Analysis of coupled cluster methods. II. What is the best way to account for triple excitations in coupled cluster theory?

Summary

Various coupled cluster (CC) and quadratic CI (QCI) methods are compared in terms of sixth, seventh, eighth, and infinite order Møller-Plesset (MPn, n=6, 7, 8, ∞) perturbation theory. By partitioning the MPn correlation energy into contributions resulting from combinations of single (S), double (D), triple (T), quadruple (Q), pentuple (P), hextuple (H), etc. excitations, it has been determined how many and which of these contributions are covered by CCSD, QCISD, CCSD(T), QCISD(T), CCSD(TQ), QCISD(TQ), and CCSDT. The analysis shows that QCISD is inferior to CCSD because of three reasons: a) With regard to the total number of energy contributions QCI rapidly falls behind CC for largen. b) Part of the contributions resulting from T, P, and higher odd excitations are delayed by one order of perturbation theory. c) Another part of the T, P, etc. contributions is missing altogether. The consequence of reason a) is that QCISD(T) covers less infinite order effects than CCSD does, and QCISD(TQ) less than CCSD(T), which means that the higher investment on the QCI side (QCISD(T) :O(M ⁷), CCSD :O(M ⁶), QCISD(TQ) :O(M ⁸), CCSD(T) :O(M ⁷),M: number of basis functions) does not compensate for its basic deficiencies. Another deficiency of QCISD(T) is that it does not include a sufficiently large number of TT coupling terms to prevent an exaggeration of T effects in those cases where T correlation effects are important. The best T method in terms of costs and efficiency should be CCSD(T).