Polarization consistent basis set

Jensen, F. Polarization consistent basis sets principles, J. Chem. Phys. 2001,115, 9113-9125. 

The polarization consistent basis sets again employ an energetic criterion for determining the importance of each type of basis function. The level of polarization beyond the isolated atom is indicated by a value after the acronym, i.e. a pc-0 basis set is... 

Table 5.4 Composition in terms of contracted and primitive basis functions for the polarization consistent basis sets...

We will look at the convergence as a function of basis set and amount of electron correlation (Figure 4.3). For independent-particle methods (FIF and DFT) we will use the polarization consistent basis sets (pc-n), while for correlated methods (MP2 and CCSD(T)) we will use the correlation consistent basis sets (cc-pVXZ, X = D,T, Q, 5, 6). Table 11.1 shows how the geometry changes as a function of basis set at the HF level of theory, where the quality of the basis sets is indicated by the maximum angular momentum function included in the basis set. 

T. Kupka, From correlation-consistent to polarization-consistent basis sets estimation ofNMR spin—spin coupling constant in the B3LYP Kohn—Sham basis sethmit, Chem. Phys. Lett. 461 (2008) 33. 

The perturbation operator in the calculation of electric dipole moments, electric dipole polarizabilities and hyperpolarizabilities, i.e. the electric dipole moment operator Eq. (4.30), contains the position vector r of the electrons, which implies that the tail of the wavefunction becomes important. However, this is not well described in GTOs as discussed before and it is therefore essential to include additional valence functions with very small exponents C - so-called diffuse basis functions. In the Pople-style basis sets this is done in the 6-31G-I- and 6-31G- -- - basis sets, where in the -h basis set one diffuse function is added only for second- and third-row atoms, while in the - -+ basis set one diffuse function is also added for hydrogen (Clark et al., 1983). In the series of correlation consistent and polarization consistent basis sets one set of diffuse functions of each type present in the basis set is added in the aug-cc-pVXZ (Kendall et at, 1992 Woon and Dunning Jr., 1993, 1994 Balabanov and Peterson, 2005) and aug-pc-n (Jensen, 2002c) version of these basis sets. In the series of correlation consistent basis sets it is also possible to add two or more sets of diffuse functions in the d-aug , t-aug and so forth versions. 

Jensen, F. (2003). Polarization consistent basis sets. IV. The basis set convergence of equilibrium geometries, harmonic vibrational frequencies, and intensities. J. Chem. Phys., 118, 2459-2463. 

To cut down on the resources needed for the large substrates, we made use of the hierarchical polarization consistent basis set from Jensen [5] PC-2 for the region of interest, i.e. the atoms directly involved in the reaction and up to the second nearest neighbours from these, also indicated with a yellow halo in Fig. 2 and PC-1 for the rest of the system. 

One advantage of Ax is its relatively low cost. The cc-pVTZ basis set may still be out of reach for many practical problems, however, and therefore, the basis set dependence of the diagnostic is of interest. Table 3 lists correlation coefficients and deviation statistics (from near-basis-set-limit values with Jensen s pc-3 polarization consistent basis set [49-55]) for the LANL2DZ, 6-3IG, and 6-3IIG basis sets. It is shown there that > 0.98 for basis sets of at least polarized double-zeta quality, while > 0.995 can be reached for triple-zeta double polarization or better basis sets. Only for small double-zeta basis sets like LANL2DZ or SDD could basis set dependence potentially become an issue. 

The polarization-consistent basis sets pc-x x = 0-4) have been designed along similar hnes as the correlation-consistent basis sets but with special emphasis on the extrapolation to the basis set hmit in connection with DFT calculations. The different convergence behavior (exponential versus inverse polynomial) suggests that high angular momentum functions are less important in HF and DFT procedures than in correlated methods. 

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