Localized orbitals for optimal decomposition of molecular properties

We present the procedure for transforming delocalized molecular orbitals into the localized property‐optimized orbitals (LPOs) designed 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 monoatomic and diatomic terms. In this way, a decomposition of molecular properties into contributions associated with individual atoms and the pairs of atoms is obtained with the a priori known upper bound for the decomposition accuracy. Additional algorithm is proposed for obtaining the set of “the Chemist's LPOs” (CLPOs) containing a single localized orbital, with nearly double occupancy, per a pair of electrons. CLPOs form an idealized Lewis structure optimized for the closest possible reproduction of one‐electron properties derived from the original many‐electron wavefunction. The computational algorithms for constructing LPOs and CLPOs from a general wavefunction are presented and their implementation within the open‐source freeware program JANPA (http://janpa.sourceforge.net/) is discussed. The performance of the proposed procedures is assessed using the test set of density matrices of 33 432 small molecules obtained at both Hartree‐Fock and second‐order Moller‐Plesset theory levels and excellent agreement with the chemist's Lewis‐structure picture is found. Algorithms for transforming molecular orbitals to localized form are presented. The orbitals created by the proposed algorithms provide the basis for accuracy‐optimized decomposition of any one‐electron molecular property into contributions associated with individual atoms and the pairs of atoms. In this way, the “property‐optimal” Lewis structure is recovered from a general wavefunction obtained from quantum‐chemical calculations. The algorithms are implemented in an open‐source freeware program JANPA (http://janpa.sourceforge.net/) and tested on 33 432 small molecules.