Joshua D. Coe

Optimal sampling efficiency in Monte Carlo simulation with an approximate potential.

Building on the work of Iftimie et al. [J. Chem. Phys. 113, 4852 (2000)] and Gelb [J. Chem. Phys. 118, 7747 (2003)], Boltzmann sampling of an approximate potential (the reference system) is used to build a Markov chain in the isothermal-isobaric ensemble. At the end points of the chain, the energy is evaluated at a more accurate level (the full system) and a composite move encompassing all of the intervening steps is accepted on the basis of a modified Metropolis criterion. For reference system chains of sufficient length, consecutive full energies are statistically decorrelated and thus far fewer are required to build ensemble averages with a given variance. Without modifying the original algorithm, however, the maximum reference chain length is too short to decorrelate full configurations without dramatically lowering the acceptance probability of the composite move. This difficulty stems from the fact that the reference and full potentials sample different statistical distributions. By manipulating the thermodynamic variables characterizing the reference system (pressure and temperature, in this case), we maximize the average acceptance probability of composite moves, lengthening significantly the random walk between consecutive full energy evaluations. In this manner, the number of full energy evaluations needed to precisely characterize equilibrium properties is dramatically reduced. The method is applied to a model fluid, but implications for sampling high-dimensional systems with ab initio or density functional theory potentials are discussed.

The influence of morphology on the low- and high-strain-rate compaction response of CeO2 powders

The low- and high-strain-rate compaction response of three distinct morphology CeO2 powders was measured experimentally. At low-strain-rates, the compression path was found to vary with initial particle morphology as a result of differences in initial packing structure and particle rearrangement at low stresses. However, similar compression responses were observed at higher stresses under low-strain-rate loading. Dynamic experiments were performed at impact velocities between 0.15 and 0.78u2009km/s, and resulted in compaction stresses of 0.51-4.59u2009GPa in the powders. In contrast to the behavior observed at low stresses and low-strain-rates, dynamic loading resulted in a similar compaction response for all morphology powders. The dynamic results were treated with a Hayes equation of state augmented with a P-α compaction model, and good agreement between experimental and theoretical results was achieved. From the observed similarities in compressibility for the three morphology powders at elevated stresses at b...

Nested Markov chain Monte Carlo sampling of a density functional theory potential: Equilibrium thermodynamics of dense fluid nitrogen

An optimized variant of the nested Markov chain Monte Carlo [n(MC)(2)] method [J. Chem. Phys. 130, 164104 (2009)] is applied to fluid N(2). In this implementation of n(MC)(2), isothermal-isobaric (NPT) ensemble sampling on the basis of a pair potential (the reference system) is used to enhance the efficiency of sampling based on Perdew-Burke-Ernzerhof density functional theory with a 6-31G(*) basis set (PBE6-31G(*), the full system). A long sequence of Monte Carlo steps taken in the reference system is converted into a trial step taken in the full system; for a good choice of reference potential, these trial steps have a high probability of acceptance. Using decorrelated samples drawn from the reference distribution, the pressure and temperature of the full system are varied such that its distribution overlaps maximally with that of the reference system. Optimized pressures and temperatures then serve as input parameters for n(MC)(2) sampling of dense fluid N(2) over a wide range of thermodynamic conditions. The simulation results are combined to construct the Hugoniot of nitrogen fluid, yielding predictions in excellent agreement with experiment.

Shockwave response of two carbon fiber-polymer composites to 50 GPa

Shock compression of two molded, carbon fiber-filled polymer composites was performed in gas gun-driven plate impact experiments at impact velocities up to ≈5u2009km/s. Hugoniot states for both composites were obtained from <5u2009GPa to nearly 50u2009GPa. The two materials contained a high fill percentage of chopped carbon fibers, bound by either phenolic or cyanate ester polymeric resins. Their dynamic responses were similar, although the 10u2009wt.u2009% difference of carbon fill produced measureable divergence in shock compressibility. The chopped carbon fibers in the polymer matrix led to moderately anisotropic shocks, particularly when compared with the more commonly encountered filament-wound carbon fiber-epoxy composites. A discontinuity, or cusp, was observed in the principal Hugoniot of both materials near 25u2009GPa. We attribute the accompanying volume collapse to shock-driven chemical decomposition above this condition. Inert and reacted products equations of state were used to capture the response of the two materi...

Chemical stability of molten 2,4,6-trinitrotoluene at high pressure

2,4,6-trinitrotoluene (TNT) is a molecular explosive that exhibits chemical stability in the molten phase at ambient pressure. A combination of visual, spectroscopic, and structural (x-ray diffraction) methods coupled to high pressure, resistively heated diamond anvil cells was used to determine the melt and decomposition boundaries to >15u2009GPa. The chemical stability of molten TNT was found to be limited, existing in a small domain of pressure-temperature conditions below 2u2009GPa. Decomposition dominates the phase diagram at high temperatures beyond 6u2009GPa. From the calculated bulk temperature rise, we conclude that it is unlikely that TNT melts on its principal Hugoniot.

Reactive Monte Carlo sampling with an ab initio potential

We present the first application of reactive Monte Carlo in a first-principles context. The algorithm samples in a modified NVT ensemble in which the volume, temperature, and total number of atoms of a given type are held fixed, but molecular composition is allowed to evolve through stochastic variation of chemical connectivity. We discuss general features of the method, as well as techniques needed to enhance the efficiency of Boltzmann sampling. Finally, we compare the results of simulation of NH3 to those of ab initio molecular dynamics (AIMD). We find that there are regions of state space for which RxMC sampling is much more efficient than AIMD due to the rare-event character of chemical reactions.

Optimized nested Markov chain Monte Carlo sampling: theory

Metropolis Monte Carlo sampling of a reference potential is used to build a Markov chain in the isotherm al‐isobaric ensemble. At the endpoints of the chain, the energy is reevaluated at a different level of approximation (the “full” energy) and a composite move encompassing all of the intervening steps is accepted on the basis of a modified Metropolis criterion. By manipulating the thermodynamic variables characterizing the reference system we maximize the average acceptance probability of composite moves, lengthening significantly the random walk made between consecutive evaluations of the full energy at a fixed acceptance probability. This provides maximally decorrelated samples of the full potential, thereby lowering the total number required to build ensemble averages of a given variance. The efficiency of the method is illustrated using model potentials appropriate to molecular fluids at high pressure. Implications for ab initio or density functional theory (DFT) treatment are discussed.

OPTIMIZED NESTED MARKOV CHAIN MONTE CARLO SAMPLING: APPLICATION TO THE LIQUID NITROGEN HUGONIOT USING DENSITY FUNCTIONAL THEORY

An optimized version of the Nested Markov Chain Monte Carlo sampling method is applied to the calculation of the Hugoniot for liquid nitrogen. The “full” system of interest is calculated using density functional theory (DFT) with a 6‐31G* basis set for the configurational energies. The “reference” system is given by a model potential fit to the anisotropic pair interaction of two nitrogen molecules from DFT calculations. The EOS is sampled in the isobaric‐isothermal (NPT) ensemble with a trial move constructed from many Monte Carlo steps in the reference system. The trial move is then accepted with a probability chosen to give the full system distribution. The P’s and T’s of the reference and full systems are chosen separately to optimize the computational time required to produce the full system EOS. The method is numerically very efficient and predicts a Hugoniot in excellent agreement with experimental data.

A New 5-Phase Equation of State for Carbon

We describe the development of SESAME 7835, a new tabular equation of state (EOS) for carbon containing the diamond, bc8, simple cubic, simple hexagonal, and liquid/plasma phases. We compare the EOS against a wide variety of experimental data and simulation results, including static compression, dynamic compression, specific heat, and thermal expansion. To the extent that the reference data agree amongst themselves, the results are satisfactory in all cases.