Localized molecular orbitals

Localized molecular orbitals (LMO) are obtaind by unitary transformation upon a set of canonical molecular orbitals (CMO). The tranformation normally involves the optimization (either minimization or maximization) of a specific operator. The generic form of the localization operator is the following: Failed to parse (syntax error): {\displaystyle \langle \mathcal{\hat L} \rangle = \sum_{i=1)^{n} \langle \phi_i \phi_i | \mathcal{\hat L} | \phi_i \phi_i \rangle } Many methodlogies have been devoloped during the past decades.