Jean-Louis Calais

Band structure of transition metal compounds

Abstract The article is a review of band-structure calculations for transition metal compounds (carbides and nitrides, layer compounds, A15 structures, and others).

INVERSION OF CYCLIC MATRICES

Abstract : The inversion of the overlap matrix in LCAO-cal culations of crystals is discussed for the general case, when an arbitrary number of neighbours is taken into account. Particular attention is paid to the numerical aspects of the problem. (Author)

Self-consistent-field × α cluster calculations for the ground state Ne2 molecule

Abstract The ground 1 Σ + g state potential curve for Ne 2 is calculated in the SCF × α approximation. The molecule is found to dissociate too slowly and to give no van der Waals minimum.

Convergence of direct space exchange lattice sums in polymer band structure calculations

A study of the convergence properties associated with direct lattice summations of the exchange contributions to the quantities needed in a restricted Hartree–Fock calculation for a polymer, leads to a detailed analysis of the analytic and asymptotic properties of the Fock–Dirac density matrix in the LCAO representation. The results, obtained simply by means of Fourier analysis, provide an important characterization of the restricted Hartree–Fock method as applied to chain‐like systems. As a by‐product we obtain a general proof in direct space that a partially filled band, which influences drastically the analyticity properties of the density matrix in reciprocal space, leads to a logarithmically diverging derivative of the orbital energy at the Fermi level. This in turn gives a vanishing density of states at that level. This result, well known for the electron gas model, is thus an inherent property of the restricted Hartree–Fock approximation.

Size-Consistency and Size-Intensivity Aspects of Many-Body Green's Function Calculations on Polymers : Characterization of the Convergence of Direct Lattice Self-energy Summations

Publisher Summary Today, constant refinements of experimental techniques in the field of electron spectroscopy require the development of more accurate schemes to calculate the electronic structure of polymers, going beyond the one-particle level of description. However, because of their extraordinarily heavy computational cost and, possibly, inherent size-related difficulties, correlated band structure calculations still remain as an exception. The one-particle Many-Body Greens Function (MBGF) theory, focusing on the average properties of a particle propagating in the background of an interacting many-body system, provides direct and quantitative schemes to estimate ionization and electron attachment energies. This chapter provides an outline of the diagrammatic techniques used in MBGF theory. Together with the basic crystal orbital (CO) LCAO-SCF equations for infinite systems with periodicity in one dimension, the chapter examines the implications of the linked-cluster theorem in the context of macromolecules. It also focuses on the singular divergent behavior of some specific bielectron interaction elements over crystalline orbitals and characterizes the convergence properties of various self-energy simple or coupled lattice summations.

RHF energy band shapes for metallic chains: Dependence on the summation of exchange contributions. An illustration on the linear chain of hydrogen atoms

Minimal basis set (STO‐3G) calculations on the metallic infinite chain of hydrogen atoms, (‐H‐)x, performed within the same computational framework as currently used for more realistic model systems, are reported to illustrate the dependence of the RHF energy bands on the summation of exchange contributions. The numerical results show the gradual decay of the density of states at the Fermi level as the number of terms in the exchange lattice sums is increased and rather convincingly verify the predictions of previous formal analyses.

FOURIER REPRESENTATION METHOD FOR ACCURATE EVALUATION OF THE COULOMB AND EXCHANGE LATTICE SUMS IN EXTENDED CHAINS

By considering chains of hydrogen and helium atoms with one Gaussian function centered on each atomic sites, i.e., the simplest possible metallic and insulating model systems retaining all the characteristics of the restricted Hartree–Fock–Roothaan method for extended chains, a scheme is proposed to carry out accurately and efficiently both Coulomb and exchange lattice sums which occur in a Gaussian basis set environment.

Outer Shell Overlap Integrals for Some Silver Halide Crystals

Outer shell overlap matrix elements involving ns, npσ, npπ, ndσ, ndπ, and ndδ orbitals have been calculated for the three NaCl structured silver halides AgF, AgCl, and AgBr. Hartree‐Fock‐Roothaan wave‐functions have been used in all calculations. The overlaps have been calculated for first (halogen‐silver), second (halogen‐halogen and silver‐silver), and third (halogen‐silver) neighbors at various internuclear separations. The exponential type variation of overlap with internuclear separation suggested by Hafemeister and Flygare has been utilized.

Wavelets - Something for quantum chemistry?

We propose to use the relatively new mathematical and numerical tool wavelets in quantum chemical studies. A short survey is given of the most elementary aspects of wavelet theory. The connection between wavelets and coherent states is discussed together

Simple AMO Function for the Lithium Molecule

An AMO calculation for the ground state of the Li2 molecule is described. The calculations are very simple, but quite satisfactory results are obtained. Connections with other calculations are pointed out and certain interesting problems connected with the Li2 molecule and related molecules for which the AMO method might be useful, are discussed.