Correlation consistent basis sets limit

There are two possible solutions to this problem. We may either modify our ansatz for the wavefunction, including terms that depend explicitly on the interelectronic coordinates [26-30], or we may take advantage of the smooth convergence of the correlation-consistent basis sets to extrapolate to the basis-set limit [6, 31-39], In our work, we have considered both approaches as we shall see, they are fully consistent with each other and with the available experimental data. With these techniques, the accurate calculation of AEs is achieved at a much lower cost than with the brute-force approach described in the present section. 

Table 4-4 Convergence of the (Zmax + 5) 3 extrapolated cc-pVnZ correlation-consistent basis set MP2 correlation energies (Eh) to the MP2-R12 limit see Eq. (6.2).

Table 7 Convergence of the scaled PNO extrapolated CBS/cc-pVnZ, correlation-consistent basis set higher-order [i.e. CCSD(T)-MP2] correlation energies (Eh) to the CCSD(T)-R12 limit.

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. 

For the vibrational frequencies and rotational constants, density functional theory calculations with the relatively modest 6-31IG basis set generally suffice. However, for accurate estimates of the lowest frequency modes it is occasionally necessary to include diffuse functions in the vibrational analyses and so it is perhaps better to employ the 6-311++G basis. Truhlar and coworkers have recently noted the related importance of diffuse functions in estimating relative conformational energies with density functional theory [47]. For density functional calculations there appears to be little rationale for employing the more expensive correlation-consistent basis sets, since the results are essentially converged with the 6-311-H-G basis set and since the limited accuracy of the density functional methods does not warrant extrapolation to the infinite basis set limit. 

CO Peterson and Dunning [92] have made an extensive analysis of the role of basis sets and correlation treatments in the calculation of the molecular properties of CO. By carefully controlling the errors in the calculations, it was possible to compute properties of this small molecule to an accuracy that rivals the most sophisticated experimental studies. They made use of the correlation consistent basis sets (cc). The dissociation energy with icCAS+SDQ was computed 258.5 kcal/mol with the best method, and the experimental value is 259.6 0.1 kcal/mol. The CCSD(T) yielded 258.6 kcal/mol in excellent agreement with experiment. CASSCF, MP4, and CCSD yield results with errors bigger than 4 kcal/mol. The CBS limit was obtained by exponential extrapolation of the cc-pVDZ through cc-pV6Z for all methods. 

Several points should be mentioned in this context. First, while we use QCISD(T) in our basic dehnition of G2 and G3 theories, analogous methods have been defined where the CCSD(T) method replaces QCISD(T). Both variations seem to yield very similar mean absolute deviations in most cases. However, in our most recent work on transition metal systems [78], it appears that CCSD(T) has a clear advantage over QCISD(T) and will thus become the preferred method. For the first- and second-row molecules, however, there is no clear preference. The key point to note is that the accuracy and predictive capability of these methods comes from the inherent accuracy of QCISD(T) or CCSD(T). Finally, this is one of the steps in the calculation and is likely to be rate-limiting if carried out with very large basis sets. Indeed, it is the bottleneck in CCSD(T) calculations with large correlation-consistent basis sets. In G2 theory, QCISD(T) calculations are carried out with a polarized valence triple-zeta basis set. This is a very modest basis set and this makes it possible to carry out G2 calculations on molecules of the size of naphthalene on small workstations. In our later work on G3 theory, we use even smaller 6-31G(d) calculations that makes these methods applicable for even larger molecules. 

There are two families of correlation consistent basis sets designed to recover core correlation effects, denoted cc-pCVnZ and cc-pwCVnZ [24,25]. Both add shells of functions to the standard cc-pVnZ sets in the usual correlation consistent prescription and both systematically lead to identical CBS limits. The number and type of added functions is dependent on the core definition. First-row atoms have a [He] core, so the DZ core correlation set adds a (Islp) set to the cc-pVDZ, while the TZ basis adds a (2s2pld) set, etc. In the case of the 2nd-row atoms, only 2s2p correlation is treated, i.e., the Is electrons are not correlated and the [Ne] core results in additional (Islpld), (2s2p2dlf), etc. added to the cc-pVDZ, cc-pVTZ, etc. sets to construct the core correlation basis sets. 

Del Bene JE (1993) Proton affinities of ammonia, water, and hydrogen fluoride and their anions a quest for the basis-set limit using the Dunning augmented correlation-consistent basis sets. J Phys Chem 97 107-110... 

The correlation-consistent basis sets have the advantage that as the basis-set size is expanded, the calculated values of a molecular property usually converge smoothly to a limiting value, making it easy to find this value by extrapolation. Because of this feature, these basis sets are the most widely used sets in high-level ab initio calculations. The disadvantage of these basis sets is that they are rather large. 

The correlation-consistent composite approach (ccCA) is based in part on the G3B method, but uses Dunning correlation-consistent basis sets instead of Pople basis sets, does extrapolations to the CBS limit, replaces the QCISD(T) calculation with a CCSD(T) calculation, includes a relativistic correction, and contains no empirical parameters [N. J. DeYonker et al., J. Chem. Phys., 125, 104111 (2006) Mol. Phys., 107,... 

The composite methods Wl, W2, W3, and W4 (where the W stands for the Weiz-mann Institute, where the methods were developed) use high-level coupled-cluster calculations to achieve extraordinary accuracy in thermochemical quantities [A. Karton et al., J. Chem. Phys., 125,144108 (2006) and references cited therein]. Wl has one empirically determined parameter, but W2, W3, and W4 have no empirical parameters. Wl and W2 use CCSD(T) and CCSD calculations with correlation-consistent basis sets, do exttapo-lations to the complete basis-set limit, and include relativistic corrections. W3 and W4 include CCSDT and CCSDTQ calculations, and W4 includes a CCSDTQ5 calculation with a small basis set. For various test sets of small molecules, the mean absolute deviation from experimental atomization energies or heats of formation is 0.6 kcal/mol for Wl, 0.5 kcal/mol for W2, 0.2 kcal/mol for W3, and 0.1 kcal/mol for W4. W4 also gives highly accurate bond distances, harmonic vibrational frequencies, vibrational anharmonic-ity constants, and dipole moments for small molecules [A. Karton and M. L. Marlin, J. Chem. Phys., 133, 144102 (2010) arxiv.org/abs/1008.4163]. These methods are limited to small molecules. 

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