Localized molecular orbitals

Localized molecular orbitals (LMO) are obtained by unitary transformation upon a set of canonical molecular orbitals (CMO). The transformation usually involves the optimization (either minimization or maximization) of the expectation value of a specific operator. The generic form of the localization potential is:

$\langle \hat{L} \rangle = \sum_{i=1}^{n} \langle \phi_i \phi_i | \hat{L} | \phi_i \phi_i \rangle$ ,

where $\hat{L}$ is the localization operator and $φ i$ is a molecular spatial orbital. Many methodlogies have been developed during the past decades, and they all differ in the form of $\hat{L}$ . The most commonly used localization methods are those developed by Ruedenberg et al. and by Boys et al..