Why do people prefer time reversible algorithms in Molecular Dynamics? For example Verlet integration is preferred to Runge-Kutta, Nose Hoover thermostat preferred to Andersen, etc...Are there any reasons other than the ability to reproduce the same results by different researchers with same initial conditions? Will affect the thermodynamic properties of the system?
There are different issues with different algorithms, and I don't think time reversibility can be singled out as the main criterion. For MD integrators, the main concern would be whether they are symplectic (i.e., approximately conserve the Hamiltonian during a long evolution of a chaotic system): Verlet is, while Runge-Kutta is not.
On the other hand, I think that the lack of time reversibility could affect the kinetic behavior of your system, as (for instance) in equilibrium both the forward and backward rates of any process have to be equal. It is indeed a known issue that the Andersen thermostat can give incorrect kinetic data.
In general, in chaotic systems, you hardly ever want to reproduce the same result from the same initial conditions. Rather, the main concern in MD is - as I view it - to sample the right ensemble of states in order to get correct thermodynamic properties, and to sample the right ensemble of trajectories to reproduce the correct kinetics.
@ Milosz: Thank you for the reply. Thanks for the keyword symplectic integrators. I found this link [attached] and was very helpful and answered most my doubts.
http://bionum.cs.purdue.edu/Skee98b.pdf
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