Iterative diagonalization of the non-Hermitian transcorrelated Hamiltonian using a plane-wave basis set: Application to $sp$-electron systems with deep core states

TL;DR

This paper introduces an iterative diagonalization scheme for the non-Hermitian transcorrelated Hamiltonian using a plane-wave basis, improving computational efficiency and analyzing core state effects in $sp$-electron systems.

Contribution

It develops a block-Davidson algorithm for non-Hermitian transcorrelated Hamiltonians and applies it to $sp$-electron systems to assess pseudopotential effects.

Findings

Deep valence band positions are improved by including core states explicitly.

Overall band structures are consistent whether core states are included explicitly or via pseudopotentials.

The method reduces computational costs effectively.

Abstract

We develop an iterative diagonalization scheme in solving a one-body self-consistent-field equation in the transcorrelated (TC) method using a plane-wave basis set. Non-Hermiticity in the TC method is well handled with a block-Davidson algorithm. We verify the required computational cost is efficiently reduced by our algorithm. In addition, we apply our plane-wave-basis TC calculation to some simple $sp$-electron systems with deep core states to elucidate an impact of the pseudopotential approximation to the calculated band structures. We find a position of the deep valence bands is improved by an explicit inclusion of core states, but an overall band structure is consistent with a regular setup that includes core states into the pseudopotentials. This study offers an important understanding for the future application of the TC method to strongly correlated solids.