QCISD with a correction for triples. This method is at the core of the popular G2 theory. Usually gives similar results as CCSD(T), of which it is a truncation.
(Quadratic Configuration Interaction with all Single and Double excitations and perturbative inclusion of Triple excitations) post Hartree-Fock method. Similar results to QCISDT, used in G2. Scales as n^7.