MR L-CCSD

The next step in the development and implementation of the MR ccsd method is to include the quadratic terms and, in general, non-linear terms. Here, we should mention the orthogonally spin-adapted MR ccsD-1, mr ccsd-2 and MR ccsd-3 approximations developed by Paldus et al. [105] and tested for the H4 model system. The first two approximations were designed just for testing purposes in order to better assess the importance of various non-linear terms. All three approximations are extensive. They differ by the presence of quadratic and bi-linear terms in the direct component, as well as in the coupling terms in the equation for cluster amplitudes (4.87). To be more precise, in addition to absolute and linear terms, the MR ccsd- 1 method contains the quadratic term involved in the direct term the MR ccsd-2 method contains the quadratic term involved in both the direct component, as well as in the coupling terms, and, finally, the MR ccsd-3 method represents a fully quadratic MR ccsd approximation which considers all bi-linear terms. The main conclusions to be drawn from these studies are that the inclusion of quadratic terms eliminates the singular behaviour of the linear mr ccsd approximation, mr l-ccsd, (even at the mr ccsd- 1 level) and that the inclusion of bi-linear components usually further improves the results. 

Abstract The singlet-triplet splittings of the di-radicals methylene, trimethylene-methane, ortha-, meta- and para-benzynes, and cyclobutane-l,2,3,4-tetrone have become test systems for the applications of various multi-reference (MR) coupled-cluster methods. We report results close to the basis set limit computed with double ionization potential (DIP) and double electron attachment (DBA) equation-of-motion coupled-cluster methods. These diradicals share the characteristics of a 2-hole 2-particle MR problem and are commonly used to assess the performance of MR methods, and yet require more careful study unto themselves as benchmarks. Here, using our CCSD(T)/6-311G(2d,2p) optimized geometries, we report DIP/DEA-CC results and single-reference (SR) CCSD, CCSD(T), ACCSD(T) and CCSDT results for comparison. 

A collection of previously published S-T splitting using various forms of MR-CC methods are presented in Table 1. Our DEA-CCSD results along with CCSD, CCSD(T), ACCSD(T) and CCSDT results obtained at the CCSD(T)/ 6-311-1—l-G(2d,2p) geometry in various basis sets, are shown in Table 2. 

It is interesting to compare the MR-CISD+EN(2) results with the CCSD-[MR] ones for M= 2, 4, and 8. Qualitatively, they are very similar. In both cases the smallest 2R space is not large enough to eliminate the CCSD hump, even though CCSD-[2R] yields a better result than 2R-CISD+EN(2). With 4R and 8R spaces, the MR-CISD+EN(2) absolute errors are smaller for R g [Re,l,5Re than CCSD-[MR] ones, but for R > l.SRg, the 4R-CISD+EN(2) error increases much faster than the corresponding CCSD-[4R] error. Indeed, over the interval Rgmore than 2.5 mhartree over the entire range of intemuclear separations. 

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