Coupled cluster wave function time dependent

Turning now to the specific case of a coupled cluster wave function we write the time-dependent CC wave function as... 

The simplest polarization propagator corresponds to choosing an HF reference and including only the h2 operator, known as the Random Phase Approximation (RPA), which is identical to Time-Dependent Hartree-Fock (TDHF), with the corresponding density functional version called Time-Dependent Density Functional Theory (TDDFT). For the static case co= 0) the resulting equations are identical to those obtained from a coupled Hartree-Fock approach (Section 10.5). When used in conjunction with coupled cluster wave functions, the approach is usually called Equation Of Motion (EOM) methods. ... 

Applying the time-dependent perturbation is straigthforward and leads to LR-CC methods. The nonlinear systems of equations include the normal T and Ti (for CCSD) operators-amplitudes and additionally single and double excitation (time-dependent) response amplitudes (for details the reader is referred to Refs. 1, 64, 88, 89 and references cited therein). An alternative approach, that, although conceptually different yields exactly the same excitation energies, is the equation-of-motion coupled cluster (EOM-CC) method [90]. The EOM-CC equations also contain the CC wave function 4 cc) (Eq. [50]) and a second (state-dependent) excitation operator R including single, double,. .. excitations (usually R is truncated in the same manner as T). The EOM equations read as... 

Having determined the time dependence of the coupled cluster and A wave-functions to first order, i.e. having derived expressions for the Fourier components and of the first-order time-dependent amplitudes in Eqs. (11.78)... 

Frequency-dependent response functions can only be computed within approximate electronic structure models that allow definition of the time-dependent expectation value. Hence, frequency-dependent response functions are not defined for approximate methods that provide an energy but no wave function. Such methods include MoUer-Plesset (MP) perturbation theory, multiconfigurational second-order perturbation theory (CASPT2), and coupled cluster singles and doubles with non-iterative perturbative triples [CCSD(T)]. As we shall see later, it is possible to derive static response functions for such methods. 

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