title: Order-parameter-aided temperature-accelerated sampling for the exploration of crystal polymorphism and solid-liquid phase transitions.
abstract: The problem of predicting polymorphism in atomic and molecular crystals constitutes a significant challenge both experimentally and theoretically. From the theoretical viewpoint, polymorphism prediction falls into the general class of problems characterized by an underlying rough energy landscape, and consequently, free energy based enhanced sampling approaches can be brought to bear on the problem. In this paper, we build on a scheme previously introduced by two of the authors in which the lengths and angles of the supercell are targeted for enhanced sampling via temperature accelerated adiabatic free energy dynamics [T. Q. Yu and M. E. Tuckerman, Phys. Rev. Lett. 107, 015701 (2011)]. Here, that framework is expanded to include general order parameters that distinguish different crystalline arrangements as target collective variables for enhanced sampling. The resulting free energy surface, being of quite high dimension, is nontrivial to reconstruct, and we discuss one particular strategy for performing the free energy analysis. The method is applied to the study of polymorphism in xenon crystals at high pressure and temperature using the Steinhardt order parameters without and with the supercell included in the set of collective variables. The expected fcc and bcc structures are obtained, and when the supercell parameters are included as collective variables, we also find several new structures, including fcc states with hcp stacking faults. We also apply the new method to the solid-liquid phase transition in copper at 1300 K using the same Steinhardt order parameters. Our method is able to melt and refreeze the system repeatedly, and the free energy profile can be obtained with high efficiency.
authors.affiliation: Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA.
authors.forename: Tang-Qing
authors.initials: TQ
authors.lastname: Yu
authors.affiliation: Department of Chemistry, New York University, New York, New York 10003, USA.
authors.forename: Pei-Yang
authors.initials: PY
authors.lastname: Chen
authors.affiliation: Department of Chemistry, New York University, New York, New York 10003, USA.
authors.forename: Ming
authors.initials: M
authors.lastname: Chen
authors.affiliation: Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, USA and Lawrence Livermore National Laboratory, Livermore, California 94550, USA.
authors.forename: Amit
authors.initials: A
authors.lastname: Samanta
authors.affiliation: Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA.
authors.forename: Eric
authors.initials: E
authors.lastname: Vanden-Eijnden
authors.affiliation: Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA.
authors.forename: Mark
authors.initials: M
authors.lastname: Tuckerman
mesh_terms: D003198:Computer Simulation; D003460:Crystallization; D004735:Energy Transfer; D044367:Phase Transition; D013696:Temperature; D013816:Thermodynamics