Complete basis limit

The CCSD(T) energy changes AE for reaction (7) are shown in Table 9.2. The energy changes were extrapolated to the complete basis limit using the relation of Halkieref fl/. [30] ... 

When all the Slater determinants that can be constructed from a set of Hartree-FockMOs are taken into account, the method is called full configuration interaction. It provides the best possible solutions of the non-relativistic, clamped nuclei TISE within the basis set used for the calculation. The exact solutions are thus obtained from a full configuration interaction calculation at the complete basis limit. However, the number of configurations that can be built from a set of MOs grows extremely fast with the size of the system (i.e the size of the molecule and/or of the basis set). 

This is especially troubling in view of the fact that SIE, which leads to overestimates of VDEs for doublet radical anions in the complete-basis limit (because the SIE preferentially stabilizes the anion, with its half-filled orbital), can be substantially cancelled by the incompleteness of the basis set. (Diffuse functions preferentially stabilize the anion, so their omission destabilizes the anion.) The weakly-bound (H20) 2 isomer in Figure 18(a) is a good example. In... 

In summary, our initial appUcation of the w-body decomposition procedure has proven quite promising. With further development, this approach should be able to provide near complete-basis limit binding energies for water clusters containing up to 50 monomers and enable Monte Carlo simulations to be rim for water clusters containing up to 20 monomers. 

There have been a few basis sets optimized for use with DFT calculations, but these give little if any increase in efficiency over using EIF optimized basis sets for these calculations. In general, DFT calculations do well with moderate-size HF basis sets and show a significant decrease in accuracy when a minimal basis set is used. Other than this, DFT calculations show only a slight improvement in results when large basis sets are used. This seems to be due to the approximate nature of the density functional limiting accuracy more than the lack of a complete basis set. 

The CBS models use the known asymptotic convergence of pair natural orbital expansions to extrapolate from calculations using a finite basis set to the estimated complete basis set limit. See Appendix A for more details on this technique. 

The extrapolation to the complete basis set energy limit is based upon the MoUer-Plesset expansion E= + E + E + E + E +. .. as described earlier in this appendix. Recall that E + E is the Hartree-Fock energy. We will denote E and all higher terms as E , resulting in this expression for E ... 

The filled and hollow circles indicate the contributions of each successive natural orbital. The filled circles correspond to complete shells. Only these points are useful for extrapolating to the complete basis set limit. 

First consider the dipole operator (O = r). The matrix elements on rhs of eq. 17 are thus just the dipole transition moments, and the commutator becomes C = -ip. As the exact solution (complete basis set limit) to the RPA is under consideration, we may use eq. 10 to obtain... 

Dickson and Becke, 1996, use a basis set free numerical approach for obtaining their LDA dipole moments, which defines the complete basis set limit. In all other investigations basis sets of at least polarized triple-zeta quality were employed. Some of these basis sets have been designed explicitly for electric field response properties, albeit in the wave function domain. In this category belong the POL basis sets designed by Sadlej and used by many authors as well as basis sets augmented by field-induced polarization (FTP) func-... 

C-H and N-H bond dissociation energies (BDEs) of various five- and six-membered ring aromatic compounds (including 1,2,5-oxadiazole) were calculated using composite ab initio CBS-Q, G3, and G3B3 methods. It was found that all these composite ab initio methods provided very similar BDEs, despite the fact that different geometries and different procedures in the extrapolation to complete incorporation of electron correlation and complete basis set limit were used. A good quantitive structure-activity relationship (QSAR) model for the C-H BDEs of aromatic compounds... 

The slow convergence of the correlation energy with the one-electron basis set expansion has provided the motivation for several attempts to extrapolate to the complete basis set limit [6-13], Such extrapolations require a well defined sequence of basis sets and a model for the convergence of the resulting sequence of approximations to the... 

Table 4-6 Convergence of the (Zmax + j)-3 extrapolated complete basis set second-order CBS2/cc-pVnZ correlation-consistent basis set MP2 correlation energies (Eh) to the MP2-R12 limit see Eq. (2.1), (2.2), and (6.2).

In contrast, a linear size-consistent (Zmax + )-3 extrapolation of just the MP2/cc-pVTZ and MP2/cc-pVQZ energies is accurate to 0.63 kcal/mol (Table 4.4). If we try to further reduce the basis sets to cc-pVDZ and cc-pVTZ, the error in the extrapolation increases to 6.0 kcal/mol. However, the new double extrapolation provides the complete basis set MP2 limit with an absolute accuracy of 0.86 kcal/mol without recourse to basis sets larger than cc-pVTZ [4s3p2dlf/3s2pld] (Table 4.6). 

The main feature of the CBS (complete basis set) methods (e.g. CBS-Q [15] and CBS-QB3 [20]) is extrapolation to the complete basis set limit at the UMP2 level. Additional calculations [UMP4 and UQ-CISD(T) or UCCSD(T)] are performed to estimate higher-order effects. A scaled ZPVE, together with a size-consistent empirical correction and a spin-contamination correction, are added to yield the total CBS energy of the molecule. 

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