Split-valence gaussian basis sets

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. " ... 

The structures of the surfaces, the surface adsorption and the alkali-doped crystal and the atom diffusion path (cf. Section 4) were investigated by different quantum-chemical methods. We used foremost ab initio methodologies. The main computational tool utilized was the program CRYSTAL [54]. This program makes it possible to treat molecules and in particular crystalline solids and surfaces at an ab initio level of theory for surfaces and solids the periodic boundary conditions are applied in 2 or 3 dimensions [55]. The familiar Gaussian basis sets can be used for systems ranging from crystals to isolated molecules, which enables systematic comparative studies of chemical properties in different forms of matter. In our studies, split-valence basis sets were used [56]. 

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

It is clear from this table that there is no smooth improvement in the calculated electric dipole moments as the basis set is extended from STO-3G to 6-31G. The minimal set of 0 functions generally gives values that are lower than experimental. The split valence shell basis, on the other hand, somewhat overestimates electric dipole moments. In most cases, the addition of a set of single d-gaussian polarization functions to each heavy atom produces a lowering of the 4-31G values, but... 

The solution to this problem is to use more than one basis function of each type some of them compact and others diffuse, Linear combinations of basis Functions of the same type can then produce MOs with spatial extents between the limits set by the most compact and the most diffuse basis functions. Such basis sets arc known as double is the usual symbol for the exponent of the basis function, which determines its spatial extent) if all orbitals arc split into two components, or split ualence if only the valence orbitals arc split. A typical early split valence basis set was known as 6-31G 124], This nomenclature means that the core (non-valence) orbitals are represented by six Gaussian functions and the valence AOs by two sets of three (compact) and one (more diffuse) Gaussian functions. 

Equation (2) was also used to calculate quantum chemical approach. On the basis of previous results [19], calculated electrostatic potentials were computed from ab initio wave functions obtained in the framework of the HF/SCF method using a split-valence basis set (3-21G) and a split-valence basis set plus polarisation functions on atoms other than hydrogen (6-31G ). The GAUSSIAN 90 software package [20] was used. Since ab initio calculations of the molecular wave function for the whole... 

The Gaussian 80 program l, as implemented on an IBM 370/3033 mainframe computer at the Notre Dame Computing Center, was used for most of the calculations. Calculations were also conducted with the Gaussian 86 program22a implemented on a Digital VaxStation 3200 computer. Geometric optimizations were performed with the minimal STO-3G basis set 3, 24 he split-valence... 

---