Sensitivity of Coupled Cluster Electronic Properties on the Reference Determinant: Can Kohn-Sham Orbitals Be More Beneficial than Hartree-Fock Orbitals?

TL;DR

This study compares Hartree-Fock and Kohn-Sham reference orbitals in coupled cluster calculations, finding that Kohn-Sham references generally lead to less accurate results than Hartree-Fock, except at high levels of coupled cluster theory.

Contribution

It provides a systematic comparison of HF-CC and KS-CC methods against FCI, revealing that KS references typically worsen accuracy in low-level coupled cluster calculations.

Findings

Kohn-Sham referenced CC methods are less accurate than HF-CC for electronic properties.

Errors increase with common approximations like frozen core and density fitting in KS-CC.

At high CC levels, the choice of reference has negligible impact on results.

Abstract

Coupled cluster calculations are traditionally performed over Hartree-Fock reference orbitals (HF-CC methodology). However, it has been repeatedly argued in the literature that the use of a Kohn-Sham reference (KS-CC methodology) might result in improved performance relative to HF-CC at the same computational cost. In the present theoretical study, we re-examine the relation of HF-CC and KS-CC methods by comparing the results of widely applied truncated CC calculations (CCSD, CCSD(T), CCSDT) to the limit of full configuration interaction (FCI), which in contrast to wave-function diagnostics with vague physical meaning or experimental data with considerable uncertainty serves as an undebatable reference point of accuracy. We find that apart from incidental exceptions, the Kohn-Sham referenced CC methods show systematic deterioration compared to HF-CC, that is, the KS-CC molecular properties (electronic energy and density) are always farther from the FCI limit than those obtained from HF-CC at the same coupled cluster level. Furthermore, the introduction of common approximations (frozen core, density fitting) to the CC calculation results in significantly higher errors in the case of KS reference. We conclude that the use of KS reference orbitals is not expected to increase the reliability of low-level CC energetics. Nevertheless, molecular errors from the components of the studied chemical reaction might fortunately cancel out resulting in illusory improvement compared to HF-CC. It is also notable that the choice of reference orbitals has negligible influence on the results at sufficiently high CC levels which can be estimated by test calculations or by the magnitude of double amplitudes. Therefore, the application of KS-CC is not unreasonable as it might bypass the difficulties of HF convergence.