(1) May, V.; Kühn, O. Charge and Energy Transfer Dynamics in Molecular Systems, 3rd ed.; 2011.
(2) Ullrich, C. A. Time-Dependent Density-Functional Theory: Concepts and Applications; Oxford Graduate Texts; 2011.
(3) Wigner, E. On the quantum correction for thermodynamic equilibrium. Phys. Rev. 1932, 40, 749−759.
(4) Case, W. B. Wigner functions and Weyl transforms for pedestrians. Am. J. Phys. 2008, 76, 937−946.
(5) Grunwald, R.; Kelly, A.; Kapral, R. Quantum Dynamics in Almost Classical Environments. In Energy Transfer Dynamics in Biomaterial Systems, 2009.
(6) Jasper, A. W.; Zhu, C.; Nangia, S.; Truhlar, D. G. Introductory lecture: Nonadiabatic effects in chemical dynamics. Faraday Discuss. 2004, 127, 1−22.
(7) Karsten, S.; Ivanov, S. D.; Bokarev, S. I.; Kühn, O. Quasi-classical approaches to vibronic spectra revisited. J. Chem. Phys. 2018, 102337.
(8) Tully, J. C. Mixed quantum-classical dynamics. Faraday Discussions 1998, 110, 407.
(9) Kapral, R. Progress in the theory of mixed quantum-classical dynamics. Annu. Rev. Phys. Chem. 2006, 57, 129−157.
(10) Lee, M. K.; Huo, P.; Coker, D. F. Semiclassical Path Integral Dynamics: Photosynthetic Energy Transfer With Realistic Environ- ment Interactions. Annu. Rev. Phys. Chem. 2016, 67, 639−668.
(11) Agostini, F.; Min, S. K.; Abedi, A.; Gross, E. K. U. Quantum- classical nonadiabatic dynamics: coupled- vs independent-trajectory methods. J. Chem. Theory Comput. 2016, 12, 2127−2143.
(12) Talotta, F.; Agostini, F.; Ciccotti, G. Quantum trajectories for the dynamics in the exact factorization framework: A proof-of- principle test. J. Phys. Chem. A 2020, 124, 6764−6777.
(13) Tully, J. C. Molecular dynamics with electronic transitions. J. Chem. Phys. 1990, 93, 1061−1071.
(14) Donoso, A.; Martens, C. C. Simulation of coherent non- adiabatic dynamics using classical trajectories. J. Phys. Chem. A 1998, 102, 4291−4300.
(15) Shalashilin, D. V. Multiconfigurational Ehrenfest approach to quantum coherent dynamics in large molecular systems. Faraday Discuss. 2011, 153, 105−116.
(16) Mignolet, B.; Curchod, B. F. A walk through the approximations of ab initio multiple spawning. J. Chem. Phys. 2018, 148, 134110.
(17) Nijjar, P.; Jankowska, J.; Prezhdo, O. V. Ehrenfest and classical path dynamics with decoherence and detailed balance. J. Chem. Phys. 2019, 150, 204124.
(18) Albareda, G.; Appel, H.; Franco, I.; Abedi, A.; Rubio, A. Correlated electron-nuclear dynamics with conditional wave func- tions. Phys. Rev. Lett. 2014, 113, 083003.
(19) Albareda, G.; Bofill, J. M.; Tavernelli, I.; Huarte-Larranaga, F.; Illas, F.; Rubio, A. Conditional Born-Oppenheimer dynamics: Quantum dynamics simulations for the model porphine. J. Phys. Chem. Lett. 2015, 6, 1529.
(20) Albareda, G.; Abedi, A.; Tavernelli, I.; Rubio, A. Universal steps in quantum dynamics with time-dependent potential-energy surfaces: Beyond the Born-Oppenheimer picture. Phys. Rev. A: At., Mol., Opt. Phys. 2016, 94, 062511.
(21) Albareda, G.; Kelly, A.; Rubio, A. Nonadiabatic quantum dynamics without potential energy surfaces. Physical Review Materials 2019, 3, 023803.
(22) Tokmakoff, A. Time-dependent quantum mechanics and spectroscopy. Lecture, 2014.
(23) Raab, A.; Worth, G. A.; Meyer, H.-D.; Cederbaum, L. S. Molecular dynamics of pyrazine after excitation to the S2 electronic state using a realistic 24-mode model Hamiltonian. J. Chem. Phys. 1999, 110, 936−946.
(24) Vendrell, O.; Meyer, H. D. Multilayer multiconfiguration time- dependent Hartree method: Implementation and applications to a Henon-Heiles Hamiltonian and to pyrazine. J. Chem. Phys. 2011, 134, 044135.
(25) Yabana, K.; Bertsch, G. Time-dependent local-density approximation in real time. Phys. Rev. B: Condens. Matter Mater. Phys. 1996, 54, 4484−4487.
(26) De Giovannini, U.; Brunetto, G.; Castro, A.; Walkenhorst, J.; Rubio, A. Simulating pump-probe photoelectron and absorption spectroscopy on the attosecond timescale with time-dependent density functional theory. ChemPhysChem 2013, 14, 1363−1376.
(27) McLachlan, A. D. A variational solution of the time-dependent Schrodinger equation. Mol. Phys. 1964, 8, 39−44.
(28) Vacher, M.; Bearpark, M. J.; Robb, M. A. Direct methods for non-adiabatic dynamics: connecting the single-set variational multi- configuration Gaussian (vMCG) and Ehrenfest perspectives. Theor. Chem. Acc. 2016, 135, 187.
(29) Li, X.; Tully, J. C.; Schlegel, H. B.; Frisch, M. J. Ab initio Ehrenfest dynamics. J. Chem. Phys. 2005, 123, 084106.
(30) Andrea Rozzi, C.; Maria Falke, S.; Spallanzani, N.; Rubio, A.; Molinari, E.; Brida, D.; Maiuri, M.; Cerullo, G.; Schramm, H.; Christoffers, J. Quantum coherence controls the charge separation in a prototypical artificial light-harvesting system. Nat. Commun. 2013, 4, 1602.
(31) Krumland, J.; Valencia, A. M.; Pittalis, S.; Rozzi, C. A.; Cocchi, C. Understanding real-time time-dependent density-functional theory simulations of ultrafast laser-induced dynamics in organic molecules. J. Chem. Phys. 2020, 153, 054106.
(32) Goings, J. J.; Lingerfelt, D. B.; Li, X. Can quantized vibrational effects be obtained from ehrenfest mixed quantum-classical dynamics? J. Phys. Chem. Lett. 2016, 7, 5193−5197.
(33) Kapral, R.; Ciccotti, G. Mixed quantum-classical dynamics. J. Chem. Phys. 1999, 110, 8919−8929.
(34) Broeckhove, J.; Lathouwers, L.; Kesteloot, E.; Van Leuven, P. On the equivalence of time-dependent variational principles. Chem. Phys. Lett. 1988, 149, 547−550.
(35) Lubich, C. On variational approximations in quantum molecular dynamics. Mathematics of Computation 2005, 74, 765−780.
(36) Ohta, K. Time-dependent variational principle with constraints for parametrized wave functions. Phys. Rev. A: At., Mol., Opt. Phys. 2004, 70, 022503.
(37) Kosloff, R.; Tal-Ezer, H. A direct relaxation method for calculating eigenfunctions and eigenvalues of the schrödinger equation on a grid. Chem. Phys. Lett. 1986, 127, 223.
(38) Shi, T.; Demler, E.; Ignacio Cirac, J. Variational study of fermionic and bosonic systems with non-Gaussian states: Theory and applications. Ann. Phys. 2018, 390, 245−302.
(39) Generalized Inverses; Springer: New York, NY, 2006.
(40) Kreibich, T.; Lein, M.; Engel, V.; Gross, E. K. Even-harmonic generation due to beyond-born-oppenheimer dynamics. Phys. Rev. Lett. 2001, 87, 103901.
(41) Lein, M.; Kreibich, T.; Gross, E. K.; Engel, V. Strong-field ionization dynamics of a model [Formula Presented] molecule. Phys. Rev. A: At., Mol., Opt. Phys. 2002, 65, 033403.
(42) Bandrauk, A. D.; Shon, N. H. Attosecond control of ionization and high-order harmonic generation in molecules. Phys. Rev. A: At., Mol., Opt. Phys. 2002, 66, 031401.
(43) Crespo-Otero, R.; Barbatti, M. Spectrum simulation and decomposition with nuclear ensemble: Formal derivation and application to benzene, furan and 2-phenylfuran. Theor. Chem. Acc. 2012, 131, 1237.
(44) Tancogne-Dejean, N.; Oliveira, M. J.; Andrade, X.; Appel, H.; Borca, C. H.; le Breton, G.; Buchholz, F.; Castro, A.; Corni, S.; Correa, A. A.; et al. Octopus, a computational framework for exploring light-driven phenomena and quantum dynamics in extended and finite systems. J. Chem. Phys. 2020, 152, 124119.
(45) Gross, E. K. U.; Maitra, N. T. Introduction to TDDFT. Fundamentals of Time-Dependent Density Functional Theory 2012, 837, 53−99.
(46) Pantos, E.; Philis, J.; Bolovinos, A. The extinction coefficient of benzene vapor in the region 4.6 to 36 eV. J. Mol. Spectrosc. 1978, 72, 36−43.
(47) Koch, E. E.; Otto, A. Optical absorption of benzene vapour for photon energies from 6 to 35 eV. Chem. Phys. Lett. 1972, 12, 476−480.
(48) Gingell, J. M.; Marston, G.; Mason, N. J.; Zhao, H.; Siggel, M. R. On the electronic spectroscopy of benzyl alcohol. Chem. Phys. 1998, 237, 443−449.
(49) Ridolfi, E.; Trevisanutto, P. E.; Pereira, V. M. Expeditious computation of nonlinear optical properties of arbitrary order with native electronic interactions in the time domain. Phys. Rev. B: Condens. Matter Mater. Phys. 2020, 102, 245110.
(50) Verlet, L. Computer ”experiments” on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules. Phys. Rev. 1967, 159, 98.