Static polarizabilities for excited states within the spin-conserving and spin-flipping equation-of-motion coupled-cluster singles and doubles formalism: Theory, implementation, and benchmarks

Abstract

We present the theory and implementation for calculating static polarizabilities within the equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) framework for electronically excited states and its spin-flip variant. We evaluate the second derivatives of the EOM-CCSD Lagrangian with respect to electric-field perturbations. The relaxation of reference molecular orbitals is not included. In our approach, the wave function amplitudes satisfy the 2n + 1 rule and the amplitude-response Lagrange multipliers satisfy the 2n + 2 rule. The new implementation is validated against finite-field and CCSD response-theory calculations of the excited-state polarizabilities of pyrimidine and s-tetrazine. We use the new method to compute static polarizabilities of different types of electronic states (valence, charge-transfer, singlets, and triplets) in open- and closed-shell systems (uracil, p-nitroaniline, methylene, and p-benzyne). We also present an alternative approach for calculating excited-state static polarizabilities as expectation values by using the EOM-CCSD wave functions and energies in the polarizability expression for an exact state. We find that this computationally less demanding approach may show differences up to ∼30% relative to the excited-state polarizabilities computed using the analytic-derivative formalism.

Effect of the diradical character on static polarizabilities and two-photon absorption cross sections: A closer look with spin-flip equation-of-motion coupled-cluster singles and doubles method

“…We recently discussed the effects of correlation on static polarizabilities by comparing the EOM-EE-CCSD and EOM-SF-CCSD results for methylene and p-benzyne. 53 While the EOM-SF-CCSD results agreed well with the results from an earlier study employing a multireference coupled-cluster method, 54 we found that the poor description of the multiconfigurational states with EOM-EE-CCSD had a significant effect on not only the static polarizabilities of these states but also of the states that are well described by the EOM-EE-CCSD ansatz, but are dipole-coupled to these poorly described states.…”

“…In Ref. 53, we showed that for the EOM states, polarizabilities computed with these two formulations could differ as much as by 30%. Here, we only employ the analytic-derivative approach for calculating static polarizabilities.…”

“…Our analytic-derivative implementation 53 is based on Eq. (9) and is formulated using the EOM energy Lagrangian and its second derivatives with respect to the electric-field perturbations (orbital relaxation is omitted).…”

“…52 However, nonlinear properties such as static polarizabilities and 2PA cross sections have not been investigated with the EOM-SF-CCSD method prior to Ref. 53 and this work.…”

Implementation of analytic gradients for CCSD and EOM-CCSD using Cholesky decomposition of the electron-repulsion integrals and their derivatives: Theory and benchmarks

“…The theory for analytic gradients and higher derivatives can be conveniently derived using a Lagrangian formulation. 106 The EOM-CC Lagrangian is [43][44][45]105,107…”