Bader Charge Analysis

Group members

Wenjie Tang and Samuel Chill


Richard Bader from McMaster University, developed an intuitive way of dividing molecules into atoms called the Quantum Theory of Atoms in Molecules (QTAIM). 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.

Bader's theory of atoms in molecules 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. The theory also provides a definition for chemical bonding that gives numerical values for bond strength.

Grid Method

We have developed computational method for partitioning a charge density grid into Bader volumes which is efficient, robust, and scales linearly with the number of grid points. The partitioning algorithm follows steepest ascent paths along the charge density gradient from grid point to grid point until a charge density maximum is reached. As the algorithm assigns grid points to charge density maxima, subsequent paths are terminated when they reach previously assigned grid points. It is this grid based approach which gives the algorithm its efficiency, and allows for the analysis of the large grids generated from plane wave based density functional theory calculations.


The program, code, and information about running the program can be found here.
We have a discussion forum to address issues related to the code and running the program.


W. Tang, E. Sanville, and G. Henkelman, A grid-based Bader analysis algorithm without lattice bias, J. Phys.: Compute Mater. 21 084204 (2009).

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).

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).