A finite‐difference solution of the Hartree–Fock equations for diatomic molecules

Abstract

AbstractsA more general application of the self-consistent field iteration is coupled with a finitedifference Newton-Raphson algorithm to solve the set of coupled second-order integrodifferential equations with split boundary conditions which constitutes the Hartree-Fock problem for diatomic molecules. The N orbitals are assumed to be of the form ya = La(1)Ma(~)eima~(2n)-1/2, ( x = 1, -. . , N ) , where 1, p, and 4 are the usual confocal elliptical coordinates. Requiring the expectation value of the electronic Hamiltonian to be stationary with respect to independent variations of the functions L, and M u , subject to constraints of orthonormality, leads to a set of coupled one-dimensional differential equations for the functions La and Ma . I n the new method a corresponding set of finite-difference equations including the split boundary conditions for each function, as well as the Lagrange multipliers and associated constraints on normalization and orthogonality, are incorporated into a large system of nonlinear algebraic equations which is solved by means of a coupled self-consistent field-generalized Newton-Raphson iteration. FIMPLE AND WHITEEine allgemeinere Anwendung der SCF-Iteration wird rnit einen Newton-Raphson'schen Algorithmus fur endliche Differenzen gekoppelt, urn den Satz von gekoppelten Integrodifferentialgleichungen zweiter Ordnung mit aufge-spalteten Randbedingungen zu h e n , die das Hartree-Fock-Problem fur zweiatomige Molekule bilden. Die N orbitale werden mit der Form y, = La(I)Ma (~)eima4(2.rr)-1'2, ( a = 1, . . . , 1 % '

Observations on Chatham Rise currents

“…The most suitable set of observations to allow estimation of the density field was from a station at 43°30'S, 179°00'E, occupied on 30 May 1970(G795, Heath 1973. Horizontal velocity modes calculated using the Newton-Rapson finite difference algorithm (Fimble & White 1975) are shown in Fig. 4.…”

A finite‐difference approach to the electron correlation problem

“…Recently a finite-difference Newton-Raphson algorithm, originally developed by Van Dine [l], has proven to be very successful in solving the Hartree Fock (HF) equations for atoms [2] and diatomic molecules [3].…”