Concise Physical Chemistry

c20 JWBS043-Rogers September 13, 2010 11:29 Printer Name: Yet to Come

328 QUANTUM MOLECULAR MODELING

042

0.5

1

(r)

1(r)

2(r)

1(r) 2(r)

r

FIGURE 20.6 Approximation to the 1s orbital of hydrogen by 2 Gaussians. The upper curve

is the sum of the lower two curves. The solid curve is the hydrogen 1satomic orbital.

Upon extending the basis set along the series STO-2G, STO-3G,...,STO-6G,

and more complicated functions, one reaches a point of diminishing return, beyond

which further elaboration produces little gain. On the positive side, the basis functions

fall into natural groups, which are replicated from one calculation to the next, hence a

way of using computer resources more efficiently is by treating each group as though

it were a single function. Each natural group of basis functions, treated as a unit, is

called acontracted Gaussian-type orbital(CGTO). For example, if we start out with

36 primitives (by no means a large number in this context) and segment them into

groups of 6, we have reduced the problem six-fold.

20.8 MOLECULAR ORBITALS

Extension of the method we have developed so far to molecules is quite straightfor-

ward. One simply puts a basis set into the input file for each atom in the molecule.

In a simple illustration of the transition from atomic to molecular input files, we can

convert the input file for a single hydrogen atom using our arbitrarily chosen STO-2G

atomic basis set into an input file for the H 2 molecule. The result is File 20.5.

The second atom is added to the first, inz-matrix format. This is done by selecting

the first atom as a reference point and placing the second hydrogen atom a distancer

from it. Line 7 in File 20.5 readsh1rmeaning “the distance between the second

hydrogen h and atom number 1 isr.” The approximate distance chosen is specified

in angstrom units immediately below in line 9 asr =0.7.

In the previous problem of the uncharged atom, the spin multiplicityM= 2 S+1,

whereS=± 1 /2 is the total spin of the system, was 2 (line 5 of input File 20.3), but

the multiplicity for the pairedσelectrons in molecular H 2 is 1. In molecular hydrogen

File 20.5, lines 11–15 are (almost exactly) repeated in lines 16–20. The first set of