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(2.1). This CBS extrapolation reduces the errors in the cc-pVQZ and ccpV5Z higher-order correlation energy by an order of magnitude (Table 4.7), but seriously over-corrects the cc-pVDZ and cc-pVTZ higher-order energies [50]. A simple scaling to reduce the CBS correction to the ccpVDZ and cc-pVTZ energies reduces the RMS errors below 1 kcal/mol for both (Table 4.7). This single adjustable CBS higher-order parameter might be compared to the use of a single adjustable parameter in the W1 theory [55].

7.4.Total Energies

Having established that size-consistent extrapolations of energies obtained with the cc-pVDZ and cc-pVTZ basis sets are capable of producing sub-kcal/mol absolute accuracy for SCF energies (Table 4.5),

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MP2 correlation energies (Table 4.6), and the higher-order contributions to the correlation energy (Table 4.7), we can now combine these components to obtain total electronic energies. There are many plausible combinations of basis sets and extrapolation procedures that must ultimately be explored. Efficient methods should use smaller basis sets for the CCSD(T) component than for the SCF and MP2 ones. The use of intermediate basis sets for the MP4(SDQ) component should also be explored, since we found this effective for the CBS-QB3 model (Table 4.2).

As a first try, we have elected to follow our treatment of the SCF and second-order correlation energies described above, and employ Eq. (6.2) to provide a linear extrapolation of the cc-pVDZ and cc-pVTZ total CBS-CCSD(T) energies obtained with Eq. (2.2), including the interference correction. These total energies reproduce the CCSD(T) limits estimated by Martin [55] via an extrapolation of the CCSD(T)/cc-pVDZ, TZ, QZ, 5Z, and 6Z basis sets to within 0.96 kcal/mol RMS error. The agreement with Martin’s energies for a small set of chemical reactions is even better (Table 4.8). The use of the ccpVnZ basis sets for double extrapolations is indeed promising.