Advertisement

Equilibrium Molecular Dynamics Simulations

  • Betsy M. Rice
  • Thomas D. Sewell
Part of the Shock Wave and High Pressure Phenomena book series (SHOCKWAVE)

Molecular dynamics (MD) is a widely used atomistic simulation method due to the detailed information it can provide, often with a relatively small computational investment. The most distinguishing attribute of MD among molecular simulation methods is that it provides a means to monitor the time evolution of a system of particles (usually atoms) in phase space, thus allowing for an atomic-level view of the dynamics of a material in a given equilibrium or nonequilibrium thermodynamic state. This is particularly appealing for those in the energetic materials (EM) community since such a detailed description could reveal the fundamental mechanisms controlling the initiation of an energetic material to detonation, a phenomenon for which direct experimental measurement is in short Superscriptply due to the small time and spatial scales involved and the accompanying large rates of chemical energy release. MD is not affected by any of these factors; rather, its main limitations are the description of interatomic interactions (potential energy functions) used in the simulations and the viability of using classical mechanics to study molecular-scale phenomena. MD is receiving increased use in condensed-phase EM research as interaction potentials emerge that “realistically” describe the chemistry associated with initiation of an EM. However, MD is not limited to studying nonequilibrium dynamic events only; it has proven to be extremely useful for predicting thermodynamic equilibrium properties in the condensed phase.

Often a complete mapping of the equation of state (EOS) or the shock Hugoniot locus for an EM is extremely difficult to accomplish using traditional experimental methods of diamond anvil cells or shock waves [1–3]. Further, off-Hugoniot data can be measured only through the use of specialized equipment designed to study quasi-isentropic compression or using multiple-shock methods in which experimental and analytic uncertainties multiply quickly [4, 5]. MD simulations of any of these states, on the other hand, are straightforward and can readily provide a description of the EM under conditions not amenable to experimentation. Note that in many cases, particularly ones involving dynamic phenomena, the comparison between macroscopic and atomic-based results can be complicated due to the effects of finite simulation domains or slow relaxation phenomena. However, recent increases in time and spatial resolution of experimental diagnostics such as computed microtomography [6, 7] and ultrafast dynamic ellipsometry of laser-driven shocks on thin-film samples [8], which can provide the entire shock Hugoniot based on stress-induced optical effects and low-strain particle motion within a single-shot experiment, enable measurements of properties on scales routinely accessible by molecular simulation methods.

Keywords

Molecular Dynamic Simulation Energetic Material Simulation Cell Space Group Symmetry Electronegativity Equalization Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J. C. Gump and S. M. Peiris, Isothermal equations of state of beta octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine at high temperatures, J. Appl. Phys. 97, 053513 (2005).Google Scholar
  2. 2.
    B. Olinger, B. Roof, and H. H. Cady, The linear and volume compression of β-HMX and RDX, Proc. Int. Symp. On High Dynamic Pressures (Paris, CEA, 1978) p. 3.Google Scholar
  3. 3.
    C.-S. Yoo and H. Cynn, Equation of state, phase transition, decomposition of beta-HMX (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine) at high pressures, J. Chem. Phys. 111, 10229 (1999).Google Scholar
  4. 4.
    M. R. Baer, C. A. Hall, R. L. Gustavsen, D. E. Hooks, and S. A. Sheffield, Isentropic compression experiments for mesoscale studies of energetic composites, AIP Conf. Proc. 845, 1307 (2006).Google Scholar
  5. 5.
    B. Crouzet, D. Partouche-Sebban, and N. Carion, Temperature measurements in shocked nitromethane, AIP Conf. Proc. 706, 1253 (2004).Google Scholar
  6. 6.
    S. G. Bardenhagen, A. D. Brydon, T. O. Williams, and C. Collet, Coupling grain scale and bulk mechanical response for PBXs using numerical simulations of real microstructures, AIP Conf. Proc. 845, 479 (2006).Google Scholar
  7. 7.
    A. D. Brydon, S. G. Bardenhagen, E. A. Miller, and G. T. Seidler, Simulation of the densification of real open-celled foam microstructures, J. Mech. Phys. Solids 53, 2638 (2005).Google Scholar
  8. 8.
    C. A. Bolme, S. D. McGrane, D. S. Moore, and D. J. Funk, Single shot measurements of laser driven shock waves using ultrafast dynamic ellipsometry, J. Appl. Phys. 102, 033513 (2007).Google Scholar
  9. 9.
    For instance: T. R. Gibbs and A. Popolato, LASL Explosive Property Data (University of CA, Berkeley, 1980).Google Scholar
  10. 10.
    T. D. Sewell and R. Menikoff, Complete equation of state for β-HMX and implications for initiation, AIP Conf. Proc. 706, 157 (2004).Google Scholar
  11. 11.
    G. A. Ruderman, D. S. Stewart, and J.-I. Yoh, A thermomechanical model for energetic materials with phase transformations, SIAM J. Appl. Math. 63, 510 (2002).Google Scholar
  12. 12.
    R. Menikoff and M. S. Shaw, Review of the Forest Fire Model, Combust. Theor. Mod. 12, 569 (2008).Google Scholar
  13. 13.
    W. G. Proud, M. W. Greenaway, C. R. Siviour, H. Czerski, and J. E. Field, Characterizing the response of energetic materials and polymer-bonded explosives (PBXs) to high-rate loading, Mat. Res. Soc. Symp. Proc. 896, 225 (2006).Google Scholar
  14. 14.
    S. Lecume, C. Boutry, and C. Spyckerelle, Structure of nitramines crystal defects relation with shock sensitivity, Energetic Materials: Structure and Properties, 35th International Conference of ICT, Karlsruhe, FRG, p. 2–1 (2004).Google Scholar
  15. 15.
    R. Menikoff, Pore collapse and hot spots in HMX, AIP Conf. Proc. 706, 393 (2004).Google Scholar
  16. 16.
    W. M. Trott, M. R. Baer, J. N. Castaneda, L. C. Chhabildas, and J. R. Asay, Investigation of the mesoscopic scale response of low-density pressings of granular sugar under impact, J. Appl. Phys. 101, 024917 (2007).Google Scholar
  17. 17.
    F. P. Bowden and Y. D. Yoffe, Initiation and growth of explosion in liquids and solids (Cambridge University Press, Cambridge, 1952).Google Scholar
  18. 18.
    L. Tran and H. S. Udaykumar, Simulation of void collapse in an energetic material, Part 1: Inert case, J. Propul. Pow. 22 947 (2006); ibid, Simulation of void collapse in an energetic material, Part 2: Reactive case, 22, 959 (2006).Google Scholar
  19. 19.
    R. Menikoff, Detonation waves in PBX 9501, Combust. Theor. Mod. 10, 1003 (2006).Google Scholar
  20. 20.
    R. Menikoff, Comparison of constitutive models for plastic-bonded explosives, Combust. Theor. Mod. 12, 73 (2007).Google Scholar
  21. 21.
    D. C. Sorescu, B. M. Rice, and D. L. Thompson, Molecular Dynamics Simulations of Energetic Materials, in P. Politzer and J. S. Murray (Eds.) Energetic Materials: Part 1. Decomposition, Crystal and Molecular Properties (Theoretical and Computational Chemistry) (Elsevier Science, Amsterdam, 2003) pp. 125 – 184.Google Scholar
  22. 22.
    D. A. McQuarrie, Statistical Mechanics (Harper & Row, New York, 1976).Google Scholar
  23. 23.
    J.-B. Maillet, M. Mareschal, L. Soulard, R. Ravelo, P. S. Lomdahl, T. C. Germann, and B. L. Holian, Uniaxial Hugoniostat: A method for atomistic simulations of shocked materials, Phys. Rev. E 63, 016121 (2001).Google Scholar
  24. 24.
    R. Ravelo, B. L. Holian, T. C. Germann, and P. S. Lomdahl, Constant-stress Hugoniostat method for following the dynamical evolution of shocked matter, Phys. Rev. B 70, 014103 (2004).Google Scholar
  25. 25.
    J. M. D. Lane and M. Marder, Numerical method for shock front Hugoniot states, AIP Conf. Proc. 845, 331 (2006).Google Scholar
  26. 26.
    E. J. Reed, L. E. Fried, W. D. Henshaw, and C. M. Tarver, Analysis of simulation technique for steady shock waves in materials with analytical equations of state, Phys. Rev. E 74, 056706 (2006).Google Scholar
  27. 27.
    E. J. Reed, L. E. Fried, and J. D. Joannopoulos, A method for tractable dynamical studies of single and double shock compression, Phys. Rev. Lett. 90, 235503 (2003).Google Scholar
  28. 28.
    R. Menikoff and T. D. Sewell, Constituent properties of HMX needed for mesoscale simulations, Combust. Theor. Mod. 6, 103 (2002).Google Scholar
  29. 29.
    A. Strachan and B. L. Holian, Energy exchange between mesoparticles and their internal degrees of freedom, Phys. Rev. Lett. 94, 014301 (2005).Google Scholar
  30. 30.
    Y. Guo, D. L. Thompson, and T. D. Sewell, Analysis of the zero-point energy problem in classical trajectory simulations, J. Chem. Phys. 104, 576 (1996).Google Scholar
  31. 31.
    Z. A. Dreger and Y. M. Gupta, High pressure Raman spectroscopy of single crystals of hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX), J. Phys. Chem. B 111, 3893 (2007).Google Scholar
  32. 32.
    T. R. Park, Z. A. Dreger, and Y. M. Gupta, Raman spectroscopy of pentaerythritol single crystals under high pressures, J. Phys. Chem. B 108, 3174 (2004).Google Scholar
  33. 33.
    J. A. Ciezak, T. A. Jenkins, and Z. X. Liu, Propellants Explosives Pyrotechnics 32, 472 (2007).Google Scholar
  34. 34.
    P. J. Miller, S. Block, and G. J. Piermarini, Effects of pressure on the thermal-decomposition kinetics, chemical-reactivity and phase-behavior of RDX, Combust. Flame 83, 174 (1991).Google Scholar
  35. 35.
    G. J. Piermarini, S. Block, and P. J. Miller, Effects of pressure on the thermal-decomposition kinetics and chemical-reactivity of nitromethane,J. Phys. Chem. 93, 457 (1989).Google Scholar
  36. 36.
    G. J. Piermarini, S. Block, and P. J. Miller, Effects of pressure and temperature on the thermal-decomposition rate and reaction-mechanism of beta-octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine, J. Phys. Chem. 91, 3872 (1987).Google Scholar
  37. 37.
    L. Zheng, B. M. Rice, and D. L. Thompson, Molecular dynamics simulations of the melting mechanisms of perfect and imperfect crystals of dimethylnitramine, J. Phys. Chem. B 111, 2891 (2007).Google Scholar
  38. 38.
    L. Zheng and D. L. Thompson, Molecular dynamics simulations of melting of perfect crystalline hexahydro-1,3,5-trinitro-1,3,5-s-triazine, J. Chem. Phys. 125, 084505 (2006).Google Scholar
  39. 39.
    A. Siavosh-Haghighi and D. L. Thompson, Molecular dynamics simulations of surfaceinitiated melting of nitromethane, J. Chem. Phys. 125, 184711 (2006).Google Scholar
  40. 40.
    P. M. Agrawal, B. M. Rice, L. Zheng, G. F. Velardez, and D. L. Thompson, Molecular dynamics simulations of hexahydro-1,3,5-trinitro-1,3,5-s-triazine (RDX) using a combined Sorescu-Rice-Thompson AMBER force field, J. Phys. Chem. B 110, 5721 (2006).Google Scholar
  41. 41.
    L. Zheng, S. N. Luo, and D. L. Thompson, Molecular dynamics simulations of melting and the glass transition of nitromethane, J. Chem. Phys. 124, 154504 (2006).Google Scholar
  42. 42.
    P. M. Agrawal, B. M. Rice, and D. L. Thompson, Molecular dynamics study of the melting of nitromethane, J. Chem. Phys. 119, 9617 (2003).Google Scholar
  43. 43.
    D. Cremer and J. A. Pople, General definition of ring puckering coordinates, J. Am. Chem. Soc. 97, 1354 (1975).Google Scholar
  44. 44.
    C. B. Barber, D. P. Dobkin, H. T. Huhdanpaa, Quickhull algorithm for convex hulls, ACM Trans. Math. Softw. 22, 469 (1996).Google Scholar
  45. 45.
    M. J. Cawkwell, T. D. Sewell, K. J. Ramos, and D. E. Hooks, Shock-induced anomalous plastic hardening in an energetic molecular crystal (Phys. Rev. B, submitted).Google Scholar
  46. 46.
    K. Kadau, T. C. Germann, and P. S. Lomdahl, Molecular dynamics comes of age: 320 billion atom simulation on BlueGene/L, Int. J. Mod. Phys. C 17, 1755 (2006).Google Scholar
  47. 47.
    K. Kadau, C. Rosenblatt, J. L. Barber, T. C. Germann, Z. B. Huang, P. Carles, and B. J. Alder, The importance of fluctuations in fluid mixing, Proc. Nat. Acad. Sci. USA 104, 7741 (2007).Google Scholar
  48. 48.
    D. Frenkel and B. Smit, Understanding Molecular Simulation (Academic Press, San Diego, 2002).Google Scholar
  49. 49.
    A. Gavezzotti, Are crystal-structures predictable?, Accounts Chem. Res. 27, 309 (1994).Google Scholar
  50. 50.
    P. Verwer and F. J. J. Leusen, Computer simulation to predict possible crystal polymorphs, in Reviews in Computational Chemistry, K. B. Lipkowitz and D. B. Boyd (Eds.) (Wiley-VCH, New York, 1998), p. 327.Google Scholar
  51. 51.
    R. J. Gdanitz, Ab initio prediction of molecular crystal structures, Curr. Opn. Solid State Mater. Sci. 3, 414 (1998).Google Scholar
  52. 52.
    A. Gavezzotti, The chemistry of intermolecular bonding: Organic crystals, their structures and transformations. Synlett 2, 201 (2002).Google Scholar
  53. 53.
    T. Beyer, T. Lewis, and S. L. Price, Which organic crystal structures are predictable by lattice energy minimisation?, Cryst. Eng. Comm. 44, 1 (2001).Google Scholar
  54. 54.
    J. P. M. Lommerse, W. D. S. Motherwell, H. L. Ammon, J. D. Dunitz, A. Gavezzotti, D. W. M. Hofmann, F. J. J. Leusen, W. T. M. Mooij, S. L. Price, B. Schweizer, M. U. Schmidt, B. P. van Eijck, P. Verwer, and D. E. Williams, A test of crystal structure prediction of small organic molecules, Acta Cryst. B 56, 697 (2002).Google Scholar
  55. 55.
    W. D. S. Motherwell, H. L. Ammon, J. D. Dunitz, A. Dzyabchenko, P. Erk, A. Gavezzotti, D. W. M. Hofmann, F. J. J. Leusen, J. P. M. Lommerse, W. T. M. Mooij, S. L. Price, H. Scheraga, B. Schweizer, M. U. Schmidt, B. P. van Eijck, P. Verwer, and D. E. Williams, Crystal structure prediction of small organic molecules: a second blind test, Acta Cryst. B 58, 647 (2002).Google Scholar
  56. 56.
    W. T. M. Mooij, B. P. van Eijck, S. L. Price, P. Verwer, and J. Kroon, Crystal structure predictions for acetic acid, J. Comput. Chem. 19, 459 (1998).Google Scholar
  57. 57.
    D. W. M. Hofmann and T. Lengauer, Crystal structure prediction based on statistical potentials, J. Mol. Model. 4, 132 (1998).Google Scholar
  58. 58.
    A. Gavezzotti, Generation of possible crystal-structures from the molecular-structure for lowpolarity organic-compounds, J. Am. Chem. Soc. 113, 4622 (1991).Google Scholar
  59. 59.
    H. R. Karfunkel, F. J. Leusen, and R. J. Gdanitz, The ab initio prediction of yet unknown molecular crystal structures by solving the crystal packing problem, J. Comput.-Aided Mater. Des. 1, 177 (1993).Google Scholar
  60. 60.
    D. J. Willock, S. L. Price, M. Leslie, and C. R. A. Catlow, The relaxation of molecularcrystal structures using a distributed multipole electrostatic model, J. Comput. Chem. 16, 628 (1995).Google Scholar
  61. 61.
    D. E. Williams, Ab initio molecular packing analysis, Acta Cryst. A 52 326 (1996).Google Scholar
  62. 62.
    A. V. Dzyabchenko, T. S. Pivina, and E. A. Arnautova, Prediction of structure and density for organic nitramines, J. Mol Struct. 378, 67 (1996).Google Scholar
  63. 63.
    M. U. Schmidt and U. Englert, Prediction of crystal structures, J. Chem. Soc. Dalton Trans. 10, 2077 (1996).Google Scholar
  64. 64.
    A. M. Chaka, R. Zaniewski, W. Youngs, C. Tessier, and G. Klopman, Predicting the crystal structure of organic molecular materials, Acta Cryst. B 52, 165 (1996).Google Scholar
  65. 65.
    D. W. M. Hofmann and T. Lengauer, A discrete algorithm for crystal structure prediction of organic molecules, Acta Cryst. A 53, 225 (1997).Google Scholar
  66. 66.
    G. M. Day, W. D. S. Motherwell, H. L. Ammon, S. X. M. Boerrigter, R. G. Della Valle, E. Venuti, A. Dzyabchenko, J. D. Dunitz, B. Schweizer, B. P. van Eijck, P. Erk, J. C. Facelli, V. E. Bazterra, M. B. Ferraro, D. W. M. Hofmann, F. J. J. Leusen, C. Liang, C. C. Pantelides, P. G. Karamertzanis, S. L. Price, T. C. Lewis, H. Nowell, A. Torrisi, H. A. Scheraga, Y. A. Arnautova, M. U. Schmidt, and P. Verwer, A third blind test of crystal structure prediction, Acta Cryst. B 61, 511 (2005).Google Scholar
  67. 67.
    P. Erk, Crystal engineering: from molecules and crystals to materials, NATO Sci. Ser. C 538, 143 (1999).Google Scholar
  68. 68.
    B. P. van Eijck and J. Kroon, UPACK program package for crystal structure prediction: Force fields and crystal structure generation for small carbohydrate molecules, J. Comput. Chem. 20, 799 (1999).Google Scholar
  69. 69.
    A. V. Dzyabchenko, V. Agafonov, and V. A. Davydov, A theoretical study of the pressureinduced dimerization of C-60 fullerene, J. Phys. Chem. A 103, 2812 (1999).Google Scholar
  70. 70.
    W. T. M. Mooij, F. B. van Duijneveldt, J. G. C. M. van Duijneveldt-van de Rijdt, and B. P. van Eijck, Transferable ab initio intermolecular potentials. 1. Derivation from methanol dimer and trimer calculations, J. Phys. Chem. A 103, 9872 (1999).Google Scholar
  71. 71.
    W. D. S. Motherwell, Crystal structure prediction and the Cambridge Structural Database, Nova Acta Leopoldina 79, 89 (1999).Google Scholar
  72. 72.
    B. P. van Eijck and J. Kroon, Structure predictions allowing more than one molecule in the asymmetric unit, Acta Cryst. B 56, 535 (2000).Google Scholar
  73. 73.
    T. Beyer and S. L. Price, Dimer or catemer? Low-energy crystal packings for small carboxylic acids, J. Phys. Chem. B 104, 2647 (2000).Google Scholar
  74. 74.
    T. Beyer, G. M. Day, and S. L. Price, The prediction, morphology, and mechanical properties of the polymorphs of paracetamol, J. Am. Chem. Soc. 123, 5086 (2001).Google Scholar
  75. 75.
    J. Pillardy, Y. A. Arnautova, C. Czaplewski, K. D. Gibson, and H. A. Scheraga, Conformation-family Monte Carlo: A new method for crystal structure prediction, Proc. Nat. Acad. Sci. USA 98, 12351 (2001).Google Scholar
  76. 76.
    C. Mellot-Draznieks, S. Girard, G. Ferey, J. C. Schon, Z. Cancarevic, and M. Jansen, Computational design and prediction of interesting not-yet-synthesized structures of inorganic materials by using building unit concepts, Chem. Eur. J. 8, 4103 (2002).Google Scholar
  77. 77.
    E. Pidcock and W. D. S. Motherwell, A new model of crystal packing, Chem. Commun. 24, 3028 (2003).Google Scholar
  78. 78.
    E. Pidcock and W. D. S. Motherwell, A novel description of the crystal packing of molecules, Cryst. Growth Des. 4, 611 (2004).Google Scholar
  79. 79.
    J. R. Holden, Z. Y. Du, and H. L. Ammon, Prediction of possible crystal-structures for C-containing, H-containing, N-containing, O-containing and F-containing organiccompounds, J. Comput. Chem. 14 422 (1993).Google Scholar
  80. 80.
    D. Q. Gao and D. E. Williams, Molecular packing groups and ab initio crystal-structure prediction, Acta Cryst. A 55, 621 (1999).Google Scholar
  81. 81.
    A. D. Mighell, V. L. Himes, and J. R. Rodgers, Space-group frequencies for organic-compounds, Acta Cryst. A 39 737 (1983).Google Scholar
  82. 82.
    For example: J. A. Moriarty, L. X. Benedict, J. N. Glosli, R. Q. Hood, D. A. Orlikowski, M. V. Patel, P. Soderlind, F. H. Streitz, M. J. Tang, and L. H. Yang, Robust quantum-based interatomic potentials for multiscale modeling in transition metals, J. Mat. Res. 21, 563 (2006).Google Scholar
  83. 83.
    For example: A. J. Pertsin and A. I. Kitaigorodskii, The Atom-Atom Potential Method: Applications to Organic Molecular Solids. Springer Series in Chemical Physics 43. (Springer, Heidelberg, 1987).Google Scholar
  84. 84.
    A. M. N. Niklasson, C. J. Tymczak, and M. Challacombe, Time-reversible ab initio molecular dynamics, J. Chem. Phys. 126, 114103 (2007).Google Scholar
  85. 85.
    D. C. Sorescu, B. M. Rice, and D. L. Thompson, Intermolecular potential for the hexahydro-1,3,5-trinitro-1,3,5-s-triazine crystal (RDX): A crystal packing, Monte Carlo, and molecular dynamics study, J. Phys. Chem. B 101, 798 (1997).Google Scholar
  86. 86.
    D. C. Sorescu and D. L. Thompson, Classical and quantum mechanical studies of crystalline ammonium nitrate, J. Phys. Chem. A 105, 720 (2001).Google Scholar
  87. 87.
    D. C. Sorescu, J. A. Boatz, and D. L. Thompson, Classical and quantum-mechanical studies of crystalline FOX-7 (1,1-diamino-2,2-dinitroethylene), J. Phys. Chem.A 105, 5010 (2001).Google Scholar
  88. 88.
    D. C. Sorescu and D. L. Thompson, Classical and quantum mechanical studies of crystalline ammonium dinitramide, J. Phys. Chem. B 103, 6774 (1999).Google Scholar
  89. 89.
    G. D. Smith and R. K. Bharadwaj, Quantum chemistry based force field for simulations of HMX, J. Phys. Chem. B 103, 3570 (1999).Google Scholar
  90. 90.
    J. Seminario, M. C. Concha, and P. Politzer, A density-functional molecular-dynamics study of the structure of liquid nitromethane, J. Chem. Phys. 102 8281 (1995).Google Scholar
  91. 91.
    S. W. Bunte and H. Sun, Molecular modeling of energetic materials: The parameterization and validation of nitrate esters in the COMPASS force field, J. Phys. Chem. B 104, 2477 (2000).Google Scholar
  92. 92.
    D. C. Sorescu, B. M. Rice, and D. L. Thompson, Theoretical studies of the hydrostatic compression of RDX, HMX, HNIW, and PETN crystals, J. Phys. Chem. B 103, 6783 (1999).Google Scholar
  93. 93.
    J. P. Agrawal and R. D. Hodgson, Organic Chemistry of Explosives (Wiley, Chichester, 2007).Google Scholar
  94. 94.
    H. H. Cady and L. C. Smith, Studies on the polymorphs of HMX, LANL report LA-MS-2652 (Los Alamos National Laboratory, 1962).Google Scholar
  95. 95.
    H. H. Cady, A. C. Larson, and D. T. Cromer, The crystal structure of α-HMX and a refinement of the structure of β-HMX, Acta Crystallogr. 16, 617 (1963).Google Scholar
  96. 96.
    C. S. Choi and H. P. Boutin, A study of the crystal structure of β-cyclotetramethylene tetranitramine by neutron diffraction, Acta Cryst. B 26, 1235 (1970).Google Scholar
  97. 97.
    R. E. Cobbledick and R. W. H. Small, The crystal structure of the δ-form of 1,3,5,7-tetranitro-1,3,5,7-tetraazacyclooctane (8-HMX), Acta Cryst. B 30, 1918 (1974).Google Scholar
  98. 98.
    D. W. Brenner, D. H. Robertson, M. L. Elert, and C. T. White, Detonations at nanometer resolution using molecular dynamics, Phys. Rev. Lett. 70, 2174 (1993); ibid., Detonations at nanometer resolution using molecular dynamics,Phys. Rev. Lett. 76, 2202 (1996).Google Scholar
  99. 99.
    J. Tersoff, Empirical interatomic potential for carbon, with applications to amorphous carbon, Phys. Rev. Lett. 61, 2879 (2003).Google Scholar
  100. 100.
    R. L. Martin, Electronic Structure: Basic Theory and Practical Methods (Cambridge University Press, New York, 2004).Google Scholar
  101. 101.
    R. G. Parr and W Yang, Density-Functional Theory of Atoms and Molecules (Oxford University Press, New York, 1989).Google Scholar
  102. 102.
    H. Liu, J. J. Zhao, D. Q. Wei, and Z. Z. Gong, Structural and vibrational properties of solid nitromethane under high pressure by density functional theory, J. Chem. Phys. 124, 12450 (2006).Google Scholar
  103. 103.
    E. F. C. Byrd, G. E. Scuseria, and C. F. Chabalowski, An ab initio study of solid nitromethane, HMX, RDX, and CL20: Successes and failures of DFT, J. Phys. Chem. B 108,13100 (2004).Google Scholar
  104. 104.
    E. F. C. Byrd and B. M. Rice, Ab initio study of compressed 1,3,5,7-tetranitro-1,3,5,7-tetraazacyclooctane (HMX), cyclotrimethylenetrinitramine (RDX), 2,4,6,8,10,12-hexanitro-hexaazaisowurzitane (CL-20), 2,4,6-trinitro-1,3,5-benzenetriamine (TATB), and pentaery-thritol tetranitrate (PETN), J. Phys. Chem. C 111, 2787 (2007).Google Scholar
  105. 105.
    V. I. Levitas, L. B. Smilowitz, B. F. Henson, and B. W Asay, Interfacial and volumetric kinetics of the beta - › delta phase transition in the energetic nitramine octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine based on the virtual melting mechanism, J. Chem. Phys. 124, 025101 (2006).Google Scholar
  106. 106.
    A. C. T. van Duin, S. Dasgupta, F. Lorant, and W A. Goddard III, ReaxFF: A reactive force field for hydrocarbons, J. Phys. Chem. A 105, 9396 (2001).Google Scholar
  107. 107.
    A. Strachan, A. C. T. van Duin, D. Chakraborty, S. Dasgupta, and W A. Goddard III, Shock waves in high-energy materials: The initial chemical events in nitramine RDX, Phys. Rev. Lett. 91, 098301 (2003).Google Scholar
  108. 108.
    A. Strachan, E. M. Kober, A. C. T. van Duin, J. Oxgaard, and W A. Goddard III, Thermal decomposition of RDX from reactive molecular dynamics, J. Chem. Phys. 122, 054502 (2005).Google Scholar
  109. 109.
    A. C. T. van Duin, Y. Zeiri, F. Dubnikova, R. Kosloff, and W. A. Goddard III, Atomistic-scale simulations of the initial chemical events in the thermal initiation of triacetonetriperoxide, J. Am. Chem. Soc. 127, 11053 (2005).Google Scholar
  110. 110.
    W. J. Mortier, S. K. Ghosh, and S. Shankar, Electronegativity equalization method for the calculation of atomic charges in molecules, J. Am. Chem. Soc. 108, 4315 (1986).Google Scholar
  111. 111.
    M. J. Buehler, A. C. T. van Duin, and W. A. Goddard III, Multiparadigm modeling of dynamical crack propagation in silicon using a reactive force field, Phys. Rev. Lett. 96, 095505 (2006).Google Scholar
  112. 112.
    K. Chenoweth, S. Cheung, A. C. T. van Duin, W. A. Goddard III, and E. M. Kober, Simulations on the thermal decomposition of a poly(dimethylsiloxane) polymer using the ReaxFF reactive force field, J. Am. Chem. Soc. 127, 7192 (2005).Google Scholar
  113. 113.
    Q. Zhang, Y. Qi, L. G. Hector, T. Cagin, and W. A. Goddard III, Atomic simulations of kinetic friction and its velocity dependence at Al/Al and alpha-Al2O3/alpha-Al2O3 interfaces, Phys. Rev. B 72, 045406 (2005).Google Scholar
  114. 114.
    K. D. Nielson, A. C. T. van Duin, J. Oxgaard, W. Q. Deng, and W. A. Goddard III, Development of the ReaxFF reactive force field for describing transition metal catalyzed reactions, with application to the initial stages of the catalytic formation of carbon nanotubes, J. Phys. Chem. A 109, 493 (2005).Google Scholar
  115. 115.
    J. Ludwig, D. G. Vlachos, A. C. T. van Duin, and W. A. Goddard III, Dynamics of the dissociation of hydrogen on stepped platinum surfaces using the ReaxFF reactive force field, J. Phys. Chem. B 110, 4274 (2006).Google Scholar
  116. 116.
    W. A. Goddard III, A. C. T. van Duin, K. Chenoweth, M. J. Cheng, S. Pudar, J. Oxgaard, B. Merinov, Y. H. Jang, and P. Persson, Development of the ReaxFF reactive force field for mechanistic studies of catalytic selective oxidation processes on BiMoOx, Topics Catalysis 38, 93 (2006).Google Scholar
  117. 117.
    S. S. Han, J. K. Kang, H. M. Lee, A. C. T. van Duin, and W. A. Goddard III, The theoretical study on interaction of hydrogen with single-walled boron nitride nanotubes. I. The reactive force field ReaxFF(HBN) development, J. Chem. Phys. 123, 114703 (2005).Google Scholar
  118. 118.
    S. S. Han, A. C. T. van Duin, W. A. Goddard III, and H. M. Lee, Optimization and application of lithium parameters for the reactive force field, ReaxFF, J. Phys. Chem. A 109, 4575 (2005).Google Scholar
  119. 119.
    S. Cheung, W. Q. Deng, A. C. T. van Duin, and W. A. Goddard III, ReaxFF(MgH) reactive force field for magnesium hydride systems, J. Phys. Chem. A 109, 851 (2005).Google Scholar
  120. 120.
    W. A. Goddard III, O. Zhang, M. Uludogan, A. Strachan, and T. Cagin, The ReaxFF polarizable reactive force fields for molecular dynamics simulation of ferroelectrics, AIP Conf. Proc. 626, 45 (2002).Google Scholar
  121. 121.
    I. I. Oleynik, M. Conroy, S. V. Zybin, L. Zhang, A. C. T. van Duin, W. A. Goddard III, and C. T. White, Energetic materials at high compression: first-principles density functional theory and reactive force field studies, AIP Conf. Proc. 845, 573 (2006).Google Scholar
  122. 122.
    SeqQuest Electronic Structure Code, http://dft.sandia.gov/Quest/Google Scholar
  123. 123.
    D. C. Langreth and J. P. Perdew, Theory of nonuniform electronic systems. 1. Analysis of the gradient approximation and a generalization that works, Phys. Rev. B 21, 5469 (1980).Google Scholar
  124. 124.
    J. P. Perdew and W. Yue W, Accurate and simple density functional for the electronic exchange energy: Generalized gradient approximation, Phys. Rev. B 33, 8800 (1986); ibid., Erratum: Accurate and simple density functional for the electronic exchange energy: Generalized gradient approximation, Phys. Rev. B 40, 3399 (1989).Google Scholar
  125. 125.
    J. P. Perdew, Density-functional approximation for the correlation-energy of the inhomogeneous electron-gas, Phys. Rev. B 33, 8822 (1986); ibid., Correction, Phys. Rev. B 34, 7406 (1986).Google Scholar
  126. 126.
    D. C. Langreth and M. J. Mehl, Beyond the local-density approximation in calculations of ground-state electronic-properties, Phys. Rev. B 28, 1809 (1983); ibid., Erratum: Beyond the local-density approximation in calculations of ground-state electronic properties, Phys. Rev. B 29, 2310 (1984).Google Scholar
  127. 127.
    J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996); ibid., Generalized gradient approximation made simple, Phys. Rev. Lett. 78, 1396 (1997).Google Scholar
  128. 128.
    A. C. T. van Duin, S. V. Zybin, K. Chenoweth, L. Zhang, S. P. Han, A. Strachan, and W. A. Goddard III, Reactive force fields based on quantum mechanics for applications to materials at extreme conditions, AIP Conf. Proc. 845, 581 (2006).Google Scholar
  129. 129.
    A. C. T. van Duin, S. V. Zybin, K. Chenoweth, S. P. Han, and W. A. Goddard III, Reactive force fields based on quantum mechanics for applications to materials at extreme conditions. Lecture Series on Computer and Computational Sciences 4 (Brill Academic Publishers, Amsterdam, 2005) p. 1109.Google Scholar
  130. 130.
    L. Zhang, S. V. Zybin, A. C. T. van Duin, S. Dasgupta, and W. A. Goddard III, Thermal decomposition of energetic materials by ReaxFF reactive molecular dynamics, AIP Conf. Proc. 845, 589 (2006).Google Scholar
  131. 131.
    O. Borodin, G. D. Smith, D. Bedrov, and T. D. Sewell, Polarizable and non-polarizable force fields for alkylnitrates, J. Phys. Chem. B 112, 734 (2008).Google Scholar
  132. 132.
    D. C. Sorescu, B. M. Rice, and D. L. Thompson, Molecular packing and NPT molecular dynamics investigation of the transferability of the RDX intermolecular potential to 2,3,6,8,10,12-hexanitrohexaazaisowurtzitane, J. Phys. Chem. B 102, 948 (1998).Google Scholar
  133. 133.
    D. C. Sorescu, B. M. Rice, and D. L. Thompson, Isothermal-isobaric molecular dynamics simulations of 1,3,5,7-tetranitro-1,3,5,7-tetraazacyclooctane (HMX) crystals, J. Phys. Chem. B 102, 6692 (1998).Google Scholar
  134. 134.
    D. C. Sorescu, B. M. Rice, and D. L. Thompson, A transferable intermolecular potential for nitramine crystals, J. Phys. Chem. A 102, 8386 (1998).Google Scholar
  135. 135.
    D. C. Sorescu, B. M. Rice, and D. L. Thompson, Molecular packing and molecular dynamics study of the transferability of a generalized nitramine intermolecular potential to non-nitramine crystals, J. Phys. Chem. A 103, 989 (1999).Google Scholar
  136. 136.
    B. M. Rice and D. C. Sorescu, Assessing a generalized CHNO intermolecular potential through ab initio crystal structure prediction, J. Phys. Chem. B 108, 17730 (2004).Google Scholar
  137. 137.
    L. Q. Zheng and D. L. Thompson, On the accuracy of force fields for predicting the physical properties of dimethylnitramine, J. Phys. Chem. B 110, 16082 (2006).Google Scholar
  138. 138.
    D. C. Sorescu, B. M. Rice, and D. L. Thompson, Theoretical studies of solid nitromethane, J. Phys. Chem. B 104, 8406 (2000).Google Scholar
  139. 139.
    D. C. Sorescu, B. M. Rice, and D. L. Thompson, Molecular dynamics simulations of liquid nitromethane, J. Phys. Chem. A 105, 9336 (2001).Google Scholar
  140. 140.
    A. Siavosh-Haghighi and D. L. Thompson, Melting point determination from solid-liquid coexistence initiated by surface melting, J. Phys. Chem. C 111, 7980 (2007).Google Scholar
  141. 141.
    T. Megyes, S. Bálint, T. Grósz, T. Radnai, I. Bakó, and L. Almásy, Structure of liquid nitromethane: Comparison of simulation and diffraction studies, J. Chem. Phys. 126, 164507 (2007).Google Scholar
  142. 142.
    P. M. Agrawal, B. M. Rice, L. Zheng, and D. L. Thompson, Molecular dynamics simulations of hexahydro-1,3,5-trinitro-1,3,5-s-triazine (RDX) using a combined Sorescu-Rice-Thompson AMBER force field, J. Phys. Chem. B 110, 26185 (2006).Google Scholar
  143. 143.
    N. Goto, H. Yamawaki, K. Wakabayashi, Y. Nakayama, M. Yoshida, and M. Koshi, High pressure phase of RDX, Sci. Tech. Energ. Mater. 66, 291 (2005).Google Scholar
  144. 144.
    D. A. Case, D. A. Pearlman, J. W. Caldwell, T. E. Cheatham, J. Wang, W. S. Ross, C. L. Simmerling, T. A. Darden, K. M. Merz, R. V. Stanton, A. L. Cheng, J. J. Vincent, M. Crowley, V. Tsui, H. Gohlke, R. J. Radmer, Y. Duan, J. Pitera, I. Massova, G. L. Seibel, U. C. Singh, P. K. Weiner, and P. A. Kollman, AMBER 7 (University of California, San Francisco, 2002).Google Scholar
  145. 145.
    J. M. Wang, R. M. Wolf, J. W. Caldwell, P. A. Kollman, and D. A. Case, Development and testing of a general amber force field, J. Comput. Chem. 25, 1157 (2004).Google Scholar
  146. 146.
    S. J. Weiner, P. A. Kollman, D. T. Nguyen, and D. A. Case, An all atom force-field for simulations of proteins and nucleic-acids, J. Comput. Chem. 7, 230 (1986).Google Scholar
  147. 147.
    S. Ye, K. Tonokura, and M. Koshi, Theoretical studies of pressure dependence of phonon and vibron frequency shifts of PETN, Sci. Tech. Energ. Mater. 64, 201 (2003).Google Scholar
  148. 148.
    H. E. Alper, F. Abu-Awwad, and P. Politzer, Molecular dynamics simulations of liquid nitromethane, J. Phys. Chem. B 103, 9738 (1999).Google Scholar
  149. 149.
    S. Boyd, M. Gravelle, and P. Politzer, Nonreactive molecular dynamics force field for crystalline hexahydro-1,3,5-trinitro-1,3,5 triazine, J. Chem. Phys. 124, 104508 (2006).Google Scholar
  150. 150.
    G. D. Smith, R. K. Bharadwaj, D. Bedrov, and C. Ayyagari, Quantum-chemistry-based force field for simulations of dimethylnitramine, J. Phys. Chem. B 103, 705 (1999).Google Scholar
  151. 151.
    H. Davande, O. Borodin, G. D. Smith, and T. D. Sewell, Quantum chemistry-based force field for simulations of energetic dinitro compounds, J. Energ. Mater. 23, 205 (2005).Google Scholar
  152. 152.
    R. I. Hiyoshi, Y. Kohno, O. Takahashi, J. Nakamura, Y. Yamaguchi, S. Matsumoto, N. Azuma, and K. Ueda, Effect of pressure on the vibrational structure of insensitive energetic material 5-nitro-2,4-dihydro-1,2,4-triazole-3-one, J. Phys. Chem. A 110, 9816 (2006).Google Scholar
  153. 153.
    H. Liu, J. J. Zhao, G. F. Ji, Z. Z. Gong, and D. Q. Wei, Compressibility of liquid nitromethane in the high-pressure regime, Physica B: Condens. Mat. 382, 334 (2006).Google Scholar
  154. 154.
    B. R. Brooks, R. E. Bruccoleri, B. D. Olafson, D. J. States, S. S. Swaminathan, and M. Karplus, CHARMM: a program for macromolecular energy, minimization, and dynamics calculations, J. Comput. Chem. 4, 187187 (1983).Google Scholar
  155. 155.
    D. Bedrov, O. Borodin, B. Hanson, and G. D. Smith, Comment on “ On the accuracy of force fields for predicting the physical properties of dimethylnitramine”, J. Phys. Chem. B 111, 1900 (2007).Google Scholar
  156. 156.
    D. Bedrov, C. Ayyagari, G. D. Smith, T. D. Sewell, R. Menikoff, and J. M. Zaug, Molecular dynamics simulations of HMX crystal polymorphs using a flexible molecule force field, J. Comput. Aid. Mat. Des. 8, 77 (2001).Google Scholar
  157. 157.
    T. D. Sewell, R. Menikoff, D. Bedrov, and G. D. Smith, A molecular dynamics simulation study of elastic properties of HMX, J. Chem. Phys. 119, 7417 (2003).Google Scholar
  158. 158.
    D. Bedrov, G. D. Smith, and T. D. Sewell, Thermal conductivity of liquid octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX) from molecular dynamics simulations, Chem. Phys. Lett. 324, 64 (2000).Google Scholar
  159. 159.
    D. Bedrov, G. D. Smith, and T. D. Sewell, Temperature-dependent shear viscosity coefficient of octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX): A molecular dynamics simulation study, J. Chem. Phys. 112, 7203 (2000).Google Scholar
  160. 160.
    J. K. Dienes, Q. H. Zuo, and J. D. Kershner, Impact initiation of explosives and propellants via statistical crack mechanics, J. Mech. Phys. Solids 54, 1237 (2006).Google Scholar
  161. 161.
    B. E. Clements, E. M. Mas, J. N. Plohr, A. Ionita, and F. L. Addessio, Dynamic Response of PBX-9501 through the β—δ Phase Transition, AIP Conf. Proc. 845, 204 (2006).Google Scholar
  162. 162.
    G. D. Smith, D. Bedrov, O. Byutner, O. Borodin, C. Ayyagari, and T. D. Sewell, A quantum-chemistry-based potential for a poly(ester urethane), J. Phys. Chem. A 107, 7552 (2003).Google Scholar
  163. 163.
    R. H. Gee, S. Roszak, K. Balasubramanian, and L. E. Fried, Ab initio based force field and molecular dynamics simulations of crystalline TATB, J. Chem. Phys. 120, 7059 (2004).Google Scholar
  164. 164.
    R. Podeszwa, R. Bukowski, B. M. Rice, and K. Szalewicz, Potential energy surface for cyclotrimethylene trinitramine dimer from symmetry-adapted perturbation theory, Phys. Chem. Chem. Phys. 9, 5561 (2007).Google Scholar
  165. 165.
    C. Møller and M. S. Plesset, Note on an Approximation Treatment for Many-Electron Systems, Phys Rev. 46, 618 (1934).Google Scholar
  166. 166.
    W. J. Hehre, L. Radom, P. v. R. Schleyer, and J. A. Pople, Ab initio Molecular Orbital Theory (Wiley, New York, 1986).Google Scholar
  167. 167.
    T. D. Sewell and D. Bedrov, Elastic properties of 1,3,5-triamino-2,4,6-trinitrobenzene (TATB), (to be submitted to J. Chem. Phys., September 2008).Google Scholar
  168. 168.
    M. Pospíšil, P. Capková, P. Vavrá, and S. Zeman, Classical molecular dynamics simulations of RDX decomposition under high pressure, New Trends in Research of Energetic Materials, Proceedings of the 6th Seminar (Pardubice, Czech Republic, 2003).Google Scholar
  169. 169.
    L. Qiu, H. M. Xiao, W. H. Zhu, J. J. Xiao, and W. Zhu, Ab initio and molecular dynamics studies of crystalline TNAD (trans-1,4,5,8-tetranitro-1,4,5,8-tetraazadecalin), J. Phys. Chem. B 110, 10651 (2006).Google Scholar
  170. 170.
    X. J. Xu, H. M. Xiao, J. J. Xiao, W. Zhu, H. Huang, and J. S. Li, Molecular dynamics simulations for pure epsilon-CL-20 and epsilon-CL-20-based PBXs, J. Phys. Chem. B 110, 7203 (2006).Google Scholar
  171. 171.
    X. F. Ma, J. J. Xiao, H. Huang, X. H. Ju, J. S. Li, and H. M. Xiao, Simulative calculation of mechanical property, binding energy and detonation property of TATB/fluorine-polymer PBX, Chinese J. Chem. 24, 473 (2006).Google Scholar
  172. 172.
    K. Yin, H. Xiao, J. Zhong, and D. Xu, A new method for Calculation of Elastic Properties of Anisotropic material by constant pressure molecular dynamics. Lecture Series on Computer and Computational Sciences 1. (Brill Academic Publishers, Amsterdam, 2004) p. 586.Google Scholar
  173. 173.
    L. Qiu, W. H. Zhu, J. J. Xiao, W. Zhu, H. M. Xiao, H. Huang, and J. S. Li, Molecular dynamics simulations of trans-1,4,5,8-tetranitro-1,4,5,8-tetraazadecalin-based polymer-bonded explosives, J. Phys. Chem. B 111, 1559 (2007).Google Scholar
  174. 174.
    A. T. Hagler, E. Huler, and S. Lifson, Energy functions for peptides and proteins.1. Derivation of a consistent force-field including hydrogen-bond from amide crystals, J. Am. Chem. Soc. 96, 5319 (1974).Google Scholar
  175. 175.
    H. Sun, COMPASS: An ab initio force-field optimized for condensed-phase applications -Overview with details on alkane and benzene compounds, J. Phys. Chem. B 102, 7338 (1998).Google Scholar
  176. 176.
    R. H. Gee, A. Maiti, S. Bastea, and L. E. Fried, Molecular dynamics investigation of adhesion between TATB surfaces and amorphous fluoropolymers, .Macromolecules 40, 3422 (2007).Google Scholar
  177. 177.
    P. B. Balbuena and J. M. Seminario (Eds.), Molecular Dynamics (Theoretical and Computational Chemistry) (Elsevier Science, Amsterdam, 1999).Google Scholar
  178. 178.
    D. Marx and J. Hutter, Ab initio molecular dynamics: Theory and Implementation, J. Grotendorst J (Editor) Modern Methods and Algorithms of Quantum Chemistry (John von Neumann Institute for Computing, Jülich, 2000) NIC Series 1, 301.Google Scholar
  179. 179.
    M. E. Tuckerman and M. L. Klein ML, Ab initio molecular dynamics study of solid nitromethane, Chem. Phys. Lett. 283, 147 (1998).Google Scholar
  180. 180.
    T. Megyes, S. Bálint, T. Grósz, T. Radnai, I. Bakó, and L. Almásy, Structure of liquid nitromethane: Comparison of simulation and diffraction studies, J. Chem. Phys. 126, 164507 (2007).Google Scholar
  181. 181.
    E. J. Reed, J. D. Joannopoulos, and L. E. Fried, Electronic excitations in shocked nitromethane, Phys. Rev. B 62, 16500 (2000).Google Scholar
  182. 182.
    M. R. Manaa, L. E. Fried, C. F. Melius, M. Elstner, and T. Frauenheim, Decomposition of HMX at extreme conditions: A molecular dynamics simulation, J. Phys. Chem. A 106, 9024 (2002).Google Scholar
  183. 183.
    M. R. Manaa, E. J. Reed, L. E. Fried, G. Galli, and F. Gygi, Early chemistry in hot and dense nitromethane: Molecular dynamics simulations, J. Chem. Phys. 120, 10146 (2004).Google Scholar
  184. 184.
    S. A. Decker, T. K. Woo, D. Wei, and F. Zhang, Ab initio molecular dynamics simulations of multimolecular collisions of nitromethane and compressed liquid nitromethane, Proc. 12th Symp. (Intl.) on Detonation (San Diego, California, 2002) p. 724.Google Scholar
  185. 185.
    R. Car and M. Parrinello, Unified approach for molecular-dynamics and density-functional theory, Phys. Rev. Lett. 55, 2471 (1985).Google Scholar
  186. 186.
    M. Kamiya, T. Tsuneda, and K. Hirao, A density functional study of van der Waals interactions, J. Chem. Phys. 117, 6010 (2002).Google Scholar
  187. 187.
    R. Baer and D. Neuhauser, Density functional theory with correct long-range asymptotic behavior, Phys. Rev. Lett. 94, 043002 (2005).Google Scholar
  188. 188.
    T. Sato, T. Tsuneda, and K. Hirao, van der Waals interactions studied by density functional theory, Mol. Phys. 103, 1151 (2005).Google Scholar
  189. 189.
    H. Iikura, T. Tsuneda, T. Yanai, and K. Hirao, A long-range correction scheme for generalized-gradient-approximation exchange functionals, J. Chem. Phys. 115, 3540 (2001).Google Scholar
  190. 190.
    R. W. Williams and D. Malhotra, van der Waals corrections to density functional theory calculations: Methane, ethane, ethylene, benzene, formaldehyde, ammonia, water, PBE, and CPMD, Chem. Phys. 327, 54 (2006).Google Scholar
  191. 191.
    F. Ortmann, F. Bechstedt, and W. G. Schmidt, Semiempirical van der Waals correction to the density functional description of solids and molecular structures, Phys. Rev. B 73, 205101 (2006).Google Scholar
  192. 192.
    J. G. Angyan, I. C. Gerber, A. Savin, and J. Toulouse, van der Waals forces in density functional theory: Perturbational long-range electron-interaction corrections, Phys. Rev. A 72, 012510 (2005).Google Scholar
  193. 193.
    M. A. Neumann and M. A. Perrin, Energy ranking of molecular crystals using density functional theory calculations and an empirical van der Waals correction, J. Phys. Chem. B 109, 15531 (2005).Google Scholar
  194. 194.
    J. Kleis and E. Schroder, van der Waals interaction of simple, parallel polymers, J. Chem. Phys. 122, 164902 (2005).Google Scholar
  195. 195.
    S. Grimme, Accurate description of van der Waals complexes by density functional theory including empirical corrections, J. Comp. Chem. 25, 1463 (2004).Google Scholar
  196. 196.
    Q. Wu and W. T. Yang, Empirical correction to density functional theory for van der Waals interactions, J. Chem. Phys. 116, 515 (2002).Google Scholar
  197. 197.
    T. Sato, T. Tsuneda, and K. Hirao, A density-functional study on pi-aromatic interaction: Benzene dimer and naphthalene dimer, J. Chem. Phys. 123, 104307 (2005).Google Scholar
  198. 198.
    H. Rydberg, M. Dion, N. Jacobson, E. Schroder, P. Hyldgaard, S. I. Simak, D. C. Langreth, and B. I. Lundqvist, van der Waals density functional for layered structures, Phys. Rev. Lett. 91, 126402 (2003).Google Scholar
  199. 199.
    H. Rydberg, B. I. Lundqvist, D. C. Langreth, and M. Dion, Tractable nonlocal correlation density functionals for flat surfaces and slabs, Phys. Rev. B 62, 6997 (2000).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Betsy M. Rice
    • 1
  • Thomas D. Sewell
    • 2
  1. 1.U. S. Army Research LaboratoryAberdeen Proving GroundUSA
  2. 2.Department of ChemistryUniversity of Missouri-ColumbiaColumbiaUSA

Personalised recommendations