STO-nG basis sets

Additional recommended knowledge

Recognize and detect the effects of electrostatic charges on your balance

Weighing the right way

What is the Correct Way to Check Repeatability in Balances?

STO-nG basis sets

STO-nG basis sets are the minimal basis sets, where 'n' represents the number of primitive Gaussian functions comprising a single basis set. For minimal basis sets, the core and valence orbitals are represented by same number primitive Gaussian functions . For example, an STO-3G basis set for the 1s orbital of H atom is a linear combination of 3 primitive Gaussian functions. It is easy to calculate the energy of an electron in the 1s orbital of H atom represented by STO-nG basis sets. In the following sections, the structure of the STO-nG minimal basis sets are explained with H atom as an example.

STO-1G basis set

, where and . The optimum value of is the one which gives the minimum value for the Energy of the 1s electron of H atom. The exponent for the STO-1G basis set can be manually derived by equating the derivative of the energy with respect to the exponent to zero.
Thus and for the value , the energy of the 1s electron of H atom can be calculated as hartree. The expression for the energy of the 1s electron of H atom is a function only of , and other fundamental constants such as . For convenience, the basis set details can be represented as follows

STO-1G
	0.2829421200D+00	1.0000000000D+00

STO-2G basis set

In general an STO-nG basis set is a linear combination of 'n' primitive Gaussian functions. The STO-nG basis sets are usually represented by the exponents and the corresponding coefficients. Thus an STO-2G [Ref. 1] basis set which is a linear combination of 2 primitive Gaussian functions can be represented as follows.

STO-2G
	0.1309756377D+01	0.4301284983D+00
	0.2331359749D+00	0.6789135305D+00

Accuracy

The exact energy of the 1s electron of H atom is -0.5 hartree. Following table illustrates the increase in accuracy as the number of primitive Gaussian functions increases in the basis set.

References :

[1] http://gnode2.pnl.gov/bse/portal