Slater-type Atomic Orbital STO

The molecular orbitals x are most commonly written as linear combinations of atomic orbitals and T is then described as a LCAO wavefunction. The atomic orbitals are usually represented by Slater-type atomic orbitals (STO)... 

The first SCF wavefunctions for the ground state of N3 were calculated by Clementi. Initially he used the minimal basis set (Table 16) with Slater-type atomic orbitals (STO) The orbital exponents C (equation 20) were chosen as the best free-atom values and the internuclear distance was taken as 1T2A. (As already discussed, section II.A, this distance is erroneous.) The total electronic energy of N3 was calculated as — 162 5422// (I // = 27 209 eV/atom). 

When calculating the wavefunction it is important to make a choice of basis set J. t that is suitable for the available computing power and the accuracy desired. A straightforward early approach to basis set construction was to fit an accurate Slater-type atomic orbital (STO) with n gaussians,called STO- G. The quality of STO- G wavefunctions increases as n increases. It was determined that = 3 was a good starting point, and the STO-3G basis set has been widely used, particularly where computing resources were limited or for lai er molecules. 

The term STO-3G denotes a minimal Gaussian basis set in which each Slater-type atomic orbital (s, p or d) is approximated by a fixed block of three Gaussian functions189,... 

Each HE molecular orbital is written as a linear combination of functions describing atomic orbitals. The entire set of such equations for the atomic orbitals in a molecule is called a basis set, and each equation is called a basis set function. Ideally, these basis set fimctions would have the properties of hydrogenic wave functions, particularly with regard to the radial dependence of electron density probability as a function of distance of the electron from the nucleus, r. A type of basis set function proposed by Slater uses a radial component incorporating and such functions are called Slater t)rpe orbitals (STOs). Gaussian type orbitals (GTOs) have radial dependence and are easier to solve analytically, but they do not describe the radial dependence of electron density as well as do the STOs. 

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... 

The Slater-type orbitals are a family of functions that give us an economical way of approximating various atomic orbitals (which, for atoms other than hydrogen, we don t know anyway) in a single relatively simple form. For the general case, STOs are written... 

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. 

Minimal basis sets use fixed-size atomic-type orbitals. The STO-3G basis set is a minimal basis set (although it is not the smallest possible basis set). It uses three gaussian primitives per basis function, which accounts for the 3G in its name. STO stands for Slater-type orbitals, and the STO-3G basis set approximates Slater orbitals with gaussian functions. ... 

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... 

We have just explained that the wave equation for the helium atom cannot be solved exacdy because of the term involving l/r12. If the repulsion between two electrons prevents a wave equation from being solved, it should be clear that when there are more than two electrons the situation is worse. If there are three electrons present (as in the lithium atom) there will be repulsion terms involving l/r12, l/r13, and l/r23. Although there are a number of types of calculations that can be performed (particularly the self-consistent field calculations), they will not be described here. Fortunately, for some situations, it is not necessary to have an exact wave function that is obtained from the exact solution of a wave equation. In many cases, an approximate wave function is sufficient. The most commonly used approximate wave functions for one electron are those given by J. C. Slater, and they are known as Slater wave functions or Slater-type orbitals (usually referred to as STO orbitals). 

The two most popular basis sets consist of either Slater-type orbitals8 (STO s) or Gaussian functions. When using STO s one or more are placed on each nucleus - the more the better. The so-called minimal basis set consists of only those STO s which correspond to the occupied a.o. s in the seperated atom limit. Instead of using Slater s rules to determine orbital exponents they may be varied in order to minimize the energy. Once this optimization has been done for a small molecule the values so established can be used in bigger problems. The basis can be improved by adding additional STO s for various nuclei, e.g. with different orbital exponents. If every minimal basis a.o. is represented by two such STO s a "double Q" set is obtained. The only restriction on the number and type of STO that can be added, seems to be computer time. 

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... 

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... 

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