On the description of atomic motions in dense fluids by the generalized Langevin equation: statistical properties of random forces

Abstract

The suitability of the generalized Langevin equation (GLE) for a realistic description of the behavior of a system of interacting particles in solution is discussed. This study is focused on the GLE for a system of non-Brownian particles, i.e., the masses and the sizes of the solute particles are similar to those of the bath particles. The random and frictional forces on the atoms of the solute due to their collisions with the solvent atoms are characterized from molecular dynamics simulations of simple dense liquid mixtures. The required effective memory functions, which are dependent on the concentration of solute, are obtained by solving a generalized Volterra equation. The validity of the usual assumptions on the statistical properties of the random forces is carefully analyzed, paying special attention to their Gaussianity. The reliability of stochastic simulations based on the GLE is also discussed.

Computer simulation of macromolecules in solution: Modelling of solvent effects on ions in water

“…A similar procedure was employed for determining the friction kernel corresponding to the relative motions of ion-pairs in water from constrained MD simulations [45]. Analogously to W(r), effective memory functions dependent on the solute concentration should be used for reliable GLD simulations of systems of interacting particles [36,43].…”

“…M(t) may be also determined from the random forces on a stationary particle by using equation (2) [36,44]. A similar procedure was employed for determining the friction kernel corresponding to the relative motions of ion-pairs in water from constrained MD simulations [45].…”

“…It should be pointed out that equation (2) (2) is usually taken as an ansatz [36,49]. Despite its approximate character, it has been shown that GLD simulations can provide an accurate reproduction of different liquid properties such as the shape of atomic trajectories (fractal characteristics) [50], relative diffusion [51] or correlations in space and time [36].…”

“…Realistic M(t) functions corresponding to single solute particles can be determined from the corresponding velocity autocorrelation functions C(t) by numerical solution the Volterra equation [42] d C(t) it -M(t -t') V(t') dt' (4) J dt 0 M(t) functions for atoms in simple liquids [36,43] and single ions in water [29,44] were calculated from the C(t] results of MD simulations of the complete systems. These findings corroborate that the exponential or Gaussian M(t) functions usually assumed in theoretical treatments show marked disagreements with more realistic M(t) models.…”

“…Alternatively, electrostatic interactions can be calculated from the Poisson-Boltzmann equation [34]. Langevin dynamics (GLD) simulations [35,36] it is assumed that each component of the velocities and accelerations of each solute particle obey the equation [37,38].…”