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
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 (EOM-EE-CCSD), and its spin-flip variant (EOM-SF-CCSD). We evaluate the second derivatives of the EOM-CCSD Lagrangian with respect to electric-field perturbations. The relaxation of the reference molecular orbitals is not included. Our approach is based on the asymmetric (in terms of the interchange of the two perturbations) formulation of the second-order static properties by Stanton and Gauss; it satisfies the 2n+1 and 2n+2 rules for the wavefunction amplitudes and the Lagrange multipliers, respectively. The new implementation is validated against the finite-difference and CCSD response theory calculations for 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, 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 wavefunctions and energies in the polarizability expression for an exact state. We find that this computationally less demanding approach introduces large errors (as high as 30%) relative to the excited-state polarizabilities computed using the analytic-derivative formalism.