Coupled-cluster linear response energy

A wide range of first-order properties of the electronic excited-states of molecules in solution can be computed in terms of the gradients of the excitation energies coK with respect to external or internal perturbations. In this section, we discuss the analytical theory for the gradient of the excitation energies (4.11) computed from the coupled-cluster linear response. 

Koch H, Jensen HJA, Jorgensen P, Helgaker T (1990) Excitation-energies from the coupled cluster singles and doubles linear response function (CCSDLR) - applications to be, CH+, CO, and H2O. J Chem Phys 93 3345... 

In two recent publications we have tried to characterize the excited state properties of 1 and 3 in order to facilitate their detection by LIF-spectroscopy. Our main tool in this effort has been equation of motion coupled cluster theory (EOM-CC). The EOM-CCSD method, which is equivalent to linear response CCSD, has been shown to provide an accurate description of both valence and excited states even in systems where electron correlation effects play an important role [39]. Computed transition energies for excitations that are of mainly single substitution character are generally accurate to within 0.1 eV. We have found the EOM-CCSD method to perform particularly well in combination with the doubly-augmented cc-pVDZ (d-aug-cc-pVDZ) basis set. This basis seems to provide equally balanced descriptions of ground and excited states,... 

Sekino H, Bartlett RJ (1984) A linear response, coupled-cluster theory for excitation energy. Int J Quantum Chem Symp 18 255—265. 

X h is an eigenstate of H with eigenvalue n o>. 4 il assumed to be of the " CC-form. In the presence of interaction, the eigenstate of the composite system will not have a definite number of photons, and the extent of correlation as a result of coupling will also be modified. These changes can be induced by the action of a second cluster operator of the exponential form exp(S). The operator S destroys/creates zero, one, two,..., photons and simultaneously induce various nh-mp excitations out of 3 . The nature of the electronic part of the cluster operator in S is dictated by the nature of the energy difference we are interested in. For IP/EA calculations, V in eq. (5.3.1) will destroy/create an electron from should involve nh-(n+l)p excitations. Similarly, for EE, V will conserve the number of electrons, and S should involve nh-np excitations. For computing the linear response, it suffices to retain only the terms linear in C/CT ... 

H. Sekino and R. J. Bartlett, Int. J. Quantum Chem. Symp., 18, 255 (1984). A Linear Response, Coupled-Cluster Theory for Excitation Energy. 

H. Koch, H. J. Aa. Jensen, P. Jorgensen, and T. Helgaker, /. Chem. Phys., 93, 3345 (1990). Excitation Energies from the Coupled Cluster Singles and Doubles Linear Response Function (CCSDLR). Applications to Be, CH, CO, and H2O. 

The CC (Coupled-Cluster) method is an attempt to find such an expansion of the wave function in terms of the Slater determinants, which would preserve size consistency. In this method the wave function for the electronic ground state is obtained as a result of the operation of the wave operator exp(f) on the Hartree-Fock function (this ensures size consistency). The wave operator exp(f) contains the cluster operator T, which is defined as the sum of the operators for the /-tuple excitations, 7) up to a certain maximum I = /max- Each fi operator is the sum of the operators each responsible for a particular l-tuple excitation multiplied by its amplitude t. The aim of the CC method is to find the t values, since they determine the wave function and energy. The method generates non-linear... 

Excitation Energies from the Coupled Cluster Singles and Doubles Linear Response Function (CCSDLR). Applications to Be, CH", CO, and H2O. 

The eigenvalues > / of Eqs. (4.8) and (4.9) are the excitation energies of the molecular solute within the linear response coupled-cluster (LR-CC) approximation. They can be then written in the following functional form... 

The left and right transition moments of Eqs. (4.15a, 4.15b) determine the solute-solvent interaction in the linear response excitation energies >/ (4.11). This it can be shown by a perturbative analysis of Eq.(4.11). Let us consider as zero-order solutions the eigenvalues and eigenvector and corresponding to excited-states in the presence of the fixed reaction field of the coupled-cluster ground state. At the first order in the solvent perturbation, we can write the excitation energies as... 

Lagrangian density, 51 Linear response coupled cluster excitation energies (PCM-LRCC), 42 Local-field, 33... 

A method closely related to the CCSD linear response function approach but derived differently is the equation-of-motion coupled cluster approach (EOM-CCSD) (Sekino and Bartlett, 1984 Geertsen et al, 1989 Stanton and Bartlett, 1993). The EOM-CCSD excitation energies are identical to the excitation energies obtained from the CCSD linear response function, but the transition moments and second-order properties, like frequency-dependent polarizabihties of spin-spin coupling constants, differ somewhat. 

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