By Charles M. Quinn
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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.
Are the values of the parameters to define the primitive Gaussians and the formulae in column F, for the [2s) functions in hydrogen. $E10 -- SQRT(1/(32"PI( )))* (2-$A10)*EXP(-$A10/2) 5. 5 for this case. Again, note the normalization constant used. For the 12p) case, there is the substantial difference that the ]sto-nG:2p) Gaussians include the radial factor for 2p-like functions. $F12 = $A12*SQRT(1/(32"PI()))*EXP(-$A12/2) 6. 15a, b and c. 1, based on the criterion that good orbital energies had been calculated, except in the cases of the smallest basis sets.
This procedure has the effect of reducing the number of terms for variation in calculations, but, more particularly, philosophically, provides for the better representation of details of the atomic radial functions, such as the cusp near the origin in s-functions, since the components subject to optimization separately, can be included in the linear combination. 11. 28, which compare Huzinaga's Gaussian sets and the corresponding Slater functions for the ls and 2p orbitals in hydrogen. 27 The matchings of Huzinaga's [sto-ng:ls) basis sets to the ls [Slater] function for hydrogen.