Introduction

Many years ago, Richard Bader from McMaster University, developed an intuitive way of dividing molecules into atoms. His definition of an atom is based purely on the electronic charge density. Bader uses what are called zero flux surfaces to divide atoms. A zero flux surface is a 2-D surface on which the charge density is a minimum perpendicular to the surface. Typically in molecular systems, the charge density reaches a minimum between atoms and this is a natural place to separate atoms from each other.

Besides being an intuitive scheme for visualizing atoms in molecules, Bader's definition is often useful for charge analysis. For example, the charge enclosed within the Bader volume is a good approximation to the total electronic charge of an atom. The charge distribution can be used to determine multipole moments of interacting atoms or molecules. Bader's analysis has also been used to define the hardness of atoms, which can be used to quantify the cost of removing charge from an atom.

Program Overview

We have developed a fast algorithm for doing Bader's analysis on a charge density grid. The program (see below) can read in charge densities in the VASP CHGCAR format, or the Gaussian CUBE format. The program outputs the total charge associated with each atom, and the zero flux surfaces defining the Bader volumes.

Information about generating and analyzing charge densities from vasp is here.

Download

Select the appropriate platform to download a binary of the Bader analysis program:

• Linux x86 (ifort)
• Linux x86-64 (ifort)
• Windows (lahey)
• Mac OS X, PowerPC (xlf)
• Mac OS X, Intel (ifort)

The F90 source code is also available:

• Source Code (v0.25c 09/25/08)

Version history

Running the Program

The program can be run with the command

    bader chargefile

Command line arguments and output files

The following options can be used when running the Bader analysis program.

    bader [ -c bader | voronoi ]
          [ -n bader | voronoi ]
          [ -b neargrid | ongrid ]
          [ -r refine_edge_iterations ]
          [ -ref reference_charge ]
          [ -p all_atom | all_bader ]
          [ -p sel_atom | sel_bader ] [volume list]
          [ -p atom_index | bader_index ]
          [ -i cube | chgcar ]
          [ -h ] [ -v ]
          chargefile

To get a description of the options, run 'bader -h'.

Output files

The following output files are generated: ACF.dat, BCF.dat, AtomVolumes.dat.

ACF.dat contains the coordinates of each atom, the charge associated with it according to Bader partitioning, percentage of the whole according to Bader partitioning and the minimum distance to the surface. This distance should be compared to maximum cut-off radius for the core region if pseudo potentials have been used.

BCF.dat contains the coordinates of each Bader maxima, the charge within that volume, the nearest atom and the distance to that atom.

AtomVolumes.dat contains the number of each volume that has been assigned to each atom. These numbers correspond to the number of the BvAtxxxx.dat files.

The Bader volumes can be written using the print options.

    bader [ -p all_atom | all_bader ] chargefile
    bader [ -p sel_atom | sel_bader ] [volume list] chargefile
    bader [ -p atom_index | bader_index ] chargefile

-p none The default is to write no charge density files.

-p all_atom Combine all volumes associated with an atom and write to file. This is done for all atoms and written to files named BvAtxxxx.dat. The volumes associated with atoms are those for which the maximum in charge density within the volume is closest to the atom.

-p all_bader Write all Bader volumes (containing charge above threshold of 0.0001) to a file. The charge distribution in each volume is written to a separate file, named Bvolxxxx.dat. It will either be of a CHGCAR format or a CUBE file format, depending on the format of the initial charge density file. These files can be quite large, so this option should be used with caution.

-p sel_atom Write the selected atomic volumes, read from the subsequent list of volumes.

-p sel_bader Write the selected Bader volumes, read from the subsequent list of volumes.

-p atom_index Write the atomic volume index to a charge density file.

-p bader_index Write the Bader volume index to a charge density file.

Visualization

The Bader volumes can be written and visualized with the VASP Data Viewer, VMD, or a cube file viewer (such as GaussView) for Gaussian cube files.

Examples

• NaCl crystal (vasp chgcar)
• C₂H₄ molecule, orientation 1 (vasp chgcar)
• C₂H₄ molecule, orientation 2 (vasp chgcar)
• H₂O molecule (gaussian cube)

Discussion Forum

References

• G. Henkelman, A. Arnaldsson, and H. Jónsson, A fast and robust algorithm for Bader decomposition of charge density, Comput. Mater. Sci. 36 254-360 (2006).
  
  
• E. Sanville, S. D. Kenny, R. Smith, and G. Henkelman An improved grid-based algorithm for Bader charge allocation, J. Comp. Chem. 28 899-908 (2007).
  
  
• W. Tang, E. Sanville, and G. Henkelman A grid-based Bader analysis algorithm without lattice bias, J. Phys.: Condens. Matter (in press, 2008).

This program was written by Andri Arnaldsson, Wenjie Tang, and Graeme Henkelman.

Improvements to the original algorithm were developed by Ed Sanville (Loughborough University, UK).

With contributions from: Johannes Voss (DTU) and Erik McNellis (FHI)

The code is under development, so please send us any comments or suggestions.