Transition moments between excited electronic states from the Hermitian formulation of the coupled cluster quadratic response function

Abstract

We introduce a new method for the computation of the transition moments between the excited electronic states based on the expectation value formalism of the coupled cluster theory (XCC) [B. Jeziorski and R. Moszynski, Int. J. Quant. Chem. 48, 161 (1993)]. The working expressions of the new method solely employ the coupled cluster operator T and an auxiliary operator S that is expressed as a finite commutator expansion in terms of T and T † . In the approximation adopted in the present paper the cluster expansion is limited to single, double, and linear triple excitations.The computed dipole transition probabilities for the singlet-singlet and triplet-triplet transitions in alkali earth atoms agree well with the available theoretical and experimental data. In contrast to the existing coupled cluster response theory, the matrix elements obtained by using our approach satisfy the Hermitian symmetry even if the excitations in the cluster operator are truncated, but the operator S is exact. The Hermitian symmetry is slightly broken if the commutator series for the operator S are truncated. As a part of the numerical evidence for the new method, we report calculations of the transition moments between the excited triplet states which have not yet been reported in the literature within the coupled cluster theory. Slater-type basis sets constructed according to the correlation-consistency principle are used in our calculations.

Spin-orbit coupling matrix elements from the explicitly connected expressions of the response functions within the coupled-cluster theory

“…where X 0 = X − X and X = Ψ 0 |X|Ψ 0 . In our previous work [34] we employed the XCC formalism to express the quadratic response function in terms of the T and S operators. By using the first-order perturbed wave function Ψ (1)…”

“…The transition moment between the excited states, T X KN is obtained from the residue of the quadratic response function [34] by dividing the RHS of Eq. ( 9) by…”

“…This expression was previously used to compute numerous dipole and quadrupole transitions between electronic states [34]. In this work we employed T X KN to compute the spin-orbit transition moments.…”

“…Starting from the formula for the average value of X expressed through a finite series of commutators, the XCC method was extended to the computation of various electronic properties: electrostatic [28] and exchange [29] contributions to the interaction energies of closed-shell systems, the polarization propagator, [30] first-order molecular properties, [31] static and dynamic dipole polarizabilities, [32] and transition moments between excited states. [33,34] There is also a series of publications by Korona et al on the computation of symmetry-adapted perturbation theory (SAPT) contributions. [35][36][37][38] An extensive review of the XCC methodology was recently published.…”

Theoretical description of the ionization processes with a discrete basis set representation of the electronic continuum

“…Eq. ( 1), are obtained from rather straightforward generalizations of the linear-response CC theory [61][62][63] or the time-independent XCC theory [64][65][66].…”