ACPQ method

It can be shown [95] that in such a case the T4 contribution cancels the exclusion principle violating (EPV) quadratic terms [59]. This realization led us to the formulation of the so-called ACPQ method (CCSD with an approximate account for quadruples) [95], as well as to CCDQ and CCSDQ [86], the latter also accounting for singles. Up to a numerical factor of 9 for one term involving triplet-coupled pp-hh t2 amplitudes [95], this approach is identical with an earlier introduced CCSD-D(4,5) approach [59] and an independently developed ACCD method of Dykstra et al. [96,97]. This method arises from CCSD by simply discarding the computationally most demanding (i.e., nonfactorizable) terms (see Refs. [59,95-97] for details). 

Several possible choices of an external source have been tested so far. The basic requirement is that such a source must provide a reasonable approximation of the most important three- and four-body clusters that are missing in the SR CCSD approach. At the very least, we require it to describe the essential nondynamic correlation effects. The practical aspects require that it be easily accessible. The first attempts in this direction exploited the unrestricted Har-tree Fock (UHF) wave function [of different orbitals for different spins (DODS) type]. Its implicit exploitation lead to the so-called ACPQ (approximate coupled pairs with quadruples) method [26, 27]. Recently, its explicit version was also developed and implemented [31]. Although in many cases this source enables one to reach the correct dissociation channel, its main shortcoming is the fact that for the CS systems it can only provide T4 clusters, since the 7) contribution vanishes due to the spin symmetry of the DODS wave function. Nonetheless, the ACPQ method enabled an effective handling of extended linear systems (at the semi-empirical level), which are very demanding, since the standard CCSD method completely breaks down in this case [27]. 

T3 and T4 cluster components from some independent, yet easily accessible, wave function, which at least qualitatively describes the dissociation channel at hand. The first attempts in this direction relied on the UHF wave function (of the DODS type), leading to the so-called ACPQ method (approximate coupled pair method with quadruples) (9), and its recent explicit version referred to as the CC(S)DQ method (14). Unfortunately, for closed shell systems, the DODS-type wave function cannot provide any information about the T3 clusters. 

Two sets of results are presented in Table 4, employing two different model spaces for the RMR CCSD One involves two electrons in two active orbitals, and the other one four electrons in four active orbitals. In each case we employ a DZP basis set and label these models as S4DZP (2,2) and (4,4), respectively. We note a complete breakdown of L-CCSD and a rather poor performance of CCSD [in fact, it is interesting to point out that the two-reference state universal CCSD also breaks down in this case (32), although good results can be obtained with the 2-reference version of the ACPQ method (33)]. 

Only much later were we able to account for some of these difficulties [109-112] by developing methods that, under certain conditions, account for the T4 clusters. In cases when the projected UHF method provides the exact pair clusters, it can be shown [109] that the T4 contribution cancels the contribution from the non-linear terms representing the important exclusion-principle-violating (EPV) diagrams. Except for a numerical factor associated with the triplet-coupled pp-hh t2-amplitudes, this method—referred to as ACPQ or CCDQ —is identical to the ACCD approach that was developed independently by Dykstra s group [113-116]... 

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