Coupled-Cluster Linear Response Equations

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... 

M. Nooijen, J.G. Snijders, Int. J. Quantum Chem. 48 (1993) 15. For ionization potentials, equation-of-motion coupled-cluster, coupled-cluster linear response theory,... 

Abstract The modified equation-of-motion coupled cluster approach of Sekino and Bartlett is extended to computations of the mixed electric-dipole/magnetic-dipole polarizability tensor associated with optical rotation in chiral systems. The approach - referred to here as a linearized equation-of-motion coupled cluster (EOM-CCl) method - is a compromise between the standard EOM method and its linear response counterpart, which avoids the evaluation of computationally expensive terms that are quadratic in the field-perturbed wave functions, but still yields properties that are size-extensive/intensive. Benchmark computations on five representative chiral molecules, including (P)-hydrogen peroxide, (5)-methyloxirane, (5 )-2-chloropropioniuile, (/ )-epichlorohydrin, and (75,45)-norbornenone, demonstrate typically small deviations between the EOM-CCl results and those from coupled cluster linear response theory, and no variation in the signs of the predicted rotations. In addition, the EOM-CCl approach is found to reduce the overall computing time for multi-wavelength-specific rotation computations by up to 34%. 

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. 

Koch and Jorgensen have determined coupled cluster linear and quadratic response functions. Recently, Sekino and Bartlett have introduced an equation of motion coupled cluster method (EOM-CC)" and give results for molecules NH3 and C4H6. 

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,... 

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... 

AN INTRODUCTION TO EQUATION-OF-MOTION AND LINEAR-RESPONSE COUPLED-CLUSTER METHODS FOR ELECTRONICALLY EXCITED STATES OF MOLECULES... 

Keywords Equation-of-Motion Coupled-Cluster Theory, Linear-Response Coupled-Cluster Theory,... 

Trimerized organic conductors are of special interest, because two electrons per three sites constitute the simplest situation, where both electronic transitions resulting in single- and double-site occupation take place [21]. As one considers larger n-mers, two complications arise. First, the number of equations that should be solved sharply increases. The second complication is the increase in the number of n-meric normal modes, which are coupled to an external electromagnetic field. Recently, Yartsev et al. [22] have proposed using the linear response theory for several variables to describe the optical properties of trimers with arbitrary equilibrium charge density distribution. This approach can be extended to any cluster—the size is limited only by computer facilities. 

Keywords Coupled cluster theory linear response theory equation-of-motion coupled cluster theory optical rotation chirality... 

In this section we will introduce some wavefunction-based methods to calculate photoabsorption spectra. The Hartree-Fock method itself is a wavefunction-based approach to solve the static Schrodinger equation. For excited states one has to account for time-dependent phenomena as in the density-based approaches. Therefore, we will start with a short review of time-dependent Hartree-Fock. Several more advanced methods are available as well, e.g. configuration interaction (Cl), multireference configuration interaction (MRCI), multireference Moller-Plesset (MRMP), or complete active space self-consistent field (CASSCF), to name only a few. Also flavours of the coupled-cluster approach (equations-of-motion CC and linear-response CQ are used to calculate excited states. However, all these methods are applicable only to fairly small molecules due to their high computational costs. These approaches are therefore discussed only in a more phenomenological way here, and many post-Hartree-Fock methods are explicitly not included. 

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. 

At the wavefunction level methods based on coupled cluster (CC) theory are among the most reliable ones. For ground-state energetics the CCSD(T) approach is the gold standard of chemistry, whereas for excited states one can use the equation-of-motion (EOM) CC (EOM-CC) method or CC linear response theory (CC-LRT) [4] approaches. Note that the CC-LRT is size-extensive for both energies and properties such as intensities, however for EOM-CC this is true only for energies (unless one uses the closely related similarity transformed (ST)EOM-CC method [18]). As the computational cost of fully iterative (e.g., CCSD, CCSDT, etc.) methods can quickly become prohibitive, perturbative methods [4]... 

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