Stockholder partitioning

Different studies have appeared on fragment similarity using all the three partitioning schemes mentioned above, although in the case of the Hirshfeld method, the stockholder partitioning has also been applied directly to the similarity index [46,66,67]. 

Figure 6.1 shows the stockholder decomposition of the theoretical deformation density of the cyanoacetylene molecule, H—Cs=C—C=N (Hirshfeld 1977b). The overlap density in the bonds is distributed between the bonded atoms. The assignment of part of the density near the hydrogen nucleus to the adjacent carbon atom manifests the difference between fuzzy and discrete boundary partitioning methods. 

Net atomic charges based on the stockholder partitioning of theoretical densities for a number of linear molecules containing N, C, and H are listed in Table 6.1. For these molecules, the charge transfer between atoms is relatively small. Much larger values are obtained for more electronegative atoms, such as oxygen and fluorine bonded to carbon atoms. 

The stockholder recipe partitions the density according to each atom s contribution to the promolecule density. The partitioned fragment distributions... 

TABLE 6.1 Net Charges q (e) from the Stockholder Partitioning. Charges in the Second Row are from a Discrete Boundary Partitioning by Politzer (1971) and Politzer and Reggio (1972)... 

On the other hand, dipole moments obtained with stockholder partitioning tend to be systematically low for pyridinium dicyanomethylide, the value is... 

Hirshfeld s stockholder partitioning applied to a theoretical density of hydrogen cyanide, HCN, gives the following values for the atomic charges, dipole moments, and second moments /i ... 

R.F. Nalewajski, E. Broniatowska, Atoms-in-molecules from the stockholder partition of molecular two-electron distribution, Theret. Chem. Acc. 117 (2007) 7. 

Let us begin a survey of this development with a brief reminder of the Hirshfeld (H) partition scheme and its information-theoretic justification. The stockholder division [34] of the molecular electron density p(r). experimental or theoretical, into the AIM densities, p(r) = X< Pa(r)>... 

Postulate I. Among all possible partitions of the molecular ground-state density p into densities of molecular fragments [ p , for the fixed promolecule (free atom) reference, a natural choice in chemistry, there exists the equilibrium division into the stockholder fragments, that are characterized completely by p and by the reference densities alone. 

Hirshfeld (or stockholder) charges are based on using atomic densities for partitioning the molecular electron density. The promolecular density is defined as the sum of atomic densities placed at the nuclear geometries in the molecule. The actual molecular electron density at each point in space is then partitioned by weighting factors according to the promolecular contributions. 

It has been amply demonstrated elsewhere [10-15] that many classical problems of theoretical chemistry can be approached afresh using this novel IT perspective. For example, displacements in information distribution in molecules relative to the promolecular reference consisting of nonbonded constituent atoms have been investigated [10-18], and the least biased partition of molecular electron distributions into subsystem contributions (e.g., densities of AIM) has been investigated as well [10,19-26], The IT approach has been shown to lead to the stockholder molecular fragments of Hirshfeld [27], These optimum density pieces have been derived from alternative global and local variational principles of IT. 

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... 

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