Extrapolations to the complete-basis-set

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. 

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... 

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. 

Hypoiodous acid and iodine nitrate have been investigated with coupled cluster theory and the results extrapolated to the complete basis set limit. Together with revised thermochemistry for several ancillary molecules, the enthalpy changes of working reactions yields new thermochemistry for HOI and IONO2. The latter data, employed in unimolecular rate theory, appear to be consistent with kinetic measurements on the lO -l- NO2 reaction to within the uncertainties of the kinetic analysis. 

RI-MP2/TZVPP, extrapolating to the complete basis set and including corrections fromCCSD(T). 

Extrapolated to the complete basis set limit and corrected for CCSD(T). 

Jurecka et al have published a database of accurate benchmark quality interaction energies of small model complexes, DNA base pairs, and amino acid pairs obtained from MP2 and CCSD(T) calculations together with estimates of the complete basis set limit. They examine interaction energies and geometries for more than 100 DNA base pairs, amino acid pairs and model complexes. Extrapolation to the complete basis set limit was carried out by these researchers using a two-point method in conjunction with correlation consistent basis sets. 

The CCSD(T)//MP4(SDQ)/aug-cc-pVTZ method, with the extrapolation to the complete basis set limit using the aug-cc-pVTZ and aug-cc-pVQZ basis sets, yielded a standard deviation of 0.58kcal/mol when compared to a select set of experimental values of gas-phase deprotonation reactions compiled in the NIST online database, a data set with uncertainty of values extremely useful in determining accurate pKa calculations and will be referenced throughout the review. 

Note should be made of the fact that the choice of the definition of the (-contributions may be relevant in computations of accurate MP2/CA energies. This is especially true if one would like to take advantage of the knowledge of the theoretical AECs in extrapolations to the complete-basis-set (CBS) limit. We have found that, in this case, using the AE (T ) definition leads to the most accurate results. Therefore, we have used this definition in all computations below. 

As mentioned in Section 15.4, the cc basis sets can be used to extrapolate to the complete-basis-set (CBS) limit for molecular properties. Energies in hartrees for SCF MO H2O optimized-geometry calculations with the cc-pVnZ basis sets for n = 2,3,4,5,6 are -76.02705, -76.05777, -76.06552, -76.06778, -76.06810, respectively. The following empirical formula has been found to work rather well for extrapolating cc-pVnZ SCF MO energies to the CBS limit ... 

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