Calculation of velocities in Langevin Dynamics - 06/01/15 08:37 AM

Dear advanced users,

Recently I am studying the source code of CHARMM (c36b2) and get a little confused of the calculation of velocities in Langevin Dynamics.

Based on the equations provided in reference [1], one can readily figure out the algorithm of the coordinate propagation.

However, for the calculation of velocities, the code provided for the LEAP method is :

------------------dynlng.src--------------------

gam=timfac*fbeta(i)*delta

gamma(i+natom3)=half*sqrt(one+gam*half)/delta

------------------dynamc.src--------------------

fact=gamma(i+natom3)

vx(i)=(xnew(i)+xold(i))*fact

Thus, there seems to be an additional coefficient, sqrt(one+gam*half), comparing to typical Verlet methods (as in reference [2]).

So I was wondering if there is any theoretical foundation of this coefficient.

Any suggestions would be greatly appreciated.

References:

[1] A. BrĂ¼nger, C. L. Brooks III, M. Karplus, Stochastic boundary conditions for molecular dynamics simulations of ST2 water. Chem. Phys. Letters, 1984, 105 (5) 495-500.

[2] L. Verlet, Computer experiments on classical fluids: I. Thermodynamical properties of Lennard-Jones molecules. Phys. Rev., 1967, 159 (1) 98-103

Recently I am studying the source code of CHARMM (c36b2) and get a little confused of the calculation of velocities in Langevin Dynamics.

Based on the equations provided in reference [1], one can readily figure out the algorithm of the coordinate propagation.

However, for the calculation of velocities, the code provided for the LEAP method is :

------------------dynlng.src--------------------

gam=timfac*fbeta(i)*delta

gamma(i+natom3)=half*sqrt(one+gam*half)/delta

------------------dynamc.src--------------------

fact=gamma(i+natom3)

vx(i)=(xnew(i)+xold(i))*fact

Thus, there seems to be an additional coefficient, sqrt(one+gam*half), comparing to typical Verlet methods (as in reference [2]).

So I was wondering if there is any theoretical foundation of this coefficient.

Any suggestions would be greatly appreciated.

References:

[1] A. BrĂ¼nger, C. L. Brooks III, M. Karplus, Stochastic boundary conditions for molecular dynamics simulations of ST2 water. Chem. Phys. Letters, 1984, 105 (5) 495-500.

[2] L. Verlet, Computer experiments on classical fluids: I. Thermodynamical properties of Lennard-Jones molecules. Phys. Rev., 1967, 159 (1) 98-103