Dynamic Monte Carlo method
Encyclopedia
In chemistry
, dynamic Monte Carlo (DMC) is a method for modeling the dynamic behaviors of molecule
s by comparing the rates of individual steps with random number
s. Unlike the Metropolis Monte Carlo method, which has been employed to study systems at equilibrium
, the DMC method is used to investigate non-equilibrium systems such as a reaction
, diffusion
, and so-forth (Meng and Weinberg 1994). This method is mainly applied to analyze adsorbates' behavior on surfaces. The DMC method is very similar to the kinetic Monte Carlo
method.
There are several well-known methods for performing DMC simulations, including the First Reaction Method (FRM) and Random Selection Method (RSM). Although the FRM and RSM give the same results from a given model, the computer resource
s are different depending on the applied system.
In the FRM, the reaction whose time is minimum on the event list is advanced. In the event list, the tentative times for all possible reactions are stored. After the selection of one event, the system time is advanced to the reaction time, and the event list is recalculated. This method is efficient in computation time because the reaction always occurs in one event. On the other hand, it consumes a lot of computer memory
because of the event list. Therefore, it is difficult to apply to large-scale systems.
The RSM decides whether the reaction of the selected molecule proceeds or not by comparing the transition probability with a random number. In this method, the reaction does not necessarily proceed in one event, so it needs significantly more computation time than FRM. However, this method saves computer memory because it does not use an event list. Large-scale systems are able to be calculated by this method.
Chemistry
Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....
, dynamic Monte Carlo (DMC) is a method for modeling the dynamic behaviors of molecule
Molecule
A molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...
s by comparing the rates of individual steps with random number
Random number
Random number may refer to:* A number generated for or part of a set exhibiting statistical randomness.* A random sequence obtained from a stochastic process.* An algorithmically random sequence in algorithmic information theory....
s. Unlike the Metropolis Monte Carlo method, which has been employed to study systems at equilibrium
Chemical equilibrium
In a chemical reaction, chemical equilibrium is the state in which the concentrations of the reactants and products have not yet changed with time. It occurs only in reversible reactions, and not in irreversible reactions. Usually, this state results when the forward reaction proceeds at the same...
, the DMC method is used to investigate non-equilibrium systems such as a reaction
Chemical reaction
A chemical reaction is a process that leads to the transformation of one set of chemical substances to another. Chemical reactions can be either spontaneous, requiring no input of energy, or non-spontaneous, typically following the input of some type of energy, such as heat, light or electricity...
, diffusion
Diffusion
Molecular diffusion, often called simply diffusion, is the thermal motion of all particles at temperatures above absolute zero. The rate of this movement is a function of temperature, viscosity of the fluid and the size of the particles...
, and so-forth (Meng and Weinberg 1994). This method is mainly applied to analyze adsorbates' behavior on surfaces. The DMC method is very similar to the kinetic Monte Carlo
Kinetic Monte Carlo
The kinetic Monte Carlo method is a Monte Carlo method computer simulation intended to simulate the time evolution of some processes occurring in nature. Typically these are processes that occur with a given known rate...
method.
There are several well-known methods for performing DMC simulations, including the First Reaction Method (FRM) and Random Selection Method (RSM). Although the FRM and RSM give the same results from a given model, the computer resource
Computational resource
In computational complexity theory, a computational resource is a resource used by some computational models in the solution of computational problems....
s are different depending on the applied system.
In the FRM, the reaction whose time is minimum on the event list is advanced. In the event list, the tentative times for all possible reactions are stored. After the selection of one event, the system time is advanced to the reaction time, and the event list is recalculated. This method is efficient in computation time because the reaction always occurs in one event. On the other hand, it consumes a lot of computer memory
Computer memory
In computing, memory refers to the physical devices used to store programs or data on a temporary or permanent basis for use in a computer or other digital electronic device. The term primary memory is used for the information in physical systems which are fast In computing, memory refers to the...
because of the event list. Therefore, it is difficult to apply to large-scale systems.
The RSM decides whether the reaction of the selected molecule proceeds or not by comparing the transition probability with a random number. In this method, the reaction does not necessarily proceed in one event, so it needs significantly more computation time than FRM. However, this method saves computer memory because it does not use an event list. Large-scale systems are able to be calculated by this method.