Walter England

Localized charge distributions

A localized molecular orbital has been found to extend slightly and regularly into regions away from the chemical bond which contains most of its charge cloud. This was made the basis for a method of transferring localized orbitals among similar molecules. Each localized orbital induces a set of so-called molecule invariant fragments consisting of one bond fragment and collections of geminal fragments, vicinal fragments, and third and fourth neighbor fragments. Localized orbital expansion coefficients in a hybrid basis can be calculated for these molecule invariant fragments without solving any equations or performing any laborious computations.The present work is an application to acylic hydrocarbons. The results are based on the analysis of 33 INDO-SCF molecular orbital wavefunctions in the localized representation. Computational methods for obtaining close approximations to localized orbitals are also discussed. The application of a suggested pseudo-eigenvalue localization method and its accompanying self-consistent iteration process are found to not converge.

Electronic structure of VS

Energy bands, density of states, Fermi surfaces, and wavefunction populations are calculated for VS in the hexagonal phase. Purely metallic, mixed metal‐nonmetal, and purely nonmetallic bands are observed. The Fermi level intersects the almost pure vanadium 3d bands so the compound should exhibit electrical conductivity like typical d band metals. The vanadium s and p and sulfur p bands are hybridized and lie well below the Fermi energy, and they give rise to the strong covalent bonds and the nonmetallic mechanical properties of the compound.

Localized charge distributions. The internal rotation barrier in borazane

Abstract The barrier to internal rotation in borazane is analyzed in terms of the localized charge distribution defined in previous papers. The origin of the barriers is found to be similar to that in ethane. Upon rotation from staggered to eclipsed, the vicinal H-H one-electron interference energies within the NH and BH bonds change from binding to antibinding, the BH contribution being considerably larger. The calculated and interference barriers are, respectively, 1.98 and 1.89 kcal/mole. As in ethane, it is found that while repulsion and quasi-classical two-center attractions are changed drastically by geometry optimization, the interference analysis of the barrier is relatively insensitive to geometry changes.

Quantum field theoretical methods in chemically bonded systems. II : Diagrammatic perturbation theory

SummaryMany-body perturbation theory is derived for chemical bonds. Paired quasiparticles represent the bonds. Products of the paired quasiparticles define a model Bardeen-Cooper-Schrieffer function. The pairing force is added as a model interaction to the self-consistent problem. The starting model is based on valency and adiabatic symmetry correlation. Symmetries are enforced by the model Hamiltonian. Perturbative corrections are expressed as ordinary Feynman diagrams. The number of diagrams needed is the same as for particle-hole theory.

Quantum field theoretical methods in chemically bonded systems. III : BCSLN-HL(N) potential energy curves for the ground states of H2, LiH, FH and F2

SummaryA new perturbative method is applied to single bonds. The starting model is the second-quantized self-consistent Heitler-London model. The unperturbed function is a four-determinant Bardeen-Cooper-Schrieffer function. Perturbative corrections are computed with renormalized Feynman diagrams. Convergence is satisfactory by third order. Calculated (experimental) dissociation energies in eV are 4.61 (4.75) for H2, 2.37 (2.52) for LiH, 6.22 (6.13) for FH, and 1.88 (1.66) for F2. Calculated (experimental) equilibrium bond distances in Å are 0.739 (0.741) for H2, 1.598 (1.596) for LiH, 0.903 (0.917) for FH, and 1.395 (1.412) for F2. Calculated (experimental) vibrational frequencies in cm−1 are 4578 (4401) for H2, 1396 (1406) for LiH, 4447 (4138) for FH, and 927 (916) for F2. Other spectroscopic constants agree with experiment to within 11% except for anharmonicities which differ from experiment by up to 20%.

Quantum field theoretical methods in chemically bonded systems. IV : Analysis of perturbative energy terms for H2, LiH, FH and F2

SummaryA new perturbative procedure is analyzed numerically for four single bonded diatomic molecules. The starting model is the second-quantized self-consistent Heitler-London model. The unperturbed function is a four-determinant Bardeen-Cooper-Schrieffer function. The model Hamiltonian is the ordinary Hamiltonian plus linear and quadratic powers of a two-level number operator. Parameters which multiply the additional terms are chosen to enforce particle-number symmetry. Convergence of the perturbative series for the energy as a function of internuclear distance is reasonable: third-order corrections are about an order of magnitude smaller than second-order corrections; total corrections through third order are about two orders of magnitude smaller than first-order energies.

Electronic Structure and Its Relation to the Magnetic Ordering of CrB2

In an effort to understand the antiferromagnetic ordering in the hexagonal compound CrB2, we have calculated its energy band structure by using the KKR method. It is found that the energy bands consist of hybridized chromium s, p, d and boron s, p bands. The Fermi surface has a large and very flat sheet perpendicular to the c axis. It is well known that this kind of Fermi surface feature favors the formation of spin‐density‐wave state as observed below 85 K. The calculated wavevector for the spin‐density wave is 0.6l a.u., which is very close to one of the elastic neutron diffraction peaks observed in a powder sample. The density of states at the Fermi level gives a Pauli susceptibility which is one sixth of the measured paramagnetic susceptibility, and an electronic specific heat which is one half the observed value. Both discrepancies can be explained by the spin fluctuation enhancement effect. The states near the Fermi level have very small boron s character, which may explain the absence of Knight shi...