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separate shells, atomic hybridization, covalent, ionic, multicenter, and/or metallic
bonds, and steric repulsions between bonds.
Since the interactions between particles in eFF are simply pairwise forces,
the overall method is extremely fast and scales well computationally. We have
simulated on a single processor tens of thousands of electrons, and on multiple
processors millions of electrons [ 90 ].
Application Examples: Material Shock Hugoniots and Auger Decay
In one application of eFF we studied the thermodynamics of shock-compressed
liquid hydrogen, characterizing molecular, atomic, plasma, and metallic phases at
temperatures up to 200,000 K and compressions up to fivefold liquid density (see
Fig. 9 ). We found reasonable agreement with data from both static compression
(diamond anvil) and dynamic compression (shocks from explosives, magnetically
pinched wires, lasers) experiments.
We have also demonstrated the capabilities of eFF for computing single-shock
Hugoniots for lithium metal from dynamic shock wave experiments, via the shock
wave and piston kinematics and initial and final densities of a 640,000-particle
system (see Fig. 10 ). We also reported on the degree of ionization suffered by the
material, a function of the explicit nuclear delocalization of electrons [ 90 ]. A
simpler depiction of such dynamic shock experiments is shown in Fig. 11 , wherein
Fig. 9 Shock Hugoniot curve for liquid D2. We show here that eFF agrees well with most
experiments: gas gun ( red dots ), Z machine ( green dots ), convergence geometry ( orange ), and
the more recent laser data ( blue dots ) from LLNL. The PIMC results agree with eFF up to a
compression of 4.2, but leads to a lower limiting compression than eFF. To compute the Hugoniot
curve, we perform NVE simulations of D2, interpolating to temperatures such that the internal
energy, volume, and pressure satisfy the Rankine-Hyugoniot relationship. We note that the eFF
Hugoniot curve connects to an eFF low temperature starting point, while the PIMC Hugoniot curve
connects to a U 0 from a separate calculation
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