October 6, 2016
In essence, this work discusses a simple scheme to compute the fine–structure splittings (FSS) of molecules using the pp-TDA. From the converged wave function of the (+2) cation of molecular systems, the neutral excitation energies may be recovered via the pp-TDA. If the cation was converged using a relativistic Hamiltonian, orbitals with total angular momentum > 0 break degeneracy in a systematic way. As such, the pp-TDA is able to capture double ionization potentials involving each of the spilt orbitals, giving rise to FSS (see the TOC graphic of the published manuscript for a pictorial description of this procedure).
The advantage of using the pp-TDA over the ph-RPA/TDA (TDHF/CIS) is that, for some cases, the ground and excited states may be recovered with minimal spin contamination. Case and point being molecular oxygen, of which the HF ground state has broken spin symmetry. These spin contamination effects can make analysis of excited state FSS very difficult as the energetic effects may be on the same order or larger than those of the FSS themselves. It so happens that, especially for molecules with triplet ground states, the +2 cation is a singlet. Thus we were able to accurately capture the FSS in molecular oxygen with the pp-TDA, a feat impractical using the ph-RPA/TDA.