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Annual Review of Physical Chemistry

Volume 73, 2022

Calculating Multidimensional Optical Spectra from Classical Trajectories

Abstract

Multidimensional optical spectra are measured from the response of a material system to a sequence of laser pulses and have the capacity to elucidate specific molecular interactions and dynamics whose influences are absent or obscured in a conventional linear absorption spectrum. Interpretation of complex spectra is supported by theoretical modeling of the spectroscopic observable, requiring implementation of quantum dynamics for coupled electrons and nuclei. Performing numerically correct quantum dynamics in this context may pose computational challenges, particularly in the condensed phase. Semiclassical methods based on calculating classical trajectories offer a practical alternative. Here I review the recent application of some semiclassical, trajectory-based methods to nonlinear molecular vibrational and electronic spectra.

Keyword(s): nonlinear optical spectroscopy, semiclassical mechanics, two-dimensional electronic spectroscopy, two-dimensional infrared spectroscopy, two-dimensional vibrational-electronic spectroscopy
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2022-04-20
2024-04-29
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Literature Cited

  1. 1. 
    Mukamel S. 1995. Principles of Nonlinear Optical Spectroscopy New York: Oxford Univ. Press
  2. 2. 
    Scheurer C, Mukamel S. 2002. Infrared analogs of heteronuclear magnetic resonance coherence transfer experiments in peptides. J. Chem. Phys. 116:6803–16
     [Google Scholar]
  3. 3. 
    Cho M. 2009. Two-Dimensional Optical Spectroscopy Boca Raton, FL: CRC Press
  4. 4. 
    Hamm P, Zanni M. 2011. Concepts and Methods of 2D Infrared Spectroscopy New York: Cambridge Univ. Press
  5. 5. 
    Fayer MD 2013. Ultrafast Infrared Vibrational Spectroscopy Boca Raton, FL: CRC Press
  6. 6. 
    Biggs J, Healion D, Zhang Y, Mukamel S. 2013. Multidimensional attosecond resonant X-ray spectroscopy of molecules: lessons from the optical regime. Annu. Rev. Phys. Chem. 64:101–27
     [Google Scholar]
  7. 7. 
    Courtney TL, Fox ZW, Slenkamp KM, Khalil M. 2015. Two-dimensional vibrational-electronic spectroscopy. J. Chem. Phys. 143:154201
     [Google Scholar]
  8. 8. 
    Seidner L, Stock G, Domcke W. 1995. Nonperturbative approach to femtosecond spectroscopy: general theory and application to multidimensional nonadiabatic photoisomerization processes. J. Chem. Phys. 103:3998–4011
     [Google Scholar]
  9. 9. 
    Dellago C, Mukamel S. 2003. Simulation strategies and signatures of chaos in classical nonlinear response. Phys. Rev. E 67:035205
     [Google Scholar]
  10. 10. 
    Dellago C, Mukamel S. 2003. Simulation algorithms for multidimensional nonlinear response of classical many-body systems. J. Chem. Phys. 119:9344–54
     [Google Scholar]
  11. 11. 
    Mancal T, Pisliakov AV, Fleming GR. 2006. Two-dimensional optical three-pulse photon echo spectroscopy. I. Nonperturbative approach to the calculation of spectra. J. Chem. Phys. 124:234504
     [Google Scholar]
  12. 12. 
    Provazza J, Segatta F, Coker DF. 2020. Modeling nonperturbative field-driven vibronic dynamics: selective state preparation and nonlinear spectroscopy. J. Chem. Theory Comput. 17:29–39
     [Google Scholar]
  13. 13. 
    Gao X, Lai Y, Geva E 2020. Simulating absorption spectra of multiexcitonic systems via quasiclassical mapping Hamiltonian methods. J. Chem. Theory Comput. 16:6465–80
     [Google Scholar]
  14. 14. 
    Gao X, Geva E. 2020. A nonperturbative methodology for simulating multidimensional spectra of multiexcitonic molecular systems via quasiclassical mapping Hamiltonian methods. J. Chem. Theory Comput. 16:6491–502
     [Google Scholar]
  15. 15. 
    Child MS. 1991. Semiclassical Mechanics with Molecular Applications New York: Oxford Univ. Press
  16. 16. 
    Sepulveda MA, Grossmann F. 1996. Time-dependent semiclassical mechanics. Adv. Chem. Phys. 96:191–304
     [Google Scholar]
  17. 17. 
    Heller EJ. 2018. The Semiclassical Way to Dynamics and Spectroscopy Princeton, NJ/Oxford, UK: Princeton Univ. Press
  18. 18. 
    Einstein A. 1917. Zum Quantenansatz von Sommerfeld und Epstein. Dtsch. Phys. Ges. Verh. 19:82–92
     [Google Scholar]
  19. 19. 
    Stone AD. 2005. Einstein's unknown insight and the problem of quantizing chaos. Phys. Today 58:37–43
     [Google Scholar]
  20. 20. 
    Noid DW, Koszykowski ML, Marcus RA. 1981. Quasiperiodic and stochastic behavior in molecules. Annu. Rev. Phys. Chem. 32:267–309
     [Google Scholar]
  21. 21. 
    Eaker C, Schatz GC, Leon ND, Heller EJ 1984. Fourier transform methods for calculating action variables and semiclassical eigenvalues for coupled oscillator systems. J. Chem. Phys. 81:5913–19
     [Google Scholar]
  22. 22. 
    Miller WH. 1984. Calculation of semiclassical eigenvalues with one arbitrary trajectory. J. Chem. Phys. 81:3573–75
     [Google Scholar]
  23. 23. 
    Martens CC, Ezra GS. 1987. Classical and semiclassical mechanics of strongly resonant systems: a Fourier transform approach. J. Chem. Phys. 86:279–307
     [Google Scholar]
  24. 24. 
    Cundiff S. 2014. Optical three dimensional coherent spectroscopy. Phys. Chem. Chem. Phys. 16:8193–200
     [Google Scholar]
  25. 25. 
    Jonas DM. 2003. Two-dimensional femtosecond spectroscopy. Annu. Rev. Phys. Chem. 54:425–63
     [Google Scholar]
  26. 26. 
    Cowan ML, Ogilvie JP, Miller RJD. 2004. Two-dimensional spectroscopy using diffractive optics based phased-locked photon echoes. Chem. Phys. Lett. 386:184–89
     [Google Scholar]
  27. 27. 
    Brixner T, Stiopkin IV, Fleming GR. 2004. Tunable two-dimensional femtosecond spectroscopy. Opt. Lett. 29:884–86
     [Google Scholar]
  28. 28. 
    Tekavec PE, Myers JA, Lewis KLM, Ogilvie JP 2009. Two-dimensional electronic spectroscopy with a continuum probe. Opt. Lett. 34:1390–92
     [Google Scholar]
  29. 29. 
    Turner DB, Hassan Y, Scholes GD 2012. Exciton superposition states in CdSe nanocrystals measured using broadband two-dimensional electronic spectroscopy. Nano Lett 12:880–86
     [Google Scholar]
  30. 30. 
    Toa ZSD, deGolian MH, Jumper CC, Hiller RG, Scholes GD. 2019. Consistent model of ultrafast energy transfer in peridinin chlorophyll-a protein using two-dimensional electronic spectroscopy and Förster theory. J. Phys. Chem. B 123:6410–20
     [Google Scholar]
  31. 31. 
    Sardjan AS, Westerman FP, Ogilvie JP, Jansen TLC. 2020. Observation of ultrafast coherence transfer and degenerate states with polarization-controlled two-dimensional electronic spectroscopy. J. Phys. Chem. B 124:9420–27
     [Google Scholar]
  32. 32. 
    Gaynor JD, Khalil M. 2017. Signatures of vibronic coupling in two-dimensional electronic-vibrational and vibrational-electronic spectroscopies. J. Chem. Phys. 147:094202
     [Google Scholar]
  33. 33. 
    Gaynor JD, Petrone A, Li X, Khalil M 2018. Mapping vibronic couplings in a solar cell dye with polarization-selective two-dimensional electronic–vibrational spectroscopy. J. Phys. Chem. Lett 9:6289–95
     [Google Scholar]
  34. 34. 
    Fox ZW, Blair TJ, Khalil M. 2020. Determining the orientation and vibronic couplings between electronic and vibrational coordinates with polarization-selective two-dimensional vibrational-electronic spectroscopy. J. Phys. Chem. Lett. 11:1558–63
     [Google Scholar]
  35. 35. 
    Gaynor JD, Weakly RB, Khalil M. 2021. Multimode two-dimensional vibronic spectroscopy. I. Orientational response and polarization-selectivity. J. Chem. Phys. 154:184201
     [Google Scholar]
  36. 36. 
    Weakly RB, Gaynor JD, Khalil M. 2021. Multimode two-dimensional vibronic spectroscopy. II. Simulating and extracting vibronic coupling parameters from polarization-selective spectra. J. Chem. Phys. 154:184202
     [Google Scholar]
  37. 37. 
    Wang H, Thoss M, Miller WH 2000. Forward-backward initial value representation for the calculation of thermal rate constants for reactions in complex molecular systems. J. Chem. Phys. 112:47–55
     [Google Scholar]
  38. 38. 
    Wang H, Manolopoulos DE, Miller WH. 2001. Generalized Filinov transformation of the semiclassical initial value representation. J. Chem. Phys. 115:6317–26
     [Google Scholar]
  39. 39. 
    Shi Q, Geva E. 2003. A relationship between semiclassical and centroid correlation functions. J. Chem. Phys. 118:8173–84
     [Google Scholar]
  40. 40. 
    Shi Q, Geva E. 2004. Nonradiative electronic relaxation rate constants from approximations based on linearizing the path-integral forward-backward action. J. Phys. Chem. A 108:6109–16
     [Google Scholar]
  41. 41. 
    Liu J, Miller WH. 2007. Real time correlation function in a single phase space integral beyond the linearized semiclassical initial value representation. J. Chem. Phys. 126:234110
     [Google Scholar]
  42. 42. 
    Liu J, Miller WH. 2007. Linearized semiclassical initial value time correlation functions using the thermal Gaussian approximation: applications to condensed phase systems. J. Chem. Phys. 127:114506
     [Google Scholar]
  43. 43. 
    Reppert M, Brumer P. 2018. Classical coherent two-dimensional vibrational spectroscopy. J. Chem. Phys. 148:064101
     [Google Scholar]
  44. 44. 
    Wu J, Cao J. 2001. Linear and nonlinear response functions of the Morse oscillator: classical divergence and the uncertainty principle. J. Chem. Phys. 115:5381–91
     [Google Scholar]
  45. 45. 
    Cao J, Wu J, Yang S. 2002. Calculations of nonlinear spectra of liquid Xe. I. Third-order Raman response. J. Chem. Phys. 116:3739–59
     [Google Scholar]
  46. 46. 
    Cao J, Yang S, Wu J 2002. Calculations of nonlinear spectra of liquid Xe. II. Fifth-order Raman response. J. Chem. Phys. 116:3760–76
     [Google Scholar]
  47. 47. 
    Kryvohuz M, Cao J. 2005. Non-divergent classical response functions from uncertainty principle: quasi periodic systems. J. Chem. Phys. 122:024109
     [Google Scholar]
  48. 48. 
    Kryvohuz M, Cao J. 2005. Quantum-classical correspondence in response theory. Phys. Rev. Lett. 95:180405
     [Google Scholar]
  49. 49. 
    Kryvohuz M, Cao J. 2006. Classical divergence of nonlinear response functions. Phys. Rev. Lett. 96:030403
     [Google Scholar]
  50. 50. 
    Kryvohuz M, Cao J. 2006. Quantum recurrence from a semiclassical summation. Chem. Phys. 322:41–45
     [Google Scholar]
  51. 51. 
    Kryvohuz M, Cao J. 2009. The influence of dissipation on the quantum-classical correspondence: stability of stochastic trajectories. J. Chem. Phys. 130:234107
     [Google Scholar]
  52. 52. 
    Malinin SV, Chernyak VY. 2008. Collective oscillations in the classical nonlinear response of a chaotic system. Phys. Rev. E 77:025201(R)
     [Google Scholar]
  53. 53. 
    Malinin SV, Chernyak VY. 2008. Classical nonlinear response of a chaotic system. I. Collective resonances. Phys. Rev. E 77:056201
     [Google Scholar]
  54. 54. 
    Malinin SV, Chernyak VY. 2008. Classical nonlinear response of a chaotic system. II. Langevin dynamics and spectral decomposition. Phys. Rev. E 77:056202
     [Google Scholar]
  55. 55. 
    Yee TK, Gustafson TK 1978. Diagrammatic analysis of the density operator for nonlinear optical calculations: pulsed and CW responses. Phys. Rev. A 18:1597–617
     [Google Scholar]
  56. 56. 
    Jansen TLC, Saito S, Jeon J, Cho M 2019. Theory of coherent two-dimensional vibrational spectroscopy. J. Chem. Phys. 150:100901
     [Google Scholar]
  57. 57. 
    Noid WG, Ezra GS, Loring RF 2003. Optical response functions with semiclassical dynamics. J. Chem. Phys. 119:1003–20
     [Google Scholar]
  58. 58. 
    Noid WG, Ezra GS, Loring RF 2004. Semiclassical calculation of the vibrational echo. J. Chem. Phys. 120:1491–99
     [Google Scholar]
  59. 59. 
    Heller EJ. 1981. Frozen Gaussians: a very simple semiclassical approximation. J. Chem. Phys. 75:2923–31
     [Google Scholar]
  60. 60. 
    Herman MF, Kluk E. 1984. A semiclassical justification for the use of non-spreading wavepackets in dynamics calculations. Chem. Phys. 91:27–34
     [Google Scholar]
  61. 61. 
    Herman MF. 1994. Dynamics by semiclassical methods. Annu. Rev. Phys. Chem. 45:83–111
     [Google Scholar]
  62. 62. 
    Herman MF, Coker DF. 1999. Classical mechanics and the spreading of localized wave packets in condensed phase molecular systems. J. Chem. Phys. 111:1801–8
     [Google Scholar]
  63. 63. 
    Kay KG. 2006. The Herman-Kluk approximation: derivation and semiclassical corrections. Chem. Phys. 322:3–12
     [Google Scholar]
  64. 64. 
    Miller WH. 2002. An alternative derivation of the Herman-Kluk (coherent state) semiclassical initial value representation of the time-evolution operator. Mol. Phys. 100:397–400
     [Google Scholar]
  65. 65. 
    Miller WH. 2002. On the relation between the semiclassical initial value representation and an exact quantum expansion in time-dependent coherent states. J. Phys. Chem. B 106:8132–35
     [Google Scholar]
  66. 66. 
    Deshpande SA, Ezra GS. 2006. On the derivation of the Herman-Kluk propagator. J. Phys. A 39:5067–78
     [Google Scholar]
  67. 67. 
    Gruenbaum SM, Loring RF. 2008. Interference and quantization in semiclassical response functions. J. Chem. Phys. 128:124106
     [Google Scholar]
  68. 68. 
    Gruenbaum SM, Loring RF. 2008. Semiclassical mean-trajectory approximation for nonlinear spectroscopic response functions. J. Chem. Phys. 129:124510
     [Google Scholar]
  69. 69. 
    Goldstein H. 1950. Classical Mechanics Reading, MA: Addison-Wesley
  70. 70. 
    Gerace M, Loring RF. 2013. An optimized semiclassical approximation for vibrational response functions. J. Chem. Phys. 138:124104
     [Google Scholar]
  71. 71. 
    Gerace M, Loring RF. 2013. Two-dimensional spectroscopy of coupled vibrations with the optimized mean-trajectory approximation. J. Phys. Chem. B 117:15452–61
     [Google Scholar]
  72. 72. 
    Gruenbaum SM, Loring RF. 2009. Semiclassical nonlinear response functions for coupled anharmonic vibrations. J. Chem. Phys. 131:204504
     [Google Scholar]
  73. 73. 
    Gruenbaum SM, Loring RF. 2011. Semiclassical quantization in Liouville space for vibrational dynamics. J. Phys. Chem. B 115:5148–56
     [Google Scholar]
  74. 74. 
    Alemi M, Loring RF 2015. Two-dimensional vibrational spectroscopy of a dissipative system with the optimized mean-trajectory approximation. J. Phys. Chem. B 119:8950–59
     [Google Scholar]
  75. 75. 
    Alemi M, Loring RF 2015. Vibrational coherence and energy transfer in two-dimensional spectra with the optimized mean-trajectory approximation. J. Chem. Phys. 142:212417
     [Google Scholar]
  76. 76. 
    Moberg DR, Alemi M, Loring RF 2015. Thermal weights for semiclassical response functions. J. Chem. Phys. 143:084101
     [Google Scholar]
  77. 77. 
    Schatz GC, Mulloney T. 1979. Classical perturbation theory of good action angle variables: application to semiclassical eigenvalues and to collisional energy transfer in polyatomic molecules. J. Phys. Chem. 83:989–99
     [Google Scholar]
  78. 78. 
    Ishizaki A, Tanimura Y. 2006. Modeling vibrational dephasing and energy relaxation of intramolecular anharmonic modes for multidimensional infrared spectroscopies. J. Chem. Phys. 125:084501
     [Google Scholar]
  79. 79. 
    Ramesh P, Loring RF 2018. Thermal population fluctuations in two-dimensional infrared spectroscopy captured with semiclassical mechanics. J. Phys. Chem. B 122:3647–54
     [Google Scholar]
  80. 80. 
    Brinzer T, Berquist EJ, Ren Z, Dutta S, Johnson CA et al. 2015. Ultrafast vibrational spectroscopy (2D-IR) of CO2 in ionic liquids: carbon capture from carbon dioxide's point of view. J. Chem. Phys. 142:212425
     [Google Scholar]
  81. 81. 
    Daly CA Jr., Berquist EJ, Brinzer T, Garrett-Roe S, Lambrecht DS, Corcelli SA. 2016. Modeling carbon dioxide vibrational frequencies in ionic liquids: II. Spectroscopic map. J. Phys. Chem. B 120:12633–42
     [Google Scholar]
  82. 82. 
    Berquist EJ, Daly CA Jr., Brinzer T, Bullard KK, Campbell ZM et al. 2017. Modeling carbon dioxide vibrational frequencies in ionic liquids: I. Ab initio calculations. J. Phys. Chem. B 121:208–20
     [Google Scholar]
  83. 83. 
    Giammanco CH, Kramer PL, Yamada SA, Nishida J, Tamimi A, Fayer MD 2016. Coupling of carbon dioxide stretch and bend vibrations reveals thermal population dynamics in an ionic liquid. J. Phys. Chem. B 120:549–56
     [Google Scholar]
  84. 84. 
    Giammanco CH, Kramer PL, Yamada SA, Nishida J, Tamimi A, Fayer MD 2016. Carbon dioxide in an ionic liquid: structural and rotational dynamics. J. Chem. Phys. 144:104506
     [Google Scholar]
  85. 85. 
    Walters PL, Allen TC, Makri N 2017. Direct determination of discrete harmonic bath parameters from molecular dynamics simulations. J. Comput. Chem. 38:110–15
     [Google Scholar]
  86. 86. 
    Tanimura Y, Kubo RK. 1989. Time evolution of a quantum system in contact with a nearly Gaussian-Markoffian noise bath. J. Phys. Soc. Jpn. 58:101–14
     [Google Scholar]
  87. 87. 
    Tanimura Y. 1990. Nonperturbative expansion method for a quantum system coupled to a harmonic-oscillator bath. Phys. Rev. A 41:6676–87
     [Google Scholar]
  88. 88. 
    Ishizaki A, Tanimura Y. 2005. Quantum dynamics of system strongly coupled to low-temperature colored noise bath: reduced hierarchy equations approach. J. Phys. Soc. Jpn. 74:3131–34
     [Google Scholar]
  89. 89. 
    Tanimura Y. 2006. Stochastic Liouville, Langevin, Fokker–Planck, and master equation approaches to quantum dissipative systems. J. Phys. Soc. Jpn. 75:082001
     [Google Scholar]
  90. 90. 
    Tanimura Y. 2014. Reduced hierarchical equations of motion in real and imaginary time: correlated initial states and thermodynamic quantities. J. Chem. Phys. 141:044114
     [Google Scholar]
  91. 91. 
    Ishizaki A, Fleming GR. 2009. Unified treatment of quantum coherent and incoherent hopping dynamics in electronic energy transfer: reduced hierarchy equation approach. J. Chem. Phys. 130:234111
     [Google Scholar]
  92. 92. 
    Shi Q, Chen L, Nan G, Xu R-X, Yan Y 2009. Efficient hierarchical Liouville space propagator to quantum dissipative dynamics. J. Chem. Phys. 130:084105
     [Google Scholar]
  93. 93. 
    Chen L, Zheng R, Shi Q, Yan Y. 2010. Two-dimensional electronic spectra from the hierarchical equations of motion method: application to model dimers. J. Chem. Phys. 132:024505
     [Google Scholar]
  94. 94. 
    Yan Y, Jin J, Xu R-X, Zheng X 2016. Dissipation equation of motion approach to open quantum systems. Front. Phys. 11:110306
     [Google Scholar]
  95. 95. 
    Zhu J, Kais S, Rebentrost P, Aspuru-Guzik A. 2011. Modified scaled hierarchical equation of motion approach for the study of quantum coherence in photosynthetic complexes. J. Phys. Chem. B 115:1531–37
     [Google Scholar]
  96. 96. 
    Strümpfer J, Schulten K. 2012. Open quantum dynamics calculations with the hierarchy equations of motion on parallel computers. J. Chem. Theory Comput. 8:2808–16
     [Google Scholar]
  97. 97. 
    Dunn IS, Tempelaar R, Reichman DR. 2019. Removing instabilities in the hierarchical equations of motion: exact and approximate projection approaches. J. Chem. Phys. 150:184109
     [Google Scholar]
  98. 98. 
    Alemi M. 2015. The optimized mean-trajectory approximation of vibrational response functions PhD Thesis Cornell Univ. Ithaca, NY:
  99. 99. 
    Fayer MD. 2009. Dynamics of liquids, molecules, and proteins measured with ultrafast 2D IR vibrational echo chemical exchange spectroscopy. Annu. Rev. Phys. Chem. 60:21–38
     [Google Scholar]
  100. 100. 
    Bagchi S, Nebgen BT, Loring RF, Fayer MD. 2010. Dynamics of a myoglobin mutant enzyme: 2D IR vibrational echo experiments and simulations. J. Am. Chem. Soc. 132:18367–76
     [Google Scholar]
  101. 101. 
    Lee K-K, Park K-H, Joo C, Kwon H-J, Han H et al. 2012. Ultrafast internal rotational dynamics of the azido group in (4S)-azidoproline: chemical exchange 2DIR spectroscopic investigations. Chem. Phys. 396:23–29
     [Google Scholar]
  102. 102. 
    Loring RF. 2017. Mean-trajectory approximation for electronic and vibrational-electronic nonlinear spectroscopy. J. Chem. Phys. 146:144016
     [Google Scholar]
  103. 103. 
    Polley K, Loring RF. 2019. Two-dimensional vibronic spectra from classical trajectories. J. Chem. Phys. 150:164114
     [Google Scholar]
  104. 104. 
    Polley K, Loring RF. 2020. One and two dimensional vibronic spectra for an exciton dimer from classical trajectories. J. Phys. Chem. B 124:9913–20
     [Google Scholar]
  105. 105. 
    Polley K, Loring RF. 2020. Spectroscopic response theory with classical mapping Hamiltonians. J. Chem. Phys. 153:204103
     [Google Scholar]
  106. 106. 
    Polley K, Loring RF. 2021. Two-dimensional vibrational-electronic spectra with semiclassical mechanics. J. Chem. Phys. 154:194110
     [Google Scholar]
  107. 107. 
    Meyer HD, Miller WH. 1979. A classical analog for electronic degrees of freedom in nonadiabatic collision processes. J. Chem. Phys. 70:3214–23
     [Google Scholar]
  108. 108. 
    Meyer HD, Miller WH. 1979. Classical models for electronic degrees of freedom: derivation via spin analogy and application to F* + H2 → F + H2. J. Chem. Phys. 71:2156–69
     [Google Scholar]
  109. 109. 
    Meyer HD, Miller WH. 1980. Analysis and extension of some recently proposed classical models for electronic degrees of freedom. J. Chem. Phys. 72:2272–81
     [Google Scholar]
  110. 110. 
    Thoss M, Stock G. 1999. Mapping approach to the semiclassical description of nonadiabatic quantum dynamics. Phys. Rev. A 59:64–79
     [Google Scholar]
  111. 111. 
    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. 112:10282–92
     [Google Scholar]
  112. 112. 
    Ananth N. 2013. Mapping variable ring polymer molecular dynamics: a path-integral based method for nonadiabatic processes. J. Chem. Phys. 139:124102
     [Google Scholar]
  113. 113. 
    Cotton SJ, Miller WH. 2013. Symmetrical windowing for quantum states in quasi-classical trajectory simulations. J. Phys. Chem. A 117:7190–94
     [Google Scholar]
  114. 114. 
    Cotton SJ, Igumenshchev K, Miller WH. 2014. Symmetrical windowing for quantum states in quasi-classical trajectory simulations: application to electron transfer. J. Chem. Phys. 141:084104
     [Google Scholar]
  115. 115. 
    Miller WH, Cotton SJ. 2016. Wigner functions in action-angle variables, Bohr-Sommerfeld quantization, the Heisenberg correspondence principle, and a symmetrical quasi-classical approach to the full electronic density matrix. J. Chem. Phys. 145:081102
     [Google Scholar]
  116. 116. 
    Cotton SJ, Miller WH. 2019. A symmetrical quasi-classical windowing model for the molecular dynamics treatment of non-adiabatic processes involving many electronic states. J. Chem. Phys. 150:104101
     [Google Scholar]
  117. 117. 
    Cotton SJ, Miller WH. 2019. Trajectory-adjusted electronic zero point energy in classical Meyer-Miller vibronic dynamics: symmetrical quasiclassical application to photodissociation. J. Chem. Phys. 150:194110
     [Google Scholar]
  118. 118. 
    Provazza J, Coker DF. 2018. Symmetrical quasiclassical analysis of linear optical spectroscopy. J. Chem. Phys. 148:181102
     [Google Scholar]
  119. 119. 
    Kananenka AA, Hsieh C-Y, Cao J, Geva E 2018. Nonadiabatic dynamics via the symmetrical quasi-classical method in the presence of anharmonicity. J. Phys. Chem. Lett. 9:319–26
     [Google Scholar]
  120. 120. 
    Sandoval JS, Mandal A, Huo P. 2018. Symmetric quasi-classical dynamics with quasi-diabatic propagation scheme. J. Chem. Phys. 149:044115
     [Google Scholar]
  121. 121. 
    Xie Y, Zheng J, Lan Z 2018. Performance evaluation of the symmetrical quasi-classical dynamics method based on Meyer-Miller mapping Hamiltonian in the treatment of site-exciton models. J. Chem. Phys. 149:174105
     [Google Scholar]
  122. 122. 
    Saller MAC, Kelly A, Richardson JO 2019. On the identity of the identity operator in nonadiabatic linearized semiclassical dynamics. J. Chem. Phys. 150:071101
     [Google Scholar]
  123. 123. 
    Saller MAC, Kelly A, Geva E 2021. Benchmarking quasiclassical mapping Hamiltonian methods for simulating cavity-modified molecular dynamics. J. Phys. Chem. Lett. 12:3163–70
     [Google Scholar]
  124. 124. 
    Zheng J, Xie Y, Jiang S, Long Y, Ning X, Lan Z. 2019. Initial sampling in symmetrical quasiclassical dynamics based on Li-Miller mapping Hamiltonian. Phys. Chem. Chem. Phys. 21:26502–14
     [Google Scholar]
  125. 125. 
    Gao X, Saller MAC, Liu Y, Kelly A, Richardson JO, Geva E. 2020. Benchmarking quasiclassical mapping Hamiltonian methods for simulating electronically nonadiabatic molecular dynamics. J. Chem. Theory Comput. 16:2883–95
     [Google Scholar]
  126. 126. 
    Gao X, Geva E. 2020. Improving the accuracy of quasiclassical mapping Hamiltonian methods by treating the window function width as an adjustable parameter. J. Phys. Chem. A 124:11006–16
     [Google Scholar]
  127. 127. 
    Liu Y, Gao X, Lai Y, Mulvihill E, Geva E. 2020. Electronic dynamics through conical intersections via quasiclassical mapping Hamiltonian methods. J. Chem. Theory Comput. 16:4479–88
     [Google Scholar]
  128. 128. 
    Swenson DWH, Levy T, Cohen G, Rabani E, Miller WH 2011. Application of a semiclassical model to the second-quantized many-electron Hamiltonian to nonequilibrium quantum transport: the resonant level model. J. Chem. Phys. 134:164103
     [Google Scholar]
  129. 129. 
    Evans DJ, Morriss GP. 1990. Statistical Mechanics of Nonequilibrium Liquids New York: Academic Press
  130. 130. 
    Shi Q, Geva E. 2008. A comparison between different semiclassical approximations for optical response functions in nonpolar liquid solutions. II. The signature of excited state dynamics on two-dimensional spectra. J. Chem. Phys. 129:124505
     [Google Scholar]
  131. 131. 
    McRobbie PL, Geva E. 2009. A benchmark study of different methods for calculating one- and two-dimensional optical spectra. J. Phys. Chem. A 113:10425–34
     [Google Scholar]
  132. 132. 
    Chen J, Makri N. 2010. Low-temperature correlation functions via forward-backward quantum dynamics. Chem. Phys. 370:15–19
     [Google Scholar]
  133. 133. 
    Fetherolf JH, Berkelbach TC. 2017. Linear and nonlinear spectroscopy from quantum master equations. J. Chem. Phys. 147:244109
     [Google Scholar]
  134. 134. 
    Huo P, Coker DF. 2011. Partial linearized density matrix dynamics for dissipative, non-adiabatic quantum evolution. J. Chem. Phys. 135:201101
     [Google Scholar]
  135. 135. 
    Huo P, Coker DF. 2012. Semi-classical path integral non-adiabatic dynamics: a partial linearized classical mapping Hamiltonian approach. Mol. Phys. 110:1035–52
     [Google Scholar]
  136. 136. 
    Provazza J, Segatta F, Garavelli M, Coker DF. 2018. Semiclassical path integral calculation of nonlinear optical spectroscopy. J. Chem. Theory Comput. 14:856–66
     [Google Scholar]
  137. 137. 
    Cho M. 2000. Triply resonant infrared-infrared-visible sum frequency generation: three-dimensional vibronic spectroscopy for the investigation of vibrational and vibronic couplings. J. Chem. Phys. 112:9002–9014
     [Google Scholar]
  138. 138. 
    Cho M. 2000. Two-dimensional vibrational spectroscopy. VII. Investigation of the vibronic and vibrational couplings by using novel triply resonant two-dimensional vibrational spectroscopies. J. Chem. Phys. 113:7746–55
     [Google Scholar]
  139. 139. 
    Bonn M, Hess C, Miners JH, Heinz TF, Bakker HJ, Cho M. 2001. Novel surface vibrational spectroscopy: infrared-infrared-visible sum-frequency generation. Phys. Rev. Lett. 86:1566–69
     [Google Scholar]
  140. 140. 
    Oliver TAA, Lewis NHC, Fleming GR 2014. Correlating the motion of electrons and nuclei with two-dimensional electronic-vibrational spectroscopy. PNAS 111:10061–66
     [Google Scholar]
  141. 141. 
    Lewis NHC, Dong H, Oliver TAA, Fleming GR 2015. Measuring correlated electronic and vibrational spectral dynamics using line shapes in two-dimensional electronic-vibrational spectroscopy. J. Chem. Phys. 142:174201
     [Google Scholar]
  142. 142. 
    Bhattacharyya P, Fleming GR. 2019. Two-dimensional electronic-vibrational spectroscopy of coupled molecular complexes: a near-analytical approach. J. Phys. Chem. Lett. 10:2081–89
     [Google Scholar]
  143. 143. 
    Wu EC, Arsenault EA, Bhattacharyya P, Lewis NHC, Fleming GR. 2019. Two-dimensional electronic vibrational spectroscopy and ultrafast excitonic and vibronic photosynthetic energy transfer. Faraday Disc 216:116–32
     [Google Scholar]
  144. 144. 
    Bhattacharyya P, Fleming GR. 2020. The role of resonant nuclear modes in vibrationally assisted energy transport: the LHCII complex. J. Chem. Phys. 153:044119
     [Google Scholar]
  145. 145. 
    Cho M, Fleming GR. 2020. Two-dimensional electronic-vibrational spectroscopy reveals cross-correlation between solvation dynamics and vibrational spectral diffusion. J. Phys. Chem. B 124:11222–35
     [Google Scholar]
  146. 146. 
    Mukamel S, Khidekel V, Chernyak V. 1996. Classical chaos and fluctuation-dissipation relations for nonlinear response. Phys. Rev. E 53:R1–4
     [Google Scholar]
  147. 147. 
    Ben-Nun M, Martinez TJ. 1999. Electronic absorption and resonance Raman spectroscopy from ab initio quantum molecular dynamics. J. Phys. Chem. A 103:10517–27
     [Google Scholar]
  148. 148. 
    Tatchen J, Pollak E. 2009. Semiclassical on-the-fly computation of the S0 → S1 absorption spectrum of formaldehyde. J. Phys. Chem. A 103:10517–27
     [Google Scholar]
  149. 149. 
    Begusic T, Vanicek J. 2020. On-the-fly ab initio semiclassical evaluation of vibronic spectra at finite temperature. J. Chem. Phys. 153:024105
     [Google Scholar]
  150. 150. 
    Begusic T, Vanicek J. 2021. Finite-temperature, anharmonicity, and Duschinsky effects on the two-dimensional electronic spectra from ab initio thermo-field Gaussian wavepacket dynamics. J. Phys. Chem. Lett. 12:2997–3005
     [Google Scholar]
/content/journals/10.1146/annurev-physchem-082620-021302
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Calculating Multidimensional Optical Spectra from Classical Trajectories
Annual Review of Physical Chemistry 73, 273 (2022); https://doi.org/10.1146/annurev-physchem-082620-021302
/content/journals/10.1146/annurev-physchem-082620-021302
/content/journals/10.1146/annurev-physchem-082620-021302
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