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 that 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 that 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.
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In the TC method, band structure calculation after the regular SCF calculation is performed self-consistently. This is because the singularities of the interaction in the k-space were handled in the manner that requires the one-body wave functions on the k-mesh used in the band-structure plot.
For LiH, note that our LDA pseudopotentials do not include the non-linear core correction55 since its meaning is ambiguous in the context of the TC method. This can be an origin of a difference for the valence bandwidths obtained by with-core and without-core LDA calculations presented in Table I. For other materials, the calculated LDA band structures are almost unchanged between with-core and without-core calculations.
