Analytic evaluation of first-order properties within the mean-field variant of spin-free exact two-component theory

Abstract

We present a scheme for the calculation of energies and analytic energy gradients within spin-free exact two-component (SFX2C) theory in its mean-field variant, which we refer to as SFX2C-mf. In the presented scheme, the Foldy-Wouthuysen transformation is carried out after the spin-free four-component Hartree-Fock treatment such that in electron-correlated calculations only the non-mean-field part of the two-electron interactions is handled in an untransformed manner. The formulation of analytic gradients requires some adjustments in comparison with the nonrelativistic case, i.e., the additional solution of the spin-free Dirac Coulomb coupled-perturbed Hartee-Fock equations together with a simplified treatment of orbital relaxation at the SFX2C-mf level. The improved accuracy of SFX2C-mf in comparison with SFX2C-1e is demonstrated in the calculation of energies, dipole moments, and electric-field gradients for the hydrogen halides HX, X = F-At. It is shown that the main contribution to the improvement stems from the elimination of the error at the Hartree-Fock (HF) level; however, the corresponding correlation contribution is also improved such that SFX2C-mf can be considered a suitable scheme for the treatment of heavy-element compounds for which the error of SFX2C-1e is rather substantial.

Coupled-cluster techniques for computational chemistry: The CFOUR program package

“…SFDC is available in the released version of CFOUR for calculations of energies and first-order electrical properties (RELATIVISTIC=SFREE). 55 The SFX2C-mf scheme recently implemented 284 in CFOUR per-This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.…”

Cholesky Decomposition-Based Implementation of Relativistic Two-Component Coupled-Cluster Methods for Medium-Sized Molecules

“…Specifically, the evaluation of orbitalrelaxation contributions to analytic X2CMMF derivatives requires including the response of the molecular mean-field spin−orbit integrals. An analytic evaluation of electrical properties for the spin-free version of X2CMMF-CC with a solution of coupled-perturbed HF equations to account for the response of mean-field integrals 58 and an unrelaxed version of analytic X2CMMF-CCSD first derivatives 38 have been reported so far.…”

Relativistic coupled‐cluster and equation‐of‐motion coupled‐cluster methods

“…CC calculations using the spin-free version of X2C theory in its mean-field variant (the SFX2C-mf scheme) can provide results essentially as accurate as the SFDC-CC ones. 157 Meanwhile, the SFX2C theory in its one-electron variant (the SFX2C-1e scheme) 124,158 together with its analytic derivative formulation [159][160][161][162][163] and recontracted basis sets [164][165][166][167] offer a promising framework for scalar-relativistic CC calculations (see Refs. 168-174 for recent example applications).…”

“…Recently, a simple and accurate exact two‐component (X2C) theory 121–125,156 has been established as the method of choice for obtaining “electrons‐only” two‐component Hamiltonians. CC calculations using the spin‐free version of X2C theory in its mean‐field variant (the SFX2C‐mf scheme) can provide results essentially as accurate as the SFDC‐CC ones 157 . Meanwhile, the SFX2C theory in its one‐electron variant (the SFX2C‐1e scheme) 124,158 together with its analytic derivative formulation 159–163 and recontracted basis sets 164–167 offer a promising framework for scalar‐relativistic CC calculations (see Refs.…”