Group members
Wenjie Tang
The Program
The program, code, and information about running the program can be found here.We also have a discussion forum to address issues related to the code and running the program.
About Bader analysis
Bader analysis is a robust and fast method that is used to analyze the charge of individual atom in molecules or condensed phase systems. This algorithm carries out decomposition of electronic charge density into atomic contributions. As suggested by Bader, space is divided up into atomic regions where the dividing surfaces are at a minimum in the charge density, i.e. the gradient of the charge density is zero along the surface normal.The input for the Bader decomposition is a charge density grid, that gives the value of the electron density specified on a regular grid of points in space. The spacing between the grid points should be fine enough that a linear interpolation between the points is a sufficiently good approximation in the bonding region between atoms. In order to find out which grid points belong to each of the Bader regions, a path of steepest ascent on the charge density grid is defined for each grid point. The set of grid points that have paths ending in the same terminus of maximal charge density are members of the same Bader region. Typically, these points of charge density maxima are located at atomic nuclei. The total electronic charge within a Bader region can then be calculated as the sum over the corresponding grid points.
Improved method
There is one problem with the old Bader analysis method: it has grid bias (left picture). The method has been improved recently to remove the grid bias of the original method. A correction step is taken when the accumulated error is larger than half of the grid length. By this way, the trajectory goes along the gradient (right picture).
Results of the Bader analysis
1. Dividing surface of charge density for water.
The left one is from the old method and the right one is from the new method. This bias is removed with the near-grid method and the surfaces become smooth.
2. Molecule orientation dependence of water molecule:
The biased Bader surfaces in the on-grid method give rise to both systematic and orientation dependent errors as compared to the near-grid method, for which the Bader surfaces and O valance charge remain constant with orientation.
3. Ionic charge in a NaCl crystal:
A fully converged charge on each Na ion is 0.828 e (blue dashed line). The (old) on-grid method deviates from this value by about 0.01 e for a fine grid with 40 million points. The (new) near-grid method rapidly converges to the correct value.
4. Scaling of computational effort:
Computer time required to analyze the charge density grid for the eight-atom NaCl cell with the near-grid algorithm. The computational cost scales linearly with the number of grid points in the charge density file, as with the on-grid method.
References
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).