Ultrafast Phenomena in Molecular Sciences pp 145-170

Part of the Springer Series in Chemical Physics book series (CHEMICAL, volume 107)

Ultrafast Laser-Induced Processes Described by Ab Initio Molecular Dynamics

  • Leticia González
  • Philipp Marquetand
  • Martin Richter
  • Jesús González-Vázquez
  • Ignacio Sola

Abstract

This chapter introduces theoretical methods that integrate the equations of motion of electrons and nuclei in molecules, including all degrees of freedom and all types of couplings. We are concerned with methods that treat the electronic motion quantum-mechanically, by expanding the electronic wave function in a relatively small basis of eigenstates of the Hamiltonian, and the nuclear motion classically, as an ensemble of trajectories each unfolding on a single electronic state at a given time, but allowing to switch between states. In particular, we focus on a quite novel method called the SHARC (Surface-Hopping in the Adiabatic Representation including arbitrary Couplings) scheme. The main novelty of SHARC consists in the evaluation of the transition probability between electronic states, which is performed by surface-hopping techniques in the adiabatic representation, essentially treating on the same footing both non-adiabatic beyond Born-Oppenheimer transitions (intersystem crossing, internal conversion) and laser-induced crossings. The choice of approximations and representation is particularly useful in evaluating the dynamics when the laser field or non-adiabatic couplings are strong. In the chapter we show examples of the performance of the scheme in two scenarios. In the first one, the dynamics of the system is simulated starting in the electronic excited state assuming an instantaneous excitation. In the second one, the interaction of the system with an external laser field is explicitly considered. This approach is necessary when deactivation occurs during the laser excitation. Moreover, the explicit consideration of the external field permits the use of quantum control schemes. We consider here two limiting cases, the impulsive and the adiabatic time-evolution, represented by two paradigmatic control schemes, the ultrafast pump-dump control and the APLIP (Adiabatic Passage by Light Induced Potentials) scheme, respectively.

References

  1. 1.
    S.A. Rice, M. Zhao, Optical Control of Molecular Dynamics (Wiley, New York, 2000) Google Scholar
  2. 2.
    M. Shapiro, P. Brumer, Principles of Quantum Control of Molecular Processes (Wiley, New York, 2003) Google Scholar
  3. 3.
    L. Wöste, J. Manz (eds.), Femtosecond Chemistry, Vols. I, II (VCH, Weinheim, 1995) Google Scholar
  4. 4.
    B. Whitaker (ed.), Femtosecond Chemistry, Vols. I, II (Cambridge University Press, Cambridge, 2003) Google Scholar
  5. 5.
    V. Sundström (ed.), Femtochemistry and Femtobiology: Ultrafast Reaction Dynamics at Atomic-Scale Resolution (Imperial College Press, London, 1996) Google Scholar
  6. 6.
    F.C.D. Schryver, S. DeFeyter, G. Schweitzer (eds.), Femtochemistry (Wiley-VCH, Weinheim, 2001) Google Scholar
  7. 7.
    M. Martin, J.T. Hynes (eds.), Femtochemistry and Femtobiology: Ultrafast Events in Molecular Science (Elsevier, Oxford, 2004) Google Scholar
  8. 8.
    A. Douhal, J. Santamaria (eds.), Femtochemistry and Femtobiology (World Scientific, Singapore, 2002) Google Scholar
  9. 9.
    W. Domcke, D.R. Yarkony, H. Köppel (eds.), Conical Intersections: Electronic Structure, Dynamics and Spectroscopy (World Scientific, Singapore, 2004) Google Scholar
  10. 10.
    M. Chergui (ed.), Femtochemistry—Ultrafast Chemical and Physical Processes in Molecular Systems (World Scientific, Singapore, 1996) Google Scholar
  11. 11.
    A.H. Zewail, Femtochemistry, Vols. I, II (World Scientific, Singapore, 1994) Google Scholar
  12. 12.
    A.H. Zewail, Femtochemistry: atomic-scale dynamics of the chemical bond. J. Phys. Chem. 104, 5660–5694 (2000) Google Scholar
  13. 13.
    A. Assion, T. Baumert, M. Bergt, T. Brixner, V. Seyfried, M. Strehle, G. Gerber, Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses. Science 282, 919–922 (1998) Google Scholar
  14. 14.
    C. Daniel, J. Full, L. González, C. Lupulescu, J. Manz, A. Merli, Štefan Vajda, L. Wöste, Deciphering the reaction dynamics underlying optimal control laser fields. Science 299, 536–539 (2003) Google Scholar
  15. 15.
    M. Dantus, Ultrafast four-wave mixing in the gas phase. Annu. Rev. Phys. Chem. 52, 639–679 (2001) Google Scholar
  16. 16.
    I.V. Hertel, W. Radloff, Ultrafast dynamics in isolated molecules and molecular clusters. Rep. Prog. Phys. 69, 1897–2003 (2006) Google Scholar
  17. 17.
    A.D. Bandrauk (ed.), Molecules in Laser Fields (Marcel Dekker, New York, 1994) Google Scholar
  18. 18.
    R.J. Levis, G.M. Menkir, H. Rabitz, Selective bond dissociation and rearrangement with optimally tailored, Strong-field laser pulses. Science 292, 709–713 (2001) Google Scholar
  19. 19.
    B.J. Sussman, D. Townsend, M.Y. Ivanov, A. Stolow, Dynamic Stark control of photochemical processes. Science 314, 278–281 (2006) Google Scholar
  20. 20.
    O. Smirnova, S. Patchkovskii, Y. Mairesse, N. Dudovich, M.Y. Ivanov, Strong-field control and spectroscopy of attosecond electron-hole dynamics in molecules. Proc. Natl. Acad. Sci. USA 106, 16556–16561 (2009) Google Scholar
  21. 21.
    K. Yamanouchi, The next frontier. Science 295, 1659–1660 (2002) Google Scholar
  22. 22.
    L. González, D. Escudero, L. Serrano-Andrés, Progress and challenges in the calculation of electronic excited states. Comput. Phys. Commun. 13, 28–51 (2012) Google Scholar
  23. 23.
    F. Martín, J. Fernández, T. Havermeier, L. Foucar, T. Weber, K. Kreidi, M. Schöffler, L. Schmidt, T. Jahnke, O. Jagutzki, A. Czasch, E.P. Benis, T. Osipov, A.L. Landers, A. Belkacem, M.H. Prior, H. Schmidt-Böcking, C.L. Cocke, R. Dörner, Single photon-induced symmetry breaking of H2 dissociation. Science 315, 629–633 (2007) Google Scholar
  24. 24.
    H.-D. Meyer, F. Gatti, G.A. Worth (eds.), Multidimensional Quantum Dynamics (Wiley, Weinheim, 2009) Google Scholar
  25. 25.
    M. Ben-Nun, J. Quenneville, T.J. Martinez, Ab initio multiple spawning: photochemistry from first principles quantum molecular dynamics. J. Phys. Chem. A 104, 5161 (2000) Google Scholar
  26. 26.
    M. Ben-Nun, T.J. Martínez, Ab Initio Quantum Molecular Dynamics (Wiley, New York, 2002), pp. 439–512 Google Scholar
  27. 27.
    A.M. Virshup, C. Punwong, T.V. Pogorelov, B.A. Lindquist, C. Ko, T.J. Martínez, Photodynamics in complex environments: ab initio multiple spawning quantum Mechanical/Molecular mechanical dynamics. J. Phys. Chem. B 113, 3280–3291 (2009) Google Scholar
  28. 28.
    G.A. Worth, M.A. Robb, I. Burghardt, A novel algorithm for non-adiabatic direct dynamics using variational Gaussian wavepackets. Faraday Discuss. 127, 307–323 (2004) Google Scholar
  29. 29.
    V.A. Rassolov, S. Garashchuk, Semiclassical nonadiabatic dynamics with quantum trajectories. Phys. Rev. A 71, 032511 (2005) Google Scholar
  30. 30.
    J. Li, C. Woywod, V. Vallet, C. Meier, Investigation of the dynamics of two coupled oscillators with mixed quantum-classical methods. J. Chem. Phys. 124, 184105 (2006) Google Scholar
  31. 31.
    R. Spezia, I. Burghardt, J.T. Hynes, Conical intersections in solution: non-equilibrium versus equilibrium solvation. Mol. Phys. 104, 903–914 (2006) Google Scholar
  32. 32.
    B. Lasorne, M.A. Robb, G.A. Worth, Direct quantum dynamics using variational multi-configuration Gaussian wavepackets. Implementation details and test case. Phys. Chem. Chem. Phys. 9, 3210–3227 (2007) Google Scholar
  33. 33.
    T. Yonehara, S. Takahashi, K. Takatsuka, Non-Born–Oppenheimer electronic and nuclear wavepacket dynamics. J. Chem. Phys. 130, 214113 (2009) Google Scholar
  34. 34.
    T. Yonehara, K. Takatsuka, Non-Born–Oppenheimer quantum chemistry on the fly with continuous path branching due to nonadiabatic and intense optical interactions. J. Chem. Phys. 132, 244102 (2010) Google Scholar
  35. 35.
    G. Granucci, M. Persico, A. Zoccante, Including quantum decoherence in surface hopping. J. Chem. Phys. 133, 134111 (2010) Google Scholar
  36. 36.
    B.F.E. Curchod, I. Tavernelli, U. Rothlisberger, Trajectory-based solution of the nonadiabatic quantum dynamics equations: an on-the-fly approach for molecular dynamics simulations. Phys. Chem. Chem. Phys. 13, 3231–3236 (2011) Google Scholar
  37. 37.
    J. Caillat, J. Zanghellini, M. Kitzler, O. Koch, W. Kreuzer, A. Scrinzi, Correlated multielectron systems in strong laser fields: a multiconfiguration time-dependent Hartree-Fock approach. Phys. Rev. A 71, 012712 (2005) Google Scholar
  38. 38.
    T. Yonehara, K. Takatsuka, Nonadiabatic electron wavepacket dynamics of molecules in an intense optical field: an ab initio electronic state study. J. Chem. Phys. 128, 154104 (2008) Google Scholar
  39. 39.
    J. Kim, H. Tao, J.L. White, V.S. Petrović, T.J. Martinez, P.H. Bucksbaum, Control of 1,3-cyclohexadiene photoisomerization using light-induced conical intersections. J. Phys. Chem. A Google Scholar
  40. 40.
    L. Wang, H.-D. Meyer, V. May, Femtosecond laser pulse control of multidimensional vibrational dynamics: computational studies on the pyrazine molecule. J. Chem. Phys. 125, 014102 (2006) Google Scholar
  41. 41.
    T.J. Penfold, G.A. Worth, C. Meier, Local control of multidimensional dynamics. Phys. Chem. Chem. Phys. 12, 15616–15627 (2010) Google Scholar
  42. 42.
    C. Sanz-Sanz, G.W. Richings, G.A. Worth, Dynamic Stark control: model studies based on the photodissociation of IBr. Faraday Discuss. 153, 275–291 (2011) Google Scholar
  43. 43.
    M. Schröder, J.-L. Carreon-Macedo, A. Brown, Implementation of an iterative algorithm for optimal control of molecular dynamics into MCTDH. Phys. Chem. Chem. Phys. 10, 850–856 (2008) Google Scholar
  44. 44.
    M. Schröder, A. Brown, Realization of the cnot quantum gate operation in six-dimensional ammonia using the OCT-MCTDH approach. J. Chem. Phys. 131, 034101 (2009) Google Scholar
  45. 45.
    R. Car, M. Parrinello, Unified approach for molecular dynamics and density-functional theory. Phys. Rev. Lett. 55, 2471–2474 (1985) Google Scholar
  46. 46.
    N. Doltsinis, D. Marx, First principles molecular dynamics involving excited states and nonadiabatic transitions. J. Theor. Comput. Chem. 1, 319–349 (2002) Google Scholar
  47. 47.
    D. Marx, J. Hutter (eds.), Ab Initio Molecular Dynamics: Basic Theory and Advanced Methods (Cambridge University Press, Cambridge, 2009) Google Scholar
  48. 48.
    J.C. Tully, Molecular dynamics with electronic transitions. J. Chem. Phys. 93, 1061–1071 (1990) Google Scholar
  49. 49.
    N. Doltsinis, in Computational Nanoscience: Do It Yourself!, NIC Series, vol. 31 (John von Neumann Institute for Computing, Jülich, 2006), pp. 389–409 Google Scholar
  50. 50.
    E. Tapavicza, I. Tavernelli, U. Rothlisberger, Trajectory surface hopping within linear response time-dependent density-functional theory. Phys. Rev. Lett. 98, 023001 (2007) Google Scholar
  51. 51.
    M. Baer, Beyond Born-Oppenheimer: Electronic Nonadiabatic Coupling Terms and Conical Intersections (Wiley, Hoboken, 2006) Google Scholar
  52. 52.
    V. Chernyak, S. Mukamel, Density-matrix representation of nonadiabatic couplings in time-dependent density functional (TDDFT) theories. J. Chem. Phys. 112, 3572–3579 (2000) Google Scholar
  53. 53.
    R. Baer, Non-adiabatic couplings by time-dependent density functional theory. Chem. Phys. Lett. 364, 75–79 (2002) Google Scholar
  54. 54.
    I. Tavernelli, B.F.E. Curchod, U. Rothlisberger, On nonadiabatic coupling vectors in time-dependent density functional theory. J. Chem. Phys. 131, 196101 (2009) Google Scholar
  55. 55.
    I. Tavernelli, E. Tapavicza, U. Rothlisberger, Nonadiabatic coupling vectors within linear response time-dependent density functional theory. J. Chem. Phys. 130, 124107 (2009) Google Scholar
  56. 56.
    M.S. Topaler, T.C. Allison, D.W. Schwenke, D.G. Truhlar, What is the best semiclassical method for photochemical dynamics of systems with conical intersections? J. Chem. Phys. 109, 3321–3345 (1998) Google Scholar
  57. 57.
    G.A. Worth, M.A. Robb, Applying Direct Molecular Dynamics to Non-adiabatic Systems (Wiley, New York, 2003), pp. 355–431 Google Scholar
  58. 58.
    M. Barbatti, Nonadiabatic dynamics with trajectory surface hopping method. WIREs Comput. Mol. Sci. 1, 620–633 (2011) Google Scholar
  59. 59.
    S. Garashchuk, V.A. Rassolov, G.C. Schatz, Semiclassical nonadiabatic dynamics based on quantum trajectories for the O(3 P,1 D)+H2 system. J. Chem. Phys. 124, 244307 (2006) Google Scholar
  60. 60.
    W. Hu, G. Lendvay, B. Maiti, G.C. Schatz, Trajectory surface hopping study of the o(3p) + ethylene reaction dynamics. J. Phys. Chem. A 112, 2093–2103 (2008) Google Scholar
  61. 61.
    I. Tavernelli, B.F.E. Curchod, U. Rothlisberger, Nonadiabatic molecular dynamics with solvent effects: a LR-TDDFT QM/MM study of ruthenium (II) tris (bipyridine) in water. Chem. Phys. 391, 101–109 (2011) Google Scholar
  62. 62.
    M. Odelius, C. Ribbing, J. Kowalewski, Molecular dynamics simulation of the zero-field splitting fluctuations in aqueous Ni(II). J. Chem. Phys. 103, 1800–1811 (1995) Google Scholar
  63. 63.
    D.S.N. Parker, R.S. Minns, T.J. Penfold, G.A. Worth, H.H. Fielding, Ultrafast dynamics of the s1 excited state of benzene. Chem. Phys. Lett. 469, 43–47 (2009) Google Scholar
  64. 64.
    R.S. Minns, D.S.N. Parker, T.J. Penfold, G.A. Worth, H.H. Fielding, Competing ultrafast intersystem crossing and internal conversion in the “channel 3” region of benzene. Phys. Chem. Chem. Phys. 12, 15607–15615 (2010) Google Scholar
  65. 65.
    B. Fu, B.C. Shepler, J.M. Bowman, Three-state trajectory surface hopping studies of the photodissociation dynamics of formaldehyde on ab initio potential energy surfaces. J. Am. Chem. Soc. 133, 7957–7968 (2011) Google Scholar
  66. 66.
    K. Yamashita, K. Morokuma, Theoretical study of laser-catalyzed Na + HCl reaction: a possibility of transition state spectroscopy. Chem. Phys. Lett. 169, 263–268 (1990) Google Scholar
  67. 67.
    H. Gai, G.A. Voth, A computer simulation method for studying the ablation of polymer surfaces by ultraviolet laser radiation. J. Appl. Phys. 71, 1415–1420 (1992) Google Scholar
  68. 68.
    M. Thachuk, M.Y. Ivanov, D.M. Wardlaw, A semiclassical approach to intense-field above-threshold dissociation in the long wavelength limit. J. Chem. Phys. 105, 4094–4104 (1996) Google Scholar
  69. 69.
    K. Yagi, K. Takatsuka, Nonadiabatic chemical dynamics in an intense laser field: electronic wave packet coupled with classical nuclear motions. J. Chem. Phys. 123, 224103 (2005) Google Scholar
  70. 70.
    G.A. Jones, A. Acocella, F. Zerbetto, On-the-fly, electric-field-driven, coupled electron-nuclear dynamics. J. Phys. Chem. A 112, 9650–9656 (2008) Google Scholar
  71. 71.
    R. Mitrić, J. Petersen, V. Bonačić-Koutecký, Laser-field-induced surface-hopping method for the simulation and control of ultrafast photodynamics. Phys. Rev. A 79, 053416 (2009) Google Scholar
  72. 72.
    I. Tavernelli, B.F.E. Curchod, U. Rothlisberger, Mixed quantum-classical dynamics with time-dependent external fields: a time-dependent density-functional-theory approach. Phys. Rev. A 81, 052508 (2010) Google Scholar
  73. 73.
    B.F.E. Curchod, T.J. Penfold, U. Rothlisberger, I. Tavernelli, Local control theory in trajectory-based nonadiabatic dynamics. Phys. Rev. A 84, 042507 (2011) Google Scholar
  74. 74.
    M. Richter, P. Marquetand, J. González-Vázquez, I. Sola, L. González, SHARC—ab initio molecular dynamics with surface hopping in the adiabatic representation including arbitrary couplings. J. Chem. Theory Comput. 7, 1253–1258 (2011) Google Scholar
  75. 75.
    M. Richter, P. Marquetand, J. González-Vázquez, I. Sola, L. González, Correction to SHARC: ab initio molecular dynamics with surface hopping in the adiabatic representation including arbitrary couplings [J. Chem. Theory Comput. 2011, 7, 1253–1258]. J. Chem. Theory Comput. 8, 374 (2012) Google Scholar
  76. 76.
    J. Petersen, R. Mitrić, V. Bonačić-Koutecký, J. Wolf, J. Roslund, H. Rabitz, How shaped light discriminates nearly identical biochromophores. Phys. Rev. Lett. 105, 073003 (2010) Google Scholar
  77. 77.
    R. Mitrić, J. Petersen, M. Wohlgemuth, U. Werner, V. Bonačić-Koutecký, Field-induced surface hopping method for probing transition state nonadiabatic dynamics of Ag3. Phys. Chem. Chem. Phys. 13, 8690–8696 (2011) Google Scholar
  78. 78.
    R. Mitrić, J. Petersen, M. Wohlgemuth, U. Werner, V. Bonačić-Koutecký, L. Wöste, J. Jortner, Time-resolved femtosecond photoelectron spectroscopy by field-induced surface hopping. J. Phys. Chem. A 115, 3755–3765 (2011) Google Scholar
  79. 79.
    P. Lisinetskaya, R. Mitrić, Simulation of laser-induced coupled electron-nuclear dynamics and time-resolved harmonic spectra in complex systems. Phys. Rev. A 83(3) (2011) Google Scholar
  80. 80.
    X. Li, J.C. Tully, H.B. Schlegel, M.J. Frisch, Ab initio ehrenfest dynamics. J. Chem. Phys. 123, 084106 (2005) Google Scholar
  81. 81.
    J. González-Vázquez, I.R. Sola, J. Santamaria, V.S. Malinovsky, Quantum control of spin-orbit coupling by dynamic Stark-shifts induced by laser fields. Chem. Phys. Lett. 431, 231–235 (2006) Google Scholar
  82. 82.
    B.Y. Chang, S. Shin, J. Santamaria, I.R. Sola, Bond breaking in light-induced potentials. J. Chem. Phys. 130, 124320 (2009) Google Scholar
  83. 83.
    B.Y. Chang, S. Shin, I.R. Sola, Further aspects on the control of photodissociation in light-induced potentials. J. Chem. Phys. 131, 204314 (2009) Google Scholar
  84. 84.
    A. Präkelt, M. Wollenhaupt, C. Sarpe-Tudoran, T. Baumert, Phase control of a two-photon transition with shaped femtosecond laser-pulse sequences. Phys. Rev. A 70, 063407 (2005) Google Scholar
  85. 85.
    J.J. Bajo, J. González-Vázquez, I.R. Sola, J. Santamaria, M. Richter, P. Marquetand, L. González, Mixed quantum-classical dynamics in the adiabatic representation to simulate molecules driven by strong laser pulses. J. Phys. Chem. A Google Scholar
  86. 86.
    P. Marquetand, M. Richter, J. González-Vázquez, I. Sola, L. González, Nonadiabatic ab initio molecular dynamics including spin-orbit coupling and laser fields. Faraday Discuss. 153, 261–273 (2011) Google Scholar
  87. 87.
    O.V. Prezhdo, P.J. Rossky, Mean-field molecular dynamics with surface hopping. J. Chem. Phys. 107, 825–834 (1997) Google Scholar
  88. 88.
    L. Verlet, Computer “experiments” on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules. Phys. Rev. 159, 98–103 (1967) Google Scholar
  89. 89.
    L. Verlet, Computer “experiments” on classical fluids. ii. Equilibrium correlation functions. Phys. Rev. 165, 201–214 (1968) Google Scholar
  90. 90.
    M.D. Feit, J.A. Fleck Jr., A. Steiger, Solution of the Schrödinger equation by a spectral method. J. Comput. Phys. 47, 412–433 (1982) Google Scholar
  91. 91.
    M.D. Feit, J.A. Fleck Jr., Solution of the Schrödinger equation by a spectral method ii: Vibrational energy levels of triatomic molecules. J. Chem. Phys. 78, 301–308 (1983) Google Scholar
  92. 92.
    M.D. Feit, J.A. Fleck Jr., Wave packet dynamics and chaos in the Hénon-Heiles system. J. Chem. Phys. 80, 2578–2584 (1984) Google Scholar
  93. 93.
    B.J. Sussman, M.Y. Ivanov, A. Stolow, Nonperturbative quantum control via the nonresonant dynamic Stark effect. Phys. Rev. A 71, 051401 (2005) Google Scholar
  94. 94.
    D. Townsend, B.J. Sussman, A. Stolow, A Stark future for quantum control. J. Phys. Chem. A 1154, 357–373 (2011) Google Scholar
  95. 95.
    S. Patchkovskii, Ab initio investigation of potential energy curves of the 23 electronic states of IBr correlating to neutral 2P atoms. Phys. Chem. Chem. Phys. 8, 926–940 (2006) Google Scholar
  96. 96.
    H. Guo, The effect of nonadiabatic coupling in the predissociation dynamics of IBr. J. Chem. Phys. 99, 1685–1692 (1993) Google Scholar
  97. 97.
    R. Kosloff, H. Tal-Ezer, A direct relaxation method for calculating eigenfunctions and eigenvalues of the Schrödinger equation on a grid. Chem. Phys. Lett. 127, 223–230 (1986) Google Scholar
  98. 98.
    R.D. Levine, Molecular Reaction Dynamics (Cambridge University Press, Cambridge, 2005) Google Scholar
  99. 99.
    B.J. Sussman, Five ways to the nonresonant dynamic Stark effect. Am. J. Phys. 79, 477–484 (2011) Google Scholar
  100. 100.
    L.D. Landau, Theory of energy transfer. Phys. Z. Sowjetunion 1, 89 (1932) Google Scholar
  101. 101.
    C. Zener, Non-adiabatic crossing of energy levels. Proc. R. Soc. Lond. A 137, 696–701 (1932) Google Scholar
  102. 102.
    B.M. Garraway, K. Suominen, Adiabatic passage by light-induced potentials in molecules. Phys. Rev. Lett. 80, 932–935 (1998) Google Scholar
  103. 103.
    I.R. Solá, J. Santamaría, V.S. Malinovsky, Efficiency and robustness of adiabatic passage by light-induced potentials. Phys. Rev. A 61, 043413 (2000) Google Scholar
  104. 104.
    I.R. Solá, B.Y. Chang, J. Santamaría, V.S. Malinovsky, J.L. Krause, Selective excitation of vibrational states by shaping of light-induced potentials. Phys. Rev. Lett. 85, 4241–4244 (2000) Google Scholar
  105. 105.
    J.-L. Chang, R. Li, J.-C. Wu, J.-C. Shieh, Y.-T. Chen, Two-photon vibronic spectra of vinyl chloride at 7.3–10 eV. J. Chem. Phys. 115, 5925–5931 (2001) Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Leticia González
    • 1
  • Philipp Marquetand
    • 1
  • Martin Richter
    • 1
  • Jesús González-Vázquez
    • 2
  • Ignacio Sola
    • 2
  1. 1.Institute of Theoretical ChemistryUniversity of ViennaViennaAustria
  2. 2.Departamento de Química Física IUniversidad ComplutenseMadridSpain

Personalised recommendations