Quantum molecular dynamics simulations of shocked nitrogen oxide S. Mazevet, 1 P. Blottiau, 2 J. D. Kress, 1 and L. A. Collins 1 1 Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA 2 CEA/DIF, Boîte Postale 12 Bruyère Le Chatel, France (Received 7 January 2004; published 22 June 2004) Using quantum molecular dynamics, we study the dissociation of nitrogen oxide along the principal and reshocked Hugoniots. We obtain good agreement with available experimental data for the first and highest second-shock Hugoniots. Reminiscent of the experimental and theoretical findings for shocked liquid nitrogen, the calculation indicates little temperature variation along the second shock as the fluid dissociates. The analysis of the concentration of molecular species along both Hugoniots indicates, as expected, that for low final shock densities molecular nitrogen is forming when nitrogen oxide dissociates. In contrast to basic assumptions used for high pressure modeling of nitrogen oxide, we find, however, that oxygen mostly stays in an atomic state for the whole density-temperature range studied. DOI: 10.1103/PhysRevB.69.224207 PACS number(s): 71.15.Pd, 62.50.1p, 61.20.Ja I. INTRODUCTION The study of materials under extreme conditions of tem- perature and pressure has made significant progress in the past few years, due to noticeable advances in both the ex- perimental and theoretical techniques. On the experimental side, Z pinch and laser-driven experimental setups have pushed Hugoniot measurements into the megabar range. 1,2 On the theoretical side, simulation methods, such as quantum molecular dynamics and path-integral Monte Carlo, 3–7 now allow the study of materials under such conditions from a mostly ab initio standpoint. However, the application of these methods has up to now primarily focused on pure sys- tems such as hydrogen, nitrogen, and oxygen, and lately on complementing the study of the equation of state (EOS) with the determination of the associated optical and electrical properties. 8–12 In the present work, we study the EOS and dissociation of NO along the principal and second-shock Hugoniots using quantum molecular dynamics (QMD). While NO presents a natural extension to study the EOS of multicomponent systems, 13 it also serves as a prototype for the study of ex- plosive compounds and their associated reactive chemistry. Furthermore, the determination of reactive potentials, 14,15 necessary for the study of technologically relevant and more complex systems such as H-C-N-O, also requires first a cali- bration to the NO system. Up to now, this calibration has been solely supported by the experimental measurements of the first (principal) and second-shock Hugoniots. 13 To complement the latter, we first calculate the principal and second-shock Hugoniots as well as the corresponding tem- perature up to pressures of, respectively, 83 GPa and 65 GPa. We further paid particular attention to the constituency of the fluid along each Hugoniot as the chemistry induced by such an increase of pressure and temperature remains among the most challenging aspects in the modeling of such sys- tems. Quantum molecular dynamics methods, where the electrons receive a fully quantum mechanical treatment, are particularly suited for the study of such chemical processes as ionization, recombination, dissociation, and association of the various atomic species present in the media, as well as many-body effects, which are treated on an equal footing within the framework of the density-functional theory (DFT). Using this parameter-free method, we show that for these overdriven experiments, where the shock front propa- gates faster than the reaction front, the dissociation of nitro- gen oxide leads, as expected, to the formation of molecular nitrogen at the lowest density. In contrast, we find that oxy- gen mostly stays in an atomic state for the density- temperature range covered by the principal and highest second-shock Hugoniots. This challenges the basic assump- tion used in the modeling of the high-pressure behavior of nitrogen oxide 13,16 where molecular nitrogen and molecular oxygen are both assumed to be the only products of the reaction. II. PRINCIPAL AND RESHOCKED HUGONIOTS In the present application, the molecular dynamics trajec- tories were calculated using the VASP plane-wave pseudopo- tential code, which was developed at the Technical Univer- sity of Vienna. 17 This code implements the Vanderbilt ultrasoft pseudopotential scheme 18 in a form supplied by Kresse and Hafner 19 and the Perdew-Wang 91 parametriza- tion of the generalized gradient approximation (GGA). 20 Tra- jectories were calculated at fixed volume and at separate den- sity and temperature points, selected to span a range of densities from r =1.90 to r =3.2 g/cm 3 and temperatures from T =1000 K to T = 14 000 K to highlight the first and second-shock Hugoniot regions. We used both 27/ 27 and 54/ 54 nitrogen/oxygen atoms in the unit cell and fixed the plane-wave cutoff at 495 eV. All the simulations were started using molecular NO as initial conditions. Integration of the equations of motion proceeded with time steps of 2 fs and for a total simulation time of up to 6 ps. During the simula- tions, the ion temperature T i was kept constant at every time step using velocity scaling. The validity of this assumption for the calculation of Hugoniot points was tested for the case of nitrogen using microcanonical simulations. 22 In turn, the assumption of local thermodynamical equilibrium sets the PHYSICAL REVIEW B 69, 224207 (2004) 0163-1829/2004/69(22)/224207(6)/$22.50 ©2004 The American Physical Society 69 224207-1