Extension of selected configuration interaction for transcorrelated methods

Abstract

In this work we present an extension of the popular selected configuration interaction (SCI) algorithms to the Transcorrelated (TC) framework. Although we used in this work the recently introduced one-parameter correlation factor [E. Giner, J. Chem. Phys., 154, 084119 (2021)], the theory presented here is valid for any correlation factor. Thanks to the formalization of the non Hermitian TC eigenvalue problem as a search of stationary points for a specific functional depending both on left-and right-functions, we obtain a general framework allowing different choices for both the selection criterion in SCI and the second order perturbative correction to the energy. After numerical investigations on different second-row atomic and molecular systems in increasingly large basis sets, we found that taking into account the non Hermitian character of the TC Hamiltonian in the selection criterion is mandatory to obtain a fast convergence of the TC energy. Also, selection criteria based on either the first order coefficient or the second order energy lead to significantly different convergence rates, which is typically not the case in the usual Hermitian SCI. Regarding the convergence of the total second order perturbation energy, we find that the quality of the left-function used in the equations strongly affects the quality of the results. Within the near-optimal algorithm proposed here we find that the SCI expansion in the TC framework converges faster than the usual SCI both in terms of basis set and number of Slater determinants.

TC++: First-principles calculation code for solids using the transcorrelated method

“…Because of this construction, several post-HF methods can be applied to the TC Hamiltonian in a straightforward manner. For example, the TC method was combined with the coupled-cluster theory [22,23], Møller-Plesset (MP) perturbation theory [7,8], and configuration interaction (CI) theory [24,25,26,27,28] for atomic and molecular systems. The combination of the TC method with the post-HF methods was also reported for solid-state calculations: calculation of optical absorption spectra by TC-CI singles [29], and TC-MP2 calculation for simple solids [30].…”