Quasi-linear buildup of Coulomb integrals via the coupling strength parameter in the non-relativistic electronic Schrödinger equation

Kristyán, Sándor (2020) Quasi-linear buildup of Coulomb integrals via the coupling strength parameter in the non-relativistic electronic Schrödinger equation. In: AIP Conference Proceedings. American Institute of Physics, p. 420006. ISBN 978-0-7354-4025-8

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Abstract

Abstract. The non-relativistic electronic Hamiltonian, HHne+aHee, is linear in coupling strength parameter (a), but its eigenvalues (electronic energies) have only quasi-linear dependence on it. Detailed analysis is given on the participation of electron-electron repulsion energy (Vee) in total electronic energy (Etotal electr,k) in addition to the wellknown virial theorem and standard algorithm for vee(a=1)=Vee calculated during the standard- and post HF-SCF routines. Using a particular modification in the SCF part of the Gaussian package, we have analyzed the ground state solutions via the parameter “a”. Technically, with a single line in the SCF algorithm, operator was changed as 1/rija/rij with input “a”. The most important findings are, 1, vee(a) is quasi-linear function of “a”, 2, the extension of 1 st Hohenberg-Kohn theorem (0(a=1)  Hne  Y0(a=0)) and its consequences in relation to “a”. The latter allows an algebraic transfer from the simpler solution of case a=0 (where the single Slater determinant Y0 is the accurate form) to the physical case a=1. Moreover, we have generalized the emblematic Hund’s rule, virial-, Hohenberg-Kohnand Koopmans theorems in relation to the coupling strength parameter.

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