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On Increasing the Timestep in Molecular Dynamics.

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We examine how the two properties of the Langevin/implicit-Euler scheme
for molecular dynamics (MD) - stability over large time steps and damping
of high-frequency vibrations greater than some cutoff frequency c_{
}-
affect the dynamics of a liquid butane model. For time steps t__<__20
fs with a "natural" cutoff _{c}=k_{b}T/
(k_{b
}and are
Boltzmann's and Planck's constants, T=temperature ), the associated kinetic
energy is greater than 85% of its value at t=1
fs, where the connection to a heat bath is weak and the generated trajectories
by our scheme and conventional MD are similar. At larger t
the connection to the heat bath is much stronger, and for t>20
fs, the intrinsic damping of the scheme sets in. The comparison of bond-length
and dihedral-angle distributions at three different time steps reveals
a small, broadening trend at larger t.
The differences in a dynamic property, the velocity autocorrelation function,
are however much larger. There is a drastic difference for 2 and 20 fs,
and for t>40 fs most of the
motion between time steps is damped and more random. Thus while the Langevin
equation per se gives a Boltzmann distribution, the expected configurational
sampling can be obtained as long as the numerical damping does not disturb
the balance between the random and damping terms. Consequently, for studying
certain dynamic functions time steps in the same range as in conventional
MD are needed, but for static properties larger time steps can be used.

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