Dynamic friction on rigid and flexible bonds

Abstract

A wide variety of problems involving molecular motion in liquids can be formulated in terms of the generalized Langevin equation (GLE). The friction coefficient on a molecular bond or on some more complicated reaction coordinate is then required. An often used approximation is to set the dynamic friction constant equal to the autocorrelation function of the fluctuating force exerted on the frozen bond by the remaining unfrozen coordinates. The true friction involves projection operators and should differ from this approximation. In this paper we derive various identities and show that the rigid bond approximation is the high frequency limit of the true dynamic friction coefficient. We compute the ‘‘true’’ dynamic friction and the friction approximated on the basis of the rigid or frozen bond and show that the asymptotic limit is very accurate even for frequencies not much larger than the peak frequency of the solvent spectral density. Two different dynamical systems are studied using MD simulations with our newly devised NAPA integrator for systems with disparate time scales. In one the molecule is not allowed to rotate and in the other it is allowed to rotate. Interestingly, even for very long rotational reorientation times, small but significant differences in the long time decay of the bond dynamic friction are observed for rotational and nonrotational molecules—differences, however, that do not produce large differences in the static friction constants.

Molecular dynamics simulations of sodium chloride solutions in water–dimethyl sulphoxide mixtures: Potentials of mean force and solvation structures

“…The potential of mean force, W͑r͒, of the ion pair in the presence of the solvent can then be calculated as 39 W͑r ͒ϭϪ ͵ F͑r ͒drϭW͑ r 0 ͒Ϫ ͵ r 0 r F͑r ͒dr. ͑7͒…”

“…35 The equations of motion were solved numerically using the Verlet algorithm 38 using a time step of 0.5 fs. For the system consisting of two ions ͑A,B͒ and N solvent molecules, the force due to the solute-solvent interactions, acting along the interionic axis is evaluated as 39 ⌬F͑r,t ͒ϭ ͫ where F AS (r,t) and F BS (r,t) are the total forces on the solute particles A and B due to the solvent molecules; m A and m B are the individual masses of the ions; is the reduced mass of the ion pair and r is the unit vector along the AB direction. The ⌬F(r,t) values are calculated at each time step and then averaged over the whole simulation.…”

The Role of Attractive Interactions in Self-Diffusion

“…The simplest (and least chemically important) process of this type is self-diffusion. Other, more complicated (and, chemically, more important) examples include vibrational relaxation, [1][2][3][4] solvation dynamics, 5,6 and quadrupolar relaxation. 7,8 A starting point for many theories of self-diffusion is kinetic theory.…”

The Enskog theory for classical vibrational energy relaxation in fluids with continuous potentials

“…The atomic mass and size of the diatomic solute are the same as those of an argon atom. In this table, the theoretical prediction is compared both with the simulation results of Berne et al 5 and the INM predictions. 6 In Ref.…”

“…2 Equation ͑4͒ gives a simple way to relate the solvent dynamic response to the VER rate. The validity of the freedraining approximation is systematically examined by Berne et al using molecular dynamics simulations 5 and the Zwanzig-Bixon model based on the continuous hydrodynamic equation, 8 and it is found that the approximation is not verified for a short bond length. However, this approximation is still semiquantitatively reliable, and so is the LandauTeller expression, at least for the low-frequency mode.…”