Concise Physical Chemistry

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

326 QUANTUM MOLECULAR MODELING

042

0.5

1

STO(r)

(r)

r

FIGURE 20.5 Comparison of the 1sSTO of hydrogen with an arbitrarily parameterized

two-Gaussian functionφ(r):= 0. 40 e−^1.^0 r

2

+ 0. 60 e−^0.^25 r

2

.

The fit is certainly not perfect, but it is better than what we got with a single basis

function. The energy obtained from this basis set isHF=-0.4572106which is

91.4% of the defined value of 0.5Eh. The error has been reduced from about 15%

to about 8.5%. Variational optimization in theCparameters takes place during the

program run as we see by addingGFInputto the#geninput line in File 20.1.

This change produces the output shown in File 20.2.

AO basis set in the form of general basis input:

10

S 2 1.00 0.000000000000

0.1000000000D+01 0.4304660143D+00

0.2500000000D+00 0.6456990214D+00

****

FILE 20.2 (Output) The STO-2G basis set written as a 1s orbital consisting of functions

with arbitrarily selected exponents 1.00 and 0.25.

20.7 STORED PARAMETERS

We can also run an STO-2Gab initiocalculation on the hydrogen atom using the

GAUSSIAN stored parameters rather than supplying our own. The input file is shown

in file 20.3. We find that there are two Gaussian primitives and one unpaired electron

from the output:

1 basis functions 2 primitive gaussians

1 alpha electrons 0 beta electrons

which agrees with the picture of the STO-2G basis set that we are trying to build. Of

course we want to know what the parameters are for the two Gaussians. The keyword