Time-dependent coupled cluster approach: Excitation energy calculation using an orthogonally spin-adapted formalism

In the time-dependent coupled cluster approach the excitation energies can be obtained as eigenvalues of a generally non-Hermitian matrix characterizing the homogeneous part of a linear response equation. This matrix consists of the Hermitian configuration interaction part as well as of a non-Hermitian part which describes the ‘‘renormalization’’ due to ground state correlations. The relationship between a singular behavior of the ground state coupled cluster equations and the existence of vanishingly small excitation energies in the linear response formalism is pointed out. The explicit form of the required matrix elements in the orthogonally spin-adapted version of the theory is given for configuration spaces restricted to single and double excitations. A numerical test of the formalism for π-electron models of trans-butadiene and benzene is carried out and the relationship of the time-dependent coupled cluster approach with other many body approaches to excitation energies calculation is discussed.