Basis sets Double-zeta STOs

The starting point to obtain a PP and basis set for sulphur was an accurate double-zeta STO atomic calculation4. A 24 GTO and 16 GTO expansion for core s and p orbitals, respectively, was used. For the valence functions, the STO combination resulting from the atomic calculation was contracted and re-expanded to 3G. The radial PP representation was then calculated and fitted to six gaussians, serving both for s and p valence electrons, although in principle the two expansions should be different. Table 3 gives the numerical details of all these functions. 

In the early calculations of IR spectra of molecules, small basis sets (e.g., STO-3G, 3-21G, or 4-31G) were used because of limitations of computational power. At present typically a basis set consists of split valence functions (double zeta) with polarization functions placed on the heavy atoms (i.e., non-hydrogens) of the molecule (the so-called DZ+P or 6-31 G basis set). Such basis sets have been... 

In order to have a better basis set, we can replace each STO of a minimal basis set by two STOs with different orbital exponent f (zeta). This is known as a double zeta basis set. In this basis, there is a linear combination of a contracted function (with a larger zeta) and a diffuse function (with a smaller zeta) and the coefficients of these combinations are optimized by the SCF procedure. Using H2O as an example, a double zeta set has two Is STOs on each H, two Is STOs, two 2s STOs, two 2px, two 2pv and two 2pz STOs on oxygen, making a total of 14 basis functions. 

Full ab initio optimizations of molecular geometries of enamines (and of any other kind of molecules) depend strongly on the kind of applied basis sets application of STO-3G 2 3, 3-21G 3-2lG 4-3lG 6-3lG 6-31G " and 6-31G basis sets leads to optimizations for the coplanar framework of all atoms of vinylamine, but it was not stated in these references whether coplanarity was assumed by input constraint or not. Contrary to that, the use of a double-zeta basis set with heavy atom polarization functions as well as 6-31 - -G ° based optimization yielded a non-planar amino group for 115. 

Because of the complexity of the PHF function, only very small electronic systems were initially considered. As first example, the electronic energy of some four electron atomic systems was calculated using the Brillouin procedure [8]. For this purpose, a short double zeta STO basis set. Is, Is , 2s and 2s , with optimized exponents was used. The energy values obtained are given in Table 1. In the same table, the RHF energy values calculated with the same basis are gathered for comparison. It is seen that the PHF model introduces some electronic correlation in the wave-function. Because of the nature of the basis set formed by only s-type orbitals, only radial correlation is included which account for about 30% of the electronic correlation energy. 

A double-zeta (DZ) basis set is obtained by replacing each STO of a minimal basis set by two STOs that differ in their orbital exponents ((zeta). (Recall that a single STO is not an accurate representation of an AO use of two STOs gives substantial improvement.) For example, for QHa a double-zeta set consists of two Is STOs on each H, two Is STOs, two 2s STOs, two 2p two 2py, and two 2p STOs on each carbon, for a total of 24 basis functions this is a (4s /2s) basis set. (Recall that we did a double-zeta SCF calculation on He in Section 13.16.) Since each basis function Xr in < i = 2, CriXr has its own independently determined variational coefficient c , the number of variational parameters in a double-zeta-basis-set wave function is twice that in a minimal-basis-set wave function. A triple-zeta (TZ) basis set replaces each STO of a minimal basis set by three STOs that differ in their orbital exponents. 

Double zeta valence or triple zeta valence calculations can be carried out by putting DZV or TZV in place of STO NGAUSS = 3 in the second line of the INPUT file in the GAMESS implementation. The calculated energies become progressively lower (better) for double and triple zeta basis sets... 

Plot the curve of the bond energy of H2 vs. intemuclear distance for the H2 molecule using the STO-3G, double zeta valence (DZV), and triple zeta valence (TZV) basis sets in the GAMESS implementation. 

More definite evidence comes from an MO study of the S—O stretching in dimethyl sulphoxide9, where three basis sets were employed a STO-3G one (I), a 4-31G one (double-zeta, II) and a 3G + d one (III). Table 6 reports the main results the small effect of the double-zeta, and the dramatic effect of the 3d functions, are clearly visible. Notice also how the C—S bond length and the bond angles are by far less sensitive to basis set changes. 

Each CGTO can be considered as an approximation to a single Slater-type orbital (STO) with effective nuclear charge f (zeta). The composition of the basis set can therefore be described in terms of the number of such effective zeta values (or STOs) for each electron. A double-zeta (DZ) basis includes twice as many effective STOs per electron as a single-zeta minimal basis (MB) set, a triple-zeta (TZ) basis three times as many, and so forth. A popular choice, of so-called split-valence type, is to describe core electrons with a minimal set and valence electrons with a more flexible DZ (or higher) set. 

Many calculations for atoms have led to the development of a number of recipes for deciding the best values of and n. A further important issue is the size of the basis set. A minimal basis set of STOs for an atom would include one function for each SCF occupied orbital with different n and / quantum numbers in equation (6.56) for the chlorine atom, therefore, the minimal basis set would include s, 2s, 2p, 3s and 3p functions, each with an optimised Slater orbital exponent . A higher order of approximation would be to double the number of STOs (the double zeta basis set), with orbital exponents optimised ultimately the Hartree-Fock limit is reached, as it has been for all atoms from He to Xe [13]. 

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