QMMCC methods

The method of moments of coupled-cluster equations (MMCC) is extended to potential energy surfaces involving multiple bond breaking by developing the quasi-variational (QV) and quadratic (Q) variants of the MMCC theory. The QVMMCC and QMMCC methods are related to the extended CC (ECC) theory, in which products involving cluster operators and their deexcitation counterparts mimic the effects of higher-order clusters. The test calculations for N2 show that the QMMCC and ECC methods can provide spectacular improvements in the description of multiple bond breaking by the standard CC approaches. 

Because of the apparent relationship between the QVMMCC or QMMCC methods and ECC/XCC approaches, we also explore the usefulness of the ECC theory in studies of multiple bond breaking, using N2 as an example. Instead of the strictly bi-variational ECC method of Arponen and Bishop 114-123), we... 

Thus, we can expect further improvements in the description of multiple bond breaking by the QMMCC method. This statement parallels similar findings by Head-Gordon et al. (27, 28, 128, 129), who considered the quadratic variant of the ECC theory of Arponen and Bishop (114 -123), in which the energy is calculated by imposing the stationary conditions for the asymmetric, doubly connected, energy functional... 

Based on the nature of the triple bond in N2, which requires, at least in principle, some hextuply excited configurations in the Cl expansion of the ground-state wave function, one might expect that the lower-order QMMCC methods, such as QMMCC(2,5), should not work well at larger N-N separations. Interestingly enough, this is not the case. As demonstrated in Table I, the QMMCC(2,5) approach, which does not require the calculation of the hextuply excited (2) moments, provides the results of the... 

We will continue testing the QMMCC methods by performing the calculations for other systems and larger basis sets. 

The positive answer to this question is provided by the QMMCC approaches. In analogy to the CR-CCSD(T) and CR-CCSD(TQ) methods, the QMMCC methods are based on the idea of adding noniterative corrections to the CCSD energies. As in the CR-CCSD(T) and CR-CCSD(TQ) approaches, the QMMCC corrections are calculated using only the T and T2 clusters obtained in the CCSD calculations. The difference between the CR-CCSD(T) and CR-CCSD(TQ) approaches on the one hand and the QMMCC approximations on the other hand is in the presence of the additional high-order terms in the QMMCC energy expressions (see Section 2.2.2). 

All of the above examples clearly demonstrate that the CR-CC and QMMCC methods are capable of eliminating the pervasive failing of the standard CC methods at larger internuclear separations. Aside from the... 

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