Hartree-Fock-Slater LCAO calculations

Figure 3.47. The geometries of lr4 and Iri > clusters used in the Hartree-Fock-Slater LCAO calculations with results presented in table (3.17)1 1.

Geurts, P. J. M., Bouten, P. C. P., 8 van der Avoird, A. (1980). Hartree-Fock-Slater-LCAO calculations on the Cu(II) bis(dithiocarbamate) complex Magnetic coupling parameters and optical spectrum. Journal of Chemical Physics, 73,1306. 

Ravenek W and Geurts EMM 1986 Hartree-Fock-Slater-LCAO implementation of the moderately large-embedded-cluster approach to chemisorption. Calculations for hydrogen on lithium (100) J. Chem. Phys. 84 1613-23... 

LCAO expansion of the MOs [15]. In the DV-Xa MO method based on the Hartree-Fock-Slater approach, the exchange-correlation potential is approximated by the simple Slater form [16] Vxc(r) = —3a 3p(r)/47i 1/3, where the coefficient a is a scaling parameter (fixed at 0.7 in the present study) and p(r) is the local electron density at a position r. The basis functions for the MO calculation consisted of atomic orbital wave eigenfunctions obtained in numerical form, which included the ls-6s, ls-5s, ls-6p, ls-4p, and ls-2p orbitals for Ba, Sr, Pb, Ti, and O ions, respectively... 

The formal analysis of the mathematics required incorporating the linear combination of atomic orbitals molecular orbital approximation into the self-consistent field method was a major step in the development of modem Hartree-Fock-Slater theory. Independently, Hall (57) and Roothaan (58) worked out the appropriate equations in 1951. Then, Clement (8,9,63) applied the procedure to calculate the electronic structures of many of the atoms in the Periodic Table using linear combinations of Slater orbitals. Nowadays linear combinations of Gaussian functions are the standard approximations in modem LCAO-MO theory, but the Clement atomic calculations for helium are recognized to be very instructive examples to illustrate the fundamentals of this theory (67-69). 

Other calculations tested using this molecule include two-dimensional, fully numerical solutions of the molecular Dirac equation and LCAO Hartree-Fock-Slater wave functions [6,7] local density approximations to the moment of momentum with Hartree-Fock-Roothaan wave functions [8] and the effect on bond formation in momentum space [9]. Also available are the effects of information theory basis set quality on LCAO-SCF-MO calculations [10,11] density function theory applied to Hartree-Fock wave functions [11] higher-order energies in... 

While in principle all of the methods discussed here are Hartree-Fock, that name is commonly reserved for specific techniques that are based on quantum-chemical approaches and involve a finite cluster of atoms. Typically one uses a standard technique such as GAUSSIAN-82 (Binkley et al., 1982). In its simplest form GAUSSIAN-82 utilizes single Slater determinants. A basis set of LCAO-MOs is used, which for computational purposes is expanded in Gaussian orbitals about each atom. Exchange and Coulomb integrals are treated exactly. In practice the quality of the atomic basis sets may be varied, in some cases even including d-type orbitals. Core states are included explicitly in these calculations. 

The key to most covalent models is the Linear Combination of Atomic Orbitals treatment or LCAO. Its principles, as carefully detailed by Roothaan (1951) are closely connected to Hartree-Fock calculations described by Slater (1960) and Cowan (1981). Let us recall the basic formulae and hypothesis ... 

Quantum chemistry calculations are currently quite common and we recall the excitement this author experienced when first reading Roberts Notes on Molecular Orbital Theory [2] in the early 1960s. Therefore, we include some modern but simple examples here in the hope that the amazement factor is still possible for undergraduates eager to learn up-to-date material. First we can write down the main Hartree-Fock-Roothaan energy operator and at least interpret the various terms. We have used Slater s derivation [1] of the Roothaan LCAO form of the Hartree-Fock equations but prefer Pople s implementation [3] for computer code. First, the one-electron operator... 

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