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Piskulich ZA, Laage D, Thompson WH. A structure-dynamics relationship enables prediction of the water hydrogen bond exchange activation energy from experimental data. Chem Sci 2024; 15:2197-2204. [PMID: 38332825 PMCID: PMC10848719 DOI: 10.1039/d3sc04495e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/27/2023] [Accepted: 12/23/2023] [Indexed: 02/10/2024] Open
Abstract
It has long been understood that the structural features of water are determined by hydrogen bonding (H-bonding) and that the exchange of, or "jumps" between, H-bond partners underlies many of the dynamical processes in water. Despite the importance of H-bond exchanges there is, as yet, no direct method for experimentally measuring the timescale of the process or its associated activation energy. Here, we identify and exploit relationships between water's structural and dynamical properties that provide an indirect route for determining the H-bond exchange activation energy from experimental data. Specifically, we show that the enthalpy and entropy determining the radial distribution function in liquid water are linearly correlated with the activation energies for H-bond jumps, OH reorientation, and diffusion. Using temperature-dependent measurements of the radial distribution function from the literature, we demonstrate how these correlations allow us to infer the value of the jump activation energy, Ea,0, from experimental results. This analysis gives Ea,0 = 3.43 kcal mol-1, which is in good agreement with that predicted by the TIP4P/2005 water model. We also illustrate other approaches for estimating this activation energy consistent with these estimates.
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Affiliation(s)
- Zeke A Piskulich
- Department of Chemistry, University of Kansas Lawrence KS 66045 USA
| | - Damien Laage
- PASTEUR, Départment de Chimie, École Normale Supérieure, PSL University, Sorbonne Université, CNRS Paris 75005 France
| | - Ward H Thompson
- Department of Chemistry, University of Kansas Lawrence KS 66045 USA
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Heyes DM, Dini D, Pieprzyk S, Brańka AC. Departures from perfect isomorph behavior in Lennard-Jones fluids and solids. J Chem Phys 2023; 158:134502. [PMID: 37031156 DOI: 10.1063/5.0143651] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/05/2023] Open
Abstract
Isomorphs are lines on a fluid or solid phase diagram along which the microstructure is invariant on affine density scaling of the molecular coordinates. Only inverse power (IP) and hard sphere potential systems are perfectly isomorphic. This work provides new theoretical tools and criteria to determine the extent of deviation from perfect isomorphicity for other pair potentials using the Lennard-Jones (LJ) system as a test case. A simple prescription for predicting isomorphs in the fluid range using the freezing line as a reference is shown to be quite accurate for the LJ system. The shear viscosity and self-diffusion coefficient scale well are calculated using this method, which enables comments on the physical significance of the correlations found previously in the literature to be made. The virial–potential energy fluctuation and the concept of an effective IPL system and exponent, n′, are investigated, particularly with reference to the LJ freezing and melting lines. It is shown that the exponent, n′, converges to the value 12 at a high temperature as ∼ T−1/2, where T is the temperature. Analytic expressions are derived for the density, temperature, and radius derivatives of the radial distribution function along an isomorph that can be used in molecular simulation. The variance of the radial distribution function and radial fluctuation function are shown to be isomorph invariant.
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Affiliation(s)
- D. M. Heyes
- Department of Mechanical Engineering, Imperial College London, Exhibition Road, South Kensington, London SW7 2AZ, United Kingdom
| | - D. Dini
- Department of Mechanical Engineering, Imperial College London, Exhibition Road, South Kensington, London SW7 2AZ, United Kingdom
| | - S. Pieprzyk
- Institute of Molecular Physics, Polish Academy of Sciences, M. Smoluchowskiego 17, 60-179 Poznań, Poland
| | - A. C. Brańka
- Institute of Molecular Physics, Polish Academy of Sciences, M. Smoluchowskiego 17, 60-179 Poznań, Poland
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Siderius DW, Hatch HW, Shen VK. Temperature Extrapolation of Henry's Law Constants and the Isosteric Heat of Adsorption. J Phys Chem B 2022; 126:7999-8009. [PMID: 36170675 PMCID: PMC9808984 DOI: 10.1021/acs.jpcb.2c04583] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
Abstract
Computational screening of adsorbent materials often uses the Henry's law constant (KH) (at a particular temperature) as a first discriminator metric due to its relative ease of calculation. The isosteric heat of adsorption in the limit of zero pressure (qst∞) is often calculated along with the Henry's law constant, and both properties are informative metrics of adsorbent material performance at low-pressure conditions. In this article, we introduce a method for extrapolating KH as a function of temperature, using series-expansion coefficients that are easily computed at the same time as KH itself; the extrapolation function also yields qst∞. The extrapolation is highly accurate over a wide range of temperatures when the basis temperature is sufficiently high, for a wide range of adsorbent materials and adsorbate gases. Various results suggest that the extrapolation is accurate when the extrapolation range in inverse-temperature space is limited to |β - β0 | < 0.5 mol/kJ. Application of the extrapolation to a large set of materials is shown to be successful provided that KH is not extremely large and/or the extrapolation coefficients converge satisfactorily. The extrapolation is also able to predict qst∞ for a system that shows an unusually large temperature dependence. The work provides a robust method for predicting KH and qst∞ over a wide range of industrially relevant temperatures with minimal effort beyond that necessary to compute those properties at a single temperature, which facilitates the addition of practical operating (or processing) conditions to computational screening exercises.
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Affiliation(s)
- Daniel W. Siderius
- Chemical Sciences Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8320, United States,Corresponding Author:
| | - Harold W. Hatch
- Chemical Sciences Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8320, United States
| | - Vincent K. Shen
- Chemical Sciences Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8320, United States
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Katiyar A, Thompson WH. Temperature Dependence of Peptide Conformational Equilibria from Simulations at a Single Temperature. J Phys Chem A 2021; 125:2374-2384. [PMID: 33720712 DOI: 10.1021/acs.jpca.1c00150] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Understanding the structure of proteins is key to unraveling their function in biological processes. Thus, significant attention has been paid to the calculation of conformational free energies. In this paper, we demonstrate a simple extension of fluctuation theory that permits the calculation of the temperature derivative of the conformational free energy, and hence the internal energy and entropy, from single-temperature simulations. The method further enables the decomposition into the contribution of different interactions present in the system to the internal energy surface. We illustrate the method for the canonical test system of alanine dipeptide in aqueous solution, for which we examine the free energy as a function of two dihedral angles. This system, like many, is most effectively treated using accelerated sampling methods and we show how the present approach is compatible with an important class of these, those that introduce a bias potential, by implementing it within metadynamics.
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Affiliation(s)
- Ankita Katiyar
- Department of Chemistry, University of Kansas, Lawrence, Kansas 66045, United States
| | - Ward H Thompson
- Department of Chemistry, University of Kansas, Lawrence, Kansas 66045, United States
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Saw S, Dyre JC. Structure of the Lennard-Jones liquid estimated from a single simulation. Phys Rev E 2021; 103:012110. [PMID: 33601502 DOI: 10.1103/physreve.103.012110] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/22/2020] [Accepted: 12/08/2020] [Indexed: 11/07/2022]
Abstract
Combining the recent Piskulich-Thompson approach [Z. A. Piskulich and W. H. Thompson, J. Chem. Phys. 152, 011102 (2020)JCPSA60021-960610.1063/1.5135932] with isomorph theory, from a single simulation the structure of a single-component Lennard-Jones (LJ) system is obtained at an arbitrary state point in almost the whole liquid region of the temperature-density phase diagram. The LJ system exhibits two temperature ranges where the van't Hoff assumption that energetic and entropic forces are temperature independent is valid to a good approximation. A method to evaluate the structure at an arbitrary state point along an isochore from the knowledge of structures at two temperatures on the isochore is also discussed. We argue that, in general, the structure of any hidden scale-invariant system obeying the van't Hoff assumption in the whole range of temperatures can be determined in the whole liquid region of the phase diagram from a single simulation.
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Affiliation(s)
- Shibu Saw
- "Glass and Time," IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
| | - Jeppe C Dyre
- "Glass and Time," IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
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Monroe JI, Hatch HW, Mahynski NA, Shell MS, Shen VK. Extrapolation and interpolation strategies for efficiently estimating structural observables as a function of temperature and density. J Chem Phys 2020; 153:144101. [PMID: 33086808 DOI: 10.1063/5.0014282] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022] Open
Abstract
Thermodynamic extrapolation has previously been used to predict arbitrary structural observables in molecular simulations at temperatures (or relative chemical potentials in open-system mixtures) different from those at which the simulation was performed. This greatly reduces the computational cost in mapping out phase and structural transitions. In this work, we explore the limitations and accuracy of thermodynamic extrapolation applied to water, where qualitative shifts from anomalous to simple-fluid-like behavior are manifested through shifts in the liquid structure that occur as a function of both temperature and density. We present formulas for extrapolating in volume for canonical ensembles and demonstrate that linear extrapolations of water's structural properties are only accurate over a limited density range. On the other hand, linear extrapolation in temperature can be accurate across the entire liquid state. We contrast these extrapolations with classical perturbation theory techniques, which are more conservative and slowly converging. Indeed, we show that such behavior is expected by demonstrating exact relationships between extrapolation of free energies and well-known techniques to predict free energy differences. An ideal gas in an external field is also studied to more clearly explain these results for a toy system with fully analytical solutions. We also present a recursive interpolation strategy for predicting arbitrary structural properties of molecular fluids over a predefined range of state conditions, demonstrating its success in mapping qualitative shifts in water structure with density.
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Affiliation(s)
- Jacob I Monroe
- National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - Harold W Hatch
- National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - Nathan A Mahynski
- National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - M Scott Shell
- University of California - Santa Barbara, Santa Barbara, California 93106, USA
| | - Vincent K Shen
- National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
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Mahynski NA, Hatch HW, Witman M, Sheen DA, Errington JR, Shen VK. Flat-histogram extrapolation as a useful tool in the age of big data. MOLECULAR SIMULATION 2020. [DOI: 10.1080/08927022.2020.1747617] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- Nathan A. Mahynski
- Chemical Sciences Division, National Institute of Standards and Technology, Gaithersburg, MD, USA
| | - Harold W. Hatch
- Chemical Sciences Division, National Institute of Standards and Technology, Gaithersburg, MD, USA
| | | | - David A. Sheen
- Chemical Sciences Division, National Institute of Standards and Technology, Gaithersburg, MD, USA
| | - Jeffrey R. Errington
- Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, NY, USA
| | - Vincent K. Shen
- Chemical Sciences Division, National Institute of Standards and Technology, Gaithersburg, MD, USA
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Piskulich ZA, Thompson WH. On the temperature dependence of liquid structure. J Chem Phys 2020; 152:011102. [DOI: 10.1063/1.5135932] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Zeke A. Piskulich
- Department of Chemistry, University of Kansas, Lawrence, Kansas 66045, USA
| | - Ward H. Thompson
- Department of Chemistry, University of Kansas, Lawrence, Kansas 66045, USA
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Desgranges C, Delhommelle J. A new approach for the prediction of partition functions using machine learning techniques. J Chem Phys 2018; 149:044118. [DOI: 10.1063/1.5037098] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
Affiliation(s)
- Caroline Desgranges
- Department of Chemistry, University of North Dakota, 151 Cornell Street Stop 9024, Grand Forks, North Dakota 58202, USA
| | - Jerome Delhommelle
- Department of Chemistry, University of North Dakota, 151 Cornell Street Stop 9024, Grand Forks, North Dakota 58202, USA
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