On the importance of third- and fourth-order corrections in multi-reference Møller–Plesset theory

An implementation and applications of an approximate fourth-order multi-reference Møller–Plesset theory restricted to single and double excitations (MR-MP4(SD)) are presented. The results for small full CI benchmark systems indicate a substantial improvement compared to MR-MP2 and MR-MP3 treatments. For larger molecules we propose a configuration selection procedure to keep the size of the expansion spaces within the limits of personal computer capabilities. As typical applications we consider vertical excitation energies of unsaturated organic molecules (up to 66 correlated electrons) and reaction energies involving biradicals. It is found that the systematic under(over)estimation of relative energies of open- versus closed-shell states at MR-MP2(MR-MP3) levels is in most cases corrected at fourth-order.