A minimum basis set is where only sufficient orbitals are used to contain all the electrons in the neutral atom.
For example, an STO-3G basis set for the 1s, 2s and 2p orbital of the carbon atom are all linear combination of 3 primitive Gaussian functions.
)[1] This differs from the more common procedure where the criteria often used is to choose the coefficients (c's) and exponents (α's) to give the lowest energy with some appropriate method for some appropriate molecule.
A special feature of this basis set is that common exponents are used for orbitals in the same shell (e.g. 2s and 2p) as this allows more efficient computation.
[3][4] The most widely used basis set of this group is STO-3G, which is used for large systems and for preliminary geometry determinations.
[2] The exact energy of the 1s electron of H atom is −0.5 hartree, given by a single Slater-type orbital with exponent 1.0.