Transferable local density-dependent friction in tert-butanol/water mixtures.

Coarse-grained (CG) models informed from molecular dynamics simulations provide a way to represent the structure of an underlying all-atom (AA) model by deriving an effective interaction potential. However, this leads to a speed-up in dynamics due to the lost friction, which is especially pronounced in CG implicit solvent models. Applying a thermostat based on the Langevin equation (LE) provides a way to represent the long-time dynamics of CG particles by reintroducing friction to the system. To improve the representability CG models of heterogeneous molecular mixtures and their transferability over the mixture compositions, we parameterize an LE thermostat in which the friction coefficient depends on the local particle density (LD). The thermostat friction was iteratively optimized with a Markovian variant of the recently introduced Iterative Optimization of Memory Kernels (IOMK) method. We simulated tert-butanol/water mixtures over a range of compositions, which show a distinct clustering behavior. Our model with LD-dependent friction reproduces the AA diffusion coefficients well over the full range of mixtures and is, therefore, transferable with respect to dynamics.

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.

Dynamical coarse-grained models of molecular liquids and their ideal and non-ideal mixtures.

Coarse-grained (CG) simulation models of condensed-phase systems can be derived with well-established methods that perform coarse-graining in space and provide an effective Hamiltonian with which some of the structural and thermodynamic properties of the underlying fine-grained (FG) reference system can be represented. Coarse-graining in time potentially provides CG models that furthermore represent dynamic properties. However, systematic efforts in this direction have so far been limited, especially for moderately coarse-grained, chemistry-specific systems with complicated conservative interactions. With the aim of representing structural, thermodynamic, and dynamic properties in CG simulations of multi-component molecular systems, we investigated a recently introduced method in which the force on a CG particle originates from conservative interactions with surrounding particles and non-Markovian dissipative interactions, the latter introduced by means of a colored-noise thermostat. We examined two different methods to derive isotropic memory kernels required for integrating the corresponding generalized Langevin equation (GLE) of motion, based on the orthogonal dynamics of the FG forces and on an iterative optimization scheme. As a proof of concept, we coarse-grain single-component molecular liquids (cyclohexane, tetrachloromethane) and ideal and non-ideal binary mixtures of cyclohexane/tetrachloromethane and ethanol/tetrachloromethane, respectively. We find that for all systems, the FG single particle velocity auto-correlation functions and, consequently, both the short time and long time diffusion coefficients can be quantitatively reproduced with the CG-GLE models. We furthermore demonstrate that the present GLE-approach leads to an improved description of the rate with which the spatial correlations decay, which is artificially accelerated in the absence of dissipation.

Bottom-Up Informed and Iteratively Optimized Coarse-Grained Non-Markovian Water Models with Accurate Dynamics.

Molecular dynamics (MD) simulations based on coarse-grained (CG) particle models of molecular liquids generally predict accelerated dynamics and misrepresent the time scales for molecular vibrations and diffusive motions. The parametrization of Generalized Langevin Equation (GLE) thermostats based on the microscopic dynamics of the fine-grained model provides a promising route to address this issue, in conjunction with the conservative interactions of the CG model obtained with standard coarse graining methods, such as iterative Boltzmann inversion, force matching, or relative entropy minimization. We report the application of a recently introduced bottom-up dynamic coarse graining method, based on the Mori-Zwanzig formalism, which provides accurate estimates of isotropic GLE memory kernels for several CG models of liquid water. We demonstrate that, with an additional iterative optimization of the memory kernels (IOMK) for the CG water models based on a practical iterative optimization technique, the velocity autocorrelation function of liquid water can be represented very accurately within a few iterations. By considering the distinct Van Hove function, we demonstrate that, with the presented methods, an accurate representation of structural relaxation can be achieved. We consider several distinct CG potentials to study how the choice of the CG potential affects the performance of bottom-up informed and iteratively optimized models.

Cross-correlation corrected friction in generalized Langevin models: Application to the continuous Asakura-Oosawa model.

The development of dynamically consistent coarse-grained models for molecular simulations is often based on generalized Langevin equations, motivated by the application of the projection operator formalism (Mori-Zwanzig theory). While Mori's projection operator yields linear generalized Langevin equations that can be computationally efficiently implemented in numerical simulations, the downside is that Mori's generalized Langevin equation does not encompass the multi-body potential of mean force required to correctly encode structural and thermodynamic properties in coarse-grained many-body systems. Zwanzig's projection operator yields nonlinear generalized Langevin equations including the multi-body potential of mean force, while the remaining force contributions are not as cheap to implement in molecular simulation without making it formally hard to justify approximations. For many-particle coarse-grained models, due to computational and conceptual simplicity, an often used approach is to combine nonlinear conservative interactions with linear expressions to model dissipation. In a previous study [V. Klippenstein and N. F. A. van der Vegt, J. Chem. Phys. 154, 191102 (2021)], we proposed a method to parameterize such models to achieve dynamic consistency in coarse-grained models, allowing us to reconcile Mori's and Zwanzig's approach for practical purposes. In the current study, by applying the same strategy, we develop coarse-grained implicit solvent models for the continuous Asakura-Oosawa model, which under certain conditions allows us to develop very accurate coarse-grained potentials. By developing coarse-grained models for different reference systems with varying parameters, we test the broader applicability of the proposed procedure and demonstrate the relevance of accurate coarse-grained potentials in bottom-up derived dissipative models. We study how different system parameters affect the dynamic representability of the coarse-grained models. In particular, we find that the quality of the coarse-grained potential is crucial to correctly model the backscattering effect due to collisions on the coarse-grained scale. As hydrodynamic interactions are not explicitly modeled in the presented coarse-graining approach, deviations are observed in the long-time dynamics. The Asakura-Oosawa model allows for the tuning of system parameters to gain an improved understanding of this limitation. We also propose three new iterative optimization schemes to fine-tune the generalized Langevin thermostat to exactly match the reference velocity-autocorrelation function.

Cross-correlation corrected friction in (generalized) Langevin models.

We propose a route for parameterizing isotropic (generalized) Langevin [(G)LE] thermostats with the aim to correct the dynamics of coarse-grained (CG) models with pairwise conservative interactions. The approach is based on the Mori-Zwanzig formalism and derives the memory kernels from Q-projected time correlation functions. Bottom-up informed (GLE and LE) thermostats for a CG star-polymer melt are investigated, and it is demonstrated that the inclusion of memory in the CG simulation leads to predictions of polymer diffusion in quantitative agreement with fine-grained simulations. Interestingly, memory effects are observed in the diffusive regime. We demonstrate that previously neglected cross-correlations between the "irrelevant" and the CG degree of freedom are important and lie at the origin of shortcomings in previous CG simulations.

Introducing Memory in Coarse-Grained Molecular Simulations.

Preserving the correct dynamics at the coarse-grained (CG) level is a pressing problem in the development of systematic CG models in soft matter simulation. Starting from the seminal idea of simple time-scale mapping, there have been many efforts over the years toward establishing a meticulous connection between the CG and fine-grained (FG) dynamics based on fundamental statistical mechanics approaches. One of the most successful attempts in this context has been the development of CG models based on the Mori-Zwanzig (MZ) theory, where the resulting equation of motion has the form of a generalized Langevin equation (GLE) and closely preserves the underlying FG dynamics. In this Review, we describe some of the recent studies in this regard. We focus on the construction and simulation of dynamically consistent systematic CG models based on the GLE, both in the simple Markovian limit and the non-Markovian case. Some recent studies of physical effects of memory are also discussed. The Review is aimed at summarizing recent developments in the field while highlighting the major challenges and possible future directions.

Chemical bonding in initial building blocks of semiconductors: Geometrical structures and optical absorption spectra of isolated CdSe 2 + and Cd2 Se 2 + species.

We present the first experimental optical absorption spectra of isolated CdSe 2 + and Cd2 Se 2 + species in the photon energy range ℏω = 1.9-4.9 eV. We probe the optical response by measuring photodissociation cross sections and combine our results with time-dependent density functional theory and equation-of-motion coupled cluster calculations. Structural candidates for the time-dependent excited state calculations are generated by a density functional theory based genetic algorithm as a global geometry optimization tool. This approach allows us to determine the cluster geometries present in our molecular beams by a comparison of experimental spectra with theoretical predictions for putative global minimum candidates. For CdSe 2 + , an excellent agreement between the global minimum and the experimental results is presented. We identify the global minimum geometry of Cd2 Se 2 + as a trapezium, which is built up of a neutral Se2 and a cationic Cd 2 + unit, in contrast to what was previously proposed. We find an excellent overall agreement between experimental spectra and excited state calculations. We further study the influence of total and partial charges on the optical and geometric properties of Cd2Se2 and compare our findings to CdSe quantum dots and to bulk CdSe.