Tunneling in Unimolecular and Bimolecular Reactions

Chapter
Part of the Physical Chemistry in Action book series (PCIA)

Abstract

Tunneling is an important quantum phenomenon in reaction dynamics. In this chapter, the effects of tunneling on photodissociation and reactive scattering are discussed using two prototypical examples. The first deals with a unimolecular decomposition reaction, namely the photodissociation of NH3 in its first (A) absorption band and the second is concerned with an important bimolecular reaction in combustion: HO + CO → H + CO2. In the former case, the lifetimes of low-lying vibrational resonances in the predissociative excited state are influenced by tunneling through a small barrier in the dissociation (N–H) coordinate, which is also responsible for a strong H/D isotope effect. The latter, on the other hand, is affected by tunneling through a tight barrier in the exit channel primarily along the H–O dissociation coordinate, which is manifested by the non-Arrhenius rate constant at low temperatures, kinetic isotope effects, and vibrational mode selectivity. In addition, the photodetachment of HOCO produces metastable HOCO species, the decomposition of which is dominated by deep tunneling to the H + CO2 products. Since both systems are influenced by multidimensional tunneling, an accurate characterization of the dynamics requires a quantum mechanical (QM) treatment, preferably with full dimensionality. In this chapter, we review the recent advances in understanding the effects of tunneling in these two reactive systems.

References

  1. 1.
    Messiah A (1962) Quantum mechanics, vol 1. Wiley, New YorkGoogle Scholar
  2. 2.
    Cohen-Tannoudji C, Diu B, Laloe F (1992) Quantum mechanics. Wiley, New YorkGoogle Scholar
  3. 3.
    Basdevant J-L, Dalibard J (2005) Quantum mechanics. Springer, HeidelbergGoogle Scholar
  4. 4.
    Tannor DJ (2007) Introduction to Quantum Dynamics: A Time-Dependent Perspective. University Science Books, Sausalito, CAGoogle Scholar
  5. 6.
    Cohen-Tannoudji C, Grynberg G, Aspect A, Fabre C (2010) Introduction to quantum optics: From the semi-classical approach to quantized light. Cambridge University Press, CambridgeGoogle Scholar
  6. 7.
    Haroche S, Raimond J-M (2006) Exploring the quantum: Atoms, cavities, and photons. Oxford University Press, OxfordCrossRefGoogle Scholar
  7. 8.
    Pauling L, Wilson EB (1985) Introduction to quantum mechanics with applications to chemistry. Dover Publications, New YorkGoogle Scholar
  8. 9.
    Smith VH, Schaefer HF, Morokuma K (eds) (1986) Applied quantum chemistry. Springer, HeidelbergGoogle Scholar
  9. 10.
    Marcus RA (1952) Unimolecular dissociations and free radical recombination reactions. J Chem Phys 20:359CrossRefGoogle Scholar
  10. 11.
    Marcus RA (1965) On the theory of electron-transfer reactions. VI. Unified treatment for homogeneous and electrode reactions. J Chem Phys 43:679Google Scholar
  11. 12.
    Marcus RA (1993) Electron transfer reactions in chemistry. Theory and experiment. Rev Mod Phys 65:599CrossRefGoogle Scholar
  12. 13.
    Griebel M, Knapek S, Zumbusch G (2007) Numerical simulation in molecular dynamics. Springer, HeidelbergGoogle Scholar
  13. 14.
    Onuhic JN, Wolynes PG (1988) Classical and quantum pictures of reaction dynamics in condensed matter: Resonances, dephasing, and all that. J Phys Chem 92:6495CrossRefGoogle Scholar
  14. 15.
    Herzberg G (1992) Molecular spectra and molecular structure. Krieger, MalabarGoogle Scholar
  15. 16.
    Miller WH (2006) Including quantum effects in the dynamics of complex (i.e., large) molecular systems. J Chem Phys 125:132305Google Scholar
  16. 17.
    Zuev PS, Sheridan RS, Albu TV, Truhlar DG, Hrovat DA, Borden WT (2003) Carbon tunneling from a single quantum state. Science 299:867CrossRefGoogle Scholar
  17. 18.
    McMahon RJ (2003) Chemical reactions involving quantum tunneling. Science 299:833CrossRefGoogle Scholar
  18. 19.
    Espinosa-García J, Corchado JC, Truhlar DG (1997) The importance of quantum effects for C-H bond activation reactions. J Am Chem Soc 119:9891CrossRefGoogle Scholar
  19. 22.
    Cha Y, Murray CJ, Klinman JP (1989) Hydrogen tunneling in enzyme-reaction. Science 243:1325CrossRefGoogle Scholar
  20. 24.
    Truhlar DG, Gao J, Alhambra C, Garcia-Viloca M, Corchado J, Sánchez ML, Villà J (2002) The incorporation of quantum effects in enzyme kinetics modeling. Acc Chem Res 35:341CrossRefGoogle Scholar
  21. 25.
    Truhlar DG, Gao J, Alhambra C, Garcia-Viloca M, Corchado J, Sánchez ML, Villà J (2004) Ensemble-averaged variational transition state theory with optimized multidimensional tunneling for enzyme kinetics and other condensed-phase reactions. Int J Quant Chem 100:1136CrossRefGoogle Scholar
  22. 26.
    Hammer-Schiffer S (2002) Impact of enzyme motion on activity. Biochemistry 41:13335CrossRefGoogle Scholar
  23. 27.
    Antoniou D, Caratzoulas S, Mincer J, Schwartz SD (2002) Barrier passage and protein dynamics in enzymatically catalyzed reactions. Eur J Biochem 269:3103CrossRefGoogle Scholar
  24. 29.
    Domcke W, Yarkony DR, Köppel H (eds) (2004) Conical intersections, electronic strucutre, dynamics and spectroscopy. World Scientific, New JerseyGoogle Scholar
  25. 30.
    Domcke W, Yarkony DR, Köppel H (eds) (2004) Conical intersections, theory, computation and experiment. World Scientific, New JerseyGoogle Scholar
  26. 33.
    Polli D, Altoè P, Weingart O, Spillane KM, Manzoni C, Brida D, Tomasello G, Orlandi G, Kukura P, Mathies RA, Garavelli M, Cerullo G (2010) Conical intersection dynamics of the primary photoisomerization event in vision. Nature 467:440CrossRefGoogle Scholar
  27. 34.
    Lan Z, Frutos LM, Sobolewski AL, Domcke W (2008) Photochemistry of hydrogen-bonded aromatic pairs: quantum dynamical calculations for the pyrrole-pyridine complex. Proc Natl Acad Sci USA 105:12707CrossRefGoogle Scholar
  28. 35.
    Schultz T, Samoylova E, Radloff W, Hertel IV, Sobolewski AL, Domcke W (2004) Efficient deactivation of a model base pair via excited-state hydrogen transfer. Science 306:1765CrossRefGoogle Scholar
  29. 36.
    Wolynes PG (2009) Some quantum weirdness in physiology. Proc Natl Acad Sci USA 106:17247–17248CrossRefGoogle Scholar
  30. 37.
    Engel GS, Calhoun TR, Read EL, Ahn T-K, Mancal T, Cheng Y-C, Blankenship RE, Fleming GR (2007) Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems. Nature 446:782–786CrossRefGoogle Scholar
  31. 38.
    Lee H, Cheng Y-C, Fleming GR (2007) Coherence dynamics in photosynthesis: Protein protection of excitonic coherence. Science 316:1462CrossRefGoogle Scholar
  32. 39.
    Collini E, Wong CY, Wilk KE, Curmi PMG, Brumer P, Scholes GD (2010) Coherently wired light-harvesting in photosynthetic marine algae at ambient temperature. Nature 463:644CrossRefGoogle Scholar
  33. 40.
    Wang Q, Schoenlein RW, Peteanu LA, Shank RA (1994) Vibrationnaly coherent photochemistry in the femtosecond primary event of vision. Science 266:422–424CrossRefGoogle Scholar
  34. 41.
    Brumer P, Shapiro M (2012) Molecular response in one-photon absorption via natural thermal light vs. pulsed laser excitation. Proc Natl Acad Sci USA 109:19575Google Scholar
  35. 42.
    Gross A, Scheffer M (1998) Ab initio quantum and molecular dynamics of the dissociative adsorption on Pd(100). Phys Rev B 57:2493CrossRefGoogle Scholar
  36. 43.
    Marx D, Parrinello M (1996) The effect of quantum and thermal fluctuations on the structure of the floppy molecule C2H3 +. Science 271:179CrossRefGoogle Scholar
  37. 44.
    Arndt M, Nairz O, Voss-Andreae J, Keller C, van der Zouw G, Zeillinger A (1999) Wave-particle duality of c60 molecules. Nature 401:680CrossRefGoogle Scholar
  38. 45.
    Gerlich S, Eibenberger S, Tomand M, Nimmrichter S, Hornberger K, Fagan PJ, Tüxen J, Mayor M, Arndt M (2011) Quantum interference of large organic molecules. Nat Phys 2:263Google Scholar
  39. 46.
    Chatzidimitriou-Dreismann A, Arndt M (2004) Quantum mechanics and chemistry: The relevance of nonlocality and entanglement for molecules. Angew Chem Int Ed 335:144CrossRefGoogle Scholar
  40. 47.
    Chergui M (ed) (1996) Femtochemistry. World Scientific, SingaporeGoogle Scholar
  41. 48.
    Zewail AH (1994) Femtochemistry: ultrafast dynamics of the chemical bond. World Scientific, SingaporeGoogle Scholar
  42. 49.
    Ihee H, Lobastov V, Gomez U, Goodson B, Srinivasan R, Ruan C-Y, Zewail AH (2001) Science 291:385CrossRefGoogle Scholar
  43. 50.
    Drescher M, Hentschel M, Kienberger R, Uiberacker M, Scrinzi A, Westerwalbesloh T, Kleineberg U, Heinzmann U, Krausz F (2002) Time-resolved atomic inner-shell spectroscopy. Nature 419:803CrossRefGoogle Scholar
  44. 51.
    Goulielmakis E, Loh Z-H, Wirth A, Santra R, Rohringer N, Yakovlev VS, Zherebtsov S, Pfeifero T, Azzeer AM, Kling MF, Leone SR, Krausz F (2010) Real-time observation of valence electron motion. Nature 466:739CrossRefGoogle Scholar
  45. 52.
    Krausz F, Ivanov M (2009) Attosecond physics. Rev Mod Phys 81:163–234CrossRefGoogle Scholar
  46. 53.
    Kling MF, Siedschlag C, Verhoef AJ, Khan JI, Schultze M, Uphues T, Ni Y, Uiberacker M, Drescher M, Krausz F, Vrakking MJJ (2006) Control of electron localization in molecular dissociation. Science 312:246CrossRefGoogle Scholar
  47. 54.
    Niikura H, Légaré F, Hasbani R, Bandrauk AD, Ivanov MY, Villeneuve DM, Corkum PB (2002) Sub-laser-cycle electron pulse for probing molecular dynamics. Nature 417:917CrossRefGoogle Scholar
  48. 55.
    Stolow A, Jonas DM (2004) Muldimensional snapshots of chemical dynamics. Science 305:1575CrossRefGoogle Scholar
  49. 58.
    Brixner T, Damreuer NH, Niklaus P, Gerber G (2001) Photoselective adaptative femtosecond quantum control in the liquid phase. Nature 414:57CrossRefGoogle Scholar
  50. 59.
    Herek JL, Wohlleben W, Cogdell RJ, Zeidler D, Motzus M (2002) Quantum control of energy flow in light harvesting. Nature 417:533CrossRefGoogle Scholar
  51. 60.
    Levis RJ, Menkir GM, Rabitz H (2001) Selective bond dissociation and rearrangement with optimally tailored, strong-field laser pulses. Science 292:709CrossRefGoogle Scholar
  52. 61.
    Daems D, Guérin S, Hertz E, Jauslin HR, Lavorel B, Faucher O (2005) Field-free two-direction alignement alternation of linear molecules by elliptic laser pulses. Phys Rev Lett 95:063005CrossRefGoogle Scholar
  53. 62.
    Madsen CB, Madsen LB, Viftrup SS, Johansson MP, Poulsen TB, Holmegaard L, Kumarappan V, Jorgensen KA, Stapelfeldt H (2009) Manipulating the torsion of molecules by strong laser pulses. Phys Rev Lett 102:073007CrossRefGoogle Scholar
  54. 63.
    Holmegaard L, Hansen JL, Kalhøj L, Kragh SL, Stapelfeldt H, Filsinger F, Küpper J, Meijer G, Dimitrovski D, Martiny C, Madsen LB (2010) Photoelectron angular distributions from strong-field ionization of oriented molecules. Nat Phys 6:428CrossRefGoogle Scholar
  55. 65.
    Bethlem HL, Berden G, Crompvoets FM, Jongma RT, van Roij AJA, Meijer G (2000) Electrostatic trapping of ammonia molecules. Nature 406:491CrossRefGoogle Scholar
  56. 66.
    Kreckel H, Bruhns H, Open image in new window M, Glover SCO, Miller KA, Urbain X, Savin DW (2010) Experimental results for H2 formation from H and H and implications for first star formation. Science 329:69Google Scholar
  57. 67.
    Clary DC (1998) Quantum theory of chemical reaction dynamics. Science 279:1879CrossRefGoogle Scholar
  58. 68.
    Schnieder L, Seekamp-Rahn K, Borkowski J, Wrede E, Welge KH, Aoiz FJ, Bañares L, D’Mello MJ, Herrero VJ, Rábanos VS, Wyatt RE (1995) Experimental studies and theoretical predictions for the H + D2 → HD + D reaction. Science 269:207CrossRefGoogle Scholar
  59. 69.
    Qui M, Ren Z, Che L, Dai D, Harich SA, Wang X, Yang X, Xu C, Xie D, Gustafsson M, Skodje RT, Sun Z, Zhang DH (2006) Observation of Feshbach resonances in the F + H2 → HF + H reaction. Science 311:1440CrossRefGoogle Scholar
  60. 70.
    Dong W, Xiao C, Wang T, Dai D, Yang X, Zhang DH (2010) Transition-state spectroscopy of partial wave resonances in the F + HD. Science 327:1501CrossRefGoogle Scholar
  61. 71.
    Dyke TR, Howard BJ, Klemperer W. Radiofrequency and microwave spectrum of the hydrogen fluoride dimer; a nonrigid molecule. J Chem Phys 56:2442Google Scholar
  62. 72.
    Howard BJ, Dyke TR, Klemperer W (1984) The molecular beam spectrum and the structure of the hydrogen fluoride dimer. J Chem Phys 81:5417CrossRefGoogle Scholar
  63. 80.
    Zhang JZH (1999) Theory and application of uantum molecular dynamics. World Scientific, SingaporeGoogle Scholar
  64. 81.
    McCullough EA, Wyatt RE (1969) Quantum dynamics of the collinear (H,H2) reaction. J Chem Phys 51:1253CrossRefGoogle Scholar
  65. 82.
    McCullough EA, Wyatt RE (1971) Dynamics of the collinear (H,H2) reaction. I. Probability density and flux. J Chem Phys 54:3578Google Scholar
  66. 93.
    Heller EJ. Time-dependent approach to semiclassical dynamics. J Chem Phys 62:1544Google Scholar
  67. 94.
    Heller EJ. Time-dependent variational approach to semiclassical dynamics. J Chem Phys 64:63Google Scholar
  68. 95.
    Heller EJ () Wigner phase space method: Analysis for semiclassical applications. J Chem Phys 65:1289Google Scholar
  69. 98.
    Kosloff D, Kosloff R (1983) A Fourier-method solution for the time-dependent Schrödinger equation as a tool in molecular dynamics. J Comput Phys 52:35CrossRefGoogle Scholar
  70. 99.
    Wang X-G, Carrington Jr T (2003) A contracted basis-Lanczos calculation of vibrational levels of methane: Solving the Schrödinger equation in nine dimensions. J Chem Phys 119:101CrossRefGoogle Scholar
  71. 100.
    Wang X-G, Carrington Jr T (2004) Contracted basis lanczos methods for computing numerically exact rovibrational levels of methane. J Chem Phys 121(7):2937–2954CrossRefGoogle Scholar
  72. 101.
    Tremblay JC, Carrington Jr T (2006) Calculating vibrational energies and wave functions of vinylidene using a contracted basis with a locally reorthogonalized coupled two-term lanczos eigensolver. J Chem Phys 125:094311CrossRefGoogle Scholar
  73. 102.
    Wang X, Carrington Jr T (2008) Vibrational energy levels of CH5 +. J Chem Phys 129:234102CrossRefGoogle Scholar
  74. 103.
    Norris LS, Ratner MA, Roitberg AE, Gerber RB (1996) Moller-plesset perturbation theory applied to vibrational problems. J Chem Phys 105:11261CrossRefGoogle Scholar
  75. 104.
    Christiansen O (2003) Moller-plesset perturbation theory for vibrational wave functions. J Chem Phys 119:5773CrossRefGoogle Scholar
  76. 105.
    Christiansen O (2004) Vibrational coupled cluster theory. J Chem Phys 120:2149CrossRefGoogle Scholar
  77. 106.
    Christiansen O, Luis J (2005) Beyond vibrational self-consistent-field methods: Benchmark calculations for the fundamental vibrations of ethylene. Int J Quant Chem 104:667CrossRefGoogle Scholar
  78. 107.
    Scribano Y, Benoit D (2007) J Chem Phys 127:164118CrossRefGoogle Scholar
  79. 108.
    Barone V (2005) Anharmonic vibrational properties by a fully automated second-order perturbative aproach. J Chem Phys 122:014108CrossRefGoogle Scholar
  80. 109.
    Bowman J (1978) Self-consistent field energies and wavefunctions for coupled oscillators. J Chem Phys 68:608CrossRefGoogle Scholar
  81. 110.
    Bowman J, Christoffel K, Tobin F. Application of SCF-SI theory to vibrational motion in polyatomic molecules. J Phys Chem 83:905Google Scholar
  82. 111.
    Bégué D, Gohaud N, Pouchan C, Cassam-Chenaï P, Liévin J (2007) A comparison of two methods for selecting vibrational configuration interaction spaces on a heptatomic system: Ethylene oxide. J Chem Phys 127:164115CrossRefGoogle Scholar
  83. 112.
    Carter S, Bowman JM, Handy NC (1998) Extensions and tests of “multimodes”: a code to obtain accurate vibration/rotation energies of many-mode molecules. Theor Chem Acc 100:191CrossRefGoogle Scholar
  84. 113.
    Bowman JM (2000) Chemistry—beyond platonic molecules. Science 290:724CrossRefGoogle Scholar
  85. 114.
    Culot F, Laruelle F, Liévin J (1995) A vibrational CASSCF study of stretch-bend interactions and their influence on infrared intensities in the water molecule. Theor Chem Acc 92:211Google Scholar
  86. 115.
    Heislbetz S, Rauhut G (2010) Vibrational multiconfiguration self-consistent field theory: Implementation and test calculations. J Chem Phys 132:124102CrossRefGoogle Scholar
  87. 116.
    Meyer H-D, Le Quéré F, Léonard C, Gatti F (2006) Calculation and selective population of vibrational levels with the Multiconfiguration Time-Dependent Hartree (MCTDH) algorithm. Chem Phys 329:179–192CrossRefGoogle Scholar
  88. 117.
    Joubert Doriol L, Gatti F, Iung C, Meyer H-D (2008) Computation of vibrational energy levels and eigenstates of fluoroform using the multiconfiguration time-dependent Hartree method. J Chem Phys 129:224109CrossRefGoogle Scholar
  89. 118.
    Gerber RB, Buch V, Ratner MA (1982) Time-dependent self-consistent field approximation for intramolecular energy transfer. I. Formulation and application to dissociation of van der Waals molecules. J Chem Phys 77:3022Google Scholar
  90. 119.
    Gerber RB, Ratner MA (1988) Self-consistent-field methods for vibrational excitations in polyatomic systems. Adv Chem Phys 70:97Google Scholar
  91. 120.
    Makri N, Miller WH (1987) Time-dependent self-consistent (TDSCF) approximation for a reaction coordinate coupled to a harmonic bath: Single and multiconfiguration treatments. J Chem Phys 87:5781CrossRefGoogle Scholar
  92. 121.
    Kotler Z, Nitzan A, Kosloff R (1988) Multiconfiguration time-dependent self-consistent field approximation for curve crossing in presence of a bath. A Fast Fourier Transform study. Chem Phys Lett 153:483Google Scholar
  93. 122.
    Meyer H-D, Manthe U, Cederbaum LS (1990) The multi-configurational time-dependent Hartree approach. Chem Phys Lett 165:73–78CrossRefGoogle Scholar
  94. 123.
    Manthe U, Meyer H-D, Cederbaum LS (1992) Wave-packet dynamics within the multiconfiguration Hartree framework: General aspects and application to NOCl. J Chem Phys 97:3199–3213CrossRefGoogle Scholar
  95. 124.
    Beck MH, Jäckle A, Worth GA, Meyer H-D (2000) The multi-configuration time-dependent Hartree (MCTDH) method: A highly efficient algorithm for propagating wave packets. Phys Rep 324:1–105CrossRefGoogle Scholar
  96. 126.
    Worth GA, Beck MH, Jäckle A, Meyer H-D (2007) The MCTDH Package, Version 8.2, (2000). Meyer HD, Version 8.3 (2002), Version 8.4 (2007). See http://mctdh.uni-hd.de/
  97. 127.
    Jolicard G, Austin E (1985) Optical potential stabilisation method for predicting resonance level. Chem Phys Lett 121:106CrossRefGoogle Scholar
  98. 128.
    Jolicard G, Austin E (1986) Optical potential method of caculating resonance energies and widths. Chem Phys 103:295CrossRefGoogle Scholar
  99. 129.
    Riss UV, Meyer H-D (1993) Calculation of resonance energies and widths using the complex absorbing potential method. J Phys B 26:4503CrossRefGoogle Scholar
  100. 130.
    Riss UV, Meyer H-D (1996) Investigation on the reflection and transmission properties of complex absorbing potentials. J Chem Phys 105:1409CrossRefGoogle Scholar
  101. 131.
    Moiseyev N (1998) Quantum theory of resonances: calculating energies, widths and cross-sections by complex scaling. Phys Rep 302:211CrossRefGoogle Scholar
  102. 132.
    Moiseyev N (2011) Non-Hermitian quantum mechanics. Cambridge University Press, Cambridge, UKCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of Chemistry and Chemical BiologyUniversity of New MexicoAlbuquerqueUSA
  2. 2.Institute of Atomic and Molecular PhysicsSichuan UniversityChengduChina

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