ANALYSIS OF COUPLED-CLUSTER METHODS .2. WHAT IS THE BEST WAY TO ACCOUNT FOR TRIPLE EXCITATIONS IN COUPLED-CLUSTER THEORY

Various coupled cluster (CC) and quadratic CI (QCI methods are compare d in terms of sixth, seventh, eighth, and infinite order Moller-Plesse t (MPn, n = 6, 7, 8, infinity) perturbation theory. By partitioning th e MPn correlation energy into contributions resulting from combination s of single (S), double (D), triple (T), quadruple (Q), pentuple (P), hextuple (H), etc. excitations, it has been determined how many and wh ich of these contributions are covered by CCSD, QCISD, CCSD(T), QCISD( T), CCSD(TQ), QCISD(TQ), and CCSDT. The analysis shows that QCISD is i nferior to CCSD because of three reasons: a) With regard to the total number of energy contributions QCI rapidly falls behind CC for large n . b) Part of the contributions resulting from T, P, and higher odd exc itations are delayed by one order of perturbation theory. c) Another p art of the T, P, etc. contributions is missing altogether. The consequ ence 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(M7), CCSD: O(M6), QCISD (TQ): O(M8), CCSD(T): O(M7), M: number of basis functions) does not co mpensate for its basic deficiencies. Another deficiency of QCISD(T) is that it does not include a sufficiently large number of TT coupling t erms to prevent an exaggeration of T effects in those cases where T co rrelation effects are important. The best T method in terms of costs a nd efficiency should be CCSD(T).