Second-order variational coupled-cluster linear-response method: A Hermitian time-dependent theory

The formalism is presented for the linear response of a time-dependent (TD) variational coupled cluster (VCC), truncated according to Moller-Plesset perturbation theory, i.e., a TD-VCC[n] linear response, where n denotes the order of the corresponding quasienergy with respect to the fluctuation potential. The resulting eigenvalue problem determining the excitation energies is Hermitian and of the simple Tamm-Dancoff form. The VCC[1] excitation energies are equivalent to those of the configuration-interaction singles (CIS) model, while the Casida equation for the TD-Hartree-Fock approach is an approximation to it. The TD-VCC[2] response, the lowest-order method including electron correlation, is discussed in detail and the relations to other second-order methods, such as the CC2 linear response and the algebraic diagrammatic construction at second order [ADC(2)] are explored.