In this work, we study the interlayer interactions between sheets of blue phosphorus with quantum Monte Carlo (QMC) methods. We find that as previously observed in black phosphorus, interlayer binding of blue phosphorus cannot be described by van der Waals (vdW) interactions alone within the density functional theory framework. Specifically, while some vdW density functionals produced reasonable binding curves, none of them could provide a correct, even qualitatively, description of charge redistribution due to interlayer binding. We also show that small systematic errors in common practice QMC calculations, such as the choice of optimized geometry and finite-size corrections, are non-negligible given the energy and length scales of this problem. We mitigate some of the major sources of error and report QMC-optimized lattice constant, stacking, and interlayer binding energy for blue phosphorus. It is strongly suggested that these considerations are important and quite general in the modeling of two-dimensional phosphorus allotropes.
Kim, Jeongnim; Baczewski, Andrew D.; Beaudet, Todd D.; Benali, Anouar; Bennett, Michael; Berrill, Mark A.; Blunt, Nick S.; Casula, Michele; Ceperley, David M.; Chiesa, Simone; Clark, Bryan K.; Clay III, Raymond C.; Delaney, Kris T.; Dewing, Mark; Esler, Kenneth P.; Hao, Hongxia; Hein, Olle; Kent, Paul R.C.; Krogel, Jaron T.; Kylanpaa, Ilkka; Li, Ying W.; Lopez, M.G.; Luo, Ye; Martin, Richard M.; Mathuriya, Amrita; Mcminis, Jeremy; Melton, Cody A.; Mitas, Lubos; Neuscamman, Eric; Parker, William D.; Pineda Flores, Sergio D.; Romero, Nichols A.; Rubenstein, Brenda M.; Shea, Jacqueline A.R.; Shin, Hyeondeok; Shulenburger, Luke N.; Tillack, Andreas F.; Townsend, Joshua P.; Tubman, Norm M.; Van Der Goetz, Brett; Vincent, Jordan E.; Yang, Yubo; Zhang, Shuai; Morales, Miguel A.; Zhao, Luning
QMCPACK is an open source quantum Monte Carlo package for ab-initio electronic structure calculations. It supports calculations of metallic and insulating solids, molecules, atoms, and some model Hamiltonians. Implemented real space quantum Monte Carlo algorithms include variational, diffusion, and reptation Monte Carlo. QMCPACK uses Slater-Jastrow type trial wave functions in conjunction with a sophisticated optimizer capable of optimizing tens of thousands of parameters. The orbital space auxiliary field quantum Monte Carlo method is also implemented, enabling cross validation between different highly accurate methods. The code is specifically optimized for calculations with large numbers of electrons on the latest high performance computing architectures, including multicore central processing unit (CPU) and graphical processing unit (GPU) systems. We detail the program’s capabilities, outline its structure, and give examples of its use in current research calculations. The package is available at http://www.qmcpack.org.
