Types of Basis Sets and Their Uses

The basis sets described here in most detail are those developed by Pople3 and coworkers [40], which are probably the most popular now, but most general-purpose (those not used just on small molecules or on atoms) basis sets utilize some sort of contracted Gaussian functions to simulate Slater orbitals. A brief discussion of basis sets and references to many, including the widely-used Dunning 

3John Pople, bom in Bumham-on-Sea, Somerset, England, 1925. Ph.D. (Mathematics) Cambridge, 1951. Professor, Camegie-Mellon University, 1960-1986, Northwestern University (Evanston, Illinois) 1986-present. Nobel Prize in chemistry 1998 (with Walter Kohn, Chapter 5, Section 7.1). Died Chicago, 2004. 

This is called a minimal basis set, although some atoms actually have more basis functions (which for this basis can be equated with atomic orbitals) than are needed 

The STO-3G basis introduces us to the concept of contraction shells in constructing contracted Gaussians from primitive Gaussians (Section 5.3.2). The Gaussians of a contraction shell share common exponents. Carbon, for example, has one s shell and one sp shell. This means that the 2s and 2p Gaussians (belonging to the 2sp shell) share common oc exponents (which differ from those of the Is function). Consider the contracted Gaussians 

Basis set Single point Time (s) Geometry optimization Time (s) Geometry optimization + frequencies Time (s)  

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