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

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 [B. Jeziorski and R. Moszynski, Int. J. Quantum 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.