Extrapolations to the complete-basis-set limit

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. 

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. 

Mayeux C, Burk P. Evaluation of alkali metal cation affinities and basicities using extrapolation to the complete basis set limit. J Phys Chem A. 2014 118 1906-17, and references therein. 

In the present discussion it has to be noted that the availability of a theoretically justified formula for the extrapolation to the complete basis set limit [70] allows us to improve even more the accuracy reachable by quantum chemistry in estimating this property. Another issue that should be taken into account in predicting molecular properties is the zero-point vibrational effect, as quantum chemical results are equilibrium values, whereas experimental data usually refer to the vibrational ground state. 

Values extrapolated to the complete basis set limit (CBS) plus core correlation corrections (CV). Zero-point vibrational corrections (ZPV) added to the CBS + CV values. 

With the possible exception of the new def2-style basis sets of Weigend and co-workers [34] for the lanthanide atoms as discussed above, there have not been any standard PP-based basis sets reported in the literature for the /-block elements that are amenable to reliable extrapolation to the complete basis set limit, e.g., correlation consistent basis sets. This is currently being mitigated by work in one of the authors groups whereby the cc-pVnZ-PP basis set family (n=D, T, Q, etc.), which have been previously developed for... 

A detailed description for the CCSD(T)/CBS approach is found elsewhere [26, 59-61]. Briefly, the single-point electronic energies are calculated by using the restricted/ unrestricted coupled-cluster R/UCCSD(T) formalism [62-64] and extrapolated to the complete basis set limit (CBS) based on the correlation-consistent aug-cc-pVnZ n = D, T, and Q) basis sets [65, 66]. The CCSD(T) energies are then extrapolated to the CBS limit energies using expression (1) [67] ... 

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