CCSD approach

As in the recent QCCD study by Head-Gordon et al. (28, 128), we tested the ECCSD, LECCSD, and QECCSD methods, based on eqs (52)-(59), using the minimum basis set STO-3G (145) model of N2. In all correlated calculations, the lowest two core orbitals were kept frozen. As in the earlier section, our discussion of the results focuses on the bond breaking region, where the standard CCSD approach displays, using a phrase borrowed from ref 128, a colossal failure (see Table II and Figure 2). 

All of the levels of theory listed in Table 1.1 predict the C-H bond length with accuracy within 1 %. One piece of cheering information from Table 1.1 is that the DFT method predicts this bond length as accurately as the much more computationally expensive CCSD approach. The error in the ionization energy predicted by HF is substantial, but all three of the other methods give better predictions. The higher levels of theory (MP2 and CCSD) give considerably more accurate results for this quantity than DFT. 

Let us recall, finally, that ec CCSD approaches exploit the complementarity of the Cl and CC methods in their handling of the dynamic and nondynamic correlations. While we use the Cl as an external source of higher than pair clusters, Meissner et al. [10,72-74] exploit the CC method to correct the Cl results (thus designing the CC-based Davidson-type corrections). This aspect will also be addressed below. 

Let us, finally, reiterate that, similarly as the MR CISD method can serve as an external source for correcting CCSD approaches, we can conversely use CCSD to formulate Davidson-type corrections for MR CISD, both for the lowest-lying [72,74] and the higher-lying states [73]. 

Del Bene et al.22S have studied, from a theoretical viewpoint, the 4hJ(P, P) value in [12] intending to mimic the similar coupling in the cationic system [13], which was measured some years ago.229 To this end, they employed the EOM-CCSD approach implemented in the ACESII program.45 Del Bene... 

Correlation contributions to the Ne polarizabilities were estimated using the CCSD approach with the same basis sets as used above [81]. (We note in passing that these Ne CCSD hyperpolarizability results [81] are all somewhat too large, as is the CCSD(T) value. Details are given in an erratum that will be published in early 1992.) The results are given in Table 5.9. 

Perhaps the most severe test of the proposed scheme was encountered in our study of the radicaloid mode of benzene dissociation or, equivalently, a recombination of two allylic radicals [67]. Since the separated limit involves open shell subsystems, standatrd CCSD approaches an incorrect channel. However, when VB corrected CCSD is used, we obtain practically the FCI result. 

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]. 

The CAS FCI or SOCI corrected CCSD results represent a definite improvement over the standard SR CCSD results. Nonetheless, for a given choice of the active-space, the performance of the ASTQ CCSD approaches deteriorates with the increasing size of the basis set. This is easily understood, since the external source does not include excitations out of the active-space, which are more important for larger basis sets. We should also mention that computationally much more demanding CAS SCF wave functions are about as effective as CAS FCI ones (cf., e.g., Tables II and III of [33]). 

The RMR CCSD approach certainly represents the optimal ecCCSD method relying on the Cl-type wave function. In particular, we must emphasize its conceptual simplicity and the fact that the method is unambiguously defined by the choice of the reference space, whose dimension can be very small indeed. Already a 2-dimensional 2R-RMR CCSD often provides excellent results. This is important, since the computational cost, in contrast to ASTQ approaches, is proportional to the number of references employed. On the other hand, in view of the fact that in computing a subset of r3<0) and T4<0) amplitudes we... 

CC method A is a standard CCSD approach, in which ota is set at 2, Na equals 6 (in this case, moments 97tX.X(OTA) also vanish for n = 1 and 2, since, by definition, the ground-state CCSD equations that are used to determine the corresponding 7j and 72 clusters are obtained by zeroing moments 9Jta "an(2) with n = 1,2 cf. Eq. (5)). 

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