A modification of the nudged elastic band method for finding minimum energy paths is presented. One of the images is made to climb up along the elastic band to converge rigorously on the highest saddle point. Also, variable spring constants are used to increase the density of images near the top of the energy barrier to get an improved estimate of the reaction coordinate near the saddle point. Applications to CH 4 dissociative adsorption on Ir͑111͒ and H 2 on Si͑100͒ using plane wave based density functional theory are presented.

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An improved way of estimating the local tangent in the nudged elastic band method for finding minimum energy paths is presented. In systems where the force along the minimum energy path is large compared to the restoring force perpendicular to the path and when many images of the system are included in the elastic band, kinks can develop and prevent the band from converging to the minimum energy path. We show how the kinks arise and present an improved way of estimating the local tangent which solves the problem. The task of finding an accurate energy and configuration for the saddle point is also discussed and examples given where a complementary method, the dimer method, is used to efficiently converge to the saddle point. Both methods only require the first derivative of the energy and can, therefore, easily be applied in plane wave based density-functional theory calculations. Examples are given from studies of the exchange diffusion mechanism in a Si crystal, Al addimer formation on the Al͑100͒ surface, and dissociative adsorption of CH 4 on an Ir͑111͒ surface.

A computational method for partitioning a charge density grid into Bader volumes is presented which is efficient, robust, and scales linearly with the number of grid points. The partitioning algorithm follows the steepest ascent paths along the charge density gradient from grid point to grid point until a charge density maximum is reached. In this paper, we describe how accurate off-lattice ascent paths can be represented with respect to the grid points. This improvement maintains the efficient linear scaling of an earlier version of the algorithm, and eliminates a tendency for the Bader surfaces to be aligned along the grid directions. 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.

An improvement to the grid-based algorithm of Henkelman et al. for the calculation of Bader volumes is suggested, which more accurately calculates atomic properties as predicted by the theory of Atoms in Molecules. The CPU time required by the improved algorithm to perform the Bader analysis scales linearly with the number of interatomic surfaces in the system. The new algorithm corrects systematic deviations from the true Bader surface, calculated by the original method and also does not require explicit representation of the interatomic surfaces, resulting in a more robust method of partitioning charge density among atoms in the system. Applications of the method to some small systems are given and it is further demonstrated how the method can be used to define an energy per atom in ab initio calculations.