  Localized orbitals are important for modeling and interpreting complicated
electronic structures of atoms and molecules in a chemically meaningful way.
Here, we present the parameter-free procedure for transforming delocalized
molecular orbitals (either canonical self-consistent field orbitals, or Lowdin
natural orbitals obtained from a general wavefunction) into the localized
property-optimized orbitals (LPOs), which can be used for building the most
accurate (in the Frobenius norm sense) approximation to the first-order reduced
density matrix in form of the sum of localized mono- and diatomic terms. In
this way any, any one-electron molecular property can be decomposed into
contributions associated with individual atoms and the pairs of atoms, with the
upper bound for the decomposition acucracy known in advance due to
Cauchy-Bunyakovsky-Schwarz inequality. In addition, an algorithm is proposed
for obtaining 'the Chemist's LPOs' (CLPOs) set of localized orbitals containing
a single orbital per a pair of electrons and forming an idealized Lewis
structure with the one-electron properties which are closest to the properties
obtained from the original many-electron wavefunction. The computational
algorithms for constructing LPOs and CLPOs as well as their underlying atomic
hybrid orbitals (AHOs and LHOs respectively) from the results of
quantum-chemical calculations are presented and their implementation within the
open-source freeware program JANPA (http://janpa.sourceforge.net/ ) is
discussed. The performance of the proposed orbital localization procedures is
assessed using the test set of density matrices of 33432 small molecules
obtained at Hartree-Fock and 2-nd order Moller-Plesset theory levels.
