Position-Dependent Diffusion Constant of Molecules in Heterogeneous Systems as Evaluated by the Local Mean Squared Displacement

Abstract

The authors propose a novel method to evaluate the position-dependent diffusion constant by analyzing unperturbed segments of a trajectory determined by the additional flat-bottom potential. The accuracy of this novel method is first established by studying homogeneous systems, where the reference value can be obtained by the Einstein relation. The applicability of this new method to heterogeneous systems is then demonstrated by studying a hydrophobic solute near a hydrophobic wall. The proposed method is also comprehensively compared with popular conventional methods, whereby the significance of the present method is illustrated. The novel method is powerful and useful for studying kinetics in heterogeneous systems based on molecular dynamics calculations.

Momentum Removal to Obtain the Position-Dependent Diffusion Constant in Constrained Molecular Dynamics Simulation

“…The temperature was controlled by a Nosé-Hoover thermostat 31,32 at 300 K with a time constant of 100 fs. The effect of the thermostat on the resultant diffusion constant has been shown to be negligible in these conditions 20 for various methods, thus allowing us to get the position-dependent diffusion constant. The total force acting on the COM of the methane molecule was sampled every 1 fs.…”

“…Because of its importance, many methods [10][11][12][13][14][15][16][17][18][19] have been proposed to obtain the position-dependent diffusion coefficient. Two of us and other coworkers have also previously proposed a method for obtaining the positiondependent diffusion coefficient with high accuracy in any heterogeneous system 20 . Among the methods proposed so far, the Marrink-Berendsen (MB) method is one of the best-known methods used to calculate the position-dependent diffusion coefficient [21][22][23][24][25][26] .…”

“…Despite systematic underestimation 27,20 , the method is widely used these days because the position-dependent diffusion coefficient can be calculated easily by the MB method with existing MD calculation packages. In the MB method, the center of mass (COM) of the molecule is constrained to a certain position, and the diffusion coefficient can be obtained by the force autocorrelation function (FACF) of the COM of the molecule.…”

Momentum removal to obtain the position‐dependent diffusion constant in constrained molecular dynamics simulation

“…Because of its importance, many methods 10–19 have been proposed to obtain the position‐dependent diffusion coefficient. Two of us and other coworkers have also previously proposed a method for obtaining the position‐dependent diffusion coefficient with high accuracy in any heterogeneous system 20 …”

“…In this method, the center of mass (COM) of the molecule is constrained to a certain position, and the diffusion coefficient can be obtained by the force autocorrelation function (FACF) of the COM of the molecule. A downside is systematic underestimation of the resultant diffusion coefficient, 27,20 which can be attributed to perturbation of dynamics arising from constraints. In other words, the memory kernel of a freely moving particle may not always be well approximated by that of a constrained particle.…”