A new expression for the correlation energy of closed-shell systems is presented. This correlation energy, obtained from the random phase approximation, is size consistent, invariant to unitary transformations of degenerate orbitals, and has the important property that at long range it yields the coupled Hartree-Fock dispersion force between interacting systems. Since ordinary second-order many-body perturbation theory, when applied to the same problem, gives uncoupled Hartree-Fcck dispersion forces, calculations based on our formula, which still requires only particle-hole twoelectron integrals. are expected to lead to significantly improved potential energy curves.

A general method is proposed for quantum-mechanical study of physical properties of molecules involving polarization or distortion of the electronic structure. This consists of the calculation of self-consistent molecular orbital wavefunctions (single determinants) in the presence of small but finite perturbations. The general theory of such methods is presented together with a preliminary discussion of numerical error.

A new expression for the correlation energy within the random phase approximation (RPA) is presented. It has the following properties: it is (1) size consistent, (2) invariant to unitary transformations of degenerate orbitals, (3) correct to second order in perturbation theory, and (4) when applied to a supermolecule comprised of two interacting closed-shells, it describes the dispersive part of the interaction at the coupled Hartree–Fock (HF) level, i.e., the van der Waals’ coefficient extracted from its long-range behavior is identical to that obtained from the Casimir–Polder expression using the dynamic coupled Hartree–Fock polarizabilities of the isolated systems. This expression, which requires only particle–hole two-electron integrals for its evaluation, is expected to yield considerably more accurate potential energy curves between closed-shell systems than second-order Moller–Plesset perturbation theory which, as is shown, describes dispersion forces at the less accurate uncoupled HF level. In addition, since it is shown how this RPA correlation energy can be obtained from the zeroth iteration of a self-consistent RPA procedure such as that of McKoy and co-workers, our result can be systematically improved. Finally, illustrative calculations of He and (He)2 are presented.

The finite pertubation method developed in the first paper of this series is applied to isotropic nuclear-spin coupling constants, assuming that only a Fermi contact mechanism couples the electron and nuclear spins. Results for some simple systems are calculated using self-consistent molecular orbital methods involving the neglect of differential overlap, and on the basis of these results, certain points regarding the mechanisms of spin coupling are discussed. A detailed discussion of the sources and magnitudes of the errors is also presented.

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, Jch values are calculated for a wide variety of compounds. Regarding hydrogen Is 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 -1+ substituents (-F, -OR, -NR2, -O, etc.), but not for molecules with -Isubstituents (-CF3, -C(0)X, -N02, -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 parameter.2-20The early hybridization arguments were (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)

The SCF finite perturbation method is applied to the calculation of geminal proton-proton coupling constants in 19 compounds with saturated >CH2 groups, and 22 compounds with unsaturated =CH2 groups. The calculations were based on the Fermi contact mechanism and the INDO molecular orbital approximation. Generally good agreement is obtained with experimental trends of substituent effects. The results are discussed in terms of the more qualitative Pople-Bothner-By theory, with which good agreement is obtained. Angular and conformational dependences of the computed couplings are explored.The chemical literature of the past 10 years contains a large body of experimental and theoretical work on correlating the signs and magnitudes of proton-proton coupling constants with molecular structure. Much attention has focused upon coupling between protons bonded to the same carbon atom.These geminal proton-proton coupling constants (denoted here by Vhh) have been the subject of frequent studies and critical review.1 2Early valence-bond calculations generally provided qualitatively correct predictions on the dependences of the magnitude of VHh on the HCH angle and on the conformations of adjacent conjugating groups.8'4 However, these apparent early correlations required reexamination5-7 when the assumed positive sign for (1) (a) Research supported in part by a grant from the National Science Foundation; (b) papers I and II in the series are given in ref 24 and 25; (c) Special NIH Fellow, on leave from the University of California, Davis; (d) Postgraduate Scholar of the National Research

The general conditions under which real, restricted Hartree-Fock wavefunctions become unstable with respect to variation of the orbitals are derived. It is shown that complex solutions to the Hartree-Fock equations are associated with a singlet instability in the usual real, restricted solution. A comment is made concerning the complex wavefunctions found by Harris and Pohl for hydrogen halides at short internuclear distances.

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