Slater type orbitals radial part

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. 

The theory (7, 8, 9,10,11,12) will be outlined for molecules having n atoms with a total of P valence shell electrons. We seek a set of molecular orbitals (LCAO-MO s), that are linear combinations of atomic orbitals centered on the atoms in the molecule. Since we shall not ignore overlap, the geometry of the molecule must be known, or one must guess it. The molecule is placed in an arbitrary Cartesian coordinate system, and the coordinates of each atom are determined. Orbitals of the s and p Slater-type (STO) make up the basis orbitals, and as indicated above we restrict ourselves to the valence-shell electrons for each of the atoms in the molecule. The STOs have the following form for the radial part of the function (13,18) ... 

The main ZDO parameters for each orbital type are the orbital exponent ( entering the radial part of Slater-type AOs, the diagonal matrix elements of the interaction of an electron occupying AO Xn with its own core expressed through electronegativity + of this the resonance integrals (3 depending... 

The Slater-type functions (STF) with the radial part in the form (8.3) and integer n can be used as the basis functions in Hartree-Fock-Roothaan calculations of atomic waveftmctions. The radial dependence of the atomic orbitals is an expansion in the radial Slater-type basis functions ipimp whose indices are I, running over s,p, symmetries, and p counting serially over basis-set members for a given s3Tnmetry ... 

The most familiar atomic orbitals are those for the hydrogen atom which are usually designated according to their angular parts as s for / = 0, p for / = 1, d for Z = 2, and so on where there are 2/ -t 1 orbitals of each type. For calculational purposes Slater proposed that the radial part of the orbital, while stiU centered upon the nucleus, should be of the form... 

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