Pictorial Representation of MOs for Molecules

STO-3G. STO-3G is a minimum basis set consisting of Is orbitals for hydrogen and 2s and 2p orbitals for second-row elements, described by Gaussian functions. 

Split-Valence Gaussian Orbitals. (3-21G, 4-31G, 6-31G) Split-valence orbitals are described by two or more Gaussian functions. Also in this category are Dunning-Huzinaga orbitals. 

Polarized Orbitals. These basis sets add further orbitals, such as p for hydrogen and d for carbon that allow for change of shape and separation of centers of charge. Numbers in front of the d, f designations indicate inclusion of multiple orbitals of each type. For example, 6-3 2df, 2pd) orbitals have two d functions and one / function on second-row elements and two p functions and one d function on hydrogen. 

Dijfuse Basis Sets. (6-31-l-G, 6-31 ++ G ) Diffuse basis sets include expanded orbitals that are used for molecules with relatively loosely bound electrons, such as anions and excited states. 6-31+G have diffuse p orbitals on second-row elements. 6-31+ + G orbitals have diffuse orbitals on both second-row elements and hydrogen. 

MP (Moeller-Plesset) calculations treat correlation by a perturbation method based on adding excited state character. MP2 includes a contribution from the interaction of doubly excited states with the ground state. MP4 includes, single, double, and quadruple excited states in the calculation. 

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