Analysis of Coupled Cluster and Quadratic Configuration Interaction Theory in Terms of Sixth-Order Perturbation Theory

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 ( N 9 ) method, but less costly approximations to M P ~ are possible. M P ~ 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. Introduction Nowadays electron correlation methods are routinely applied for many chemical problems with generally available computer packages. Most work has been done in the framework of many-body perturbation theory ( MBPT ) using the MsllerPlesset ( MP) perturbation operator [ 11. MP perturbation theory offers a hierarchy of well defined methods that allow one to calculate correlation corrections in single, noniterative steps with increasing accuracy the higher the order of perturbation theory applied. Today computer programs are available to calculate second-order ( M P ~ ) [ 21, third-order (MP3) [ 31, fourth-order ( M P ~ ) [ 4,5 1, and fifth-order ( M P ~ ) [ 6,7] correlation corrections to the energy. At MP2 and MP3, double (D) excitations are included; at MP4 and MP5, single ( S) , D, triple ( T ) , and quadruple ( Q) excitations are included. MP methods yield large parts of dynamical correlation corrections; they are economical to use; and they are size-consistent [ 3,8] or, even more gen* Corresponding author. International Journal of Quantum Chemistry: Quantum Chemistry Symposium 2 5 , 4 3 7 0 (1991)