Compactification of Determinant Expansions via Transcorrelation

TL;DR

This paper introduces a transcorrelated approach to selected configuration interaction that significantly reduces the determinant space needed for accurate electronic structure calculations and accelerates energy convergence with basis set size.

Contribution

The study demonstrates that transcorrelation compresses the determinant space and improves energy convergence in SCI, with the extent depending on the correlation factor accuracy.

Findings

Transcorrelation reduces the number of determinants needed for accuracy.

Energy convergence accelerates with basis set size in TC-SCI.

Compression effectiveness depends on the correlation factor accuracy.

Abstract

Although selected configuration interaction (SCI) algorithms can tackle much larger Hilbert spaces than the conventional full CI (FCI) method, the scaling of their computational cost with respect to the system size remains inherently exponential. Additionally, inaccuracies in describing the correlation hole at small interelectronic distances lead to the slow convergence of the electronic energy relative to the size of the one-electron basis set. To alleviate these effects, we show that the non-Hermitian, transcorrelated (TC) version of SCI significantly compactifies the determinant space, allowing to reach a given accuracy with a much smaller number of determinants. Furthermore, we note a significant acceleration in the convergence of the TC-SCI energy as the basis set size increases. The extent of this compression and the energy convergence rate are closely linked to the accuracy of the correlation factor used for the similarity transformation of the Coulombic Hamiltonian. Our systematic investigation of small molecular systems in increasingly large basis sets illustrates the magnitude of these effects.