Analysis of coupled cluster and quadratic configuration interaction theory in terms of sixth‐order perturbation theory

The energy at sixth‐order Møller‐Plesset ( MP 6) perturbation theory is given and dissected into 36 size‐consistent energy contributions resulting from single ( S ), double ( D ), triple ( T ), quadruple ( Q ), pentuple ( P ), and hextuple ( H ) excitations. It is shown that MP 6 is an O ( N 9 ) method, but less costly approximations to MP 6 are possible. MP 6 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: MP 4( SDTQ ) < QCISD ( T ) < CCSD ( T ) < QCISD ( TQ ), CCSD ( TQ ) < CCSDT . None of the methods investigated is correct in sixth order. Only if CCSDT is extended to CCSDT ( QPH ), which is also an O ( N 9 ) method, are all MP 6 energy contributions then covered.