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

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.