The equation of motion coupled-cluster method. A systematic biorthogonal approach to molecular excitation energies, transition probabilities, and excited state properties

A comprehensive overview of the equation of motion coupled-cluster (EOM-CC) method and its application to molecular systems is presented. By exploiting the biorthogonal nature of the theory, it is shown that excited state properties and transition strengths can be evaluated via a generalized expectation value approach that incorporates both the bra and ket state wave functions. Reduced density matrices defined by this procedure are given by closed form expressions. For the root of the EOM-CC effective Hamiltonian that corresponds to the ground state, the resulting equations are equivalent to the usual expressions for normal single-reference CC density matrices. Thus, the method described in this paper provides a universal definition of coupled-cluster density matrices, providing a link between EOM-CC and traditional ground state CC theory. Excitation energy, oscillator strength, and property calculations are illustrated by means of several numerical examples, including comparisons with full configuration interaction calculations and a detailed study of the ten lowest electronically excited states of the cyclic isomer of C4.