Slater-type orbitals STO basis sets

ADF) (26). We described the electronic states of the clusters with a triple- Slater-type orbital (STO) basis set. With the exception of K and Ca, polarization functions were included in the basis set. For Li, Na, Be and Mg the Lr orbitals were treated with the frozen core approximation. For K and Ca, the Lf 2p shells were regarded as the frozen core. 

Many types of basis set have been examined and two of these have come to dominate the area of ab initio molecular calculations. These two, which we refer to as the gaussian and the Slater-type-orbital (STO) basis sets, are actually very similar in many important respects. 

Among the gradient-corrected functionals, B-LYP is superior to B-P, and the inclusion of HF exchange in the hybrid methods (B3-P and B3-LYP) improves the agreement with experiment. The B-P functional, combined with a Slater-type orbital (STO) basis set, unlike B-P and B3-P using GTO basis sets, predicts Aiso which are nearly as accurate as those from CCSD(T). The reason for this significant improvement using the STO basis set is that electron density can better satisfy the cusp condition... 

For both types of orbitals, the coordinates r, 0, and (j) refer to the position of the electron relative to a set of axes attached to the center on which the basis orbital is located. Although Slater-type orbitals (STOs) are preferred on fundamental grounds (e.g., as demonstrated in Appendices A and B, the hydrogen atom orbitals are of this form and the exact solution of the many-electron Schrodinger equation can be shown to be of this form (in each of its coordinates) near the nuclear centers), STOs are used primarily for atomic and linear-molecule calculations because the multi-center integrals < XaXbl g I XcXd > (each... 

These atomic orbitals, called Slater Type Orbitals (STOs), are a simplification of exact solutions of the Schrodinger equation for the hydrogen atom (or any one-electron atom, such as Li" ). Hyper-Chem uses Slater atomic orbitals to construct semi-empirical molecular orbitals. The complete set of Slater atomic orbitals is called the basis set. Core orbitals are assumed to be chemically inactive and are not treated explicitly. Core orbitals and the atomic nucleus form the atomic core. 

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. 

A minimum basis set of Slater-type orbitals (STO) is used. 

All these calculations require a set of atomic orbitals from which MOs can be calculated (the basis set). The earliest to be used were Slater-type orbitals (STOs) but these are mathematically inconvenient, and the STO-3G minimal basis set, which uses gaussian functions to mimic Slater orbitals, is commonly used. More sophisticated gaussian basis sets, which lead to improved accuracy, carry labels such as 6-31G(d) and 6-31++G(dp). Successive increases in basis set size (STO-3G—>3-21G—>3-31G(d)—>6-311G(3df)) give improved bond-length accuracy. 

Slater type orbital (STO) functions will be presented here. They are well known fimctions since their description made by Slater around sixty years ago [43a] and heavily studied and used as atomic basis sets [43b,43c]. In this section the connection of STO with CETO functions is analyzed. 

We use three different basis sets in this work. The first is the minimal STO-3G basis 5) consisting of a least squares fit of three gaus-sian functions to each function in a minimal basis set (Is on H Is, 2s, 2fx, 2py, 2pz on C, N, 0) of Slater-type orbitals. This basis has been successfully used to calculate geometries of a large number of acyclic molecules and some cyclic hydrocarbons. We therefore use it here to obtain optimized structures for each of the three-membered ring molecules. 

The entries in the first columns of the two tables are total energies of atoms given by the SCF calculations with the minimal basis set of Slater-type orbitals (STO, see Section 2.B.). The entries in the second columns are energies given by the calculations in which each STO was replaced by two Slater-type functions with the exponents so optimized to give the minimum total energy. From Tables 2.1 and... 

An example of how ab initio calculations may be applied to the study of fragments of polymer chains is given by Jaffe, Yoon, and McLean, who studied a series of mono- and diphenyl molecules containing up to 35 atoms. These compounds are models for a variety of important polymers such as polycarbonates (see Figure 1), polyimides, aromatic polyamides, aromatic polyesters, and polyether sulfone. A variety of basis sets, representing linear combination of Gaussian functions to approximate Slater-type orbitals (STOs) as compiled in Table 1, were employed. 

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