DZ model

Figure 1. The PECs for the DZ model of N2 as obtained with the PCI and CCSD methods.

The above outlined almost-linear (AL) versions of the RMR CCSD method have been applied to several model systems involving four and eight hydrogen atoms, as well as to a double zeta (DZ) model of the water molecule at both the equilibrium and stretched geometries. 

The results for this model considered at the minimum basis set (MBS) and double zeta (DZ) levels are given in Tables 2 and 3, respectively. In both cases, the (2,2) model space is used in multireference calculations. Again, both AL-RMR-CCSD-1 and AL-RMR-CCSD-2 represent a good approximation to the full RMR CCSD (both differing by only a few /lihartree at the MBS level and by 10-60 /ihartree at the DZ level). In turn, RMR CCSD represents a significant improvement over the standard CCSD (by more than 7 mhartree for a 0 for a DZ model). 

Comparison of correlation energies (all signs reversed) for the ground state of the H8 DZ model (in mhartree). The multireference methods use a (2,2) model space. The acronym AL-RMR-CCSD-i is abbreviated to AL-RMR-f. 

We now proceed to the other option of improving on standard CCSD via various energy corrections and focus on the very recently proposed schemes that are based on the asymmetric energy formula of CC theory (9,34), We first very briefly present the basic formalism and refer the reader to the original papers for detail (34) [see also Refs. (31-33)]. At the same time we also present yet another perturbative energy correction, this time for MR CISD. We then compare the performance of these corrections using the same DZ models of HF and N2 as in Refs. (9,34). 

We first consider the standard double-zeta (DZ) model of the HE molecule. Relying on the minimal 2-electron/2-active-orbital space, we employ both the 2R space spanned by IOq) = laaaP) and WE>i) = la (xa P), and the 4R space spanned by IOo>, lOi), = iaaa p), and lOa) = la ocap). In Table IV, we list the FCI energies for the five geometries (namely for R=Re=l.l33 bohr, 1.5/ , 2Rg, 2,5Rg, and 3Re), and the energy differences relative to the FCI as obtained with the CCSD, 2R-CISD, 2R-CISD+EN(2), CCSD-[2R], and with 4R-CISD, 4R-CISD+EN(2), and CCSD-[4R] methods. 

Table IV. The total FCI energies (in hartree) and the energy differences relative to FCI, E-E(FCT) (in mhartree), for the DZ model of the HF molecule, as obtained with various mediods (i die text for the definition of acron3m(is). All electrons were correlated. Rg = 1.733 bohr.

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