Concise Physical Chemistry

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

THE GAUSSIAN BASIS SET 325

The next step is to take two Gaussian functions, calledprimitives, parameterized

so that one fits the STO close to the nucleus and the other contributes to the part away

from the nucleus. We seek a function

STO-2G=C 1 e−α^1 r

2

+C 2 e−α^2 r

2

But how shall we apportion this linear combination so that we have one tall basis

function contributing to the orbital near the nucleus and one for a “fat” tail? Let us take

α 1 = 1 .0 andα 2 = 0 .25. BothC 1 e−r

2

andC 2 e−^0.^25 r

2

contribute to the sum. The larger

negative exponent is tall near the nucleus but drops off faster than the small negative

exponent. Nowφ(r) will extend to larger values ofrand give us the fat tail we seek:

φ(r)=C 1 e−r

2

+C 2 e−^0.^25 r

2

But we still have two parameters to worry aboutC 1 andC 2. They control the relative

contribution of each primitive to the final wave function. Let us take a 60/40 split and

favor the fat tail:

φ(r)= 0. 40 e−^1.^0 r

2

+ 0. 60 e−^0.^25 r

2

We now have a four-parameter basis set for use with thegenkeyword (File 20.1).

They are entered in the format

α 1 C 1

α 2 C 2

The GAUSSIAN©Cinput file becomes File 20.1. The STO curve fit is shown in

Fig. 20.5.

STO(r):=e−r

φ(r):= 0. 40 e−^1.^0 r

2

+ 0. 60 e−^0.^25 r

2

.

# gen

hatom gen

02

h

1

S2

1.0 0.40

0.25 0.60

****

FILE 20.1 (Input) A four-parameter Gaussian File for the hydrogen atom. Line 8 designates

the first center (the only one in this case) and line 9 identifies it as an s orbital with 2 basis

functions.