Slater-type orbitals overlap integral

The coefficients and the exponents are found by least-squares fitting, in which the overlap between the Slater type function and the Gaussian expansion is maximised. Thus, for the Is Slater type orbital we seek to maximise the following integral ... 

Two Slater type orbitals, i andj, centered on the same point results in the following overlap integrals ... 

In equations 31 and 32 Pv and pp. are semiempirical parameters, represents the two electron two center repulsion integrals and Spv is the overlap of Slater type orbitals of the form,... 

In order to interpret these values further, it is necessary to have values for the overlap integrals (10). We obtained these as follows An approximate real wavefunction which fits the outer regions of the 5/function well (within 0.4% for af,nonlinear least squares procedure. The square of a function composed of Slater-type orbitals was fit to the probability amplitude calculated from a relativistic SCF wavefunction. The result is... 

Fig. R.2. The hydrogen molecule in the simplest basis set of two Is Slater type orbitals (STO). (a) The overlap integral S as a function of the intemuclear distance R. (b) The penetration energy represents the difference between the eleetron- roton interaction calculated assuming the eleetronie eharge distribution and the same energy ealculated with the point charges (the eleetron is loeated on nucleus a), (c) The energies + and E- of the bonding (lower curve and of the antibonding (upper curve) orbitals. Energies and distances in a.u.

Coulomb Sturmians (CSs) are an exponential-type complete set of basis functions which satisfy a Sturm-Liouville equation [2]. The main objective of the present work is to derive an ADT for the Slater-type orbitals (STOs), which are the fundamental ETO, and thereby for the CSs, which are a linear combination of STOs. The expression for the two-center overlap integral is then worked out for the CSs as an illustration and numerical results and conclusions are presented. 

A similar SCF calculation of ferrocene has been made by Shustorovich and Dyatkina (73) in which Slater functions were used for the iron orbitals. These calculations gave an exactly opposite charge distribution to that of Dahl and Ballhausen, owing to the more contracted metal orbitals used by the latter authors. Because values of overlap integrals of the type S (2pa3da) and S(2p7T3d7T) calculated by the latter authors are almost identical with those calculated directly from the Watson functions (74), it seems that the charge distribution calculated by Dahl and Ballhausen is the correct one. 

Explicit formulas and numerical tables for the overlap integral S between AOs (atomic orbitals) of two overlapping atoms a and b are given. These cover all the most important combinations of AO pairs involving ns, npSlater type, each containing two parameters i [equal to Z/( - 5)], and n — S, where n — S is an effective principal quantum number. The S formulas are given as functions of two parameters p and t, where p = p- + p,s)R/ao, R being the interatomic distance, and t = — Mb)/(ma + Mb)- Master tables of... 

It is in the definition of the integrals or the lack of it, that most m.o. methods differ. The overlap integrals are easy to compute and were, indeed, tabulated for Slater-type atomic orbitals a long time ago (ref. 79). In some simple calculations, namely extended Huckel-type calculations a rough estimation of Hmn is as follows (see also page 79). 

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