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Theoretical Chemistry Accounts

, Volume 116, Issue 1–3, pp 60–74 | Cite as

Novel perspectives in quantum dynamics

  • Fabien GattiEmail author
Regular Article

Abstract

In the field of theoretical chemistry, we focus on the sub-discipline of quantum dynamics. Special emphasis is placed on novel methods which can provide predictions for medium-sized and large systems and on the difficulties encountered when facing the huge dimension of the primitive basis within a quantum mechanical framework. We try to highlight the possibilities of applications of these methods to atmospheric or astrophysical spectroscopy and organic chemistry and to bring out general perspectives, in particular via comparisons with the electronic structure theory.

Keywords

Potential Energy Surface Chem Phys Quantum Dynamic Conical Intersection HONO 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Schinke R (1993) Photodissociation dynamics. Cambridge University Press, CambridgeGoogle Scholar
  2. 2.
    Wyatt RE, Zhang JZH (eds) (1996) Dynamics of molecules and chemical reactions. Marcel Dekker, New YorkGoogle Scholar
  3. 3.
    Chergui M (eds) (1996) Femtochemistry. World Scientific, SingaporeGoogle Scholar
  4. 4.
    Zewail AH (1994) Femtochemistry – ultrafast dynamics of the chemical bond. World Scientific, SingaporeGoogle Scholar
  5. 5.
    Ihee H, Lobastov V, Gomez U, Goodson B, Srinivasan R, Ruan C-Y, Zewail AH (2001). Science 291:385Google Scholar
  6. 6.
    Saykally RJ, Blake GA (1993). Science 259:1570Google Scholar
  7. 7.
    Fellers RS, Braly LB, Saykally RJ, Leforestier C (1999). Science 284:6306CrossRefGoogle Scholar
  8. 8.
    Boyarkin O, Kowalszyk M, Rizzo T (2003). J Chem Phys 118:93CrossRefGoogle Scholar
  9. 9.
    Romanini D, Campargue A (1996). Chem Phys Lett 254:52CrossRefGoogle Scholar
  10. 10.
    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
  11. 11.
    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 35:341CrossRefPubMedGoogle Scholar
  12. 12.
    Truhlar DG, Gao J, Alhambra C, Garcia-Viloca M, Alhambra C, 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
  13. 13.
    Frisch MJ, Trucks GW, Schlegel HB, Gill PMW, Johnson BG, Robb MA, Cheeseman JR, Keith T, Petersson GA, Montgomery JA, Raghavachari K, Al-Laham MA, Zakrzewski VG, Ortiz JV, Foresman JB, Cioslowski J, Stefanov BB, Nanayakkara A, Challacombe M, Peng CY, Ayala PY, Chen W, Wong MW, Andres JL, Replogle ES, Gomperts R, Martin RL, Fox DJ, Binkley JS, Defrees DJ, Baker J, Stewart JP, Head-Gordon M, Gonzalez C, Pople JA (1995) GAUSSIAN 94, revision C.2Google Scholar
  14. 14.
    Werner H-J, Knowles PJ MOLPRO is a package of ab initio programs. Further information can be obtained from http://www.tc.bham.ac.uk/molproGoogle Scholar
  15. 15.
    Miller WH (1975). J Chem Phys 62:1899CrossRefGoogle Scholar
  16. 16.
    Heller EJ (1975) Time-dependent approach to semiclassical dynamics. J Chem Phys 62:1544CrossRefGoogle Scholar
  17. 17.
    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 112:10282–10292CrossRefGoogle Scholar
  18. 18.
    Miller WH (2001). J Phys Chem 105:2942CrossRefGoogle Scholar
  19. 19.
    Billing GD, Balakrishnan N, Marković N (1996) Application of semiclassical dynamics to chemical reactions. In: Wyatt RE, Zhang JZH (eds) Dynamics of molecules and chemical reactions. Marcel Dekker, New York, pp 531–560Google Scholar
  20. 20.
    Tully JC (1998) Mixed quantum–classical dynamics. Farad Discuss 110:407–419CrossRefGoogle Scholar
  21. 21.
    Köppel H, Domcke W, Cederbaum LS (1984) Multimode molecular dynamics beyond the Born-Oppenheimer approximation. Adv Chem Phys 57:59Google Scholar
  22. 22.
    Sidis V (1992). Adv Chem Phys 82:73Google Scholar
  23. 23.
    Cederbaum LS (2004) Born-oppenheimer approximation and beyond. In: Domcke W, Yarkony DR, Köppel H (eds) Conical intersections. World Scientific, Singapore, pp 3–40Google Scholar
  24. 24.
    Köppel H (2004) Diabatic representation: methods for the construction of diabatic states. In: Domcke W, Yarkony DR, Köppel H (eds) Conical intersections. World Scientific, Singapore, pp 175–204Google Scholar
  25. 25.
    Neuhauser D (1990) Bound state eigenfunctions from wave packets: Time → energy resolution. J Chem Phys 93:2611CrossRefGoogle Scholar
  26. 26.
    Mandelshtam VA, Taylor HS (1998) Multidimensional harmonic inversion by filter-diagonalization. J Chem Phys 108:9970CrossRefGoogle Scholar
  27. 27.
    Narevicius E, Neuhauser D, Korsch HJ, Moiseyev N (1997) Resonances from short time complex-scaled cross-correlation probability amplitudes by the filter-diagonalization method. Chem Phys Lett 276:250CrossRefGoogle Scholar
  28. 28.
    Beck MH, Meyer H-D (1998) Extracting accurate bound-state spectra from approximate wave packet propagation using the filter-diagonalization method. J Chem Phys 109:3730–3741CrossRefGoogle Scholar
  29. 29.
    Gatti F, Beck MH, Worth GA, Meyer H-D (2001) A hybrid approach of the multi-configuration time-dependent Hartree and filter-diagonalisation methods for computing bound-state spectra. Application to HO2. PCCP 3:1576–1582Google Scholar
  30. 30.
    Chakraborty A, Truhlar DG (2005). Proc Nat Acad Sci USA 102:6744CrossRefPubMedGoogle Scholar
  31. 31.
    Routberg A, Gerber RB, Elber R, Ratner MA (1995). Science 268:1319PubMedGoogle Scholar
  32. 32.
    Li ZM, Gerber RB (1995). Chem Phys Lett 243:257CrossRefGoogle Scholar
  33. 33.
    Jung JO, Gerber RB (1996). J Chem Phys 105:10682CrossRefGoogle Scholar
  34. 34.
    Bihary Z, Gerber RB, Apkarian VA (2001) Vibrational self-consistent field approach to anharmonic spectroscopy of molecules in solids: application to iodine in argon matrix. J Chem Phys 115:2695CrossRefGoogle Scholar
  35. 35.
    Bowman JM (1986). Acc Chem Res 19:202CrossRefGoogle Scholar
  36. 36.
    Carter S, Culik SJ, Bowman JM (1997) Vibrational self-consistent field method for many-mode systems: a new approach and application to the vibrations of co adsorbed on cu(100). J Chem Phys 107:10458CrossRefGoogle Scholar
  37. 37.
    Chakraborty A, Truhlar DG, Bowman JM, Carter S (2004). J Chem Phys 121:2071CrossRefPubMedGoogle Scholar
  38. 38.
    Bowman JM (2000). Science 290:724CrossRefPubMedGoogle Scholar
  39. 39.
    Wilson E, Decius J, Cross P (1955) Molecular vibrations. McGraw-Hill, New YorkGoogle Scholar
  40. 40.
    Culot F, Liévin J (1994). J Theor Chim Acta 89:227CrossRefGoogle Scholar
  41. 41.
    Culot F, Laruelle F, Liévin J (1995). J Theor Chim Acta 92:211Google Scholar
  42. 42.
    Bačić Z, Light JC (1986) Highly excited vibrational levels of “floppy” triatomic molecules: a discrete variable representation – distributed Gaussian approach. J Chem Phys 85:4594CrossRefGoogle Scholar
  43. 43.
    Qiu Y, Bačić Z (1997). J Chem Phys 106:2158CrossRefGoogle Scholar
  44. 44.
    Lanczos C (1950) An iterative method for the solution of the eigenvalue problem of linear differential and integral operators. J Res Natl Bur Stand 45:255Google Scholar
  45. 45.
    Köppel H, Cederbaum LS, Domcke W (1982). J Chem Phys 77:2014CrossRefGoogle Scholar
  46. 46.
    Nauts A, Wyatt RE (1983). Phys Rev Lett 51:2238CrossRefGoogle Scholar
  47. 47.
    Huang S-W, Carrington T Jr (1999) A comparison of filter diagonalisation methods with the Lanczos method for calculating vibrational energy levels. Chem Phys Lett 312:311CrossRefGoogle Scholar
  48. 48.
    Davidson E (1975). J Comp Phys 17:87CrossRefGoogle Scholar
  49. 49.
    Ribeiro F, Iung C, Leforestier C (2002). Chem Phys Lett 362:199CrossRefGoogle Scholar
  50. 50.
    Feit MD, Fleck JA Jr, Steiger A (1982) Solution of the Schrödinger equation by a spectral method. J Comp Phys 47:412–433CrossRefGoogle Scholar
  51. 51.
    Kosloff R, Kosloff D (1983). J Chem Phys 79:1823CrossRefGoogle Scholar
  52. 52.
    Light JC, Hamilton IP, Lill JV (1985) Generalized discrete variable approximation in quantum mechanics. J Chem Phys 82:1400CrossRefGoogle Scholar
  53. 53.
    Corey GC, Lemoine D (1992) Pseudospectral method for solving the time-dependent Schrödinger equation in spherical coordinates. J Chem Phys 97:4115CrossRefGoogle Scholar
  54. 54.
    Bramley MJ, Tromp JW, Carrington T, Corey RC (1994). J Chem Phys 100:6175CrossRefGoogle Scholar
  55. 55.
    Leforestier C (1994). J Chem Phys 101:7357CrossRefGoogle Scholar
  56. 56.
    Leforestier C, Braly LB, Liu K, Matthew MJ, Saykally RJ (1997) Fully coupled six-dimensional calculations of the water dimer vibration-rotation-tunneling states with a split wigner pseudo spectral approach. J Chem Phys 106:8527CrossRefGoogle Scholar
  57. 57.
    Harris DO, Engerholm GG, Gwinn GW (1965) Calculation of matrix elements for one-dimensional quantum-mechanical problems and the application to anharmonic oscillators. J Chem Phys 43:1515CrossRefGoogle Scholar
  58. 58.
    Wei H, Carrington T (1992). J Chem Phys 97:3029CrossRefGoogle Scholar
  59. 59.
    Echave J, Clary DC (1994) Quantum theory of planar four-atom reactions. J Chem Phys 100:402CrossRefGoogle Scholar
  60. 60.
    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 111:7236–7243CrossRefGoogle Scholar
  61. 61.
    Leforestier C, Viel A, Gatti F, Munoz C, Iung C (2001) The Jacobi-Wilson method: a new approach to the description of polyatomic molecules. J Chem Phys 114:2099CrossRefGoogle Scholar
  62. 62.
    Yu H-G (2002). J Chem Phys 117:2030CrossRefGoogle Scholar
  63. 63.
    Wang X, Carrington T (2003). J Chem Phys 118:6946CrossRefGoogle Scholar
  64. 64.
    Yu H-G (2004). J Chem Phys 120:2270CrossRefPubMedGoogle Scholar
  65. 65.
    McCoy AB, Sibert EL (1996) Canonical van vleck perturbation theory and its application to studies of higly vibrationally excited states of polyatomic molecules. In: Wyatt RE, Zhang JZH (eds) Dynamics of molecules and chemical reactions. Marcel Dekker, New York, pp 151–184Google Scholar
  66. 66.
    Ramesh SG, Sibert EL (2004). J Chem Phys 120:11011CrossRefPubMedGoogle Scholar
  67. 67.
    Castillo-Chará J, Sibert EL (2003). J Chem Phys 119:11671CrossRefGoogle Scholar
  68. 68.
    Bloch C (1958). Nucl Phys 6:329CrossRefGoogle Scholar
  69. 69.
    Durand P, Malrieu JP (1987) Ab initio methods in quantum chemistry. In: Lawley KP (ed) Wiley, New YorkGoogle Scholar
  70. 70.
    Wyatt RE, Iung C (1996) Quantum mechanical studies of molecular sepctra and dynamics. In: Wyatt RE, Zhang JZH (eds) Dynamics of molecules and chemical reactions. Marcel Dekker, New York, pp 59–122Google Scholar
  71. 71.
    Wyatt RE, Iung C, Leforestier C (1992) Quantum dynamics of overtone relaxation in benzene. I. 5 and 9 modes models for relaxation from CH(ν=3). J Chem Phys 97:3458CrossRefGoogle Scholar
  72. 72.
    Wyatt RE, Iung C, Leforestier C (1992) Quantum dynamics of overtone relaxation in benzene. II. 16 mode models for relaxation from CH(ν=3). J Chem Phys 97:3477CrossRefGoogle Scholar
  73. 73.
    Iung C, Leforestier C, Wyatt RE (1993). J Chem Phys 98:6722CrossRefGoogle Scholar
  74. 74.
    Wyatt RE, Iung C (1993) Quantum dynamics of overtone relaxation in benzene. V. CH(ν=3) dynamics computed with a new ab initio force field. J Chem Phys 98:6758CrossRefGoogle Scholar
  75. 75.
    Wyatt RE, Iung C(1994). J Chem Phys 101:3671CrossRefGoogle Scholar
  76. 76.
    Iung C, Wyatt RE (1993) Time-dependent quantum mechanical study of intramolecular vibrational energy redistribution in benzene. J Chem Phys 99:2261–2264CrossRefGoogle Scholar
  77. 77.
    Wyatt RE, Iung C, Leforestier C (1995). Acc Chem Res 28:423CrossRefGoogle Scholar
  78. 78.
    Maynard A, Wyatt RE, Iung C (1997) A quantum dynamical study of CH overtones in fluoroform. II. Eigenstate analysis of the v(CH) = 1 and v(CH) = 2 regions. J Chem Phys 106:9483CrossRefGoogle Scholar
  79. 79.
    Minehardt TJ, Wyatt RE (1998) Quasiclassical dynamics of benzene overtone relaxation on an ab initio force field. I. Energy flow and survival probabilities in planar benzene for CH(v = 2,3). J Chem Phys 109:8330CrossRefGoogle Scholar
  80. 80.
    Iung C, Leforestier C (1995). J Chem Phys 102:8453CrossRefGoogle Scholar
  81. 81.
    Leforestier C, Bisseling RH, Cerjan C, Feit MD, Friesner R, Guldenberg A, Hammerich A, Jolicard G, Karrlein W, Meyer H-D, Lipkin N, Roncero O, Kosloff R (1991) A comparison of different propagation schemes for the time dependent Schrödinger equation. J Comp Phys 94:59CrossRefGoogle Scholar
  82. 82.
    Worth GA, Beck MH, Jäckle A, Meyer H-D (2002) The MCTDH Package, Version 8.2, (2000). Meyer H-D, Version 8.3 (2002). See http://www.pci.uni-heidelberg.de/tc/usr/mctdh/Google Scholar
  83. 83.
    Meyer H-D, Manthe U, Cederbaum LS (1990) The multi-configurational time-dependent Hartree approach. Chem Phys Lett 165:73–78CrossRefGoogle Scholar
  84. 84.
    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
  85. 85.
    Beck MH, Jäckle A, Worth GA, Meyer H-D (2000) The multiconfiguration time-dependent Hartree method: a highly efficient algorithm for propagating wavepackets. Phys Rep 324:1–105CrossRefGoogle Scholar
  86. 86.
    Meyer H-D, Worth GA (2003) Quantum molecular dynamics: Propagating wavepackets and density operators using the multiconfiguration time-dependent Hartree (MCTDH) method. Theor Chem Acc 109:251–267CrossRefGoogle Scholar
  87. 87.
    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
  88. 88.
    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 153:483CrossRefGoogle Scholar
  89. 89.
    Moiseyev N, Schatzberger R, Froelich P, Goscinski O (1985). J Chem Phys 83:3924CrossRefGoogle Scholar
  90. 90.
    Moiseyev N, Brown RC, Wyatt RE (1986). Chem Phys Lett 127:37CrossRefGoogle Scholar
  91. 91.
    Worth GA, Meyer H-D, Cederbaum LS (1996) The effect of a model environment on the S2 absorption spectrum of pyrazine: a wavepacket study treating all 24 vibrational modes. J Chem Phys 105:4412CrossRefGoogle Scholar
  92. 92.
    Worth GA, Meyer H-D, Cederbaum LS (1998) Relaxation of a system with a conical intersection coupled to a bath: a benchmark 24-dimensional wavepacket study treating the environment explicitly. J Chem Phys 109:3518–3529CrossRefGoogle Scholar
  93. 93.
    Raab A, Worth G, Meyer H-D, Cederbaum LS (1999) Molecular dynamics of pyrazine after excitation to the S2 electronic state using a realistic 24-mode model Hamiltonian. J Chem Phys 110:936–946CrossRefGoogle Scholar
  94. 94.
    Worth GA (2000) Accurate wave packet propagation for large molecular systems: The multi-configuration time-dependent Hartree (MCTDH) method with selected configurations. J Chem Phys 112:8322–8329CrossRefGoogle Scholar
  95. 95.
    Wang H, Thoss M (2003) Multilayer formulation of the multiconfiguration time-dependent Hartree theory. J Chem Phys 119:1289CrossRefGoogle Scholar
  96. 96.
    Nest M, Meyer H-D (2002) Benchmark calculations on high-dimensional Henon-Heiles potentials with the Multi-Configuration Time-Dependent Hartree (MCTDH) Method. J Chem Phys 117:10499–10505CrossRefGoogle Scholar
  97. 97.
    Hammerich AD, Manthe U, Kosloff R, Meyer H-D, Cederbaum LS (1994) Time-dependent photodissociation of methyl iodide with five active modes. J Chem Phys 101:5623CrossRefGoogle Scholar
  98. 98.
    Liu L, Fang J-Y, Guo H (1995) How many configurations are needed in a time-dependent Hartree treatment of the photodissociation of ICN?. J Chem Phys 102:2404CrossRefGoogle Scholar
  99. 99.
    Trin J, Monerville M, Pouilly B, Meyer H-D (2003) Photodissociation of the ArHBr complex investigated with the Multi–Configuration Time–Dependent Hartree (MCTDH) approach. J Chem Phys 118:600–609CrossRefGoogle Scholar
  100. 100.
    Pouilly B, Monnerville M, Gatti F, Meyer H-D (2005). J Chem Phys 122:1843–13CrossRefGoogle Scholar
  101. 101.
    Fang J-Y, Guo H (1994) Multiconfiguration time-dependent Hartree studies of the CH3I/MgO photodissociation dynamics. J Chem Phys 101:5831CrossRefGoogle Scholar
  102. 102.
    Jansen APJ, Burghgraef H (1995) MCTDH study of CH4 dissociation on Ni (111). Surf Sci 344:149CrossRefGoogle Scholar
  103. 103.
    Gromov EV, Trofimov AB, Vitkovskaya NM, Köppel H, Schirmer J, Meyer H-D, Cederbaum LS (2004) Theoretical study of excitations in furan: Spectra and molecular dynamics. J Chem Phys 121:4585CrossRefPubMedGoogle Scholar
  104. 104.
    Fang J-Y, Guo H (1995) Multiconfiguration time-dependent Hartree studies of the Cl2Ne vibrational predissociation dynamics. J Chem Phys 102:1944CrossRefGoogle Scholar
  105. 105.
    Cattarius C, Worth GA, Meyer H-D, Cederbaum LS (2001) All mode dynamics at the conical intersection of an octa-atomic molecule: multi-configuration time-dependent Hartree (MCTDH) investigation on the butatriene cation. J Chem Phys 115:2088–2100CrossRefGoogle Scholar
  106. 106.
    Köppel H, Döscher M, Baldea I, Meyer H-D, Szalay PG (2002) Multistate vibronic interactions in the benzene radical cation. II. Quantum dynamical simulations. J Chem Phys 117:2657–2671CrossRefGoogle Scholar
  107. 107.
    Gerdts T, Manthe U (1997) The resonance Raman spectrum of CH3I: an application of the MCTDH approach. J Chem Phys 107:6584CrossRefGoogle Scholar
  108. 108.
    Jäckle A, Meyer H-D (1995) Reactive scattering using the multiconfiguration time-dependent Hartree approximation: General aspects and application to the collinear H+H2 → H2+H reaction. J Chem Phys 102:5605CrossRefGoogle Scholar
  109. 109.
    Sukiasyan S, Meyer H-D (2001) On the effect of initial rotation on reactivity. A multi-configuration time-dependent Hartree (MCTDH) wave-packet propagation study on the H+D2 and D+H2 reactive scattering systems. J Phys Chem A 105:2604–2611Google Scholar
  110. 110.
    Sukiasyan S, Meyer H-D (2002) Reaction cross section for the H+D20=1) → HD+D and D+H20=1) → DH+H systems. A multi-configuration time-dependent Hartree (MCTDH) wave-packet propagation study. J Chem Phys 116:10641–10647Google Scholar
  111. 111.
    Ehara M, Meyer H-D, Cederbaum LS (1996) Multiconfiguration time-dependent Hartree (MCTDH) study on the rotational and diffractive inelastic molecule-surface scattering. J Chem Phys 105:8865CrossRefGoogle Scholar
  112. 112.
    Heitz M-C, Meyer H-D (2001) Rotational and diffractive inelastic scattering of a diatom on a corrugated surface: A multiconfiguration time-dependent Hartree (MCTDH) study on N2/LiF(001). J Chem Phys 114:1382–1392CrossRefGoogle Scholar
  113. 113.
    van Harrevelt R, Manthe U (2004) Degeneracy in discrete variable representations: General considerations and applications to the multiconfigurational time-dependent hartree approach. J Chem Phys 121:5623CrossRefPubMedGoogle Scholar
  114. 114.
    Milot R, Jansen APJ (2000) Energy distribution analysis of the wavepacket simulations of CH4 and CD4 scattering. Surf Sci 452:179CrossRefGoogle Scholar
  115. 115.
    Manthe U, Matzkies F (1996) Iterative diagonalization within the multi-configurational time-dependent Hartree approach: Calculation of vibrationally excited states and reaction rates. Chem Phys Lett 252:71CrossRefGoogle Scholar
  116. 116.
    Huarte-Larrañaga F, Manthe U (2002) Vibrational excitation in the transition state: The CH4+H → CH3+H2 reaction rate constant in an extended temperature interval. J Chem Phys 116:2863CrossRefGoogle Scholar
  117. 117.
    Huarte-Larrañaga F, Manthe U (2002) Accurate quantum dynamics of a combustion reaction: Thermal rate constants of O(3P) + CH4(X1A1) → OH(X2Π) + CH3(X2 A2''). J Chem Phys 117:4635CrossRefGoogle Scholar
  118. 118.
    Lasorne B, Gatti F, Baloitcha E, Meyer H-D, Desouter-Lecomte M (2004) Cumulative isomerization probability studied by various transition state wave packet methods including the mctdh algorithm. benchmark: HCN → CNH. J Chem Phys 121:644–654CrossRefPubMedGoogle Scholar
  119. 119.
    Worth G, Cederbaum L (2001) Electron transfer along a conjugated chain: the allene radical cation. Chem Phys Lett 348:477–482CrossRefGoogle Scholar
  120. 120.
    Rescigno TN, Isaacs WA, Orel AE, Meyer H-D, McCurdy CW (2002) Theoretical study of resonant excitation of CO2 by electron impact. Phys Rev A 65:32716CrossRefGoogle Scholar
  121. 121.
    Nauendorf H, Worth G, Meyer H-D, Kühn O (2002) Multi-configuration time-dependent Hartree dynamics on an ab initio reaction surface: Ultrafast laser -driven proton motion in Phthalic Acid Monomethylester. J Phys Chem 106:719–724Google Scholar
  122. 122.
    Beck MH, Meyer H-D (2001) Efficiently computing bound-state spectra: a hybrid approach of the multi-configuration time- dependent Hartree and filter-diagonalization methods. J Chem Phys 114:2036–2046CrossRefGoogle Scholar
  123. 123.
    Leforestier C, Wyatt RE (1983) Optical potential for laser induced dissociation. J Chem Phys 78:2334CrossRefGoogle Scholar
  124. 124.
    Riss UV, Meyer H-D (1993) Calculation of resonance energies and widths using the complex absorbing potential method. J Phys B 26:4503CrossRefGoogle Scholar
  125. 125.
    Riss UV, Meyer H-D (1995) Reflection-free complex absorbing potentials. J Phys B 28:1475CrossRefGoogle Scholar
  126. 126.
    Riss UV, Meyer H-D (1996) Investigation on the reflection and transmission properties of complex absorbing potentials. J Chem Phys 105:1409CrossRefGoogle Scholar
  127. 127.
    Moiseyev N (1998). Phys Rep 302:211CrossRefGoogle Scholar
  128. 128.
    Richter F, Hochlaf M, Rosmus P, Gatti F, Meyer H-D (2004) A study of mode–selective trans–cis isomerisation in HONO using ab initio methodology. J Chem Phys 120:1306–1317CrossRefPubMedGoogle Scholar
  129. 129.
    Richter F, Rosmus P, Gatti F, Meyer H-D (2004) Time-dependent wavepacket study on trans–cis isomerisation of HONO. J Chem Phys 120:6072–6084CrossRefPubMedGoogle Scholar
  130. 130.
    Gatti F, Meyer H-D (2004) Intramolecular vibrational energy redistribution in Toluene: a nine dimensional quantum mechanical study using the MCTDH algorithm. Chem Phys 304:3–15CrossRefGoogle Scholar
  131. 131.
    Iung C, Gatti F, Meyer H-D (2004) Intramolecular vibrational energy redistribution in the highly excited Fluoroform molecule: a quantum mechanical study using the MCTDH algorithm. J Chem Phys 120:6992–6998CrossRefPubMedGoogle Scholar
  132. 132.
    Feynman RP (1948). Rev Mod Phys 20:367CrossRefGoogle Scholar
  133. 133.
    Feynman RP, Hibbs AR (1965) Quantum mechanics and path integrals. McGraw-Hill, New YorkGoogle Scholar
  134. 134.
    Feynman RP (1972) Statistical mechanics. W. A. Benjamin Inc., Reading MassachusettsGoogle Scholar
  135. 135.
    Makri N (1991). Computer Phys Comm 63:389CrossRefGoogle Scholar
  136. 136.
    Shao J, Makri N (2002). J Chem Phys 116:507CrossRefGoogle Scholar
  137. 137.
    Topaler M, Makri N (1992). J Chem Phys 97:9001CrossRefGoogle Scholar
  138. 138.
    Makarov DE, Makri N (1994). Chem Phys Lett 221:482CrossRefGoogle Scholar
  139. 139.
    Makri N, Makarov DE (1995). J Chem Phys 102:4611CrossRefGoogle Scholar
  140. 140.
    Makri N (1997) Path integral simulation of long-time dynamics in quantum dissipative systems. In: De Witt-Morette (eds) Functional integration: basics and applications. Plenum, New York, pp 193–211Google Scholar
  141. 141.
    Makri N (1998). J Phys Chem 102:4414Google Scholar
  142. 142.
    Nakayama A, Makri N (2003). J Chem Phys 119:8592CrossRefGoogle Scholar
  143. 143.
    Wright NJ, Makri N (2004). J Phys Chem B 108:6816CrossRefGoogle Scholar
  144. 144.
    Doll JD, Freeman DL, Beck TL (1990). Adv Chem Phys 78:61Google Scholar
  145. 145.
    Winterstetter M, Domcke W (1995). Chem Phys Lett 236:445CrossRefGoogle Scholar
  146. 146.
    Mielke SL, Truhlar DG (2003) A ‘path-by-path’ monotone extrapolation sequence for feynman path integral calculations of quantum mechanical free energy. Chem Phys Lett 378:317CrossRefGoogle Scholar
  147. 147.
    Lynch VA, Mielke SL, Truhlar DG (2004). J Chem Phys 121:5148CrossRefPubMedGoogle Scholar
  148. 148.
    Jang S, Voth GA (1999). J Chem Phys 111:2357CrossRefGoogle Scholar
  149. 149.
    Cao J, Voth GA (1993). J Chem Phys 99:10070CrossRefGoogle Scholar
  150. 150.
    Cao J, Voth GA (1994). J Chem Phys 100:5106CrossRefGoogle Scholar
  151. 151.
    Cao J, Voth GA (1994). J Chem Phys 101:6168CrossRefGoogle Scholar
  152. 152.
    Lobaugh J, Voth GA (1996). J Chem Phys 104:2056CrossRefGoogle Scholar
  153. 153.
    Lobaugh J, Voth GA (1997). J Chem Phys 106:2400CrossRefGoogle Scholar
  154. 154.
    Sibert EL (1989). J Chem Phys 90:2672CrossRefGoogle Scholar
  155. 155.
    Podolsky B (1928). Phys Rev 32:812CrossRefGoogle Scholar
  156. 156.
    Nauts A, Chapuisat X (1985). Mol Phys 55:1287Google Scholar
  157. 157.
    Sutcliffe BT, Tennyson J (1986). Mol Phys 58:1053Google Scholar
  158. 158.
    Chapuisat X, Nauts A, Brunet J-P (1991). Mol Phys 72:1Google Scholar
  159. 159.
    Bramley MJ, Handy NC (1993). J Chem Phys 98:1378CrossRefGoogle Scholar
  160. 160.
    Wolfram S (1991) Mathematica, a system for doing mathematics by computer 2nd ed. Addison-Wesley, Reading, Mass, USAGoogle Scholar
  161. 161.
    Menou M, Chapuisat X (1993). J Mol Spec 300:300CrossRefGoogle Scholar
  162. 162.
    Lauvergnat D, Nauts A (2002). J Chem Phys 116:8560CrossRefGoogle Scholar
  163. 163.
    Chapuisat X, Iung C (1992). Phys Rev A 45:6217CrossRefPubMedGoogle Scholar
  164. 164.
    Gatti F, Justum Y, Menou M, Nauts A, Chapuisat X (1997). Quantum-mechanical description of rigidly or adiabatically constrained molecular systems. J Mol Spec 373:403CrossRefGoogle Scholar
  165. 165.
    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 108:8821CrossRefGoogle Scholar
  166. 166.
    Gatti F, Iung C, Menou M, Chapuisat X (1998) Vector parametrization of the n-atom problem in quantum mechanics. II. Coupled-angular-momentun spectral representations for four atom systems. J Chem Phys 108:8821CrossRefGoogle Scholar
  167. 167.
    Gatti F (1999) Vector parametrization of the n-atom problem in quantum mechanics. iii separation into two sub-systems. J Chem Phys 111:7225CrossRefGoogle Scholar
  168. 168.
    Iung C, Gatti F, Viel A, Chapuisat X (1999) Vector parametrization of the n-atom problem in quantum mechanics. non-orthogonal coordinates. PCCP 1:3377Google Scholar
  169. 169.
    Mladenović, M (2000) Rovibrational hamiltonians for general polyatomic molecules in spherical polar parametrization. I. Orthogonal representations. J Chem Phys 112:1070–1081CrossRefGoogle Scholar
  170. 170.
    Gatti F, Munoz C, Iung C (2001) A general expression of the exact kinetic energy operator in polyspherical coordinates. J Chem Phys 114:8275Google Scholar
  171. 171.
    Gatti F, Nauts A (2003) Vector parametrization, partial angular momenta and unusual commutation relations in molecular physics. Chem Phys 295:167–174CrossRefGoogle Scholar
  172. 172.
    Gatti F, Iung C (2003) Exact and constrained kinetic energy operators in polyspherical coordinates. J Theor Comp Chem 2:507–522CrossRefGoogle Scholar
  173. 173.
    Iung C, Gatti F, Ortiz J-M, Meyer H-D (2004) in preparationGoogle Scholar
  174. 174.
    Yu H-G, Muckerman JT (2002). J Mol Spec 214:11Google Scholar
  175. 175.
    Yu H-G (2002). J Chem Phys 117:8190CrossRefGoogle Scholar
  176. 176.
    Costa LS, Clary DC (2002). J Chem Phys 117:7512CrossRefGoogle Scholar
  177. 177.
    Goldfield EM, Gray SK (2002) A quantum dynamics study of H2+OH→H2O+H employing Wu-Schatz-Lendvay-Fang- Harding potential function and a four-atom implementation of the real wave packet method. J Chem Phys 117:1604Google Scholar
  178. 178.
    Lin SY, Guo H (2002). J Chem Phys 117:5183CrossRefGoogle Scholar
  179. 179.
    Frederick JH, Woywod C (1999). J Chem Phys 111:7255CrossRefGoogle Scholar
  180. 180.
    van der Avoird A, Wormer PES, Moszynski R (1994). Chem Rev 94:1931CrossRefGoogle Scholar
  181. 181.
    Gatti F (2003) Flexible monomer formulation for non-rigid systems. Chem Phys Lett 373:146–152CrossRefGoogle Scholar
  182. 182.
    Nauts A, Chapuisat X (1987). Chem Phys Lett 136:164Google Scholar
  183. 183.
    Hadder JE, Frederick JH (1992). J Chem Phys 97:3500CrossRefGoogle Scholar
  184. 184.
    Leforestier C, Gatti F, Fellers RS, Saykally RJ (2002). J Chem Phys 117:8710CrossRefGoogle Scholar
  185. 185.
    Thompson KC, Jordan MJT, Collins MA (1998) Polyatomic molecular potential energy surfaces by interpolation in local internal coordinates. J Chem Phys 108:8302–8316CrossRefGoogle Scholar
  186. 186.
    Crespos C, Collins MA, Pijper E, Kroes GJ (2003). Chem Phys Lett 376:566Google Scholar
  187. 187.
    Crespos C, Collins MA, Pijper E, Kroes GJ (2004). J Chem Phys 120:2392CrossRefPubMedGoogle Scholar
  188. 188.
    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 205Google Scholar
  189. 189.
    Miller WH, Handy NC, Adams JE (1980). J Chem Phys 72:99CrossRefGoogle Scholar
  190. 190.
    Ruf BA, Miller WH (1988). J Chem Soc Faraday Trans 84:1523Google Scholar
  191. 191.
    Seidner L, Stock G, Domcke W (1994). Chem Phys Lett 228:665CrossRefGoogle Scholar
  192. 192.
    Stock G, Domcke W (2004) Femtosecond time-resolved spectroscopy of the dynamics at conical intersections. In: Stock G, Domcke W (eds) Conical Intersections. World Scientific, Singapore, pp 739–801Google Scholar
  193. 193.
    Manthe U (1996) A time-dependent discrete variable representation for (multi-configuration) Hartree methods. J Chem Phys 105:6989Google Scholar
  194. 194.
    van Harrevelt R, Manthe U (2004) Multiconfigurational time-dependent Hartree calculations for dissociative adsorption of H2 on Cu(100). J Chem Phys 121:3829PubMedGoogle Scholar
  195. 195.
    Jäckle A, Meyer H-D (1996) Product representation of potential energy surfaces. J Chem Phys 104:7974Google Scholar
  196. 196.
    Jäckle A, Meyer H-D (1998) Product representation of potential energy surfaces II. J Chem Phys 109:3772CrossRefGoogle Scholar
  197. 197.
    Remacle F, Levine RD (1996) Spectra, rates, and intramolecular dynamics. In: Wyatt RE, Zhang JZH (eds) Dynamics of molecules and chemical reactions. Marcel Dekker, New York, pp 1–58Google Scholar
  198. 198.
    Zewail AH (2001) Femtochemistry. In: De Schryver, FC, De Feyter S, Schweitzer G (ed) Wiley-VCH, New YorkGoogle Scholar
  199. 199.
    Brixner T, Damreuer NH, Niklaus P, Gerber G (2001). Nature 414:57CrossRefPubMedGoogle Scholar
  200. 200.
    Levis RJ, Menkir GM, Rabitz H (2001). Science 292:709CrossRefPubMedGoogle Scholar
  201. 201.
    McDonald PA, Shirk JS (1982) The infrared laser photoisomerization of HONO in solid N2 and Ar. J Chem Phys 77:2355Google Scholar
  202. 202.
    Shirk AE, Shirk JS (1983) Isomerization of HONO in solid nitrogen by selective vibrational excitation. Chem Phys Lett 97:549–552Google Scholar
  203. 203.
    Khriatchev L, Lundell J, Isoniemi E, Räsänen M (2000) HONO in solid Kr: Site-selective transcis isomerization with narrow-band infrared radiation. J Chem Phys 113:4265–4273CrossRefGoogle Scholar
  204. 204.
    Bernstein HJ, Herzberg G (1948). J Phys Chem 16:4765Google Scholar
  205. 205.
    Dubal HR, Quack M (1984). J Chem Phys 81:3779CrossRefGoogle Scholar
  206. 206.
    Segall J, Zare RN, Dubal HR, Lewerentz M, Quack M (1987). J Chem Phys 86:634Google Scholar
  207. 207.
    Quack M, Willeke M (1999). J Chem Phys 110:11958CrossRefGoogle Scholar
  208. 208.
    Gough KM, Henry BR (1984). J Phys Chem 88:1298CrossRefGoogle Scholar
  209. 209.
    Zhu C, Kjaergaard HG, Henry BR (1997). J Chem Phys 107:691Google Scholar
  210. 210.
    Léonard, Chambaud G, Rosmus P, Carter S, Handy NC (2001). PCCP 3:508Google Scholar
  211. 211.
    Lequéré F, Léonard C, Rosmus P, Meyer H-D, Gatti F (2004) (in preparation)Google Scholar
  212. 212.
    Cooper AC, Clot E, Huffman JC, Streib WE, Maseras F, Eisenstein O, Caulton KG (1999). J Am Chem Soc 121:97Google Scholar
  213. 213.
    Clot E, Eisenstein O (2004) Agostic interactions from a computational perspective: one name, many interpretations. In: Kaltsoyannis N, McGrady JE (eds) Principles and applications of density functional theory in inorganic chemistry II. Springer, Berlin Heidelberg New York, pp 2–36Google Scholar
  214. 214.
    Torrent M, Solà M, Frenking G (2000). Chem Rev 100:439–493CrossRefPubMedGoogle Scholar
  215. 215.
    Bittner M, Köppel H (2004). J Phys Chem A 108:11116Google Scholar
  216. 216.
    Garavelli M, Celani P, Bernardi F, Robb MR, Olivucci M (1997). J Am Chem Soc 119:6891Google Scholar
  217. 217.
    Garavelli M, Negri F, Olivucci M (1999). J Am Chem Soc 121:1023Google Scholar
  218. 218.
    Migani A, Robb MA, Olivucci M (2003). J Am Chem Soc 125:2804PubMedGoogle Scholar
  219. 219.
    Worth GA, Cederbaum LS (2001) Mediation of ultrafast electron transfer in biological systems by conical intersections. Chem Phys Lett 338:219–223CrossRefGoogle Scholar
  220. 220.
    Vendrell O, Galabert R, Moreno M, Lluch JM (2004). Chem Phys Lett 396:202Google Scholar
  221. 221.
    Robb MA, Bernardi F, Olivucci M (1985). Pure Appl Chem 67:783Google Scholar
  222. 222.
    Bonacic-Koutecky V, Schoffel K, Michl J (1987). Theor Chem Acc 72:459CrossRefGoogle Scholar
  223. 223.
    Sobolewski AL, Woywod C, Domcke W (1993). J Chem Phys 98:5627Google Scholar
  224. 224.
    Migani A, Sinicropi A, Ferré N, Cembran A, Garavelli M (2004). Faraday Discuss 127:179CrossRefPubMedGoogle Scholar
  225. 225.
    Migani A, Olivucci M (2004) Conical intersections and organic reaction mechanisms. In: Domcke W, Yarkony DR, Köppel H (eds) Conical Intersections. World Scientific, Singapore, p 271Google Scholar
  226. 226.
    Goldman N, Fellers RS, Leforestier C, Saykally RJ (2001). J Phys Chem A 105:515Google Scholar
  227. 227.
    Christiansen O (2004). J Chem Phys 120:2149PubMedGoogle Scholar
  228. 228.
    Jasper AW, Truhlar DG (2005). J Chem Phys 122:044101Google Scholar
  229. 229.
    Burghardt I, Meyer H-D, Cederbaum LS (1999) Approaches to the approximate treatment of complex molecular systems by the multiconfiguration time-dependent Hartree method. J Chem Phys 111:2927–2939Google Scholar
  230. 230.
    Burghardt I, Nest M, Worth GA (2003). J Chem Phys 119:5364CrossRefGoogle Scholar
  231. 231.
    Worth G, Burghardt I (2003) Full quantum mechanical molecular dynamics using Gaussian wavepackets. Chem Phys Lett 368:502–508Google Scholar
  232. 232.
    Worth GA (2001) Quantum dynamics using pseudo-particle trajectories: a new approach based on the multi-configuration time-dependent Hartree method. J Chem Phys 114:1524–1532Google Scholar
  233. 233.
    Wang H, Thoss M, Miller W (2001) Systematic convergence in the dynamical hybrid approach for complex systems: a numerical exact methodology. J Chem Phys 115:2979Google Scholar
  234. 234.
    Thoss M, Wang H, Miller WH (2001) Self-consistent hybrid approach for complex systems: application to the spin-boson model with debye spectral density. J Chem Phys 115:2991Google Scholar

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© Springer-Verlag 2005

Authors and Affiliations

  1. 1.LSDSMS (UMR-CNRS 5636), CC 014Université Montpellier IIMontpellier Cédex 05France

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