Molecular dynamics (MD) simulations have been performed for highly compressed fluid deuterium, nitrogen, and oxygen, in the density and temperature regime of shock-compression experiments, using density functional (DF) electronic structure techniques to describe the interatomic forces. The Hugoniots derived from the calculated equation-of-state for deuterium does not exhibit the large compression predicted by the recently reported laser-driven experiments. However, the Hugoniot derived for nitrogen and oxygen agree well with explosively-driven and gas-gun experiments. The nature of the fluid along the Hugoniot, as calculated with DF-MD, has been analyzed. All three species (D2, N2, amd 02) undergo a continuous transition from a molecular to a partially dissociated fluid containing a mixture of atoms and molecules

Collins, L. A. (Lee A.)

Kress, J. D. (Joel D.)

Mazevet, S. (Stephane)

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0 1 -  c./ LA-U R- Approved for public release; distribution is unlimited. Title: Au thor(s): Subrnitfed to: DENSITY-FUNCTIONAL MOLECULAR DYNAMICS SIMULATIONS OF SHOCKED MOLECULAR LIQUIDS Joel D. Kress Stephane Mazevet Lee A. Collins CONFERENCE ON SHOCK COMPRESSION OF CONDENSED MATTER, JUNE 24-29,2001, ATLANTA, GA Los Alamos N AT I 0 N A L LA 6 0 R AT0 RY Los Aiamos National Laboratory, an affirmative actionhqual opportunity employer, is operated by the University of California for the US. Department of Energy under contract VI/-7405-ENG-36. By acceptance of this article, the publisher recognizes that the US. Government retains a nonexclusive, royalty-free license to publish or reproduce the published form of this contribution, orto allow others to do so, for US. Government purposes. Los Alamos National Laboratory requests that the publisher identify this article as work performed under the auspices of the US. Department of Energy. Los Alamos National Laboratory strongly supports academic freedom and a researcher's right to publish: as an institution, however, the Laboratorydoes not endorse theviewpoint of a publication or guarantee its technical correctness. Form 836 (1 0/96) DENSITY-FUNCTIONAL MOLECULAR DYNAMICS SIMULATIONS OF SHOCKED MOLECULAR LIQUIDS J. D. Kress, S. Mazevet, and L. A. Collins Theoretical Division, Los Alamos National Luboratory, Los Alamos, NM 87545 Abstract. Molecular dynamics (MD) simulations have been performed for highly compressed fluid deuterium, nitrogen, and oxygen, in the density and temperature regime of shock-compression experiments, using density functional (DF) electronic structure techniques to describe the interatomic forces. The Hugoniots derived from the calculated equation-of-state for deuterium does not exhibit the large compression predicted by the recently reported laser-driven experiments. However, the Hugoniot derived for nitrogen and oxygen agree well with explosively-driven and gas-gun experi- ments. The nature of the fluid along the Hugoniot, as calculated with DF-MD, has been analyzed. All three species (D2, N2, amd 02) undergo a continuous transition from a molecular to a partially dissociated fluid containing a mixture of atoms and molecules. Density Functional Molecular Dynamics (DFMD) simulations provide an extremely penetrat- ing probe of a variety of enviroments in which dense matter at elevated temperatures plays a significant role, including solids, fluids, gases, plasmas, and especially mixtures of these variouri states of matter. In many circumstances, a quantum ("ab initio") treatment of the interaction between electrons and ions provides the only reliable procedure for gaining information and understanding on the state and interaction of matter in these extreme conditions in which experiments remain difficult. Renewed interest in shocked-compressed ni- trogen and oxygen has arisen fiom an unlikely source, namely, laser-driven shock. experiments on deuterium( 1). These experiments have indicated that the deuterium Hugoniot appears much softer than originally predicted by a conventional EOS such as the SESAME table(2), allowing a maximum com- pression ratio (q- = p-/po) of a factor of six from the liquid state at po. This value (qmax=6) more re- sembles that of an ideal diatomic rigid-rotor molec- ular fluid than an atomic one (qm=4). These find- ings have immense ramifications for many areas of science including the modeling of planetary interi- ors. As a further complication, considerable dis- agreement exists among the theoretical methods for the case of deuterium. While the various ab initio simulation approaches (3,4) now show considerable concurrence, the high compressibility measured ex- perimentally can only be reproduced with fluid theo- ries based on effective pair potentials(5). Since close parallels exist between deuterium, ni- trogen, and oxygen in this compressed-fluid regime, a study using ab initio molecular dynamics(MD) simulations might not only elucidate many interest- ing aspects of compressed nitrogen but also provide further insight into the deuterium dilemma. All three species have natural(cryogenic) fluid states com- posed of diatomic molecules, and all form molecules with large dissociation energies [4.5,9.8 and 5.1 eV, respectively, for Dz, Nz, and 021  and moderately high ionization energies [12 - 15 eV]. Since the ab initio MD simulations for deuterium show consid- erable disagreement with laser experiments at high compression(q,, > 4), trials on similars system with established shock data provides a critical test of the theoretical approaches, especially those without tunable parameters. The past few years have witnessed the develop- ment of a variety of large-scale simulation methods to treat fluid systems over a broad range of con- ditions. In DF methods, the total energy is writ- ten as a functional of the electron density, which is obtained by summing the probability density over the occupied orbitals. Further, for the Generalized Gradient Approximation (GGA), the electronic ex- change and correlation energy are approximated us- ing a functional which depends only on the elec- tron density and its spatial derivatives. GGA meth- ods provide a highly accurate means of studying the thermochemistry of chemical bonding by repre- senting the inhomogeneities inherent in the electron charge density relative to the homogeneous electron gas. In addition, the method encompasses all man- ner of transient effects such as dissociation and as- sociation of chemical bonds, quasi-molecular forma- tion, and ionization and recombination. Finally, a semi-empirical tight-binding (TB) electronic struc- ture model for deuterium has been developed(6). The TB method presents an effective compromise, giving a reasonable accurate representation of the principal mechanisms while consuming conderably less com- putational resources than the DF approaches. For the DF calculations, we employed the VASP planewave pseudopotential code, which was devel- oped at the Technical University of Vienna (7). This code implements the Vanderbilt ultrasoft pseudopo- tential scheme in a form supplied by G. Kresse and J. Hafner and the Perdew-Wang 91 parameterization of GGA. A finite-temperature density functional pro- cedure (8) is employed by setting the electron and ion temperatures equal (local thermodynamic equi- librium) using a Fermi-Dirac distribution. Finite-temperature, fixed-volume molecular dy- namics simulations were performed for density and temperature points selected to span the range of the singleshock Hugoniot experiments. A simulation cell with periodic boundary conditions with a fixed number of atoms was employed. For nitrogen and oxygen we used 32 atoms (160 and 192 valence elec- trons, respectively), while for deuterium, 128 atoms (128 valence electrons) Further details can be found in (3) and (10). The Rankine-Hugoniot equation 1 (U1 - U2) e p 1  -V2)(Pl +P2) = 0, (1) describes the shock adiabat through a relation be- tween initial (VI = l /pl ,  U1, PI) and final(V2 = l/p2, U2, P2) volume, internal energy, and pressure. The internal energy per atom U consists of the sum of the ion kinetic energy (3 k~ Z) and the time aver- age of the DF potential energy Em, where kB is the Boltzmann constant. The pressure P is computed us- ing the Hellmann-Feynman forces derived from the DF potential energy. We have chosen P1 = 0, and U1 so that the energy of the isolated molecule is zero. The initial densities were set to pl=0.171,0.808, and 1.2 g/cm3, respectively, for &, N2, and 0 2 ,  To find the Hugoniot point for a given VZ, P and U derived from the DF-MD results were fit by a least-squares prescription to a quadratic function in T. P2 and T2 were found by substituting these functions and solv- ing Eq. 1. The DF-MD Hugoniot points appear in Fig. 1 along with the experimental data for &, N2, and 02. We first focus on the results for deuterium (Fig. 1 a). The system starts as a cryogenically-cooled liq- uid. The points in pressure-density space then fol- low from the application of the single-shock Rankin- Hugoniot conditions based on the equation-of-state for a given theoretical model. At present, a large dif- ference exists among various methods and the laser- driven NOVA experiments( 1). The SESAME(2) (not shown), tight-binding-MD (TB)(6), DF-MD(3), and path integral Monta Carlo (PIMC)(4) approaches all appear in generally good agreement, giving a maxi- mum compression q = p/po of around 4. This value closely matches that for an ideal atomic fluid. How- ever, they differ substantially from the linear-mixing model@) and the lone experimental (laser-driven) results(1) above P = 50 GPa; both yield q=6 - more like an ideal molecular fluid. We emphasize a point that appears to cause con- siderable confusion in the general literature. All the models discussed from SESAME to the DF-GGA and PIMC include dissociation at some level of ap- proximation. The large compressions seen in the laser experiments cannot be solely attributed to dis- sociation. Some additional mechanism must also be at work. Furthermore, all of these models have a rep- resentation, at some level, of the basic physical pro- cesses that govern Hydrogen in this regime. Identify- ing the precise physical mechanisms that lead to such differences in the theoretical models has remained elusive. We next return to the principal Hugoniots for N2 (Fig. lb) and 02 (Fig. IC). (Further DF-MD calcu- lations on double-shocked Hugoniots for N2 are re- I GGA-MDD, I) 4 GGA-MD 0, rn TBD, IC GGA-MD N, 0 GASGUNO, Rwis D, I PlhllC D, mm Compression Compression Compression FIGURE 1. Hugoniots (compression = p/p~). (a) Deuterium. DP-MD [purple long-dashed h e ,  Ref. (3)]. PIMC [magenta solid line, Ref. (411. Tight-binding (n3) [green dashed-line, Ref. (6)]. Linear-mixing model (Ross) [yellow short-dashed line, Ref. (J)]. Laser-drvien experiments (NOVA) [purple open circles, Ref. (l)]. Gas-gun experiments [green closed circles, Ref. (9)]. @I) Nitrogen. DF-MD [orange closed squares, Ref. (10) 1. Experiments [black closed circles, Refs. (l l) ,  (12) and (13))]. (c) Oxygen. DF-MD [orange closed squares]. Explosively-driven experiments [purple open circles, Ref. (14)]. Gas-gun experiments [green closed circles, Ref. (12)]. ported elsewhere in these proceedings( 19.) We find very good agreement between the IDF-MD calcula- tions and the explosively-driven and gas-gun exper- imental results all along the single-shock Hugoniot. In particular, the calculations reproduce the distinc- tive inflection associated with dissociation, centered about q = 4,3, and 2.5, respectively, for 9, N2, and 02. These comparisons with available experimental results demonstrate that the MD simulations can rea- sonably reproduce the major trends along the prin- cipal Hugoniot. We now explore the explicit nature of the fluid for which the experiments can offer only indirect evidence. In order to place these results on a more quan- titative basis, we have performed a standard clus- ter analysis of the MD trajectories. An effective ra- dius is selected, and and all atoms within this dis- tance are considered bound to a reference atom. This produces, at a selected time step in the MD trajec- tory, a distribution of monomers, dimers, and larger molecules. We then average the distributions over the extent of the MD trajectory. Figure 2 shows the variation of the dissociation fraction p, the ratio of monomers to the total number of particles, along the principal Hugoniot. For N2, the value for p at a fixed density was calculated as an average of two temper- atures (approximately 500 K above and below the Hugoniot), with the error bars indicating the spread between these two results. Figure 2 gives clear indi- cations of the general trends in the evolution of the fluid. The system appears to undergo a continuous transition from a molecular to a nearly fully dissoci- ated fluid, As the fluid starts to dissociate (at around q = 4,2.2,  and 2, respectively, for a, Nz, and a), trimers and larger clusters appear. (Note that this dis- sociation region coincides with the inflection region in Fig. 1.) However, these trimers survive for less than a vibrational period of the ground state dimer REFERENCES compression FIGURE 2. Variation of the average dissociation fraction p along the principal Hugoniot as a function of shock com- pression (q = p/po). D2 [trianlges, adapted from Ref. (?)I; N2 [circles, Ref. (lo)]; 0 2  (squares). and are thus highly transient. By contrast, the dimers hold together for many such periods. As the tem- perature and density increase, the lifetimes of the molecular species will decline since the collisional frequency will likewise rise, facilitating the breaking of the chemical bonds. This behavior becomes even more apparent from movies of the particle motions, The continuous dissociation and the transient charac- ter along the principal Hugoniot for Dz, Nz, and 02 all closely resemble each other. In summary, we have calculated equation-of-state properties for deuterium, nitrogen, and oxygen us- ing density functional molecular dynamics simula- tions at the GGA level. We obtain very good agree- ment (for pressure vs. density) with the gas-gun ex- periments along the principal Hugoniot. As density and pressure increase along the Hugoniot, the sys- tem appears to undergo a continuous transition from a molecular to a partially dissociated fluid containing a mixture of atoms and molecules. A small fraction of clusters larger than dimers were found; however, these larger clusters were of a highly transient nature, with lifetimes of a few femtoseconds, This work was supported under the auspices of the U.S. Dept. of Energy at Los Alamos National Laboratory (LANL) under Contract W-7405-ENG- 36. 1.  2. 3. 4. 5. 6. 7. 8. 9. L. B. DaSilva et al., Phys. Rev. Lett. 78,483 (1997); G. W. Collins it et al., Science 281(5380) 1178 (1998). 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DENSITY-FUNCTIONAL MOLECULAR DYNAMICS SIMULATIONS OF SHOCKED MOLECULAR LIQUIDS

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