LR-CCSD

Inclusion of single and double excitations EOM-CCSD and LR-CCSD... 

Using the complete form of the LR-CCSD (linear response CC formalism with single and double excitations) theory in combination with the ZPolC perturbation-tailored basis set Kowalski et have provided accurate estimates for the static and dynamic electronic polarizabilities of Ceo and have showed that the T2-dependent terms not included in CC2 play in important role in estimating these properties since they lead to a reduction of the polarizability by 12 13%. In the static limit, their estimate amounts to 82.23 in comparison with the 76.5 8 measured value. Note also that in the static limit the vibrational contribution is not necessary negligible. For a wavelength of 1064 nm, their estimate amounts to 83.62 A in comparison with the experimental value of 79 4 A. ... 

A break through for the application of the CC methods to excited states of large systems has recently been obtained by Christiansen et al. These authors introduced a simplified LR-CCSD method termed CC2, where the doubles excitation operator is taken from second-order perturbation theory (Qi)- The CC2 ground-state wave function can be written as... 

We developed expressions for EOM-CCSD-PCM in the SS formalism, and a series of approximations to reduce the considerable computational cost of this approach. Christiansen and Mikkelsen originally developed the LR formalism for the CCSD wave function in solution for a simple continuum solvation model. Later, they extended it to their flavour of explicit polarizable solvation model. Cammi has also presented several interesting developments in this research area, including a rederivation of the LR-CCSD expressions for PCM, and we presented the first implementation of the method. Other examples of CC methods combined with (non-)polarizable solvation models [e.g., fixed point charges) are also available in the literature. ... 

Table 1 The trace of the 355 nm Rosenfeld tensor of Eq. (24) (in atomic units) and the corresponding specific rotation [in deg dm (g/mL) ] for the (P) enantiomer of the hydrogen peroxide monomer and dimer in the CCSD/aug-cc-pVDZ hnear reponse (LR) and EOM-CCl approximations ...

The effects of including the triple excitations in coupled cluster linear response theory for evaluating the dynamic polarizabilities have been assessed for a set of closed-shell (Ne, HF, N2, CO) and open-shell (CN, CO, O2) systems, in view of exploring a new accuracy regime for molecular properties. The main conclusions include that i) for systems with little or no static correlation, CC3 is nearly identical to CCSDT, ii) CC3 and PS(T) [pole shifted technique where the CCSD-LR poles are corrected by adding a noniterative correction due to the triples] methods perform better than CCSD but their relative accuracy is not determined yet, iii) differences between CCSD and CC3 results as well as the errors with respect to CCSDT drop when the basis set is increased, and iv) ROHF-based CC-LR approaches should be favored over their UHF counterparts while the dilfer-ences between the ROHF and UHF appear as an appropriate criterion for determining whether higher-order UHF-based CC calculations can be used. 

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... 

IPDM. The cost of evaluating these charges is negligible compared to the leading terms in the CC equations, thus, the excited state part of the calculation in solution is equivalent to that of an isolated molecule. Due to this inherent computational efficiency, the LR formalism is used in the numerical results section, where the CCSD-PCM and DFT-PCM results are compared to experiment. 

Fig.l Flow chart for the solution of the EOM-CCSD-PCM equations in the SS formalism (left) and LR formalism (right). See text for details. 

DCB CCSD calculations [122] confirmed this result. The next excited state of Lr, 7s 6d3/2 ( 03/2), was found to he at 0.16 eV higher in energy in good agreement with the corrected value of 0.186 eV of the MCDF calculations [23]. 

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