Computational Methods for the Assignment of Vibrational Modes in Crystalline Materials

Chapter
Part of the Springer Series in Optical Sciences book series (SSOS, volume 171)

Abstract

In this chapter we provide a description of the computational tools used for the calculation of the terahertz absorption spectrum of a crystalline material, with a particular focus on molecular crystals. We explain using examples why it is not correct to use the normal modes of vibration of an isolated molecule to understand the vibrational spectrum of a material in the terahertz range, but that the features in this spectral region are largely related to intermolecular interactions. It is, therefore, necessary to use methods that consider the periodicity of the crystal structure. We describe the two main methods used for the calculation of the vibrational frequencies and their absorption intensities of a crystal: lattice dynamics and molecular dynamics, providing examples showing the benefits and limitations of each method.

References

  1. 1.
    P.F. Bernath, The spectroscopy of water vapour: Experiment, theory and applications. Phys. Chem. Chem. Phys. 4, 1501–1509 (2002)CrossRefGoogle Scholar
  2. 2.
    O. Pirali, N.-T. Van-Oanh, P. Parneix, M. Vervloet, P. Brechignac, Far-infrared spectroscopy of small polycyclic aromatic hydrocarbons. Phys. Chem. Chem. Phys. 8, 3707–3714 (2006)CrossRefGoogle Scholar
  3. 3.
    S.C. Capelli, A. Albinati, S.A. Mason, B.T.M. Willis, Molecular motion in crystalline naphthalene: analysis of multi-temperature X-ray and neutron diffraction data. J. Phys. Chem. A 110(41), 11695–11703 (2006)CrossRefGoogle Scholar
  4. 4.
    I. Harada, T. Shimanouchi, Normal vibrations and intermolecular forces of crystalline benzene and naphthalene. J. Chem. Phys. 44(5), 2016–2028 (1966)ADSCrossRefGoogle Scholar
  5. 5.
    G. Taddei, H. Bonadeo, S. Califano, The calculation of the normal coordinates of molecular crystals using pairwise potential functions. Chem. Phys. Lett. 13(2), 136–139 (1972)ADSCrossRefGoogle Scholar
  6. 6.
    P. Hermet, J.-L. Bantignies, A. Rahmani, J.-L. Sauvajol, M.R. Johnson, F. Serein, Far- and mid-Infrared of crystalline 2,2’-Bithiophene: Ab initio analysis and comparison with infrared response. J. Phys. Chem. A 109(8), 1684–1691 (2005)CrossRefGoogle Scholar
  7. 7.
    G. Wang, J. Shen, Y. Jia, Vibrational spectra of ketamine hydrochloride and 3,4-methylenedioxymethamphetamine in terahertz range. J. Appl. Phys. 102(1), 013106 (2007)ADSCrossRefGoogle Scholar
  8. 8.
    D.G. Allis, P.M. Hakey, T.M. Korter, The solid-state terahertz spectrum of MDMA (Ecstasy)–a unique test for molecular modeling assignments. Chem. Phys. Lett. 463(4–6), 353–356 (2008)ADSCrossRefGoogle Scholar
  9. 9.
    P. Hakey, D. Allis, M. Hudson, T. Korter, Density functional dependence in the theoretical analysis of the terahertz spectrum of the illicit drug MDMA (Ecstasy). IEEE Sens. J. 10(3), 478–484 (2010)CrossRefGoogle Scholar
  10. 10.
    G. Grosso, G.P. Parravicini, Solid State Physics, 1st edn. (Academic Press, New York, 2000)Google Scholar
  11. 11.
    E.W. Kellermann, Theory of the vibrations of the sodium chloride lattice. Philos. Trans. R. Soc. Lond. Ser. A, Math. Phys. Sci. 238(798), 513–548 (1940)Google Scholar
  12. 12.
    G. Raunio, S. Rolandson, Lattice dynamics of NaCl, KCl, RbCl, and RbF. Phys. Rev. B 2(6), 2098–2103 (1970)ADSCrossRefGoogle Scholar
  13. 13.
    M.P. Verma, B. Dayal, Lattice dynamics of MgO. Phys. Status Solidi (B) 19(2), 751–756 (1967)ADSCrossRefGoogle Scholar
  14. 14.
    G. Raunio, L. Almqvist, R. Stedman, Phonon dispersion relations in NaCl. Phys. Rev. 178(3), 1496–1501 (1969)ADSCrossRefGoogle Scholar
  15. 15.
    A.M. Karo, J.R. Hardy, Precise vibrational frequency distributions and the second-order Raman spectrum and specific heat of NaCl. Phys. Rev. 141(2), 696–710 (1966)ADSCrossRefGoogle Scholar
  16. 16.
    U. Schröder, A new model for lattice dynamics (“breathing shell model”). Solid State Commun. 4(7), 347–349 (1966)ADSCrossRefGoogle Scholar
  17. 17.
    W. Dyck, Lattice dynamics of alkali hydrides and euterides with the NaCl type structure. . J. Phys. C: Solid State Phys. 14(29), 4193 (1981)ADSCrossRefGoogle Scholar
  18. 18.
    S. Baroni, P. Giannozzi, A. Testa, Green’s-function approach to linear response in solids. Phys. Rev. Lett. 58(18), 1861–1864 (1987)ADSCrossRefGoogle Scholar
  19. 19.
    A.J. Pertsin, A.I. Kitaigorodskii, in The Atom-Atom Potential Method: Applications to Organic Molecular Solids, vol. 43 (Springer Series in Chemical Physics (Springer, Heidelberg, 1987)Google Scholar
  20. 20.
    D.E. Williams, Nonbonded potential parameters derived from crystalline aromatic hydrocarbons. J. Chem. Phys. 45, 3770–3779 (1966)ADSCrossRefGoogle Scholar
  21. 21.
    S.R. Cox, L.-Y. Hsu, D.E. Williams, Nonbonded potential function models for crystalline oxohydrocarbons. Acta Crystallogr. Sect. A 37(3), 293–301 (1981)ADSCrossRefGoogle Scholar
  22. 22.
    D.E. Williams, S.R. Cox, Nonbonded potentials for azahydrocarbons: the importance of the Coulombic interaction. Acta Crystallogr. Sect. B 40(4), 404–417 (1984)CrossRefGoogle Scholar
  23. 23.
    D.E. Williams, D.J. Houpt, Fluorine nonbonded potential parameters derived from crystalline perfluorocarbons. Acta Crystallogr. Sect. B 42(3), 286–295 (1986)CrossRefGoogle Scholar
  24. 24.
    G.M. Day, S.L. Price, A nonempirical anisotropic atom-atom model potential for chlorobenzene crystals. J. Am. Chem. Soc. 125(52), 16434–16443 (2003)CrossRefGoogle Scholar
  25. 25.
    R. Righini, N. Neto, S. Califano, S. Walmsley, Lattice dynamics of crystalline ammonia and deutero-ammonia. Chem. Phys. 33(3), 345–353 (1978)CrossRefGoogle Scholar
  26. 26.
    S.H. Walmsley, Basic theory of the lattice dynamics of molecular crystals, in Lattice dynamics and Intermolecular Forces. Proceedings of the International School of Physics “Enrico Fermi”, vol. 55. (Academic Press, New York, 1975), p. 82Google Scholar
  27. 27.
    P.D. DeCicco, F.A. Johnson, The quantum theory of lattice dynamics. IV. Proc. R. Soc. Lond. A. Math. Phys. Sci. 310(1500), 111–119 (1969)ADSCrossRefGoogle Scholar
  28. 28.
    P. Hohenberg, W. Kohn, Inhomogeneous electron gas. Phys. Rev. 136(3B), B864–B871 (1964)Google Scholar
  29. 29.
    W. Kohn, L.J. Sham, Self-consistent equations including exchange and correlation effects. Phys. Rev. 140(4A), A1133–A1138 (1965)Google Scholar
  30. 30.
    S.G. Boyd, K.J. Boyd, A computational analysis of the interaction of lattice and intramolecular vibrational modes in crystalline \(\alpha \)-RDX. J. Chem. Phys. 129(13), 134502 (2008)ADSCrossRefGoogle Scholar
  31. 31.
    F. Shimojo, Z. Wu, A. Nakano, R.K. Kalia, P. Vashishta, Density functional study of 1,3,5-trinitro-1,3,5-triazine molecular crystal with van der Waals interactions. J. Chem. Phys. 132(9), 094106 (2010)ADSCrossRefGoogle Scholar
  32. 32.
    S. Grimme, J. Antony, S. Ehrlich, H. Krieg, A consistent and accurate ab initio parametrization of density functional dispersion correction (dft-d) for the 94 elements H-Pu. J. Chem. Phys. 132, 154104 (2010)ADSCrossRefGoogle Scholar
  33. 33.
    B. Delley, An all-electron numerical method for solving the local density functional for polyatomic molecules. J. Chem. Phys. 92, 508–518 (1990)ADSCrossRefGoogle Scholar
  34. 34.
    J.M. Soler, E. Artacho, J.D. Gale, A. García, J. Junquera, P. Ordejón, D. Sánchez-Portal, The SIESTA method for ab initio order-N materials simulation. J. Phys.: Conden. Matter 14(11), 2745 (2002).Google Scholar
  35. 35.
    J. Junquera, O. Paz, D. Sánchez-Portal, E. Artacho, Numerical atomic orbitals for linear-scaling calculations. Phys. Rev. B 64(23), 235111 (2001)ADSCrossRefGoogle Scholar
  36. 36.
    R. Dovesi, R. Orlando, B. Civalleri, C. Roetti, V.R. Saunders, C.M. Zicovich-Wilson, CRYSTAL: a computational tool for the ab initio study of the electronic properties of crystals. Zeitschrift für Kristallographie 220, 571–573 (2005)ADSCrossRefGoogle Scholar
  37. 37.
    S.J. Clark, M.D. Segall, C.J. Pickard, P.J. Hasnip, M.I.J. Probert, K. Refson, M.C. Payne, First principles methods using CASTEP. Zeitschrift für Kristallographie 220, 567–570 (2005)ADSCrossRefGoogle Scholar
  38. 38.
    G. Kresse, J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54(16), 11169–11186 (1996)ADSCrossRefGoogle Scholar
  39. 39.
    G. Taddei, H. Bonadeo, M.P. Marzocchi, S. Califano, Calculation of crystal vibrations of benzene. J. Chem. Phys. 58(3), 966–978 (1973)ADSCrossRefGoogle Scholar
  40. 40.
    G.S. Pawley, A model for the lattice dynamics of naphthalene and anthracene. Phys. Status Solidi (b) 20(1), 347–360 (1967)ADSCrossRefGoogle Scholar
  41. 41.
    R. Li, J.A. Zeitler, D. Tomerini, E.P.J. Parrott, L.F. Gladden, G.M. Day, A study into the effect of subtle structural details and disorder on the terahertz spectrum of crystalline benzoic acid. Phys. Chem. Chem. Phys. 12, 5329–5340 (2010)CrossRefGoogle Scholar
  42. 42.
    I. Harada, T. Shimanouchi, Far-infrared spectra of crystalline benzene at 138K and intermolecular forces. J. Chem. Phys. 46(7), 2708–2714 (1967)ADSCrossRefGoogle Scholar
  43. 43.
    H. Bonadeo, M.P. Marzocchi, E. Castellucci, S. Califano, Raman spectrum of a single crystal of benzene. J. Chem. Phys. 57(10), 4299–4303 (1972)ADSCrossRefGoogle Scholar
  44. 44.
    D.E. Williams, Nonbonded potential parameters derived from crystalline hydrocarbons. J. Chem. Phys. 47, 4680–4684 (1967)ADSCrossRefGoogle Scholar
  45. 45.
    M. Majoube, G. Vergoten, Lattice vibrations of crystalline imidazole and 15N and D substituted analogs. J. Chem. Phys. 76(6), 2838–2847 (1982)ADSCrossRefGoogle Scholar
  46. 46.
    C. Perchard, A. Novak, Far-infrared spectra and hydrogen-bond frequencies of imidazole. J. Chem. Phys. 48(7), 3079–3084 (1968)ADSCrossRefGoogle Scholar
  47. 47.
    G. Filippini, A. Gavezzotti, Empirical intermolecular potentials for organic crystals: the ‘6-exp’ approximation revisited. Acta Crystallogr. B49, 868–880 (1993)Google Scholar
  48. 48.
    D.S. Coombes, S.L. Price, D.J. Willock, M. Leslie, Role of electrostatic interactions in determining the crystal structures of polar organic molecules. A distributed multipole study. J. Phys. Chem. 100(18), 7352–7360 (1996)CrossRefGoogle Scholar
  49. 49.
    D.E. Williams, Improved intermolecular force field for crystalline oxohydrocarbons including O-H\(\cdots \)O hydrogen bonding. J. Comput. Chem. 22(1), 1–20 (2001)CrossRefGoogle Scholar
  50. 50.
    D.E. Williams, Improved intermolecular force field for molecules containing H, C, N, and O atoms, with applications to nucleoside and peptide crystals. J. Comput. Chem. 22(11), 1154–1166 (2001)CrossRefGoogle Scholar
  51. 51.
    A.J. Stone, M. Alderton, Distributed multipole analysis: methods and applications. Mol. Phys. 56(5), 1047–1064 (1985)ADSCrossRefGoogle Scholar
  52. 52.
    G.M. Day, S.L. Price, M. Leslie, Atomistic calculations of phonon frequencies and thermodynamic quantities for crystals of rigid organic molecules. J. Phys. Chem. B 107, 10919–10933 (2003)CrossRefGoogle Scholar
  53. 53.
    A.E. Gray, G.M. Day, M. Leslie, S.L. Price, Dynamics in crystals of rigid organic molecules: contrasting the phonon frequencies calculated by molecular dynamics with harmonic lattice dynamics for imidazole and 5-azauracil. Mol. Phys. 102, 1067–1083 (2004)ADSCrossRefGoogle Scholar
  54. 54.
    Z. Gamba, H. Bonadeo, Lattice dynamical calculations on azabenzene crystals: the distributed dipole model. J. Chem. Phys. 75(10), 5059–5066 (1981)ADSCrossRefGoogle Scholar
  55. 55.
    G.M. Day, J.A. Zeitler, W. Jones, T. Rades, P.F. Taday, Understanding the influence of polymorphism on phonon spectra: lattice dynamics calculations and terahertz spectroscopy of carbamazepine. J. Phys. Chem. B 110, 447–456 (2006)CrossRefGoogle Scholar
  56. 56.
    K. Parlinski, J. Lazewski, Y. Kawazoe, Ab initio studies of phonons in MgO by the direct method including LO mode. J. Phys. Chem. Solids 61, 87–90 (2000)Google Scholar
  57. 57.
    P.M. Hakey, D.G. Allis, M.R. Hudson, W. Ouellette, T.M. Korter, Terahertz spectroscopic investigation of S-(+)-ketamine hydrochloride and vibrational assignment by density functional theory. J. Phys. Chem. A 114(12), 4364–4374 (2010)CrossRefGoogle Scholar
  58. 58.
    S. Baroni, S. de Gironcoli, A. Dal Corso, P. Giannozzi, Phonons and related crystal properties from density-functional perturbation theory. Rev. Mod. Phys. 73(2), 515–562 (2001)ADSCrossRefGoogle Scholar
  59. 59.
    Y. Noel, M. Catti, P. D’Arco, R. Dovesi, The vibrational frequencies of forsterite \({Mg}_{2}{SiO}_{4}\): an all-electron ab initio study with the CRYSTAL code. Phys. Chem. Miner. 33, 383–393 (2006)ADSCrossRefGoogle Scholar
  60. 60.
    D.G. Allis, J.A. Zeitler, P.F. Taday, T.M. Korter, Theoretical analysis of the solid-state terahertz spectrum of the high explosive RDX. Chem. Phys. Lett. 463(1–3), 84–89 (2008)ADSCrossRefGoogle Scholar
  61. 61.
    J.A. Ciezak, S.F. Trevino, Inelastic neutron scattering spectrum of cyclotrimethylenetrinitramine: a comparison with solid-state electronic structure calculations. J. Phys. Chem. A 110(15), 5149–5155 (2006)CrossRefGoogle Scholar
  62. 62.
    M.S. Miao, Z.A. Dreger, J.M. Winey, Y.M. Gupta, Density functional theory calculations of pressure effects on the vibrational structure of \(\alpha \)-RDX. J. Phys. Chem. A 112(47), 12228–12234 (2008)CrossRefGoogle Scholar
  63. 63.
    M.D. King, W.D. Buchanan, T.M. Korter, Application of London-type dispersion corrections to the solid-state density functional theory simulation of the terahertz spectra of crystalline pharmaceuticals. Phys. Chem. Chem. Phys. 13, 4250–4259 (2011)CrossRefGoogle Scholar
  64. 64.
    R. Car, M. Parrinello, Unified approach for molecular dynamics and density-functional theory. Phys. Rev. Lett. 55(22), 2471–2474 (1985)ADSCrossRefGoogle Scholar
  65. 65.
    A.M. Reilly, D.S. Middlemiss, M.M. Siddick, D.A. Wann, G.J. Ackland, C.C. Wilson, D.W.H. Rankin, C.A. Morrison, The phonon spectrum of phase-I ammonia: reassignment of lattice mode symmetries from combined molecular and lattice dynamics calculations. J. Phys. Chem. A 112(6), 1322–1329 (2008)CrossRefGoogle Scholar
  66. 66.
    N.L. Allinger, Conformational analysis. 130. MM2. A hydrocarbon force field utilizing V1 and V2 torsional terms. J. Am. Chem. Soc. 99(25), 8127–8134 (1977)CrossRefGoogle Scholar
  67. 67.
    S.O. Jonsdottir, K. Rasmussen, The consistent force field. Part 6: an optimized set of potential energy functions for primary amines. N. J. Chem. 24, 243–247 (2000)Google Scholar
  68. 68.
    A. MacKerel Jr., C. Brooks III, L. Nilsson, B. Roux, Y. Won, M. Karplus, in CHARMM: The Energy Function and Its Parameterization with an Overview of the Program, vol. 1. The Encyclopedia of Computational Chemistry (Wiley, Chichester, 1998), pp. 271–277Google Scholar
  69. 69.
    B. Hess, C. Kutzner, D. van der Spoel, E. Lindahl, Gromacs 4: algorithms for highly efficient, load-balanced, and scalable molecular simulation. J. Chem. Theory Comput. 4(3), 435–447 (2008)CrossRefGoogle Scholar
  70. 70.
    A.K. Rappe, C.J. Casewit, K.S. Colwell, W.A. Goddard, W.M. Skiff, UFF, a full periodic table force field for molecular mechanics and molecular dynamics simulations. J. Am. Chem. Soc. 114(25), 10024–10035 (1992)CrossRefGoogle Scholar
  71. 71.
    B. Qiu, X. Ruan, Molecular dynamics simulations of lattice thermal conductivity of bismuth telluride using two-body interatomic potentials. Phys. Rev. B 80(16), 165203 (2009)ADSCrossRefGoogle Scholar
  72. 72.
    M.M. Siddick, G.J. Ackland, C.A. Morrison, Constrained dynamics and extraction of normal modes from ab initio molecular dynamics: application to ammonia. J. Chem. Phys. 125(6), 064707 (2006)ADSCrossRefGoogle Scholar
  73. 73.
    H. Zhang, E. Zukowski, R. Balu, S.K. Gregurick, A dynamics study of the a-chain of ricin by terahertz vibrational calculation and normal modes analysis. J. Mol. Graph. Model. 27(5), 655–663 (2009)CrossRefGoogle Scholar
  74. 74.
    S. Thirumuruganandham, H. Urbassek, Low-frequency vibrational modes and infrared absorbance of red, blue and green opsin. J. Mol. Model. 15, 959–969 (2009)CrossRefGoogle Scholar
  75. 75.
    A.Y. Zasetsky, A.S. Lileev, A.K. Lyashchenko, Molecular dynamic simulations of terahertz spectra for water-methanol mixtures. Mol. Phys.: Int. J. Interface. Chem. Phys. 108, 649–656 (2010)ADSGoogle Scholar
  76. 76.
    H. Schober, D. Strauch, Investigation of the LO-TO splitting in complex binary crystals. J. Phys.: Conden. Matter 5(34), 6165 (1993)Google Scholar
  77. 77.
    R. Ruppin, R. Englman, Optical phonons of small crystals. Rep. Prog. Phys. 33(1), 149–196 (1970)ADSCrossRefGoogle Scholar
  78. 78.
    E. Balan, A.M. Saitta, F. Mauri, G. Calas, First-principles modeling of the infrared spectrum of kaolinite. Am. Mineral. 86(11–12), 1321–1330 (2001)Google Scholar
  79. 79.
    C.C. Wilson, N. Shankland, A.J. Florence, Direct determination of the temperature dependence of proton transfer in the benzoic acid dimer by single crystal neutron diffraction. Chem. Phys. Lett. 253(1–2), 103–107 (1996)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of ChemistryUniversity of CambridgeCambridgeUK

Personalised recommendations