By Warren J Hehre

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Discussion is provided in Section II. STO-3G Minimal Basis Set The simplest possible atomic orbital representation is termed a minimal basis set. This comprises only those functions required to accommodate all of the electrons of the atom, while still maintaining its overall spherical symmetry. In practice, this involves a single (1s) function for hydrogen and helium, a set of five functions (1s, 2s, 2px, 2py, 2pz) for lithium to neon and a set of nine functions (1s, 2s, 2px, * The reason that Gaussian functions are used in place of exponential functions is that integrals, in particular electron repulsion integrals, which arise in approximate treatments are very difficult to evaluate using exponential functions but relatively easy to evaluate using Gaussian functions.

Hartree-Fock models are well defined and yield unique properties. They are both size consistent and variational. Not only may energies and wavefunctions be evaluated from purely analytical (as opposed to numerical) methods, but so too may first and second energy derivatives. This makes such important tasks as geometry optimization (which requires first derivatives) and determination of vibrational frequencies (which requires second derivatives) routine. Hartree-Fock models and are presently applicable to molecules comprising upwards of 50 to 100 atoms.

Hydrogen is provided by two s-type functions, and main-group elements are provided two sets of valence s and p-type functions. Among the simplest split-valence basis sets are 3-21G and 6-31G. Each core atomic orbital in the 3-21G basis set is expanded in terms of three Gaussians, while basis functions representing inner and outer components of valence atomic orbitals are expanded in terms of two and one Gaussians, respectively. 6-31G basis sets are similarly constructed, with core orbitals represented in terms of six Gaussians and valence orbitals split into three and one Gaussian components.

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