him and his co-worker~.’~ The assistance of Drs. John and Louise Hanson in helping to establish working versions of the code at BNL is also acknowledged. We thank Prof. M. Weaver for sending us a preprint of ref 29. Registry No. Fe(H20)62+,15365-81-8; R u ( N H 3 ) 2 + , 19052-44-9; Co(NH,),*+, 15365-75-0. (36) Newton, M. D. In Chemical Reacarions in the Liquid State; Moreau, M., Turq, P., Eds.; Plenum: New York, in press. (37) Binkley, S.; Whiteside, R. A.; Krishnan, R.; Schlegel, H. B.; Seeger, R.; DeFrees, D. J.; Pople, J. A . Quanrum Chemistry Program Exchange; Indiana University: Blwmington, IN, 1982.
Nuclear Spin-Spin Coupling Constant of HD Jens Oddershede,* Jan Geertsen, Department of Chemistry, Odense University, DK-5230 Odense M , Denmark
and Gustavo E. Scuseria Department of Chemistry, University of California, Berkeley, California 94720 (Received: August 17, 1987; In Final Form: November 11, 1987)
Using the coupled cluster, singles and doubles, polarization propagator approximation, we have calculated the nuclear spinspin coupling constant of HD. We find that JHD = 42.79 Hz, including all four terms (Fermi contact, spin-dipole, paramagnetic spin-orbit, and diamagnetic spin-orbit) as well as vibrational and Boltzmann averaging at 40 K. This is in good agreement with experiment,Ia 42.94 f 0.04 Hz. Inclusion of very tight basis functions in the basis set is essential, as is a numerical determination of the vibrational correction amounting to I .81 Hz. The improved treatment of the vibrational averaging also leads to an increase in literature values for the isotope shifts of J H D (AJHD = 0.30 Hz).
1. Introduction The nuclear spin-spin coupling constant of the H D molecule, JHD, was measured more than 20 years ago with an accuracy of f O . l Hz.Ib Despite the simplicity of the electronic structure of HD, none of the numerous calculations2-6 of J H D have yet been able to reproduce the experimental coupling constant. It is the intention of the present paper to investigate whether pushing present theory to the limit in fact now makes it possible to calculate JHD with experimental accuracy. In order to do so, we need to determine all known contributions’ to the coupling constant, including vibrational averaging. We must also apply an accurate method of calculation. We have used the polarization propagator method which has been demonstrated to yield reliable coupling constants in several other instance^.^^^-'^ However, the second-order polarization ~~
(1) (a) Beckett, J. R. Ph.D. Thesis, Rutgers University, 1979. (b) Benoit, H.; Piejus, P.C . R . Seances Acad. Sci., Ser. B 1967, 265, 101. (2) For reviews covering until 1982, see: Kowalewski, J. f r o g . N M R Spectrosc. 1977, 1 1 , 1; Annu. Rep. N M R Spectrosc. 1982, 12, 81 (3) Iwai, M.; Saika, A. Phys. Rev. A 1983, 28, 1924. (4) Geertsen, J. Chem. Phys. Lett. 1985, 116, 89. (5) Saika, A. Bull. Magn. Reson. 1985, 7 , 100. (6) Sekino, H.; Bartlett, R. J . J . Chem. Phys. 1986, 85, 3945. (7) Ramsey, N. F. Phys. Rev. 1953, 91, 303. (8) Geertsen, J.; Oddershede, J. Chem. Phys. 1984, 90, 301. (9) Geertsen, J . ; Oddershede, J. Chem. Phys. 1986, 104, 67. (10) Geertsen, J.; Oddershede, J.; Scuseria, G. E. J . Chem. Phys. 1987, 87, 2138. ( 1 1 ) Geertsen, J.; Oddershede, J.; Scuseria, G. E. Int. J . Quantum Chem., Quantum Chem. S y m p . , in press.
0022-3654/88/2092-3056$01 SO10
propagator approach (SOPPA) which was apt in the previous applications is not sufficiently accurate for our present purpose. Even though the difference between J H D in SOPPA and in the coupled cluster polarization propagator approach12 is only of the order 2 Hz, this difference is essential when we are aiming for experimental accuracy. We are thus using a polarization propagator method based on a singles and doubles coupled clusterI3 (CCSD) reference state in the present study. The basis set error is one of the primary sources of error in calculations of spin-spin coupling constants, and we have hence performed an extensive basis set variation to check the stability of our result. We have included vibrational and rotational corrections to J H D in our calculation. These corrections turn out to be rather important, nearly 2 Hz, which is about 0.5 H z larger than the bestI4 previous calculation of the vibrational correction for HD. Furthermore, from the vibrational averaged results we have calculated the isotope effect of the spin-spin coupling constant15 for isotopomers of H, (H2, HD, HT, D,, DT, and T2). 2. Method The field-independent splitting of N M R lines, the indirect nuclear spin-spin coupling constant JNN’, has four different contribution^,^^' all of which are electron coupled interactions (12) Geertsen, J.; Oddershede, J. J . Chem. Phys. 1986, 85, 2112. (13) Purvis, G. D.; Bartlett, R. J . J . Chem. Phys. 1982, 76, 1910. (14) Schulman, J. M.; Lee, W. S . J . Chem. Phys. 1980, 73, 1350. (1 5) Forsyth, D. A. In Isotopes in Organic Chemistry; Buncel, E.; Lee, C. C.; Eds.; Elsevier: Amsterdam, 1984; Vol. 6, p 1. Q 1988 American Chemical Societv
The Journal of Physical Chemistry, Vol. 92, No. 11, 1988 3057
Nuclear Spin-Spin Coupling Constant of H D TABLE I: Nuclear Spin-Spin Coupling Constant of basis set' A: 1 0 ~ 6 0 B: 1 0 ~ 6 i l d({d = 1.0) C: 10~6p2d({d = 0.5 and 1.5) D: 10s6p2d ([d = 2.0 and 5.0) E: lls6p2d (lS= 5000) F: 12s6p2d (lS= 15000) G: 13s6p2d (lS = 50000) H: 14s6p2d (lS= 150000) I: 15s6p2d (lS = 500000) J: H + lS = 0.025 = 8.0 K: H L: H lP = 0.1 M: H + {d = 12.6
+ [, +
numerical Hartree-Fock experimental l a
GTO's
50 62 74 74 76 78 80 82 84 84 88 88 94
HD (in Hz)as a Function of the One-Electron Basis Set' ESCF,
au
wH)b
-1.133 560 -1.133599 -1.1 33 615 -1.133619 -1.133619 -1.133619 -1.133619 -1.133619 -1.133619 -1.133619 -1.133622 -1.133620 -1.133619
0.4440 0.4440 0.4440 0.4440 0.4455 0.4480 0.4485 0.4494 0.4495 0.4494 0.4494 0.4494 0.4494
-1.133 63023a
0.450023b
JFCC
JsDc
JpsOc
jDS0d
38.68 38.63 38.62 38.98 39.24 39.69 39.77 39.93 39.94 39.93 39.93 39.92 39.93
0.39 0.57 0.45 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.55
0.73 0.77 0.78 0.82 0.82 0.82 0.82 0.82 0.82 0.82 0.83 0.82 0.82
-0.32 -0.32 -0.33 -0.33 -0.33 -0.33 -0.33 -0.33 -0.33 -0.33 -0.33 -0.33 -0.33
JtO"1
39.48 39.65 39.52 39.96 40.22 40.67 40.75 40.9 1 40.92 40.91 40.91 40.90 40.97 42.94 f 0.04
'Van D ~ i j n e v e l d (10s) t ~ ~ and Schulman and KaufmanZ5(5p) basis set augmented with extra functions as indicated. b S C F density (in au) at the nuclear positions. cCalculated in the coupled cluster (CCSD) polarization propagator approximation at R = 1.40 au. d S C F average value, as discussed in section 2.
between the two nuclear spins, I N and ZN,. Three of these terms can be expressed as a sum over states
where In) are the excited states and 10) is the ground state of the system. The individual interactions are specified by HN: HN represents Fermi contact (FC), spin-dipole (SD), and paramagnetic spin-orbit (PSO). The last contribution to J",, the diamagnetic spin-orbit (DSO) term, is of a different form, being an average value of an operator containing reference to both nuclei The actual expressions for HN and H", are given in several place~.~9'9~ It is generally argued that the Fermi contact term gives the dominant contribution to the coupling constant. This holds for H D even though there are several examples of molecules for which this statement is not true.'0~11J6However, none of the three other terms can be neglected when we are aiming for experimental accuracy in JHD. Our method of calculations-10is based on the observation that the sum-over-states expression in eq 1 is the zero-energy value of the polarization propagator. The polarization propagator is evaluated directly from orbital energies and two-electron integrals without ever computing the excitation energies, E , - Eo, that appear in the denominator in eq 1. Furthermore, the most time-consuming step in the evaluation of the polarization propagator does not depend upon the form of HN and HN,. Thus, the cost of a polarization propagator calculation of coupling constants is not, like in the corresponding finite-field method," proportional to the number of components of the coupling operators (HN)that we wish to determine. However, we must perform one calculation in singlet (En- Eo is a singlet-to-singlet excitation energy) to evaluate PSO terms and one in triplet (singlet-to-triplet excitation energy) to determine FC and SD terms. The general aspects of the polarization propagator method have been reviewed recently18 while Geertsen and Oddershede8 have given details for coupling constant calculations. The coupled cluster (CC) polarization propagator methodl2 is an extension of the second-order polarization propagator approximation (SOPPA). Like SOPPA, it is consistent through second order in perturbation theory, but it contains in addition several extra self-energy diagrams (many of which are summed to infinite order) that are not included in SOPPA. This means that the C C propagator method is superior to SOPPA in cases where the Rayleigh-Schrodinger (RS) perturbation expansion is slowly convergent. For such ~~~
~~
(16) Galasso, V.; Fronzoni, G. J . Chem. Phys. 1986, 84, 3215. (17) Guest, M. F.; Saunders, V. R.; Overill, R. E. Mol. Phys. 1978, 35, 427. (18) Oddershede, J. M u . Chem. Phys. 1987, 69, 201.
TABLE II: Nuclear Spin-Spin Coupling Constant' of HD (in Hz)at R = 1.40 au C H F b HRPAC SOPPAd CCSDPPAe exptlf FC 53.11 42.62 42.60 39.93 SD 0.57 0.52 0.5 1 0.49 PSO 0.83 0.82 0.83 0.82 DSOg -0.33 -0.33 -0.33 -0.33 total 54.18 43.63 43.61 40.91 42.94 0.04
*
"Calculated using basis set H of Table I. bCoupled Hartree-Fock or RPA. cHigher RPA, see ref 27. dSecond-order polarization propagator approximation. Coupled cluster polarization propagator approximation based on a reference state that includes both single and double substitutions." fReference l a (T = 40 K). ZSCF average value used at all levels of approximation.
s y s t e m ~ ~ ~we . ' ~find J ~ a substantial improvement in calculated molecular properties when the C C method is applied. Even though H, is a favorable case for R S perturbation theory, we still find a small effect of including the many extra terms in the C C propagator method as we will see later.
3. Basis Set We have computed the basis set dependence of the coupling constant of HD. The results for the coupled cluster singles and doubles polarization propagator approximation' (CCSDPPA) are given in Table I. The basis set dependence is not as pronounced as we have seen in other cases.I0 However, the usual trends prevail with no basis set dependence of the DSO term and with the FC term showing the largest basis set variations. The basis sets are constructed from the uncontracted 10s basis set of van D ~ i j n e v e l d and t ~ ~ the 5p basis set used by Schulman and Kaufmanz5in an earlier calculation of JHD. The 10s5p basis set is then augmented with d-functions, more tight s-functions, p-functions, as well as diffuse functions. The addition of the large-exponent s-functions has the expectedz6 effect on the FC term and the density at the nuclei but leaves everything else, including the total energy, invariant. Only the GTO with the largest exponent, lS= 500 000, does not seem to influence the value of JHD. Since only minor effects are seen from adding diffuse functions and extra p- and d-functions (the last four rows in Table I), we are using basis set H , Le., a 14s6p2d basis set, in the
'
(19) Geertsen, J. Chem. Phys. Lett. 1987, 134, 400. (20) Overill, R. E.; Saunders, V. R. Chem. Phys. Lett. 1984, 106, 197. (21) Scuseria, G. E. Chem. Phys. 1986, 107, 417. (22) Matsuoka, 0.;Aoyama, T. J . Chem. Phys. 1980, 73, 5718. (23) (a) Laaksonen, L.; Pyykko, P.; Sundholm, D. Comput. Phys. Rep. 1986, 4, 313. (b) Laaksonen, L.; private communication. (24) van Duijneveldt, F. B.; IBM Technical Report, RJ 945, 1971. (25) Schulman, J . M.; Kaufman, D. N. J . Chem. Phys. 1970, 53, 477. (26) Schulman, J. M.; Kaufman, D. N. J . Chem. Phys. 1972, 57, 2328.
3058
The Journal of Physical Chemistry, Vol. 92, No. 11, 1988
TABLE III: Internuclear Dependence of the Nuclear Spin-Spin Coupling Constant of H D (in Hz) Calculated in the Coupled Cluster Singles and Doubles Polarization Propagator Approximation (CCSDPPA)" R. au JFC JSD JPSO JDSO fotal 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.70 1.80
27.56 30.99 34.15 37.11 39.93 42.64 45.28 47.88 50.49 55.76 61.28
0.83 0.74 0.65 0.57 0.49 0.42 0.37 0.33 0.30 0.25 0.22
1.16 1.06 0.97 0.89 0.82 0.76 0.70
0.64 0.59 0.51 0.44
-0.25 -0.29 -0.31 -0.32 -0.33 -0.33 -0.32 -0.32 -0.31 -0.29 -0.27
29.30 32.50 35.46 38.25 40.91 43.49 46.03 48.53 5 1.07 56.23 61.67
Oddershede et al. TABLE IV: Internuclear Derivatives of the Spin-Spin Coupling Constant of HD Hz $2),b Hz CHF' 204.823 178.6 SOPPAC 86.602 -13.4 CCSDPPA' 73.297 -63.1 Raynes and Rileyd 72.2 -84 Schulman and Lee' 75.684 -95 Kowalewski et a l f 78.33 -111.7 Ishigurog 53.00 -379.1
*e)
= (aJ/af)R,Rc, where f = (R - R,)/R,. bJ(e2) = (a2J/a2[),=,c. 'Present calculation at Re = 1.40 au. The acronyms are defined in footnotes b, d, and e of Table 11. dReference 30, Re = 1.401 au; the derivatives are computed by using J ( R ) from Schulman and Kaufman.26 'Reference 14, Re = 1.40 au. fReference 31, R, = 1.40 au. EReference 32, Re = 1.40 au.
"Using basis set H of Table I.
calculation. Based on the changes in POta1 caused by addition of more functions to this basis set, it seems likely that the remaining basis set error in basis set H should be within the desired accuracy of f0.1 Hz in POta'. 4. Correlation Effects
The spin-spin coupling constant was calculated in coupled H F (CHF) and several post-CHF methods. From Table I1 we see that it is essential to add electronic correlation beyond C H F to obtain acceptable results. Addition of the vibrational correction (see section 5) to the equilibrium values in Table I1 shows that the CCSD results is closest to the experimental' coupling constant. Unlike most other cases,lo-llwe find that the second-order polarization propagator approximation (SOPPA) and an approximation to SOPPA, the higher random phase approximation (HRPA),27v28give nearly the same JHD. From this we infer that the two-particle, two-hole corrections and the second-order corrections to the transition moments are vanishingly small for H2. However, the contributions to the second-order A and B matrices that come from inclusion of double substitutions to infinite orders are of some importance. These terms constitute the main difference between SOPPA and CCSDPPA. The present value of JHD in SOPPA is about 1 Hz larger than that previously reported by Geertsen4 using the same method. The difference is almost solely due to nearly I-Hz increase in the FC term, the origin of which is the basis set effect. Almost the whole increase in J& originates from the addition of the very tight s-functions, as we can see from Table I. A similar effect of addition of large-exponent basis function was seen by Schulman and Kaufman.26 These kinds of basis functions were not part of the basis sets used in the previous4 calculation. The global representation of the Dirac delta function that was applied by Geertsen is apparently not able to overcome this deficiency of the basis set. The noncontact terms have nearly the same values in the previous4 and in the present SOPPA calculation, as well as in the coupled cluster approximation (Table 11). The sum of all noncontact terms (CCSDPPA) is 0.98 Hz, which is somewhat different from the "estimated" value of Schulman and LeeI4 of 0.61 Hz but very close to that actually contained in Table I of the same r e f e r e n ~ e ,0.97 ' ~ Hz. 5. Vibrational Corrections The internuclear dependence of the four terms contributing to the spin-spin coupling constants is displayed in Table 111. We see nearly the same trend as reported previously1° for C O and N,: a strong increase in pc and a weak decrease in p Dand Po as R increases. (For CO and N2Poshowed a weak increase.) The diamagnetic term goes through a minimum right around the internuclear equilibrium (Re= 0.7416 A), but it is also a slowly varying function of R. This means that the FC term dominates (27) Galasso, V. J . Chem. Phys. 1985, 82, 899. (28) Shibuya, T.; McKoy, V. Phys. Reo. A 1970, 2, 2208. (29) Deleted in proof.
TABLE V Rotationally and Vibrationally Averaged Nuclear Spin-Spin Coupling Constant of H B (in Hz) Calculated by Using the Coupled Cluster Singles and Doubles Polarization Propagator Method (CCSDPPA) J(R,=0.7416 40.98 42.79 J ( u =N = 0) 42.79 J(T=40 K)b J(expt) 42.94 f 0.04c 42.94 f O . l d Nonvibrationally averaged equilibrium value. bTemperature averaged over the three lowest rotational states N = 0, 1 , 2 as described in eq 3. 'Reference la; gas-phase data at 40 K. dReference lb; liquidphase data at 20.4 K.
the internuclear dependence of J H D , and our result can therefore be compared to previous investigations that only considered the contact term. This is done in Table IV where we are comparing first and second derivatives. In the present calculation the derivatives are obtained from a parabolic fit to the three values of J computed for R = 1.35, 1.40, and 1.45 au (see Table 111). We see a substantial deviation between the C H F and the post-CHF method, and even the derivatives in SOPPA and CCSDPPA are rather different. Of the previous calculations, those of Riley and Raynes30 (which actually use data of Schulman and Kaufman26) and of Schulman and Lee14 give the best overall agreement with our post-CHF calculations. Using the C ~ o l e method, y ~ ~ we have calculated the (numerical) vibrational-rotational wave functions that reproduce the experimenta134spectroscopic energies of the ground state of HD. We have used these numerical wave functions to integrate the Rdependent coupling constants and thereby obtained the rotational and vibrational averaged quantities in Table V. The temperature averaging is performed as a Boltzmann averaging over three rotational states
J H D ( T= )
When all corrections are added, we see that the nuclear spinspin coupling constant calculated at the highest level of theory (CCSDPPA) comes close to experiment.' However, mainly due to the remaining basis set error (see section 3), the calculated coupling constant is still too small by about 0.1 Hz. It is instructive to look a little more in detail at the results of the vibrational averaging. In Table VI we have compared various (30) Raynes, W. T.; Riley, J. P. Mol. Phys. 1974, 27, 331. (31) Kowalewski, J.; Roos, B.; Siegbahn, P.; Vestin, R. Chem. Phys. 1974, 3, 70. (32) Ishiguro, E. Phys. Reu. 1958, I 1 I , 203. (33) Cooley, J. Math. Comput. 1961, 15, 363. (34) Huber, K. P.; Herzberg, G. Molecular Spectra and Molecular Structure. IV. Constants of Diatomic Molecules: van Nostrand Reinhold: New York, 1979.
The Journal of Physical Chemistry, Vol. 92, No. 11, 1988 3059
Nuclear Spin-Spin Coupling Constant of H D
TABLE VII: Isotope Shifts" for Isotowmers of H, (in Hz)
TABLE V I Vibrational Correction"to the Nuclear Spin-Spin Coupline Constant of HD (in I&) method vib cor Raynes and Riley30 Schulman and Lee14 Facelli et aLb this calc, CCSDPPA
" For u = N
Dunham expansion Dunham expansion expansion of Morse potential Morse potential numerical integration
Raynes and
0.30 0.40 0.63 0.77 0.92
1.36 1.39 1.4 0.21 1.81
" u = N = 0.
= 0 (excluding Boltzmann averaging).
Facelli et used the same derivatives as Raynes and Riley (see footnote d of Table IV).
calculations of the vibrational corrections to JHD. The first, third, and fourth entry in Table IV all use the same26J(R) curve. This clearly shows that the vibrational correction depends strongly upon the methods used to perform the integration over nuclear coordinates as also previously pointed out by Facelli et The present CCSDPPA calculation and Raynes and Riley30 and Schulman and Led4 give nearly the same derivatives of J (see Table IV). Still, th5re is about -0.45-Hz difference in the vibrational correction. Raynes and Riley30 as well as Schulman and Lee14 determine the correction from the expansion (4)
(r)
where are calculated from a Dunham expansion using the ao-a4 coefficients of the expanded potential energy c ~ r v e . ~ ~One ,~' may thus ask whether the reason for the deviation between our result and their calculations lies in the expansion in eq 4 or in the use of the Dunham expansion to calculate (p).Using values of ( calculated from the numerical nuclear wave function together with CCSD derivatives (see Table IV), we find that the vibrational correction calculated from eq 4 is 1.72 Hz. Thus, the use of the expansion in eq 4 rather than the numerical integration reduces the vibrational correction by 0.09 Hz. On the other hand, comparison of ( p)oo gives ( {)oo = 0.029 11 (0.026 59) and ([*), = 0.01323 (0.01322) where the numbers in parentheses are obtained from the Dunham expansion36and the others from the numerical integration. This implies that the use of the Dunham expansion lowers the vibrational correction by 0.185 H z (for 4') = 73.297, see Table IV). The remaining difference between the vibrational correction of Raynes and Riley30 (1.36 Hz) and our calculated value of 1.81 H z is due to changes in 4')which increases the vibrational correction given by Raynes and Riley by 0.03 Hz and to changes in 4') which increases ( J ) o oby 0.14 Hz. Thus, we see that all corrections to the result of Raynes and Riley30 point in the same direction, namely, to an increase of (J)oo. The largest change originate from the errors introduced by using (35) Facelli, J. C.; Contreras, R. H.; Scuseria, G.E.; Engelmann, A. R. J. Mol. Struct. 1979, 57, 299. (36) Raynes, W. T.; Davies, A. M.; Cook, D. 8. Mol.Phys. 1971,21, 123. (37) Herman, R. M.; Short, S. J . Chem. Phys. 1968,48, 1266; 1969,50, 272.
this calc, CCSDPPA
the Dunham expansion for potential energy curves for systems with light nuclei. However, the different curvatures of the two J(R) calculations and the numerical integration scheme also give important corrections to the literature value of ( J ) o o . 6. Isotope Effects The isotope effect on spinspin coupling constant^^^^^* expresses the changes in J o n isotopic substitution (other than that originating for the change in gyromagnetic ratios). Thus, for H D the isotope shift is
AJ(Hz,HD) = (YD/YH)JHH- JHD
(6)
and similarly for other isotopomers of HD. AJ is solely determined by the isotopic difference in the vibrational wavefunction as the electronic contributions to the coupling constants are the same for all isotopomers when multiplied by the appropriate Y~ factors. Isotope effects for HD isotopomers have previously been calculated by Raynes and Riley.30 However, due to the problems with the vibrational averaging (see section 5 ) , their calculated isotope shifts will be modified. The results of both calculations are given in Table VII. As expected, we find that A J increases relative to increases). The the results of Raynes and Riley30 (since ( oo0 predicted isotope shifts are now so large that some of them should be amenable to experimental determinations.
7. Conclusions Using the most advanced form of the perturbative polarization propagator methods, a method based on a singles and doubles coupled cluster reference state (CCSDPPA),I2 we have calculated the nuclear spin-spin coupling constant of H D to be J H D = 42.79 Hz, in good agreement with experiment,Ia J H D = 42.94 f 0.04 Hz. The electronic contributions to J H D amount to 40.98 Hz while the correction for nuclear motion is 1.8 1 Hz. The Fermi contact term is 39.93 Hz, leaving 0.98 Hz for the noncontact contributions. Clearly, inclusion of the vibrational correction is important for obtaining agreement between theory and experiment. We have shown that the use of a Dunham expansion of the potential energy curve for H D leads to unsatisfactory large errors in the average values and also in the calculated isotope shifts for isotopomers of H,.
Acknowledgment. We thank Dr. W. T. Raynes for making us aware of ref la. Registry No. HD, 13983-20-5. ~~
(38) Jameson, C. J.; Osten, H.-J. J . Am. Chem. SOC.1986, 108, 2497.
