By Charles M. Quinn
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Additional info for Computational Quantum Chemistry: An Interactive Guide to Basis Set Theory
10a. 19: comparison of the numerical radial functions for boron ls based on Slater and the Hehre, Stewart and Pople Isto-3g) approximations to these Slater functions. 10c. In the first part, comparisons are made between the Slater functions and the numerical outputs of the Herman-Skillman program. In the second, the comparisons are between the Slater functions and their Gaussian representations. Finally, the role of the Slater exponent is emphasized by the restoration of the hydrogenic results using the hydrogenic Slater exponents.
Note this is the F A C T D O U B L E ( ) intrinsic function in the 'Engineering Function library' in EXCEL. So, if this library is not present on your basic version, add it under the TOOLS menu using the EXCEL CD. 19a Detail from the worksheet for the matching of the Slater and Isto-3g) approximations to the l s orbital for boron as the output of the Herman-Skillman program. 19b for the match to the hydrogen function. 19b Restoration of the match to the hydrogen ls orbital simply by changing the entries for the Slater exponents in cells $G$3 and $G$7.
For applications in molecular orbital theory, we need, in addition, to make allowance for the evident fact that an atom in a molecule is in a different environment to the isolated atom in free space, since any other atoms in a molecule give rise to extra potentials disturbing the free space electron distribution for that atom. 22 is the key to the generation of modem Gaussian basis sets. It is not too much of an extrapolation to develop this approach in the direction that different 'effective' Slater exponents might be appropriate in the molecular environment.
Computational Quantum Chemistry: An Interactive Guide to Basis Set Theory by Charles M. Quinn