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STO-nG basis setsAdditional recommended knowledge
STO-nG basis setsSTO-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.
STO-2G basis setIn 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.
AccuracyThe 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 |
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This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "STO-nG_basis_sets". A list of authors is available in Wikipedia. |