c20 JWBS043-Rogers September 13, 2010 11:29 Printer Name: Yet to Come
332 QUANTUM MOLECULAR MODELINGradius. One way to improve our basis set is recognize the shell structure for atoms Li
and higher by splitting it into a part for the inner shellcoreelectrons and a part for
the outer shellvalenceelectrons. An example is the 3–21G split valence basis set,
which consists of core electrons expressed by 3 basis functions followed by 2 and 1
separate orbitals for the valence electrons. The single valence basis function 1 has a
larger excursion from the nucleus than the double basis function 2. The total orbital
is the sum of all the basis functions. Addition of new basis functions leads to larger
basis sets, which we hope will be more complete and will be a better representation
of the actual orbital. Larger split valence basis sets become complicated as can be
seen from the response toGFInputin the route section of a relatively simple 6-31G
calculation for methane:17 basis functions 38 primitive Gaussians20.11 POLARIZED BASIS FUNCTIONS
The electron probability density of an atom participating in a chemical bond is
distorted somewhat into the region between the atoms participating in that bond. It
is not spherically symmetrical. The new probability density can be represented by
adding some kind of a directional basis function to the spherical orbitals already used.
The new orbital is said to bepolarized. A convenient change in the basis set is ap
orbital added to the sphericalsorbital of a bonded H atom. This would be denoted,
for example, 6–31G(p). It turns out that addingdorbitals to theporbitals of carbon in
aCH bond has a greater effect on the energy than does the thep-hydrogen addition.
Thus we see the more common notation 6–31G(d). A step further is to add basis
functions for both distortions, resulting in the widely used 6–31G(d,p) basis set. The
notation 6–31G** is also used.
By the time split basis sets were being used, the development ofab initiomolecular
orbital theory had shifted from an effort to reproduce Slater-type orbitals to an effort
to reproduce the results of experimental measurements of the chemical and physical
properties of the molecules themselves. Basis sets were further improved by adding
new functions, each representing some refined aspect of the physics of the molecular
orbital. Electrons do not have a very high probability density far from the nuclei
in a molecule, but the little probability that they do have is important in chemical
bonding, sodiffuse functions, denoted+as in 6-311+G(d,p), were added in some
very high level basis sets. While these basis set extensions were being made, the
power of computing hardware was growing to accommodate them.20.12 HETEROATOMS: OXYGEN
We shall extend our calculations to the STO-3G methanol input file given as
File 20.9. The stored basis functions for H, C, and O are used. For this calcula-
tion, STO-3G is requested in the#route section of the input file. The keyword