4.12. CHARGE: Atomic charges from difference density
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 (
mol) is partitioned
according to the Hirshfeld method.
4.12.1. Hirshfeld Partitioning
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 QA, is derived from the integration of the difference density fragment, An alternative scheme is based on the atomic contributions to the total promolecular potential Vpro defined as the sum of the electronic and nuclear contributions.
4.12.2. Density And Potential Profiles
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 Ak, nk and zk 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/bohr3) and potential profiles (e/bohr) are stored at 44 discrete values of r (bohrs) for the points,
r1 = 0. ; rk+1 = 1.15(rk + .01); 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.
4.12.3. Density, Distances And Errors
The difference density (mol) must be input from the
FOURR file map. CHARGE partitions this density into atomic
contributions and integrates over the input region to obtain a charge. If the
input map is the asymmetric unit the values obtained are total atomic charges
for atoms at general positions or fractions governed by the site symmetry for
atoms at special positions. The user must determine the fraction of an atom
present in the input map and calculate the total charge accordingly.
The user may specify the effective range of atom contributions in two ways. The border option in the program initiation line determines the region beyond the input map for which atom contributions are included. The default value of 6Å implies that any atom within this distance of the input map edges is included. Also the distance beyond which an atom contribution is zero may be set by the contact option.
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.
4.12.4. File Assignments
Reads lrcell: and symmetry data from the input archive bdf
Reads difference density from a map file
Reads profile data base from the file designated by the macro profile: