Re: CCL:Energy conservation of molecular dynamics in the presence of electrostatic forces

 Charles:  I am a bit confused by your results. The factor that most
 influences integration step size is how rapidly the potential changes
 with distance, not its magnitude. Electrostatic forces are much smoother
 and change more slowly than van der Waal's terms (1/r vs 1/r^10 or 1/r^14).
 A step size of 1fs should give you good energy conservation. You did not
say what code you were using. The usual cause of energy conservation problems 
 is the "stiff" nature of C-H and other similar bonds.
 Here are a few possible problems:
1. Numerically check the correctness of your derivatives in the force calculation. Symmetric finite difference is simple and usually works very well for this and can help track down 
    problems. If you are using someone else's code, then you can skip this.
2. Are you using periodic boundary conditions? If one atom of a neutral dipole pair crosses the periodic boundary, you get a sudden discontinuity in the energy since the charges are now separated by a large distance. You need to apply periodic boundaries to neutral charge groups as a whole. A traditional way of dealing with this is by using cutoffs with a smooth ramp to zero at some large distance based on distance between centers of charge groups. Nowdays, folks use particle mesh Ewald or some other summation method to handle electrostatics. 
 3. Does the energy drift or does it just fluctuate a lot around an average?
    Methods like Gear and Runge-Cutta  are not used in MD because,
though they give very good short-time accuracy, they lack long term stability you get with a symplectic integration scheme like Verlet. If you come from a Physics background you may be accustomed to running much more accurate integrations with tighter error control. This is usually not appropriate for large-scale MD since the exponential divergence of trajectories from their initial conditions renders coordinate accuracy meaningless in less than a picosecond. MD is used mainly for sampling coordinates. Nonetheless, your energy should be stable and not drift with time. Running equivalent time periods with different time steps should 
    show improvement in conservation as steps get small.
 Good luck.
   Richard Gillilan
   MacCHESS, Cornell
 
 Dear CCLers,
 I have a general question about totoal energy conservation of classical
 molecular dynamics (MD) in the presence of electrostatic forces.
 Total energy is perfectly conserved when we do a typical MD with
 only the wan der Waals (Lennard-Jones) potentials, using a time
 step of one femtosecond (e.g. for the Argon gas as a classical example).
 Problems, however, arise when molecules are charged. Because
 electrostatic forces are much more long-ranged (1/r dependence) and
 typically stronger, the magnitude of electrostatic forces on atoms can
 be several hundred (or even thousand) times greater than that of van
 der Waals forces. As a result, the time step has to be accordingly
 reduced for two or three orders of magnitude, in order for the total
 energy to conserve. This means a time step of 0.001-0.01 femtosecond
 has to be applied.
 (EXPLAIN: Most standard algorithms, such as the Verlet method, the Gear
 predictor-corrector method and the Runge-Cutta method, depend on using
the term a*dt^2 to compute the solution stepwisely, where a is the acceleration, dt is the time step. If this term is too large, the numerical error will rapidly propogate, and the solution will diverge. Compared with pure Lennard-Jones simulations, adding the electrostatic forces increase accelerations. Therefore, 
 dt must be decreased in order to keep a*dt^2 down.)
I can see only two ways to solve this problem, both of which turn out to be 
 impractical, as you will see later.
One is to accept the reality, use a smaller time step. But, reducing the time 
 step to 0.001 femtosecond will slow down the simulation 1000 times (in
comparison to pure Lennard-Jones simulations). You will probably never see 
 any emerging behavior of the model because losing your temper.
The other way around is to use smaller charges, as most molecular mechanics force fields do. For example, instead of using 1 for a free radical's charge, one can use 0.01 (and self-explain that this is an effective-field approximation). 
 While this would maintain energy conservation, you might not see the
emerging behaviors due to charges either --- because the electrostatic forces 
 are so weaker than they ought to be, they might not be able to produce
results that only strong interactions can exhibit, such as self-organization.
Energy conservation is generally not an concern for most classic molecular dynamics simulations that assume a heat bath (for controlling the temperature to a desired value, thus remove the numerical errors resulted from large a*dt^2). However, getting the energetics right is of paramount importance to modeling exoergicity/endoergicity of chemical reactions. Unfortunately, I am not aware of anyone mentioning this before. All the molecular simulation books I have (Allen and Tildesley, Leach, Rapaport and so on) do not even mention it at all. My prior experience with CHARMm v27, if I was doing it right, is that it doesn't seem to do energy conservation, even though the NVE protocol is literally specified. 
 I would greatly appreciate any advice and opinion.