Comparison of Friction Parametrization from Dynamics and Material Properties for a Coarse-Grained Polymer Melt

A Gauss-Newton method for iterative optimization of memory kernels for generalized Langevin thermostats in coarse-grained molecular dynamics simulations

In molecular dynamics simulations, dynamically consistent coarse-grained (CG) models commonly use stochastic thermostats to model friction and fluctuations that are lost in a CG description. While Markovian, i.e., time-local, formulations of such thermostats allow for an accurate representation of diffusivities/long-time dynamics, a correct description of the dynamics on all time scales generally requires non-Markovian, i.e., non-time-local, thermostats. These thermostats typically take the form of a Generalized Langevin Equation (GLE) determined by a memory kernel. In this work, we use a Markovian embedded formulation of a position-independent GLE thermostat acting independently on each CG degree of freedom. Extracting the memory kernel of this CG model from atomistic reference data requires several approximations. Therefore, this task is best understood as an inverse problem. While our recently proposed approximate Newton scheme allows for the iterative optimization of memory kernels (IOMK), Markovian embedding remained potentially error-prone and computationally expensive. In this work, we present an IOMK-Gauss-Newton scheme (IOMK-GN) based on IOMK that allows for the direct parameterization of a Markovian embedded model.

Chemically Specific Systematic Coarse-Grained Polymer Model with Both Consistently Structural and Dynamical Properties

The coarse-grained (CG) model serves as a powerful tool for the simulation of polymer systems; its reliability depends on the accurate representation of both structural and dynamical properties. However, strong correlations between structural and dynamical properties on different scales and also a strong memory effect, enforced by chain connectivity between monomers in polymer systems, render developing a chemically specific systematic CG model a formidable task. In this study, we report a systematic CG approach that combines the iterative Boltzmann inversion (IBI) method and the generalized Langevin equation (GLE) dynamics. Structural properties are ensured by using conservative CG potentials derived from the IBI method. To retrieve the correct dynamical properties in the system, we demonstrate that using a combination of a Rouse-type delta function and a time-dependent short-time kernel in the GLE simulation is practically efficient. The former can be used to adjust the long-time diffusion dynamics, and the latter can be reconstructed from an iterative procedure according to the velocity autocorrelation function (ACF) from all-atomistic (AA) simulations. Taking the polystyrene as an example, we show that not only structural properties of radial distribution function, intramolecular bond, and angle distributions can be reproduced but also dynamical properties of mean-square displacement, velocity ACF, and force ACF resulted from our CG model have quantitative agreement with the reference AA model. In addition, reasonable agreements are observed in other collective properties between our GLE-CG model and the AA simulations as well.

Theory and modeling of molecular modes in the NMR relaxation of fluids

Traditional theories of the nuclear magnetic resonance (NMR) autocorrelation function for intra-molecular dipole pairs assume a single-exponential decay, yet the calculated autocorrelation of realistic systems displays a rich, multi-exponential behavior, resulting in anomalous NMR relaxation dispersion (i.e., frequency dependence). We develop an approach to model and interpret the multi-exponential intra-molecular autocorrelation using simple, physical models within a rigorous statistical mechanical development that encompasses both rotational diffusion and translational diffusion in the same framework. We recast the problem of evaluating the autocorrelation in terms of averaging over a diffusion propagator whose evolution is described by a Fokker-Planck equation. The time-independent part admits an eigenfunction expansion, allowing us to write the propagator as a sum over modes. Each mode has a spatial part that depends on the specified eigenfunction and a temporal part that depends on the corresponding eigenvalue (i.e., correlation time) with a simple, exponential decay. The spatial part is a probability distribution of the dipole pair, analogous to the stationary states of a quantum harmonic oscillator. Drawing inspiration from the idea of inherent structures in liquids, we interpret each of the spatial contributions as a specific molecular mode. These modes can be used to model and predict the NMR dipole-dipole relaxation dispersion of fluids by incorporating phenomena on the molecular level. We validate our statistical mechanical description of the distribution in molecular modes with molecular dynamics simulations interpreted without any relaxation models or adjustable parameters: the most important poles in the Padé-Laplace transform of the simulated autocorrelation agree with the eigenvalues predicted by the theory.