Hirshfeld partitioning

Several forms of wf have already been used within the field of MQS. These methods include the Hirshfeld partitioning [30], Bader s partitioning based on the virial theorem within atomic domains in a molecule [64], and the Mulliken approach [65]. For more information on all the three methods, refer to Chapter 15. 

Let us again examine the A-B reactive system and its A°-B° promolecule reference, the latter consisting of the free reactant densities brought to their current positions in A-B, for the finite separation between the two subsystems. It should be observed, that this hypothetical state also corresponds to the electrostatic stage of the interaction between reactants, when the electron distributions and internal subsystem geometries are held frozen at finite inter-reactant separations. When the subsequent Hirshfeld partitioning of the known overall ground-state density of A-B is performed, one obtains the uniquely defined, equilibrium subsystems in the reactive system. 

As expected by analogy to the ordinary Hirshfeld partitioning problem of equation (93a), the solution of this modified missing information variational principle gives ... 

De Profit F, Alsenoy CV, Peelers A, Langenaeker W, Geerlings P. Atomic charges, dipole moments, and Fukui functions using Hirshfeld partitioning of the electron density. J Corn-put Chem. 2002 23 1198-209. 

Approximations for these spin Fukui functions were computed using the approximations introduced by Galvan et al. (eqns (136) and (137)) the condensed values of densities of these orbitals on the different atoms were obtained using the Hirshfeld partitioning scheme. " The global... 

Several other definitions of atomic charges have been published in the chemical literature. Among those, two methods have gained some popularity. Hirshfeld partitioning is based upon the stockholder principle . According to that principle, p(r) at each point is partitioned into atomic contributions, called densities of bonded. atoms , that are given by... 

Figure 2 also presented the Hirshfeld partitioning [23] of the total charge, as a function of time. The Hirshfeld partitioning attributes the charge at each point in space... 

Recently, Ayers et al. [24] have used sound mathematical arguments to recommend using Hirshfeld partitioning to compute the charges, and in our approach. 

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