1
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Bartlett ER, Borkowski AK, Nilles CK, Blakemore JD, Thompson WH. Entropy Drives Accelerated Ion Diffusion upon Carbon Dioxide Expansion of Electrolytes. J Phys Chem B 2024. [PMID: 38703113 DOI: 10.1021/acs.jpcb.4c00540] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/06/2024]
Abstract
Carbon dioxide-expanded liquids, organic solvents with high concentrations of soluble carbon dioxide (CO2) at mild pressures, have gained attention as green catalytic media due to their improved properties over traditional solvents. More recently, carbon dioxide-expanded electrolytes (CXEs) have demonstrated improved reaction rates in the electrochemical reduction of CO2, by increasing the rate of delivery of CO2 to the electrode while maintaining facile charge transport. However, recent studies indicate that the limiting behavior of CXEs at higher CO2 pressures is a decline in solution conductivity due to reduced polarity, leading to poorer charge screening and greater ion pairing. In this article, we employ molecular dynamics simulations to investigate the energetic driving forces behind the diffusive properties of an acetonitrile and tetrapropylammonium hexafluorophosphate (TPrAPF6) CXE with increasing CO2 concentration. Our results indicate that entropy drives solvent and electrolyte diffusion with increasing CO2 pressure. The activation energy of ion diffusion increases with higher concentrations of CO2, indicating that increasing the temperature may improve solution conductivity in these systems. This trend in the activation energies is traced to stronger cation-anion Coulombic interactions due to weaker solvent screening at high CO2 concentrations, suggesting that the choice of ion may provide a route to diminish this effect.
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Affiliation(s)
- Elizabeth R Bartlett
- Department of Chemistry, University of Kansas, Lawrence, Kansas 66045, United States
| | - Ashley K Borkowski
- Department of Chemistry, University of Kansas, Lawrence, Kansas 66045, United States
| | - Christian K Nilles
- Department of Chemistry, University of Kansas, Lawrence, Kansas 66045, United States
| | - James D Blakemore
- 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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2
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Rick SW, Thompson WH. Effects of polarizability and charge transfer on water dynamics and the underlying activation energies. J Chem Phys 2023; 158:2890774. [PMID: 37191215 DOI: 10.1063/5.0151253] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2023] [Accepted: 05/02/2023] [Indexed: 05/17/2023] Open
Abstract
A large number of force fields have been proposed for describing the behavior of liquid water within classical atomistic simulations, particularly molecular dynamics. In the past two decades, models that incorporate molecular polarizability and even charge transfer have become more prevalent, in attempts to develop more accurate descriptions. These are frequently parameterized to reproduce the measured thermodynamics, phase behavior, and structure of water. On the other hand, the dynamics of water is rarely considered in the construction of these models, despite its importance in their ultimate applications. In this paper, we explore the structure and dynamics of polarizable and charge-transfer water models, with a focus on timescales that directly or indirectly relate to hydrogen bond (H-bond) making and breaking. Moreover, we use the recently developed fluctuation theory for dynamics to determine the temperature dependence of these properties to shed light on the driving forces. This approach provides key insight into the timescale activation energies through a rigorous decomposition into contributions from the different interactions, including polarization and charge transfer. The results show that charge transfer effects have a negligible effect on the activation energies. Furthermore, the same tension between electrostatic and van der Waals interactions that is found in fixed-charge water models also governs the behavior of polarizable models. The models are found to involve significant energy-entropy compensation, pointing to the importance of developing water models that accurately describe the temperature dependence of water structure and dynamics.
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Affiliation(s)
- Steven W Rick
- Department of Chemistry, University of New Orleans, New Orleans, Louisiana 70148, USA
| | - Ward H Thompson
- Department of Chemistry, University of Kansas, Lawrence, Kansas 66045, USA
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3
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Piskulich ZA, Borkowski AK, Thompson WH. A Maxwell relation for dynamical timescales with application to the pressure and temperature dependence of water self-diffusion and shear viscosity. Phys Chem Chem Phys 2023; 25:12820-12832. [PMID: 37129891 DOI: 10.1039/d3cp01386c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
A Maxwell relation for a reaction rate constant (or other dynamical timescale) obtained under constant pressure, p, and temperature, T, is introduced and discussed. Examination of this relationship in the context of fluctuation theory provides insight into the p and T dependence of the timescale and the underlying molecular origins. This Maxwell relation motivates a suggestion for the general form of the timescale as a function of pressure and temperature. This is illustrated by accurately fitting simulation results and existing experimental data on the self-diffusion coefficient and shear viscosity of liquid water. A key advantage of this approach is that each fitting parameter is physically meaningful.
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Affiliation(s)
- Zeke A Piskulich
- Department of Chemistry, University of Kansas, Lawrence, KS 66045, USA.
| | | | - Ward H Thompson
- Department of Chemistry, University of Kansas, Lawrence, KS 66045, USA.
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4
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Borkowski AK, Campbell NI, Thompson WH. Direct calculation of the temperature dependence of 2D-IR spectra: Urea in water. J Chem Phys 2023; 158:064507. [PMID: 36792517 DOI: 10.1063/5.0135627] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023] Open
Abstract
A method for directly calculating the temperature derivative of two-dimensional infrared (2D-IR) spectra from simulations at a single temperature is presented. The approach is demonstrated by application to the OD stretching spectrum of isotopically dilute aqueous (HOD in H2O) solutions of urea as a function of concentration. Urea is an important osmolyte because of its ability to denature proteins, which has motivated significant interest in its effect on the structure and dynamics of water. The present results show that the temperature dependence of both the linear IR and 2D-IR spectra, which report on the underlying energetic driving forces, is more sensitive to urea concentration than the spectra themselves. Additional physical insight is provided by calculation of the contributions to the temperature derivative from different interactions, e.g., water-water, water-urea, and urea-urea, present in the system. Finally, it is demonstrated how 2D-IR spectra at other temperatures can be obtained from only room temperature simulations.
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Affiliation(s)
- Ashley K Borkowski
- Department of Chemistry, University of Kansas, Lawrence, Kansas 66045, USA
| | - N Ian Campbell
- 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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5
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Borkowski AK, Thompson WH. Shining (Infrared) Light on the Hofmeister Series: Driving Forces for Changes in the Water Vibrational Spectra in Alkali-Halide Salt Solutions. J Phys Chem B 2022; 126:6700-6712. [PMID: 36004804 DOI: 10.1021/acs.jpcb.2c03957] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The Hofmeister series is frequently used to rank ions based on their behavior from chaotropes ("structure breakers"), which weaken the surrounding hydrogen-bond network, to kosmotropes ("structure makers"), which enhance it. Here, we use fluctuation theory to investigate the energetic and entropic driving forces underlying the Hofmeister series for aqueous alkali-halide solutions. Specifically, we exploit the OH stretch infrared (IR) spectrum in isotopically dilute HOD/D2O solutions as a probe of the effect of the salt on the water properties for different concentrations and choice of halide anion. Fluctuation theory is used to calculate the temperature derivative of these IR spectra, including decomposition of the derivative into different energetic contributions. These contributions are used to determine the thermodynamic driving forces in terms of effective internal energy and entropic contributions. This analysis implicates entropic contributions as the key factor in the Hofmeister series behavior of the OH stretch IR spectra, while the effective internal energy is nearly ion-independent.
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Affiliation(s)
- Ashley K Borkowski
- 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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6
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Piskulich ZA, Laage D, Thompson WH. Using Activation Energies to Elucidate Mechanisms of Water Dynamics. J Phys Chem A 2021; 125:9941-9952. [PMID: 34748353 DOI: 10.1021/acs.jpca.1c08020] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Recent advances in the calculation of activation energies are shedding new light on the dynamical time scales of liquid water. In this Perspective, we examine how activation energies elucidate the central, but not singular, role of the exchange of hydrogen-bond (H-bond) partners that rearrange the H-bond network of water. The contributions of other motions to dynamical time scales and their associated activation energies are discussed along with one case, vibrational spectral diffusion, where H-bond exchanges are not mechanistically significant. Nascent progress on outstanding challenges, including descriptions of non-Arrhenius effects and activation volumes, are detailed along with some directions for future investigations.
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Affiliation(s)
- Zeke A Piskulich
- Department of Chemistry, University of Kansas, Lawrence, Kansas 66045, United States
| | - Damien Laage
- PASTEUR, Department de Chimie, École Normale Supérieure, PSL University, Sorbonne Université, CNRS, Paris 75005, France
| | - Ward H Thompson
- Department of Chemistry, University of Kansas, Lawrence, Kansas 66045, United States
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7
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Piskulich ZA, Thompson WH. Examining the Role of Different Molecular Interactions on Activation Energies and Activation Volumes in Liquid Water. J Chem Theory Comput 2021; 17:2659-2671. [PMID: 33819026 DOI: 10.1021/acs.jctc.0c01217] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
There are a large number of force fields available to model water in molecular dynamics simulations, which each have their own strengths and weaknesses in describing the behavior of the liquid. One particular weakness in many of these models is their description of dynamics away from ambient conditions, where their ability to reproduce measurements is mixed. To investigate this issue, we use the recently developed fluctuation theory for dynamics to directly evaluate measures of the local temperature and pressure dependence: the activation energy and the activation volume. We examine these activation parameters for hydrogen-bond jump exchange times, OH reorientation times, and diffusion coefficients calculated from the SPC/E, SPC/Fw, TIP3P-PME, TIP3P-PME/Fw, OPC3, TIP4P/2005, TIP4P/Ew, E3B2, and E3B3 water models. Activation energy decompositions available through the fluctuation theory approach provide mechanistic insight into the origins of different temperature dependences between the various models, as well as the influence of three-body effects and flexibility.
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Affiliation(s)
- Zeke A Piskulich
- 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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8
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Piskulich ZA, Laage D, Thompson WH. On the role of hydrogen-bond exchanges in the spectral diffusion of water. J Chem Phys 2021; 154:064501. [PMID: 33588543 DOI: 10.1063/5.0041270] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The dynamics of a vibrational frequency in a condensed phase environment, i.e., the spectral diffusion, has attracted considerable interest over the last two decades. A significant impetus has been the development of two-dimensional infrared (2D-IR) photon-echo spectroscopy that represents a direct experimental probe of spectral diffusion, as measured by the frequency-frequency time correlation function (FFCF). In isotopically dilute water, which is perhaps the most thoroughly studied system, the standard interpretation of the longest timescale observed in the FFCF is that it is associated with hydrogen-bond exchange dynamics. Here, we investigate this connection by detailed analysis of both the spectral diffusion timescales and their associated activation energies. The latter are obtained from the recently developed fluctuation theory for the dynamics approach. The results show that the longest timescale of spectral diffusion obtained by the typical analysis used cannot be directly associated with hydrogen-bond exchanges. The hydrogen-bond exchange time does appear in the decay of the water FFCF, but only as an additional, small-amplitude (<3%) timescale. The dominant contribution to the long-time spectral diffusion dynamics is considerably shorter than the hydrogen-bond exchange time and exhibits a significantly smaller activation energy. It thus arises from hydrogen-bond rearrangements, which occur in between successful hydrogen-bond partner exchanges, and particularly from hydrogen bonds that transiently break before returning to the same acceptor.
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Affiliation(s)
- Zeke A Piskulich
- Department of Chemistry, University of Kansas, Lawrence, Kansas 66045, USA
| | - Damien Laage
- PASTEUR, Department of Chemistry, École Normale Supérieure, PSL University, Sorbonne Université, CNRS, 75005 Paris, France
| | - Ward H Thompson
- Department of Chemistry, University of Kansas, Lawrence, Kansas 66045, USA
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9
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Borkowski AK, Piskulich ZA, Thompson WH. Examining the Hofmeister Series through Activation Energies: Water Diffusion in Aqueous Alkali-Halide Solutions. J Phys Chem B 2021; 125:350-359. [PMID: 33382267 DOI: 10.1021/acs.jpcb.0c09965] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The effect of ions on the properties of aqueous solutions is often categorized in terms of the Hofmeister series that ranks them from chaotropes ("structure-breakers"), which weaken the surrounding hydrogen-bond network to kosmotropes ("structure-makers"), which enhance it. Here, we investigate the Hofmeister series in ∼1 M sodium-halide solutions using molecular dynamics simulations to calculate the effect of the identity and proximity of the halide anion on both the water diffusion coefficient and its activation energy. A recently developed method for calculating the activation energy from a single-temperature simulation is used, which also permits a rigorous decomposition into contributions from different interactions and motions. The mechanisms of the salt effects on the water dynamics are explored by separately considering water molecules based on their location relative to the ions. The results show that water diffusion is accelerated moving down the halide group from F- to I-. The behavior of the diffusion activation energy, Ea, is more complex, indicating a significant role for entropic effects. However, water molecules in the first or second solvation shell of an ion exhibit a decrease in Ea moving down the halide series and Na+ exhibits a larger effect than any of the anions. The Ea for water molecules within the second solvation shell of an ion are modest, indicating a short-ranged nature of the ion influence.
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Affiliation(s)
- Ashley K Borkowski
- Department of Chemistry, University of Kansas, Lawrence, Kansas 66045, United States
| | - Zeke A Piskulich
- 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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10
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Piskulich ZA, Thompson WH. Temperature Dependence of the Water Infrared Spectrum: Driving Forces, Isosbestic Points, and Predictions. J Phys Chem Lett 2020; 11:7762-7768. [PMID: 32852956 DOI: 10.1021/acs.jpclett.0c02301] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
The temperature derivative of the infrared (IR) spectrum of HOD/D2O is directly calculated from simulations at a single temperature using a fluctuation theory approach. It is demonstrated, on the basis of an energetic decomposition of the derivative, that the blue shift with increasing temperature is associated with the competition between electrostatic and Lennard-Jones interactions. The same competition gives rise, where their contributions cancel, to a near isosbestic point. The derivative is further used to define an effective internal energy (and entropy) associated with the IR spectrum, and it is shown how a van't Hoff relation can be used to accurately predict the spectrum over a wide range of temperatures. These predictions also explain why a precise isosbestic point is not observed.
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Affiliation(s)
- Zeke A Piskulich
- 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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11
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Piskulich ZA, Laage D, Thompson WH. Activation energies and the extended jump model: How temperature affects reorientation and hydrogen-bond exchange dynamics in water. J Chem Phys 2020; 153:074110. [DOI: 10.1063/5.0020015] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [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
| | - 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, Kansas 66045, USA
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12
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Piskulich ZA, Thompson WH. The dynamics of supercooled water can be predicted from room temperature simulations. J Chem Phys 2020; 152:074505. [DOI: 10.1063/1.5139435] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [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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13
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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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14
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Mendis CH, Piskulich ZA, Thompson WH. Tests of the Stokes–Einstein Relation through the Shear Viscosity Activation Energy of Water. J Phys Chem B 2019; 123:5857-5865. [DOI: 10.1021/acs.jpcb.9b04647] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023]
Affiliation(s)
- Camina H. Mendis
- Department of Chemistry, University of Kansas, Lawrence, Kansas 66045, United States
| | - Zeke A. Piskulich
- 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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15
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Affiliation(s)
- Zeke A. Piskulich
- Department of Chemistry, University of Kansas, Lawrence, Kansas 66045, United States
| | - Oluwaseun O. Mesele
- 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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16
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Schile AJ, Limmer DT. Rate constants in spatially inhomogeneous systems. J Chem Phys 2019; 150:191102. [DOI: 10.1063/1.5092837] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Addison J. Schile
- Department of Chemistry, University of California, Berkeley, California 94720-1460, USA
- Lawrence Berkeley National Laboratory, University of California, Berkeley, California 94720-1460, USA
| | - David T. Limmer
- Department of Chemistry, University of California, Berkeley, California 94720-1460, USA
- Lawrence Berkeley National Laboratory, University of California, Berkeley, California 94720-1460, USA
- Kavli Energy NanoSciences Institute, University of California, Berkeley, California 94720-1460, USA
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17
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Piskulich ZA, Thompson WH. The activation energy for water reorientation differs between IR pump-probe and NMR measurements. J Chem Phys 2018; 149:164504. [DOI: 10.1063/1.5050203] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [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
- Center for Environmentally Beneficial Catalysis, University of Kansas, Lawrence, Kansas 66047, USA
| | - Ward H. Thompson
- Department of Chemistry, University of Kansas, Lawrence, Kansas 66045, USA
- Center for Environmentally Beneficial Catalysis, University of Kansas, Lawrence, Kansas 66047, USA
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18
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Piskulich ZA, Mesele OO, Thompson WH. Expanding the calculation of activation volumes: Self-diffusion in liquid water. J Chem Phys 2018; 148:134105. [DOI: 10.1063/1.5023420] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023] Open
Affiliation(s)
- Zeke A. Piskulich
- Department of Chemistry, University of Kansas, Lawrence, Kansas 66045, USA
- Center for Environmentally Beneficial Catalysis, University of Kansas, Lawrence, Kansas 66047, USA
| | | | - Ward H. Thompson
- Department of Chemistry, University of Kansas, Lawrence, Kansas 66045, USA
- Center for Environmentally Beneficial Catalysis, University of Kansas, Lawrence, Kansas 66047, USA
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19
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Piskulich ZA, Mesele OO, Thompson WH. Removing the barrier to the calculation of activation energies: Diffusion coefficients and reorientation times in liquid water. J Chem Phys 2017; 147:134103. [DOI: 10.1063/1.4997723] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Affiliation(s)
- Zeke A. Piskulich
- Department of Chemistry, University of Kansas, Lawrence, Kansas 66045, USA
- Center for Environmentally Beneficial Catalysis, University of Kansas, Lawrence, Kansas 66047, USA
| | | | - Ward H. Thompson
- Department of Chemistry, University of Kansas, Lawrence, Kansas 66045, USA
- Center for Environmentally Beneficial Catalysis, University of Kansas, Lawrence, Kansas 66047, USA
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20
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Junginger A, Duvenbeck L, Feldmaier M, Main J, Wunner G, Hernandez R. Chemical dynamics between wells across a time-dependent barrier: Self-similarity in the Lagrangian descriptor and reactive basins. J Chem Phys 2017; 147:064101. [DOI: 10.1063/1.4997379] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Andrej Junginger
- Institut für Theoretische Physik 1, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Lennart Duvenbeck
- Institut für Theoretische Physik 1, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Matthias Feldmaier
- Institut für Theoretische Physik 1, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Jörg Main
- Institut für Theoretische Physik 1, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Günter Wunner
- Institut für Theoretische Physik 1, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Rigoberto Hernandez
- Department of Chemistry, Johns Hopkins University, Baltimore, Maryland 21218, USA
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