1
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Goswami Y, Sastry S. Kinetic reconstruction of free energies as a function of multiple order parameters. J Chem Phys 2023; 158:144502. [PMID: 37061464 DOI: 10.1063/5.0144338] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/17/2023] Open
Abstract
A vast array of phenomena, ranging from chemical reactions to phase transformations, are analyzed in terms of a free energy surface defined with respect to a single or multiple order parameters. Enhanced sampling methods are typically used, especially in the presence of large free energy barriers, to estimate free energies using biasing protocols and sampling of transition paths. Kinetic reconstructions of free energy barriers of intermediate height have been performed, with respect to a single order parameter, employing the steady state properties of unconstrained simulation trajectories when barrier crossing is achievable with reasonable computational effort. Considering such cases, we describe a method to estimate free energy surfaces with respect to multiple order parameters from a steady state ensemble of trajectories. The approach applies to cases where the transition rates between pairs of order parameter values considered is not affected by the presence of an absorbing boundary, whereas the macroscopic fluxes and sampling probabilities are. We demonstrate the applicability of our prescription on different test cases of random walkers executing Brownian motion in order parameter space with an underlying (free) energy landscape and discuss strategies to improve numerical estimates of the fluxes and sampling. We next use this approach to reconstruct the free energy surface for supercooled liquid silicon with respect to the degree of crystallinity and density, from unconstrained molecular dynamics simulations, and obtain results quantitatively consistent with earlier results from umbrella sampling.
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Affiliation(s)
- Yagyik Goswami
- Theoretical Sciences Unit and School of Advanced Materials, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur Campus, Bengaluru 560064, India
| | - Srikanth Sastry
- Theoretical Sciences Unit and School of Advanced Materials, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur Campus, Bengaluru 560064, India
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2
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Reiner M, Bachmair B, Tiefenbacher MX, Mai S, González L, Marquetand P, Dellago C. Nonadiabatic Forward Flux Sampling for Excited-State Rare Events. J Chem Theory Comput 2023; 19:1657-1671. [PMID: 36856706 PMCID: PMC10061683 DOI: 10.1021/acs.jctc.2c01088] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2022] [Indexed: 03/02/2023]
Abstract
We present a rare event sampling scheme applicable to coupled electronic excited states. In particular, we extend the forward flux sampling (FFS) method for rare event sampling to a nonadiabatic version (NAFFS) that uses the trajectory surface hopping (TSH) method for nonadiabatic dynamics. NAFFS is applied to two dynamically relevant excited-state models that feature an avoided crossing and a conical intersection with tunable parameters. We investigate how nonadiabatic couplings, temperature, and reaction barriers affect transition rate constants in regimes that cannot be otherwise obtained with plain, traditional TSH. The comparison with reference brute-force TSH simulations for limiting cases of rareness shows that NAFFS can be several orders of magnitude cheaper than conventional TSH and thus represents a conceptually novel tool to extend excited-state dynamics to time scales that are able to capture rare nonadiabatic events.
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Affiliation(s)
- Madlen
Maria Reiner
- Research
Platform on Accelerating Photoreaction Discovery (ViRAPID), University of Vienna, Währinger Strasse 17, 1090 Vienna, Austria
- Vienna
Doctoral School in Physics, University of
Vienna, Boltzmanngasse
5, 1090 Vienna, Austria
| | - Brigitta Bachmair
- Research
Platform on Accelerating Photoreaction Discovery (ViRAPID), University of Vienna, Währinger Strasse 17, 1090 Vienna, Austria
- Vienna
Doctoral School in Chemistry, University
of Vienna, Währinger
Strasse 42, 1090 Vienna, Austria
| | - Maximilian Xaver Tiefenbacher
- Research
Platform on Accelerating Photoreaction Discovery (ViRAPID), University of Vienna, Währinger Strasse 17, 1090 Vienna, Austria
- Vienna
Doctoral School in Chemistry, University
of Vienna, Währinger
Strasse 42, 1090 Vienna, Austria
| | - Sebastian Mai
- Institute
of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Strasse 17, 1090 Vienna, Austria
| | - Leticia González
- Research
Platform on Accelerating Photoreaction Discovery (ViRAPID), University of Vienna, Währinger Strasse 17, 1090 Vienna, Austria
- Institute
of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Strasse 17, 1090 Vienna, Austria
| | - Philipp Marquetand
- Research
Platform on Accelerating Photoreaction Discovery (ViRAPID), University of Vienna, Währinger Strasse 17, 1090 Vienna, Austria
- Institute
of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Strasse 17, 1090 Vienna, Austria
| | - Christoph Dellago
- Research
Platform on Accelerating Photoreaction Discovery (ViRAPID), University of Vienna, Währinger Strasse 17, 1090 Vienna, Austria
- Faculty
of Physics, University of Vienna, Kolingasse 14-16, 1090 Vienna, Austria
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3
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Appeldorn JH, Lemcke S, Speck T, Nikoubashman A. Employing Artificial Neural Networks to Identify Reaction Coordinates and Pathways for Self-Assembly. J Phys Chem B 2022; 126:5007-5016. [DOI: 10.1021/acs.jpcb.2c02232] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Affiliation(s)
- Jörn H. Appeldorn
- Institute of Physics, Johannes Gutenberg-University Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
| | - Simon Lemcke
- Institute of Physics, Johannes Gutenberg-University Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
| | - Thomas Speck
- Institute of Physics, Johannes Gutenberg-University Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
| | - Arash Nikoubashman
- Institute of Physics, Johannes Gutenberg-University Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
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4
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Mehdi S, Wang D, Pant S, Tiwary P. Accelerating All-Atom Simulations and Gaining Mechanistic Understanding of Biophysical Systems through State Predictive Information Bottleneck. J Chem Theory Comput 2022; 18:3231-3238. [PMID: 35384668 DOI: 10.1021/acs.jctc.2c00058] [Citation(s) in RCA: 28] [Impact Index Per Article: 14.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023]
Abstract
An effective implementation of enhanced sampling algorithms for molecular dynamics simulations requires a priori knowledge of the approximate reaction coordinate describing the relevant mechanisms in the system. In this work, we focus on the recently developed artificial intelligence-based State Predictive Information Bottleneck (SPIB) approach and demonstrate how SPIB can learn such a reaction coordinate as a deep neural network even from undersampled trajectories. We exemplify its usefulness by achieving more than 40 times acceleration in simulating two model biophysical systems through well-tempered metadynamics performed by biasing along the SPIB-learned reaction coordinate. These include left- to right-handed chirality transitions in a synthetic helical peptide (Aib)9 and permeation of a small benzoic acid molecule through a synthetic, symmetric phospholipid bilayer. In addition to significantly accelerating the dynamics and achieving back and forth movement between different metastable states, the SPIB-based reaction coordinate gives mechanistic insights into the processes driving these two important problems.
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Affiliation(s)
- Shams Mehdi
- Biophysics Program and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, United States
| | - Dedi Wang
- Biophysics Program and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, United States
| | - Shashank Pant
- Center for Biophysics and Quantitative Biology, Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
| | - Pratyush Tiwary
- Department of Chemistry and Biochemistry and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, United States
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5
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Russo JD, Zhang S, Leung JMG, Bogetti AT, Thompson JP, DeGrave AJ, Torrillo PA, Pratt AJ, Wong KF, Xia J, Copperman J, Adelman JL, Zwier MC, LeBard DN, Zuckerman DM, Chong LT. WESTPA 2.0: High-Performance Upgrades for Weighted Ensemble Simulations and Analysis of Longer-Timescale Applications. J Chem Theory Comput 2022; 18:638-649. [PMID: 35043623 DOI: 10.1021/acs.jctc.1c01154] [Citation(s) in RCA: 15] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
Abstract
The weighted ensemble (WE) family of methods is one of several statistical mechanics-based path sampling strategies that can provide estimates of key observables (rate constants and pathways) using a fraction of the time required by direct simulation methods such as molecular dynamics or discrete-state stochastic algorithms. WE methods oversee numerous parallel trajectories using intermittent overhead operations at fixed time intervals, enabling facile interoperability with any dynamics engine. Here, we report on the major upgrades to the WESTPA software package, an open-source, high-performance framework that implements both basic and recently developed WE methods. These upgrades offer substantial improvements over traditional WE methods. The key features of the new WESTPA 2.0 software enhance the efficiency and ease of use: an adaptive binning scheme for more efficient surmounting of large free energy barriers, streamlined handling of large simulation data sets, exponentially improved analysis of kinetics, and developer-friendly tools for creating new WE methods, including a Python API and resampler module for implementing both binned and "binless" WE strategies.
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Affiliation(s)
- John D Russo
- Department of Biomedical Engineering, Oregon Health and Science University, Portland, Oregon 97239-3098, United States
| | - She Zhang
- OpenEye Scientific, Santa Fe, New Mexico 87508, United States
| | - Jeremy M G Leung
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, United States
| | - Anthony T Bogetti
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, United States
| | - Jeff P Thompson
- OpenEye Scientific, Santa Fe, New Mexico 87508, United States
| | - Alex J DeGrave
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, United States
| | - Paul A Torrillo
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, United States
| | - A J Pratt
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, United States
| | - Kim F Wong
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, United States
| | - Junchao Xia
- OpenEye Scientific, Santa Fe, New Mexico 87508, United States
| | - Jeremy Copperman
- Department of Biomedical Engineering, Oregon Health and Science University, Portland, Oregon 97239-3098, United States
| | - Joshua L Adelman
- Department of Biological Sciences, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, United States
| | - Matthew C Zwier
- Department of Chemistry, Drake University, Des Moines, Iowa 50311-4505, United States
| | - David N LeBard
- OpenEye Scientific, Santa Fe, New Mexico 87508, United States
| | - Daniel M Zuckerman
- Department of Biomedical Engineering, Oregon Health and Science University, Portland, Oregon 97239-3098, United States
| | - Lillian T Chong
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, United States
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6
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Zou Z, Tsai ST, Tiwary P. Toward Automated Sampling of Polymorph Nucleation and Free Energies with the SGOOP and Metadynamics. J Phys Chem B 2021; 125:13049-13056. [PMID: 34788047 DOI: 10.1021/acs.jpcb.1c07595] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Understanding the driving forces behind the nucleation of different polymorphs is of great importance for material sciences and the pharmaceutical industry. This includes understanding the reaction coordinate that governs the nucleation process and correctly calculating the relative free energies of different polymorphs. Here, we demonstrate, for the prototypical case of urea nucleation from the melt, how one can learn such a one-dimensional reaction coordinate as a function of prespecified order parameters and use it to perform efficient biased all-atom molecular dynamics simulations. The reaction coordinate is learnt as a function of the generic thermodynamic and structural order parameters using the "spectral gap optimization of order parameters (SGOOP)" approach [Tiwary, P. and Berne, B. J. Proc. Natl. Acad. Sci. U.S.A. (2016)] and is biased using well-tempered metadynamics simulations. The reaction coordinate gives insights into the role played by different structural and thermodynamics order parameters, and the biased simulations obtain accurate relative free energies for different polymorphs. This includes an accurate prediction of the approximate pressure at which urea undergoes a phase transition and one of the metastable polymorphs becomes the most stable conformation. We believe the ideas demonstrated in this work will facilitate efficient sampling of nucleation in complex, generic systems.
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Affiliation(s)
- Ziyue Zou
- Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland 20742, United States
| | - Sun-Ting Tsai
- Department of Physics, University of Maryland, College Park, Maryland 20742, United States.,Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, United States
| | - Pratyush Tiwary
- Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland 20742, United States.,Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, United States
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7
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Tsai ST, Smith Z, Tiwary P. SGOOP-d: Estimating Kinetic Distances and Reaction Coordinate Dimensionality for Rare Event Systems from Biased/Unbiased Simulations. J Chem Theory Comput 2021; 17:6757-6765. [PMID: 34662516 DOI: 10.1021/acs.jctc.1c00431] [Citation(s) in RCA: 17] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Abstract
Understanding kinetics including reaction pathways and associated transition rates is an important yet difficult problem in numerous chemical and biological systems, especially in situations with multiple competing pathways. When these high-dimensional systems are projected on low-dimensional coordinates, which are often needed for enhanced sampling or for interpretation of simulations and experiments, one can end up losing the kinetic connectivity of the underlying high-dimensional landscape. Thus, in the low-dimensional projection, metastable states might appear closer or further than they actually are. To deal with this issue, in this work, we develop a formalism that learns a multidimensional yet minimally complex reaction coordinate (RC) for generic high-dimensional systems. When projected along this RC, all possible kinetically relevant pathways can be demarcated and the true high-dimensional connectivity is maintained. One of the defining attributes of our method lies in that it can work on long unbiased simulations as well as biased simulations often needed for rare event systems. We demonstrate the utility of the method by studying a range of model systems including conformational transitions in a small peptide Ace-Ala3-Nme, where we show how two-dimensional and three-dimensional RCs found by our previously published spectral gap optimization method "SGOOP" [Tiwary, P. and Berne, B. J. Proc. Natl. Acad. Sci. 2016, 113, 2839] can capture the kinetics for 23 and all 28 out of the 28 dominant state-to-state transitions, respectively.
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Affiliation(s)
- Sun-Ting Tsai
- Department of Physics and Institute for Physical Science and Technology, University of Maryland, College Park 20742, Maryland, United States
| | - Zachary Smith
- Biophysics Program and Institute for Physical Science and Technology, University of Maryland, College Park 20742, Maryland, United States
| | - Pratyush Tiwary
- Department of Chemistry and Biochemistry and Institute for Physical Science and Technology, University of Maryland, College Park 20742, Maryland, United States
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8
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Clark AE, Adams H, Hernandez R, Krylov AI, Niklasson AMN, Sarupria S, Wang Y, Wild SM, Yang Q. The Middle Science: Traversing Scale In Complex Many-Body Systems. ACS CENTRAL SCIENCE 2021; 7:1271-1287. [PMID: 34471670 PMCID: PMC8393217 DOI: 10.1021/acscentsci.1c00685] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/04/2023]
Abstract
A roadmap is developed that integrates simulation methodology and data science methods to target new theories that traverse the multiple length- and time-scale features of many-body phenomena.
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Affiliation(s)
- Aurora E. Clark
- Department of Chemistry, Washington State University, Pullman, Washington 99163, United States
| | - Henry Adams
- Department of Mathematics, Colorado State
University, Fort Collins, Colorado 80523, United States
| | - Rigoberto Hernandez
- Departments
of Chemistry, Chemical and Biomolecular Engineering, and Materials
Science and Engineering, Johns Hopkins University, Baltimore, Maryland 21218, United States
| | - Anna I. Krylov
- Department of Chemistry, University of Southern California, Los Angeles, California 90089, United States
| | - Anders M. N. Niklasson
- Theoretical
Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Sapna Sarupria
- Department of Chemical and Biomolecular Engineering, Center for Optical
Materials Science and Engineering Technologies (COMSET), Clemson University, Clemson, South Carolina 29670, United States
- Department
of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455, United States
| | - Yusu Wang
- Halıcıŏglu Data Science Institute, University of California, San Diego, La Jolla, California 92093, United States
| | - Stefan M. Wild
- Mathematics
and Computer Science Division, Argonne National
Laboratory, Lemont, Illinois 60439, United
States
| | - Qian Yang
- Computer Science and Engineering Department, University of Connecticut, Storrs, Connecticut 06269-4155, United States
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9
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DeGrave AJ, Bogetti AT, Chong LT. The RED scheme: Rate-constant estimation from pre-steady state weighted ensemble simulations. J Chem Phys 2021; 154:114111. [PMID: 33752378 PMCID: PMC7972523 DOI: 10.1063/5.0041278] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2020] [Accepted: 02/11/2021] [Indexed: 12/13/2022] Open
Abstract
We present the Rate from Event Durations (RED) scheme, a new scheme that more efficiently calculates rate constants using the weighted ensemble path sampling strategy. This scheme enables rate-constant estimation from shorter trajectories by incorporating the probability distribution of event durations, or barrier-crossing times, from a simulation. We have applied the RED scheme to weighted ensemble simulations of a variety of rare-event processes that range in complexity: residue-level simulations of protein conformational switching, atomistic simulations of Na+/Cl- association in explicit solvent, and atomistic simulations of protein-protein association in explicit solvent. Rate constants were estimated with up to 50% greater efficiency than the original weighted ensemble scheme. Importantly, our scheme accounts for the systematic error that results from statistical bias toward the observation of events with short durations and reweights the event duration distribution accordingly. The RED scheme is relevant to any simulation strategy that involves unbiased trajectories of similar length to the most probable event duration, including weighted ensemble, milestoning, and standard simulations as well as the construction of Markov state models.
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Affiliation(s)
| | - Anthony T. Bogetti
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
| | - Lillian T. Chong
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
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10
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Torrillo PA, Bogetti AT, Chong LT. A Minimal, Adaptive Binning Scheme for Weighted Ensemble Simulations. J Phys Chem A 2021; 125:1642-1649. [PMID: 33577732 PMCID: PMC8091492 DOI: 10.1021/acs.jpca.0c10724] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Abstract
A promising approach for simulating rare events with rigorous kinetics is the weighted ensemble path sampling strategy. One challenge of this strategy is the division of configurational space into bins for sampling. Here we present a minimal adaptive binning (MAB) scheme for the automated, adaptive placement of bins along a progress coordinate within the framework of the weighted ensemble strategy. Results reveal that the MAB binning scheme, despite its simplicity, is more efficient than a manual, fixed binning scheme in generating transitions over large free energy barriers, generating a diversity of pathways, estimating rate constants, and sampling conformations. The scheme is general and extensible to any rare-events sampling strategy that employs progress coordinates.
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Affiliation(s)
- Paul A Torrillo
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, United States
| | - Anthony T Bogetti
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, United States
| | - Lillian T Chong
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, United States
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11
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Khan SA, Dickson BM, Peters B. How fluxional reactants limit the accuracy/efficiency of infrequent metadynamics. J Chem Phys 2020; 153:054125. [DOI: 10.1063/5.0006980] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Affiliation(s)
- Salman A. Khan
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106-5080, USA
| | | | - Baron Peters
- Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
- Department of Chemistry and Biochemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
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12
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Hussain S, Haji-Akbari A. Studying rare events using forward-flux sampling: Recent breakthroughs and future outlook. J Chem Phys 2020; 152:060901. [DOI: 10.1063/1.5127780] [Citation(s) in RCA: 27] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Sarwar Hussain
- Department of Chemical and Environmental Engineering, Yale University, New Haven, Connecticut 06520, USA
| | - Amir Haji-Akbari
- Department of Chemical and Environmental Engineering, Yale University, New Haven, Connecticut 06520, USA
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13
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Solvent fluctuations in the solvation shell determine the activation barrier for crystal growth rates. Proc Natl Acad Sci U S A 2019; 116:23954-23959. [PMID: 31712439 DOI: 10.1073/pnas.1910691116] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Solution crystallization is a common technique to grow advanced, functional crystalline materials. Supersaturation, temperature, and solvent composition are known to influence the growth rates and thereby properties of crystalline materials; however, a satisfactory explanation of how these factors affect the activation barrier for growth rates has not been developed. We report here that these effects can be attributed to a previously unrecognized consequence of solvent fluctuations in the solvation shell of solute molecules attaching to the crystal surface. With increasing supersaturation, the average hydration number of the glutamic acid molecule decreases and can reach an asymptotic limit corresponding to the number of adsorption sites on the molecule. The hydration number of the glutamic acid molecule also fluctuates due to the rapid exchange of solvent in the solvation shell and local variation in the supersaturation. These rapid fluctuations allow quasi-equilibrium between fully solvated and partially desolvated states of molecules, which can be used to construct a double-well potential and thereby to identify the transition state and the required activation barrier. The partially desolvated molecules are not stable and can attach spontaneously to the crystal surface. The activation barrier versus hydration number follows the Evans-Polanyi relation. The predicted absolute growth rates of the α-glutamic acid crystal at lower supersaturations are in reasonable agreement with the experimental observations.
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14
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Tsai ST, Smith Z, Tiwary P. Reaction coordinates and rate constants for liquid droplet nucleation: Quantifying the interplay between driving force and memory. J Chem Phys 2019; 151:154106. [PMID: 31640371 DOI: 10.1063/1.5124385] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022] Open
Abstract
In this work, we revisit the classic problem of homogeneous nucleation of a liquid droplet in a supersaturated vapor phase. We consider this at different extents of the driving force, or equivalently the supersaturation, and calculate a reaction coordinate (RC) for nucleation as the driving force is varied. The RC is constructed as a linear combination of three order parameters, where one accounts for the number of liquidlike atoms and the other two for local density fluctuations. The RC is calculated from biased and unbiased molecular dynamics (MD) simulations using the spectral gap optimization approach "SGOOP" [P. Tiwary and B. J. Berne, Proc. Natl. Acad. Sci. U. S. A. 113, 2839 (2016)]. Our key finding is that as the supersaturation decreases, the RC ceases to simply be the number of liquidlike atoms, and instead, it becomes important to explicitly consider local density fluctuations that correlate with shape and density variations in the nucleus. All three order parameters are found to have similar barriers in their respective potentials of mean force; however, as the supersaturation decreases, the density fluctuations decorrelate slower and thus carry longer memory. Thus, at lower supersaturations, density fluctuations are non-Markovian and cannot be simply ignored from the RC by virtue of being noise. Finally, we use this optimized RC to calculate nucleation rates in the infrequent metadynamics framework and show that it leads to a more accurate estimate of the nucleation rate with four orders of magnitude acceleration relative to unbiased MD.
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Affiliation(s)
- Sun-Ting Tsai
- Department of Physics and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
| | - Zachary Smith
- Biophysics Program and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
| | - Pratyush Tiwary
- Department of Chemistry and Biochemistry and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
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