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Structure and properties of (AlB2)n and (MgB2)n (n = 1, …, 10) clusters

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Abstract

A systematic search for energetically lowest lying structures of neutral (AlB2)n and (MgB2)n clusters with n = 1, …, 10 is performed using density functional theory within a multistep hierarchical algorithm specially adapted for the global optimization of relatively large structures. For obtained clusters, different physical properties (energetic, electrostatic, electronic, and thermodynamic) are determined. The variation of these properties with increasing cluster size is discussed in detail. The bulk values of binding energy, specific zero point energy, ionization potential, electron affinity, collision diameter and formation enthalpy for aluminum and magnesium diborides have been obtained by means of physically sound extrapolation of the calculated data to the particles of infinite size. The temperature-dependent thermodynamic functions of (AlB2)n and (MgB2)n clusters, such as enthalpy, entropy, specific heat capacity, and reduced Gibbs energy, are evaluated with allowance for vibrational anharmonicity and for the existence of excited electronic states. The appropriate data are fitted to seven-parameter NASA (Chemkin) polynomials. The approximations of the reduced Gibbs energy applicable for extrapolation towards large clusters and even small nanoparticles are also elaborated.

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References

  1. J. Nagamatsu, N. Nakagawa, T. Muranaka, Y. Zenitani, J. Akimitsu, Nature 410, 63 (2001)

    Article  ADS  Google Scholar 

  2. N.I. Medvedeva, A.L. Ivanovskii, J.E. Medvedeva, A.J. Freeman, Phys. Rev. B 64, 020502 (2001)

    Article  ADS  Google Scholar 

  3. J. Nakamura, S.Y. Nasubida et al., Phys. Rev. B 68, 064515 (2003)

    Article  ADS  Google Scholar 

  4. V.V. Ivanovskaya, A.N. Enyashin, A.L. Ivanovskii, Inorg. Mater. 40, 134 (2004)

    Article  Google Scholar 

  5. U. Burkhardt, V. Gurin, F. Haarmann, H. Borrmann, W. Schnelle, A. Yaresko, Y. Grin, J. Solid State Chem. 177, 389 (2004)

    Article  ADS  Google Scholar 

  6. G. Severa, E. Rönnebro, C.M. Jensen, Chem. Commun. 46, 421 (2010)

    Article  Google Scholar 

  7. T.R. Galeev, C. Romanescu, W.L. Li, L.S. Wang, A.I. Boldyrev, J. Chem. Phys. 135, 104301 (2011)

    Article  ADS  Google Scholar 

  8. W.L. Li, C. Romanescu, T.R. Galeev, L.S. Wang, A.I. Boldyrev, J. Phys. Chem. A 115, 10391 (2011)

    Article  Google Scholar 

  9. M.J. van Setten, G.A. de Wijs, M. Fichtner, G. Brocks, Chem. Mater. 20, 4952 (2008)

    Article  Google Scholar 

  10. G.L. Soloveichik, Y. Gao, J. Rijssenbeek, M. Andrus, S. Kniajanski, R.C. Bowman Jr, S.J. Hwang, J.C. Zhao, Int. J. Hydrogen Energy 34, 916 (2009)

    Article  Google Scholar 

  11. K.T. Möller, A.S. Fogh, M. Paskevicius, J. Skibsted, T.R.R. Jensen, Phys. Chem. Chem. Phys. 18, 27545 (2016)

    Article  Google Scholar 

  12. M.L. Whittaker, R.A. Cutler, P.E. Anderson, Mater. Res. Soc. Symp. Proc. 1405, Mrsf111405y1102 (2012)

    Article  Google Scholar 

  13. Y. Guo, W. Zhang, X. Zhou, B. Bao, J. Therm. Anal. Calorim. 113, 787 (2013)

    Article  Google Scholar 

  14. M.N. Makhov, Rus. J. Phys. Chem. B 9, 50 (2015)

    Article  Google Scholar 

  15. S. Xu, Y. Chen, X. Chen, D. Wu, D. Liu, Combust. Explos. Shock Waves 52, 342 (2016)

    Article  Google Scholar 

  16. D.A. Yagodnikov, A.V. Voronetskii, V.I. Sarab’ev, Combust. Explos. Shock Waves 52, 300 (2016)

    Article  Google Scholar 

  17. X. Liu, K.L. Chintersingh, M. Schoenitz, E.L. Dreizin, J. Propul. Power 34, 787 (2018)

    Article  Google Scholar 

  18. B.I. Lukhovitskii, A.S. Sharipov, J. Eng. Phys. Thermophys. 91, 766 (2018)

    Article  Google Scholar 

  19. M.A. Korchagin, A.I. Gavrilov, B.B. Bokhonov, N.V. Bulina, V.E. Zarko, Combust. Expl. Shock Waves 54, 424 (2018)

    Article  Google Scholar 

  20. S. Polarz, in Encyclopedia of Nanoscience and Nanotechnology (American Scientific Publishers, 2004), Vol. 6, pp. 179–196

  21. F. Baletto, R. Ferrando, Rev. Mod. Phys. 77, 371 (2005)

    Article  ADS  Google Scholar 

  22. E. Roduner, Chem. Soc. Rev. 35, 583 (2006)

    Article  Google Scholar 

  23. R.S. Berry, B.M. Smirnov, Comput. Theor. Chem. 1021, 2 (2013)

    Article  Google Scholar 

  24. A.W. Castleman Jr S.N. Khanna, J. Phys. Chem. C 113, 2664 (2009)

    Article  Google Scholar 

  25. Z. Wei, W. Jiang, Z. Bai, Z. Lian, Z. Wang, F. Song, Eur. Phys. J. D 71, 237 (2017)

    Article  ADS  Google Scholar 

  26. A. Pinkard, A.M. Champsaur, X. Roy, Acc. Chem. Res. 51, 919 (2018)

    Article  Google Scholar 

  27. E. Roduner, Phys. Chem. Chem. Phys. 20, 23812 (2018)

    Article  Google Scholar 

  28. A.M. Starik, A.S. Sharipov, B.I. Loukhovitski, A.M. Savelév, Phys. Scr. 91, 013004 (2016)

    Article  ADS  Google Scholar 

  29. D. Sundaram, V. Yang, R.A. Yetter, Prog. Energy Combust. Sci. 61, 293 (2017)

    Article  Google Scholar 

  30. S. Zhou, T. Nozaki, X. Pi, J. Phys. D: Appl. Phys 51, 025305 (2017)

    Article  ADS  Google Scholar 

  31. I. Moullet, J.L. Martins, F. Reuse, J. Buttet, Phys. Rev. Lett. 65, 476 (1990)

    Article  ADS  Google Scholar 

  32. S. Neukermans, N. Veldeman, E. Janssens, P. Lievens, Z. Chen, P.v.R. Schleyer, Eur. Phys. J. D 45, 301 (2007)

    Article  ADS  Google Scholar 

  33. X.J. Feng, Y.H. Luo, J. Phys. Chem. A 111, 2420 (2007)

    Article  Google Scholar 

  34. M. Boyukata, Z.B. Guvenc, J. Alloys Compd. 509, 4214 (2011)

    Article  Google Scholar 

  35. X.L. Lei, J. Clust. Sci. 22, 159 (2011)

    Article  Google Scholar 

  36. J.Z. Yu, F.Q. Zhao, S.Y. Xu, X.H. Ju, J. Serb. Chem. Soc. 82, 163 (2017)

    Article  Google Scholar 

  37. B.I. Loukhovitski, A.S. Sharipov, A.M. Starik, Chem. Phys. 493, 61 (2017)

    Article  Google Scholar 

  38. Q.L. Lu, Q.Q. Luo, Chem. Phys. Lett. 710, 26 (2018)

    Article  ADS  Google Scholar 

  39. D. Rodriguez, D. Soto, E. Ramirez, A. Cruz, A. Santana, G.E. Lopez, Res. Lett. Phys. 2008, 879017 (2008)

    Article  Google Scholar 

  40. Y.Y. Wu, F.Q. Zhao, X.H. Ju, Comput. Theor. Chem. 1027, 151 (2014)

    Article  Google Scholar 

  41. Y.Y. Wu, S.Y. Xu, F.Q. Zhao, X.H. Ju, J. Clust. Sci. 26, 983 (2015)

    Article  Google Scholar 

  42. A.C. Reber, S.N. Khanna, J. Chem. Phys. 142, 054304 (2015)

    Article  ADS  Google Scholar 

  43. Y.J. Wang, L.Y. Feng, J.C. Guo, H.J. Zhai, Chem. Asian J. 12, 2899 (2017)

    Article  Google Scholar 

  44. G. Rossi, R. Ferrando, J. Phys.: Condens. Matter 21, 084208 (2009)

    ADS  Google Scholar 

  45. F. Avaltroni, C. Corminboeuf, J. Comput. Chem. 33, 502 (2012)

    Article  Google Scholar 

  46. S. Heiles, R.L. Johnston, Int. J. Quantum Chem. 113, 2091 (2013)

    Article  Google Scholar 

  47. H. Yang, H. Chen, Eur. Phys. J. D 71, 191 (2017)

    Article  ADS  Google Scholar 

  48. B. Hartke, Eur. Phys. J. D 24, 57 (2003)

    Article  ADS  Google Scholar 

  49. S.E. Schönborn, S. Goedecker, S. Roy, A.R. Oganov, J. Chem. Phys. 130, 144108 (2009)

    Article  ADS  Google Scholar 

  50. R.P.F. Kanters, K.J. Donald, J. Chem. Theory Comput. 10, 5729 (2014)

    Article  Google Scholar 

  51. B.I. Loukhovitski, A.S. Sharipov, A.M. Starik, Eur. Phys. J. D 70, 250 (2016)

    Article  ADS  Google Scholar 

  52. R.H. Leary, J. Global Optim. 11, 35 (1997)

    Article  MathSciNet  Google Scholar 

  53. M.J.S. Dewar, E.G. Zoebisch, E.F. Healy, J.J.P. Stewart, J. Am. Chem. Soc. 107, 3902 (1985)

    Article  Google Scholar 

  54. D.N. Laikov, J. Chem. Phys. 135, 134120 (2011)

    Article  ADS  Google Scholar 

  55. D.N. Laikov, Priroda 14, Quantum Chemical Program (Lomonosov Moscow State University, Moscow (Russian Federation), 2014)

  56. S.H. Vosko, L. Wilk, M. Nusair, Can. J. Phys. 58, 1200 (1980)

    Article  ADS  Google Scholar 

  57. P.J. Wilson, T.J. Bradley, D.J. Tozer, J. Chem. Phys. 115, 9233 (2001)

    Article  ADS  Google Scholar 

  58. Y. Tantirungrotechai, K. Phanasant, S. Roddecha, P. Surawatanawong, V. Sutthikhum, J. Limtrakul, J. Mol. Struct. (Theochem.) 760, 189 (2006)

    Article  Google Scholar 

  59. A.A. Granovsky, Firefly V. 8.2.0, https://doi.org/classic.chem.msu.su/gran/firefly/index.html

  60. M.W. Schmidt, K.K. Baldridge, J.A. Boatz, S.T. Elbert, M.S. Gordon, J.H. Jensen, S. Koseki, N. Matsunaga, K.A. Nguyen, S. Su, T.L. Windus, M. Dupuis, J.A. Montgomery, J. Comput. Chem. 14, 1347 (1993)

    Article  Google Scholar 

  61. N.E. Schultz, Y. Zhao, D.G. Truhlar, J. Phys. Chem. A 109, 11127 (2005)

    Article  Google Scholar 

  62. A.S. Sharipov, B.I. Loukhovitski, A.M. Starik, Eur. Phys. J. D 69, 211 (2015)

    Article  ADS  Google Scholar 

  63. L.A. Curtiss, P.C. Redfern, K. Raghavachari, J. Chem. Phys. 127, 124105 (2007)

    Article  ADS  Google Scholar 

  64. C.W. Bauschlicher Jr, S.R. Langhoff, J. Chem. Phys. 101, 80 (1994)

    Article  ADS  Google Scholar 

  65. G.L. Gutsev, P. Jena, R.J. Bartlett, J. Chem. Phys. 110, 2928 (1999)

    Article  ADS  Google Scholar 

  66. E.P.F. Lee, T.G. Wright, J. Phys. Chem. A 108, 7424 (2004)

    Article  Google Scholar 

  67. M. Pelegrini, O. Roberto-Neto, F.B.C. Machado, Int. J. Quantum Chem. 95, 205 (2003)

    Article  Google Scholar 

  68. D. Tzeli, A. Mavridis, J. Phys. Chem. A 109, 10663 (2005)

    Article  Google Scholar 

  69. I.M. Alecu, J. Zheng, Y. Zhao, D.G. Truhlar, J. Chem. Theory Comput. 6, 2872 (2010)

    Article  Google Scholar 

  70. A.S. Sharipov, B.I. Loukhovitski, C.J. Tsai, A.M. Starik, Eur. Phys. J. D 68, 99 (2014)

    Article  ADS  Google Scholar 

  71. G.A. Andrienko, Chemcraft version 1.8, https://doi.org/www.chemcraftprog.com

  72. H.A. Kurtz, J.J. Stewart, K.M. Dieter, J. Comput. Chem. 11, 82 (1990)

    Article  Google Scholar 

  73. M.G. Medvedev, I.S. Bushmarinov, J. Sun, J.P. Perdew, K.A. Lyssenko, Science 355, aah5975 (2017)

    Article  Google Scholar 

  74. D. Hait, M. Head-Gordon, J. Chem. Theory Comput. 14, 1969 (2018)

    Article  Google Scholar 

  75. A.S. Sharipov, B.I. Loukhovitski, A.M. Starik, J. Phys. B: At. Mol. Opt. Phys. 50, 165101 (2017)

    Article  ADS  Google Scholar 

  76. B.I. Loukhovitski, S.A. Torokhov, E.E. Loukhovitskaya, A.S. Sharipov, Struct. Chem. 29, 49 (2018)

    Article  Google Scholar 

  77. A. Aguado, A. Vega, L.C. Balbas, Phys. Rev. B 84, 165450 (2011)

    Article  ADS  Google Scholar 

  78. F. Egidi, T. Giovannini, M. Piccardo, J. Bloino, C. Cappelli, V. Barone, J. Chem. Theory Comput. 10, 2456 (2014)

    Article  Google Scholar 

  79. P. Jaque, A. Toro-Labbe, J. Chem. Phys. 117, 3208 (2002)

    Article  ADS  Google Scholar 

  80. F. Jensen, Introduction to Computational Chemistry, 2nd edn. (John Wiley & Sons, Ltd, 2007)

  81. J.C. Rienstra-Kiracofe, G.S. Tschumper, H.F. Schaefer, S. Nandi, G.B. Ellison, Chem. Rev. 102, 231 (2002)

    Article  Google Scholar 

  82. A.A. Zavitsas, J. Phys. Chem. 91, 5573 (1987)

    Article  Google Scholar 

  83. A. Dreuw, M. Head-Gordon, Chem. Rev. 105, 4009 (2005)

    Article  Google Scholar 

  84. M. Gronowski, Comput. Theor. Chem. 1108, 50 (2017)

    Article  Google Scholar 

  85. W.M.F. Fabian, Monatsh. Chem. 139, 309 (2008)

    Article  Google Scholar 

  86. A. Gany, D.W. Netzer, Int. J. Turbo Jet Eng. 2, 157 (1985)

    ADS  Google Scholar 

  87. D.C. Young, Computational chemistry: A Practical Guide for Applying Techniques to Real-World Problems (John Wiley & Sons, Inc., 2004)

  88. R.L. Johnston, Phil. Trans. R. Soc. Lond. A 356, 211 (1998)

    Article  ADS  Google Scholar 

  89. M.J. van Setten, M. Fichtner, J. Alloys Compd. 477, L11 (2009)

    Article  Google Scholar 

  90. J. Wang, G. Wang, J. Zhao, Phys. Rev. B 66, 035418 (2002)

    Article  ADS  Google Scholar 

  91. B. Assadollahzadeh, S. Schafer, P. Schwerdtfeger, J. Comput. Chem. 31, 929 (2010)

    Google Scholar 

  92. C. Buzea, T. Yamashita, Supercond. Sci. Technol. 14, R115 (2001)

    Article  ADS  Google Scholar 

  93. Z. Xiao-Lin, L. Ke, C. Xiang-Rong, Z. Jun, Chin. Phys. 15, 3014 (2006)

    Article  ADS  Google Scholar 

  94. L.D. Landau, E.M. Lifshitz, Statistical physics Part 1. V. 5: Course of theoretical physics (Pergamon Press, 1968)

  95. B. Farid, R.W. Godby, Phys. Rev. B 43, 14248 (1991)

    Article  ADS  Google Scholar 

  96. W.A. de Heer, Rev. Mod. Phys. 65, 611 (1993)

    Article  ADS  Google Scholar 

  97. S. Heiles, R. Schäfer, Dielectric Properties of Isolated Clusters: Beam Deflection Studies (Springer, Dordrecht, Netherlands, 2014)

  98. S. Schäfer, B. Assadollahzadeh, M. Mehring, P. Schwerdtfeger, R. Schäfer, J. Phys. Chem. A 112, 12312 (2008)

    Article  Google Scholar 

  99. K.D. Bonin, V.V. Kresin, Electric-dipole polarizabilities of atoms, molecules, and clusters (World Scientific, Singapore, 1997)

  100. I.G. Kaplan, Intermolecular Interactions: Physical Picture, Computational Methods and Model Potentials (Wiley, Hoboken, NJ, 2006)

  101. E. Benichou, R. Antoine, D. Rayane, B. Vezin, F.W. Dalby, P. Dugourd, M. Broyer, C. Ristori, F. Chandezon, B.A. Huber, J.C. Rocco, S.A. Blundell, C. Guet, Phys. Rev. A 59, R1 (1999)

    Article  ADS  Google Scholar 

  102. S.A. Blundell, C. Guet, R.R. Zope, Phys. Rev. Lett. 84, 4826 (2000)

    Article  ADS  Google Scholar 

  103. D.R. Snider, R.S. Sorbello, Phys. Rev. B 28, 5702 (1983)

    Article  ADS  Google Scholar 

  104. V.S. Fomenko, Handbook of thermionic properties: electronic work functions and Richardson constants of elements and compounds (Plenum Press Data Division, 1966)

  105. A. Mezzi, P. Soltani, S. Kaciulis, A. Bellucci, M. Girolami, M. Mastellone, D.M. Trucchi, Surf. Interface Anal. 50, 1138 (2018)

    Article  Google Scholar 

  106. L.V. Gurvich, I.V. Veyts, C.B. Alcock, Thermodynamics Properties of Individual Substances (Hemisphere Pub. Co., New York, New York, 1989)

  107. I. Glassman, R.A. Yetter, Combustion, 4th edn. (Elsevier, 2008)

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Sharipov, A.S., Loukhovitski, B.I. Structure and properties of (AlB2)n and (MgB2)n (n = 1, …, 10) clusters. Eur. Phys. J. D 73, 14 (2019). https://doi.org/10.1140/epjd/e2018-90574-y

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