Gaussian basis sets polarization functions

Basis sets for use in practical Hartree-Fock, density functional, Moller-Plesset and configuration interaction calculations make use of Gaussian-type functions. Gaussian functions are closely related to exponential functions, which are of the form of exact solutions to the one-electron hydrogen atom, and comprise a polynomial in the Cartesian coordinates (x, y, z) followed by an exponential in r. Several series of Gaussian basis sets now have received widespread use and are thoroughly documented. A summary of all electron basis sets available in Spartan is provided in Table 3-1. Except for STO-3G and 3 -21G, any of these basis sets can be supplemented with additional polarization functions and/or with diffuse functions. It should be noted that minimal (STO-3G) and split-valence (3-2IG) basis sets, which lack polarization functions, are unsuitable for use with correlated models, in particular density functional, configuration interaction and Moller-Plesset models. Discussion is provided in Section II. 

However, especially for core AOs, where an exponential function has a very sharp cusp at the nucleus, several Gaussian functions are required even to begin to represent an exponential function accurately. For example, a split-valence basis set, developed by John Pople s group and widely employed in current calculations, uses six Gaussian functions to represent the H core orbitals on first row atoms whereas, a set of only three Gaussians, plus one more independent Gaussian, is used to represent the valence 2s and 2p AOs. With 3d functions included, to serve as polarization functions for the valence orbitals on the heavy atoms, Pople denotes this Gaussian basis set as 6-31G(d) or, more commonly, 6-31G. " ... 

Accordingly, dipole moment and polarizability calculations are sensitive to both the quantum chemistry method and the basis set used. Accurate calculations typically require the use of D FTor Hartree-Fock methods with the inclusion of M P2 treatment of electron correlation [53, 54]. Furthermore, Gaussian basis sets should be augmented with diffuse polarization functions to provide an adequate description of the tail regions of density (the most easily polarized regions of the molecule). 

This is a split valence basis set with polarization functions (these terms were explained in connection with the 3-21 G( ) basis set, above). The valence shell of each atom is split into an inner part composed of three Gaussians and an outer part composed of one Gaussian (hence 31 ), while the core orbitals are each represented by one basis function, each composed of six Gaussians ( 6 ). The polarization functions ( ) are present on heavy atoms - those beyond helium. Thus H and He... 

An important issue of the application of electronic structure theory to polyatomic systems is the selection of the appropriate basis set. As usual in quantum chemistry, a compromise between precision and computational cost has to be achieved. It is generally accepted that in order to obtain qualitatively correct theoretical results for valence excited states of polyatomic systems, a Gaussian basis set of at least double-zeta quality with polarization functions on all atoms (or at least on the heavy atoms) is necessary. For a correct description of Rydberg-type excited states, the basis set has to be augmented with additional diffuse Gaussian functions. Such basis sets were used in the calculations discussed below. 

Examine now the determination of exponents for polarization functions. Obviously, the atomic ground state calculations that are so useful in the optimization of valence shell exponents cannot help us. There is a possibility of performing calculations for excited states of atoms. This approach is, however, not appropriate. The role of polarization functions is to polarize valence orbitals in bonds so that the excited atomic orbitals are not very suitable for this purpose. Chemically, more well-founded polarization functions are obtained by direct exponent optimization in molecules. Actually, this was done for a series of small molecules in both Slater and Gaussian basis sets. Among the published papers, we cite. Since expo-... 

G - ab initio HF calculation using split-valence contracted Gaussian basis set with polarization functions,... 

Significant experience exists with Gaussian basis sets and they are available in a number of formats [1,15]. Polarization and diffuse functions can normally be adopted from published basis sets. For all electron GAPW calculations also the core part of the basis can be used un-altered. The use of GTH PP requires adapted basis sets. A systematically improving sequence of basis sets for use with the GTH PP was optimized for all first- and second-row elements, using the procedure detailed below. 

Table II shows that Simons basis set (set I) reproduces the experimental values rather accurately for the and 2 ionization potentials, the errors being 0.14 and 0.22 eV, respectively. These results represent vast improvements over the Koopmans theorem values of 17.58 and 21.75 eV. However, the n state is grossly in error, being 1.11 eV different from experiment. (Simons, at first, mistakenly reported his value to be 1 eV lower than this, leading him to conclude, erroneously, that the EOM method gave accurate IPs for all three states with this basis set. ) Adding the polarization functions to Simons basis set (giving basis set II) lowers the calculation of the troublesome IP by 0.36 eV and leaves the other states relatively unaffected. The EOM results with Nesbet s basis (set III) are much better still all the IPs are within 0.34 eV of experiment. The calculations employing basis set IV indicate that the EOM Gaussian basis set calculations are of comparable accuracy to the double zeta Slater basis sets with polarization functions. ...

POLARIZATION FUNCTIONS, GAUSSIAN LOBES AND HIGHER-ORDER GAUSSIAN BASIS SETS... 

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