arXiv subjects

Jaehyeok Jin

Publications and source records attributed to Jaehyeok Jin.

11 recordsLinked to original sources

arXiv2026

A Bottom-Up Field-Theoretic Framework via Hierarchical Coarse-Graining: Generalized Mode Theory

Multiscale simulations facilitate the efficient exploration of large spatiotemporal scales in chemical and physical systems, yet particle-based simulations become prohibitively expensive at time and length scales beyond the molecular level. Field-theoretic simulations offer an attractive alternative, but most existing formulations rely on top-down approximations and are not systematically connected to atomistic interactions. Here, we present a hierarchical bottom-up framework for constructing auxiliary field representations of molecular liquids directly from microscopic models. We introduce a hierarchical coarse-graining framework that constructs field-theoretic models directly from atomistic liquids. The method first maps atomistic interactions to coarse-grained center-of-mass potentials and regularizes short-range divergences through a perturbative expansion in reciprocal space. Building on the auxiliary field formulation developed in polymer field-theoretic simulations, we then generalize the Hubbard-Stratonovich transformation to arbitrary pair potentials by separating positive and negative Fourier modes and introducing two auxiliary fields. The resulting generalized mode theory extends bottom-up field-theoretic modeling beyond positive-definite kernels and is compatible with existing field-theoretic sampling strategies. By combining formal derivations with numerical regularization and mode-truncation procedures, this work provides the theoretical foundation for scalable, bottom-up field-theoretic simulations of molecular systems.

physics.chem-ph↗

arXiv2025

Microscopic Phase-Field Modeling

Phase-field methods offer a versatile computational framework for simulating large-scale morphological evolution. However, the applicability and predictability of phase-field models are inherently limited by their ad hoc nature, and there is currently no version of this approach that enables truly first-principles predictive modeling of large-scale non-equilibrium processes. Here, we present a bottom-up framework that provides a route to the construction of mesoscopic phase-field models entirely based on atomistic information. Leveraging molecular coarse-graining, we describe the formulation of an order parameter-based free energy functional appropriate for a phase-field description via the enhanced sampling of rare events. We demonstrate our approach on ice nucleation dynamics, achieving a spatiotemporal scale-up of nearly $10^8$ times compared to the microscopic model. Our framework offers a unique approach for incorporating atomistic details into mesoscopic models and systematically bridges the gap between microscopic particle-based simulations and field-theoretic models.

cond-mat.mtrl-sci↗

arXiv2025

Field-Theoretic Simulation of Dean-Kawasaki Dynamics for Interacting Particles

The formulation of a fluctuating hydrodynamic theory for interacting particles is a crucial step in the theoretical description of liquids. The microscopic mappings proposed decades ago by Dean and Kawasaki have played a central role in the analytical treatment of such problems. However, the singular mathematical nature of the density distributions used in these derivations raises concerns about the validity and practical utility of the resulting stochastic partial differential equations, particularly for direct numerical simulations. Recent efforts have centered on establishing a rigorous coarse-graining procedure to regularize the effective Dean-Kawasaki equation. Building on this foundation, we numerically investigate weakly interacting fluids within such a regularized framework for the first time. Our work reveals, at the level of structural correlations, the effects of regularization on the Dean-Kawasaki formalism and paves the way for improved numerical approaches to simulate fluctuating hydrodynamics in liquids.

cond-mat.stat-mech↗

arXiv2025

Understanding Dynamics in Coarse-Grained Models: V. Extension of Coarse-Grained Dynamics Theory to Non-Hard Sphere Systems

Coarse-grained (CG) modeling has gained significant attention in recent years due to its wide applicability in enhancing the spatiotemporal scales of molecular simulations. While CG simulations, often performed with Hamiltonian mechanics, faithfully recapitulate structural correlations at equilibrium, they lead to ambiguously accelerated dynamics. In the first paper of this series [J. Chem. Phys. 158, 034103 (2023)], we proposed the excess entropy scaling relationship to understand the CG dynamics. Then, in the following companion paper [J. Chem. Phys. 158, 034104 (2023)], we developed a theory to map the CG system into a dynamically-consistent hard sphere system to analytically derive an expression for fast CG dynamics. However, many chemical and physical systems do not exhibit hard sphere-like behavior, limiting the extensibility of the developed theory. In this paper, we aim to generalize the theory to the non-hard sphere system based on the Weeks-Chandler-Andersen perturbation theory. Since non-hard sphere-like CG interactions affect the excess entropy term as it deviates from the hard sphere description, we explicitly account for the extra entropy to correct the non-hard sphere nature of the system. This approach is demonstrated for two different types of interactions seen in liquids, and we further provide a generalized description for any CG models using the generalized Gaussian CG models using Gaussian basis sets. Altogether, this work allows for extending the range and applicability of the hard sphere CG dynamics theory to a myriad of CG liquids.

physics.chem-ph↗

arXiv2024

Microscopic Theory of Density Scaling: Coarse-Graining in Space and Time

Understanding the structure and dynamics of liquids is pivotal for the study of larger spatiotemporal processes, especially in glass-forming materials at low temperatures. Density scaling, observed in many molecular systems through experiments, offers an efficient means for exploring a vast range of time scales along a one-dimensional phase diagram. However, the theoretical foundation provided by isomorph theory is of limited use for molecular systems, since currently no first-principles theory exists that can explain the origins of density scaling or make predictions based on it. In this work, we propose a first-principles framework employing coarse-graining in space and time. Spatial coarse-graining reduces a molecule to a center-of-mass-level description by eliminating fast degrees of freedom, while temporal coarse-graining involves averaging fluctuations or correlation functions over characteristic time scales. We show that both approaches enable ab initio estimation of the density scaling coefficient for ortho-terphenyl, consistent with experimental values. Building on these findings, we employ excess entropy scaling to derive a microscopic theory that underpins density scaling from fully atomistic simulations. Our results illuminate the role of coarse-graining in assessing slow fluctuations in molecules and unravel the microscopic nature of density scaling. Ultimately, our proposed framework enables systematic bottom-up approaches for predicting transport coefficients that are otherwise experimentally inaccessible and computationally prohibitive.

cond-mat.soft↗

arXiv2024

Understanding Dynamics in Coarse-Grained Models: IV. Connection of Fine-Grained and Coarse-Grained Dynamics with the Stokes-Einstein and Stokes-Einstein-Debye Relations

Applying an excess entropy scaling formalism to the coarse-grained (CG) dynamics of liquids, we discovered that missing rotational motions during the CG process are responsible for artificially accelerated CG dynamics. In the context of the dynamic representability between the fine-grained (FG) and CG dynamics, this work introduces the well-known Stokes-Einstein and Stokes-Einstein-Debye relations to unravel the rotational dynamics underlying FG trajectories, thereby allowing for an indirect evaluation of the effective rotations based only on the translational information at the reduced CG resolution. Since the representability issue in CG modeling limits a direct evaluation of the shear stress appearing in the Stokes-Einstein and Stokes-Einstein-Debye relations, we introduce a translational relaxation time as a proxy to employ these relations, and we demonstrate that these relations hold for the ambient conditions studied in our series of work. Additional theoretical links to our previous work are also established. First, we demonstrate that the effective hard sphere radius determined by the classical perturbation theory can approximate the complex hydrodynamic radius value reasonably well. Also, we present a simple derivation of an excess entropy scaling relationship for viscosity by estimating the elliptical integral of molecules. In turn, since the translational and rotational motions at the FG level are correlated to each other, we conclude that the "entropy-free" CG diffusion only depends on the shape of the reference molecule. Our results and analyses impart an alternative way of recovering the FG diffusion from the CG description by coupling the translational and rotational motions at the hydrodynamic level.

physics.chem-ph↗

arXiv2024

Hierarchical Framework for Predicting Entropies in Bottom-Up Coarse-Grained Models

The thermodynamic entropy of coarse-grained (CG) models stands as one of the most important properties for quantifying the missing information during the CG process and for establishing transferable (or extendible) CG interactions. However, performing additional CG simulations on top of model construction often leads to significant additional computational overhead. In this work, we propose a simple hierarchical framework for predicting the thermodynamic entropies of various molecular CG systems. Our approach employs a decomposition of the CG interactions, enabling the estimation of the CG partition function and thermodynamic properties a priori. Starting from the ideal gas description, we leverage classical perturbation theory to systematically incorporate simple yet essential interactions, ranging from the hard sphere model to the generalized van der Waals model. Additionally, we propose an alternative approach based on multiparticle correlation functions, allowing for systematic improvements through higher-order correlations. Numerical applications to molecular liquids validate the high fidelity of our approach, and our computational protocols demonstrate that a reduced model with simple energetics can reasonably estimate the thermodynamic entropy of CG models without performing any CG simulations. Overall, our findings present a systematic framework for estimating not only the entropy but also other thermodynamic properties of CG models, relying solely on information from the reference system.

physics.chem-ph↗

arXiv2023

Perturbative Expansion in Reciprocal Space: Bridging Microscopic and Mesoscopic Descriptions of Molecular Interactions

Determining the Fourier representation of various molecular interactions is important for constructing density-based field theories from a microscopic point of view, enabling a multiscale bridge between microscopic and mesoscopic descriptions. However, due to the strongly repulsive nature of short-ranged interactions, interparticle interactions cannot be formally defined in Fourier space, which renders coarse-grained approaches in $\textit{k}$-space somewhat ambiguous. In this paper, we address this issue by designing a perturbative expansion of pair interactions in reciprocal space. Our perturbation theory, starting from reciprocal space, elucidates the microscopic origins underlying zeroth-order (long-range attractions) and divergent repulsive interactions from higher-order contributions. We propose a systematic framework for constructing a faithful Fourier space representation of molecular interactions, capturing key structural correlations in various systems, including simple model systems and molecular coarse-grained models of liquids. Building upon the Ornstein-Zernike equation, our approach can be combined with appropriate closure relations, and to further improve the closure approximations, we develop a bottom-up parametrization strategy for inferring the bridge function from microscopic statistics. By incorporating the bridge function into the Fourier representation, our findings suggest a systematic, bottom-up approach to performing coarse-graining in reciprocal space, leading to the systematic construction of a bottom-up classical field theory of complex aqueous systems.

physics.chem-ph↗

arXiv2023

Understanding Dynamics in Coarse-Grained Models: III. Roles of Rotational Motion and Translation-Rotation Coupling in Coarse-Grained Dynamics

This paper series aims to establish a complete correspondence between fine-grained (FG) and coarse-grained (CG) dynamics by way of excess entropy scaling (introduced in Paper I). While Paper II successfully captured translational motions in CG systems using a hard sphere mapping, the absence of rotational motions in single-site CG models introduces differences between FG and CG dynamics. In this third paper, our objective is to faithfully recover atomistic diffusion coefficients from CG dynamics by incorporating rotational dynamics. By extracting FG rotational diffusion, we unravel, for the first time reported to our knowledge, a universality in excess entropy scaling between the rotational and translational diffusion. Once the missing rotational dynamics are integrated into the CG translational dynamics, an effective translation-rotation coupling becomes essential. We propose two different approaches for estimating this coupling parameter: the rough hard sphere theory with acentric factor (temperature-independent) or the rough Lennard-Jones model with CG attractions (temperature-dependent). Altogether, we demonstrate that FG diffusion coefficients can be recovered from CG diffusion coefficients by (1) incorporating "entropy-free" rotational diffusion with translation-rotation coupling and (2) recapturing the missing entropy. Our findings shed light on the fundamental relationship between FG and CG dynamics in molecular fluids.

physics.chem-ph↗

arXiv2023

Understanding Dynamics in Coarse-Grained Models: I. Universal Excess Entropy Scaling Relationship

Coarse-grained (CG) models facilitate an efficient exploration of complex systems by reducing the unnecessary degrees of freedom of the fine-grained (FG) system while recapitulating major structural correlations. Unlike structural properties, assessing dynamic properties in CG modeling is often unfeasible due to the accelerated dynamics of the CG models, which allows for more efficient structural sampling. Therefore, the ultimate goal of the present series of articles is to establish a better correspondence between the FG and CG dynamics. To assess and compare dynamical properties in the FG and the corresponding CG models, we utilize the excess entropy scaling relationship. For Paper I of this series, we provide evidence that the FG and the corresponding CG counterpart follow the same universal scaling relationship. By carefully reviewing and examining the literature, we develop a new theory to calculate excess entropies for the FG and CG systems while accounting for entropy representability. We demonstrate that the excess entropy scaling idea can be readily applied to liquid water and methanol systems at both the FG and CG resolutions. For both liquids, we reveal that the scaling exponents remain unchanged from the coarse-graining process, indicating that the scaling behavior is universal for the same underlying molecular systems. Combining this finding with the concept of mapping entropy in CG models, we show that the missing entropy plays an important role in accelerating the CG dynamics.

physics.chem-ph↗

arXiv2023

Understanding Dynamics in Coarse-Grained Models: II. Coarse-Grained Diffusion Modeled Using Hard Sphere Theory

The first paper of this series [J. Chem. Phys. 158, 034103 (2023)] demonstrated that excess entropy scaling holds for both fine-grained and corresponding coarse-grained (CG) systems. Despite its universality, a more exact determination of the scaling relationship was not possible due to the semi-empirical nature. In this second paper, an analytical excess entropy scaling relation is derived for bottom-up CG systems. At the single-site CG resolution, effective hard sphere systems are constructed that yield near-identical dynamical properties as the target CG systems by taking advantage of how hard sphere dynamics and excess entropy can be analytically expressed in terms of the liquid packing fraction. Inspired by classical equilibrium perturbation theories and recent advances in constructing hard sphere models for predicting activated dynamics of supercooled liquids, we propose a new approach for understanding the diffusion of molecular liquids in the normal regime using hard sphere reference fluids. The proposed "fluctuation matching" is designed to have the same amplitude of long wavelength density fluctuations (dimensionless compressibility) as the CG system. Utilizing the Enskog theory to derive an expression for hard sphere diffusion coefficients, a bridge between the CG dynamics and excess entropy is then established. The CG diffusion coefficient can be roughly estimated using various equations of the state, and an accurate prediction of accelerated CG dynamics at different temperatures is also possible in advance of running any CG simulation. By introducing another layer of coarsening, these findings provide a more rigorous method to assess excess entropy scaling and understand the accelerated CG dynamics of molecular fluids.

physics.chem-ph↗