Atomic and ionic orbitals

Charge and configurational variations of atomic orbitals Although oversimplified treatments commonly speak of the atomic orbitals for a given atom, it is clear that AOs must depend on the charge state and specific configuration of the atom. Thus, the (N)AOs of an anionic atom A- will tend to be markedly more diffuse (i.e., spread out to greater distances from the nucleus) than those of a cationic A+. 

The naive concept that a fixed set of valence AOs suffices for all charge states and bonding environments is equivalent to the use of a minimum basis set (e.g., STO-3G), which is known to be quite inadequate for quantitative purposes. Nevertheless, if the AOs are properly allowed to adjust dynamically in the molecular environment, one recovers a minimal-basis description that is surprisingly accurate the natural minimal basis. In the NBO framework the effective natural atomic orbitals are continually optimized in the molecular environment, and the number of important NAOs therefore remains close to minimal, greatly simplifying the description of bonding. 

In the following sections we shall primarily focus on the linear combinations of NAOs that lead to optimal hybrids and NBOs, rather than on the forms of the NAOs 

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