arXiv subjects

Ralf Ludwig

Publications and source records attributed to Ralf Ludwig.

10 recordsLinked to original sources

arXiv2026

Computing Shear Viscosities from Molecular Dynamics Simulation: Comparing the OrthoBoXY Approach with the Green-Kubo Method

We calculated shear viscosities of 15 neat molecular liquids from equilibrium molecular dynamics (MD) simulations using the OrthoBoXY approach and compare them to viscosities calculated via the Green-Kubo method. Data from both methods agree very well. Here, we show how to avoid pitfalls while computing the OrthoBoXY-data to obtain optimal results. From simulations of multiple system sizes, we could verify that the viscosity of molecular liquids is not influenced by finite size effects down to systems as small as 250 molecules. Moreover, we demonstrate that also the standard error of the viscosity is nearly independent of the system size. This is shown to be a consequence of a compensation effect of an increasing accuracy of the self-diffusion coefficients with increasing systems-size and the system-size dependent weighting according to the OrthoBoXY-equation. As a consequence, we suggest that it is preferable to run simulations of smaller systems with longer simulation times rather than larger systems with shorter simulation runs. In addition, we discuss a refinement of the recently introduced "recipe" for OrthoBoXY simulations block-lengths $\tau_\mathrm{block}$. Based on data from simulations with varying run-lengths, we suggest the following modification: for highly viscous systems, the value of $\tau_\mathrm{block}$ might safely be scaled by a factor of $1/8$, significantly reducing the computational resources needed. For less viscous systems, the value of $\tau_\mathrm{block}$ might safely be scaled by a factor of $1/4$. For systems with high fluidity, the value of $\tau_\mathrm{block}$ should not be scaled down in order to achieve reliable results. When using a smaller system size of 250 molecules, these refinements are leading up to a 24-fold reduction in computational cost compared to the previous recommended set-up without sacrificing numerical accuracy.

cond-mat.stat-mech↗

arXiv2024

When Theory Meets Experiment: What Does it Take to Accurately Predict $^1$H NMR Dipolar Relaxation Rates in Neat Liquid Water from Theory?

In this contribution, we compute the $^1$H nuclear magnetic resonance (NMR) relaxation rate of liquid water at ambient conditions. We are using structural and dynamical information from Coupled Cluster Molecular Dynamics (CCMD) trajectories generated at CCSD(T) electronic structure accuracy while considering also nuclear quantum effects in addition to consulting information from X-ray and neutron scattering experiments. Our analysis is based on a recently presented computational framework for determining the frequency-dependent NMR dipole-dipole relaxation rate of spin $1/2$ nuclei from Molecular Dynamics (MD) simulations, which allows for an effective disentanglement of its structural and dynamical contributions, and is including a correction for finite-size effects inherent to MD simulations with periodic boundary conditions. A close to perfect agreement with experimental relaxation data is achieved if structural and dynamical informations from CCMD trajectories are considered including a re-balancing of the rotational and translational dynamics, according to the product of the self-diffusion coefficient and the reorientational correlation time of the H-H vector $D_0\times\tau_\mathrm{HH}$. The simulations show that this balance is significantly altered when nuclear quantum effects are taken into account. Our analysis suggests that the intermolecular and intramolecular contribution to the $^1$H NMR relaxation rate of liquid water are almost similar in magnitude, unlike to what was predicted earlier from classical MD simulations.

physics.chem-ph↗

arXiv2024

Towards more realistic climate model outputs: A multivariate bias correction based on zero-inflated vine copulas

Climate model large ensembles are an essential research tool for analysing and quantifying natural climate variability and providing robust information for rare extreme events. The models simulated representations of reality are susceptible to bias due to incomplete understanding of physical processes. This paper aims to correct the bias of five climate variables from the CRCM5 Large Ensemble over Central Europe at a 3-hourly temporal resolution. At this high temporal resolution, two variables, precipitation and radiation, exhibit a high share of zero inflation. We propose a novel bias-correction method, VBC (Vine copula bias correction), that models and transfers multivariate dependence structures for zero-inflated margins in the data from its error-prone model domain to a reference domain. VBC estimates the model and reference distribution using vine copulas and corrects the model distribution via (inverse) Rosenblatt transformation. To deal with the variables' zero-inflated nature, we develop a new vine density decomposition that accommodates such variables and employs an adequately randomized version of the Rosenblatt transform. This novel approach allows for more accurate modelling of multivariate zero-inflated climate data. Compared with state-of-the-art correction methods, VBC is generally the best-performing correction and the most accurate method for correcting zero-inflated events.

stat.AP↗

arXiv2023

Computing the Frequency-Dependent NMR Relaxation of $^1$H Nuclei in Liquid Water

It is the purpose of this paper to present a computational framework for reliably determining the frequency-dependent intermolecular and intramolecular NMR dipole-dipole relaxation rate of spin $1/2$ nuclei from MD simulations. The approach avoids alterations caused by well-known finite-size effects of the translational diffusion. Moreover, a procedure is derived to control and correct for effects caused by fixed distance-sampling cutoffs and periodic boundary conditions. By construction, this approach is capable of accurately predicting the correct low-frequency scaling behavior of the intermolecular NMR dipole-dipole relaxation rate and thus allows the reliable calculation of the frequency-dependent relaxation rate over many orders of magnitude. Our approach is based on the utilisation of the theory of Hwang and Freed for the intermolecular dipole-dipole correlation function and its corresponding spectral density [J. Chem. Phys. 63, 4017 (1975)] and its combination with data from molecular dynamics (MD) simulations. The deviations from the Hwang and Freed theory caused by periodic boundary conditions and sampling distance cutoffs are quantified by means of random walker Monte Carlo simulations. An expression based on the Hwang and Freed theoryis also suggested for correcting those effects. As a proof of principle, our approach is demonstrated by computing the frequency-dependent inter- and intramolecular dipolar NMR relaxation rate of the $^1$H nuclei in liquid water at $273\,\mbox{K}$ and $298\,\mbox{K}$ based on simulations of the TIP4P/2005 model. Our calculations are suggesting that the intermolecular contribution to the $^1$H NMR relaxation rate of the TIP4P/2005 model in the extreme narrowing limit has previously been substantially underestimated.

cond-mat.soft↗

arXiv2023

Physics-aware Machine Learning Revolutionizes Scientific Paradigm for Machine Learning and Process-based Hydrology

Accurate hydrological understanding and water cycle prediction are crucial for addressing scientific and societal challenges associated with the management of water resources, particularly under the dynamic influence of anthropogenic climate change. Existing reviews predominantly concentrate on the development of machine learning (ML) in this field, yet there is a clear distinction between hydrology and ML as separate paradigms. Here, we introduce physics-aware ML as a transformative approach to overcome the perceived barrier and revolutionize both fields. Specifically, we present a comprehensive review of the physics-aware ML methods, building a structured community (PaML) of existing methodologies that integrate prior physical knowledge or physics-based modeling into ML. We systematically analyze these PaML methodologies with respect to four aspects: physical data-guided ML, physics-informed ML, physics-embedded ML, and physics-aware hybrid learning. PaML facilitates ML-aided hypotheses, accelerating insights from big data and fostering scientific discoveries. We first conduct a systematic review of hydrology in PaML, including rainfall-runoff hydrological processes and hydrodynamic processes, and highlight the most promising and challenging directions for different objectives and PaML methods. Finally, a new PaML-based hydrology platform, termed HydroPML, is released as a foundation for hydrological applications. HydroPML enhances the explainability and causality of ML and lays the groundwork for the digital water cycle's realization. The HydroPML platform is publicly available at https://hydropml.github.io/.

cs.LG↗

arXiv2021

Structure, hydrogen bond dynamics and phase transition in a prototypical ionic liquid electrolyte

Ionic liquids (ILs) gain much interest as possible electrolytes in the next generation of mixed-solid Li-ion batteries. However, such properties of ionic liquids as melting transition, diffusion, strength and structure of hydrogen bond network remain poorly investigated. Here 2H NMR study of a prototypical ionic liquid [TEA][NTf2] has been performed. We show that the dynamical melting occurs through a dynamically heterogeneous phase stable between 223-277 K and the transition process is characterized by two standard molar enthalpy changes indicating to the multistage nature of the melting. The spin relaxation analysis allowed determining geometry, rates and energetics of IL mobility in both solid and liquid state. We compare these properties with previously reported data on [TEA][OTf] and [TEA][OMs] ILs that share cation but have anions of varying strength. Our results prove that the stronger hydrogen bonds between cation and anion lead to the lower enthalpy change between solid and liquid state, higher activation barrier of tumbling motion and lower amplitude of libration motion.

cond-mat.mtrl-sci↗

arXiv2017

Revisiting Imidazolium Based Ionic Liquids: Effect of the Conformation Bias of the [NTf$_{2}$] Anion Studied By Molecular Dynamics Simulations

We study ionic liquids composed 1-alkyl-3-methylimidazolium cations and bis(trifluoromethyl-sulfonyl)imide anions ([C$_n$MIm][NTf$_2$]) with varying chain-length $n\!=\!2, 4, 6, 8$ by using molecular dynamics simulations. We show that a reparametrization of the dihedral potentials as well as charges of the [NTf$_2$] anion leads to an improvment of the force field model introduced by Köddermann {\em et al.} [ChemPhysChem, \textbf{8}, 2464 (2007)] (KPL-force field). A crucial advantage of the new parameter set is that the minimum energy conformations of the anion ({\em trans} and {\em gauche}), as deduced from {\em ab initio} calculations and {\sc Raman} experiments, are now both well represented by our model. In addition, the results for [C$_n$MIm][NTf$_2$] show that this modification leads to an even better agreement between experiment and molecular dynamics simulation as demonstrated for densities, diffusion coefficients, vaporization enthalpies, reorientational correlation times, and viscosities. Even though we focused on a better representation of the anion conformation, also the alkyl chain-length dependence of the cation behaves closer to the experiment. We strongly encourage to use the new NGKPL force field for the [NTf$_2$] anion instead of the earlier KPL parameter set for computer simulations aiming to describe the thermodynamics, dynamics and also structure of imidazolium based ionic liquids.

cond-mat.soft↗

arXiv2017

Hydrogen Bonding in Protic Ionic Liquids: Structural Correlations, Vibrational Spectroscopy, and Rotational Dynamics of Liquid Ethylammonium Nitrate

The properties of the hydrogen bonds in ethylammonium nitrate are analyzed by using molecular dynamics simulations and infrared as well as nuclear magnetic resonance experiments. Ethylammonium nitrate features a flexible three-dimensional network of hydrogen bonds with moderate strengths, which makes it distinct from related triethylammonium-based ionic liquids. First, the network's flexibility is manifested in a not very pronounced correlation of the hydrogen bond geometries, which is caused by rapid interchanges of bonding partners. The large flexibility of the network leads to a substantial broadening of the mid-IR absorption band, with the contributions due to N-H stretching motions ranging from 2800 to 3250~\cm. Finally, the different dynamics are also seen in the rotational correlation of the N-H bond vector, where a correlation time as short as 16.1~ps is observed.

physics.chem-ph↗

arXiv2015

A Simple Guiding Principle for the Temperature Dependence of the Solubility of Light Gases in Imidazolium-based Ionic Liquids Derived from Molecular Simulations

We have determined the temperature dependence of the solvation behavior of a large collection of light gases in imidazolium-based Ionic Liquids (ILs) with the help of extensive molecular dynamics simulations. The solubility of molecular hydrogen, oxygen, nitrogen, methane, krypton, argon, neon and carbon dioxide in the imidazolium based ILs of type 1-n-alkyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([C$_n$mim][NTf$_2$]) with varying chain lengths $n\!=\!2,4,6,8$ are computed for a temperature range between $300\,\mbox{K}$ and $500\,\mbox{K}$ at $1\,\mbox{bar}$. By applying Widom's particle insertion technique and Bennet's overlapping distribution method, we are able to determine the temperature dependent solvation free energies for those selected light gases in simulated imidazolium based ILs with high statistical accuracy. Our simulations show that the magnitude of the solvation free energy of a gas molecule at a chosen reference temperature and its temperature-derivatives are intimately related with respect to oneanother. We conclude that this "universal" behavior is rooted in a solvation entropy-enthalpy compensation effect, which seems to be a defining feature of the solvation of small molecules in Ionic Liquids. We argue that this feature is based on a hypothesized funnel-like shape of the free energy landscape of a solvated gas molecule. The observations lead to simple analytical relations, determining the temperature dependence of the solubility data based on the absolute solubility at a certain reference temperature, which we call "solvation funnel" model. By comparing our results with available experimental data from many sources, we can show that the "solvation funnel" model is particularly helpful for providing reliable estimates for the solvation behavior of very light gases, such as hydrogen, where conflicting experimental data exist.

physics.chem-ph↗

arXiv2008

The Solvophobic Solvation and Interaction of Small Apolar Particles in Imidazolium-Based Ionic Liquids is Characterized by Enthalpy-/Entropy-Compensation

We report results of molecular dynamics simulations characterizing the solvation and interaction of small apolar particles such as methane and Xenon in imidazolium-based ionic liquids (ILs). The simulations are able to reproduce semi-quantitatively the anomalous temperature dependence of the solubility of apolar particles in the infinite dilution regime. We observe that the ``solvophobic solvation'' of small apolar particles in ILs is governed by compensating entropic and enthalpic contributions, very much like the hydrophobic hydration of small apolar particles in liquid water. In addition, our simulations clearly indicate that the solvent mediated interaction of apolar particles dissolved in ILs is similarly driven by compensating enthalpic/entropic contributions, making the ``solvophobic interaction'' thermodynamically analogous to the hydrophobic interaction.

cond-mat.soft↗