Michael Barfield

Valence‐Bond Studies of Contact Nuclear Spin–Spin Coupling. II. Long‐Range Pi‐Electron Coupling between Protons

A theoretical study of long‐range proton coupling is presented in terms of a semiempirical valence‐bond formalism which does not invoke the approximation of a “mean excitation energy” in the second‐order perturbation sum. Using the spin coupling theory which includes an explicit sum over the triplet‐state valence‐bond wavefunctions, π‐electron contributions to long‐range couplings are calculated for a large number of unsaturated molecules in which the protons are separated by four to seven bonds. The calculated results are shown to be in reasonably good agreement with the available experimental data and are of importance in discussing mechanisms of contact nuclear spin–spin coupling.

Erratum: Anisotropy of the Carbon‐13 and Proton Hyperfine Coupling Constants in Organic Radicals

A theoretical study of the anisotropy of the carbon‐13 and proton hyperfine coupling constants in organic radicals is presented in terms of a spin density formulation which uses the generalized product approximation specialized to valence‐bond wavefunctions. Both isotropic and anisotropic components of the 13C and 1H hyperfine coupling tensors are obtained for the methyl and ethyl radicals with inclusion of all valence electrons. Theoretical results for the methyl radical are also based on spin densities from self‐consistent‐field (SCF) molecular‐orbital theory in the approximation of intermediate neglect of differential overlap and from nonempirical spin‐restricted SCF calculations with configuration interaction. The calculated results are compared with the available experimental data, and they indicate that inclusion of contributions from the σ‐electron framework is essential. But in contrast to isotropic hyperfine coupling constants, components of the anisotropic hyperfine tensor are relatively insensi...

Valence‐Bond Studies of Contact Nuclear Spin–Spin Coupling. I. A Truncated Matrix Sum Method

A theoretical description of contact nuclear spin–spin coupling is presented in terms of a valence‐bond formalism which does not invoke the approximation of a “mean excitation energy” in the second‐order perturbation sum. By explicitly including a sum over the valence‐bond triplet‐state wavefunctions, a general expression for the contact nuclear spin coupling constant is obtained in a theory which uses a bond diagram formalism. The relationship of this extended theory to existing valence‐bond descriptions is investigated. As examples of the applicability of the method, detailed results are given for the contributions of the individual triplet states to the long‐range proton coupling constants in eight electron fragments of the butadiene and allene molecules.

Theoretical Studies of Solvent Effects on Nuclear Spin–Spin Coupling Constants. I. The Reaction Field Model

A theoretical study of the solvent dependence of nuclear spin–spin coupling constants is presented in terms of Onsagers reaction field model and self‐consistent perturbation theory in the semiempirical INDO (intermediate neglect of differential overlap) approximation of self‐consistent‐field molecular orbital theory. A possible mechanism for reaction field induced changes in coupling constants is discussed in terms of the sum over virtual orbital method, corresponding to the uncoupled Hartree–Fock approximation. Although the latter method does not give satisfactory values for coupling constants, the reaction field induced shifts are reasonable. Finite perturbation theory, which corresponds to the coupled Hartree–Fock approximation, gives much better coupling constant results. Calculated reaction field induced shifts for a variety of H–H and H–F coupling constants are compared with the experimental results in a variety of solvents. Although the calculated results are linear functions for very large values...

Anisotropy of the indirect nuclear spin-spin coupling constant

Abstract Anisotropies in the indirect nuclear spin-spin coupling constants arise from cross-terms between the contact and dipolar terms in the electron-nuclear Hamiltonian. Calculated anisotropic H-H and 13 C-H coupling constants, which are based on valence-bond wavefunctions, are non-negligible in comparison with the isotropic coupling constants, but are much smaller than the direct dipole-dipole coupling constants.

The conformational dependence of vicinal 15N-C-C-H coupling constants in peptides

The conformational dependence of vicinal 15N-C-C-H coupling in N-methylacetamide as a model compound for coupling in the peptide backbone is investigated by means of the self-consistent perturbation formulation for coupling constants in the INDO approximation of self-consistent-field molecular orbital theory. Because the calculated coupling constants cover a range of at least 7 Hz, they should be useful in determining the ψ angles in peptides. The prediction of opposite signs for gauche and trans coupling indicates the need for sign determination. Non-negligible coupling constants of positive sign for the gauche arrangements are undoubtedly due to a substituent effect involving the lone pair electrons on the nitrogen and the π-electrons of the carbonyl group. Calculated results are compared with the available experimental data.

Calculations of deuterium quadrupole coupling constants employing semiempirical molecular orbital theory

Deuterium quadrupole coupling constants (DQCC) for deuterium nuclei in a variety of bonding situations have been obtained by means of semiempirical molecular orbital wavefunctions in the INDO approximation. All integrals of the operator entering the electronic contributions have been included with no approximations in their evaluation. Analytical expressions are tabulated for the relevant two‐center integrals; three‐center integrals were obtained by numerical integration techniques. The factors responsible for the very strong dependence of deuterium QCC on internuclear distance, and the relative constancy of the parameters for a given bonding situation are discussed with regard to the types of terms which enter the integral expressions and the molecular electronic distributions. Some interesting and possibly useful predictions are also included in the tabulated results; the DQCC for the bridging deuterium in diborane is predicted to have a value of −110 kHz, which may be the first negative value for a DQC...

Magnetic shielding and shielding anisotropies by semiempirical molecular orbital theory. I. Inclusion of two‐center integrals of the type 〈φB‖OA‖φB〉

Magnetic shielding components are obtained for a number of molecules by means of semiempirical molecular orbital theory in the INDO approximation with inclusion of two‐center integrals of the type 〈φμB‖OA‖φνB〉. Exceedingly good results are obtained for calculated values of the diamagnetic shielding as these . 98195

Erratum: Electron Correlation and the Nuclear Spin–Spin Coupling Constant. II. The Generalized Product Approximation with Intergroup Configuration Interaction

A generalization of a number of existing theoretical descriptions of contact nuclear spin–spin coupling is presented in terms of a density matrix formalism and the generalized product approximation. The recognition of distinct groups such as bonds, σ electrons, or π electrons by this method permits a simplification of the discussion of many electron systems, but for an adequate description of spin coupling in many cases in which there is more than one group, it is essential to introduce intergroup configuration interaction. The resulting theoretical expressions provide a generalization of those descriptions which use second‐order perturbation theory and do not invoke the approximation of a “mean excitation energy” in the second‐order perturbation sum. The applicability of the method is demonstrated for cases in which the groups are described by both molecular‐orbital and valence‐bond (VB) wavefunctions. Using VB wavefunctions, specific π‐electron coupling constant results are reported for fragments of the butadiene and allene molecules. In the generalized product approximation, each of these fragments is described in terms of two groups of four electrons. Although considerably less computational effort is required by this method, the calculated results are in substantially good agreement with previous results based on eight‐electron VB calculations. With the computational simplification provided by the generalized product approximation, theoretical results are obtained for the π‐electron coupling between protons separated by from two to nine bonds in octatetraene.

Valence‐Bond Calculations of Triplet‐State Energies and Spin Densities of Unsaturated Organic Molecules

A theoretical study of triplet‐state organic molecules is given by means of the semiempirical valence‐bond (VB) method. Triplet‐state energies and spin densities are calculated by means of a VB bond‐diagram method with integral parameters from studies of ground‐state and spin‐dependent properties. For the two‐ to eight‐carbon polyenes reasonable agreement is obtained between the calculated ground to lowest triplet‐state energy separations and the experimental absorption maxima. It is found that a reversal of the polyene single and double bond lengths significantly lowers the triplet‐state energy because of effective correlation which tends to concentrate the positive spin density on the terminal carbons. A discussion is given of the various factors which influence dihedral twisting in the polyenes.