The Kinetic Monte Carlo (KMC) Method

A core strength of the Theoretical Chemical and Quantum Physics Group


The well known Molecular Dynamics method calculates detailed trajectories for all the atoms in a simulation. Molecular Dynamics requires the use of small time steps to accurately solve the equations of motion and forces must be calculated between each pair of atoms at each time step. Consequently Molecular Dynamics can effectively only simulate a relatively small number of atoms for relatively short durations.

A popular and powerful approach to simulations involving large numbers of atoms or longer timescales or both, is the Kinetic Monte Carlo method. In Kinetic Monte Carlo the system is evolved by simulating the key atomistic processes for the system under study, in accordance with the probability of occurrence of these processes. Kinetic Monte Carlo needs to be suitably parameterised from detailed Molecular Dynamics or Ab-Initio studies. In its usual lattice approximation for atomic positions, Kinetic Monte Carlo coarse grains detailed atomic motions and avoids force calculations between pairs of atoms. This makes Kinetic Monte Carlo much cheaper computationally than Molecular Dynamics, so enabling the simulation of larger size and longer time scales compared to Molecular Dynamics. In particular Kinetic Monte Carlo can simulate the mesoscopic regime in which nanostructure growth occurs.

We have applied the Kinetic Monte Carlo method to model the development of metallic nanostructures on surfaces. Through Kinetic Monte Carlo simulations, we can investigate the influence of factors such as: adatom deposition rate, adatom mobility, substrate temperature and surface topography, on the assembly of nanostructures.

A recent Kinetic Monte Carlo study has been the growth of Pt nanostructures on Au, as potential bimetallic nano-catalysts [1].

In suitable circumstances Kinetic Monte Carlo and Molecular Dynamics can be combined together in a hybrid domain decomposition scheme, gaining benefits from each method [2].

Pt nanostructure on Au surface.

A Platinum (Pt) nanostructure (coloured silver) formed on a Gold (Au) step edge.

Recent Publications

[1] P Zoontjens, G Grochola, I K Snook and S P Russo, A Kinetic Monte Carlo study of Pt on Au(111) with applications to bimetallic catalysis, J. Phys.: Condens. Matter 23, 015302 (2011)

[2] P Zoontjens, T P Schulze and S C Hendy, Hybrid method for modelling epitaxial growth: Kinetic Monte Carlo plus Molecular Dynamics, Phys. Rev. B 76, 245418 (2007)

For more information about this technique, please contact Salvy Russo.

The Hybrid Reverse Monte Carlo (HRMC) Method

A core strength of the Theoretical Chemical and Quantum Physics Group


The Hybrid Reverse Monte Carlo method is a fitting routine which aims to produce three dimensional atomic coordinates of disordered materials which are consistent with a variety of experimental data while ensuring a low energy local bonding environment. Experimental data may include electron, x-ray and neutron diffraction, EXAFS and porosity information.

The HRMC methodology was developed to address two critical shortcomings in two fields employing the Metropolis-Hastings algorithm.

  • Traditional energy minimizing Metropolis Monte Carlo (MMC) method which produces atomic configurations by minimizing an empirical potential energy function. This methodology lacks a direct connection to experimental data.
  • The Reverse Monte Carlo (RMC) method which fits only experimental data such as the radial distribution function G(r) or structure factor S(q). This methodology tends to produce unphysical local bonding environments for materials that have significant bond angle dependence.

The HRMC method addresses both issues by simultaneously minimizing the potential energy as well as the discrepancy between simulation and experimental data. This methodology was pioneered within our group.

A comparison of HRMC and RMC

A comparison of HRMC (left) and RMC (right) resulting structures for amorphous carbon. While both configurations are consistent with experimental diffraction data, the RMC local bonding environment is physically unrealistic. The empirical potential in HRMC ensures that the bond angles are realistic.

Recent Publicatios

G. Opletal, T. Petersen, B. O'Malley, I. Snook, D. G. McCulloch, N. A. Marks and I. Yarovsky, Hybrid approach for generating realistic amorphous carbon structures using metropolis and reverse Monte Carlo, Mol. Sim. 28, 927 (2002)

T. Petersen, I. Yarovsky, I. Snook, D. G. McCulloch and G. Opletal, Structural analysis of carbonaceous solids using an adapted reverse Monte Carlo algorithm, Carbon 41, 2403 (2003)

T. Petersen, I. Yarovsky, I. Snook, D. G. McCulloch and G. Opletal, Microstructure of an industrial char by diffraction techniques and a Reverse Monte Carlo modeling, Carbon 42, 2457 (2004)

G. Opletal, T. C. Petersen, D. G. McCulloch, I. K. Snook and I. Yarovsky, The structure of disordered carbon solids studied using a hybrid reverse Monte Carlo algorithm, J. Phys.: Condens. Matter 17, 2605 (2005)

G. Opletal, T. C. Petersen, I. K. Snook and D. G. McCulloch, Modeling of structure and porosity in amorphous silicon systems using Monte Carlo methods, J. Chem. Phys. 126, 214705 (2007)

G. Opletal, T. C. Petersen, B. O'Malley, I. K. Snook, D. G. McCulloch and I. Yarovsky, HRMC: Hybrid Reverse Monte Carlo method with silicon and carbon potentials, Comp. Phys. Comm. 178, 777 (2008)

For more information about this technique, please contact George Opletal or visit http://www.hrmccode.com