A study of the ionisation and excitation energies of core electrons using a unitary group adapted state universal approach

The unitary group adapted state universal multi-reference coupled cluster (UGA-SUMRCC) theory, recently developed by us using a normal-ordered multi-exponential wave operator Ansatz with spin-free excitations in the cluster operators, has the twin advantages of generating a spin-adapted coupled-cluster (CC) function and having a terminating expression of the so-called direct term' at the quartic power of cluster amplitudes. Not having any valence spectators, it also has the potentiality to describe orbital- and correlation-relaxation effectively. We illustrate this aspect by applying our formalism to study ionised/excited state energies involving core electrons. The high degree of orbital relaxation attendant on removal of a core electron and the consequent correlation relaxation of the ionised state are demonstrated to be captured very effectively with the Hartree-Fock orbitals for the neutral ground state.Three different formalisms have been used: (1) the ionisation potential/excitation energies (IP/EE) are computed as difference between state energies of the concerned states; (2) a quasi-Fock extension of the UGA-SUMRCC theory, which computes IP/EE directly and (3) use of a special model space to describe both the ground and the excited states such that EE is obtained directly. The model spaces for EE are incomplete and we have indicated the necessary modifications needed to have extensive energies. The results obtained by all the three approaches are very similar but they usually outperform the current CC-based allied theories with roughly the same computational effort.