By Charles M. Quinn
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Extra info for Computational Quantum Chemistry: An Interactive Guide to Basis Set Theory
H u z i n a g a pointed out that multiple m i n i m a occur in the a p p r o x i m a t e e i g e n v a l u e calculations based on the use of linear c o m b i n a tions of G a u s s i a n s and so it is not surprising that Cauchy's elephant can be drawn in m a n y ways. The ( 4 - 3 1 ) basis set for the l s orbital in h y d r o g e n is an early e x a m p l e of a splitbasis set 22. 01330, r) + 0 . 0 1 9 0 6 g ~ ( 1 3 . 23 22Since the basis set can be applied to other atoms using a suitable ~', the notation has a more general meaning: 4-31 is accepted to mean a 4-term contraction of primitives for the core orbitals and then a split into a single term and a 3-term contraction for the valence orbitals.
Apply the chart wizard to generate the chart shown. xls, simply by changing the Slater exponent to the value for the hydrogen 1s orbital. Note, how the spreadsheet responds to this simple change of input. 00. 10b. 1. 2. 3. 4. 20: comparison of the numerical radial functions for boron 2s based on Slater functions and the Hehre, Stewart and Pople Isto-3g) approximations to these Slater functions. xls. This establishes the general form of the spreadsheet and the chart, which changes, as before, when the appropriate data and formulae for the 2s orbital are applied.
Thus, in this chapter you will learn: 1. 2. 3. 4. 5. 6. 1 using the spreadsheet method; how to calculate an overlap integral between two l s atomic orbitals in H2; how to calculate the same integral using the ]sto-3g) basis to approximate the hydrogen ls orbitals; how to determine the 'best' linear combinations of Gaussian functions for the modelling of Slater functions. NUMERICAL INTEGRATION The trapezium rule and Simpson's rule are the two standard procedures for numerical integration (53). 1.