Ab Initio Molecular Dynamics Studies of Fast Ion Conductors

  • Zhuoying Zhu
  • Zhi Deng
  • Iek-Heng Chu
  • Balachandran Radhakrishnan
  • Shyue Ping Ong


Ab initio molecular dynamics (AIMD) is emerging as a computational technique of choice in the study of the kinetics of materials, especially fast ionic conductors that are of immense interest to energy storage and other application. In this chapter, we will first provide an introduction of the theoretical underpinnings of AIMD, including both the Car-Parrinello and Born-Oppenheimer variants and the analysis of such simulations for diffusion properties. As for defects that are frequently introduced via aliovalent doping and are crucial for tuning the ionic conductivity in the conductors, we will briefly discuss the first principles techniques that allow us to measure the dopability of materials. Finally, we will review several application-driven examples, such as electrolytes for solid oxide fuel cells and rechargeable alkali-ion batteries, wherein AIMD techniques have provided useful insights for materials design.


  1. 1.
    Minh, N.Q.: Ceramic fuel cells. J. Am. Ceram. Soc. 76, 563–588 (1993)CrossRefGoogle Scholar
  2. 2.
    Rhodes, W.: Agglomerate and particle size effects on sintering yttria-stabilized zirconia. J. Am. Ceram. Soc. 64, 19–22 (1981)CrossRefGoogle Scholar
  3. 3.
    Logothetis, E.M.: ZrO2 oxygen sensors in automotive applications. ‘Science and Technology of Zirconia’. In: Proceedings of the 1st International Conference Held at Cleveland. Advances in Ceramics, p. 388 (1980)Google Scholar
  4. 4.
    Singhal, S.C.: Advances in solid oxide fuel cell technology. Solid State Ionics 135, 305–313 (2000)CrossRefGoogle Scholar
  5. 5.
    Deng, Z., Mo, Y., Ong, S.P.: Computational studies of solid-state alkali conduction in rechargeable alkali-ion batteries. NPG Asia Mater. 8, e254 (2016)CrossRefGoogle Scholar
  6. 6.
    Hayashi, A., Noi, K., Sakuda, A., Tatsumisago, M.: Superionic glass-ceramic electrolytes for room-temperature rechargeable sodium batteries. Nat. Commun. 3, 856 (2012)CrossRefGoogle Scholar
  7. 7.
    Knauth, P.: Inorganic solid Li ion conductors: an overview. Solid State Ionics 180, 911–916 (2009)CrossRefGoogle Scholar
  8. 8.
    Bachman, J.C., Muy, S., Grimaud, A., Chang, H.-H., Pour, N., Lux, S.F., Paschos, O., Maglia, F., Lupart, S., Lamp, P., Giordano, L., Shao-Horn, Y.: Inorganic solid-state electrolytes for lithium batteries: mechanisms and properties governing ion conduction. Chem. Rev. 116, 140–162 (2016)CrossRefGoogle Scholar
  9. 9.
    Kamaya, N., Homma, K., Yamakawa, Y., Hirayama, M., Kanno, R., Yonemura, M., Kamiyama, T., Kato, Y., Hama, S., Kawamoto, K., Mitsui, A.: A lithium superionic conductor. Nat. Mater. 10, 682–686 (2011)CrossRefGoogle Scholar
  10. 10.
    Seino, Y., Ota, T., Takada, K., Hayashi, A., Tatsumisago, M.: A sulphide lithium super ion conductor is superior to liquid ion conductors for use in rechargeable batteries. Energy Environ. Sci. 7, 627–631 (2014)CrossRefGoogle Scholar
  11. 11.
    Vineyard, G.H.: Frequency factors and isotope effects in solid state rate processes. J. Phys. Chem. Solids 3, 121–127 (1957)CrossRefGoogle Scholar
  12. 12.
    Jónsson, H., Mills, G., Jacobsen, K.W.: Nudged elastic band method for finding minimum energy paths of transitions. In: Classical and Quantum Dynamics in Condensed Phase Simulations: Proceedings of the International School of Physics. World Scientific Publishing, Singapore (1998)Google Scholar
  13. 13.
    Voter, A.F.: Introduction to the kinetic Monte Carlo method. Radiat. Eff. Solids 235, 1–23 (2007)CrossRefGoogle Scholar
  14. 14.
    Ryckaert, J.P., Ciccotti, G., Berendsen, H.J.C.: Numerical integration of the cartesian equations of motion of a system with constraints: molecular dynamics of n-alkanes. J. Comput. Phys. 23, 327–341 (1977)CrossRefGoogle Scholar
  15. 15.
    Berendsen, H.J.C., Postma, J.P.M., van Gunsteren, W.F., DiNola, A., Haak, J.R.: Molecular dynamics with coupling to an external bath. J. Chem. Phys. 81, 3684–3690 (1984)CrossRefGoogle Scholar
  16. 16.
    Car, R., Parrinello, M.: Unified approach for molecular dynamics and density-functional theory. Phys. Rev. Lett. 55, 2471–2474 (1985)CrossRefGoogle Scholar
  17. 17.
    Chroneos, A., Yildiz, B., Tarancón, A., Parfitt, D., Kilner, J.A.: Oxygen diffusion in solid oxide fuel cell cathode and electrolyte materials: mechanistic insights from atomistic simulations. Energy Environ. Sci. 4, 2774 (2011)CrossRefGoogle Scholar
  18. 18.
    Urban, A., Seo, D.-H., Ceder, G.: Computational understanding of Li-ion batteries. NPJ Comput. Mater. 2, 16002 (2016)CrossRefGoogle Scholar
  19. 19.
    Pedone, A., Malavasi, G., Menziani, M.C., Cormack, A.N., Segre, U.: A new self-consistent empirical interatomic potential model for oxides, silicates, and silicas-based glasses. J. Phys. Chem. B 110, 11780–11795 (2006)CrossRefGoogle Scholar
  20. 20.
    Adams, S., Prasada Rao, R.: Structural requirements for fast lithium ion migration in Li10GeP2S12. J. Mater. Chem. 22, 7687 (2012)CrossRefGoogle Scholar
  21. 21.
    Islam, M.S., Fisher, C.A.J., Islam, S.M., Fisher, C.A.J.: Lithium and sodium battery cathode materials: computational insights into voltage, diffusion and nanostructural properties. Chem. Soc. Rev. 43, 185–204 (2014)CrossRefGoogle Scholar
  22. 22.
    Hutter, J.: Car-Parrinello molecular dynamics. Wiley Interdiscip. Rev. Comput. Mol. Sci. 2, 604–612 (2012)CrossRefGoogle Scholar
  23. 23.
    Gibson, D.A., Ionova, I.V., Carter, E.A.: A comparison of Car-Parrinello and Born-Oppenheimer generalized valence bond molecular dynamics. Chem. Phys. Lett. 240, 261–267 (1995)CrossRefGoogle Scholar
  24. 24.
    Wentzcovitch, R.M., Martins, J.L.: First principles molecular dynamics of Li: test of a new algorithm. Solid State Commun. 78, 831–834 (1991)CrossRefGoogle Scholar
  25. 25.
    Barnett, R.N., Landman, U.: Born-Oppenheimer molecular-dynamics simulations of finite systems: structure and dynamics of (H˙2O)˙2. Phys. Rev. B 48, 2081 (1993)CrossRefGoogle Scholar
  26. 26.
    Marx, D., Hutter, J.: Ab Initio Molecular Dynamics: Basic Theory and Advanced Methods. Cambridge University Press, Cambridge (2009)CrossRefGoogle Scholar
  27. 27.
    Murch, G.: The haven ratio in fast ionic conductors. Solid State Ionics 7, 177–198 (1982)CrossRefGoogle Scholar
  28. 28.
    Bron, P., Johansson, S., Zick, K., auf der Günne, J.S., Dehnen, S.S., Roling, B.: Li10SnP2S12 – an affordable lithium superionic conductor Li10SnP2S12 – an affordable lithium superionic conductor. J. Am. Chem. Soc. 135, 15694–15697 (2013)Google Scholar
  29. 29.
    Morgan, B.J., Madden, P.A.: Relationships between atomic diffusion mechanisms and ensemble transport coefficients in crystalline polymorphs. Phys. Rev. Lett. 112, 145901 (2014)CrossRefGoogle Scholar
  30. 30.
    Zhu, Z., Chu, I.-H., Deng, Z., Ong, S.P.: Role of Na+ interstitials and dopants in enhancing the Na+ conductivity of the cubic Na3PS4 superionic conductor. Chem. Mater. 27, 8318–8325 (2015)CrossRefGoogle Scholar
  31. 31.
    Richards, W.D., Tsujimura, T., Miara, L., Wang, Y., Kim, J.C., Ong, S.P., Uechi, I., Suzuki, N., Ceder, G.: Design and synthesis of the superionic conductor Na10SnP2S12. Nat. Commun. 7, 1–8 (2016)CrossRefGoogle Scholar
  32. 32.
    Wang, Y., Richards, W.D., Ong, S.P., Miara, L.J., Kim, J.C., Mo, Y., Ceder, G.: Design principles for solid-state lithium superionic conductors. Nat. Mater. 14, 1026–1031 (2015)CrossRefGoogle Scholar
  33. 33.
    Nosé, S.: A unified formulation of the constant temperature molecular dynamics methods. J. Chem. Phys. 81, 511 (1984)CrossRefGoogle Scholar
  34. 34.
    Hoover, W.G.: Canonical dynamics: equilibrium phase-space distributions. Phys. Rev. A 31, 1695–1697 (1985)CrossRefGoogle Scholar
  35. 35.
    Tanibata, N., Noi, K., Hayashi, A., Kitamura, N., Idemoto, Y., Tatsumisago, M.: X-ray crystal structure analysis of sodium-ion conductivity in 94Na3PS4•6Na4SiS4 glass-ceramic electrolytes. ChemElectroChem 1, 1130–1132 (2014)CrossRefGoogle Scholar
  36. 36.
    Tanibata, N., Noi, K., Hayashi, A., Tatsumisago, M.: Preparation and characterization of highly sodium ion conducting Na3PS4-Na4SiS4 solid electrolytes. RSC Adv. 4, 17120 (2014)CrossRefGoogle Scholar
  37. 37.
    Kato, Y., Hori, S., Saito, T., Suzuki, K., Hirayama, M., Mitsui, A., Yonemura, M., Iba, H., Kanno, R.: High-power all-solid-state batteries using sulfide superionic conductors. Nat. Energy 1, 16030 (2016)CrossRefGoogle Scholar
  38. 38.
    Ishihara, T., Matsuda, H., Takita, Y.: Doped LaGaO3 perovskite type oxide as a new oxide ionic conductor. J. Am. Chem. Soc. 116, 3801–3803 (1994)CrossRefGoogle Scholar
  39. 39.
    Bo, S.H., Wang, Y., Kim, J.C., Richards, W.D., Ceder, G.: Computational and experimental investigations of Na-ion conduction in cubic Na3PSe4. Chem. Mater. 28, 252–258 (2016)CrossRefGoogle Scholar
  40. 40.
    Zhang, Y., Zhao, Y., Chen, C.: Ab initio study of the stabilities of and mechanism of superionic transport in lithium-rich antiperovskites. Phys. Rev. B 87, 134303 (2013)CrossRefGoogle Scholar
  41. 41.
    Deng, Z., Radhakrishnan, B., Ong, S.P.: Rational composition optimization of the lithium-rich Li˙3OCl˙1 − xBr˙x anti-perovskite superionic conductors. Chem. Mater. 27, 3749–3755 (2015)CrossRefGoogle Scholar
  42. 42.
    Murugan, R., Thangadurai, V., Weppner, W.: Fast lithium ion conduction in garnet-type Li7La3Zr2O12. Angew. Chem. Int. Ed. 46, 7778–7781 (2007)CrossRefGoogle Scholar
  43. 43.
    Allen, J.L., Wolfenstine, J., Rangasamy, E., Sakamoto, J.: Effect of substitution (Ta, Al, Ga) on the conductivity of Li7La3Zr2O12. J. Power Sources 206, 315–319 (2012)CrossRefGoogle Scholar
  44. 44.
    Kuhn, A., Gerbig, O., Zhu, C., Falkenberg, F., Maier, J., Lotsch, B.V.: A new ultrafast superionic Li-conductor: ion dynamics in Li11Si2PS12 and comparison with other tetragonal LGPS-type electrolytes. Phys. Chem. Chem. Phys. 16, 14669–14674 (2014)CrossRefGoogle Scholar
  45. 45.
    Zhou, P., Wang, J., Cheng, F., Li, F., Chen, J.: A solid lithium superionic conductor Li11AlP2S12 with thio-LISICON analogous structure. Chem. Commun. 52, 6091–6094 (2016)CrossRefGoogle Scholar
  46. 46.
    Wei, S.-H., Zhang, S.: Chemical trends of defect formation and doping limit in II–VI semiconductors: the case of CdTe. Phys. Rev. B 66, 1–10 (2002)Google Scholar
  47. 47.
    Mellander, B.-E.: Electrical conductivity and activation volume of the solid electrolyte phase a-AgI and the high-pressure phase fcc AgI. Phys. Rev. B 26, 5886 (1982)CrossRefGoogle Scholar
  48. 48.
    Kvist, A., Josefson, A.-M.: The electrical conductivity of solid and molten silver iodide. Zeitschriftfir Naturforschung 23, 625 (1968)Google Scholar
  49. 49.
    Funke, K.: AgI-type solid electrolytes. Prog. Solid State Chem. 11, 345–402 (1976)CrossRefGoogle Scholar
  50. 50.
    Kawakita, Y., Enosaki, T., Takeda, S., Maruyama, K.: Structural study of molten Ag halides and molten AgCl–AgI mixture. J. Non-Cryst. Solids 353, 3035–3039 (2007)CrossRefGoogle Scholar
  51. 51.
    Shimojo, F., Aniya, M., Hoshino, K.: Anomalous cation-cation interactions in molten CuI: Ab initio molecular-dynamics simulations. J. Phys. Soc. Jpn. 73, 2148–2153 (2004)CrossRefGoogle Scholar
  52. 52.
    Mohn E.C., Stolen, S., Hull, S.: Diffusion within α-CuI studied using ab initio molecular dynamics simulations. J. Phys. Condens. Matter 21, 335403 (2009)CrossRefGoogle Scholar
  53. 53.
    Shimojo, F., Inoue, T., Aniya, M., Sugahara, T., Miyata, Y.: Ab initio molecular-dynamics study of static structure and bonding properties of molten AgI. J. Phys. Soc. Jpn. 75, 1–7 (2006)CrossRefGoogle Scholar
  54. 54.
    Wood, B.C., Marzari, N.: Dynamical structure, bonding, and thermodynamics of the superionic sublattice in α-AgI. Phys. Rev. Lett. 97, 1–4 (2006)CrossRefGoogle Scholar
  55. 55.
    Sun, S.-R., Xia, D.-G.: An ab-initio calculation study on the super ionic conductors α-AgI and Ag2X (X = S, Se) with BCC structure. Solid State Ionics 179, 2330–2334 (2008)CrossRefGoogle Scholar
  56. 56.
    Steele, B.C., Heinzel, A.: Materials for fuel-cell technologies. Nature 414, 345–352 (2001)CrossRefGoogle Scholar
  57. 57.
    Lacorre, P., Goutenoire, F., Bohnke, O., Retoux, R., Laligant, Y.: Designing fast oxide-ion conductors based on La2Mo2O9. Nature 404, 856–858 (2000)CrossRefGoogle Scholar
  58. 58.
    Wachsman, E.D., Lee, K.T.: Lowering the temperature of solid oxide fuel cells. Science 334, 935–939 (2011)CrossRefGoogle Scholar
  59. 59.
    Goodenough, J.B.: Ceramic technology: oxide-ion conductors by design. Nature 404, 821–823 (2000)CrossRefGoogle Scholar
  60. 60.
    Zhu, B., Li, S., Mellander, B.E.: Theoretical approach on ceria-based two-phase electrolytes for low temperature (300–600 C) solid oxide fuel cells. Electrochem. Commun. 10, 302–305 (2008)Google Scholar
  61. 61.
    Mogensen, M., Lindegard, T., Hansen, U.R.: Physical properties of mixed conductor solid oxide fuel cell anodes of doped CeO2. J. Electrochem. Soc. 141, 2122–2128 (1994)CrossRefGoogle Scholar
  62. 62.
    Huang, K., Wan, J.-H., Goodenough, J.B.: Increasing power density of LSGM-based solid oxide fuel cells using new anode materials. J. Electrochem. Soc. 148, A788 (2001)CrossRefGoogle Scholar
  63. 63.
    Ishihara, T., Tabuchi, J., Ishikawa, S., Yan, J., Enoki, M., Matsumoto, H.: Recent progress in LaGaO3 based solid electrolyte for intermediate temperature SOFCs. Solid State Ionics 177, 1949–1953 (2006)CrossRefGoogle Scholar
  64. 64.
    Chaopradith, D.T., Scanlon, D.O., Catlow, C.R.A.: Adsorption of water on yttria-stabilized zirconia. J. Phys. Chem. C 119, 22526–22533 (2015)CrossRefGoogle Scholar
  65. 65.
    An, W., Turner, C.H.: One-dimensional Ni-based nanostructures and their application as solid oxide fuel cell anodes: a DFT investigation. 117, 1315–1322 (2013)Google Scholar
  66. 66.
    Pietrucci, F., Bernasconi, M., Laio, A., Parrinello, M.: Vacancy-vacancy interaction and oxygen diffusion in stabilized cubic ZrO2 from first principles. Phys. Rev. B Condens. Matter Mater. Phys. 78, 1–7 (2008)Google Scholar
  67. 67.
    He, X., Mo, Y.: Accelerated materials design of Na˙0. 5Bi˙0. 5TiO˙3 oxygen ionic conductors based on first principles calculations. Phys. Chem. Chem. Phys. 17, 18035–18044 (2015)Google Scholar
  68. 68.
    Li, M., Pietrowski, M.J., De Souza, R.A., Zhang, H., Reaney, I.M., Cook, S.N., Kilner, J.A., Sinclair, D.C.: A family of oxide ion conductors based on the ferroelectric perovskite Na˙0. 5Bi˙0. 5TiO3. Nat. Mater. 13, 31–5 (2014)Google Scholar
  69. 69.
    Haavik, C., Ottesen, E.M., Nomura, K., Kilner, J.A., Norby, T.: Temperature dependence of oxygen ion transport in Sr+Mg-substituted LaGaO3 (LSGM) with varying grain sizes. Solid State Ionics 174, 233–243 (2004)CrossRefGoogle Scholar
  70. 70.
    Jung, D.W., Duncan, K.L., Wachsman, E.D.: Effect of total dopant concentration and dopant ratio on conductivity of (DyO˙1. 5)˙x−(WO˙3)˙y−(BiO˙1. 5)˙1 − xy. Acta Mater. 58, 355–363 (2010)Google Scholar
  71. 71.
    Thangadurai, V., Kaack, H., Weppner, W.J.F.: Novel fast lithium ion conduction in garnet-type Li5La3M2O12 (M: Nb, Ta). ChemInform 34, 437–440 (2003)Google Scholar
  72. 72.
    Ong, S.P., Mo, Y., Richards, W.D., Miara, L., Lee, H.S., Ceder, G.: Phase stability, electrochemical stability and ionic conductivity of the Li10±1MP2X12 (M = Ge, Si, Sn, Al or P, and X = O, S or Se) family of superionic conductors. Energy Environ. Sci. 6, 148–156 (2013)CrossRefGoogle Scholar
  73. 73.
    Chu, I.-H., Nguyen, H., Hy, S., Lin, Y.-C., Wang, Z., Xu, Z., Deng, Z., Meng, Y.S., Ong, S.P.: Insights into the performance limits of the Li7P3S11 superionic conductor: a combined first-principles and experimental study. ACS Appl. Mater. Interfaces 8, 7843–7853 (2016)CrossRefGoogle Scholar
  74. 74.
    Bernstein, N., Johannes, M., Hoang, K.: Origin of the structural phase transition in Li7La3Zr2O12. Phys. Rev. Lett. 109, 205702 (2012)CrossRefGoogle Scholar
  75. 75.
    Jalem, R., Yamamoto, Y., Shiiba, H., Nakayama, M., Munakata, H., Kasuga, T., Kanamura, K.: Concerted migration mechanism in the Li ion dynamics of garnet-type Li7La3Zr2O12. Chem. Mater. 25, 425–430 (2013)CrossRefGoogle Scholar
  76. 76.
    Mo, Y., Ong, S.P., Ceder, G.: First principles study of the Li10GeP2S12 lithium super ionic conductor material. Chem. Mater. 24, 15–17 (2012)CrossRefGoogle Scholar
  77. 77.
    Radhakrishnan, B., Ong, S.P.: Aqueous stability of alkali superionic conductors from first principles calculations. Front. Energy Res. 4, 1–12 (2016)CrossRefGoogle Scholar
  78. 78.
    Richards, W.D., Miara, L.J., Wang, Y., Kim, J.C., Ceder, G.: Interface stability in solid-state batteries. Chem. Mater. 28, 266–273 (2015)CrossRefGoogle Scholar
  79. 79.
    Zhu, Y., He, X., Mo, Y.: Origin of outstanding stability in the lithium solid electrolyte materials: insights from thermodynamic analyses based on first principles calculations. ACS Appl. Mater. Interfaces 7, 23685–23693 (2015)CrossRefGoogle Scholar
  80. 80.
    Zhu, Y., He, X., Mo, Y.: First principles study on electrochemical and chemical stability of the solid electrolyte-electrode interfaces in all-solid-state Li-ion batteries. J. Mater. Chem. A 4, 1–14 (2015)Google Scholar
  81. 81.
    Goodenough, J., Hong, H.-P., Kafalas, J.: Fast Na+-ion transport in skeleton structures. Mater. Res. Bull. 11, 203–220 (1976)CrossRefGoogle Scholar
  82. 82.
    Inaguma, Y., Liquan, C., Itoh, M., Nakamura, T.: High ionic conductivity in lithium lanthanum titanate. Solid State Commun. 86, 689–693 (1993)CrossRefGoogle Scholar
  83. 83.
    Deviannapoorani, C., Dhivya, L., Ramakumar, S., Murugan, R.: Lithium ion transport properties of high conductive tellurium substituted Li7La3Zr2O12 cubic lithium garnets. J. Power Sources 240, 18–25 (2013)CrossRefGoogle Scholar
  84. 84.
    Awaka, J., Kijima, N., Hayakawa, H., Akimoto, J.: Synthesis and structure analysis of tetragonal Li7La3Zr2O12 with the garnet-related type structure. J. Solid State Chem. 182, 2046–2052 (2009)CrossRefGoogle Scholar
  85. 85.
    Meier, K., Laino, T., Curioni, A.: Solid-state electrolytes: revealing the mechanisms of Li-Ion conduction in tetragonal and cubic LLZO by first-principles calculations. J. Phys. Chem. C 118, 6668–6679 (2014)CrossRefGoogle Scholar
  86. 86.
    Rangasamy, E., Wolfenstine, J., Sakamoto, J.: The role of Al and Li concentration on the formation of cubic garnet solid electrolyte of nominal composition Li7La3Zr2O12. Solid State Ionics 206, 28–32 (2012)CrossRefGoogle Scholar
  87. 87.
    Geiger, C.A., Alekseev, E., Lazic, B., Fisch, M., Armbruster, T., Langner, R., Fechtelkord, M., Kim, N., Pettke, T., Weppner, W.: Crystal chemistry and sability of “Li7La3Zr2O12” garnet: a fast lithium-ion conductor. Inorg. Chem. 50, 1089–1097 (2011)CrossRefGoogle Scholar
  88. 88.
    Miara, L.J., Ong, S.P., Mo, Y., Richards, W.D., Park, Y., Lee, J.-M., Lee, H.S., Ceder, G.: Effect of Rb and Ta doping on the ionic conductivity and stability of the garnet Li˙7 + 2xy(La˙3 − xRb˙x)(Zr˙2 − yTa˙y)O˙12 (0 ≤ x ≤ 0.375, 0 ≤ y ≤ 1) superionic conductor: a first principles investigation. Chem. Mater. 25, 3048–3055 (2013)Google Scholar
  89. 89.
    Zhu, Z., Chu, I.-H., Ong, S.P.: Li3Y(PS4)2 and Li5PS4Cl2: new lithium superionic conductors predicted from silver thiophosphates using efficiently tiered Ab initio molecular dynamics simulations. Chem. Mater. 29, 2474–2484 (2017)CrossRefGoogle Scholar
  90. 90.
    Deng, Z., Zhu, Z., Chu, I.-H., Ong, S.P.: Data-driven first-principles methods for the study and design of alkali superionic conductors. Chem. Mater. 29, 281–288 (2017)CrossRefGoogle Scholar
  91. 91.
    Sankey, O.F., Niklewski, D.J.: Ab initio multicenter tight-binding model for molecular-dynamics simulations and other applications in covalent systems. Phys. Rev. B 40, 3979–3995 (1989)CrossRefGoogle Scholar
  92. 92.
    Field, M.J., Bash, P.A., Karplus, M.: A combined quantum mechanical and molecular mechanical potential for molecular dynamics simulations. J. Comp. Chem. 11, 700–733 (1990)CrossRefGoogle Scholar
  93. 93.
    Woo, T.K., Margl, P.M., Blöchl, P.E., Ziegler, T.: A combined car-parrinello QM/MM implementation for ab initio molecular dynamics simulations of extended systems: application to transition metal catalysis. J. Phys. Chem. B 101, 7877–7880 (1997)CrossRefGoogle Scholar
  94. 94.
    Marx, D., Parrinello, M.: Ab initio path integral molecular dynamics: basic ideas. J. Chem. Phys. 104, 4077 (1996)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Zhuoying Zhu
    • 1
  • Zhi Deng
    • 1
  • Iek-Heng Chu
    • 1
  • Balachandran Radhakrishnan
    • 1
  • Shyue Ping Ong
    • 1
  1. 1.Department of NanoEngineeringUniversity of California San DiegoLa JollaUSA

Personalised recommendations