A spin-adapted linear response theory in a coupled-cluster framework for direct calculation of spin-allowed and spin-forbidden transition energies

TLDR: In this paper, a spin-adapted linear response theory in a coupled-cluster framework was proposed to calculate the spin-allowed and spin-forbidden transition energies from a single methodology.

Abstract: In this paper, we have spin-adapted our recently formulated linear response theory in a coupled-cluster framework. This allows us to calculate directly both the spin-allowed and the spin-forbidden transition energies from a single methodology. We have introduced rank-zero and rank-one spin operators to construct excitation operators for singlet-singlet and singlet-triplet transitions respectively and utilised the graphical methods of spin algebra to integrate the spin variables. It has been shown how a suitable parameterisation of the reduced Hugenholtz matrix elements of the excitation operator in terms of Goldstone matrix elements makes the resulting system of equations simple, compact and suitable for computer implementation. A pilot calculation has been performed to test the applicability of the theory.