Quasi-linear dependence of Coulomb forces on coupling strength parameter in the non-relativistic electronic Schrödinger equation and its consequences in Hund’s rule, Mølle -Plesset perturbation- , virial - , Hohenberg-Kohn - and Koopmans theorem
Sandor Kristyan
10.26434/chemrxiv.5371507.v1
https://chemrxiv.org/articles/Quasi-linear_dependence_of_Coulomb_forces_on_coupling_strength_parameter_in_the_non-relativistic_electronic_Schr_dinger_equation_and_its_consequences_in_Hund_s_rule_M_lle_-Plesset_perturbation-_virial_-_Hohenberg-Kohn_-_and_Koopmans_theorem/5371507
<p> The extended non-relativistic electronic
Hamiltonian, H<sub>Ñ</sub>+ H<sub>ne</sub>+ aH<sub>ee</sub>, is linear in coupling strength
parameter (a), but its eigenvalues (interpreted as electronic energies) have
only quasi-linear dependence on “a”. No detailed analysis has yet been
published on the ratio or participation of electron-electron repulsion energy (V<sub>ee</sub>)
in total electronic energy – apart from virial theorem and the highly detailed
and well-known algorithm for V<sub>ee</sub>, which is calculated during the standard
HF-SCF and post-HF-SCF routines. Using a particular modification of the SCF
part in the Gaussian package we have analyzed the ground state solutions via
the parameter “a”. Technically, this modification was essentially a
modification of a single line in an SCF algorithm, wherein the operator r<sub>ij</sub><sup>-1</sup>
was overwritten as r<sub>ij</sub><sup>-1</sup> ® ar<sub>ij</sub><sup>-1</sup>, and used “a” as input. The most important finding
beside that the repulsion energy V<sub>ee</sub>(a) is a quasi-linear function
of “a”, is that the extended 1<sup>st</sup> Hohenberg-Kohn theorem (Y<sub>0</sub>(a=1) Û H<sub>ne</sub> Û Y<sub>0</sub>(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 is the accurate form) to the realistic
wanted case a=1. Moreover,
we have generalized the emblematic theorems
in the title in relation to the coupling strength parameter. </p>
2017-09-07 20:40:28
electron-electron repulsion energy participation in ground states
coupling strength parameter
totally non-interacting reference system
evolution of LCAO parameters in HF-SCF algorithm
generalization of Hundu2019s rule, Mu00f8ller-Plesset perturbation-, virial-, Hohenberg-Kohn- and Koopmans theorem
Chemistry