DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Toward Automated Sampling of Polymorph Nucleation and Free Energies with the SGOOP and Metadynamics

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. Here, we believe the ideas demonstrated in this work will facilitate efficient sampling of nucleation in complex, genericmore » systems.« less

Authors:
 [1];  [1]; ORCiD logo [1]
  1. University of Maryland, College Park, MD (United States)
Publication Date:
Research Org.:
Univ. of Maryland, College Park, MD (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1991192
Grant/Contract Number:  
SC0021009
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Physical Chemistry. B
Additional Journal Information:
Journal Volume: 125; Journal Issue: 47; Journal ID: ISSN 1520-6106
Publisher:
American Chemical Society
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; Computer simulations; Entropy; Free energy; Nucleation; Urea

Citation Formats

Zou, Ziyue, Tsai, Sun-Ting, and Tiwary, Pratyush. Toward Automated Sampling of Polymorph Nucleation and Free Energies with the SGOOP and Metadynamics. United States: N. p., 2021. Web. doi:10.1021/acs.jpcb.1c07595.
Zou, Ziyue, Tsai, Sun-Ting, & Tiwary, Pratyush. Toward Automated Sampling of Polymorph Nucleation and Free Energies with the SGOOP and Metadynamics. United States. https://doi.org/10.1021/acs.jpcb.1c07595
Zou, Ziyue, Tsai, Sun-Ting, and Tiwary, Pratyush. Wed . "Toward Automated Sampling of Polymorph Nucleation and Free Energies with the SGOOP and Metadynamics". United States. https://doi.org/10.1021/acs.jpcb.1c07595. https://www.osti.gov/servlets/purl/1991192.
@article{osti_1991192,
title = {Toward Automated Sampling of Polymorph Nucleation and Free Energies with the SGOOP and Metadynamics},
author = {Zou, Ziyue and Tsai, Sun-Ting and Tiwary, Pratyush},
abstractNote = {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. Here, we believe the ideas demonstrated in this work will facilitate efficient sampling of nucleation in complex, generic systems.},
doi = {10.1021/acs.jpcb.1c07595},
journal = {Journal of Physical Chemistry. B},
number = 47,
volume = 125,
place = {United States},
year = {Wed Nov 17 00:00:00 EST 2021},
month = {Wed Nov 17 00:00:00 EST 2021}
}

Works referenced in this record:

Polymorph control: past, present and future
journal, March 2008


Giant Anomalous Strain between High-Pressure Phases and the Mesomers of Urea
journal, January 2017

  • Roszak, Kinga; Katrusiak, Andrzej
  • The Journal of Physical Chemistry C, Vol. 121, Issue 1
  • DOI: 10.1021/acs.jpcc.6b11454

High-Pressure High-Temperature Structural Properties of Urea
journal, January 2017

  • Dziubek, Kamil; Citroni, Margherita; Fanetti, Samuele
  • The Journal of Physical Chemistry C, Vol. 121, Issue 4
  • DOI: 10.1021/acs.jpcc.6b11059

Overcoming time scale and finite size limitations to compute nucleation rates from small scale well tempered metadynamics simulations
journal, December 2016

  • Salvalaglio, Matteo; Tiwary, Pratyush; Maggioni, Giovanni Maria
  • The Journal of Chemical Physics, Vol. 145, Issue 21
  • DOI: 10.1063/1.4966265

Conformational Polymorphism
journal, December 2013

  • Cruz-Cabeza, Aurora J.; Bernstein, Joel
  • Chemical Reviews, Vol. 114, Issue 4
  • DOI: 10.1021/cr400249d

Nonphysical sampling distributions in Monte Carlo free-energy estimation: Umbrella sampling
journal, February 1977


Reaction coordinates and rate constants for liquid droplet nucleation: Quantifying the interplay between driving force and memory
journal, October 2019

  • Tsai, Sun-Ting; Smith, Zachary; Tiwary, Pratyush
  • The Journal of Chemical Physics, Vol. 151, Issue 15
  • DOI: 10.1063/1.5124385

Entropy from Correlations in TIP4P Water
journal, February 2010

  • Giuffré, Emanuela; Prestipino, Santi; Saija, Franz
  • Journal of Chemical Theory and Computation, Vol. 6, Issue 3
  • DOI: 10.1021/ct900627q

Role of Polymorphism in Materials Science
journal, August 2014

  • Mondal, Pradip; Chopra, Deepak
  • Material Science Research India, Vol. 11, Issue 1
  • DOI: 10.13005/msri/110106

Polymorphism at High Pressures
journal, January 1916

  • Bridgman, P. W.
  • Proceedings of the American Academy of Arts and Sciences, Vol. 52, Issue 3
  • DOI: 10.2307/20025675

H-Bond Breaking in High-Pressure Urea
journal, August 2009

  • Olejniczak, Anna; Ostrowska, Kinga; Katrusiak, Andrzej
  • The Journal of Physical Chemistry C, Vol. 113, Issue 35
  • DOI: 10.1021/jp904942c

Polymorphism of pharmaceutical molecules: perspectives on nucleation
journal, January 2010

  • Lu, Jie; Li, Zhen; Jiang, Xiaolin
  • Frontiers of Chemical Engineering in China, Vol. 4, Issue 1
  • DOI: 10.1007/s11705-009-0294-2

The Amber biomolecular simulation programs
journal, January 2005

  • Case, David A.; Cheatham, Thomas E.; Darden, Tom
  • Journal of Computational Chemistry, Vol. 26, Issue 16
  • DOI: 10.1002/jcc.20290

Polymorphism as an additional functionality of materials for technological applications at surfaces and interfaces
journal, January 2019

  • Gentili, Denis; Gazzano, Massimo; Melucci, Manuela
  • Chemical Society Reviews, Vol. 48, Issue 9
  • DOI: 10.1039/c8cs00283e

Obtaining reaction coordinates by likelihood maximization
journal, August 2006

  • Peters, Baron; Trout, Bernhardt L.
  • The Journal of Chemical Physics, Vol. 125, Issue 5
  • DOI: 10.1063/1.2234477

Predicting polymorphism in molecular crystals using orientational entropy
journal, September 2018

  • Piaggi, Pablo M.; Parrinello, Michele
  • Proceedings of the National Academy of Sciences, Vol. 115, Issue 41
  • DOI: 10.1073/pnas.1811056115

Orientational correlations and entropy in liquid water
journal, September 1996

  • Lazaridis, Themis; Karplus, Martin
  • The Journal of Chemical Physics, Vol. 105, Issue 10
  • DOI: 10.1063/1.472247

Sampling Rare Switching Events in Biochemical Networks
journal, January 2005


Entropy of Liquid Water from Ab Initio Molecular Dynamics
journal, December 2011

  • Zhang, Cui; Spanu, Leonardo; Galli, Giulia
  • The Journal of Physical Chemistry B, Vol. 115, Issue 48
  • DOI: 10.1021/jp204981y

P-LINCS:  A Parallel Linear Constraint Solver for Molecular Simulation
journal, December 2007

  • Hess, Berk
  • Journal of Chemical Theory and Computation, Vol. 4, Issue 1
  • DOI: 10.1021/ct700200b

A practical guide to pharmaceutical polymorph screening & selection
journal, August 2014


A general set of order parameters for molecular crystals
journal, February 2011

  • Santiso, Erik E.; Trout, Bernhardt L.
  • The Journal of Chemical Physics, Vol. 134, Issue 6
  • DOI: 10.1063/1.3548889

Numerical study of the effect of thiol–disulfide exchange in the cluster phase of β-lactoglobulin aggregation
journal, January 2012

  • Zeiler, Rosanne N. W.; Bolhuis, Peter G.
  • Faraday Discussions, Vol. 158
  • DOI: 10.1039/c2fd20030a

Promoting transparency and reproducibility in enhanced molecular simulations
journal, July 2019


Principles of maximum entropy and maximum caliber in statistical physics
journal, July 2013


GROMACS: High performance molecular simulations through multi-level parallelism from laptops to supercomputers
journal, September 2015


Author Correction: VAMPnets for deep learning of molecular kinetics
journal, October 2018


Direct calculation of ice homogeneous nucleation rate for a molecular model of water
journal, August 2015

  • Haji-Akbari, Amir; Debenedetti, Pablo G.
  • Proceedings of the National Academy of Sciences, Vol. 112, Issue 34
  • DOI: 10.1073/pnas.1509267112

Molecular-dynamics simulations of urea nucleation from aqueous solution
journal, December 2014

  • Salvalaglio, Matteo; Perego, Claudio; Giberti, Federico
  • Proceedings of the National Academy of Sciences, Vol. 112, Issue 1
  • DOI: 10.1073/pnas.1421192111

A Review of Classical and Nonclassical Nucleation Theories
journal, October 2016

  • Karthika, S.; Radhakrishnan, T. K.; Kalaichelvi, P.
  • Crystal Growth & Design, Vol. 16, Issue 11
  • DOI: 10.1021/acs.cgd.6b00794

Past–future information bottleneck for sampling molecular reaction coordinate simultaneously with thermodynamics and kinetics
journal, August 2019

  • Wang, Yihang; Ribeiro, João Marcelo Lamim; Tiwary, Pratyush
  • Nature Communications, Vol. 10, Issue 1
  • DOI: 10.1038/s41467-019-11405-4

Urea and deuterium mixtures at high pressures
journal, March 2015

  • Donnelly, M.; Bull, C. L.; Husband, R. J.
  • The Journal of Chemical Physics, Vol. 142, Issue 12
  • DOI: 10.1063/1.4915523

PLUMED 2: New feathers for an old bird
journal, February 2014

  • Tribello, Gareth A.; Bonomi, Massimiliano; Branduardi, Davide
  • Computer Physics Communications, Vol. 185, Issue 2
  • DOI: 10.1016/j.cpc.2013.09.018

Development and testing of a general amber force field
journal, January 2004

  • Wang, Junmei; Wolf, Romain M.; Caldwell, James W.
  • Journal of Computational Chemistry, Vol. 25, Issue 9
  • DOI: 10.1002/jcc.20035

DeepIce: A Deep Neural Network Approach To Identify Ice and Water Molecules
journal, March 2019

  • Fulford, Maxwell; Salvalaglio, Matteo; Molteni, Carla
  • Journal of Chemical Information and Modeling, Vol. 59, Issue 5
  • DOI: 10.1021/acs.jcim.9b00005

Spectral gap optimization of order parameters for sampling complex molecular systems
journal, February 2016

  • Tiwary, Pratyush; Berne, B. J.
  • Proceedings of the National Academy of Sciences, Vol. 113, Issue 11
  • DOI: 10.1073/pnas.1600917113

Crystal phase transition of urea: what governs the reaction kinetics in molecular crystal phase transitions
journal, January 2017

  • Shang, Cheng; Zhang, Xiao-Jie; Liu, Zhi-Pan
  • Physical Chemistry Chemical Physics, Vol. 19, Issue 47
  • DOI: 10.1039/c7cp07060h

High-Pressure Sorption of Hydrogen in Urea
journal, March 2021

  • Safari, F.; Tkacz, M.; Katrusiak, A.
  • The Journal of Physical Chemistry C, Vol. 125, Issue 14
  • DOI: 10.1021/acs.jpcc.1c00138

Enhancing Entropy and Enthalpy Fluctuations to Drive Crystallization in Atomistic Simulations
journal, July 2017


Crystal Nucleation in Liquids: Open Questions and Future Challenges in Molecular Dynamics Simulations
journal, May 2016


Intrinsic map dynamics exploration for uncharted effective free-energy landscapes
journal, June 2017

  • Chiavazzo, Eliodoro; Covino, Roberto; Coifman, Ronald R.
  • Proceedings of the National Academy of Sciences, Vol. 114, Issue 28
  • DOI: 10.1073/pnas.1621481114

Reinforcement Learning Based Adaptive Sampling: REAPing Rewards by Exploring Protein Conformational Landscapes
journal, August 2018

  • Shamsi, Zahra; Cheng, Kevin J.; Shukla, Diwakar
  • The Journal of Physical Chemistry B, Vol. 122, Issue 35
  • DOI: 10.1021/acs.jpcb.8b06521

Bond-orientational order in liquids and glasses
journal, July 1983

  • Steinhardt, Paul J.; Nelson, David R.; Ronchetti, Marco
  • Physical Review B, Vol. 28, Issue 2
  • DOI: 10.1103/physrevb.28.784

Expression in Terms of Molecular Distribution Functions for the Entropy Density in an Infinite System
journal, December 1958

  • Nettleton, R. E.; Green, M. S.
  • The Journal of Chemical Physics, Vol. 29, Issue 6
  • DOI: 10.1063/1.1744724

Ion dissolution mechanism and kinetics at kink sites on NaCl surfaces
journal, January 2018

  • Joswiak, Mark N.; Doherty, Michael F.; Peters, Baron
  • Proceedings of the National Academy of Sciences, Vol. 115, Issue 4
  • DOI: 10.1073/pnas.1713452115

Nucleation mechanism of clathrate hydrates of water-soluble guest molecules
journal, November 2017

  • DeFever, Ryan S.; Sarupria, Sapna
  • The Journal of Chemical Physics, Vol. 147, Issue 20
  • DOI: 10.1063/1.4996132

The seven deadly sins: When computing crystal nucleation rates, the devil is in the details
journal, July 2021

  • Blow, Katarina E.; Quigley, David; Sosso, Gabriele C.
  • The Journal of Chemical Physics, Vol. 155, Issue 4
  • DOI: 10.1063/5.0055248

Fast recovery of free energy landscapes via diffusion-map-directed molecular dynamics
journal, January 2014

  • Preto, Jordane; Clementi, Cecilia
  • Phys. Chem. Chem. Phys., Vol. 16, Issue 36
  • DOI: 10.1039/c3cp54520b

Canonical sampling through velocity rescaling
journal, January 2007

  • Bussi, Giovanni; Donadio, Davide; Parrinello, Michele
  • The Journal of Chemical Physics, Vol. 126, Issue 1
  • DOI: 10.1063/1.2408420

Reweighted autoencoded variational Bayes for enhanced sampling (RAVE)
journal, August 2018

  • Ribeiro, João Marcelo Lamim; Bravo, Pablo; Wang, Yihang
  • The Journal of Chemical Physics, Vol. 149, Issue 7
  • DOI: 10.1063/1.5025487

Mining of effective local order parameters for classifying crystal structures: A machine learning study
journal, June 2020

  • Doi, Hideo; Takahashi, Kazuaki Z.; Aoyagi, Takeshi
  • The Journal of Chemical Physics, Vol. 152, Issue 21
  • DOI: 10.1063/5.0005228

Analyzing and Driving Cluster Formation in Atomistic Simulations
journal, February 2017

  • Tribello, Gareth A.; Giberti, Federico; Sosso, Gabriele C.
  • Journal of Chemical Theory and Computation, Vol. 13, Issue 3
  • DOI: 10.1021/acs.jctc.6b01073

Well-Tempered Metadynamics: A Smoothly Converging and Tunable Free-Energy Method
journal, January 2008


Raman and X-Ray Scattering Studies of High-Pressure Phases of Urea
journal, April 2005

  • Lamelas, F. J.; Dreger, Z. A.; Gupta, Y. M.
  • The Journal of Physical Chemistry B, Vol. 109, Issue 16
  • DOI: 10.1021/jp040760m

Enhancing Important Fluctuations: Rare Events and Metadynamics from a Conceptual Viewpoint
journal, May 2016


Dynamical Nucleation Theory: A New Molecular Approach to Vapor-Liquid Nucleation
journal, April 1999

  • Schenter, Gregory K.; Kathmann, Shawn M.; Garrett, Bruce C.
  • Physical Review Letters, Vol. 82, Issue 17
  • DOI: 10.1103/physrevlett.82.3484

Polymorph specific RMSD local order parameters for molecular crystals and nuclei: α-, β-, and γ-glycine
journal, October 2011

  • Duff, Nathan; Peters, Baron
  • The Journal of Chemical Physics, Vol. 135, Issue 13
  • DOI: 10.1063/1.3638268

Modified genetic algorithm to model crystal structures. I. Benzene, naphthalene and anthracene
journal, April 2002

  • Bazterra, Victor E.; Ferraro, Marta B.; Facelli, Julio C.
  • The Journal of Chemical Physics, Vol. 116, Issue 14
  • DOI: 10.1063/1.1458547

Crystal nucleation along an entropic pathway: Teaching liquids how to transition
journal, December 2018


Inferring Transition Rates of Networks from Populations in Continuous-Time Markov Processes
journal, October 2015

  • Dixit, Purushottam D.; Jain, Abhinav; Stock, Gerhard
  • Journal of Chemical Theory and Computation, Vol. 11, Issue 11
  • DOI: 10.1021/acs.jctc.5b00537

How to quantify and avoid finite size effects in computational studies of crystal nucleation: The case of heterogeneous ice nucleation
journal, January 2021

  • Hussain, Sarwar; Haji-Akbari, Amir
  • The Journal of Chemical Physics, Vol. 154, Issue 1
  • DOI: 10.1063/5.0026355

Insight into the nucleation of urea crystals from the melt
journal, January 2015

  • Giberti, Federico; Salvalaglio, Matteo; Mazzotti, Marco
  • Chemical Engineering Science, Vol. 121
  • DOI: 10.1016/j.ces.2014.08.032

Polymorphic transitions in single crystals: A new molecular dynamics method
journal, December 1981

  • Parrinello, M.; Rahman, A.
  • Journal of Applied Physics, Vol. 52, Issue 12
  • DOI: 10.1063/1.328693

Seeding approach to nucleation in the N V T ensemble: The case of bubble cavitation in overstretched Lennard Jones fluids
journal, February 2020


tICA-Metadynamics: Accelerating Metadynamics by Using Kinetically Selected Collective Variables
journal, May 2017

  • M. Sultan, Mohammad; Pande, Vijay S.
  • Journal of Chemical Theory and Computation, Vol. 13, Issue 6
  • DOI: 10.1021/acs.jctc.7b00182

Global Optimization by Basin-Hopping and the Lowest Energy Structures of Lennard-Jones Clusters Containing up to 110 Atoms
journal, July 1997

  • Wales, David J.; Doye, Jonathan P. K.
  • The Journal of Physical Chemistry A, Vol. 101, Issue 28
  • DOI: 10.1021/jp970984n

Microscopic Mechanism and Kinetics of Ice Formation at Complex Interfaces: Zooming in on Kaolinite
journal, June 2016

  • Sosso, Gabriele C.; Li, Tianshu; Donadio, Davide
  • The Journal of Physical Chemistry Letters, Vol. 7, Issue 13
  • DOI: 10.1021/acs.jpclett.6b01013

A Time-Independent Free Energy Estimator for Metadynamics
journal, July 2014

  • Tiwary, Pratyush; Parrinello, Michele
  • The Journal of Physical Chemistry B, Vol. 119, Issue 3
  • DOI: 10.1021/jp504920s

Metadynamics: Metadynamics
journal, February 2011

  • Barducci, Alessandro; Bonomi, Massimiliano; Parrinello, Michele
  • Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 1, Issue 5
  • DOI: 10.1002/wcms.31

Towards a quantification of disorder in materials: Distinguishing equilibrium and glassy sphere packings
journal, July 2000

  • Truskett, T. M.; Torquato, S.; Debenedetti, P. G.
  • Physical Review E, Vol. 62, Issue 1
  • DOI: 10.1103/physreve.62.993

The Maximum Caliber Variational Principle for Nonequilibria
journal, April 2020


Characterization of the Local Structure in Liquid Water by Various Order Parameters
journal, June 2015

  • Duboué-Dijon, Elise; Laage, Damien
  • The Journal of Physical Chemistry B, Vol. 119, Issue 26
  • DOI: 10.1021/acs.jpcb.5b02936

SGOOP-d: Estimating Kinetic Distances and Reaction Coordinate Dimensionality for Rare Event Systems from Biased/Unbiased Simulations
journal, October 2021

  • Tsai, Sun-Ting; Smith, Zachary; Tiwary, Pratyush
  • Journal of Chemical Theory and Computation, Vol. 17, Issue 11
  • DOI: 10.1021/acs.jctc.1c00431

A smooth particle mesh Ewald method
journal, November 1995

  • Essmann, Ulrich; Perera, Lalith; Berkowitz, Max L.
  • The Journal of Chemical Physics, Vol. 103, Issue 19
  • DOI: 10.1063/1.470117

Contour forward flux sampling: Sampling rare events along multiple collective variables
journal, January 2019

  • DeFever, Ryan S.; Sarupria, Sapna
  • The Journal of Chemical Physics, Vol. 150, Issue 2
  • DOI: 10.1063/1.5063358

Escaping free-energy minima
journal, September 2002

  • Laio, A.; Parrinello, M.
  • Proceedings of the National Academy of Sciences, Vol. 99, Issue 20
  • DOI: 10.1073/pnas.202427399

Collective variables for the study of crystallisation
journal, March 2021


High-pressure polymorphism in deuterated urea
journal, August 2002

  • Weber, H. P.; Marshall, W. G.; Dmitriev, V.
  • Acta Crystallographica Section A Foundations of Crystallography, Vol. 58, Issue s1
  • DOI: 10.1107/s0108767302091985

Predicting reaction coordinates in energy landscapes with diffusion anisotropy
journal, October 2017

  • Tiwary, Pratyush; Berne, B. J.
  • The Journal of Chemical Physics, Vol. 147, Issue 15
  • DOI: 10.1063/1.4983727

VMD: Visual molecular dynamics
journal, February 1996


CrystalExplorer : a program for Hirshfeld surface analysis, visualization and quantitative analysis of molecular crystals
journal, April 2021

  • Spackman, Peter R.; Turner, Michael J.; McKinnon, Joshua J.
  • Journal of Applied Crystallography, Vol. 54, Issue 3
  • DOI: 10.1107/S1600576721002910