The adaptive kinetic Monte Carlo (aKMC) method is a method to coarse grain molecular dynamics for rare event systems. 1 2 A rare event system is one in which the interesting dynamics is governed by short transitions between stable states. The fast vibrational motion within a stable state is considered to be in equilibrium and described statisitcally. A transition between states is assumed to be first order, since it is a rare events, and the rate of the transition is calculated from the harmonic approximation to transition state theory (hTST).

The hTST approximation of a transition rate is calculated from the energy difference between the saddle point along the minimum energy path for the transition and the initial minimum. The vibrational modes at these points are also used to calculate the prefactor. An hTST rate is of the standard Arrhenius form $$R = v \exp (-\Delta E/kT)$$ where $$v$$ is the product of all positive modes at the minimum divided by those at the saddle, $$\Delta E$$ is the energy barrier, and $$kT$$ is the thermal enregy.

In order to propogate the dynamics within aKMC, a list of all possible rates leading away from the current stable state to any other state is required. Formally, there are an enourmously large number of such transitions (also called processes) available in a typical atomic system, but in fact only the transitions with the fastest rates with the highest probability of happening are required. The search for processes is then limited to those with rates on the same order as the fastest processes found.

The search for possible processes is the primary task of the aKMC simulations. Each client does a minimum mode (minmode) following search from the miminum of the current state and tries to find a saddle point which connects from the minimum in the current state to an adjacent state. 3 A saddle point is connected to a state if a minimization initiated along the negative mode at the saddle converges to the minimum of that state.

Each client is tasked with one or more such searches. It climbs from the minimum to a saddle, and if successful, it minimizes on either side of the saddle to determine the connecting states. The prefactor for the transition is also calculated by finite difference and the hTST rate is calculated. These data are reported back to the server.

The server is reponsible for the time evolution of the system by the KMC algorithm. Each process leading to a new state is tabulated in a rate table and one transition is selected stochastically with a probability proportional to its rate. The transition time is drawn from a first-order distribution for the total rate of escape from the state.

The following describes options for running an aKMC simulation, including both KMC options on the server-side and minmode following saddle point searching options on the client-side. Each option is specified in the config.ini file under the section name given. Default values for each option is given along with a brief description.

## [AKMC] Options¶

confidence_scheme

default: new

options: old, new

confidence: The confidence (out of 1.0) criterion for moving to the next state.

default: 0.99

confidence_correction:

default: False

thermally_accessible_window: Processes with barriers within this number of kT above the lowest barrier will be used in the rate table and for confidence calculations.

default: 20.0

thermally_accessible_buffer: Processes with barriers of thermally_accessible_window + thermally_accessible_buffer will be stored , in the event that they are thermally accessible later, but are not used in the rate table or for the confidence calculations. Processes with barriers higher than the sum of these two values will be discarded.

default: 0.0

server_side_process_search: If true the server does not send out “process_search” jobs instead it manages individual dimer, minimization, and hessian calculations. This option is usually used when a single “process_search” job will take a long time (hours or longer).

default: False

max_kmc_steps: The maximum number of KMC transitions in a row. In MPI or continuous mode, EON will exit after performing this many KMC steps. If this is set to 0, EON will run forever.

default: 0

References

1
1. Henkelman and H. Jónsson, “Long time scale kinetic Monte Carlo simulations without lattice approximation and predefined event table” J. Chem. Phys. 115, 9657-9666 (2001). doi:10.1063/1.1415500

2
1. Xu and G. Henkelman, “Adaptive kinetic Monte Carlo for first-principles accelerated dynamics” J. Chem. Phys. 129, 114104 (2008). doi:10.1063/1.2976010

3
1. Henkelman and H. Jónsson, “A dimer method for finding saddle points on high dimensional potential surfaces using only first derivatives” J. Chem. Phys. 111, 7010-7022 (1999).