On the AB initio crystal orbital method

Abstract

A new computer realization of the LCAO Hartree--Fock crystal orbital method using contracted Gaussian orbitals is reported. AH integrals over the atomie orbitals are ealculated explieitly within a finite interaction range. No approximation with respeet to exchange is used. The spin-unrestricted Hartree--Fock-type crystal orbital formalism has been programmed, too. Both programs are limited to quasi one-dimensional systems at present, provide nevertheless a useful tool for the theoretical investigation of the eleetronic strueture of simple polymers and one-dimensional models of solids. Basic information on both programs is documented.Some numerieal aspeets, especially the convergency properties of the methods with respect to the number of grid points in the Brillouin zone, the shape of the Fermi surfaee in the special case of partly filled bands, the starting density matrices in the self-eonsistent field iteration procedure and the size of the finite interactiort range taken into account are diseussed. The specific problem of the starting density matrices in the unrestricted HF case are also dealt with. Finally comparison is made with semi-empirical ealculations. lntroductionThe linear eombination of atomic orbitals (LCAO) Hartree--Fock (HF) molecular orbital (MO) as well as crystal orbital (CO) methods appear nowadays well established calculational tools for the investigation of the electronic structure of molecules and solids, respectively. A number of physical observables can be estimated well even from approximate HF wave functions (especially one-particle properties) while others await correlation corrections. Thus it is easy to understand that a large effort has been devoted to the calculation of the LCAO HF CO-s (and energy bands) of many systems. It Ÿ not the aim of the present work to review this s we refcr to two review papers only, eovering part of the actual caleulations [1]. From the methodological point of view these calculations are either semi-empirical using usually one of the integral approximation schemes of the approximate quantum chemical MO methods of are of nonempirical nature. The lattcr are often termed ab initio but use in fact in the majority of cases some kind of approximation scheme [2] for the integrals over the atomic orbitals (AO-s) entering in the LCAO CO formalista. In this paper we shall use the term ab initio (in close *

Symmetric and symmetry‐broken Hartree–Fock solutions of one‐dimensional models

“…For the UHF case the corresponding equations are quite similar, the difference is only the exchange term in the Fock operator. In the case of the UHF scheme we can write the following coupled matrix eigenvalue equations [4] : F"(k)Cz(k) = ~z(k)S(k)Cz(k) (a = a,P; n = 1,2,. . .…”

On the Role of the Nonlocal Hartree-Fock (HF) Exchange in Narrow-Band Materials

“…One of the first contributions had been given by Fujita and Imamura [15]. Subsequent calculations based on ab initio CO procedures showed alternatively pronounced long-range effects of the exchange potential [2,3,[5][6][7][8][16][17][18] or the absence of significant LR contributions (i.e. interactions beyond the third or fourth nearest neighbors) [4,19].…”

Convergence of LCAO density matrices in Hartree—Fock calculations on extended model chains

“…Zl; is nothing else that the jth coefficient of the complex Fourier series representing D,,(k') [Eq. (7)]. D,(k') being constructed from the solutions of the Fock equations, can be expected to be infinitely differentiable functions of k', except possibly at the Brillouin zone boundaries or at those k' values at which the Hartree-Fock orbital occupancy changes discontinuously.…”