How important is floating-point precision in molecular dynamics?

as usual the short answer is: it depends ...

the slightly longer answer is: Practically all systems you'd simulate with MD are chaotic, meaning that your results depend sensitively on the initial conditions. So, no matter how precise your hardware is, you will ALWAYS end up with noticeably different trajectories after a very short time span, but your averages should not be affected. For example if you simulate a small sample of liquid water in the NVT ensemble, you will end up with totally different coordinates of individual water molecules, depending on the random seed of the algorithm that generates your initial velocities, but the total energy and pressure you get should be the same (inside small error bars if you allow for sufficient total simulation time)

In practice we are using either single or double precision. If single precision is used its typically faster (very much so with GPUs). As for the results, as stated above by Vadim, the problem are the round of errors. If you do MD of a protein in solution, and you are merely interested in the protein structure (the coordinates that are the result of a rather simple set of equations), you are certainly fine with single precision. But the more "higher order" the terms you are interested in are, the more pronounced the round-off errors get. For example if you consider things like free energies or thermal conductivity, you calculate numbers based on coordinates, so you add another round of calculations on top of the first one (the calculation of the coordinates) and with each such manipulation you lose at least one digit of precision. However, for most practical purposes it will never get as far as you ending up with random numbers when you use single precision. A good way to combine speed and precision is to work with mixed precision (single for coordinates and velocities, double for higher order terms) as for example done in Gromacs - see: http://manual.gromacs.org/current/reference-manual/definitions.html#mixed-or-double-precision

mic