Evaluation of the grand-canonical partition function using Expanded Wang-Landau simulations. IV. Performance of many-body force fields and tight-binding schemes for the fluid phases of Silicon

Abstract

We extend Expanded Wang-Landau (EWL) simulations beyond classical systems and develop the EWL method for systems modeled with a tight-binding Hamiltonian. We then apply the method to determine the partition function and thus all thermodynamic properties, including the Gibbs free energy and entropy, of the fluid phases of Si. We compare the results from quantum many-body (QMB) tight binding models, which explicitly calculate the overlap between the atomic orbitals of neighboring atoms, to those obtained with classical many-body force fields (CMB), which allow to recover the tetrahedral organization in condensed phases of Si through e.g. a repulsive 3-body term that favors the ideal tetrahedral angle. Along the vapor-liquid coexistence, between 3000K and 6000K, the densities for the two coexisting phases are found to vary significantly (by $5$ orders of magnitude for the vapor and by up to 25% for the liquid) and to provide a stringent test of the models. Transitions from vapor to liquid are predicted to occur for chemical potentials that are $10-15$% higher for CMB models than for QMB models, and a ranking of the force fields is provided by comparing the predictions for the vapor pressure to the experimental data. QMB models also reveal the formation of a gap in the electronic density of states of the coexisting liquid at high temperatures. Subjecting Si to a nanoscopic confinement has a dramatic effect on the phase diagram, with e.g. at 6000K a decrease in liquid densities by about 50% for both CMB and QMB models and an increase in vapor densities between 90% (CMB) and 170% (QMB). The results presented here provide a full picture of the impact of the strategy (CMB or QMB) chosen to model many-body effects on the thermodynamic properties of the fluid phases of Si.

References in corpus (13)

• An efficient, multiple range random walk algorithm to calculate the density of states
• Determining the density of states for classical statistical models: A random walk algorithm to produce a flat histogram
• On the Wang-Landau Method for Off-Lattice Simulations in the "Uniform" Ensemble
• Optimizing the ensemble for equilibration in broad-histogram Monte Carlo simulations
• An improved Monte Carlo method for direct calculation of the density of states
• Transitions of tethered polymer chains: A simulation study with the bond fluctuation lattice model
• Multicritical Points and Crossover Mediating the Strong Violation of Universality: Wang-Landau Determinations in the Random-Bond $d=2$ Blume-Capel model
• Phase diagram of silicon from atomistic simulations
• Stabilized silicene within bilayer graphene: A proposal based on molecular dynamics and density-functional tight-binding calculations
• Relations between the diffusion anomaly and cooperative rearranging regions in a hydrophobically nanoconfined water monolayer
• The long-range non-additive three-body dispersion interactions for the rare gases, alkali and alkaline-earth atoms
• Effects of three-body interactions on the structure and thermodynamics of liquid krypton
• Toward transferable interatomic van der Waals interactions without electrons: The role of multipole electrostatics and many-body dispersion

Cited by in corpus (8)

• Scaling Laws and Critical Properties for $FCC$ and $HCP$ Metals
• Free energy calculations along entropic pathways: I. Homogeneous vapor-liquid nucleation for atomic and molecular systems
• Crystal nucleation along an entropic pathway: Teaching liquids how to transition
• Evaluation of the grand-canonical partition function using Expanded Wang-Landau simulations. V. Impact of an electric field on the thermodynamic properties and ideality contours of water
• Free energy calculations along entropic pathways: II. Droplet nucleation in binary mixtures
• Benchmark free energies and entropies for saturated and compressed water
• Impact of Friedel oscillations on vapor-liquid equilibria and supercritical properties in 2D and 3D
• Ginzburg-Landau free energy for molecular fluids: determination and coarse-graining