Equation-of-motion coupled-cluster EOM-CC

The vertical IPs of CO deserve special attention because carbon monoxide is a reference compound for the application of photoelectron spectroscopy (PES) to the study of adsorption of gases on metallic surfaces. Hence, the IP of free CO is well-known and has been very accurately measured [62]. A number of very efficient theoretical methods specially devoted to the calculation of ionization energies can be found in the literature. Most of these are related to the so-called random phase approximation (RPA) [63]. The most common formulations result in the equation-of-motion coupled-cluster (EOM-CC) equations [59] and the one-particle Green s function equations [64,65] or similar formalisms [65,66]. These are powerful ways of dealing with IP calculations because the ionization energies are directly obtained as roots of the equations, and the repolarization or relaxation of the MOs upon ionization is implicitly taken into account [59]. In the present work we remain close to the Cl procedures so that a separate calculation is required for each state of the cation and of the ground state of the neutral to obtain the IP values. 

Abstract This chapter presents a review of equation-of-motion coupled-cluster (EOM-CC) and... 

The results are summarized in Tables 20.3 and 20.4. The calculations with CAS-SCF and CAS-QDPT are far too large to be done. We, therefore, compare the results with available experimental results and some recent theoretical results, i.e. MR-Cl results by Hachey et al. [39], the second-order complete active space perturbation theory (CASPT2) calculations by Merchan and Roos [40], and the equation of motion coupled cluster (EOM-CC) calculations by Gwaltney and Bartlett [41]. 

As follows from the form of the QM/MM Hamiltonian (Eq. 5.8), any electronic structure method can be used for describing the QM and MM parts of the system. Applications discussed in the following session mainly deal with understanding photochemistry in the condensed phase, with a common choice of the excited state methods from the equation of motion coupled cluster (EOM-CC) family [61-64], time-dependent density functional theory (TD-DFT) [65-66], or configuration interaction (Cl) methods. The MM Hamiltonian is represented by either EFPl or EFP Hamiltonian from Eq. 5.1 or Eq. 5.7. //qm-mm coupling term in the QM/EFPl... 

The CC method is used to calculate the ground-state energy and wave function. What about the excited states This is a task for the equation-of-motion coupled cluster (EOM-CC) method, the primary goal being not the excited states themselves, but the excitation energies with respect to the ground state. 

The equation-of-motion coupled-cluster (EOM-CC) method is based on the CC wave function obtained for the ground state and is designed to provide the electronic excitation energies and the corresponding excited-state wave functions. 

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... 

Excited states may be studied using the general post-Hartree-Fock methods listed above, or some specialized techniques, such as configmation interaction with single substitutions (CIS) (Foresman et al. 1992), time-dependent density functional theory (TDDFT) (Dreuw and Head-Cordon 2005 Elliott et al. 2009), equations-of-motion coupled cluster (EOM-CC) (Kowalski and Piecuch 2004 Wloch et al. 2005). 

Excited states may be treated using the CIS, TDDFT, multi-configurational quasidegenerate perturbation theory (MCQDPT) (Nakano 1993a, b), and equation-of-motion coupled-cluster (EOM-CC) methodologies. 

Another category of approaches that avoids the symmetry breaking problem of the orbitals for the target state is based on using a related, well-behaved HF reference instead. Examples of such techniques include quasi-restricted Hartree-Fock coupled-cluster (QRHF CC) (11,19), symmetry adapted cluster configuration interaction (SAC-CI) (22,23), coupled-cluster linear response theory (CCLRT) (24-26) or equivalently equation-of-motion coupled-cluster (EOM-CC) (27-32), Fock space multi-reference coupled-cluster (FSMRCC) (33-37), and similarity transformed equation-of-motion coupled-cluster (STEOM-CC) (38-40). In the case of NO3 and N03, the restricted Hartree-Fock (RHF) orbitals of the closed-shell N03 anion system can be used as the reference. The anion orbitals are stable with respect to symmetry perturbations, and the system does not suffer from the artifactual symmetry breaking of the neutral and cation. 

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