Calculation of size-intensive transition moments from the coupled cluster singles and doubles linear response function

Abstract

Coupled cluster singles and doubles linear response (CCLR) calculations have been carried out for excitation energies and dipole transition strengths for the lowest excitations in LiH, CH+, and C4 and the results compared with the results from a CI-like approach to equation of motion coupled cluster (EOMCC) . The transition strengths are similar in the two approaches for single molecule calculations on small systems. However, the CCLR approach gives size-intensive dipole transition strengths, while the EOMCC formalism does not. Thus, EOMCC calculations can give unphysically dipole transition strengths, e.g., in EOMCC calculations on a sequence of noninteracting LiH systems we obtained a negative dipole strength for the lowest totally symmetric dipole allowed transition for 19 or more noninteracting LiH systems. The CCLR approach is shown to be a very attractive "black box" approach for the calculation of transition moments.

Assessment of low-scaling approximations to the equation of motion coupled-cluster singles and doubles equations

“…The mathematical difference between LR and EOM formalisms arises when they are used to compute excitation properties, such as transition dipole and oscillator strengths. Jørgensen and coworkers have shown that the transition moment in LR-CC is size-intensive whereas EOM formalism is not, 13 although the difference in intensity between LR and EOM is very small for most computationally tractable systems. 27 In this work, we focus only on analyzing the performance of low-scaling alternatives to EOM-CCSD and LR-CCSD on excitation energies where these two formalisms are equivalent.…”

“…15 Despite their formal differences, LR-CC and EOM-CC when truncated at the same level of cluster operator will give the same value for excitation energies, although they differ with respect to transition properties. 13 In particular, the EOM-CC formalism 16,17 has led to extremely accurate and robust descriptions of excited states, yet may be prohibitively costly. The equation of motion coupled cluster singles and doubles (EOM-CCSD) 14,18 gives accurate qualitative and quantitative energies for most molecular systems, yet scales as O(N 6 ), making its application to large molecules difficult.…”

“…The first application of coupled cluster theory to electronic excited states was based off of the response formalism, and is known as linear response coupled cluster a) Email: xsli@uw.edu (LR-CC). [9][10][11][12][13] This was followed by the equation of motion coupled cluster formalism (EOM-CC), 14 as well as symmetry adapted cluster configuration interaction (SAC-CI). 15 Despite their formal differences, LR-CC and EOM-CC when truncated at the same level of cluster operator will give the same value for excitation energies, although they differ with respect to transition properties.…”

The integral-direct coupled cluster singles and doubles model

“…The analytical calculation of molecular properties must be implemented using integral-direct techniques, as the CCSD approach has proven to be successful in calculating several molecular properties in the framework of the response function formalism. 11 Particularly excitation energies 12 and transition matrix elements 13 have been computed, as well as frequency-dependent polarizabilities 14 and magnetic shielding tensors. 15 We have already implemented the calculation of the coupled cluster linear response ͑CCLR͒ excitation energies 16 directly from the AO integral distributions.…”

Transition moments between excited electronic states from the Hermitian formulation of the coupled cluster quadratic response function

“…There exists two coupled cluster approaches for the computation of the transition moments between the ground and excited states, the linear response coupled cluster theory (LRCC) of Koch et al 16,17,19,20 and the coupled cluster expectation value formulation of the linear response function (XCC) of Tucholska et al 21 As already stated above, for the transition moments between the excited states, the only available approach is based on the quadratic response coupled cluster (QRCC) theory of Koch et al 16,17,19,20 In the present work we generalize the approach of Refs. 22 and 21 to the calculation of transition properties between the excited states.…”