STO-nG basis sets

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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