We present a current, up-to-date review of the surface hopping methodology for solving nonadiabatic problems, 25 years after Tully published the fewest switches surface hopping algorithm. After reviewing the original motivation for and failures of the algorithm, we give a detailed examination of modern advances, focusing on both theoretical and practical issues. We highlight how one can partially derive surface hopping from the Schrödinger equation in the adiabatic basis, how one can change basis within the surface hopping algorithm, and how one should understand and apply the notions of decoherence and wavepacket bifurcation. The question of time reversibility and detailed balance is also examined at length. Recent applications to photoexcited conjugated polymers are discussed briefly.


Article metrics loading...

Loading full text...

Full text loading...


Literature Cited

  1. Closs GL, Piotrowiak P, MacInnis JM, Fleming GR. 1.  1988. Determination of long distance intramolecular triplet energy-transfer rates. Quantitative comparison with electron transfer. J. Am. Chem. Soc. 110:2652–53 [Google Scholar]
  2. Closs GL, Johnson M, Miller JR, Piotrowiak P. 2.  1989. A connection between intramolecular long-range electron, hole, and triplet energy transfers. J. Am. Chem. Soc. 111:3751–53 [Google Scholar]
  3. Landry BR, Subotnik JE. 3.  2014. Quantifying the lifetime of triplet energy transfer processes in organic chromophores: a case study of 4-(2-naphthylmethyl)benzaldehyde. J. Chem. Theory Comp. 10:4253–63 [Google Scholar]
  4. Lengsfield BH, Yarkony DR. 4.  1992. Nonadiabatic interactions between potential energy surfaces: theory and applications. Adv. Chem. Phys. 82:Part 21–71 [Google Scholar]
  5. Lengsfield BH, Saxe P, Yarkony DR. 5.  1984. On the evaluation of nonadiabatic coupling matrix elements using SA-MCSCF/CI wave functions and analytic gradient methods. I. J. Chem. Phys. 81:4549–53 [Google Scholar]
  6. Li X, Tully JC, Schlegel HB, Frisch MJ. 6.  2005. Ab initio Ehrenfest dynamics. J. Chem. Phys. 123:084106 [Google Scholar]
  7. Cotton SJ, Igumenshchev K, Miller WH. 7.  2014. Symmetrical windowing for quantum states in quasi-classical trajectory simulations: application to electron transfer. J. Chem. Phys. 141:084104 [Google Scholar]
  8. Martínez TJ, Ben-Nun M, Levine RD. 8.  1996. Multi-electronic-state molecular dynamics: a wave function approach with applications. J. Phys. Chem. 100:7884–95 [Google Scholar]
  9. Ben-Nun M, Martínez TJ. 9.  2000. A multiple spawning approach to tunneling dynamics. J. Chem. Phys. 112:6113–21 [Google Scholar]
  10. Tully JC. 10.  1990. Molecular dynamics with electronic transitions. J. Chem. Phys. 93:1061–71 [Google Scholar]
  11. Malhado JP, Bearpark MJ, Hynes JT. 11.  2014. Non-adiabatic dynamics close to conical intersections and the surface hopping perspective. Front. Chem. 2:97 [Google Scholar]
  12. Jasper AW, Truhlar DG. 12.  2011. Non-Born–Oppenheimer molecular dynamics for conical intersections, avoided crossings, and weak interactions. Conical Intersections: Theory, Computation and Experiment W Domcke, DR Yarkony, H Koppel 375–414 New Jersey: World Sci. [Google Scholar]
  13. Barbatti M. 13.  2011. Nonadiabatic dynamics with trajectory surface hopping method. Wiley Interdiscip. Rev. Comput. Mol. Sci. 1:620–33 [Google Scholar]
  14. Doltsinis N. 14.  2002. Nonadiabatic dynamics: mean-field and surface hopping. Quantum Simulations of Complex Many-Body Systems: From Theory to Algorithms J Grotendorst, D Marx, A Muramatsu 377–97 Jülich, Germany: John von Neumann Inst. Comput. [Google Scholar]
  15. Coker DF. 15.  1993. Computer simulation methods for nonadiabatic dynamics in condensed systems. Computer Simulation in Chemical Physics MP Allen, DJ Tildesley 315–78 Jülich, Germany: John von Neumann Inst. Comput. [Google Scholar]
  16. de Carvalho FF, Bouduban MEF, Curchod BFE, Tavernelli I. 16.  2014. Nonadiabatic molecular dynamics based on trajectories. Entropy 16:62–85 [Google Scholar]
  17. Makri N, Makarov DE. 17.  1995. Tensor propagator for iterative quantum time evolution of reduced density matrices. I. Theory. J. Chem. Phys. 102:4600–10 [Google Scholar]
  18. Makri N, Makarov DE. 18.  1995. Tensor propagator for iterative quantum time evolution of reduced density matrices. II. Numerical methodology. J. Chem. Phys. 102:4611–18 [Google Scholar]
  19. Tanimura Y. 19.  2012. Reduced hierarchy equations of motion approach with Drude plus Brownian spectral distribution: probing electron transfer processes by means of two-dimensional correlation spectroscopy. J. Chem. Phys. 137:22A550 [Google Scholar]
  20. Bittner ER. 20.  2000. Quantum tunneling dynamics using hydrodynamic trajectories. J. Chem. Phys. 112:9703–10 [Google Scholar]
  21. Miller WH. 21.  2001. The semiclassical initial value representation: a potentially practical way for adding quantum effects to classical molecular dynamics simulations. J. Phys. Chem. A 105:2942–55 [Google Scholar]
  22. Miller WH. 22.  2012. Perspective: quantum or classical coherence?. J. Chem. Phys. 136:210901 [Google Scholar]
  23. Makri N, Thompson K. 23.  1998. Semiclassical influence functionals for quantum systems in anharmonic environments. Chem. Phys. Lett. 291:101–9 [Google Scholar]
  24. Herman MF, Kluk E. 24.  1984. A semiclassical justification for the use of non-spreading wavepackets in dynamics calculations. Chem. Phys. 91:27–34 [Google Scholar]
  25. Kay KG. 25.  1994. Integral expressions for the semiclassical time dependent propagator. J. Chem. Phys. 100:4377–92 [Google Scholar]
  26. Meyer HD, Miller WH. 26.  1979. A classical analog for electronic degrees of freedom in nonadiabatic collision processes. J. Chem. Phys. 70:3214–23 [Google Scholar]
  27. Meyer HD, Miller WH. 27.  1980. Analysis and extension of some recently proposed classical models for electronic degrees of freedom. J. Chem. Phys. 72:2272–81 [Google Scholar]
  28. Stock G, Thoss M. 28.  1997. Semiclassical description of nonadiabatic quantum dynamics. Phys. Rev. Lett. 78:578 [Google Scholar]
  29. Miller WH. 29.  2009. Electronically nonadiabatic dynamics via semiclassical initial value methods. J. Phys. Chem. A 113:1405–15 [Google Scholar]
  30. Kim H, Nassimi A, Kapral R. 30.  2008. Quantum-classical Liouville dynamics in the mapping basis. J. Chem. Phys. 129:084102 [Google Scholar]
  31. Nassimi A, Bonella S, Kapral R. 31.  2010. Analysis of the quantum-classical Liouville equation in the mapping basis. J. Chem. Phys. 133:134115 [Google Scholar]
  32. Kim HW, Rhee YM. 32.  2014. Improving long time behavior of Poisson bracket mapping equation: a non-Hamiltonian approach. J. Chem. Phys. 140:184106 [Google Scholar]
  33. Gherib R, Ryabinkin IG, Izmaylov AF. 33.  2015. Why do mixed quantum-classical methods describe short-time dynamics through conical intersections so well? Analysis of geometric phase effects. J. Chem. Theory Comp. 11:1375–82 [Google Scholar]
  34. Schwartz BJ, Rossky PJ. 34.  1994. Aqueous solvation dynamics with a quantum mechanical solute: computer simulation studies of the photoexcited hydrated electron. J. Chem. Phys. 101:6902–15 [Google Scholar]
  35. Bittner ER, Rossky PJ. 35.  1995. Quantum decoherence in mixed quantum-classical systems: nonadiabatic processes. J. Chem. Phys. 103:8130–43 [Google Scholar]
  36. Schwartz BJ, Bittner ER, Prezhdo OV, Rossky PJ. 36.  1996. Quantum decoherence and the isotope effect in condensed phase nonadiabatic molecular dynamics simulations. J. Chem. Phys. 104:5942–55 [Google Scholar]
  37. Prezhdo OV, Rossky PJ. 37.  1997. Evaluation of quantum transition rates from quantum-classical molecular dynamics simulations. J. Chem. Phys. 107:5863–78 [Google Scholar]
  38. Wong KF, Rossky PJ. 38.  2002. Dissipative mixed quantum-classical simulation of the aqueous solvated electron system. J. Chem. Phys. 116:8418–28 [Google Scholar]
  39. Wong KF, Rossky PJ. 39.  2002. Solvent-induced electronic decoherence: configuration dependent dissipative evolution for solvated electron systems. J. Chem. Phys. 116:8429–38 [Google Scholar]
  40. Horenko I, Salzmann C, Schmidt B, Schutte C. 40.  2002. Quantum-classical Liouville approach to molecular dynamics: surface hopping Gaussian phase-space packets. J. Chem. Phys. 117:11075–88 [Google Scholar]
  41. Subotnik JE, Shenvi N. 41.  2011. Decoherence and surface hopping: When can averaging over initial conditions help capture the effects of wave packet separation?. J. Chem. Phys. 134:244114 [Google Scholar]
  42. Subotnik JE, Shenvi N. 42.  2011. A new approach to decoherence and momentum rescaling in the surface hopping algorithm. J. Chem. Phys. 134:024105 [Google Scholar]
  43. Landry BR, Subotnik JE. 43.  2012. How to recover Marcus theory with fewest switches surface hopping: Add just a touch of decoherence. J. Chem. Phys. 137:22A513 [Google Scholar]
  44. Fang JY, Hammes-Schiffer S. 44.  1999. Improvement of the internal consistency in trajectory surface hopping. J. Phys. Chem. A 103:9399–407 [Google Scholar]
  45. Fang JY, Hammes-Schiffer S. 45.  1999. Comparison of surface hopping and mean field approaches for model proton transfer reactions. J. Chem. Phys. 110:11166–75 [Google Scholar]
  46. Bedard-Hearn MJ, Larsen RE, Schwartz BJ. 46.  2005. Mean-field dynamics with stochastic decoherence (MF-SD): a new algorithm for nonadiabatic mixed quantum/classical molecular-dynamics simulations with nuclear-induced decoherence. J. Chem. Phys. 123:234106 [Google Scholar]
  47. Hack MD, Truhlar DG. 47.  2001. Electronically nonadiabatic trajectories: continuous surface switching II. J. Chem. Phys. 114:2894–902 [Google Scholar]
  48. Volobuev YL, Hack MD, Topaler MS, Truhlar DG. 48.  2000. Continuous surface switching: an improved time-dependent self-consistent-field method for nonadiabatic dynamics. J. Chem. Phys. 112:9716–26 [Google Scholar]
  49. Jasper AW, Truhlar DG. 49.  2005. Electronic decoherence time for non-Born–Oppenheimer trajectories. J. Chem. Phys. 123:064103 [Google Scholar]
  50. Prezhdo OV, Rossky PJ. 50.  1997. Mean-field molecular dynamics with surface hopping. J. Chem. Phys. 107:825–34 [Google Scholar]
  51. Tully JC. 51.  1998. Mixed quantum-classical dynamics. Faraday Discuss. 110:407–19 [Google Scholar]
  52. Müller U, Stock G. 52.  1997. Surface-hopping modeling of photoinduced relaxation dynamics on coupled potential-energy surfaces. J. Chem. Phys. 107:6230–45 [Google Scholar]
  53. Kelly A, Markland TE. 53.  2013. Efficient and accurate surface hopping for long time nonadiabatic quantum dynamics. J. Chem. Phys. 139:014104 [Google Scholar]
  54. Hazra A, Soudackov AV, Hammes-Schiffer S. 54.  2010. Role of solvent dynamics in ultrafast photoinduced proton-coupled electron transfer reactions in solution. J. Phys. Chem. B 114:12319–32 [Google Scholar]
  55. Schwerdtfeger CA, Soudackov AV, Hammes-Schiffer S. 55.  2014. Nonadiabatic dynamics of electron transfer in solution: explicit and implicit solvent treatments that include multiple relaxation time scales. J. Chem. Phys. 140:034113 [Google Scholar]
  56. Landry BR, Subotnik JE. 56.  2011. Standard surface hopping predicts incorrect scaling for Marcus golden-rule rate: The decoherence problem cannot be ignored. J. Chem. Phys. 135:191101 [Google Scholar]
  57. Fuji T, Suzuki YI, Horio T, Suzuki T, Mitri R. 57.  et al. 2010. Ultrafast photodynamics of furan. J. Chem. Phys. 133:234303 [Google Scholar]
  58. Parandekar PV, Tully JC. 58.  2005. Mixed quantum-classical equilibrium. J. Chem. Phys. 122:094102 [Google Scholar]
  59. Schmidt JR, Parandekar PV, Tully JC. 59.  2008. Mixed quantum-classical equilibrium: surface hopping. J. Chem. Phys. 129:044104 [Google Scholar]
  60. Landry BR, Falk MJ, Subotnik JE. 60.  2013. Communication: the correct interpretation of surface hopping trajectories: how to calculate electronic properties. J. Chem. Phys. 139:211101 [Google Scholar]
  61. Worth GA, Bearpark MJ, Robb MA. 61.  2005. Semiclassical nonadiabatic trajectory computations in photochemistry: Is the reaction path enough to understand a photochemical reaction mechanism. ? In Computational Photochemistry M Olivucci 171–90 Amsterdam: Elsevier [Google Scholar]
  62. Berendsen HJC, Mavri J. 62.  1995. Quantum dynamics simulation of a small quantum system embedded in a classical environment. Quantum Mechanical Simulation Methods for Studying Biological Systems D Bicout, M Field 157–178 Berlin: Springer-Verlag [Google Scholar]
  63. Martens CC, Fang JY. 63.  1997. Semiclassical-limit molecular dynamics on multiple electronic surfaces. J. Chem. Phys. 106:4918–30 [Google Scholar]
  64. Donoso A, Martens CC. 64.  1998. Simulation of coherent nonadiabatic dynamics using classical trajectories. J. Phys. Chem. A 102:4291–300 [Google Scholar]
  65. Kapral R, Ciccotti G. 65.  1999. Mixed quantum-classical dynamics. J. Chem. Phys. 110:8919–29 [Google Scholar]
  66. Nielsen S, Kapral R, Ciccotti G. 66.  2000. Mixed quantum-classical surface hopping dynamics. J. Chem. Phys. 112:6543–53 [Google Scholar]
  67. Aleksandrov IVZ. 67.  1981. The statistical dynamics of a system consisting of a classical and a quantum subsystem. Z. Naturforsch. A 36:902–8 [Google Scholar]
  68. Boucher W, Traschen J. 68.  1988. Semiclassical physics and quantum fluctuations. Phys. Rev. D 37:3522–32 [Google Scholar]
  69. Zhang WY, Balescu R. 69.  1988. Statistical mechanics of a spin-polarized plasma. J. Plasma Phys. 40:199–213 [Google Scholar]
  70. Anderson A. 70.  1995. Quantum back reaction on ``classical’’ variables. Phys. Rev. Lett. 74:621–25 [Google Scholar]
  71. Prezhdo OV, Kisil VV. 71.  1997. Mixing quantum and classical mechanics. Phys. Rev. A 56:162–75 [Google Scholar]
  72. Micha DA, Thorndyke B. 72.  2002. Dissipative dynamics in many-atom systems: a density matrix treatment. Int. J. Quant. Chem. 90:759–771 [Google Scholar]
  73. Ouyang W, Subotnik JE. 73.  2014. Estimating the entropy and quantifying the impurity of a swarm of surface-hopping trajectories: a new perspective on decoherence. J. Chem. Phys. 140:204102 [Google Scholar]
  74. Shi Q, Geva E. 74.  2004. A derivation of the mixed quantum-classical Liouville equation from the influence functional formalism. J. Chem. Phys. 121:3393–404 [Google Scholar]
  75. Mukamel S. 75.  1982. On the semiclassical calculation of molecular absorption and fluorescence spectra. J. Chem. Phys. 77:173–181 [Google Scholar]
  76. Shemetulskis NE, Loring RF. 76.  1992. Semiclassical theory of the photon echo: applications to polar fluids. J. Chem. Phys. 97:1217–25 [Google Scholar]
  77. Egorov SA, Rabani E, Berne BJ. 77.  1998. Vibronic spectra in condensed matter: a comparison of exact quantum mechanical and various semiclassical treatments for harmonic baths. J. Chem. Phys. 108:1407–22 [Google Scholar]
  78. Egorov SA, Rabani E, Berne BJ. 78.  1999. Nonradiative relaxation processes in condensed phases: quantum versus classical baths. J. Chem. Phys. 110:5238–48 [Google Scholar]
  79. Bursulaya BD, Kim HJ. 79.  1996. Effects of solute electronic structure variation on photon echo spectroscopy. J. Phys. Chem. 100:16451–56 [Google Scholar]
  80. Subotnik JE, Ouyang W, Landry BR. 80.  2013. Can we derive Tully's surface-hopping algorithm from the semiclassical quantum Liouville equation: almost, but only with decoherence. J. Chem. Phys. 139:214107 [Google Scholar]
  81. Horsfield AP, Bowler DR, Fisher AJ, Todorov TN, Sanchez CG. 81.  2004. Beyond Ehrenfest: correlated non-adiabatic molecular dynamics. J. Phys. Cond. Matter 16:8251–66 [Google Scholar]
  82. Stella L, Meister M, Fisher AJ, Horsfield AP. 82.  2007. Robust nonadiabatic molecular dynamics for metals and insulators. J. Chem. Phys. 127:214104 [Google Scholar]
  83. McEniry EJ, Bowler DR, Dundas D, Horsfield AP, Sanchez CG, Todorov TN. 83.  2007. Dynamical simulation of inelastic quantum transport. J. Phys. Cond. Matter 19:196201 [Google Scholar]
  84. Prezhdo O, Pereverzev YV. 84.  2000. Quantized Hamilton dynamics. J. Chem. Phys. 113:6557–65 [Google Scholar]
  85. Onuchic JN, Wolynes PG. 85.  1988. Classical and quantum pictures of reaction dynamics in condensed matter: resonances, dephasing, and all that. J. Phys. Chem. 92:6495–503 [Google Scholar]
  86. Petit AS, Subotnik JE. 86.  2014. How to calculate linear absorption spectra with lifetime broadening using fewest switches surface hopping trajectories: a simple generalization of ground-state Kubo theory. J. Chem. Phys. 141:014107 [Google Scholar]
  87. Petit AS, Subotnik JE. 87.  2014. Calculating time-resolved differential absorbance spectra for ultrafast pump–probe experiments with surface hopping trajectories. J. Chem. Phys. 141:154108 [Google Scholar]
  88. Petit AS, Subotnik JE. 88.  2105. Appraisal of surface hopping as a tool for modeling condensed phase linear absorption spectra. J. Chem. Theory Comp. 11:4328–41 [Google Scholar]
  89. Tanimura Y, Kubo R. 89.  1989. Time evolution of a quantum system in contact with a nearly Gaussian–Markovian noise bath. J. Phys. Soc. Jpn. 58:101–114 [Google Scholar]
  90. Ishizaki A, Fleming GR. 90.  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]
  91. Cline RE, Wolynes PG. 91.  1987. Stochastic dynamic models of curve crossing phenomena in condensed phases. J. Chem. Phys. 86:3836–44 [Google Scholar]
  92. Warshel A, Hwang JK. 92.  1986. Simulation of the dynamics of electron transfer reactions in polar solvents: semiclassical trajectories and dispersed polaron approaches. J. Chem. Phys. 84:4938–57 [Google Scholar]
  93. Jain A, Subotnik JE. 93.  2015. Surface hopping, transition state theory, and decoherence. II. Thermal rate constants and detailed balance. J. Chem. Phys. 143:134107 [Google Scholar]
  94. Ben-Nun M, Martínez TJ. 94.  2007. A continuous spawning method for nonadiabatic dynamics and validation for the zero temperature spin boson problem. Isr. J. Chem. 47:75–88 [Google Scholar]
  95. Chen H-T, Reichman DR. 95.  2016. On the accuracy of surface hopping dynamics in condensed phase non-adiabatic problems. J. Chem. Phys. 144:094104 [Google Scholar]
  96. Xie W, Baj S, Zhu L, Shi Q. 96.  2013. Calculation of electron transfer rates using mixed quantum classical approaches: nonadiabatic limit and beyond. J. Phys. Chem. A 117:6196–204 [Google Scholar]
  97. Zhu X, Yarkony DR. 97.  2014. Fitting coupled potential energy surfaces for large systems: method and construction of a 3-state representation for phenol photodissociation in the full 33 internal degrees of freedom using multireference configuration interaction determined data. J. Chem. Phys. 140:024112 [Google Scholar]
  98. Sterpone F, Bedard-Hearn MJ, Rossky PJ. 98.  2009. Nonadiabatic mixed quantum-classical dynamic simulation of π-stacked oligophenylenevinylenes. J. Phys. Chem. A 113:3427–30 [Google Scholar]
  99. Nelson T, Fernandez-Alberti S, Roitberg AE, Tretiak S. 99.  2014. Nonadiabatic excited-state molecular dynamics: modeling photophysics in organic conjugated materials. Acc. Chem. Res. 47:1155–64 [Google Scholar]
  100. Plasser F, Crespo-Otero R, Pederzoli M, Pittner J, Lischka H, Barbatti M. 100.  2014. Surface hopping dynamics with correlated single-reference methods: 9H-adenine as a case study. J. Chem. Theory Comp. 10:1395–405 [Google Scholar]
  101. Barbatti M, Paier J, Lischka H. 101.  2004. Photochemistry of ethylene: a multireference configuration interaction investigation of the excited-state energy surfaces. J. Chem. Phys. 121:11614 [Google Scholar]
  102. Barbatti M, Granucci G, Persico M, Ruckenbauer M, Vazdar M. 102.  et al. 2007. The on-the-fly surface-hopping program system Newton-X: application to ab initio simulation of the nonadiabatic photodynamics of benchmark systems. J. Photochem. Photobiol. A Chem. 190:228–40 [Google Scholar]
  103. Subotnik JE, Alguire EC, Ou Q, Landry BR, Fatehi S. 103.  2015. The requisite electronic structure theory to describe photoexcited nonadiabatic dynamics: nonadiabatic derivative couplings and diabatic electronic couplings. Acc. Chem. Res. 48:1340–50 [Google Scholar]
  104. Tavernelli I, Curchod BFE, Rothlisberger U. 104.  2009. On nonadiabatic coupling vectors in time-dependent density functional theory. J. Chem. Phys. 131:196101 [Google Scholar]
  105. Hu C, Sugino O, Tateyama Y. 105.  2009. All-electron calculation of nonadiabatic couplings from time-dependent density functional theory: probing with the Hartree–Fock exact exchange. J. Chem. Phys. 131:114101 [Google Scholar]
  106. Send R, Furche F. 106.  2010. First-order nonadiabatic couplings from time-dependent hybrid density functional response theory: consistent formalism, implementation, and performance. J. Chem. Phys. 132:044107 [Google Scholar]
  107. Fatehi S, Alguire E, Shao Y, Subotnik JE. 107.  2011. Analytical derivative couplings between configuration interaction singles states with built-in translation factors for translational invariance. J. Chem. Phys. 135:234105 [Google Scholar]
  108. Li Z, Liu W. 108.  2014. First-order nonadiabatic coupling matrix elements between excited states: a Lagrangian formulation at the CIS, RPA, TD-HF, and TD-DFT levels. J. Chem. Phys. 141:014110 [Google Scholar]
  109. Zhang X, Herbert JM. 109.  2014. Analytic derivative couplings for spin-flip configuration interaction singles and spin-flip time-dependent density functional theory. J. Chem. Phys. 141:064104 [Google Scholar]
  110. Martínez TJ. 110.  1997. Ab initio molecular dynamics around a conical intersection: Li(2p) + H2. Chem. Phys. Lett. 272:139–47 [Google Scholar]
  111. Martínez TJ, Levine RD. 111.  1996. First-principles molecular dynamics on multiple electronic states: a case study of NaI. J. Chem. Phys. 105:6334–41 [Google Scholar]
  112. Ou Q, Fatehi S, Alguire E, Subotnik JE. 112.  2014. Derivative couplings between TDDFT excited states obtained by direct differentiation in the Tamm–Dancoff approximation. J. Chem. Phys. 141:024114 [Google Scholar]
  113. Ou Q, Alguire E, Subotnik JE. 113.  2015. Derivative couplings between time-dependent density functional theory excited states in the random-phase approximation based on pseudowavefunctions: behavior around conical intersections. J. Phys. Chem. B 119:7150–61 [Google Scholar]
  114. Alguire E, Ou Q, Subotnik JE. 114.  2015. Calculating derivative couplings between time-dependent Hartree–Fock excited states with pseudo-wavefunctions. J. Phys. Chem. B 119:7140–49 [Google Scholar]
  115. Shao Y, Gan Z, Epifanovsky E, Gilbert AT, Wormit M. 115.  et al. 2015. Advances in molecular quantum chemistry contained in the Q-Chem 4 program package. Mol. Phys. 113:184–215 [Google Scholar]
  116. Mahan BH. 116.  1975. Microscopic reversibility and detailed balance. An analysis. J. Chem. Ed. 52:299–302 [Google Scholar]
  117. Sherman MC, Corcelli SA. 117.  2015. Thermal equilibrium properties of surface hopping with an implicit Langevin bath. J. Chem. Phys. 142:024110 [Google Scholar]
  118. Subotnik JE, Rhee YM. 118.  2015. On surface hopping and time-reversal. J. Phys. Chem. A 119:990–95 [Google Scholar]
  119. Tannor D. 119.  2006. Introduction to Quantum Mechanics: A Time-Dependent Perspective Univ. Sci. Books [Google Scholar]
  120. Jain A, Herman MF, Ouyang W, Subotnik JE. 120.  2015. Surface hopping, transition state theory and decoherence. I. Scattering theory and time-reversibility. J. Chem. Phys. 143:134106 [Google Scholar]
  121. Hammes-Schiffer S, Tully J. 121.  1994. Proton transfer in solution: molecular dynamics with quantum transitions. J. Chem. Phys. 101:4657–67 [Google Scholar]
  122. Coker DF, Xiao L. 122.  1995. Methods for molecular dynamics with nonadiabatic transitions. J. Chem. Phys. 102:496–510 [Google Scholar]
  123. Jasper AW, Hack MD, Truhlar DG. 123.  2001. The treatment of classically forbidden electronic transitions in semiclassical trajectory surface hopping calculations. J. Chem. Phys. 115:1804–16 [Google Scholar]
  124. Huo P, Miller TF, Coker DF. 124.  2013. Communication: predictive partial linearized path integral simulation of condensed phase electron transfer dynamics. J. Chem. Phys. 139:151103 [Google Scholar]
  125. Strümpfer J, Schulten K. 125.  2012. Open quantum dynamics calculations with the hierarchy equations of motion on parallel computers. J. Chem. Theory Comp. 8:2808–16 [Google Scholar]
  126. Strümpfer J, Schulten K. 126.  2009. Light harvesting complex II B850 excitation dynamics. J. Chem. Phys. 131:225101 [Google Scholar]
  127. Tully JC, Preston RK. 127.  1971. Trajectory surface hopping approach to nonadiabatic molecular collisions: the reaction of H+with D2. J. Chem. Phys. 55:562–72 [Google Scholar]
  128. Tempelaar R, van der Vegte CP, Knoester J, Jansen TLC. 128.  2013. Surface hopping modeling of two-dimensional spectra. J. Chem. Phys. 138:164106 [Google Scholar]
  129. Tempelaar R, Spano FC, Knoester J, Jansen TLC. 129.  2014. Mapping the evolution of spatial exciton coherence through time-resolved fluorescence. J. Phys. Chem. Lett. 5:1505–10 [Google Scholar]
  130. Zimmermann T, Vanicek J. 130.  2014. Efficient on-the-fly ab initio semiclassical method for computing time-resolved nonadiabatic electronic spectra with surface hopping or Ehrenfest dynamics. J. Chem. Phys. 141:134102 [Google Scholar]
  131. Dorfman KE, Fingerhut BP, Mukamel S. 131.  2013. Broadband infrared and Raman probes of excited-state vibrational molecular dynamics: simulation protocols based on loop diagrams. Phys. Chem. Chem. Phys. 15:12348–59 [Google Scholar]
  132. Fingerhut BP, Dorfman KE, Mukamel S. 132.  2014. Probing the conical intersection dynamics of the RNA base uracil by UV-pump stimulated-Raman-probe signals: ab initio simulations. J. Chem. Theory Comp. 10:1172–88 [Google Scholar]
  133. Martínez-Mesa A, Saalfrank P. 133.  2015. Semiclassical modelling of finite-pulse effects on nonadiabatic photodynamics via initial condition filtering: the predissociation of NaI as a test case. J. Chem. Phys. 142:194107 [Google Scholar]
  134. Shen YC, Cina JA. 134.  1999. What can short-pulse pump–probe spectroscopy tell us about Franck–Condon dynamics?. J. Chem. Phys. 110:9793–806 [Google Scholar]
  135. Richter M, Marquetand P, González-Vázquez J, Sola I, González L. 135.  2011. SHARC: ab initio molecular dynamics with surface hopping in the adiabatic representation including arbitrary couplings. J. Chem. Theory Comp. 7:1253–58 [Google Scholar]
  136. Hammes-Schiffer S, Tully JC. 136.  1995. Nonadiabatic transition state theory and multiple potential energy surface molecular dynamics of infrequent events. J. Chem. Phys. 103:8528–37 [Google Scholar]
  137. Ouyang W, Dou W, Subotnik JE. 137.  2015. Surface hopping with a manifold of electronic states. I. Incorporating surface-leaking to capture lifetimes. J. Chem. Phys. 142:084109 [Google Scholar]
  138. Shenvi N, Roy S, Tully JC. 138.  2009. Nonadiabatic scattering at metal surfaces: independent electron surface hopping. J. Chem. Phys. 130:174107 [Google Scholar]
  139. Shenvi N, Roy S, Tully JC. 139.  2009. Dynamical steering and electronic excitation in NO scattering from a gold surface. Science 326:829–32 [Google Scholar]
  140. Dou W, Nitzan A, Subotnik JE. 140.  2015. Surface hopping with a manifold of electronic states. II. Application to the many-body Anderson–Holstein model. J. Chem. Phys. 142:084110 [Google Scholar]
  141. Dou W, Nitzan A, Subotnik JE. 141.  2015. Surface hopping with a manifold of electronic states. III. Transients, broadening, and the Marcus picture. J. Chem. Phys. 142:234106 [Google Scholar]
  142. Granucci G, Persico M, Toniolo A. 142.  2001. Direct semiclassical simulation of photochemical processes with semiempirical wave functions. J. Chem. Phys. 114:10608–15 [Google Scholar]
  143. Fernandez-Alberti S, Roitberg AE, Nelson T, Tretiak S. 143.  2012. Identification of unavoided crossings in nonadiabatic photoexcited dynamics involving multiple electronic states in polyatomic conjugated molecules. J. Chem. Phys. 137:014512 [Google Scholar]
  144. Meek GA, Levine BG. 144.  2014. Evaluation of the time-derivative coupling for accurate electronic state transition probabilities from numerical simulations. J. Phys. Chem. Lett. 5:2351–56 [Google Scholar]
  145. Wang L, Prezhdo OV. 145.  2014. A simple solution to the trivial crossing problem in surface hopping. J. Phys. Chem. Lett. 5:713–19 [Google Scholar]
  146. Meek GA, Levine BG. 146.  2014. Evaluation of the time-derivative coupling for accurate electronic state transition probabilities from numerical simulations. J. Phys. Chem. Lett. 5:2351–56 [Google Scholar]
  147. Herman MF. 147.  1982. Generalization of the geometric optical series approach for non-adiabatic scattering problems. J. Chem. Phys. 76:2949–58 [Google Scholar]
  148. Gorshkov VN, Tretiak S, Mozyrsky D. 148.  2013. Semiclassical Monte-Carlo approach for modelling non-adiabatic dynamics in extended molecules. Nature 4:2144 [Google Scholar]
  149. Zhu C, Nangia S, Jasper AW, Truhlar DG. 149.  2004. Coherent switching with decay of mixing: an improved treatment of electronic coherence for non-Born–Oppenheimer trajectories. J. Chem. Phys. 121:7658–70 [Google Scholar]
  150. Zhu C, Jasper AW, Truhlar DG. 150.  2005. Non-Born–Oppenheimer Liouville–von Neumann dynamics. Evolution of a subsystem controlled by linear and population-driven decay of mixing with decoherent and coherent switching. J. Chem. Theory Comp. 1:527–40 [Google Scholar]
  151. Granucci G, Persico M, Zoccante A. 151.  2010. Including quantum decoherence in surface hopping. J. Chem. Phys. 133:134111 [Google Scholar]
  152. Xia SH, Xie BB, Fang Q, Cui G, Thiel W. 152.  2015. Excited-state intramolecular proton transfer to carbon atoms: nonadiabatic surface-hopping dynamics simulations. Phys. Chem. Chem. Phys. 17:9687–97 [Google Scholar]
  153. Falk MJ, Landry BR, Subotnik JE. 153.  2014. Can surface hopping sans decoherence recover Marcus theory? Understanding the role of friction in a surface hopping view of electron transfer. J. Phys. Chem. B 118:8108–17 [Google Scholar]
  154. Landry BR, Subotnik JE. 154.  2015. Surface hopping outperforms secular Redfield theory when reorganization energies range from small to moderate (and nuclei are classical). J. Chem. Phys. 142:104102 [Google Scholar]

Data & Media loading...

  • Article Type: Review Article
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error