Double-zeta plus polarization calculations

Although there is no strict relationship between the basis sets developed for, and used in, conventional ah initio calculations and those applicable in DFT, the basis sets employed in molecular DFT calculations are usually the same or highly similar to those. For most practical purposes, a standard valence double-zeta plus polarization basis set (e.g. the Pople basis set 6-31G(d,p) [29] and similar) provides sufficiently accurate geometries and energetics when employed in combination with one of the more accurate functionals (B3LYP, PBEO, PW91). A somewhat sweeping statement is that the accuracy usually lies mid-way between that of M P2 and that of the CCSD(T) or G2 conventional wave-function methods. 

Comparison of the experimental potential in a crystal and the theoretical potential for an isolated molecule is an excellent test for the transferability of theoretical isolated molecule densities to problems such as molecular packing and protein folding. A systematic study of this kind was done on L-alanine. Figure 8.3 shows a comparison between theory and experiment for a plane containing the C—N bond in this molecule. The comparison is with the 6-3IG basis set of double-zeta-plus-polarization quality. The agreement of experiment with more modest basis-set calculations was found to be inferior, which gives confidence in the experimental results. Both in the plane shown, and in the plane of the carboxyl... 

Table 2.2. A double-zeta plus polarization (DZP) basis forH2 calculations.

The factorial growth of the FCI treatment with basis set and number of electrons clearly limits its applicability. However, FCI calculations can be performed in moderate-sized (double-zeta plus polarization (DZP) or better) basis sets to calibrate approximate methods of including electron correlation. Thus there is considerable incentive to utilize these FCI methods and the capabilities of modern supercomputers to perform large-scale benchmark calculations. In this section we consider several examples of the insight obtained from FCI benchmark calculations. In the sections dealing with applications, we consider additional FCI benchmark calculations in conjunction with specific applications. 

The full Cl is impractical except as a reference because the number of determinants is asymptotically N . That means its application is possible only for small molecules and small basis sets. In praaice, calculations using 25 x 10 determinants for H O in a double zeta plus polarization (DZP) basis have been made and —10 determinants for CH3 in a triple zeta plus polarization (TZP) basis. ... 

Calculation has been performed mainly at the HF level with the double-zeta plus polarization quality basis sets and ECP for Pd, P, Si, and Sn. The energetics for R = Me has been recalculated at the MPn (n = 2-4) level at the HF geometries. The overall reactions for various RCCH (R = CN, H, CH3, and OCH3) and H3SiSnH3 with the model catalyst Pd(PH3)2 have been studied. It has been shown that H3Si-SnH3 easily, with a few kilocalories per mole barrier, adds oxidatively to the catalyst Pd(PH3)2 and the resultant complex lies only 5.9 kcal/mol lower than the reactants. The next step, acetylene coordination to the catalyst, causes with the dissociation of... 

This section demonstrates the generality of the rules for degenerate excitations numerically. The data are partially taken from the literature. Some data are newly obtained by the SAC-CI calculations [1, 2] with Huzinaga-Dunning double-zeta plus polarization (DZP) basis sets [6, 7] and/or by the time-dependent density... 

All the calculations have been performed within the Density Functional Hybrid Approximation, using the B3LYP parametrization [47]. A double zeta plus polarization Gaussian Type Orbital basis set has been adopted (6-31g(dp) [48]). 

More recent ab initio calculations on the formation of the adduct H3P BH3 applied basis sets of double zeta [95], double zeta plus polarization [96], and 4-31G quality (including counterpoise corrections) [97]. A slightly exothermal decomposition of the adduct is predicted at the CEPA level and agrees with the observed instability of the adduct in the gas phase at ambient temperature [96]. A recent ab intio MO calculation for the 1 1 adduct H3P - BF3 at the SCF and MP2 levels with basis sets of triple zeta quality gave a very large P-B distance. The adduct can thus be considered only a weak van der Waals complex which should not easily be observable in experiments. The calculated results therefore disagree [98] with the alleged experimental observation of this adduct in the gas phase [99]. 

In calculations on molecules within the matrix Hartree-Fock approximation, it is found to be important to add polarization functions to double-zeta basis sets. Such basis functions do not improve the energies of the isolated component atomic species but contribute significantly to calculated bond energies and to the accuracy of calculated equilibrium bond angles. Double-zeta plus polarization basis sets (usually designated DZP or DZ + P) became widespread in quantum chemistry in the 1970s. In such a basis set the hydrogen atom is described by two s functions and one set of p functions the... 

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