Time-propagation algorithms in molecular dynamics: Difference between revisions

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{{TAG|IBRION}}, {{TAG|MDALGO}}, [[Thermostats]]
{{TAG|IBRION}}, {{TAG|MDALGO}}, [[Thermostats]]


[[Category:Theory]][[Category:Molacular dynamics]][[Category:Thermostats]]
[[Category:Theory]][[Category:Molecular dynamics]][[Category:Thermostats]]

Latest revision as of 10:28, 18 October 2024

In molecular dynamics simulations, the ionic positions and velocities are monitored as functions of time . This time dependence is obtained by integrating Newton's equations of motion. When integrating the equations of motions it is important to use symplectic algorithms which conserve the phase-space volume. To solve the equations of motion under symplectic conditions, various integration algorithms have been developed. The time dependence of a particle can be expressed in a Taylor expansion

A backward propagation in time by a time step can be obtained in a similar way

Adding these two equation gives and rearrangement gives the Verlet algorithm

The Verlet algorithm can be rearranged to the Velocity-Verlet algorithm by inserting

Velocity-Verlet integration scheme

The Velocity-Verlet algorithm can be decomposed into the following steps:

  1. compute forces from density functional theory or machine learning

From these equations it can be seen that the velocity and the position vectors are synchronous in time.

Leap-Frog integration scheme

Another form of the Verlet algorithm can be written in the form of the Leap-Frog algorithm. The Leap-Frog algorithm consists of the following steps:

  1. compute forces from density functional theory or machine learning

In this form the velocity and the position vectors are asynchronous in time.

Thermostats and used integrators

MDALGO thermostat integration algorithm
0 Nose-Hoover Velocity-Verlet
1 Andersen Leap-Frog
2 Nose-Hoover Leap-Frog
3 Langevin Velocity-Verlet
4 NHC Velocity-Verlet
5 CSVR Leap-Frog
5 Multiple Andersen Leap-Frog

Related tags and articles

IBRION, MDALGO, Thermostats