Abstract
An attempt to generalize the Langevin dynamics simulation method is presented based on the generalized Langevin theory of liquids, in which the dynamics of both solute and solvent is treated by the generalized Langevin equations, but the integration of the equation of motion of solute is made in the manner similar to the ordinary molecular dynamics simulation with discretized time steps along a trajectory. A preliminary result is derived based on an assumption of the uniform solvent density. The result is regarded to be a microscopic generalization of the phenomenological Langevin theory for the harmonic oscillator immersed in a continuum solvent developed by Wang and Uhlenbeck.
Highlights
It has been five decades since the molecular dynamics simulation scored its first step in the study of liquids and solutions [1]
We have proposed theories to describe the dynamics of molecular liquids, which combines the reference interactionsite method (RISM) with the generalized Langevin equation (GLE): the liquid structure by RISM and the dynamics by GLE [4]
That is our motivation to formulate the “generalized Langevin dynamics simulation” in which the dynamics of both solute and solvent is treated on equal footing by the generalized Langevin equations, but the integration of the equation of motion of solute is made in the manner similar to the ordinary molecular dynamics simulation with discretized time steps along a trajectory
Summary
It has been five decades since the molecular dynamics simulation scored its first step in the study of liquids and solutions [1]. The method is facing a high barrier which may not be overcome by the improvement of computing power alone One of these problems is the phenomena related to the thermodynamic limit essentially such as the phase transition and separation. It is an essential requirement to describe the liquid dynamics subject to the field from protein in order to be able to handle the higher order moments of the density fluctuations. The new theory has a potential capability of describing the higher order moment of the density fluctuations if it is incorporated into the generalized Langevin treatment of liquids. That is our motivation to formulate the “generalized Langevin dynamics simulation” in which the dynamics of both solute and solvent is treated on equal footing by the generalized Langevin equations, but the integration of the equation of motion of solute is made in the manner similar to the ordinary molecular dynamics simulation with discretized time steps along a trajectory. We consider the limit of uniform solvent density in order to make contact with the classical Langevin treatment
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