JOURNAL O F T H E A M E R I C A N C H E M I C A L SOCIETY Registered i n U.S. Paten1 Ofice.
@ CopTight, 1970, by the American
VOLUME92, NUMBER 1
Chemical Society
JANUARY 14, 1970
Physicd und Inorgunic Chemistry Approximate Self-consistent Molecular Orbital Theory of Nuclear Spin Coupling. I. Directly Bonded Carbon-Hydrogen Coupling Constants’” G . E. Maciel,lb J. W. McIver, Jr., N. S. Ostlund,’c and J. A. Pople Contribution from the Department of Chemistry, Carnegie-Mellon University, Pittsburgh, Pennsylvania 15213. Received February 7, 1969 Abstract: With the employment of finite perturbation methods, a self-consistent perturbation theory is applied in
the INDO molecular orbital approximation to the calculation of isotropic nuclear spin coupling between directly bonded carbon and hydrogen for a series of molecules. Including perturbations associated only with the Fermi contact mechanism, JCHvalues are calculated for a wide variety of compounds. Regarding hydrogen 1 s and carbon 2s atomic orbital densities at the nuclei as fixed parameters, good agreement with experimental trends is obtained for hydrocarbons and for molecules with -I+ substituents (-F, -OR, -NRz, =0, etc.), but not for molecules with -I- substituents (-CF8, -C(O)X, -NOz, -CN, etc.). The correspondence between calculated and experimental results is improved qualitatively when these densities are varied in accordance with a simple correction based on Slater’s rules. For those molecules for which the experimental trends are qualitatively reproduced, a sensitivity to substituent effects is predicted which is closer to the experimental results than what would be predicted by simple arguments based on carbon s character. ne of the most frequently studied classes of nuclear spin-spin coupling constants, and one which has appeared quite frequently in qualitative theoretical arguments, is the directly bonded C-H constant. Relatively straightforward experimental access via satellite experiments and intriguing early interpretations in terms of carbon hybridization generated a great deal of experimental activity directed toward this nmr paramThe early hybridization arguments were eter. 2-20
0
(1) Research supported in part by Grant GP6458 from the National Science Foundation; (b) Special National Institutes of Health Fellow, on leave from the University of California, Davis; (c) Postgraduate Scholar of the National Research Council of Canada. (2) (a) J. N. Shoolery, J . Chem. Phys., 31, 1427 (1959); (b) N. Muller and D. E. Pritchard, ibid., 31,768,1471 (1959). (3) P. T. Inglefield and L. W. Reeves, ibid., 40,2424 (1964). (4) N. Muller, ibid., 36, 359 (1962). (5) (a) J. H. Goldstein and G. S. Reddy, ibid., 36, 2644 (1962); (b) G. S. Reddy, R. T. Hobgood, Jr., and J. H. Goldstein, J . A m . Chem. Soc., 84,336 (1962). (6) N. Muller, J . Chem. Phys., 37,2729 (1962). (7) N. Muller and P. I. Rose, J . Am. Chem. SOC.,84,3973 (1962). (8) G. J. Karabatsos, ibid., 83, 1230 (1961). (9) E.R. Malinowski, ibid., 83,4479(1961). (10) E. R. Malinowski, L. Z. Pollara, and J. P. Larmann, ibid., 84, 2649 (1962).
based largely upon valence-bond2 or molecular orbital (MO)zbJ3developments from Ramsey’sZ4 secondorder perturbation formula for the Fermi contact term, 1122
(11) S. G. Frankiss,J. Phys. Chem., 67,752(1963). (12) G. P. VanDerKelen and Z. Eeckhaut, J. Mol. Spectry., 10, 141 (1963). (13) R.M. Hammaker, ibid., 15,506 (1965). (14) P. C. Lauterbur in “Determination of Organic Structure by Physical Methods,” Vol. 2, F. C. Nachod and W. D. Phillips, Ed,, Academic Press, New York. N. Y..1962. Chauter 7. (15) H.M. Hutton, W. F. Reynoids, and T. Schaefer, Can. J . Chem., 40, 1758 (1962). (16) R: M. ’Lynden-Bell and N. Sheppard, Proc. Roy. Soc., A269, 385 (1962); D. M. Graham and C. E. Holloway, Can. J . Chem., 41, 21 14 (1963). (17) K. Frei and H. I. Bernstein, J . Chem. Phys., 48, 1216 (1963). (18) (a) V. S. Watts and J. H. Goldstein, Theoret. Chim. Acta, 4, 265 (1966); (b) T.Yonezawa and I. Morishima, J . Mol. Spectry., 27, 210(1968). (19) T.F. Page, Jr., Mol. Phys., 13,523 (1967). (20) (a) G. A. Gray, Ph.D. Dissertation, University of California, Davis, 1967; (b) G. A. Olah and T. E. Kiovsky, J . Am. Chem. SOC.,90, 4666 (1968). (21) M. Karplus and D. M. Grant, Proc. Natl. Acad. Sci. Li. S., 45, 1269 (1959). (22) H.S. Gutowsky and C. Juan, J . Chem. Phys., 37,2198 (1962). (23) H.M.McConnell, ibid., 24,460 (1956). (24) N.F. Ramsey, Phys. Rev., 91,303 (1953).
1
2
using the average A E approximation. One of the several largely equivalent forms which result from such developments is given in eq l , which results from a MO treatment in which the average AE is i n v 0 k e d . ~ ~ *In ~5
termines the coupling constant. This basic approach is equivalent in principle to a complete, self-consistent perturbation calculation involving the sum over all appropriate excited states ; however, it is computationally easier than the alternative, which has not yet been employed for molecules of typical chemical interest. In a preliminary survey, the trends in coupling constants calculated by this method were in good general agreement with established trends in experimental valu e ~ The . ~present ~ ~paper, ~ ~ devoted to directly bonded C-H couplings, is the first in a series concerned with applying this method systematically t o a variety of spinspin systems.
( 4 / 3 ) 2 h h ~ 7 ~ ( A E ) -21(f0~) S ~ 2 ( O ) P s c ~ ~(1) 2 this expression p is the Bohr magneton, sC2(O) is the carbon 2s orbital density at the carbon nucleus, and P,,,, is the carbon 2s-hydrogen 1s element of the first-order density matrix (sometimes referred t o as the chargedensity, bond-order matrix). Interpretations of J c H in terms of only hybridization, or "carbon s character," arguments largely pivot on the factor Pscsa2, and effectively assume the factor Results (AE)-'sc~(O)SH~(O) to be constant. Such assumptions All calculations were based on eq 3, the numerical have been c r i t i ~ i z e d . ~ "Indeed, , ~ ~ ~ ~ alternative views evaluation being carried out as described previously.33 based on assuming a dominant importance of variations The computations, performed on the CDC 1604A comin AE or in sc2(0) have been presented for substituted puter, required run times typified by the 32 min involved methanes. 2 8 , 2 9 The more general MO approach which does not make in one pyridine calculation. Except for a few explicitly noted cases, all calculations were based on the standard the average AE approximationz5is difficult to apply satgeometrical model used previously in this laboraisfactorily because of problems associated with contory, 3, * structing good excited-state wave functions, and beThe computed coupling constants are presented in cause of serious cancellation difficulties. The analogous valence-bond treatment, also avoiding the average Tables I-IV. Table I contains results for compounds AE approximation, appears to share the cancellation of the type CHXYZ, i.e., substituted methanes. Calculations on molecules not possessing sufficient symdifficulty. 30 metry generally give computed JCHvalues which are difRecently a conceptually simple theoretical method for calculating second-order properties, utilizing finite ferent for different C-H bonds. In such cases the valperturbation techniques, has been under development ues given in Table I are the weighted averages. Table I1 presents analogous results for XHC=Y compounds, in this laboratory. In its initial applications it has emLe., substituted ethylenes, formaldehydes, and formalployed INDO (intermediate neglect of differential overdimines. Table I11 give results for compounds with lap) molecular orbital wave functions31 in an approxitriple bonds, H b X , and Table IV, the results for mate SCF f r a m e ~ o r k . ~ ~ , 3Details 3 of this general apsome aromatic compounds. In addition to the comproach to perturbation calculations and its application t o the Fermi contact spin-coupling i n t e r a c t i ~ nhave ~ ~ , ~ ~ puted J C H values, Tables I-IV also give the computed These were obtained from the calculavalues of P,,,,. been discussed previously. Briefly, it involves the comtions on the perturbed molecules. However, they are putation of an unrestricted, single determinant, I N D 0 3 nearly equivalent to values obtained in the absence of molecular orbital wave function in the presence of a the perturbation. The computed bond orders for a contact perturbation of the form given by and /3 spins usually differ by less than 0.1 %, and resulAB = (8T/3)PE1.BSB '(O) (2) tant P,,,, values are nearly independent of the position or presence of the perturbation. For a few clearly due to presence of the nuclear moment pB. Then, using specified cases, C-H coupling constants calculated at the Hellmen-Feynmann theorem, it is shown that the the CNDO level of approximation are given in Tables ~ be expressed as reduced coupling constant K A can I-IV. Also included in Tables I-IV are the available experimental results relevant to the computed JCHvalues. where psasAis the diagonal spin density matrix element Discussion corresponding to the valence s orbital of atom A, and Overall Trends. In agreement with experimental K A B is defined as (~T/~YA')'B)JAB. Thus, within the experience, a general tendency toward increasing framework of the approximations employed, it is the JCH values is noted in progressing from Table I t o Table sensitivity of the spin density in the orbital SA to the I1 (or IV) to Table 111. This corresponds to the wellpresence of the nuclear spin perturbation p B which deknown crude relationship between JCHand carbon coordination or hybridization. It is particularly evident (25) J. A. Pople and D. P. Santry, Mol. Phys., 8, l (1963). (26) J. I. Musher, Proceedings of the XIIIth Colloque Ampere, if closely analogous compounds are considered, Le., the University of Leuven, 1964. hydrocarbons ethane (16), ethylene (60), and acetylene (27) A. Saika, J . Chem. Phys., 45, 2715 (1966). ( 9 3 , the fluoro compounds ethyl fluoride (41) and vinyl (28) N. Cyr and T. J. R. Cyr, ibid., 47,3082 (1967). (29) D. M. Grant and W. M. Litchman, J . Am. Chem. Soc., 81,3994 fluoride (69), or the nitrogen compounds methylamine (1965). (27), formaldimine (75-76), and hydrogen cyanide (96). (30) M. Barfield, J . Chem. Phys., 48,4458, 4463 (1968). (31) J . A. Pople, D. L. Beveridge, and P. A. Dobosh, ibid., 47, 2026 The MO parameter P,,,,, which conveys information (1967). on the "hybridization or carbon s character" from these (32) J. A. Pople, J. W. McIver, Jr., and N. S . Ostlund, Chem. Phys., MO calculations, is given in Tables 1-111; in these Letters, 1, 465 (1967). JCH
=
(33) J. A. Pople, J. W. McIver, Jr., and N. S . Ostlund, J . Chem. Phys., 49,2960,2965 (1968).
Journal of the American Chemical Society
(34) J. A. Pople and M. Gordon, J. Am. Chem. SOC.,89,4253 (1967).
92:I / January 14, 1970
3 Table I. JCHin HCXYZ Compounds Calculated Compoundb
1. 2. 3.* 4. 5.* 6.* 7.* 8. 9.* IO.* 11. * 12.* 13.* 14.* 15.* 16. 17. 18.* 19. 20. 21.* 22. 23. 24. 25.* 26. 27. 28. 29. 30. 31. 32. 33.* 34. 35.* 36. 37.* 38. 39. 40. 41. 42. 43.* 44. 44a. 45. 46. 47.* 48. 49. 50. 51. 52.
HCH3 (CNDO) HCHzCH3 (CNDO) HCH(C0ZHh HC(CH3)B HC(CN)3 HC(CH3)zCN HC(CN)zCHa HCH(CH8)z HCH(CN)z HCH(CN)CH3 HCHzCOzGHb HCHzCOCaH5 HCHzCOzH HCHzCHO HCHzCkCH HCHzCH3 HCHzCH=CHa HCHzCN HCH3 HC(CH&OH HC(OH)(CH3)CsH5 HC(OH)[CH(CH,)z]z HCH(CH3)NHz HCH(OH)CH(CHah HCHzNOz HCF(CH3)z HCHzNHz HCH(OH)C(CH3)8 HCHzN=CHz HCH*N(CH3KHO HCHzNfH3 HCH(CH3)0CHzCH3 HCH(0H)CFa HCHzOH HCH(N0z)z HCHzOCH3 HCHFCaHb HCH[N(CH3)z]z HCHzOCHO HC(OH)&H, HCHFCH, HCHzOCsHs HCHFCN HCHzF HCH(OH)2 HCH(OCH& HCF2CH3 HCFzCN HCHF, HC(0H)z HC(OCH3)3 HCF(OCH3)Z HCFi
Experimental
JCH
PWsH
UCH"
JCH
UCH"
Ref
93.19 93.31 111.12 114.17 114.44 114.69 114.79 119.37 119.67 119.84 120.15 120.29 120.61 121.36 122.01 122.12 122.44 122.47 122.91 123.03 123.69 125.35 126.30 128.22 129.78 129.80 129.92 130.18 131.95 132.04 132.13 133.25 133.11 135.27 135.33 135.50 136.33 136.44 136.89 137.07 137.13 138.21 138.63 140.08 150.05 151.67 156.98 159.98 166.79 169.48 170.75 180.95 212.29
0.4992 0.4918 0.4726 0.4679 0.4604 0.4656 0.4631 0.4809 0.4756 0.4784 0.4890 0.4870 0.4895 0.4891 0.4878 0.4910 0.4896 0.4884 0.4985 0.4844 0.4831 0.4850 0,4920 0.4974 0.5042 0.4926 0,5032 0.4985 0.5020 0.5050 0.5053 0.5000 0.5035 0.5125 0.5076 0.5114 0.5064 0.5044 0.5125 0.5073 0.5082 0.5105 0.5050 0.5191 0.5251 0.5270 0.5283 0.5246 0.5466 0.5463 0.5443 0.5527 0.5828
-29.72 -29.60 -11.79 -8.74 -8.47 -8.22 -8.12 -3.54 -3.24 -3.07 -2.86 -2.62 -2.30 -1.55 -0.90 -0.79 -0.47 -0.44 0 0.12 0.78 2.44 3.39 5.41 6.78 6.89 7.01 7.27 9.04 9.13 9.22 10.34 10.20 12.36 12.42 12.59 13.42 13.52 13.98 14.16 14.22 15.30 15.72 17.17 27.14 28.76 34.07 37.07 43.88 46.57 47.84 58.04 89.38
125.0 124.9 132.0
0.0 -0.1 7.0
2b 16 7
135.5
10.5
20a
145.2 135.5 130.3 125.7 130.0 127.0 132.0 124.9
20.2 10.5 5.3 0.7 5.0 2.0 7.0 -0.1
12 20a 20a 17 2b 2b 2b 16
136.1 125.0
11.1 0
20a 2b
142.5 136.0
17.5 11.0
17 8
140.0 146.7
15.0 21.7
8 11
133.0 132.0
8.0 7.0
2b 8
138.0 145.0
13.0 20.0
4
147.5 141 .O 169.4 140.0 151 .O 136.6 147.0
22.5 16.0 44.0 15.0 26.0 11.6 22.0
12 2b 11 7 7 11 2b
143.0 166.0 149.1
18.0 41 .O 24.1
2b 12 11
161.8
36.8
11
205.5 184.5
80.5 59.5
12 11
186.0
61 .O
7
239.1
114.1
11
Difference between JCHfor a given compound and that of methane. is not connected directly to the C-H carbon are marked with an asterisk.
Compounds in which the most electronegative substituent atom
terms the relationship between calculated values of J C ~ should lead t o a decrease in JCH is generally paralleled by a decrease in P,,,,, so that the direct application of and carbon s character is demonstrated in Figure 1, eq 1 using the INDO values of PscsH2would also give which shows a trend of increasing J C H with increasing the qualitatively incorrect prediction of J C H . Possible PsCsH2.This trend is in rough qualitative agreement with the popular view which interprets changes of JCH reasons for such failures are discussed in a later section. with changes of carbon s character. However, some Another relevant aspect of the trend shown in Figure 1 concerns the relative sensitivities of the computed JCH aspects of this apparent trend require further informaand PscsH2values to structural changes. If only the hytion, especially for molecules which are not hydrocardrocarbons are considered, a nearly linear plot is obbons. tained, as shown in Figure 2, which shows that both The apparent tendency of the present method to yield values for substituent changes which corJCH,calcd and PscsH2vary with about the same sensitiviincreased JCH respond to substantial increases in computed P,,,, valties to structural changes. Hence, in the special case of ues holds even in those cases for which this method prehydrocarbons, the simple "s-character view" is in close dicts the incorrect sign of the increment in J C H . Thus, agreement with the results obtained by eq 3. However, an incorrect prediction that a given substituent effect viewing the HCXYZ, HXC=Y, H G X compounds of Maciel, Mclver, Ostlund, Pople / MO Theory of Nuclear Spin Coupling
4 Table II. JCHin
,"!=Y Compounds Calculated
Compound
\ 54*
-Experimental
\
JCH
PmCIH
127.63
0.5484
-29.07
151.15
0.5417
-5.55
149.24
0.5392
-7.46
163.36
0.5513
155.22
0.5338
-1.48
155.50
0.5490
-1.20
156.34
0.5454
-0.36
156.70
0.5471
0.0
153.26
0.5444
162.36
0.5536
159.08
dlCH"
JCH
UGH'
Ref
156.2
0.0
16
168.2
12.0
5
156.2
0.0
16
159.18
2.98
18'
5.66
162.16
5.96
18'
0.5493
2.38
173.7
17.5
10
160.11
0.5523
3.41
178.83
0.5881
22.13
194.8
38.6
13
179.51
0.5704
22.81
180.51
0.5794
23.81
172.0
15.8
10
164.51
0.5571
7.81
172.4
16.2
10
183.11
0.5731
26.41
200.2
44.0
18
/
/-\
H H
CHa
H
\
55:
/
c=c
/
\
56.b H
CH=CHz
6.66
H
\
57.
(J=CH2 CHz=CH H
\
58.
/
=C+CHa
/
H H
\
59.
/c=c(cHa)z H
H
\
60.
/
C=CH2
H H
F
\
/
61.b /-\ 62.b H H
\
63.
H
c=O
-3.44
\ 64*
H
H
\ 65.
/-O 0H
\ 66.
67.
(as)
F
/
/-\
F H \
H
H
H
\ 68.
/"" CHa
H
\
69.
F
/
/
(1.0
{ sC 2(o)sH2(o) 1 0
=
- 0.304~)~([3.25- O.354~]/3.25)~( 5 )
the nonpolar, neutral case and where 4 H and 4c refer to the net electron densities on hydrogen and carbon, respectively. Results obtained by this formula for a sample of compounds chosen from Table I are presented in Table VI. There it is demonstrated that this sort of adjustment leads to improved general agreement with experimental results. Focusing attention on the
0.00
Figure 3. Plot of calculated JCHvalues us. experimental JCHvalues for compounds of Table I with no -I- substituents (entries in Table I without asterisk).
factors fc and fH leads one t o the conclusion that the correction could be improved if a modified approach were employed in which the hydrogen Is shielding constant (0.30) was increased relative to the carbon 2s shielding constant (0.35), i.e., if the effective nuclear charge and s2(0)values for hydrogen Is were even more sensitive t o local atomic charge density, relative to the sensitivities of the carbon 2s values, than predicted by eq 5. However, justification for any such modification would involve considerations beyond the scope of the present application. Nevertheless, these qualitative results suggest that the major source of disagreement for the starred compounds in Table I may be due to the fact that constant values were chosen for sc2(0) and sH2(0). Furthermore, in making this type of correction, the variation of SH~(O) may be at least as important as the changes in sc*(O). Litchman and Grant39 have recently questioned their earlier neglect of sH2(0)variation in substituted methanes. 2 9 HXC=Y Compounds. The comparisons between experimental and computed JcHvalues for the HXC=Y (39) W. M. Litchman and D. M. Grant, J . Am. Chem. Soc., 89, 6775 (1967).
Maciel, Mclver, Ostlund, Pople / MO Theory of Nuclear Spin Coupling
10
Figure 4. Plot of calculated Jcn values us. experimental JCHvalues for compounds in Table 11.
system available in Table I1 reveal a considerably better qualitative agreement than that experienced with the substituted methanes of Table I. These comparisons are shown graphically in Figure 4, which displays an approximate correspondence with the experimental trend. While the agreement is not as close as that represented for HCXYZ compounds in Figure 3, it must be emphasized that the results plotted in Figure 4 have not been selected from Table I1 in an arbitrary way. All available comparisons were included in Figure 4, and it seems likely that fair qualitative agreement is possible only because experimental data are not available for compounds containing the more troublesome -I- substituents of Table I, except for entries 61 and 62. For entry 61, the experimental order with respect t o ethylene is not reproduced by the theory. However, ~ these calculations do place the three distinct J C values of vinyl fluoride (61, 62, and 69) in the correct experimental order. It is interesting to note that the computed JCHvalues listed in Table I1 for formic acid (72) and the formate ion (65) were obtained from calculations on structures with rather arbitrary but hopefully representative intermolecular interactions included. Thus, in the formic acid case, a dimer geometry was adopted which is consistent with the available electron diffraction data.40 A calculation for a formic acid monomer using “standard geometry” yields the value 219.2 Hz, clearly out of line with respect t o the ester value. For the formate ion, a geometry of the type 111, including two interacting /H H-C
/O
H-o
\
Li
0 H-0
‘ H I11
water molecules and a lithium cation, was employed. 4 1 This configuration gave a J c H value of 178.8 Hz. A calculation on an isoIated formate ion with “standard (40) J. Karle and L.0. Brockway, J . Am. Chem. Soc., 66, 574 (1944). The 0...H-0 distance and the 0-H distance employed in the calculation are 2.70and 1.08 A, respectively. (41) Distances (A) employed in the calculation: RCH = 1-08, Rco = 1.31, R o . . . H = 1.30, Ro...H-o = 2.40, ROH = 1.08, ROLI = 2.01.
Journal of the American Chemical Society
geometry” yielded the value 106.5 Hz. Thus, the inclusion of the types of interactions represented in structure I, hydrogen bonding and the field of a cation, bring the calculated result from a value corresponding to serious disagreement into the correct range. This does not imply that such a structure is representative of the “average” configuration, but suggests that such interactions may be important in the calculations of properties of solutes. The general significance and potential usefulness of such calculations which include solvent molecules along with the solutes of primary interest are under investigation. The inclusion of hydrogen-bonding configurations for formaldehyde, with water reflecting the presence of the aqueous solvent used in the experiment, are incapable of improving the agreement significantly for that species; only small reductions in the coupling constant are obtained. However, it is of interest that the JCH value computed for the hydrate, with which formaldehyde might be in rapid equilibrium in aqueous solution, is only 150.0 Hz. In the last section of Table I1 is a collection of calculated JCHvalues for systems in which C H fragments occur in cisjtrans pairs with respect to some substituent. Substantial cisjtrans differences are noted for most cases. Of particular interest because of possible practical value in structure determinations are the geometrical effects in oximes (81-88). The predicted JCH values for the hydrogen cis with respect to the OH group are between 10 and 20 Hz smaller than those for the hydrogen in the corresponding trans relationship. Recently there has appeared one example of relevant experimental data,18b and this case supports the predicted trend. H - C s X Compounds. It is difficult to evaluate the relative success of the present method in accounting for substituent effects on JCHin the HC=X systems reported in Table 111. Thus, for those compounds for which both calculated and experimental values are available, the ranges of each cover only a few hertz. Furthermore, some of the experimental values were obtained by the early rapid-passage, dispersion-mode technique for which uncertainties of this magnitude can be expected. l 4 Aromatic Compounds. Relatively few accurate experimental data are available for comparison with the calculated results on six-membered-ring aromatic compounds given in Table IV. Some values have been reported on the basis of rapid-passage, dispersion-mode experiments but these have been excluded from the table because of the relatively large uncertainties frequently associated with them. Both promising trends and incorrect predictions are apparent in the comparisons which are available in Table IV. The calculated JCH values for fluorobenzene are in the experimentally correct order with respect to each other and the value for benzene. The same is true of the J C H 1values of compounds 111-1 13. In addition, the calculated JCH values for pyridine (1 13) are in good experimental correspondence with respect to both their internal order and their relationships to the benzene value. The reasonable qualitative agreement for the widely different JcH1 values in the series benzene, pyridine, pyrimidine may again be associated with the fact that the most electronegative atoms in the latter two compounds are attached directly to the C H fragment of interest. More experimental data are required before a more meaning-
/ 92:l / January 14, 1970
11
ful evaluation of the present method can be made for aromatic systems. Summary and Conclusion Application of approximate self-consistent molecular orbital theory with the INDO and finite perturbation approximations is moderately successful in accounting for the available experimental results on directly bonded C-H coupling constants in terms of a Fermi contact mechanism. The method is quite successful in predicting substituent effects on JCH in methanes which con-
tain no substituents of the -I- type, and in accounting for gross structural (hybridization) changes. Improved results appear likely, especially for compounds containing such substituents, if corrections can be made for variation of atomic s-orbital densities at both nuclei. The present results indicate that it is unnecessary to invoke such large changes in carbon s character as would be necessary in the popular hybridization view of JcH. It should be kept in mind that some errors are likely to result from the use of “standard geometries’’ rather than actual geometries in the calculations.
Approximate Self-consistent Molecular Orbital Theory of Nuclear Spin Coupling. 11. Fermi Contact Contributions to Coupling between Carbon and Directly Bonded Atoms’” G.E. Maciel,lb J. W. McIver, Jr., N. S. Ostlund,“ and J. A. Pople Contributionfrom the Department of Chemistry, Carnegie-Mellon University, Pittsburgh, Pennsylvania 15213. Received February 7, 1969 Abstract: The SCF finite perturbation method is applied to the Fermi contact contributions to spin-spin coupling between directly bonded CC, CN, and CF in a wide variety of molecules. The INDO molecular orbital approximation is used. Computed values of Jcc are in qualitatively good agreement with experimental values for noncyclic systems, especially if intermolecular interactions are included in appropriate cases. The method is far less successful in accounting for JcN and JCF;possible reasons for these difficulties are discussed.
great deal of interest has been focused upon the measurement and interpretation of spin-spin coupling constants between directly bonded atoms. Much of this interest has centered upon couplings between carbon and another atom, most frequently hydrogen, and the suggested relationships between the coupling constants and bond hybridization parameters. On the assumption of the dominance of the Fermi contact mechanism, such relationships were predicted from the early ~ a l e n c e - b o n dand ~ ~ molecular ~ orbital (MO)6,7 approximations of Ramsey’s formulation, using the average excitation energy (AE) approximation. A molecular orbital form of this approximate approach yields a proportionality between the coupling constant JAB and the parameter P , sB2, where P,,,, is the element of the first-order density matrixs between the valence-shell s orbitals of the atoms A and B involved in the coupling. In part I of this series3 detailed consideration was given to directly bonded C-H coupling constants.
A
(1) (a) Research supported in part by Grant GP6458 from the National Science Foundation; (b) Special National Institutes of Health Fellow, on leave from the University of California, Davis; (c) Postgraduate Scholar of the National Research Council of Canada. (2) J. W.Emsley, J. Feeney, and L. H. Sutcliffe, “High Resolution Nuclear Magnetic Resonance Spectroscopy,” Vol. 2, Pergamon Press, New York, N. Y.,1966,Chapter 12. (3) G. E. Maciel, J. W. McIver, Jr., N. S. Ostlund, and J. A. Pople, J . Am. Chem. Soc., 92, 1 (1970), for a summary of pertinent references. (4) M. Karplus and D. M. Grant, Proc. Natl. Acad. Sei. U.S., 45, 1269 (1959). (5) H. S. Gutowsky and C. Jaun, J . Chem. Phys., 37,2198 (1962). (6) N. Muller and D. E. Pritchard, ibid., 31,768 (1959). (7) K. Frei and H. J. Bernstein, ibid., 38, 1216 (1963). (8) Sometimes referred to, in the neglect of overlap approximation, as the charge-density, bond-order matrix.
There it was shown that the P,,,, parameters, as computed by the INDO$ molecular orbital method, do not manifest sufficient sensitivity to substituent effects t o account well for experimental trends inJCH. However, promising results were obtained by application of the approximate SCF finite perturbation method reported recently by Pople, McIver, and Ostlund. This method is based on a general framework for the calculation of second-order properties which has been described in detail elsewhere. 11,12 In its application to the Fermi contact spin-coupling interaction, l 2 it involves the calculation of an open-shell molecular orbital wave function under the influence of the perturbation
hB = (8r/3)PFBsB2(o) due t o the presence of a nuclear moment p B . It has been shown12 that in the INDO approximation this leads to an expression for the reduced coupling KAB given by
where /?is the Bohr magneton, S A ~ ( O is ) the valence-shell s-orbital density of atom A at its nucleus, psAsAis the (9) J. A. Pople, D. L. Beveridge, and P. A. Dobosh, J . Chem. Phys., 47,2026 (1967). (10) J. A. Pople, J. W. McIver, Jr., and N. S. Ostlund, Chem. Phys. Letters, 1,465 (1967). (1 1) J. A. Pople, J. W. McIver, Jr., and N. S. Ostlund, J. Chem. Phys., 49. 2960 f1968). (12) J.‘A. Pople, J. W. McIver, Jr., and N. S . Ostlund, ibid., 49, 2965 (1968).
Maciel, McIver, Ostlund, Pople / MO Theory of Nuclear Spin Coupling
