Double zeta and split valence basis sets

2 Double zeta and split valence basis sets 

In order to have a better basis set, we can replace each STO of a minimal basis set by two STOs with different orbital exponent f (zeta). This is known as a double zeta basis set. In this basis, there is a linear combination of a contracted function (with a larger zeta) and a diffuse function (with a smaller zeta) and the coefficients of these combinations are optimized by the SCF procedure. Using H2O as an example, a double zeta set has two Is STOs on each H, two Is STOs, two 2s STOs, two 2px, two 2pv and two 2pz STOs on oxygen, making a total of 14 basis functions. 

If only valence orbitals are described by double zeta basis, while the inner shell (or core) orbitals retain their minimal basis character, a split valence basis set is obtained. In the early days of computational chemistry, the 3-21G basis was fairly popular. In this basis set, the core orbitals are described by three Gaussian functions. The valence electrons are also described by three Gaussians the inner part by two Gaussians and the outer part by one Gaussian. More recently, the popularity of this basis set is overtaken by the 6-31G set, where the core orbitals are a contraction of six Gaussians, the inner part of the valence orbitals is a contraction of three Gaussians, and the outer part is represented by one Gaussian. 

Similarly, the basis set can be further improved if three STOs (with three different zetas, of course) are used to describe each orbital in an atom. Such a basis is called a triple zeta set. Correspondingly, the 6-311G set is a triplesplit valence basis, with the core orbitals still described by six Gaussians and the valence orbitals split into three functions described by three, one, and one Gaussians, respectively. 

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