Advertisement

TDDFT and Quantum-Classical Dynamics: A Universal Tool Describing the Dynamics of Matter

  • Federica Agostini
  • Basile F. E. Curchod
  • Rodolphe Vuilleumier
  • Ivano Tavernelli
  • E. K. U. Gross
Living reference work entry

Latest version View entry history

Abstract

Time-dependent density functional theory (TDDFT) is currently the most efficient approach allowing to describe electronic dynamics in complex systems, from isolated molecules to the condensed phase. TDDFT has been employed to investigate an extremely wide range of time-dependent phenomena, as spin dynamics in solids, charge and energy transport in nanoscale devices, and photoinduced exciton transfer in molecular aggregates. It is therefore nearly impossible to give a general account of all developments and applications of TDDFT in material science, as well as in physics and chemistry. A large variety of aspects are covered throughout these volumes. In the present chapter, we will limit our presentation to the description of TDDFT developments and applications in the field of quantum molecular dynamics simulations in combination with trajectory-based approaches for the study of nonadiabatic excited-state phenomena. We will present different quantum-classical strategies used to describe the coupled dynamics of electrons and nuclei underlying nonadiabatic processes. In addition, we will give an account of the most recent applications with the aim of illustrating the nature of the problems that can be addressed with the help of these approaches. The potential, as well as the limitations, of the presented methods is discussed, along with possible avenues for future developments in TDDFT and nonadiabatic dynamics.

References

  1. Abedi A, Maitra NT, Gross EKU (2010) Exact factorization of the time-dependent electron-nuclear wave function. Phys Rev Lett 105(12):123002ADSCrossRefGoogle Scholar
  2. Abedi A, Maitra NT, Gross EKU (2012) Correlated electron-nuclear dynamics: exact factorization of the molecular wave-function. J Chem Phys 137(22):22A530CrossRefGoogle Scholar
  3. Abedi A, Agostini F, Suzuki Y, Gross EKU (2013a) Dynamical steps that bridge piecewise adiabatic shapes in the exact time-dependent potential energy surface. Phys Rev Lett 110(26):263001ADSCrossRefGoogle Scholar
  4. Abedi A, Maitra NT, Gross EKU (2013b) Reply to comment on “correlated electron-nuclear dynamics: exact factorization of the molecular wave-function”. J Chem Phys 139(8):087102ADSCrossRefGoogle Scholar
  5. Abedi A, Agostini F, Gross EKU (2014) Mixed quantum-classical dynamics from the exact decomposition of electron-nuclear motion. Europhys Lett 106(3):33001ADSCrossRefGoogle Scholar
  6. Adamo C, Jacquemin D (2013) The calculations of excited-state properties with time-dependent density functional theory. Chem Soc Rev 42(3):845–856CrossRefGoogle Scholar
  7. Agostini F, Abedi A, Suzuki Y, Gross EKU (2013) Mixed quantum-classical dynamics on the exact time-dependent potential energy surfaces: a novel perspective on non-adiabatic processes. Mol Phys 111(22-23):3625ADSCrossRefGoogle Scholar
  8. Agostini F, Abedi A, Gross EKU (2014) Classical nuclear motion coupled to electronic non-adiabatic transitions. J Chem Phys 141(21):214101ADSCrossRefGoogle Scholar
  9. Agostini F, Abedi A, Suzuki Y, Min SK, Maitra NT, Gross EKU (2015a) The exact forces on classical nuclei in non-adiabatic charge transfer. J Chem Phys 142(8):084303ADSCrossRefGoogle Scholar
  10. Agostini F, Min SK, Gross EKU (2015b) Semiclassical analysis of the electron-nuclear coupling in electronic non-adiabatic processes. Ann Phys 527(9–10):546–555MathSciNetzbMATHCrossRefGoogle Scholar
  11. Agostini F, Min SK, Abedi A, Gross EKU (2016) Quantum-classical non-adiabatic dynamics: coupled- vs. independent-trajectory methods. J Chem Theory Comput 12(5):2127–2143CrossRefGoogle Scholar
  12. Agostini F, Tavernelli I, Ciccotti G (2018) Nuclear quantum effects in electronic (non)adiabatic dynamics. Eur Phys J B 91:139ADSMathSciNetCrossRefGoogle Scholar
  13. Akimov AV, Prezhdo OV (2014) Advanced capabilities of the PYXAID program: integration schemes, decoherence effects, multiexcitonic states, and field-matter interaction. J Chem Theory Comput 10:789CrossRefGoogle Scholar
  14. Alonso JL, Clemente-Gallardo J, Echeniche-Robba P, Jover-Galtier JA (2013) Comment on “correlated electron-nuclear dynamics: exact factorization of the molecular wave-function”. J Chem Phys 139:087101ADSCrossRefGoogle Scholar
  15. Andrade X, Castro A, Zueco D, Alonso J, Echenique P, Falceto F, Rubio A (2009) Modified Ehrenfest formalism for efficient large-scale ab initio molecular dynamics. J Chem Theory Comput 5(4):728–742CrossRefGoogle Scholar
  16. Atkins AJ, González L (2017) Trajectory surface-hopping dynamics including intersystem crossing in [ru (bpy) 3] 2+. J Phys Chem Lett 8(16):3840–3845CrossRefGoogle Scholar
  17. Baer R (2002) Non-adiabatic couplings by time-dependent density functional theory. Chem Phys Lett 364:75–79ADSMathSciNetCrossRefGoogle Scholar
  18. Baer M (2006) Beyond born-oppenheimer: electronic nonadiabatic coupling terms and conical intersections. Wiley, Hoboken, New JerseyzbMATHCrossRefGoogle Scholar
  19. Barbatti M (2011) Nonadiabatic dynamics with trajectory surface hopping method. WIREs Comput Mol Sci 1:620–633CrossRefGoogle Scholar
  20. Ben-Nun M, Martínez TJ (1998) Nonadiabatic molecular dynamics: validation of the multiple spawning method for a multidimensional problem. J Chem Phys 108:7244–7257ADSCrossRefGoogle Scholar
  21. Ben-Nun M, Martínez TJ (2002) Ab initio quantum molecular dynamics. Adv Chem Phys 121:439–512Google Scholar
  22. Ben-Nun M, Martínez TJ (2000) A multiple spawning approach to tunneling dynamics. J Chem Phys 112(14):6113–6121ADSCrossRefGoogle Scholar
  23. Ben-Nun M, Quenneville J, Martínez TJ (2000) Ab initio multiple spawning: photochemistry from first principles quantum molecular dynamics. J Phys Chem A 104:5161–5175CrossRefGoogle Scholar
  24. Bittner ER, Rossky PJ (1995) Quantum decoherence in mixed quantum-classical systems: nonadiabatic processes. J Chem Phys 103:8130ADSCrossRefGoogle Scholar
  25. Böckmann M, Doltsinis N, Marx D (2010) Unraveling a chemically enhanced photoswitch: bridged azobenzene. Angew Chemie Int Ed 49:3382CrossRefGoogle Scholar
  26. Bonella S, Coker DF (2005) LAND-map, a linearized approach to nonadiabatic dynamics using the mapping formalism. J Chem Phys 122:194102–194113ADSCrossRefGoogle Scholar
  27. Burghardt I, Meyer HD, Cederbaum LS (1999) Approaches to the approximate treatment of complex molecular systems by the multiconfiguration time-dependent Hartree method. J Chem Phys 111:2927ADSCrossRefGoogle Scholar
  28. Cannizzo A, van Mourik F, Gawelda W, Zgrablic G, Bressler C, Chergui M (2006) Broadband femtosecond fluorescence spectroscopy of [Ru(bpy)3]2+. Angew Chem Int Ed 45:3174–3176CrossRefGoogle Scholar
  29. Car R, Parrinello M (1985) Unified approach for molecular dynamics and density-functional theory. Phys Rev Lett 55:2471ADSCrossRefGoogle Scholar
  30. Casida ME (1995) Time-dependent density-functional response theory for molecules. In: Chong DP (ed) Recent advances in density functional methods. World Scientific, Singapore, p 155CrossRefGoogle Scholar
  31. Casida ME (2009) Time-dependent density-functional theory for molecules and molecular solids. J Mol Struc (Theochem) 914(1–3):3–18CrossRefGoogle Scholar
  32. Casida M, Huix-Rotllant M (2012) Progress in time-dependent density-functional theory. Annu Rev Phys Chem 63(1):287–323. http://www.annualreviews.org/doi/pdf/10.1146/annurev-physchem-032511-143803ADSCrossRefGoogle Scholar
  33. Casida ME, Gutierrez F, Guan J, Gadea FX, Salahub D, Daudey JP (2000) Charge-transfer correction for improved time-dependent local density approximation excited-state potential energy curves: analysis within the two-level model with illustration for H2O and LiH. J Chem Phys 113:7062ADSCrossRefGoogle Scholar
  34. Castro A, Marques MAL, Rubio A (2004) Propagators for the time-dependent Kohn-Sham equations. J Chem Phys 121(8):3425–3433. https://doi.org/10.1063/1.1774980ADSCrossRefGoogle Scholar
  35. Cave R, Zhang F, Maitra N, Burke K (2004) A dressed TDDFT treatment of the 21Ag states of butadiene and hexatriene. Chem Phys Lett 389(1):39–42ADSCrossRefGoogle Scholar
  36. Chernyak V, Mukamel S (1996) Size-consistent quasiparticle representation of nonlinear optical susceptibilities in many-electron systems. J Chem Phys 104(2):444–459. https://doi.org/10.1063/1.470843, http://link.aip.org/link/?JCP/104/444/1ADSCrossRefGoogle Scholar
  37. Chernyak V, Mukamel S (2000) Density-matrix representation of nonadiabatic couplings in time-dependent density functional (TDDFT) theories. J Chem Phys 112:3572–3579ADSCrossRefGoogle Scholar
  38. Cordova F, Doriol LJ, Ipatov A, Casida ME, Filippi C, Vela A (2007) Troubleshooting time-dependent density-functional theory for photochemical applications: Oxirane. J Chem Phys 127:164,111CrossRefGoogle Scholar
  39. Craig CF, Duncan WR, Prezhdo OV (2005) Trajectory surface hopping in the time-dependent kohn-sham approach for electron-nuclear dynamics. Phys Rev Lett 95:163001ADSCrossRefGoogle Scholar
  40. Curchod BFE, Agostini F, Tavernelli I (2018) CT-MQC - a coupled-trajectory mixed quantum/classical method including nonadiabatic quantum coherence effects. Eur Phys J B, 91:168ADSMathSciNetCrossRefGoogle Scholar
  41. Curchod BFE, Agostini F (2017) On the dynamics through a conical intersection. J Phys Chem Lett 8:831CrossRefGoogle Scholar
  42. Curchod BFE, Tavernelli I (2013) On trajectory-based nonadiabatic dynamics: Bohmian dynamics versus trajectory surface hopping. J Chem Phys 138:184112ADSCrossRefGoogle Scholar
  43. Curchod BFE, Tavernelli I, Rothlisberger U (2011) Trajectory-based solution of the nonadiabatic quantum dynamics equations: an on-the-fly approach for molecular dynamics simulations. Phys Chem Chem Phys 13:3231–3236CrossRefGoogle Scholar
  44. Curchod BFE, Rothlisberger U, Tavernelli I (2013) Trajectory-based nonadiabatic dynamics with time-dependent density functional theory. Chem Phys Chem 14(7):1314–1340CrossRefGoogle Scholar
  45. Curchod BFE, Agostini F, Gross EKU (2016a) An exact factorization perspective on quantum interferences in nonadiabatic dynamics. J Chem Phys 145:034103ADSCrossRefGoogle Scholar
  46. Curchod BFE, Rauer C, Marquetand P, González L, Martínez T (2016b) Communication: Gaims–generalized ab initio multiple spawning for both internal conversion and intersystem crossing processes. J Chem Phys 144(10):101102ADSCrossRefGoogle Scholar
  47. Curchod BFE , Sisto A, Martínez TJ (2016c) Ab initio multiple spawning photochemical dynamics of DMABN using GPUs. J Phys Chem A 121(1):265–276CrossRefGoogle Scholar
  48. Curchod BFE, Sisto A, Martínez TJ (2017) Ab initio multiple spawning photochemical dynamics of dmabn using GPUs. J Phys Chem A 121(1):265–276CrossRefGoogle Scholar
  49. Dancoff SM (1950) Non-adiabatic meson theory of nuclear forces. Phys Rev 78:382ADSzbMATHCrossRefGoogle Scholar
  50. Deglmann P, Furche F, Ahlrichs R (2002) An efficient implementation of second analytical derivatives for density functional methods. Chem Phys Lett 362(5–6):511–518. https://doi.org/10.1016/S0009-2614(02)01084-9, http://www.sciencedirect.com/science/article/pii/S0009261402010849ADSCrossRefGoogle Scholar
  51. Dimitrov T, Flick J, Ruggenthaler M, Rubio A (2017) Exact functionals for correlated electron-photon systems. New J Phys 19:113036CrossRefGoogle Scholar
  52. Dobson JF, Bünner MJ, Gross EKU (1997) Time-dependent density functional theory beyond linear response: an exchange-correlation potential with memory. Phys Rev Lett 79(10): 1905ADSCrossRefGoogle Scholar
  53. Doltsinis NL, Marx D (2002) Nonadiabatic Car-Parrinello molecular dynamics. Phys Rev Lett 88:166402ADSCrossRefGoogle Scholar
  54. Dreuw A, Head-Gordon M (2004) Failure of time-dependent density functional theory for long-range charge-transfer excited states: the zincbacteriochlorin-bacteriochlorin and bacteriochlorophyll-spheroidene complexes. J Am Chem Soc 126:4007–4016CrossRefGoogle Scholar
  55. Dreuw A, Head-Gordon M (2005) Single-reference ab initio methods for the calculation of excited states of large molecules. Chem Rev 105:4009CrossRefGoogle Scholar
  56. Dreuw A, Weisman J, Head-Gordon M (2003) Long-range charge-transfer excited states in time-dependent density functional theory require non-local exchange. J Chem Phys 119:2943ADSCrossRefGoogle Scholar
  57. Dunkel ER, Bonella S, Coker DF (2008) Iterative linearized approach to nonadiabatic dynamics. J Chem Phys 129:114106ADSCrossRefGoogle Scholar
  58. Eich FG, Agostini F (2016) The adiabatic limit of the exact factorization of the electron-nuclear wave function. J Chem Phys 145:054110ADSCrossRefGoogle Scholar
  59. Elliott P, Maitra NT (2012) Propagation of initially excited states in time-dependent density-functional theory. Phys Rev A 85:052510ADSCrossRefGoogle Scholar
  60. Elliott P, Furche F, Burke K (2009) 3 excited states from time-dependent density functional theory. Rev Comput Chem 26:91Google Scholar
  61. Elliott P, Goldson S, Canahui C, Maitra NT (2011) Perspectives on double-excitations in TDDFT. Chem Phys 391(1):110–119CrossRefGoogle Scholar
  62. Epstein S (1954) Note on perturbation theory. Am J Phys 22:613ADSzbMATHCrossRefGoogle Scholar
  63. Fang JY, Hammes-Schiffer S (1999) Improvement of the internal consistency in trajectory surface hopping. J Phys Chem A 103:9399–9407CrossRefGoogle Scholar
  64. Flick J, Appel H, Ruggenthaler M, Rubio A (2017a) Cavity Born-Oppenheimer approximation for correlated electron-nuclear-photon systems. J Chem Theory Comput 13:1616–1625CrossRefGoogle Scholar
  65. Flick J, Ruggenthaler M, Appel H, Rubio A (2017b) Atoms and molecules in cavities, from weak to strong coupling in quantum-electrodynamics (QED) chemistry. Proc Nat Ac Sci 114:3026–3034CrossRefGoogle Scholar
  66. Frenkel J (1934) Wave mechanics. Clarendon, OxfordzbMATHGoogle Scholar
  67. Furche F (2001) On the density matrix based approach to time-dependent density functional response theory. J Chem Phys 114:5982–5992ADSCrossRefGoogle Scholar
  68. Gaigeot MP, Lopez-Tarifa P, Martin F, Alcami M, Vuilleumier R, Tavernelli I, Hervédu Penhoat MA, Politis MF (2010) Theoretical investigation of the ultrafast dissociation of ionised biomolecules immersed in water: direct and indirect effects. Mutat Res-Rev Mutat 704(1–3): 45–53. http://www.sciencedirect.com/science/article/pii/S1383574210000086CrossRefGoogle Scholar
  69. Gao X, Thiel W (2017) Non-hermitian surface hopping. Phys Rev E 95:013308ADSCrossRefGoogle Scholar
  70. Garashchuk S, Rassolov VA (2003) Quantum dynamics with Bohmian trajectories: energy conserving approximation to the quantum potential. Chem Phys Lett 376:358ADSCrossRefGoogle Scholar
  71. Gawelda W, Johnson M, de Groot FMF, Abela R, Bressler C, Chergui M (2006) Electronic and molecular structure of photoexcited [Ru(II)(bpy)3]2+ probed by picosecond x-ray absorption spectroscopy. J Am Chem Soc 128:5001–5009CrossRefGoogle Scholar
  72. Gómez I, Reguero M, Boggio-Pasqua M, Robb MA (2005) Intramolecular charge transfer in 4-aminobenzonitriles does not necessarily need the twist. J Am Chem Soc 127(19):7119–7129CrossRefGoogle Scholar
  73. Grabo T, Petersilka M, Gross EKU (2000) Molecular excitation energies from time-dependent density functional theory. J Mol Struc (Theochem) 501–502:353–367CrossRefGoogle Scholar
  74. Grabowski ZR, Rotkiewicz K, Rettig W (2003) Structural changes accompanying intramolecular electron transfer: focus on twisted intramolecular charge-transfer states and structures. Chem Rev 103(10):3899–4032CrossRefGoogle Scholar
  75. Granucci G, Persico M (2007) Critical appraisal of the fewest switches algorithm for surface hopping. J Chem Phys 126:134114ADSCrossRefGoogle Scholar
  76. Gritsenko O, Baerends E (2004) Asymptotic correction of the exchange–correlation kernel of time-dependent density functional theory for long-range charge-transfer excitations. J Chem Phys 121:655ADSCrossRefGoogle Scholar
  77. Gross E, Kohn W (1990) Time-dependent density-functional theory. Adv Quantum Chem 21: 255–291ADSCrossRefGoogle Scholar
  78. Gross EKU, Kohn W (1985) Local density-functional theory of frequency-dependent linear response. Phys Rev Lett 55:2850–2852ADSCrossRefGoogle Scholar
  79. Gross EKU, Ullrich CA, Gossmann UJ (1994) Density functional theory of time-dependent systems. In: Gross EKU, Dreizler RM (eds) Density functional theory. Plenum, New York, pp 149–171Google Scholar
  80. Gross EKU, Dobson J, Petersilka M (1996) Density functional theory of time-dependent phenomena. In: Nalewajski RF (ed) Density functional theory II, topics in current chemistry, vol 181. Springer, Berlin, pp 81–172Google Scholar
  81. Hack MD, Wensmann AM, Truhlar DG, Ben-Nun M, Martínez TJ (2001) Comparison of full multiple spawning, trajectory surface hopping, and converged quantum mechanics for electronically nonadiabatic dynamics. J Chem Phys 115:1172ADSCrossRefGoogle Scholar
  82. Helgaker T, Jørgensen P (1989) Configuration-interaction energy derivatives in a fully variational formulation. Theor Chem Acc 75:111–127CrossRefGoogle Scholar
  83. Heller EJ (1981) Frozen gaussians: a very simple semiclassical approximation. J Chem Phys 75(6):2923–2931ADSMathSciNetCrossRefGoogle Scholar
  84. Hellgren M, Gross EKU (2012) Discontinuities of the exchange-correlation kernel and charge-transfer excitations in time-dependent density-functional theory. Phys Rev A 85:022514ADSCrossRefGoogle Scholar
  85. Hirata S, Head-Gordon M (1999) Time-dependent density functional theory within the Tamm-Dancoff approximation. Chem Phys Lett 314:291–299ADSCrossRefGoogle Scholar
  86. Hohenberg P, Kohn W (1964) Inhomogeneous electron gas. Phys Rev B 136:B864ADSMathSciNetCrossRefGoogle Scholar
  87. Hsu C, Hirata S, Head-Gordon M (2001) Excitation energies from time-dependent density functional theory for linear polyene oligomers: butadiene to decapentaene. J Phys Chem A 105(2):451–458CrossRefGoogle Scholar
  88. Hu C, Hirai H, Sugino O (2007) Nonadiabatic couplings from time-dependent density functional theory: formulation in the Casida formalism and practical scheme within modified linear response. J Chem Phys 127:064103ADSCrossRefGoogle Scholar
  89. Hu C, Hirai H, Sugino O (2008) Nonadiabatic couplings from time-dependent density functional theory. II. Successes and challenges of the pseudopotential approximation. J Chem Phys 128:154111ADSCrossRefGoogle Scholar
  90. Hu C, Sugino O, Hirai H, Tateyama Y (2010) Nonadiabatic couplings from the Kohn-Sham derivative matrix: formulation by time-dependent density-functional theory and evaluation in the pseudopotential framework. Phys Rev A 82(6):062508ADSCrossRefGoogle Scholar
  91. Hu C, Komakura R, Li Z, Watanabe K (2012) TDDFT study on quantization behaviors of nonadiabatic couplings in polyatomic systems. Int J Quantum Chem 113:263–271CrossRefGoogle Scholar
  92. Huo P, Coker DF (2012) Consistent schemes for non-adiabatic dynamics derived from partial linearized density matrix propagation. J Chem Phys 137:22A535CrossRefGoogle Scholar
  93. Hutter J (2003) Excited state nuclear forces from the Tamm-Dancoff approximation to time-dependent density functional theory within the plane wave basis set framework. J Chem Phys 118:3928–3934ADSCrossRefGoogle Scholar
  94. Iikura H, Tsuneda T, Yanai T, Hirao K (2001) A long-range correction scheme for generalized-gradient-approximation exchange functionals. J Chem Phys 115:3540ADSCrossRefGoogle Scholar
  95. Isborn CM, Luehr N, Ufimtsev IS, Martínez TJ (2011) Excited-state electronic structure with configuration interaction singles and Tamm–Dancoff time-dependent density functional theory on graphical processing units. J Chem Theory Comput 7(6):1814CrossRefGoogle Scholar
  96. Izmaylov AF, Joubert-Doriol L (2017) Quantum nonadiabatic cloning of entangled coherent states. J Phys Chem Lett 8(8):1793–1797CrossRefGoogle Scholar
  97. Jaeger HM, Fischer S, Prezhdo OV (2012) Decoherence-induced surface hopping. J Chem Phys 137:22A545CrossRefGoogle Scholar
  98. Jamorski C, Casida ME, Salahub DR (1996) Dynamic polarizabilities and excitation spectra from a molecular implementation of time-dependent density-functional response theory: N2 as a case study. J Chem Phys 104:5134ADSCrossRefGoogle Scholar
  99. Jasper AW, Truhlar DG (2007) Electronic decoherence time for non-born-oppenheimer trajectories. J Chem Phys 127:194306ADSCrossRefGoogle Scholar
  100. Jasper AW, Zhu C, Nangia S, Truhlar DG (2004) Introductory lecture: nonadiabatic effects in chemical dynamics. Faraday Discuss 127:1ADSCrossRefGoogle Scholar
  101. Jasper AW, Nangia S, Zhu C, Truhlar DG (2006) Non-born-oppenheimer molecular dynamics. Acc Chem Res 39:101CrossRefGoogle Scholar
  102. Joubert-Doriol L, Sivasubramanium J, Ryabinkin IG, Izmaylov AF (2017) Topologically correct quantum nonadiabatic formalism for on-the-fly dynamics. J Phys Chem Lett 8(2):452–456CrossRefGoogle Scholar
  103. Kapral R (2006) Progress in the theory of mixed quantum-classical dynamics. Annu Rev Phys Chem 57(1):129–157ADSCrossRefGoogle Scholar
  104. Kapral R, Ciccotti G (1999) Mixed quantum-classical dynamics. J Chem Phys 110(18):8919–8929. https://doi.org/10.1063/1.478811ADSCrossRefGoogle Scholar
  105. Kleinman L, Bylander DM (1982) Efficacious form for model pseudopotentials. Phys Rev Lett 48:1425ADSCrossRefGoogle Scholar
  106. Kurzweil Y, Baer R (2004) Time-dependent exchange-correlation current density functionals with memory. J Chem Phys 121(18):8731–8741. https://doi.org/10.1063/1.1802793, http://link.aip.org/link/?JCP/121/8731/1ADSCrossRefGoogle Scholar
  107. Lara-Astiaso M, Palacios A, Decleva P, Tavernelli I, Martín F (2017) Role of electron-nuclear coupled dynamics on charge migration induced by attosecond pulses in glycine. Cheml Phys Lett 683:357ADSCrossRefGoogle Scholar
  108. Lasorne B, Bearpark MJ, Robb MA, Worth GA (2006) Direct quantum dynamics using variational multi-configuration gaussian wavepackets. Chem Phys Lett 432(4):604–609ADSCrossRefGoogle Scholar
  109. Lasorne B, Robb M, Worth G (2007) Direct quantum dynamics using variational multi-configuration gaussian wavepackets. implementation details and test case. Phys Chem Chem Phys 9(25):3210–3227CrossRefGoogle Scholar
  110. Laurent AD, Jacquemin D (2013) Td-dft benchmarks: a review. Int J Quant Chem 113(17): 2019–2039CrossRefGoogle Scholar
  111. Lauvergnat D, Nauts A (2010) Torsional energy levels of nitric acid in reduced and full dimensionality with elvibrot and tnum. Phys Chem Chem Phys 12:8405CrossRefGoogle Scholar
  112. Lauvergnat D, Nauts A (2014) Quantum dynamics with sparse grids: a combination of Smolyak scheme and cubature. Application to methanol in full dimensionality. Spectrochim Acta Part A 119:18CrossRefGoogle Scholar
  113. Leininger T, Stoll H, Werner H, Savin A (1997) Combining long-range configuration interaction with short-range density functionals. Chem Phys Lett 275(3):151–160ADSCrossRefGoogle Scholar
  114. Levine BG, Ko C, Quenneville J, Martinez TJ (2006) Conical intersections and double excitations in density functional theory. Mol Phys 104:1039ADSCrossRefGoogle Scholar
  115. Levine BG, Coe JD, Virshup AM, Martinez TJ (2008) Implementation of ab initio multiple spawning in the molpro quantum chemistry package. Chem Phys 347(1):3–16CrossRefGoogle Scholar
  116. Li Z, Liu W (2014) First-order nonadiabatic coupling matrix elements between excited states: a lagrangian formulation at the CIS, RPA, TD-HF, and TD-DFT levels. J Chemi Phys 141(1):014110ADSCrossRefGoogle Scholar
  117. Li X, Tully JC, Schlegel HB, Frisch MJ (2005) Ab initio Ehrenfest dynamics. J Chem Phys 123(8):084106. https://doi.org/10.1063/1.2008258, http://link.aip.org/link/?JCP/123/084106/1ADSCrossRefGoogle Scholar
  118. Li Z, Suo B, Liu W (2014) First order nonadiabatic coupling matrix elements between excited states: implementation and application at the TD-DFT and PP-TDA levels. J Chem Phys 141(24):244105ADSCrossRefGoogle Scholar
  119. Liang W, Isborn CM, Lindsay A, Li X, Smith SM, Levis RJ (2010) Time-dependent density functional theory calculations of Ehrenfest dynamics of laser controlled dissociation of NO+: Pulse length and sequential multiple single-photon processes. J Phys Chem A 114(21):6201–6206CrossRefGoogle Scholar
  120. Lopez-Tarifa P, Herve du Penhoat MA, Vuilleumier R, Gaigeot MP, Tavernelli I, Le Padellec A, Champeaux JP, Alcami M, Moretto-Capelle P, Martin F, Politis MF (2011) Ultrafast nonadiabatic fragmentation dynamics of doubly charged uracil in a gas phase. Phys Rev Lett 107:023202ADSCrossRefGoogle Scholar
  121. Lopreore CL, Wyatt RE (2002) Electronic transitions with quantum trajectories. II. J Chem Phys 116(4):1228–1238ADSCrossRefGoogle Scholar
  122. Maitra NT (2005) Undoing static correlation: long-range charge transfer in time-dependent density-functional theory. J Chem Phys 122:234104ADSCrossRefGoogle Scholar
  123. Maitra NT, Wasserman A, Burke K (2003) What is time-dependent density-functional theory? successes and challenges. In: Gonis A, Kioussis N, Ciftan M (eds) Electron correlations and materials properties 2, Klewer/Plenum, New YorkGoogle Scholar
  124. Maitra NT, Zhang F, Cave RJ, Burke K (2004) Double excitations within time-dependent density functional theory linear response. J Chem Phys 120:5932ADSCrossRefGoogle Scholar
  125. Makhov DV, Glover WJ, Martinez TJ, Shalashilin DV (2014) Ab initio multiple cloning algorithm for quantum nonadiabatic molecular dynamics. J Chem Phys 141(5):054110ADSCrossRefGoogle Scholar
  126. Makhov D, Symonds C, Fernandez-Alberti S, Shalashilin D (2017) Ab initio quantum direct dynamics simulations of ultrafast photochemistry with multiconfigurational ehrenfest approach. Chem Phys 493:200–218CrossRefGoogle Scholar
  127. Marques MAL, Maitra NT, Nogueira FMDS, Gross EKU, Rubio A (2012) Fundamentals of time-dependent density functional theory, vol 837. Springer, Berlin/HeidelbergCrossRefGoogle Scholar
  128. Martínez TJ, Levine RD (1997) Non-adiabatic molecular dynamics: split-operator multiple spawning with applications to photodissociation. J Chem Soc Faraday Trans 93(5):941–947CrossRefGoogle Scholar
  129. Martínez TJ, Ben-Nun M, Levine RD (1996) Multi-electronic-state molecular dynamics: a wave function approach with applications. J Phys Chem 100(19):7884–7895CrossRefGoogle Scholar
  130. Marx D, Hutter J (2009) Ab initio molecular dynamics: basic theory and advanced methods. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  131. Meek GA, Levine BG (2016) The best of both reps—diabatized gaussians on adiabatic surfaces. J Chem Phys 145(18):184103ADSCrossRefGoogle Scholar
  132. Mendive-Tapia D, Lasorne B, Worth GA, Robb MA, Bearpark MJ (2012) Towards converging non-adiabatic direct dynamics calculations using frozen-width variational gaussian product basis functions. J Chem Phys 137(22):22A548CrossRefGoogle Scholar
  133. Meyer HD, Worth GA (2003) Quantum molecular dynamics: propagating wavepackets and density operators using the multiconfiguration time-dependent hartree method. Theor Chim Acta 109:251CrossRefGoogle Scholar
  134. Meyer HD, Manthe U, Cederbaum LS (1990) The multi-configurational time-dependent hartree approach. Chem Phys Lett 165:73–78ADSCrossRefGoogle Scholar
  135. Mignolet B, Curchod BFE, Martínez TJ (2016) Communication: Xfaims—external field ab initio multiple spawning for electron-nuclear dynamics triggered by short laser pulses. J Chem Phys 145(19):191104ADSCrossRefGoogle Scholar
  136. Min SK, Agostini F, Gross EKU (2015) Coupled-trajectory quantum-classical approach to electronic decoherence in nonadiabatic processes. Phys Rev Lett 115(7):073001ADSCrossRefGoogle Scholar
  137. Min SK, Agostini F, Tavernelli I, Gross EKU (2017) Ab initio nonadiabatic dynamics with coupled trajectories: a rigorous approach to quantum (de)coherence. J Phys Chem Lett 8:3048CrossRefGoogle Scholar
  138. Moss CL, Isborn CM, Li X (2009) Ehrenfest dynamics with a time-dependent density-functional-theory calculation of lifetimes and resonant widths of charge-transfer states of Li+ near an aluminum cluster surface. Phys Rev A 80:024503.  https://doi.org/10.1103/PhysRevA.80.024503, http://link.aps.org/doi/10.1103/PhysRevA.80.024503
  139. Nielsen S, Kapral R, Ciccotti G (2000) Non-adiabatic dynamics in mixed quantum-classical systems. J Stat Phys 101:225–242ADSMathSciNetzbMATHCrossRefGoogle Scholar
  140. Ou Q, Bellchambers GD, Furche F, Subotnik JE (2015) First-order derivative couplings between excited states from adiabatic TDDFT response theory. J Chem Phys 142(6):064114ADSCrossRefGoogle Scholar
  141. Parker SM, Roy S, Furche F (2016) Unphysical divergences in response theory. J Chem Phys 145(13):134105ADSCrossRefGoogle Scholar
  142. Perdew JP, Burke K, Ernzerhof M (1996) Generalized gradient approximation made simple. Phys Rev Lett 77:3865ADSCrossRefGoogle Scholar
  143. Persico M, Granucci G (2014) An overview of nonadiabatic dynamics simulations methods, with focus on the direct approach versus the fitting of potential energy surfaces. Theor Chem Acc 133(9):1–28CrossRefGoogle Scholar
  144. Petersilka M, Gossmann UJ, Gross EKU (1996) Excitation energies from time-dependent density-functional theory. Phys Rev Lett 76:1212–1215ADSCrossRefGoogle Scholar
  145. Pijeau S, Foster D, Hohenstein EG (2017) Excited-state dynamics of 2-(2’-hydroxyphenyl) benzothiazole: ultrafast proton transfer and internal conversion. J Phys Chem A 121:4595CrossRefGoogle Scholar
  146. Pulay P (1987) Analytical derivative methods in quantum chemistry. Adv Chem Phys 69: 241–286Google Scholar
  147. Rappoport D, Furche F (2005) Analytical time-dependent density functional derivative methods within the RI-J approximation, an approach to excited states of large molecules. J Chem Phys 122(6):064105. https://doi.org/10.1063/1.1844492, http://link.aip.org/link/?JCP/122/064105/1ADSCrossRefGoogle Scholar
  148. Rassolov VA, Garashchuk S (2005) Semiclassical nonadiabatic dynamics with quantum trajectories. Phys Rev A 71(3):032511ADSCrossRefGoogle Scholar
  149. Requist R, Gross EKU (2016) Exact factorization-based density functional theory of electrons and nuclei. Phys Rev Lett 117:193001ADSCrossRefGoogle Scholar
  150. Richings G, Polyak I, Spinlove K, Worth G, Burghardt I, Lasorne B (2015) Quantum dynamics simulations using gaussian wavepackets: the vMCG method. Int Rev Phys Chem 34(2): 269–308CrossRefGoogle Scholar
  151. Runge E, Gross EKU (1984) Density-functional theory for time-dependent systems. Phys Rev Lett 52:997–1000ADSCrossRefGoogle Scholar
  152. Sadri K, Lauvergnat D, Gatti F, Meyer HD (2012) Numeric kinetic energy operators for molecules in polyspherical coordinates. J Chem Phys 136:234112ADSCrossRefGoogle Scholar
  153. Sadri K, Lauvergnat D, Gatti F, Meyer HD (2014) Rovibrational spectroscopy using a kinetic energy operator in Eckart frame and the multi-configuration time-dependent hartree (MCTDH) approach. J Chem Phys 141:114101ADSCrossRefGoogle Scholar
  154. Saita K, Shalashilin DV (2012) On-the-fly ab initio molecular dynamics with multiconfigurational ehrenfest method. J Chem Phys 137(22):22A506CrossRefGoogle Scholar
  155. Scherrer A, Agostini F, Sebastiani D, Gross EKU, Vuilleumier R (2015) Nuclear velocity perturbation theory for vibrational circular dichroism: an approach based on the exact factorization of the electron-nuclear wave function. J Chem Phys 143(7):074106ADSCrossRefGoogle Scholar
  156. Scherrer A, Agostini F, Sebastiani D, Gross EKU, Vuilleumier R (2017) On the mass of atoms in molecules: beyond the born-oppenheimer approximation. Phys Rev X 7:031035Google Scholar
  157. Schild A, Agostini F, Gross EKU (2016) Electronic flux density beyond the born-oppenheimer approximation. J Phys Chem A 120:3316CrossRefGoogle Scholar
  158. Schwartz BJ, Bittner ER, Prezhdo OV, Rossky PJ (1996) Quantum decoherence and the isotope effect in condensed phase nonadiabatic molecular dynamics simulations. J Chem Phys 104:5942ADSCrossRefGoogle Scholar
  159. Send R, Furche F (2010) First-order nonadiabatic couplings from time-dependent hybrid density functional response theory: Consistent formalism, implementation, and performance. J Chem Phys 132(4):044107. https://doi.org/10.1063/1.3292571ADSCrossRefGoogle Scholar
  160. Shalashilin D (2009) Quantum mechanics with the basis set guided by ehrenfest trajectories: theory and application to spin-boson model. J Chem Phys 130:244101ADSCrossRefGoogle Scholar
  161. Shalashilin DV (2010) Nonadiabatic dynamics with the help of multiconfigurational ehrenfest method: improved theory and fully quantum 24d simulation of pyrazine. J Chem Phys 132(24):244111ADSCrossRefGoogle Scholar
  162. Shenvi N, Yang W (2012) Achieving partial decoherence in surface hopping through phase correction. J Chem Phys 137:22A528CrossRefGoogle Scholar
  163. Shenvi N, Subotnik JE, Yang W (2011a) Phase-corrected surface hopping: correcting the phase evolution of the electronic wavefunction. J Chem Phys 135:024101ADSCrossRefGoogle Scholar
  164. Shenvi N, Subotnik JE, Yang W (2011b) Simultaneous-trajectory surface hopping: a parameter-free algorithm for implementing decoherence in nonadiabatic dynamics. J Chem Phys 134:144102ADSCrossRefGoogle Scholar
  165. Stratmann RE, Scuseria GE, Frisch MJ (1998) An efficient implementation of time-dependent density-functional theory for the calculation of excitation energies of large molecules. J Chem Phys 109(19):8218–8224ADSCrossRefGoogle Scholar
  166. Subotnik JE, Shenvi N (2011a) Decoherence and surface hopping: when can averaging over initial conditions help capture the effects of wave packet separation? J Chem Phys 134:244114ADSCrossRefGoogle Scholar
  167. Subotnik JE, Shenvi N (2011b) A new approach to decoherence and momentum rescaling in the surface hopping algorithm. J Chem Phys 134:024105ADSCrossRefGoogle Scholar
  168. Subotnik JE, Ouyang W, Landry BR (2013) Can we derive Tully’s surface-hopping algorithm from the semiclassical quantum Liouville equation? Almost, but only with decoherence. J Chem Phys 139:214107ADSCrossRefGoogle Scholar
  169. Suzuki Y, Watanabe K (2016) Bohmian mechanics in the exact factorization of electron-nuclear wave functions. Phys Rev A 94:032517ADSCrossRefGoogle Scholar
  170. Suzuki Y, Abedi A, Maitra NT, Gross EKU (2015) Laser-induced electron localization in H\(_2^+\): Mixed quantum-classical dynamics based on the exact time-dependent potential energy surface. Phys Chem Chem Phys 17:29271–29280Google Scholar
  171. Tamm I (1945) J Phys 9:449MathSciNetGoogle Scholar
  172. Tao H, Levine BG, Martínez TJ (2009) Ab initio multiple spawning dynamics using multi-state second-order perturbation theory. J Chem Phys A 113(49):13656–13662CrossRefGoogle Scholar
  173. Tapavicza E, Tavernelli I, Rothlisberger U (2007) Trajectory surface hopping within linear response time-dependent density-functional theory. Phys Rev Lett 98:023001ADSCrossRefGoogle Scholar
  174. Tapavicza E, Tavernelli I, Rothlisberger U, Filippi C, Casida ME (2008) Mixed time-dependent density-functional theory/classical trajectory surface hopping study of oxirane photochemistry. J Chem Phys 129:124108ADSCrossRefGoogle Scholar
  175. Tavernelli I (2006) Electronic density response of liquid water using time-dependent density functional theory. Phys Rev B 73:094204ADSCrossRefGoogle Scholar
  176. Tavernelli I (2013) Ab initio–driven trajectory-based nuclear quantum dynamics in phase space. Phys Rev A 87(4):042501ADSCrossRefGoogle Scholar
  177. Tavernelli I (2015) Nonadiabatic molecular dynamics simulations: synergies between theory and experiments. Acc Chem Res 48(3):792–800CrossRefGoogle Scholar
  178. Tavernelli I, Röhrig U, Rothlisberger U (2005) Molecular dynamics in electronically excited states using time-dependent density functional theory. Mol Phys 103(6–8):963–981ADSCrossRefGoogle Scholar
  179. Tavernelli I, Curchod BFE, Rothlisberger U (2009a) On nonadiabatic coupling vectors in time-dependent density functional theory. J Chem Phys 131:196101ADSCrossRefGoogle Scholar
  180. Tavernelli I, Tapavicza E, Rothlisberger U (2009b) Nonadiabatic coupling vectors within linear response time-dependent density functional theory. J Chem Phys 130:124107ADSCrossRefGoogle Scholar
  181. Tavernelli I, Curchod BFE, Laktionov A, Rothlisberger U (2010) Nonadiabatic coupling vectors for excited states within time-dependent density functional theory and beyond. J Chem Phys 133:194104–194110ADSCrossRefGoogle Scholar
  182. Tavernelli I, Curchod BFE, Rothlisberger U (2011) Nonadiabatic molecular dynamics with solvent effects: a LR-TDDFT QM/MM study of ruthenium (II) tris (bipyridine) in water. Chem Phys 391:101CrossRefGoogle Scholar
  183. Tozer D (2003) Relationship between long-range charge-transfer excitation energy error and integer discontinuity in Kohn–Sham theory. J Chem Phys 119:12697ADSCrossRefGoogle Scholar
  184. Tozer DJ, Handy NC (2000) On the determination of excitation energies using density functional theory. Phys Chem Chem Phys 2(10):2117–2121CrossRefGoogle Scholar
  185. Tully JC (1990) Molecular dynamics with electronic transitions. J Chem Phys 93:1061ADSCrossRefGoogle Scholar
  186. Tully JC (1998) Mixed quantum-classical dynamics. Faraday Discuss 110:407ADSCrossRefGoogle Scholar
  187. Ullrich CA (2012) Time-dependent density-functional theory. Oxford, Oxford University PresszbMATHGoogle Scholar
  188. Ullrich CA, Tokatly IV (2006) Nonadiabatic electron dynamics in time-dependent density-functional theory. Phys Rev B 73:235102. http://link.aps.org/doi/10.1103/PhysRevB.73.235102ADSCrossRefGoogle Scholar
  189. Vacher M, Bearpark MJ, Robb MA, Malhado JP (2017) Electron dynamics upon ionization of polyatomic molecules: Coupling to quantum nuclear motion and decoherence. Phys Rev Lett 118(8):083001ADSCrossRefGoogle Scholar
  190. van Leeuwen R (1998) Causality and symmetry in time-dependent density-functional theory. Phys Rev Lett 80(6):1280–1283ADSCrossRefGoogle Scholar
  191. van Leeuwen R (1999) Mapping from densities to potentials in time-dependent density-functional theory. Phys Rev Lett 82(19):3863–3866ADSCrossRefGoogle Scholar
  192. Van Vleck JH (1928) The correspondence principle in the statistical interpretation of quantum mechanics. Proc Nat Aca Sci USA 14(2):178ADSzbMATHCrossRefGoogle Scholar
  193. Vignale G (2008) Real-time resolution of the causality paradox of time-dependent density-functional theory. Phys Rev A 77(6):062511ADSCrossRefGoogle Scholar
  194. Virshup AM, Punwong C, Pogorelov TV, Lindquist BA, Ko C, Martínez TJ (2008) Photodynamics in complex environments: ab initio multiple spawning quantum mechanical/molecular mechanical dynamics. J Phys Chem B 113(11):3280–3291CrossRefGoogle Scholar
  195. Wang H, Thoss M (2003) Multilayer formulation of the multiconfiguration time-dependent Hartree theory. J Chem Phys 119:1289ADSCrossRefGoogle Scholar
  196. Wang F, Ziegler T (2005) A simplified relativistic time-dependent density-functional theory formalism for the calculations of excitation energies including spin-orbit coupling effect. J Chem Phys 123(15):154102ADSCrossRefGoogle Scholar
  197. Wiggins P, Williams JAG, Tozer DJ (2009) Excited state surfaces in density functional theory: a new twist on an old problem. J Chem Phys 131(9):091101ADSCrossRefGoogle Scholar
  198. Wijewardane HO, Ullrich CA (2008) Real-time electron dynamics with exact-exchange time-dependent density-functional theory. Phys Rev Lett 100:056404. http://link.aps.org/doi/10.1103/PhysRevLett.100.056404ADSCrossRefGoogle Scholar
  199. Worth G, Robb M, Burghardt I (2004) A novel algorithm for non-adiabatic direct dynamics using variational Gaussian wavepackets. Faraday Discuss 127:307–323ADSCrossRefGoogle Scholar
  200. Worth GA, Robb MA, Lasorne B (2008) Solving the time-dependent Schrödinger equation for nuclear motion in one step: direct dynamics of non-adiabatic systems. Mol Phys 106(16–18): 2077–2091ADSCrossRefGoogle Scholar
  201. Wyatt RE, Lopreore CL, Parlant G (2001) Electronic transitions with quantum trajectories. J Chem Phys 114(12):5113–5116ADSCrossRefGoogle Scholar
  202. Yagi K, Takatsuka K (2005) Nonadiabatic chemical dynamics in an intense laser field: electronic wave packet coupled with classical nuclear motions. J Chem Phys 123(22):224103ADSCrossRefGoogle Scholar
  203. Yanai T, Tew D, Handy N (2004) A new hybrid exchange-correlation functional using the coulomb-attenuating method (CAM-B3LYP). Chem Phys Lett 393:51ADSCrossRefGoogle Scholar
  204. Yang S, Coe JD, Kaduk B, Martínez TJ (2009) An “optimal” spawning algorithm for adaptive basis set expansion in nonadiabatic dynamics. J Chem Phys 130(13):04B606ADSCrossRefGoogle Scholar
  205. Zangwill A, Soven P (1980) Density-functional approach to local-field effects in finite systems: photoabsorption in the rare gases. Phys Rev A 21(5):1561ADSCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Federica Agostini
    • 1
  • Basile F. E. Curchod
    • 2
  • Rodolphe Vuilleumier
    • 3
  • Ivano Tavernelli
    • 4
  • E. K. U. Gross
    • 5
  1. 1.Laboratoire de Chimie PhysiqueUniversity Paris-SaclayOrsayFrance
  2. 2.Department of ChemistryDurham UniversityDurhamUK
  3. 3.PASTEUR, Département de chimieÉcole normale supérieure, PSL University, Sorbonne Université, CNRSParisFrance
  4. 4.Zurich Research LaboratoryIBM Research GmbHRüschlikonSwitzerland
  5. 5.Max-Planck-Institut für MikrostrukturphysikHalleGermany

Section editors and affiliations

  • Wanda Andreoni
    • 1
  • Sidney Yip
    • 2
  1. 1.Institute of PhysicsSwiss Federal Institute of Technology - LausanneLausanneSwitzerland
  2. 2.Department of Nuclear Science & EngineeringMassachusetts Institute of TechnologyCambridgeUSA

Personalised recommendations