Solving the non-relativistic electronic Schrodinger equation with manipulating the coupling strength parameter over the electron-electron Coulomb integrals

TL;DR

This paper introduces a novel approach to solving the electronic Schrödinger equation by manipulating the coupling strength parameter, enabling efficient calculation of electronic energies without relying on traditional SCF convergence methods.

Contribution

It presents a new method that solves the a=0 case and generates the a=1 solution, reducing the need for iterative SCF procedures in electronic structure calculations.

Findings

Efficient calculation of ground state energies without SCF convergence.

Reduction in computational cost by using Hamiltonian square and configuration interaction.

Accurate correction for basis set errors and electron correlation effects.

Abstract

The non-relativistic electronic Hamiltonian, H(a)= Hkin + Hne + aHee, extended with coupling strength parameter (a), allows to switch the electron-electron repulsion energy off and on. First, the easier a=0 case is solved and the solution of real (physical) a=1 case is generated thereafter from it to calculate the total electronic energy (Etotal electr,K) mainly for ground state (K=0). This strategy is worked out with utilizing generalized Moller-Plesset (MP), square of Hamiltonian (H2) and Configuration interactions (CI) devices. Applying standard eigensolver for Hamiltonian matrices (one or two times) buys off the needs of self-consistent field (SCF) convergence in this algorithm, along with providing the correction for basis set error and correlation effect. (SCF convergence is typically performed in the standard HF-SCF/basis/a=1 routine in today practice.)