By Warren J Hehre

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**Additional resources for A Guide to Molecular Mechanics and Quantum Chemical Calculations**

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Localized MP3 and MP4 models are not presently available. * Size consistency is a more important attribute than variational, and because of this, MøllerPlesset models are generally preferred over configuration interaction models. 37 Chapter 2 37 3/21/03, 11:46 AM Models for Open-Shell Molecules While the vast majority of molecules may be described in terms of closed-shell electron configurations, that is, all electrons being paired, there are several important classes of molecules with one or more unpaired electrons.

6-31G*, 6-31G**, 6-311G* and 6-311G** Polarization Basis Sets The second shortcoming of a minimal (or split-valence) basis set . . functions being centered only on atoms . . may be addressed by providing d-type functions on main-group elements (where the valence orbitals are of s and p type), and (optionally) p-type functions on hydrogen (where the valence orbital is of s type). This allows displacement of electron distributions away from the nuclear positions. , pd and sp hybrids as shown above, or alternatively in terms of a Taylor series expansion of a function (d functions are the first derivatives of p functions, p functions are the first derivatives of s functions).

Adding second, third, . . derivatives. Among the simplest polarization basis sets are 6-31G* and 6-311G*, constructed from 6-31G and 6-311G, respectively, by adding a set of d-type polarization functions written in terms of a single Gaussian for each heavy (non-hydrogen) atom. A set of six second-order Gaussians is added in the case of 6-31G* while a set of five pure d-type Gaussians is added in the case of 6-311G*. Gaussian exponents for polarization functions have been chosen to give the lowest energies for representative molecules.