Relativistic Kinetic-Balance Condition for Explicitly Correlated Basis Functions

TL;DR

This paper derives a relativistic kinetic-balance condition for explicitly correlated basis functions, ensuring variational stability in semi-classical Dirac-based calculations for many-fermion systems.

Contribution

It introduces a new kinetic-balance condition derived from row reduction, linking relativistic spinor components to the non-relativistic limit for many-electron systems.

Findings

Provides a relation for $4^N$ spinor components in N-fermion systems.

Aligns with recent developments in exact decoupling in relativistic orbital theory.

Ensures variational stability in relativistic quantum calculations.

Abstract

This paper presents the derivation of a kinetic-balance condition for explicitly correlated basis functions employed in semi-classical relativistic calculations. Such a condition is important to ensure variational stability in algorithms based on the first-quantized Dirac theory of 1/2-fermions. We demonstrate that the kinetic-balance condition can be obtained from the row reduction process commonly applied to solve systems of linear equations. The resulting form of kinetic balance establishes a relation for the $4^N$ components of the spinor of an $N$-fermion system to the non-relativistic limit, which is in accordance with recent developments in the field of exact decoupling in relativistic orbital-based many-electron theory.