Author: Nick Spadaccini, Computer Science Department, University of Western Australia, Nedlands, 6907 WA, Australia
CHARGE calculates a charge associated with an atom from the difference density. The difference density ( ) is partitioned according to the Hirshfeld method.
The Hirshfeld method apportions the electron density among the atoms by the appropriate weighting. The weights are related by the atomic contribution to the promolecular density,
The fragment of the deformation density apportioned to atom A is,
The net atomic charge, , is derived from the integration of the difference density fragment,
An alternative scheme is based on the atomic contributions to the total promolecular potential defined as the sum of the electronic and nuclear contributions.
The promolecular density or potential is the sum of the atomic densities or potentials. These latter values are derived from the Clementi and Roetti atomic wavefunctions. Associated with each atom type are the parameters , and for k=1,...,m such that the density is,
and the potential is
The last term is the nuclear contribution and (n,x) is the Incomplete Gamma Function.
The density profiles (e/ ) and potential profiles (e/bohr) are stored at 44 discrete values of r (bohrs) for the points,
; 0. ≤ r ≤ 31.2
The divisions are chosen so that the density of points is greatest in the region of steepest gradient. The density or potential value at any general point is linearly interpolated from the profile.
The difference density (
) must be input from the
The user may specify the effective range of atom
contributions in two ways. The
Estimates of (Q) are determined for spherical regions of various radii following the method of Davis and Maslen. The estimates are derived from the values of (F), the errors in the structure factor amplitudes used to derive the difference density. For each atom the program outputs a value of (Q) for a radius set within the program. The absolute radii are generated from relative radii, derived from the density profiles and stored in the database. These values are rescaled so that the total volume of the atoms in the cell equals the cell volume. The radii used are listed.
Since values of atomic radii are not unique the variation of (Q) with r is also output so that the user may determine (Q) at an alternative radius if desired. The scheme assumes a centrosymmetric structure so that phase errors are not included .
The weights here are determined from the promolecular density. The contributions of atoms up to 6Ĺ beyond the input map edges are included in the calculation. However, an atom will not contribute to the density if the point is greater than 6Ĺ away.
CHARGE poten bord 4 cont 4.5
Here the weights are determined from the promolecular potential. Atoms up to 4Ĺ from the input map edges are included in the calculation. The effective range of a atom is set to 4.5Ĺ.