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ASE Manual, Release 3.6.1.2828
7.22.6 Bader Analysis
Henkelman et. al have implemented a fast and robust algorithm for calculating the electronic charges on individual
atoms in molecules or crystals, based on the Bader partitioning scheme [Bader]. In that method, the
analysis is based purely on the electron density. The partitioning of the density is determined according to its
zero-flux surfaces. Details of their implementation can be found in [Tang]. The program is freely available at
http://theory.cm.utexas.edu/henkelman/research/bader/ where you will also find a description of the method.
The algorithm is very well suited for large solid state physical systems, as well as large biomolecular systems.
The computational time depends only on the size of the 3D grid used to represent the electron density, and scales
linearly with the total number of grid points. As the accuracy of the method depends on the grid spacing, it is
recommended to check for convergnce in this parameter (which should usually by smaller than the default value).
The program takes cube input files. It does not support units, and assumes atomic units for the density (Bohr^-3).
All ase dft calculators have a get_pseudo_density method, which can be used to get the density. A simple
python script for making a cube file, ready for the Bader program, could be:
>>> from ase import *
>>> density = calc.get_pseudo_density() * Bohr**3
>>> write(’filename.cube’, atoms, data=density)
Some calculators (e.g. gpaw) also have a method called get_all_electron_density, in which case this is
preferable to get_pseudo_density.
Note that it is strongly recommended to use version 0.26b or higher of the program, and the examples below refer
to this version.
Example: The water molecule
The following example shows how to do Bader analysis for a water molecule.
First do a ground state calculation, and save the density as a cube file:
from ase import *
from gpaw import *
atoms = molecule(’H2O’, cell=[7.5, 9, 9], calculator=GPAW(h=.17, xc=’PBE’))
atoms.center()
atoms.get_potential_energy()
rho = atoms.calc.get_all_electron_density(gridrefinement=4) * Bohr**3
write(’water_density.cube’, atoms, data=rho)
Then analyse the density cube file by running (use bader -h for a description of the possible options):
$ bader -p all_atom -p atom_index water_density.cube
This will produce a number of files. The ACF.dat file, contains a summary of the Bader analysis:
| # X Y Z CHARGE MIN DIST
| -----------------------------------------------------------------
| 1 7.0865 8.5038 9.0672 9.1121 1.3250
| 2 7.0865 9.9461 7.9403 0.4440 0.2834
| 3 7.0865 7.0615 7.9403 0.4440 0.2834
| -----------------------------------------------------------------
| NUMBER OF ELECTRONS: 9.99999
Revealing that 0.56 electrons have been transfered from each Hydrogen atom to the Oxygen atom.
The BvAtxxxx.dat files, are cube files for each Bader volume, describing the density within that volume. (I.e. it is
just the original cube file, truncated to zero outside the domain of the specific Bader volume).
AtIndex.dat is a cube file with an integer value at each grid point, describing which Bader volume it belongs to.
164 Chapter 7. Documentation for modules in ASE