Polarized basis correlated calculations

The main difference between the G2 models is tlie way in which tlie electron correlation beyond MP2 is estimated. The G2 method itself performs a series of MP4 and QCISD(T) calculations, G2(MP2) only does a single QCISD(T) calculation with tlie 6-311G(d,p) basis, while G2(MP2, SVP) (SVP stands for Split Valence Polarization) reduces the basis set to only 6-31 G(d). An even more pruned version, G2(MP2,SV), uses the unpolarized 6-31 G basis for the QCISD(T) part, which increases the Mean Absolute Deviation (MAD) to 2.1 kcal/mol. That it is possible to achieve such good performance with tliis small a basis set for QCISD(T) partly reflects the importance of the large basis MP2 calculation and partly the absorption of errors in the empirical correction. 

Dunning has developed a series of correlation-consistent polarized valence n-zeta basis sets (denoted cc-pVnZ ) in which polarization functions are systematically added to all atoms with each increase in n. (Corresponding diffuse sets are also added for each n if the prefix aug- is included.) These sets are optimized for use in correlated calculations and are chosen to insure a smooth and rapid (exponential-like) convergence pattern with increasing n. For example, the keyword label aug-cc-pVDZ denotes a valence double-zeta set with polarization and diffuse functions on all atoms (approximately equivalent to the 6-311++G set), whereas aug-cc-pVQZ is the corresponding quadruple-zeta basis which includes (3d2flg,2pld) polarization sets. 

Neither of these basis set families is satisfactory for accurate calculations without the addition of polarization functions. Various ad hoc rules have been developed over the years for polarization exponents. Since SCF polarization is less sensitive to exponent choice than correlation, it is reasonable to let the latter determine the exponents. By fitting the results of correlated calculations on closed-shell hydrides, Ahlrichs and Taylor [47] arrived at the following formulas for d exponents (ay)... 

Optimization of the basis set for atoms inevitably introduces some bias towards the atomic description, although this effect is seldom noticeable in basis sets of the traditional types described in Sec. 4.2. Bias towards the atoms can appear, however, if very small ANO sets (or, presumably, cc sets) are used. An ANO set contracted to split-valence plus polarization, [3s 2p Id], is probably too contracted to provide a good description of molecular binding. In particular, the d NO may be quite different in shape from what is required to describe polarization and correlation in the molecule. At least two d orbitals should be included to properly allow for these effects. Hence ANO or cc basis sets smaller than, say, [4s 3p 2d] should probably not be used for molecular calculations. 

A DZP or split-valence plus polarization basis is a minimal basis for correlated calculations. 

If the aim of the calculation is to describe dynamical correlation effects, there is seldom any point to using a basis that is smaller than double zeta in the valence shell and lacks polarization functions. Such a basis recovers so little of the correlation energy, and such an unrepresentative fraction (because of the poor treatment of angular correlation), that the results can be hopelessly unreliable. In this sense we should regard a DZP basis (or equivalent) as a minimal, in the sense of minimum acceptable, basis set for correlated calculations. 

The splitting factor of the d-polarization functions for the 3df basis set extension is 3 rather than the factor of 4 used for first- and second-row atoms. The 3d core orbitals and Is virtual orbitals are frozen in the single-point correlation calculations. 

A number of fullerenes have been the subject of fully ab initio theoretical studies, and no attempt will be made here to review this work. However, for any but the smallest fullerenes these remain tremendously challenging computations due to the shear size of the molecules. Were it not for the extremely high icosahedral symmetry of buckminsterfullerene, most of the ab initio calculations which have been performed on it would still be impossibly time consuming even with modem computational resources. Even the largest of these, such as the TZP-MP2 (triple zeta plus polarization basis with electron correlation at the Moeller-Plesset 2nd order level) calculation on buckminsterfullerene of Haser, Almlof, and Scuseria [3], are still short of the basis set and correlation levels normally desired to be confident that the calculation is converged to chemical accuracy. As a result, semiempirical theoretical methods have played, and likely will continue to play, a major role in theoretical work on fullerenes. 

Sadlej, A.J., Medium-size polarized basis-sets for high-level-correlated calculations of molecular electric properties. 4. Third row atoms - Ge through Br. Theor. Chim. Acta (1991) 81 45-63. 

Calculations of a similar nature have demonstrated that replacement of both hydrogens of water, yielding dimethyl ether, also has only a minor effect upon the nature of the H-bond in the water dimer. With their polarized basis set, and with inclusion of corrections for BSSE, dispersion, and intramolecular correlation effects, these authors found the first methyl substitution raises the binding energy by 0.5 kcal/mol and the second by 0.6. The authors cautioned that an unpolarized basis set would fail to pick up these small effects, which they attribute to Coulomb and dispersion components of the interaction. 

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