An Extension of the Hirshfeld Method to Open Shell Systems Using Fractional Occupations

Abstract

In this work, a new partitioning method is presented which allows one to calculate properties of radicals, in particular, atomic spin populations. The method can be seen as an extension of the Hirshfeld-I method [ Bultinck , P. et al. J. Chem. Phys. 2007 , 126 , 144111 ], in which the atomic weight functions, defining the atoms-in-molecules, are constructed by means of an iterative scheme in which the charges of the atoms-in-molecules are altered but the spin remains fixed. The Hirshfeld-I method is therefore not suitable for the calculation of atomic spin populations of open-shell systems. The new fractional occupation Hirshfeld-I (FOHI) uses an iterative scheme in which both the atomic charge and spin are optimized, resulting in a self-consistent method for the calculation of atomic spin populations. The results obtained with the FOHI method are compared with experimental results obtained using polarized neutron diffraction, thus serving as a validation of the FOHI method as well as the Hirshfeld definition of atoms-in-molecules in general.

IQA-embedded fragment attributed molecular system energy change in exploring intramolecular interactions

“…a energy term molecular fragment G {H9,H16} {C3,C12} {C4,C13} Hence, our results partly agree with the earlier reports [40][41][42] in that either only C-atoms of the bay [40,41] or only C-atoms to which ortho-H are bonded to [43] were found as main contributors to instability of planar bph. The apparent difference in conclusions arrived at [40][41][42] can be attributed to the fact that these interpretations were mainly based on C-atoms atomic energies, virial [40,41] and IQA/FOHI [42] (FOHI stands for fractional occupation iterative…”

“…term, and (ii) these atoms were indicated previously [40,41] [41], when going from ref to fin, lead to the conclusion (in agreement with the earlier report [40]) that the increase in the energy of C-atoms of the link overwrites the decrease in the atomic energies of H-atoms involved in the clash. Furthermore, a very recent report [43] pointed at the C-atoms to which ortho-hydrogens are bonded to as the main cause of destabilization of the planar form of bph.…”

“…Hirshfeld [43]). However, the FAMSEC-based interpretation, which involves all atomic energies in combination with all diatomic interactions throughout entire molecule, revealed that all C-atoms of the bay contribute (through different energy components) unfavorably to molecular energy of planar bph.…”

Hirshfeld-I charges in linear combination of atomic orbitals periodic calculations

“…As concerns the use of HI for open-shell systems, it was previously shown [11] that a rigorous application of information theory to the problem involves approaches different than what is here considered for closed-shell cases. As a first approximation to the issue, in the present work we consider a straightforward extension of the original proposal [9] in which the weight function ω A (r) in Eq.…”

“…[10] In particular efforts have been made to include open shell algorithms such as the Fractional Occupation HI (FOHI) [11,12] where both spin and atomic charges of spherical atomic densities are optimized independently. In the FOHI method, the spherical atomic densities are obtained by the equi-distribution of the occupation number of valence obitals.…”