Galerkin method for unsplit 3-D Dirac equation using atomically/kinetically balanced B-spline basis

TL;DR

This paper introduces a Galerkin numerical method employing atomically/kinetically balanced B-spline basis functions to accurately solve the time-dependent Dirac equation in prolate spheroidal coordinates for two-center systems, enabling precise spectral and dynamical analyses.

Contribution

It presents a novel Galerkin approach with balanced B-spline basis functions for efficient and accurate solutions of the 3-D Dirac equation in complex molecular geometries.

Findings

Accurate computation of the Dirac spectrum for two-center systems.

Successful simulation of eigenstate evolution under external electromagnetic fields.

Demonstration of high accuracy using B-spline basis functions.

Abstract

A Galerkin method is developed to solve the time-dependent Dirac equation in prolate spheroidal coordinates for an electron-molecular two-center system. The initial state is evaluated from a variational principle using a kinetic/atomic balanced basis, which allows for an efficient and accurate determination of the Dirac spectrum and eigenfunctions. B-spline basis functions are used to obtain high accuracy. This numerical method is used to compute the energy spectrum of the two-center problem and then the evolution of eigenstate wavefunctions in an external electromagnetic field.