Primitive GTOs

The next step was to represent each Slater atomic orbital as a fixed linear combination of Gaussian orbitals so a Slater-type orbital with exponent f is written as a sum of GTOs with exponents a, q 2, and so on. For example, in the case of three primitive GTOs we might write... 

To remind you, for an atomic STO with exponent f different from 1, the rf s remain the same but the exponents of the primitives have to be multiplied by For a carbon atom, the Is STO is represented as a combination of four primitive GTOs, whilst the 2s and 2p STO are represented by two basis functions, one consisting of three primitives and the other of one. 

The primitive GTOs with exponents 18050.0 through 0.2558 are Is type, and the remainder are 2p type. The two most diffuse s functions (those with exponents 0.7736 and 0.2558) are the main components of the 2s STO, and they are allowed to vary freely in molecular calculations. The Is primitive with exponent 2.077 turns out to make substantial contributions to both the atomic Is and 2s orbitals, so that one is also left free. The remaining seven distinct primitive Is GTOs describe the atomic Is orbital, and a careful examination of the ratios of their... 

Combining the full set of basis functions, known as the primitive GTOs (PGTOs), into a smaller set of functions by forming fixed linear combinations is known as basis set contraction, and the resulting functions are called contracted GTOs (CGTOs). 

There are two different ways of contracting a set of primitive GTOs to a set of contracted GTOs segmented and general contraction. Segmented contraction is the... 

The larger active space was then used in a new set of calculations which used a considerably larger AO basis. The 13s, 8p basis of van Duijneveldt was contracted (7,1,1,1,1,1,1/4,1,1,1,1). Additional diffuse functions were added, one of s-type (exponent 0.04) and of one p-type (exponent 0.025). Three 3d polarization functions were also included, contracted from four primitive GTOs with exponents 2.179, 0.865, 0.362 and 0.155. The exponents and the contraction coefficients were chosen according to the polarized basis-set... 

---