Density-scaling Monte Carlo

Valleau, J. P. The Coulombic phase transition density-scaling Monte Carlo. J. Chem. Phys. 1991, 95, 584-589... 

Valleau, J. P. Temperature-and-density-scaling Monte-Carlo methodology and the canonical thermodynamics of Lennard-Jonesium. Mol. Sim. 2005, 31, 223-253... 

Despite the simplicity of this lattice model, it is still a formidable problem of statistical mechanics, and its numerically exact treatment already requires large-scale Monte Carlo simulations [11-13]. Consequently, the standard approach has been [1-7] to treat this Flory-Huggins lattice model in mean-field approximation, which leads to the following expression for the excess free energy density of mixing [4] ... 

Ab initio methods allow the nature of active sites to be elucidated and the influence of supports or solvents on the catalytic kinetics to be predicted. Neurock and coworkers have successfully coupled theory with atomic-scale simulations and have tracked the molecular transformations that occur over different surfaces to assess their catalytic activity and selectivity [95-98]. Relevant examples are the Pt-catalyzed NO decomposition and methanol oxidation. In case of NO decomposition, density functional theory calculations and kinetic Monte Carlo simulations substantially helped to optimize the composition of the nanocatalyst by alloying Pt with Au and creating a specific structure of the PtgAu7 particles. In catalytic methanol decomposition the elementary pathways were identified... 

Monte Carlo simulation shows [8] that at a given instance the interface is rough on a molecular scale (see Fig. 2) this agrees well with results from molecular-dynamics studies performed with more realistic models [2,3]. When the particle densities are averaged parallel to the interface, i.e., over n and m, and over time, one obtains one-dimensional particle profiles/](/) and/2(l) = 1 — /](/) for the two solvents Si and S2, which are conveniently normalized to unity for a lattice that is completely filled with one species. Figure 3 shows two examples for such profiles. Note that the two solvents are to some extent soluble in each other, so that there is always a finite concentration of solvent 1 in the phase... 

Figure 5. Contour plots in the (110) plane of metallic magnesium (a) the bias corrected MEM density, (b) the estimated random error in the MEM density. The plots are based on 100 Monte Carlo calculations employin a uniform prior. The lots are on a linear scale, (a) 0.25 e/A3 intervals and 5.0e/A3 truncation (b) 0.1 e/A3 intervals and 1.0e/A3truncation. Maximum values in e/A3 are given at the Mg position and in the bipyramidal space. 

During the past few decades, various theoretical models have been developed to explain the physical properties and to find key parameters for the prediction of the system behaviors. Recent technological trends focus toward integration of subsystem models in various scales, which entails examining the nanophysical properties, subsystem size, and scale-specified numerical analysis methods on system level performance. Multi-scale modeling components including quantum mechanical (i.e., density functional theory (DFT) and ab initio simulation), atom-istic/molecular (i.e., Monte Carlo (MC) and molecular dynamics (MD)), mesoscopic (i.e., dissipative particle dynamics (DPD) and lattice Boltzmann method (LBM)), and macroscopic (i.e., LBM, computational... 

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