Coupled Cluster Linear Response Functions

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... 

Static charge-density susceptibilities have been computed ab initio by Li et al (38). The frequency-dependent susceptibility x(r, r cd) can be calculated within density functional theory, using methods developed by Ando (39 Zang-will and Soven (40 Gross and Kohn (4I and van Gisbergen, Snijders, and Baerends (42). In ab initio work, x(r, r co) can be determined by use of time-dependent perturbation techniques, pseudo-state methods (43-49), quantum Monte Carlo calculations (50-52), or by explicit construction of the linear response function in coupled cluster theory (53). Then the imaginary-frequency susceptibility can be obtained by analytic continuation from the susceptibility at real frequencies, or by a direct replacement co ico, where possible (for example, in pseudo-state expressions). 

Also in response theory the summation over excited states is effectively replaced by solving a system of linear equations. Spin-orbit matrix elements are obtained from linear response functions, whereas quadratic response functions can most elegantly be utilized to compute spin-forbidden radiative transition probabilities. We refrain from going into details here, because an excellent review on this subject has been published by Agren et al.118 While these authors focus on response theory and its application in the framework of Cl and multiconfiguration self-consistent field (MCSCF) procedures, an analogous scheme using coupled-cluster electronic structure methods was presented lately by Christiansen et al.124... 

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. 

A version of Coupled Cluster theory for use in the calculation of linear response functions (LRCCSD) has been developed by Piecuch et a/.135 and applied to the case of ammonia where the dipole and parallel polarizablity has been calculated as a function of the symmetric stretch and inversion internal coordinates. Coriani et a/.136 have also used CCSD response theory to calculate the electric-field-gradient induced birefringence in H2, N2, C2H2 and CH4. 

Kongsted, J., Osted, A., Mikkelsen, K. V., Christiansen, 0. (2003). Linear Response Functions for Coupled Cluster/Molecular Mechanics Including Polarization Interactions,/ Chem. Phys., 118,1620-1633. 

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

The PCM response function theory has been developed for linear and non-linear response functions and at several QM levels, including the variational wavefimctions methods (SCF,MCSCF) and the Density Functional Theory [4-18] and more recently at the Coupled-Cluster level [19, 20]. 

Continuum solvation models (QM/CSM), viii COSMO method, viii Coupled eluster Bruckner double (BD), 10 Coupled cluster linear response equations, 30 Coupled cluster linear response functions, 24 Coupled cluster method (CC), 6, 8, 20, 30, 31 Coupled cluster quadratic response functions, 31... 

Comparison with the analogous expansion of an expectation value for exact states, Elq. (3.109), shows that the coupled cluster linear response function is given as... 

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. 

LINEAR RESPONSE THEORY IN CONNECTION TO DENSITY FUNCTIONAL THEORY/MOLECULAR DYNAMICS AND COUPLED CLUSTER/MOLECULAR DYNAMICS METHODS... 

Our present focus is on density functional theory and coupled cluster methods for describing molecular systems interacting with a structured environment, and we focus on the derivation of linear response properties and compare the expressions that we obtain for the two different electronic structure methods. Based on linear response... 

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