Abstract

The energy at sixth-order Mnller-Plesset (MP6) perturbation theory is given and dissected into 36 sizeconsistent energy contributions resulting from single (S), double ( D), triple (T ), quadruple (Q), pentuple (P), and hextuple (H) excitations. It is shown that MP6 is an O(N9) method, but less costly approximations to MP~ are possible. MP~ is used to analyze and compare coupled cluster (cc ) and quadratic configuration interaction (QCI) methods, namely CCD, CCSD, CCSD(T), CCSD(TQ), CCSDT, CCSDT(Q), CCSDT(QQ), QCISD, QCISD(T), and QCISD(TQ). For larger molecules and molecules with distinct T contributions, CCSD is significantly better than QCISD because CCSD covers a relatively large number of T contributions and in particular T,T coupling effects at sixth order. Differences between the two methods become larger at higher orders of perturbation theory. If T and Q excitations are included in QcisD and CCSD in a noniterative way-thus leading to QCISD(T ), CCSD(T ), QCISD(TQ), and ccsD(TQ)-then differences between QCI and cc decrease. Hence, if a given molecular problem depends on the inclusion Of T effects, improved calculational results will be obtained in the following order: MP4(SDTQ) < QCISD(T) < CCSD(T) < QCISD(TQ), CCSD(TQ) < CCSDT. None of the methods investigated is correct in sixth order. Only ifCCsDT is extended to CCSDT(QPH), which is also an O(N9) method, are all MF6 energy contributions then covered.

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