4.43. PARTN: Hirshfield partitioning
Author: Nick Spadaccini, Computer Science Department, University of Western Australia, Nedlands 6907, Australia
PARTN partitions an input density into either the contribution of a particular atom ( fragment ) or of an atom and its symmetry equivalents ( entire ). The Hirshfeld method of partitioning is employed.
4.43.1. Hirshfeld Partitioning
The Hirshfeld (1977) 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 density apportioned to atom A is
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.
4.43.2. 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 (1974) 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.
4.43.3. Program Requirements
The structural data is read from the input archive bdf. The density must be input on file map. PARTN partitions this density into the atomic contributions. The density ascribed to the fragment atom or the entire atom specified on the site line is output to file par.
4.43.4. Contribution Distances
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. The distance beyond which an atom contribution is zero may also be set by the contact option.
4.43.5. File Assignments
Reads atom data from the input archive bdf
Reads density map from the file map
Reads profdb data base from a file defined by the macro profile:
Writes partitioned density map to the filepar
4.43.6. Examples
This example employs all the default settings. The weights are determined from the promolecular density. The contributions of atoms up to 6Å 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 6Å away. The partitioned density will include the contribution of the O12 atom at (.1234,-.1234,.7890) only.
Here the weights are determined from the promolecular potential. Atoms up to 4Å from the input map edges are included in the calculation. The effective range of an atom is set to 4.5Å. The partition density will include the contributions of all the Cu1ab atoms in the input range.
