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Reactive Scattering and Resonance

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Molecular Quantum Dynamics

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

Abstract

In this chapter, recent developments of the quantum wave packet methods for calculating differential cross sections (DCSs) of tetra-atomic reaction, for calculating DCSs of triatomic reaction using wave packet method only with reactant Jacobi coordinates, for calculating and analyzing the reactive resonance wave functions, and for simulating and explaining experimental observables of a reactive scattering, are given. Applications to the F + H2 reaction, especially some fundamental understandings of its short-lived reactive resonances, the H + O2 reaction, the H2 + OH → H + H2O reaction, and the OH + CO → H + CO2 reaction are presented for illustration.

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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

    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

    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

    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

    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

    CAS  Google Scholar 

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

    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

    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

    CAS  Google Scholar 

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

    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

    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

    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

    CAS  Google Scholar 

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

    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

    CAS  Google Scholar 

  28. Domcke W, Yarkony DR, Köppel H (eds) (2004) Conical intersections, electronic strucutre, dynamics and spectroscopy. World Scientific, New Jersey

    Google Scholar 

  29. Domcke W, Yarkony DR, Köppel H (eds) (2004) Conical intersections, theory, computation and experiment. World Scientific, New Jersey

    Google Scholar 

  30. Worth GA, Cederbaum LS (2001) Mediation of ultrafast electron transfer in biological systems by conical intersections. Chem Phys Lett 338:219–223

    CAS  Google Scholar 

  31. González-Luque M, Garavelli M, Bernardi F, Mechán M, Robb MA, Olivucci M (2010) Computational. Proc Natl Acad Sci USA 97:9379

    Google Scholar 

  32. 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

    CAS  Google Scholar 

  33. 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

    CAS  Google Scholar 

  34. 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 306:1765

    CAS  Google Scholar 

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

    CAS  Google Scholar 

  36. 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 446:782–786

    CAS  Google Scholar 

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

    CAS  Google Scholar 

  38. 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

    CAS  Google Scholar 

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

    CAS  Google Scholar 

  40. Brumer P, Shapiro M (2012) Molecular response in one-photon absorption via natural thermal light vs. pulsed laser excitation. Proc Natl Acad Sci USA 109:19575

    Google Scholar 

  41. Gross A, Scheffer M (1998) Ab initio quantum and molecular dynamics of the dissociative adsorption on Pd(100). Phys Rev B 57:2493

    CAS  Google Scholar 

  42. Marx D, Parrinello M (1996) The effect of quantum and thermal fluctuations on the structure of the floppy molecule C2H3 +. Science 271:179

    CAS  Google Scholar 

  43. 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

    CAS  Google Scholar 

  44. 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 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  49. 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

    CAS  Google Scholar 

  50. 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

    CAS  Google Scholar 

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

    Google Scholar 

  52. 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

    CAS  Google Scholar 

  53. 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

    CAS  Google Scholar 

  54. Stolow A, Jonas DM (2004) Muldimensional snapshots of chemical dynamics. Science 305:1575

    CAS  Google Scholar 

  55. Kahra S, Leschhorn G, Kowalewski M, Schiffrin A, Bothschafter E, Fuss W, de Vivie-Riedle R, Ernstorfer R, Krausz F, Kienberger R, Schaetz T (2012) Controlled delivery of single molecules into ultra-short laser pulses: a molecular conveyor belt. Nat Phys 8:238

    CAS  Google Scholar 

  56. Asssion A, Baumert T, Bergt M, Brixner T, Kiefer B, Seyfried V, Strehle M, Gerber G (1998) Control of chemical reactions by feedback-optimized phase-shaped femtocecond laser pulses. Science 282:919

    Google Scholar 

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

    CAS  Google Scholar 

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

    CAS  Google Scholar 

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

    CAS  Google Scholar 

  60. 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 95:063005

    CAS  Google Scholar 

  61. 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 102:073007

    CAS  Google Scholar 

  62. 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

    CAS  Google Scholar 

  63. 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

    CAS  Google Scholar 

  64. Bethlem HL, Berden G, Crompvoets FM, Jongma RT, van Roij AJA, Meijer G (2000) Electrostatic trapping of ammonia molecules. Nature 406:491

    CAS  Google Scholar 

  65. Kreckel H, Bruhns H, 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 329:69

    Google Scholar 

  66. Clary DC (1998) Quantum theory of chemical reaction dynamics. Science 279:1879

    CAS  Google Scholar 

  67. 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

    CAS  Google Scholar 

  68. 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

    Google Scholar 

  69. 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

    CAS  Google Scholar 

  70. 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 

  71. Howard BJ, Dyke TR, Klemperer W (1984) The molecular beam spectrum and the structure of the hydrogen fluoride dimer. J Chem Phys 81:5417

    CAS  Google Scholar 

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

    CAS  Google Scholar 

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

    CAS  Google Scholar 

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

    CAS  Google Scholar 

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

    CAS  Google Scholar 

  76. 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

    CAS  Google Scholar 

  77. 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

    CAS  Google Scholar 

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

    CAS  Google Scholar 

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

    Google Scholar 

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

    CAS  Google Scholar 

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

    CAS  Google Scholar 

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

    CAS  Google Scholar 

  83. 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

    CAS  Google Scholar 

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

    CAS  Google Scholar 

  85. 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 

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

    Google Scholar 

  87. 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

    Google Scholar 

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

    CAS  Google Scholar 

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

    CAS  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  92. 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

    Google Scholar 

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

    CAS  Google Scholar 

  94. 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

    CAS  Google Scholar 

  95. 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

    CAS  Google Scholar 

  96. 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

    CAS  Google Scholar 

  97. 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

    Google Scholar 

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

    Google Scholar 

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

    CAS  Google Scholar 

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

    CAS  Google Scholar 

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

    CAS  Google Scholar 

  102. 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

    CAS  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    CAS  Google Scholar 

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

    Google Scholar 

  107. 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

    Google Scholar 

  108. 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 100:191

    CAS  Google Scholar 

  109. Bowman JM (2000) Chemistry—beyond platonic molecules. Science 290:724

    CAS  Google Scholar 

  110. 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 92:211

    CAS  Google Scholar 

  111. Heislbetz S, Rauhut G (2010) Vibrational multiconfiguration self-consistent field theory: Implementation and test calculations. J Chem Phys 132:124102

    Google Scholar 

  112. 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 329:179–192

    CAS  Google Scholar 

  113. 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 129:224109

    Google Scholar 

  114. 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 77:3022

    Google Scholar 

  115. Gerber RB, Ratner MA (1988) Self-consistent-field methods for vibrational excitations in polyatomic systems. Adv Chem Phys 70:97

    CAS  Google Scholar 

  116. 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 87:5781

    CAS  Google Scholar 

  117. 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 153:483

    Google Scholar 

  118. Meyer H-D, Manthe U, Cederbaum LS (1990) The multi-configurational time-dependent Hartree approach. Chem Phys Lett 165:73–78

    CAS  Google Scholar 

  119. 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 97:3199–3213

    CAS  Google Scholar 

  120. 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 324:1–105

    CAS  Google Scholar 

  121. Meyer H-D, Gatti F, Worth GA (eds) (2009) Multidimensional quantum dynamics: MCTDH theory and applications. Wiley, Weinheim

    Google Scholar 

  122. 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/

  123. Jolicard G, Austin E (1985) Optical potential stabilisation method for predicting resonance level. Chem Phys Lett 121:106

    CAS  Google Scholar 

  124. Jolicard G, Austin E (1986) Optical potential method of caculating resonance energies and widths. Chem Phys 103:295

    CAS  Google Scholar 

  125. Riss UV, Meyer H-D (1993) Calculation of resonance energies and widths using the complex absorbing potential method. J Phys B 26:4503

    CAS  Google Scholar 

  126. Riss UV, Meyer H-D (1996) Investigation on the reflection and transmission properties of complex absorbing potentials. J Chem Phys 105:1409

    CAS  Google Scholar 

  127. Moiseyev N (1998) Quantum theory of resonances: calculating energies, widths and cross-sections by complex scaling. Phys Rep 302:211

    CAS  Google Scholar 

  128. Moiseyev N (2011) Non-Hermitian quantum mechanics. Cambridge University Press, Cambridge, UK

    Google Scholar 

  129. Thompson KC, Jordan MJT, Collins MA (1998) Polyatomic molecular potential energy surfaces by interpolation in local internal coordinates. J Chem Phys 108:8302–8316

    CAS  Google Scholar 

  130. Varandas AJC (2004) Modeling and interpolation of global multi-sheeted potential energy surfaces. In: Domcke W, Yarkony DR, Köppel H (eds), Conical Intersections. World Scientific, Singapore p 205

    Google Scholar 

  131. Huang X, Braams BJ, Bowman JM (2005) Ab initio potential energy and dipole moment surfaces for H5O2 +. J Chem Phys 122:044308

    Google Scholar 

  132. Miller WH, Handy NC, Adams JE (1980) Reaction path hamiltonian for polyatomic molecules. J Chem Phys 72:99

    CAS  Google Scholar 

  133. Ruf BA, Miller WH (1988) A new (cartesian) reaction-path mode for dynamics in polyatomic systems, with application to h-atom transfer in malonaldehyde. J Chem Soc Faraday Trans 84:1523

    CAS  Google Scholar 

  134. Tew D, Handy N, Carter S (2003) A reaction surface hamiltonian study of malonaldehyde. J Chem Phys 125:084313

    Google Scholar 

  135. Lauvergnat D, Nauts A, Justum Y, Chapuisat X (2001) A harmonic adiabatic approximation to calculate highly excited vibrational levels of “floppy molecules”. J Chem Phys 114:6592

    CAS  Google Scholar 

  136. Lauvergnat D, Nauts A (2004) A harmonic adiabatic approximation to calculate vibrational states of ammonia. Chem Phys 305:105

    CAS  Google Scholar 

  137. Gromov EV, Trofimov AB, Gatti F, Köppel H (2010) Theoretical study of photoinduced ring-opening in furan. J Chem Phys 133:164309

    CAS  Google Scholar 

  138. Gromov EV, Leveque C, Gatti F, Burghardt I, Köppel H (2011) Ab initio quantum dynamical study of photoinduced ring-opening in furan. J Chem Phys 135:164305

    CAS  Google Scholar 

  139. Köppel H, Domcke W, Cederbaum LS (1984) Multimode molecular dynamics beyond the Born-Oppenheimer approximation. Adv Chem Phys 57:59

    Google Scholar 

  140. Brocks G, Avoird AVD, Sutcliffe BT, Tennyson J (1983) Mol Phys 50:1025

    CAS  Google Scholar 

  141. Nauts A, Chapuisat X (1985) Momentum, quasi-momentum and hamiltonian operators in terms of arbitrary curvilinear coordinates, with special emphasis on molecular hamiltonians. Mol Phys 55:1287

    CAS  Google Scholar 

  142. Sutcliffe BT, Tennyson J (1986) A generalized approach to the calculation of ro-vibrational spectra of triatomic molecules. Mol Phys 58:1053–1066

    CAS  Google Scholar 

  143. Handy NC (1987) The derivation of vibration-rotation kinetic energy operators, in internal coordinates. Mol Phys 61:207

    CAS  Google Scholar 

  144. Lauvergnat D, Nauts A (2002) Exact numerical computation of a kinetic energy operator in curvilinear coordinates. J Chem Phys 116:8560

    CAS  Google Scholar 

  145. Ndong M, Joubert Doriol L, Meyer H-D, Nauts A, Gatti F, Lauvergnat D (2012) Automatic computer procedure for generating exact and analytical kinetic energy operators based on the polyspherical approach. J Chem Phys 136:034107

    Google Scholar 

  146. Gatti F, Iung C, Menou M, Justum Y, Nauts A, Chapuisat X (1998) Vector parametrization of the n-atom problem in quantum mechanics. I. Jacobi vectors. J Chem Phys 108:8804

    CAS  Google Scholar 

  147. Gatti F, Iung C (2009) Exact and constrained kinetic energy operators for polyatomic molecules: The polyspherical approach. Phys Rep 484:1–69

    CAS  Google Scholar 

  148. Yu H-G (2004) Full-dimensional quantum calculations of vibrational spectra of six-atom molecules. i. theory and numerical results. J Chem Phys 120:2270

    Google Scholar 

  149. Vendrell O, Gatti F, Meyer H-D. Dynamics and infrared spectroscopy of the protonated water dimer. Angew Chem Int Ed 46:6918–6921

    Google Scholar 

  150. Vendrell O, Gatti F, Meyer H-D. Strong isotope effects in the infrared spectrum of the zundel cation. Angew Chem Int Ed 48:352–355

    Google Scholar 

  151. Raab A, Worth G, Meyer H-D, Cederbaum LS. Molecular dynamics of pyrazine after excitation to the S2 electronic state using a realistic 24-mode model Hamiltonian. J Chem Phys 110:936–946

    Google Scholar 

  152. Hammer T, Manthe U (2011) Intramolecular proton transfer in malonaldehyde: Accurate multilayer multi-configurational time-dependent Hartree calculations. J Chem Phys 134:224305

    Google Scholar 

  153. Huarte-Larrañaga F, Manthe U (2000) Full dimensional quantum calculations of the CH4 + H → CH3 + H2 reaction rate. J Chem Phys 113:5115

    Google Scholar 

  154. Makri N (2008) Equilibrium and dynamical path integral methods in bacterial photosynthesis. In: Aartsma TJ, Matysik J (eds) Biophysical techniques in photosynthesis. Series advances in photosynthesis and respiration, vol 2. Springer, Dordrecht

    Google Scholar 

  155. Polyansky OL, Zobob NF, Viti S, Tennyson J, Bernath PF, Wallace L (1997) Water on the sun. Science 277:346

    CAS  Google Scholar 

  156. Callegari A, Theulé P, Muenter JS, Tolchenov RN, Zobov NF, Polyansky OL, Tennyson J, Rizzo TR (2002) Dipole moments of higly vibrationnally excited water. Science 297:993

    CAS  Google Scholar 

  157. Polyansky OL, Cászár AG, Shririn SV, Zobob NF, Barletta P, Tennyson J, Schenke DW, Knowles PJ (2003) High-accuracy ab initio rotation-vibration transitions for water. Science 299:539

    CAS  Google Scholar 

  158. Ndengué SA, Gatti F, Schinke R, Meyer H-D, Jost R (2010) Absorption cross section of ozone Isotopologues calculated with the multiconfiguration time-dependent Hartree (MCTDH) method: I. The Hartley and Huggins bands. J Phys Chem A 114:9855–9863

    Google Scholar 

  159. Ndengué SA, Schinke R, Gatti F, Meyer H-D, Jost R (2012) Comparison of the Huggins band for six ozone isotopologues: vibrational levels and Absorption Cross Section. J Phys Chem A 116:12260

    Google Scholar 

  160. Ndengué SA, Schinke R, Gatti F, Meyer H-D, Jost R (2012) Ozone photodissociation: isotopic and electronic branching ratios for asymmetric isotopologues. J Phys Chem A 116:12271

    Google Scholar 

  161. Schinke R (2011) Photodissociation of N2O: Potential energy surfaces and absorption spectrum. J Chem Phys 134:064313

    CAS  Google Scholar 

  162. Gatti F, Iung C, Leforestier C, Chapuisat X (1999) Fully coupled 6D calculations of the ammonia vibration-inversion-tunneling states with a split hamiltonian pseudospectral approach. J Chem Phys 111:7236–7243

    CAS  Google Scholar 

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Acknowledgments

We acknowledge X.M. Yang (DICP), H. Guo (UNM), D.Q. Xie (NJU), M. Alexander (UM), Soo-Y. Lee for helpful discussion and cooperated work. Funding supports from Chinese Academy of Sciences and NSFS (Grant No. 21222308, 21103187, 21133006) are acknowledged.

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Correspondence to Zhigang Sun or Dong-H. Zhang .

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Sun, Z., Zhao, B., Liu, S., Zhang, DH. (2014). Reactive Scattering and Resonance. In: Gatti, F. (eds) Molecular Quantum Dynamics. Physical Chemistry in Action. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45290-1_4

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