Unitary coupled-cluster based self-consistent polarization propagator theory: A third-order formulation and pilot applications.

In this article, the development of a third-order self-consistent polarization propagator method based on unitary coupled-cluster (UCC) parametrization of the ground-state wavefunction and the excitation manifold comprising unitary-transformed excitation operators, hereafter referred to as UCC3, is reported. The UCC3 method is designed to provide excitation energies correct up to the third order for excited states dominated by single excitations. An expansion for the UCC transformed Hamiltonian involving Bernoulli numbers as expansion coefficients is adopted in the derivation of UCC3 working equations. Interestingly, UCC-based polarization propagator theory offers an alternative derivation for the strict version of the third-order algebraic diagrammatic construction [ADC(3)-s] method. The UCC3 results for the excitation energies of excited states in HO, HF, N, Ne, CH, BH, and C molecules are compared with benchmark full configuration interaction values as well as ADC(3) and equation-of-motion coupled-cluster singles and doubles results to demonstrate the accuracy of the UCC3 method. UCC-based self-consistent polarization propagator theory appears to be a promising framework for developing non-perturbative hermitian formulations for treating electronically excited states.