Analytic evaluation of energy first derivatives for spin–orbit coupled-cluster singles and doubles augmented with noniterative triples method: General formulation and an implementation for first-order properties

Abstract

A formulation of analytic energy first derivatives for the coupled-cluster singles and doubles augmented with noniterative triples [CCSD(T)] method with spin–orbit coupling included at the orbital level and an implementation for evaluation of first-order properties are reported. The standard density-matrix formulation for analytic CC gradient theory adapted to complex algebra has been used. The orbital-relaxation contributions from frozen core, occupied, virtual, and frozen virtual orbitals to analytic spin-orbit CCSD(T) gradients are fully taken into account and treated efficiently, which is of importance to calculations of heavy elements. Benchmark calculations of first-order properties including dipole moments and electric-field gradients using the corresponding exact two-component property integrals are presented for heavy-element containing molecules to demonstrate the applicability and usefulness of the present analytic scheme.

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

“…While the implementation of AO‐based algorithms can be further improved by using density fitting or Cholesky decomposition for AO two‐electron integrals, a task with top priority is to develop analytic X2C‐CC and EOM‐CC energy derivatives. Along this direction, an analytic scheme for the evaluation of X2C‐CCSD(T) first‐order properties has recently been reported 288 . The implementation of geometrical gradients will be a next step aiming to enhance the applicability of the X2C‐CC methods.…”

“…Along this direction, an analytic scheme for the evaluation of X2C-CCSD(T) first-order properties has recently been reported. 288 The implementation of geometrical gradients will be a next step aiming to enhance the applicability of the X2C-CC methods. Another important task for further improving the efficiency of X2C-CC and EOM-CC calculations is to build an efficient computational framework using contracted basis sets for X2C calculations with spin-orbit coupling included in orbitals.…”

Calculations of Time-Reversal Symmetry Violation Sensitivity Parameters Based on Analytic Relativistic Coupled-Cluster Gradient Theory

“…The present scheme for the calculations of E eff uses the recent implementation of analytic first derivatives for X2C CCSD and CCSD(T) methods [59] and also the atomic-orbital based algorithms [69] to enhance the computational efficiency. The calculation of E eff using the X2C-CC analytic-gradient theory involves a simple contraction between the relaxed one-electron density matrix D X2C-CC and the corresponding property integrals…”

“…We refer the readers to Ref. [59] for the calculations of the relaxed one-electron density matrix D X2C-CC . We base the calculation of [V eff ] X2C on the analytic X2C gradient theory [57,58].…”

“…An analytic-gradient based scheme is not only by far more efficient than numerical differentiation of electronic energies, but is also convenient to use. In this Letter we report the development of an analytic-gradient based method for the calculations of E eff using the relativistic exact two-component (X2C) CC analytic-gradient theory, hereby combining the analytic X2C gradient theory [57,58] and the recent development [59] of analytic first derivatives [60][61][62][63] for CC singles doubles (CCSD) [64] and CCSD with a noniterative triples [CCSD(T)] [65] methods with spin-orbit coupling included at the orbital level. The development of the present analyticgradient based method aims to significantly improve the efficiency, robustness, and convenience for the calculations of E eff to enable rapid and reliable screening of candidate molecules for use in the eEDM measurements.…”