Rate constants in spatially inhomogeneous systems

Schile, Addison J.; Limmer, David T.

doi:10.1063/1.5092837

Title: Rate constants in spatially inhomogeneous systems

Journal Article · 20 May 2019 · Journal of Chemical Physics

DOI: https://doi.org/10.1063/1.5092837 · OSTI ID:1577591

Schile, Addison J. ^[1];

^[1]

Univ. of California, Berkeley, CA (United States)

Here, we introduce a theory and accompanying importance sampling method for computing rate constants in spatially inhomogeneous systems. Using the relationship between rate constants and path space partition functions, we illustrate that the relative change in the rate of a rare event through space is isomorphic to the calculation of a free energy difference, albeit in a trajectory ensemble. Like equilibrium free energies, relative rate constants can be estimated by importance sampling. An extension to transition path sampling is proposed that combines biased path ensembles and weighted histogram analysis to accomplish this estimate. We demonstrate that rate constants can also be decomposed into different contributions, including relative changes in stability, barrier height, and flux. This decomposition provides a means of interpretation and insight into rare processes in complex environments. We confirm these ideas with a simple model of diffusion with spatially varying diffusivity and illustrate their utility in a model of ion pair dissociation near an electrochemical interface.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC); Univ. of California, Oakland, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21). Scientific Discovery through Advanced Computing (SciDAC)

Grant/Contract Number:: AC02-05CH11231

OSTI ID:: 1577591

Journal Information:: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 19 Vol. 150; ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

References (78)

The missing term in effective pair potentials Berendsen, H. J. C.; Grigera, J. R.; Straatsma, T. P. The Journal of Physical Chemistry, Vol. 91, Issue 24 https://doi.org/10.1021/j100308a038	journal	November 1987
Osteoimmunology: Influence of the Immune System on Bone Regeneration and Consumption Limmer, Andreas; Wirtz, Dieter Zeitschrift für Orthopädie und Unfallchirurgie, Vol. 155, Issue 03 https://doi.org/10.1055/s-0043-100100	journal	June 2017
Atomistic understanding of kinetic pathways for single base-pair binding and unbinding in DNA Hagan, M. F.; Dinner, A. R.; Chandler, D. Proceedings of the National Academy of Sciences, Vol. 100, Issue 24 https://doi.org/10.1073/pnas.2036378100	journal	November 2003
Fabrication and Characterization of Needle-Type Katemann, Bernardo Ballesteros; Schuhmann, Wolfgang Electroanalysis, Vol. 14, Issue 1 https://doi.org/10.1002/1521-4109(200201)14:1<22::aid-elan22>3.0.co;2-f	journal	January 2002
“On Water”: Unique Reactivity of Organic Compounds in Aqueous Suspension Narayan, Sridhar; Muldoon, John; Finn, M. G. Angewandte Chemie, Vol. 117, Issue 21 https://doi.org/10.1002/ange.200462883	journal	May 2005
“On Water”: Unique Reactivity of Organic Compounds in Aqueous Suspension Narayan, Sridhar; Muldoon, John; Finn, M. G. Angewandte Chemie International Edition, Vol. 44, Issue 21 https://doi.org/10.1002/anie.200462883	journal	May 2005
Elaborating Transition Interface Sampling Methods van Erp, Titus S.; Bolhuis, Peter G. ChemInform, Vol. 35, Issue 47 https://doi.org/10.1002/chin.200447267	journal	November 2004
Fluctuating Enzymes: Lessons from Single-Molecule Studies Min, Wei; English, Brian P.; Luo, Guobin ChemInform, Vol. 37, Issue 14 https://doi.org/10.1002/chin.200614274	journal	April 2006
Settle: An analytical version of the SHAKE and RATTLE algorithm for rigid water models Miyamoto, Shuichi; Kollman, Peter A. Journal of Computational Chemistry, Vol. 13, Issue 8 https://doi.org/10.1002/jcc.540130805	journal	October 1992
THE weighted histogram analysis method for free-energy calculations on biomolecules. I. The method Kumar, Shankar; Rosenberg, John M.; Bouzida, Djamal Journal of Computational Chemistry, Vol. 13, Issue 8 https://doi.org/10.1002/jcc.540130812	journal	October 1992
Fast Parallel Algorithms for Short-Range Molecular Dynamics Plimpton, Steve Journal of Computational Physics, Vol. 117, Issue 1 https://doi.org/10.1006/jcph.1995.1039	journal	March 1995
Reaction selectivity in heterogeneous catalysis: An invited review Somorjai, Gabor A.; Kliewer, Christopher J. Reaction Kinetics and Catalysis Letters, Vol. 96, Issue 2 https://doi.org/10.1007/s11144-009-5531-7	journal	April 2009
The rate constant in the kramers multidimensional theory and the saddle-point avoidance Berezhkovskii, A. M.; Berezhkovskii, L. M.; Zitzerman, V. Yu. Chemical Physics, Vol. 130, Issue 1-3 https://doi.org/10.1016/0301-0104(89)87036-3	journal	February 1989
Transition path sampling of protein conformational changes Juraszek, Jarek; Vreede, Jocelyne; Bolhuis, Peter G. Chemical Physics, Vol. 396 https://doi.org/10.1016/j.chemphys.2011.04.032	journal	March 2012
Nanoscale heterogeneity at the aqueous electrolyte–electrode interface Limmer, David T.; Willard, Adam P. Chemical Physics Letters, Vol. 620 https://doi.org/10.1016/j.cplett.2014.11.013	journal	January 2015
Elaborating transition interface sampling methods van Erp, Titus S.; Bolhuis, Peter G. Journal of Computational Physics, Vol. 205, Issue 1 https://doi.org/10.1016/j.jcp.2004.11.003	journal	May 2005
Investigating rare events by transition interface sampling Moroni, Daniele; van Erp, Titus S.; Bolhuis, Peter G. Physica A: Statistical Mechanics and its Applications, Vol. 340, Issue 1-3 https://doi.org/10.1016/j.physa.2004.04.033	journal	September 2004
Rate processes with dynamical disorder Zwanzig, Robert Accounts of Chemical Research, Vol. 23, Issue 5 https://doi.org/10.1021/ar00173a005	journal	May 1990
Fluctuating Enzymes: Lessons from Single-Molecule Studies Min, Wei; English, Brian P.; Luo, Guobin Accounts of Chemical Research, Vol. 38, Issue 12 https://doi.org/10.1021/ar040133f	journal	December 2005
Dynamics of ligand binding to myoglobin Austin, R. H.; Beeson, K. W.; Eisenstein, L. Biochemistry, Vol. 14, Issue 24 https://doi.org/10.1021/bi00695a021	journal	December 1975
Chemical Reactions and Solvation at Liquid Interfaces: A Microscopic Perspective Benjamin, Ilan Chemical Reviews, Vol. 96, Issue 4 https://doi.org/10.1021/cr950230+	journal	January 1996
Transmission Coefficients, Committors, and Solvent Coordinates in Ion-Pair Dissociation Mullen, Ryan Gotchy; Shea, Joan-Emma; Peters, Baron Journal of Chemical Theory and Computation, Vol. 10, Issue 2 https://doi.org/10.1021/ct4009798	journal	January 2014
The missing term in effective pair potentials Berendsen, H. J. C.; Grigera, J. R.; Straatsma, T. P. The Journal of Physical Chemistry, Vol. 91, Issue 24 https://doi.org/10.1021/j100308a038	journal	November 1987
Observation of photoinduced electron transfer at a liquid-liquid interface by optical second harmonic generation Kott, Kevin L.; Higgins, Daniel A.; McMahon, Robert J. Journal of the American Chemical Society, Vol. 115, Issue 12 https://doi.org/10.1021/ja00065a075	journal	June 1993
IR−Visible SFG Investigations of Interfacial Water Structure upon Polyelectrolyte Adsorption at the Solid/Liquid Interface Kim, Joonyeong; Cremer, Paul S. Journal of the American Chemical Society, Vol. 122, Issue 49 https://doi.org/10.1021/ja003215h	journal	December 2000
The Mechanism of Cellulose Hydrolysis by a Two-Step, Retaining Cellobiohydrolase Elucidated by Structural and Transition Path Sampling Studies Knott, Brandon C.; Haddad Momeni, Majid; Crowley, Michael F. Journal of the American Chemical Society, Vol. 136, Issue 1 https://doi.org/10.1021/ja410291u	journal	December 2013
Equilibrium Time Correlation Functions from Irreversible Transformations in Trajectory Space † Geissler, Phillip L.; Dellago, Christoph The Journal of Physical Chemistry B, Vol. 108, Issue 21 https://doi.org/10.1021/jp037211l	journal	May 2004
Toward the Mechanism of Ionic Dissociation in Water Ballard, Andrew J.; Dellago, Christoph The Journal of Physical Chemistry B, Vol. 116, Issue 45 https://doi.org/10.1021/jp309300b	journal	November 2012
Solvent Structure, Dynamics, and Ion Mobility in Aqueous Solutions at 25 °C Koneshan, S.; Rasaiah, Jayendran C.; Lynden-Bell, R. M. The Journal of Physical Chemistry B, Vol. 102, Issue 21 https://doi.org/10.1021/jp980642x	journal	May 1998
Molecular Studies of Catalytic Reactions on Crystal Surfaces at High Pressures and High Temperatures by Infrared−Visible Sum Frequency Generation (SFG) Surface Vibrational Spectroscopy Somorjai, Gabor A.; Rupprechter, Günther The Journal of Physical Chemistry B, Vol. 103, Issue 10 https://doi.org/10.1021/jp983721h	journal	March 1999
Kinetic Pathways of Ion Pair Dissociation in Water Geissler, Phillip L.; Dellago, Christoph; Chandler, David The Journal of Physical Chemistry B, Vol. 103, Issue 18 https://doi.org/10.1021/jp984837g	journal	May 1999
Optimizing Nucleus Size Metrics for Liquid–Solid Nucleation from Transition Paths of Near-Nanosecond Duration Beckham, Gregg T.; Peters, Baron The Journal of Physical Chemistry Letters, Vol. 2, Issue 10 https://doi.org/10.1021/jz2002887	journal	April 2011
Nucleation and Growth in Structural Transformations of Nanocrystals Grünwald, Michael; Dellago, Christoph Nano Letters, Vol. 9, Issue 5 https://doi.org/10.1021/nl900609d	journal	May 2009
Heterogeneous catalysis Everett, D. H. Nature, Vol. 275, Issue 5680 https://doi.org/10.1038/275570b0	journal	October 1978
Spontaneous drying of non-polar deep-cavity cavitand pockets in aqueous solution Barnett, J. Wesley; Sullivan, Matthew R.; Long, Joshua A. Nature Chemistry, Vol. 12, Issue 7 https://doi.org/10.1038/s41557-020-0458-8	journal	May 2020
Forward flux sampling-type schemes for simulating rare events: Efficiency analysis Allen, Rosalind J.; Frenkel, Daan; ten Wolde, Pieter Rein The Journal of Chemical Physics, Vol. 124, Issue 19 https://doi.org/10.1063/1.2198827	journal	May 2006
Electrochemical interface between an ionic liquid and a model metallic electrode Reed, Stewart K.; Lanning, Oliver J.; Madden, Paul A. The Journal of Chemical Physics, Vol. 126, Issue 8 https://doi.org/10.1063/1.2464084	journal	February 2007
Statistically optimal analysis of samples from multiple equilibrium states Shirts, Michael R.; Chodera, John D. The Journal of Chemical Physics, Vol. 129, Issue 12 https://doi.org/10.1063/1.2978177	journal	September 2008
Statistical mechanics of isomerization dynamics in liquids and the transition state approximation Chandler, David The Journal of Chemical Physics, Vol. 68, Issue 6 https://doi.org/10.1063/1.436049	journal	January 1978
Influence of surface topology and electrostatic potential on water/electrode systems Siepmann, J. Ilja; Sprik, Michiel The Journal of Chemical Physics, Vol. 102, Issue 1 https://doi.org/10.1063/1.469429	journal	January 1995
Transition path sampling and the calculation of rate constants Dellago, Christoph; Bolhuis, Peter G.; Csajka, Félix S. The Journal of Chemical Physics, Vol. 108, Issue 5 https://doi.org/10.1063/1.475562	journal	February 1998
First spectroscopic evidence for molecular HCl on a liquid surface with sum frequency generation Baldelli, Steve; Schnitzer, Cheryl; Shultz, Mary Jane The Journal of Chemical Physics, Vol. 108, Issue 23 https://doi.org/10.1063/1.476456	journal	June 1998
On the calculation of reaction rate constants in the transition path ensemble Dellago, Christoph; Bolhuis, Peter G.; Chandler, David The Journal of Chemical Physics, Vol. 110, Issue 14 https://doi.org/10.1063/1.478569	journal	April 1999
Characterizing heterogeneous dynamics at hydrated electrode surfaces Willard, Adam P.; Limmer, David T.; Madden, Paul A. The Journal of Chemical Physics, Vol. 138, Issue 18 https://doi.org/10.1063/1.4803503	journal	May 2013
Removing the barrier to the calculation of activation energies Mesele, Oluwaseun O.; Thompson, Ward H. The Journal of Chemical Physics, Vol. 145, Issue 13 https://doi.org/10.1063/1.4964284	journal	October 2016
A one-way shooting algorithm for transition path sampling of asymmetric barriers Brotzakis, Z. Faidon; Bolhuis, Peter G. The Journal of Chemical Physics, Vol. 145, Issue 16 https://doi.org/10.1063/1.4965882	journal	October 2016
Importance sampling large deviations in nonequilibrium steady states. I Ray, Ushnish; Chan, Garnet Kin-Lic; Limmer, David T. The Journal of Chemical Physics, Vol. 148, Issue 12 https://doi.org/10.1063/1.5003151	journal	March 2018
Studying rare nonadiabatic dynamics with transition path sampling quantum jump trajectories Schile, Addison J.; Limmer, David T. The Journal of Chemical Physics, Vol. 149, Issue 21 https://doi.org/10.1063/1.5058281	journal	December 2018
Sampling the multiple folding mechanisms of Trp-cage in explicit solvent Juraszek, J.; Bolhuis, P. G. Proceedings of the National Academy of Sciences, Vol. 103, Issue 43 https://doi.org/10.1073/pnas.0606692103	journal	October 2006
Reaction coordinate of an enzymatic reaction revealed by transition path sampling Quaytman, S. L.; Schwartz, S. D. Proceedings of the National Academy of Sciences, Vol. 104, Issue 30 https://doi.org/10.1073/pnas.0704304104	journal	July 2007
Atomic detail of chemical transformation at the transition state of an enzymatic reaction Saen-oon, S.; Quaytman-Machleder, S.; Schramm, V. L. Proceedings of the National Academy of Sciences, Vol. 105, Issue 43 https://doi.org/10.1073/pnas.0808413105	journal	October 2008
Fluctuation enhanced electrochemical reaction rates at the nanoscale Garcia-Morales, V.; Krischer, K. Proceedings of the National Academy of Sciences, Vol. 107, Issue 10 https://doi.org/10.1073/pnas.0909240107	journal	February 2010
Hydration of metal surfaces can be dynamically heterogeneous and hydrophobic Limmer, David T.; Willard, Adam P.; Madden, Paul Proceedings of the National Academy of Sciences, Vol. 110, Issue 11 https://doi.org/10.1073/pnas.1301596110	journal	February 2013
Theory of amorphous ices Limmer, David T.; Chandler, David Proceedings of the National Academy of Sciences, Vol. 111, Issue 26 https://doi.org/10.1073/pnas.1407277111	journal	May 2014
Microscopic dynamics of charge separation at the aqueous electrochemical interface Kattirtzi, John A.; Limmer, David T.; Willard, Adam P. Proceedings of the National Academy of Sciences, Vol. 114, Issue 51 https://doi.org/10.1073/pnas.1700093114	journal	July 2017
Atomistic understanding of kinetic pathways for single base-pair binding and unbinding in DNA Hagan, M. F.; Dinner, A. R.; Chandler, D. Proceedings of the National Academy of Sciences, Vol. 100, Issue 24 https://doi.org/10.1073/pnas.2036378100	journal	November 2003
Activation Energies from Transition Path Sampling Simulations Dellago, Christoph; Bolhuis, Peter G. Molecular Simulation, Vol. 30, Issue 11-12 https://doi.org/10.1080/08927020412331294869	journal	September 2004
Forward flux sampling for rare event simulations Allen, Rosalind J.; Valeriani, Chantal; Rein ten Wolde, Pieter Journal of Physics: Condensed Matter, Vol. 21, Issue 46 https://doi.org/10.1088/0953-8984/21/46/463102	journal	October 2009
Charge Fluctuations in Nanoscale Capacitors Limmer, David T.; Merlet, Céline; Salanne, Mathieu Physical Review Letters, Vol. 111, Issue 10 https://doi.org/10.1103/physrevlett.111.106102	journal	September 2013
Atomistic Mechanism of NaCl Nucleation from an Aqueous Solution Zahn, Dirk Physical Review Letters, Vol. 92, Issue 4 https://doi.org/10.1103/physrevlett.92.040801	journal	January 2004
Excitations Are Localized and Relaxation Is Hierarchical in Glass-Forming Liquids Keys, Aaron S.; Hedges, Lester O.; Garrahan, Juan P. Physical Review X, Vol. 1, Issue 2 https://doi.org/10.1103/physrevx.1.021013	journal	November 2011
Autoionization in Liquid Water Geissler, P. L. Science, Vol. 291, Issue 5511 https://doi.org/10.1126/science.1056991	journal	March 2001
Single-Molecule Enzymatic Dynamics Lu, H. P. Science, Vol. 282, Issue 5395 https://doi.org/10.1126/science.282.5395.1877	journal	December 1998
Trajectory Stratification of Stochastic Dynamics Dinner, Aaron R.; Mattingly, Jonathan C.; Tempkin, Jeremy O. B. SIAM Review, Vol. 60, Issue 4 https://doi.org/10.1137/16m1104329	journal	January 2018
Heterogeneous Catalysis Weisz, P. B. Annual Review of Physical Chemistry, Vol. 21, Issue 1 https://doi.org/10.1146/annurev.pc.21.100170.001135	journal	October 1970
Transition-Path Theory and Path-Finding Algorithms for the Study of Rare Events E., Weinan; Vanden-Eijnden, Eric Annual Review of Physical Chemistry, Vol. 61, Issue 1 https://doi.org/10.1146/annurev.physchem.040808.090412	journal	March 2010
T RANSITION P ATH S AMPLING : Throwing Ropes Over Rough Mountain Passes, in the Dark Bolhuis, Peter G.; Chandler, David; Dellago, Christoph Annual Review of Physical Chemistry, Vol. 53, Issue 1 https://doi.org/10.1146/annurev.physchem.53.082301.113146	journal	October 2002
Transport Coefficients from Large Deviation Functions Gao, Chloe; Limmer, David Entropy, Vol. 19, Issue 11 https://doi.org/10.3390/e19110571	journal	October 2017
A Review of the Aqueous Aerosol Surface Chemistry in the Atmospheric Context Valsaraj, Kalliat T. Open Journal of Physical Chemistry, Vol. 02, Issue 01 https://doi.org/10.4236/ojpc.2012.21008	journal	January 2012
Forward Flux Sampling for rare event simulations Allen, Rosalind J.; Valeriani, Chantal; Wolde, Pieter Rein ten arXiv https://doi.org/10.48550/arxiv.0906.4758	text	January 2009
Excitations are localized and relaxation is hierarchical in glass-forming liquids Keys, Aaron S.; Hedges, Lester O.; Garrahan, Juan P. arXiv https://doi.org/10.48550/arxiv.1107.3628	text	January 2011
Theory of amorphous ices Limmer, David T.; Chandler, David arXiv https://doi.org/10.48550/arxiv.1306.4728	text	January 2013
Importance sampling large deviations in nonequilibrium steady states. I Ray, Ushnish; Chan, Garnet Kin-Lic; Limmer, David T. arXiv https://doi.org/10.48550/arxiv.1708.00459	text	January 2017
Studying rare nonadiabatic dynamics with transition path sampling quantum jump trajectories Schile, Addison J.; Limmer, David T. arXiv https://doi.org/10.48550/arxiv.1809.03501	text	January 2018
Investigating Rare Events by Transition Interface Sampling Moroni, Daniele; van Erp, Titus S.; Bolhuis, Peter G. arXiv https://doi.org/10.48550/arxiv.cond-mat/0311571	text	January 2003
Autoionization in liquid water Geissler, P. L.; Dellago, C.; Chandler, D. American Association for the Advancement of Science (AAAS) https://doi.org/10.5167/uzh-3197	text	January 2001
Toward a general parameterization of N ₂ O ₅ reactivity on aqueous particles: the competing effects of particle liquid water, nitrate and chloride Bertram, T. H.; Thornton, J. A. Atmospheric Chemistry and Physics, Vol. 9, Issue 21 https://doi.org/10.5194/acp-9-8351-2009	journal	January 2009
Toward a general parameterization of N ₂ O ₅ reactivity on aqueous particles: the competing effects of particle liquid water, nitrate and chloride Bertram, T. H.; Thornton, J. A. Atmospheric Chemistry and Physics Discussions, Vol. 9, Issue 4 https://doi.org/10.5194/acpd-9-15181-2009	journal	January 2009

Similar Records

Transition path sampling and the calculation of rate constants

Journal Article · 1997 · Journal of Chemical Physics · OSTI ID:773751

Dellago, C; Bolhuis, P G; Csajka, F S; +1 more

Elaborating transition interface sampling methods

Journal Article · 2005 · Journal of Computational Physics · OSTI ID:20687229

Erp, Titus S. van .; Bolhuis, Peter G

Importance sampling large deviations in nonequilibrium steady states. I

Journal Article · 2018 · Journal of Chemical Physics · OSTI ID:1543844

Ray, Ushnish; Chan, Garnet Kin-Lic; Limmer, David T.

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY

Title: Rate constants in spatially inhomogeneous systems

Citation Formats

References (78)

Similar Records

Related Subjects