CiteULike: and_ped10's Henkelman

Improved grid-based algorithm for Bader charge allocation.

E Sanville — 2007-05-23T15:55:18-00:00

J Comput Chem, Vol. 28, No. 5. (15 April 2007), pp. 899-908.

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.

A fast and robust algorithm for Bader decomposition of charge density

Graeme Henkelman — 2007-02-10T18:25:09-00:00

Computational Materials Science, Vol. 36, No. 3. (June 2006), pp. 354-360.

An algorithm is presented for carrying out decomposition of electronic charge density into atomic contributions. As suggested by Bader [R. Bader, Atoms in Molecules: A Quantum Theory, Oxford University Press, New York, 1990], 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. Instead of explicitly finding and representing the dividing surfaces, which is a challenging task, our algorithm assigns each point on a regular (x, y, z) grid to one of the regions by following a steepest ascent path on the grid. The computational work required to analyze a given charge density grid is approximately 50 arithmetic operations per grid point. The work scales linearly with the number of grid points and is essentially independent of the number of atoms in the system. The algorithm is robust and insensitive to the topology of molecular bonding. In addition to two test problems involving a water molecule and NaCl crystal, the algorithm has been used to estimate the electrical activity of a cluster of boron atoms in a silicon crystal. The highly stable three-atom boron cluster, B3I is found to have a charge of -1.5 e, which suggests approximately 50% reduction in electrical activity as compared with three substitutional boron atoms.

Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points

Graeme Henkelman — 2006-12-12T15:20:20-00:00

The Journal of Chemical Physics, Vol. 113, No. 22. (2000), pp. 9978-9985.

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 Al(100) surface, and dissociative adsorption of CH4 on an Ir(111) surface. ©2000 American Institute of Physics.

A climbing image nudged elastic band method for finding saddle points and minimum energy paths

Graeme Henkelman — 2006-12-12T15:19:22-00:00

The Journal of Chemical Physics, Vol. 113, No. 22. (2000), pp. 9901-9904.

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 CH4 dissociative adsorption on Ir(111) and H2 on Si(100) using plane wave based density functional theory are presented. ©2000 American Institute of Physics.

Exploring long-time response to radiation damage in MgO

BP Uberuaga — 2006-11-15T09:18:48-00:00

Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, Vol. 228, No. 1-4. (January 2005), pp. 260-273.

Using a variety of computational modeling and simulation methods, we examine the production and long-time evolution of damage created in irradiated MgO. We find that the damage produced in low energy (order 1 keV) collision cascades typically consists of point defects and small defect clusters. Over long times, interstitials annihilate with vacancies and aggregate with other interstitials, forming larger clusters that exhibit surprising behavior. For example, a six-atom interstitial cluster is found to have extremely high mobility. The implications of highly-mobile large clusters are explored via a rate theory model and comparison to other materials. We conclude that successful modeling of radiation damage evolution in MgO requires explicit treatment of large interstitial clusters.

MgO addimer diffusion on MgO(100): A comparison of ab initio and empirical models

G Henkelman — 2006-02-06T15:55:12-00:00

Phys. Rev. B, Vol. 72, No. 11. (September 2005), 115437.

Diffusion of a MgO dimer on a MgO(100) surface is investigated using both density functional theory (DFT) and empirical ionic potentials. Barriers for diffusion via hop and exchange mechanisms are calculated. A qualitative difference is found between DFT and the empirical potential for the oxide exchange barrier. DFT predicts a saddle point for the process with a barrier of 0.88 eV , whereas the empirical potential of Lewis and Catlow, with a formal charge of ±2.0e , finds this structure to be a stable intermediate minimum with an energy of 0.19 eV , relative to the most stable addimer structure. The empirical potential predicts that the oxide hop and exchange mechanisms are equally likely; whereas, DFT shows that the oxide adion hop mechanism has a lower energy barrier. A Bader population analysis of the DFT charge density indicates that the magnesium and oxide ions have partial charges of magnitude ±1.7e . Using an empirical potential with this partial charge, the local minimum in the oxygen exchange process becomes a saddle at 0.62 eV , which is in better agreement with DFT. The standard deviation between the energy of the DFT minima and the saddle points with those of the empirical potential was reduced from 0.32 eV when using the formal charge parameters of Lewis and Catlow to 0.15 eV using partial charges. The qualitative agreement found for each diffusion barrier using the partial charge model suggests that a Bader analysis can be used to obtain suitable partial charges for constructing empirical potentials.

Multiple Time Scale Simulations of Metal Crystal Growth Reveal the Importance of Multiatom Surface Processes

G Henkelman — 2006-01-31T20:30:41-00:00

Physical Review Letters, Vol. 90, No. 11. (March 2003), 116101.

A method for extending atomistic computer simulations of solids beyond the nanosecond time scale was used to simulate metal crystal growth on the time scale of laboratory experiments. Transitions involving concerted motion of multiple atoms on the crystal surface are found to lead to remarkably smooth growth of pure Al(100). Cu(100) is found to grow with a rougher surface, consistent with experiments. Not only is the activation energy of the multiatom Al processes surprisingly low, but vibrational entropy also favors processes where many atoms are displaced.

Long time scale kinetic Monte Carlo simulations without lattice approximation and predefined event table

Graeme Henkelman — 2006-01-31T18:10:07-00:00

The Journal of Chemical Physics, Vol. 115, No. 21. (2001), pp. 9657-9666.

We present a method for carrying out long time scale dynamics simulations within the harmonic transition state theory approximation. For each state of the system, characterized by a local minimum on the potential energy surface, multiple searches for saddle points are carried out using random initial directions. The dimer method is used for the saddle point searches and the rate for each transition mechanism is estimated using harmonic transition state theory. Transitions are selected and the clock advanced according to the kinetic Monte Carlo algorithm. Unlike traditional applications of kinetic Monte Carlo, the atoms are not assumed to sit on lattice sites and a list of all possible transitions need not be specified beforehand. Rather, the relevant transitions are found on the fly during the simulation. A multiple time scale simulation of Al(100) crystal growth is presented where the deposition event, occurring on the time scale of picoseconds, is simulated by ordinary classical dynamics, but the time interval in between deposition events, on the order of milliseconds, is simulated by the long time scale algorithm. The Al(100) surface is found to grow remarkably smooth, even at 30 K because of concerted displacements of multiple atoms with significantly lower activation energy than adatom diffusion on the flat terrace. ©2001 American Institute of Physics.

Comparison of methods for finding saddle points without knowledge of the final states

RA Olsen — 2006-01-31T18:05:04-00:00

The Journal of Chemical Physics, Vol. 121, No. 20. (2004), pp. 9776-9792.

Within the harmonic approximation to transition state theory, the biggest challenge involved in finding the mechanism or rate of transitions is the location of the relevant saddle points on the multidimensional potential energy surface. The saddle point search is particularly challenging when the final state of the transition is not specified. In this article we report on a comparison of several methods for locating saddle points under these conditions and compare, in particular, the well-established rational function optimization (RFO) methods using either exact or approximate Hessians with the more recently proposed minimum mode following methods where only the minimum eigenvalue mode is found, either by the dimer or the Lanczos method. A test problem involving transitions in a seven-atom Pt island on a Pt(111) surface using a simple Morse pairwise potential function is used and the number of degrees of freedom varied by varying the number of movable atoms. In the full system, 175 atoms can move so 525 degrees of freedom need to be optimized to find the saddle points. For testing purposes, we have also restricted the number of movable atoms to 7 and 1. Our results indicate that if attempting to make a map of all relevant saddle points for a large system (as would be necessary when simulating the long time scale evolution of a thermal system) the minimum mode following methods are preferred. The minimum mode following methods are also more efficient when searching for the lowest saddle points in a large system, and if the force can be obtained cheaply. However, if only the lowest saddle points are sought and the calculation of the force is expensive but a good approximation for the Hessian at the starting position of the search can be obtained at low cost, then the RFO approaches employing an approximate Hessian represent the preferred choice. For small and medium sized systems where the force is expensive to calculate, the RFO approaches employing an approximate Hessian is also the more efficient, but when the force and Hessian can be obtained cheaply and only the lowest saddle points are sought the RFO approach using an exact Hessian is the better choice. These conclusions have been reached based on a comparison of the total computational effort needed to find the saddle points and the number of saddle points found for each of the methods. The RFO methods do not perform very well with respect to the latter aspect, but starting the searches further away from the initial minimum or using the hybrid RFO version presented here improves this behavior considerably in most cases.©2004 American Institute of Physics.

A dimer method for finding saddle points on high dimensional potential surfaces using only first derivatives

Graeme Henkelman — 2006-01-31T17:38:35-00:00

The Journal of Chemical Physics, Vol. 111, No. 15. (1999), pp. 7010-7022.

The problem of determining which activated (and slow) transitions can occur from a given initial state at a finite temperature is addressed. In the harmonic approximation to transition state theory this problem reduces to finding the set of low lying saddle points at the boundary of the potential energy basin associated with the initial state, as well as the relevant vibrational frequencies. Also, when full transition state theory calculations are carried out, it can be useful to know the location of the saddle points on the potential energy surface. A method for finding saddle points without knowledge of the final state of the transition is described. The method only makes use of first derivatives of the potential energy and is, therefore, applicable in situations where second derivatives are too costly or too tedious to evaluate, for example, in plane wave based density functional theory calculations. It is also designed to scale efficiently with the dimensionality of the system and can be applied to very large systems when empirical or semiempirical methods are used to obtain the atomic forces. The method can be started from the potential minimum representing the initial state, or from an initial guess closer to the saddle point. An application to Al adatom diffusion on an Al(100) surface described by an embedded atom method potential is presented. A large number of saddle points were found for adatom diffusion and dimer/vacancy formation. A surprisingly low energy four atom exchange process was found as well as processes indicative of local hex reconstruction of the surface layer. ©1999 American Institute of Physics.