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

• Main Author: Kristyan, Sandor
• Format: Conference Proceeding
• Language: English
• Subjects: Algorithms; Coupling; Eigenvalues; Linear functions; Mathematical analysis; Operators (mathematics); Parameters; Relativistic effects; Schrodinger equation; Virial theorem
• ISSN: 0094-243X; 1551-7616
• DOI: 10.1063/5.0026479

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 well-known 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 1st Hohenberg-Kohn theorem (Ψ0(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-Kohn- and Koopmans theorems in relation to the coupling strength parameter.