Comparison of CCSDT-n methods with coupled-cluster theory with single and double excitations and coupled-cluster theory with single, double, and triple excitations in terms of many-body perturbation theory - what is the most effective triple-excitation method?

CCSDT-n methods (n = 1, ..., 4) are analyzed in terms of many-body perturbation theory and compared with CCSD, CCSD(T), and CCSDT. Correlation terms, which are introduced at each CCSDT-n level are identified and discussed with regard to their importance for the total energy. CCSDT-la represents the strongest improvement of CCSD since it covers 75% of the T terms added at the CCSDT level. At CCSDT-2 and CCSDT-3, only partial energy terms are added where the positive ..TQ.. coupling terms at CCSDT-2 are more important than the slightly negative ..TTS terms at CCSDT-3. CCSDT-4 leads to new ..TT.. coupling effects, which lower the energy. Calculated CCSDT-n/correlation-consistent polarized-valence triple-zeta spectra reveal that the energy changes caused by CCSDT-2, CCSDT-3, CCSDT-4. and CCSDT largely cancel each other out; however, because of a dependence of these contributions on electron clustering the importance of these effects for the correct description of certain chemical reactions must be considered. It is shown that CCSDT-1 las well as all other CCSDT-n) calculations lead to atomization energies as accurate as G2 values, where this result reflects the importance of including at least some of the T effects.