Skip to main content
SpringerLink
Log in

Non-adiabatic Photochemistry: Ultrafast Electronic State Transitions and Nuclear Wavepacket Coherence

  • Chapter
  • First Online:
Molecular Quantum Dynamics

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

Abstract

Chemistry that takes place exclusively in the ground electronic state can be well described by a reaction path in which the reactants pass over a transition state to the products. After photoexcitation, a molecule is in an excited electronic state and new topographical features joining different states, known as conical intersections, also need to be considered to describe the time-evolution from reactants to products. These intersections are due to the coupling between electrons and nuclei. In addition to providing new pathways, they provide a quantum-mechanical phase to the system which means that to describe the nuclear motion properly methods are required that include the resulting quantum-mechanical coherences in the nuclear motion. In this chapter, we review the nature and topography of conical intersections and simulation methods that have been developed to describe a molecule passing through one. These range from the full solution of the time-dependent Schrödinger equation to approximate methods based on Newtonian mechanics. Using examples the advantages and disadvantages of each are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 119.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 159.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 159.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Messiah A (1962) Quantum mechanics, vol 1. Wiley, New York

    Google Scholar 

  2. Cohen-Tannoudji C, Diu B, Laloe F (1992) Quantum mechanics. Wiley, New York

    Google Scholar 

  3. Basdevant J-L, Dalibard J (2005) Quantum mechanics. Springer, Heidelberg

    Google Scholar 

  4. Tannor DJ (2007) Introduction to Quantum Dynamics: A Time-Dependent Perspective. University Science Books, Sausalito, CA

    Google Scholar 

  5. Fox M (2006) Quantum optics: An introduction. Oxford University Press, Oxford

    Google Scholar 

  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, Cambridge

    Google Scholar 

  7. Haroche S, Raimond J-M (2006) Exploring the quantum: Atoms, cavities, and photons. Oxford University Press, Oxford

    Book  Google Scholar 

  8. Pauling L, Wilson EB (1985) Introduction to quantum mechanics with applications to chemistry. Dover Publications, New York

    Google Scholar 

  9. Smith VH, Schaefer HF, Morokuma K (eds) (1986) Applied quantum chemistry. Springer, Heidelberg

    Google Scholar 

  10. Marcus RA (1952) Unimolecular dissociations and free radical recombination reactions. J Chem Phys 20:359

    Article  CAS  Google Scholar 

  11. Marcus RA (1965) On the theory of electron-transfer reactions. VI. Unified treatment for homogeneous and electrode reactions. J Chem Phys 43:679

    Google Scholar 

  12. Marcus RA (1993) Electron transfer reactions in chemistry. Theory and experiment. Rev Mod Phys 65:599

    Article  CAS  Google Scholar 

  13. Griebel M, Knapek S, Zumbusch G (2007) Numerical simulation in molecular dynamics. Springer, Heidelberg

    Google Scholar 

  14. Onuhic JN, Wolynes PG (1988) Classical and quantum pictures of reaction dynamics in condensed matter: Resonances, dephasing, and all that. J Phys Chem 92:6495

    Article  Google Scholar 

  15. Herzberg G (1992) Molecular spectra and molecular structure. Krieger, Malabar

    Google Scholar 

  16. Miller WH (2006) Including quantum effects in the dynamics of complex (i.e., large) molecular systems. J Chem Phys 125:132305

    Google Scholar 

  17. Zuev PS, Sheridan RS, Albu TV, Truhlar DG, Hrovat DA, Borden WT (2003) Carbon tunneling from a single quantum state. Science 299:867

    Article  CAS  Google Scholar 

  18. McMahon RJ (2003) Chemical reactions involving quantum tunneling. Science 299:833

    Article  CAS  Google Scholar 

  19. Espinosa-García J, Corchado JC, Truhlar DG (1997) The importance of quantum effects for C-H bond activation reactions. J Am Chem Soc 119:9891

    Article  Google Scholar 

  20. Wonchoba SE, Hu W-P, Truhlar DG (1995) Surface diffusion of H on Ni(100). Interpretation of the transition temperature. Phys Rev B 51:9985

    Google Scholar 

  21. Hiraoka K, Sato T, Takayama T (2001) Tunneling reactions in interstellar ices. Science 292:869

    Article  CAS  Google Scholar 

  22. Cha Y, Murray CJ, Klinman JP (1989) Hydrogen tunneling in enzyme-reaction. Science 243:1325

    Article  CAS  Google Scholar 

  23. Kohen A, Cannio R, Bartolucci S, Klinman JP (1999) Enzyme dynamics and hydrogen tunnelling in a thermophilic alcohol dehydrogenase. Nature 399:496

    Article  CAS  Google Scholar 

  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 35:341

    Article  CAS  Google Scholar 

  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 100:1136

    Article  CAS  Google Scholar 

  26. Hammer-Schiffer S (2002) Impact of enzyme motion on activity. Biochemistry 41:13335

    Article  Google Scholar 

  27. Antoniou D, Caratzoulas S, Mincer J, Schwartz SD (2002) Barrier passage and protein dynamics in enzymatically catalyzed reactions. Eur J Biochem 269:3103

    Article  CAS  Google Scholar 

  28. 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 467:440

    Article  CAS  Google Scholar 

  29. 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 105:12707

    Article  CAS  Google Scholar 

  30. Wolynes PG (2009) Some quantum weirdness in physiology. Proc Natl Acad Sci USA 106:17247–17248

    Article  CAS  Google Scholar 

  31. Lee H, Cheng Y-C, Fleming GR (2007) Coherence dynamics in photosynthesis: Protein protection of excitonic coherence. Science 316:1462

    Article  CAS  Google Scholar 

  32. 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 463:644

    Article  CAS  Google Scholar 

  33. Wang Q, Schoenlein RW, Peteanu LA, Shank RA (1994) Vibrationnaly coherent photochemistry in the femtosecond primary event of vision. Science 266:422–424

    Article  CAS  Google Scholar 

  34. Arndt M, Nairz O, Voss-Andreae J, Keller C, van der Zouw G, Zeillinger A (1999) Wave-particle duality of c60 molecules. Nature 401:680

    Article  CAS  Google Scholar 

  35. 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 2:263

    Google Scholar 

  36. Chatzidimitriou-Dreismann A, Arndt M (2004) Quantum mechanics and chemistry: The relevance of nonlocality and entanglement for molecules. Angew Chem Int Ed 335:144

    Article  Google Scholar 

  37. Chergui M (ed) (1996) Femtochemistry. World Scientific, Singapore

    Google Scholar 

  38. Zewail AH (1994) Femtochemistry: ultrafast dynamics of the chemical bond. World Scientific, Singapore

    Google Scholar 

  39. Ihee H, Lobastov V, Gomez U, Goodson B, Srinivasan R, Ruan C-Y, Zewail AH (2001) Science 291:385

    Article  Google Scholar 

  40. 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 419:803

    Article  CAS  Google Scholar 

  41. 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 466:739

    Article  CAS  Google Scholar 

  42. Krausz F, Ivanov M (2009) Attosecond physics. Rev Mod Phys 81:163–234

    Article  Google Scholar 

  43. 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 312:246

    Article  CAS  Google Scholar 

  44. 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 417:917

    Article  CAS  Google Scholar 

  45. Brixner T, Damreuer NH, Niklaus P, Gerber G (2001) Photoselective adaptative femtosecond quantum control in the liquid phase. Nature 414:57

    Article  CAS  Google Scholar 

  46. Herek JL, Wohlleben W, Cogdell RJ, Zeidler D, Motzus M (2002) Quantum control of energy flow in light harvesting. Nature 417:533

    Article  CAS  Google Scholar 

  47. Levis RJ, Menkir GM, Rabitz H (2001) Selective bond dissociation and rearrangement with optimally tailored, strong-field laser pulses. Science 292:709

    Article  CAS  Google Scholar 

  48. 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 6:428

    Article  CAS  Google Scholar 

  49. Bisgaard CZ, Clarkin OJ, Wu G, Lee AMD, Gessner O, Hayden CC, Stolow A (2009) Time-resolved molecular frame dynamics of fixed-in-space CS2 molecules. Science 323:1464

    Article  CAS  Google Scholar 

  50. 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 269:207

    Article  CAS  Google Scholar 

  51. 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 311:1440

    Article  Google Scholar 

  52. 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 327:1501

    Article  CAS  Google Scholar 

  53. Dyke TR, Howard BJ, Klemperer W. Radiofrequency and microwave spectrum of the hydrogen fluoride dimer; a nonrigid molecule. J Chem Phys 56:2442

    Google Scholar 

  54. Fellers RS, Leforestier C, Braly LB, Brown MG, Saykally RJ (1999) Spectroscopic Determination of the Water Pair Potential. Science 284:945

    Article  CAS  Google Scholar 

  55. Saykally RJ, Blake GA (1993) Molecular interactions and hydrogen bond tunneling dynamics: Some new perspectives. Science 259:1570

    Article  CAS  Google Scholar 

  56. Miller WH (1974) Quantum mechanical transition state theory and a new semiclassical model for reaction rate constants. J Chem Phys 61:1823–1834

    Article  CAS  Google Scholar 

  57. Miller WH (1993) Beyond transition-state theory: a rigorous quantum theory of chemical reaction rates. Acc Chem Res 26(4):174

    Article  CAS  Google Scholar 

  58. Thoss M, Miller WH, Stock G (2000) Semiclassical description of nonadiabatic quantum dynamics: Application to the S1 – S2 conical intersection in pyrazine. J Chem Phys 112:10282–10292

    Article  CAS  Google Scholar 

  59. Wang HB, Thoss M, Sorge KL, Gelabert R, Gimenez X, Miller WH (2001) Semiclassical description of quantum coherence effects and their quenching: A forward-backward initial value representation study. J Chem Phys 114:2562–2571

    Article  CAS  Google Scholar 

  60. Bowman JM, Carrington Jr. T, Meyer H-D (2008) Variational quantum approaches for computing vibrational energies of polyatomic molecules. Mol Phys 106:2145–2182

    Article  CAS  Google Scholar 

  61. Zhang JZH (1999) Theory and application of uantum molecular dynamics. World Scientific, Singapore

    Google Scholar 

  62. McCullough EA, Wyatt RE (1969) Quantum dynamics of the collinear (H,H2) reaction. J Chem Phys 51:1253

    Article  CAS  Google Scholar 

  63. McCullough EA, Wyatt RE (1971) Dynamics of the collinear (H,H2) reaction. I. Probability density and flux. J Chem Phys 54:3578

    Google Scholar 

  64. Whitehead RJ, Handy NC (1975) J Mol Spec 55:356

    Article  CAS  Google Scholar 

  65. Schatz GC, Kuppermann A (1976) Quantum mechanical reactive scattering for three-dimensional atom plus diatom systems. I. Theory. J Chem Phys 65:4642

    Article  CAS  Google Scholar 

  66. Schatz GC, Kuppermann A (1976) Quantum mechanical reactive scattering for three-dimensional atom plus diatom systems. II. Accurate cross sections for H + H2. J Chem Phys 65:4668–4692

    Article  CAS  Google Scholar 

  67. Carter S, Handy NC (1986) An efficient procedure for the calculation of the vibrational energy levels of any triatomic molecule. Mol Phys 57:175

    Article  CAS  Google Scholar 

  68. Z, Light JC (1986) Highly excited vibrational levels of “floppy” triatomic molecules: A discrete variable representation – Distributed Gaussian approach. J Chem Phys 85:4594

    Google Scholar 

  69. Z, Light JC (1987) Accurate localized and delocalized vibrational states of HCN/HNC. J Chem Phys 86:3065

    Google Scholar 

  70. Köppel H, Cederbaum LS, Domcke W (1982) Strong nonadiabatic effects and conical intersections in molecular spectroscopy and unimolecular decay: C2H4 +. J Chem Phys 77:2014

    Article  Google Scholar 

  71. Nauts A, Wyatt RE (1983) New approach to many-state quantum dynamics: the recursive-residue-generation method. Phys Rev Lett 51:2238

    Article  CAS  Google Scholar 

  72. Sibert EL (1990) Variational and perturbative descriptions of highly vibrationally excited molecules. Int Rev Phys Chem 9:1

    Article  CAS  Google Scholar 

  73. Elkowitz AB, Wyatt RE (1975) Quantum-mechanical reaction cross-section for 3-dimensional hydrogen-exchange reaction. J Chem Phys 62:2504

    Article  CAS  Google Scholar 

  74. Heller EJ. Time-dependent approach to semiclassical dynamics. J Chem Phys 62:1544

    Google Scholar 

  75. Heller EJ. Time-dependent variational approach to semiclassical dynamics. J Chem Phys 64:63

    Google Scholar 

  76. Heller EJ () Wigner phase space method: Analysis for semiclassical applications. J Chem Phys 65:1289

    Google Scholar 

  77. Leforestier C, Bisseling RH, Cerjan C, Feit MD, Friesner R, Guldenberg A, Hammerich A, Jolicard G, Karrlein W, Meyer HD, Lipkin N, Roncero O, Kosloff R (1991) A comparison of different propagation schemes for the time dependent Schrödinger equation. J Comput Phys 94:59

    Article  Google Scholar 

  78. Kosloff R (1988) Time-dependent quantum-mechanical methods for molecular dynamics. J Phys Chem 92:2087

    Article  CAS  Google Scholar 

  79. Kosloff D, Kosloff R (1983) A Fourier-method solution for the time-dependent Schrödinger equation as a tool in molecular dynamics. J Comput Phys 52:35

    Article  CAS  Google Scholar 

  80. 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 119:101

    Article  CAS  Google Scholar 

  81. Wang X-G, Carrington Jr T (2004) Contracted basis lanczos methods for computing numerically exact rovibrational levels of methane. J Chem Phys 121(7):2937–2954

    Article  CAS  Google Scholar 

  82. 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 125:094311

    Article  Google Scholar 

  83. Wang X, Carrington Jr T (2008) Vibrational energy levels of CH5 +. J Chem Phys 129:234102

    Article  Google Scholar 

  84. Norris LS, Ratner MA, Roitberg AE, Gerber RB (1996) Moller-plesset perturbation theory applied to vibrational problems. J Chem Phys 105:11261

    Article  CAS  Google Scholar 

  85. Christiansen O (2003) Moller-plesset perturbation theory for vibrational wave functions. J Chem Phys 119:5773

    Article  CAS  Google Scholar 

  86. Christiansen O (2004) Vibrational coupled cluster theory. J Chem Phys 120:2149

    Article  CAS  Google Scholar 

  87. Christiansen O, Luis J (2005) Beyond vibrational self-consistent-field methods: Benchmark calculations for the fundamental vibrations of ethylene. Int J Quant Chem 104:667

    Article  CAS  Google Scholar 

  88. Scribano Y, Benoit D (2007) J Chem Phys 127:164118

    Article  Google Scholar 

  89. Barone V (2005) Anharmonic vibrational properties by a fully automated second-order perturbative aproach. J Chem Phys 122:014108

    Article  Google Scholar 

  90. Bowman J (1978) Self-consistent field energies and wavefunctions for coupled oscillators. J Chem Phys 68:608

    Article  CAS  Google Scholar 

  91. Bowman J, Christoffel K, Tobin F. Application of SCF-SI theory to vibrational motion in polyatomic molecules. J Phys Chem 83:905

    Google Scholar 

  92. 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 127:164115

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut Charles Gerhardt Montpellier - CNRS - Université Montpellier 2, CC 15001 Place Eugène Bataillon, 34095, Montpellier, France

    Benjamin Lasorne

  2. School of Chemistry, University of Birmingham, Edgbaston, B15 2TT, UK

    Graham A. Worth

  3. Department of Chemistry, Imperial College London, South Kensington, London, SW7 2AZ, UK

    Michael A. Robb

Authors
  1. Benjamin Lasorne
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Graham A. Worth
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Michael A. Robb
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Graham A. Worth .

Editor information

Editors and Affiliations

  1. Institut Charles GERHARDT - CNRS 5253, Université Montpellier 2, Montpellier Cedex, France

    Fabien Gatti

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Lasorne, B., Worth, G.A., Robb, M.A. (2014). Non-adiabatic Photochemistry: Ultrafast Electronic State Transitions and Nuclear Wavepacket Coherence. In: Gatti, F. (eds) Molecular Quantum Dynamics. Physical Chemistry in Action. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45290-1_7

Download citation

Publish with us

Policies and ethics

Search

Navigation