Slater-type orbitals STO

The Slater-type orbitals differ from the atomic orbitals of the hydrogen atom (see p. 178). The first difference is that the radial part is simplified in the STOs. 

Electronic Motion in the Mean Field Atoms and Molecules 

We put r, where A is a natural number or zero, instead of Laguerre polynomials given on p. 179. The second difference is in the orbital exponent, which has no constraint except that it has to be positive.  

The STOs have a great advantage they decay with distance from the centre in a similar way to the true orbitals - let us recall the ponential vanishing of the hydrogen atom orbitals (see Chapter 4). STOs would be fine, but finally we have 

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These atomic orbitals, called Slater Type Orbitals (STOs), are a simplification of exact soil tion s of the Sch rbdin ger eq nation for the... 

These functions are universally known as Slater type orbitals (STOs) and are just the leading term in the appropriate Laguerre polynomials. The first three Slater functions are as follows ... 

In quantum ehemistry it is quite eommon to use eombinations of more familiar and easy-to-handle "basis funetions" to approximate atomie orbitals. Two eommon types of basis funetions are the Slater type orbitals (STO s) and gaussian type orbitals (GTO s). STO s have the normalized form ... 

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... 

Slater type orbital (STO) mathematical function for describing the wave function of an electron in an atom, which is rigorously correct for atoms with one electron... 

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. 

Slater-type orbitals (STOs) are used to represent electron density around an atom. 

In honour of J. C. Slater, we refer to such basis functions as Slater-type orbitals (STOs). Slater orbital exponents ( = (Z — s)/n ) for atoms through neon are given in Table 9.2. 

There are two types of basis functions (also called Atomic Orbitals, AO, although in general they are not solutions to an atomic Schrodinger equation) commonly used in electronic structure calculations Slater Type Orbitals (STO) and Gaussian Type Orbitals (GTO). Slater type orbitals have die functional form... 

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. 

The atomic and molecular wave functions are usually described by a linear combination of either Gaussian-type orbitals (GTO) or Slater-type orbitals (STO). These expressions need to be multiplied by a center dependent factor expf ip-A). Further the STOs in momentum space need to be multiplied by Yim(6p,p). Examining the expressions [4], one notices the Gaussian nature of the GTOs even after the FT. The STOs are significantly altered on FT. From the expressions in Table 5.1, STOs are seen to exhibit a decay which is the decay of the slowest Is... 

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

Ab initio calculations are based on first principles using molecular orbital (MO) calculations based on Gaussian functions. Combinations of Gaussian functions yield Slater-type orbitals (STOs), also called Slater determinants. STOs are mathematical functions closely related to exact solutions for the hydrogen atom. In their ultimate applications, ab initio methods would use Gaussian-type wave functions rather than STOs. The ab initio method assumes that from the point of view of the electrons the nuclei are stationary, whereas... 

The correct limiting radial behavior of the hydrogen-like atom orbital is as a simple exponential, as in (A.62). Orbitals based on this radial dependence are called Slater-type orbitals (STOs). Gaussian functions are rounded at the nucleus and decrease faster than desirable (Figure 2.2b). Therefore, the actual basis functions are constructed by taking fixed linear combinations of the primitive Gaussian functions in such a way as to mimic exponential behavior, that is, resemble atomic orbitals. Thus... 

Each remaining valence orbital is represented by a so-called Slater-type orbital (STO). The mathematical form of a normalized STO used in EHT (in atom-centered polar coordinates) is... 

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