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J. Guan, Z. Zhu, and D. Tománek, “Phase coexistence and metal-insulator transition in few-layer phosphorene: A computational study,” Phys. Rev. Lett. 113(4), 046804 (2014).
Z. Zhu and D. Tománek, “Semiconducting layered blue phosphorus: A computational study,” Phys. Rev. Lett. 112(17), 176802 (2014).
A. H. Woomer et al., “Phosphorene: Synthesis, scale-up, and quantitative optical spectroscopy,” ACS Nano 9(9), 88698884 (2015).
J. Hu et al., “Band gap engineering in a 2D material for solar-to-chemical energy conversion,” Nano Lett. 16(1), 7479 (2016).
M. Wu, H. Fu, L. Zhou, K. Yao, and X. C. Zeng, “Nine new phosphorene polymorphs with non-honeycomb structures: A much extended family,” Nano Lett. 15(5), 35573562 (2015).
W. M. C. Foulkes, L. Mitas, R. J. Needs, and G. Rajagopal, “Quantum Monte Carlo simulations of solids,” Rev. Mod. Phys. 73(1), 3383 (2001).
Weinan E. and E. Vanden-Eijnden, “Transition-path theory and path-finding algorithms for the study of rare events,” Annu. Rev. Phys. Chem. 61(1), 391420 (2010).
G. Henkelman, B. P. Uberuaga, and H. Jónsson, “A climbing image nudged elastic band method for finding saddle points and minimum energy paths,” J. Chem. Phys. 113(22), 99019904 (2000).
Weinan E., W. Ren, and E. Vanden-Eijnden, “String method for the study of rare events,” Phys. Rev. B 66(5), 052301 (2002).
G. Henkelman and H. Jónsson, “A dimer method for finding saddle points on high dimensional potential surfaces using only first derivatives,” J. Chem. Phys. 111(15), 70107022 (1999).
N. Mousseau and G. T. Barkema, “Traveling through potential energy landscapes of disordered materials: The activation-relaxation technique,” Phys. Rev. E 57(2), 24192424 (1998).
G.-R. Qian et al., “Variable cell nudged elastic band method for studying solid–solid structural phase transitions,” Comput. Phys. Commun. 184(9), 21112118 (2013).
Y. Kanai, X. Wang, A. Selloni, and R. Car, “Testing the TPSS meta-generalized-gradient-approximation exchange-correlation functional in calculations of transition states and reaction barriers,” J. Chem. Phys. 125(23), 234104 (2006).
M. A. Morales, J. McMinis, B. K. Clark, J. Kim, and G. E. Scuseria, “Multideterminant wave functions in quantum Monte Carlo,” J. Chem. Theory Comput. 8(7), 21812188 (2012).
M. Dubecký et al., “Quantum Monte Carlo methods describe noncovalent interactions with subchemical accuracy,” J. Chem. Theory Comput. 9(10), 42874292 (2013).
M. Dubecký, L. Mitas, and P. Jurečka, “Noncovalent interactions by quantum Monte Carlo,” Chem. Rev. 116(9), 51885215 (2016).
A. Zen, E. Coccia, Y. Luo, S. Sorella, and L. Guidoni, “Static and dynamical correlation in diradical molecules by quantum Monte Carlo using the Jastrow antisymmetrized geminal power ansatz,” J. Chem. Theory Comput. 10(3), 10481061 (2014).
S. Azadi and W. M. C. Foulkes, “Systematic study of finite-size effects in quantum Monte Carlo calculations of real metallic systems,” J. Chem. Phys. 143(10), 102807 (2015).
L. M. Fraser et al., “Finite-size effects and Coulomb interactions in quantum Monte Carlo calculations for homogeneous systems with periodic boundary conditions,” Phys. Rev. B 53(4), 18141832 (1996).
A. J. Williamson et al., “Elimination of Coulomb finite-size effects in quantum many-body simulations,” Phys. Rev. B 55(8), R4851R4854 (1997).
P. R. C. Kent et al., “Finite-size errors in quantum many-body simulations of extended systems,” Phys. Rev. B 59(3), 19171929 (1999).
S. Chiesa, D. M. Ceperley, R. M. Martin, and M. Holzmann, “Finite-size error in many-body simulations with long-range interactions,” Phys. Rev. Lett. 97(7), 076404 (2006).
N. D. Drummond, R. J. Needs, A. Sorouri, and W. M. C. Foulkes, “Finite-size errors in continuum quantum Monte Carlo calculations,” Phys. Rev. B 78(12), 125106 (2008).
Y. Wu, L. K. Wagner, and N. R. Aluru, “The interaction between hexagonal boron nitride and water from first principles,” J. Chem. Phys. 142(23), 234702 (2015).
H. Kwee, S. Zhang, and H. Krakauer, “Finite-size correction in many-body electronic structure calculations,” Phys. Rev. Lett. 100(12), 126404 (2008).
C. Lin, F. H. Zong, and D. M. Ceperley, “Twist-averaged boundary conditions in continuum quantum Monte Carlo algorithms,” Phys. Rev. E 64(1), 016702 (2001).
A. R. Oganov and C. W. Glass, “Crystal structure prediction using ab initio evolutionary techniques: Principles and applications,” J. Chem. Phys. 124(24), 244704 (2006).
G. Paolo et al., “QUANTUM ESPRESSO: A modular and open-source software project for quantum simulations of materials,” J. Phys.: Condens. Matter 21(39), 395502 (2009).
J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple,” Phys. Rev. Lett. 77(18), 38653868 (1996).
D. Vanderbilt, “Soft self-consistent pseudopotentials in a generalized eigenvalue formalism,” Phys. Rev. B 41(11), 78927895 (1990).
N. Troullier and J. L. Martins, “Efficient pseudopotentials for plane-wave calculations,” Phys. Rev. B 43(3), 19932006 (1991).
L. K. Wagner, M. Bajdich, and L. Mitas, “QWalk: A quantum Monte Carlo program for electronic structure,” J. Comput. Phys. 228(9), 33903404 (2009).
R. Dovesi et al., “CRYSTAL14: A program for the ab initio investigation of crystalline solids,” Int. J. Quantum Chem. 114(19), 12871317 (2014).
M. Burkatzki, C. Filippi, and M. Dolg, “Energy-consistent pseudopotentials for quantum Monte Carlo calculations,” J. Chem. Phys. 126(23), 234105 (2007).
C. J. Umrigar, K. G. Wilson, and J. W. Wilkins, “Optimized trial wave functions for quantum Monte Carlo calculations,” Phys. Rev. Lett. 60(17), 17191722 (1988).
C. J. Umrigar, M. P. Nightingale, and K. J. Runge, “A diffusion Monte Carlo algorithm with very small time-step errors,” J. Chem. Phys. 99(4), 28652890 (1993).
A. Zen, S. Sorella, M. J. Gillan, A. Michaelides, and D. Alfè, “Boosting the accuracy and speed of quantum Monte Carlo: Size consistency and time step,” Phys. Rev. B 93(24), 241118 (2016).
W. Purwanto, H. Krakauer, and S. Zhang, “Pressure-induced diamond to β-tin transition in bulk silicon: A quantum Monte Carlo study,” Phys. Rev. B 80(21), 214116 (2009).
L. Spanu, S. Sorella, and G. Galli, “Nature and strength of interlayer binding in graphite,” Phys. Rev. Lett. 103(19), 196401 (2009).
D. M. Ceperley and B. J. Alder, “Ground state of the electron gas by a stochastic method,” Phys. Rev. Lett. 45(7), 566569 (1980).
C. Adamo and V. Barone, “Toward reliable density functional methods without adjustable parameters: The PBE0 model,” J. Chem. Phys. 110(13), 61586170 (1999).
K. Yang, J. Zheng, Y. Zhao, and D. G. Truhlar, “Tests of the RPBE, revPBE, τ-HCTHhyb, ωB97X-D, and MOHLYP density functional approximations and 29 others against representative databases for diverse bond energies and barrier heights in catalysis,” J. Chem. Phys. 132(16), 164117 (2010).
J. M. del Campo, J. L. Gázquez, S. B. Trickey, and A. Vela, “Non-empirical improvement of PBE and its hybrid PBE0 for general description of molecular properties,” J. Chem. Phys. 136(10), 104108 (2012).
T. Hu and J. Dong, “Structural phase transitions of phosphorene induced by applied strains,” Phys. Rev. B 92(6), 064114 (2015).
G. Signorello, S. Karg, M. T. Björk, B. Gotsmann, and H. Riel, “Tuning the light emission from GaAs nanowires over 290 meV with uniaxial strain,” Nano Lett. 13(3), 917924 (2013).
K. Schulten, Z. Schulten, and A. Szabo, “Dynamics of reactions involving diffusive barrier crossing,” J. Chem. Phys. 74(8), 44264432 (1981).

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Recent technical advances in dealing with finite-size errors make quantum Monte Carlo methods quite appealing for treating extended systems in electronic structure calculations, especially when commonly used density functional theory (DFT) methods might not be satisfactory. We present a theoretical study of martensitic phase transition energetics of a two-dimensional phosphorene by employing diffusion Monte Carlo (DMC) approach. The DMC calculation supports DFT prediction of having a rather diffusive barrier that is characterized by having two transition states, in addition to confirming that the so-called black and blue phases of phosphorene are essentially degenerate. At the same time, the DFT calculations do not provide the quantitative accuracy in describing the energy changes for the martensitic phase transition even when hybrid exchange-correlation functional is employed. We also discuss how mechanical strain influences the stabilities of the two phases of phosphorene.


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