CIM-CC calculations

Step 11. The PAOs x (r) defined by Eq. (43) are localized on essentially the same atomic centers as the original AOs Xpir) and, as such, can serve as a basis for constructing the unoccupied LMOs associated with the extended subsystem P, but we must perform a few additional operations on these PAOs to make them usable in the CIM-CC calculations, since they are linearly dependent and non-orthogonal. The corresponding overlap matrix S,... 

The examples included in this and the subsequent sections include the normal alkanes C H2 +2, with n = 12, 16, 20, 24, 28, and 32, and the (H20) clusters with n = 10, 12, 14, 16, and 20. All the CC calculations discussed in this chapter employ the RHF determinant as a reference and freeze the core orbitals correlating with the Is orbitals of the C and O atoms. In each case, we use the six Cartesian components of the d orbitals present in the AO basis sets used in our calculations. In this section, we focus on the CIM-CC calculations performed with the 6-3 lG(d) and 6-31G(d, p) basis sets [97, 98]. The CIM-CCSD calculations for (H20) clusters with the larger 6-3H-- -G(d, p) [97-99] and 6-31 H--1-G(d, p) [99, 100] basis sets, which contain diffuse functions and create an interesting as well as challenging situation for the CIM methodology, are discussed in the next section. 

Undoubtedly, the CIM-CCSD and CIM-CR-CC(2,3) results for the normal alkanes shown in Tables 1 and 2 are very promising, but we must keep in mind that the large fraction of the correlation energy recovered in the CIM-CC calculations may be sometimes misleading, since even a small fraction of the correlation energy, such as 0.1 %, can easily translate into differences between the CIM and the canonical CC energies on the order of a few kilocalories per mole when the molecular system... 

We have performed a number of CIM-CCSD calculations for other water clusters and other basis sets, besides the 6-31G(d, p) basis set discussed so far, with the intention of learning if we can handle more realistic basis sets with diffuse functions, such as 6-311G-I— -G(t/, p), in the CIM-CC calculations for large weakly bound molecular clusters. This has led to the discovery of challenges facing the CIM-CC theory and the development of a modified variant of CIM-CC, which has shown considerable promise in calculations with larger basis sets involving diffuse functions. This modified varianf of the CIM-CC theory is discussed in the next section. 

Before discussing the CIM-CC calculations for the (H20) clusters with basis sets containing diffuse functions, where the earlier, dual-environment CIM scheme encounters problems with accurately reproducing the relative energies of the canonical CC calculations, we examine the performance of the modified, singleenvironment CIM scheme introduced in Section 4.1 (cf., also, W. Li and P. Piecuch, unpublished manuscript) in the calculations for the ten lowest-energy stmctures of the (H20) clusters with n = 10, 12, 14, and 16, as described by the 6-31G(d) basis set. We chose the 6-31G(d) basis set, so that we could perform the canonical CCSD calculations for systems as big as (H20)i6. Due to the prohibitively large computer costs, we were unable to perform the canonical CR-CC(2,3) or CCSD(T) calculations for (H20) with n = 14 and 16 that could provide the relevant reference... 

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