|
[1] M. Baer, Beyond Born–Oppenheimer : electronic nonadiabatic coupling terms and conical intersections, (John Wiley & Sons, New Jersy, 2006). [2] L. S. Cederbaum, “Born–Oppenheimer approximation and beyond for timedependent electronic processes,” J. Chem. Phys. 128, 124101 (2008). [3] J. C. Tully, “Molecular dynamics with electronic transitions,” J. Chem. Phys. 93, 1061 (1990). [4] A. Donoso and C. C. Martens, “Semiclassical multistate Liouville dynamics in the adiabatic representation,” J. Chem. Phys. 112, 3980 (2000). [5] A. Abedi, N. T. Maitra, and E. K. U. Gross, “Exact Factorization of the Time- Dependent Electron-Nuclear Wave Function,” Phys. Rev. Lett. 105, 123002 (2010). [6] C.-Y. Zhu, “Restoring electronic coherence/decoherence for a trajectory-based nonadiabatic molecular dynamics,” Sci. Rep. 6, 24198 (2016). [7] C. L. Lopreore and R. E. Wyatt, “Quantum Wave Packet Dynamics with Trajectories,” Phys. Rev. Lett. 82, 5190 (1999). [8] C.-C. Chou, “Complex quantum Hamilton-Jacobi equation with Bohmian trajectories: Application to the photodissociation dynamics of NOCl,” J. Chem. Phys. 140, 104307 (2014). [9] C. L. Lopreore and R. E. Wyatt, “Electronic transitions with quantum trajectories. II,” J. Chem. Phys. 116, 1228 (2002). [10] R. E. Wyatt, Quantum Dynamics with Trajectories: Introduction to Quantum Hydrodynamics, (Springer, New York, 2005). [11] Y. Goldfarb, I. Degani, and D. J. Tannor, “Bohmian mechanics with complex action: A new trajectory-based formulation of quantum mechanics,” J. Chem. Phys. 125, 231103 (2006). [12] R. A. Leacock and M. J. Padgett, “Hamilton-Jacobi Theory and the Quantum Action Variable,” Phys. Rev. Lett. 50, 3 (1983). [13] R. A. Leacock and M. J. Padgett, “Hamilton-Jacobi/action-angle quantum mechanics,” Phys. Rev. D 28, 2491 (1983). [14] C. J. Trahan, K. Hughes, and R. E. Wyatt, “A new method for wave packet dynamics: Derivative propagation along quantum trajectories,” J. Chem. Phys. 118, 9911 (2003). [15] T. Azumi and K. Matsuzaki, “What Does the Term ”Vibronic Coupling” Mean?” Photochem. Photobiol. 25, 315 (1977). [16] F. T. Smith, “Diabatic and Adiabatic Representations for Atomic Collision Problems,” Phys. Rev. 179, 111 (1969). [17] M. Baer, “Electronic non-adiabatic transitions: Derivation of the general adiabatic-diabatic transformation matrix,” Mol. Phys. 40, 1011 (1980). [18] B. T. Sutcliffe and R. G. Woolley, “Molecular structure calculations without clamping the nuclei,” Phys. Chem. Chem. Phys. 7, 3664 (2005). [19] Á. S. Sanz and S. Miret-Artés, A Trajectory Description of Quantum Processes. I. Fundamentals, (Springer, Berlin, 2012). [20] R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics, volume 3, (Addison-Wesley, San Francisco, 2013). [21] E. R. Bittner and R. E. Wyatt, “Integrating the quantum Hamilton–Jacobi equations by wavefront expansion and phase space analysis,” J. Chem. Phys. 113, 8888 (2000). [22] N. Zamstein and D. J. Tannor, “Non-adiabatic molecular dynamics with complex quantum trajectories. I. The diabatic representation,” J. Chem. Phys. 137, 22A517 (2012). [23] R. L. Burden and J. D. Faires, Numerical Analysis, 9th edition, (Brooks/Cole, Boston, 2011). [24] W. E. Boyce and R. C. DiPrima, Elementary Differential Equations and Boundary Value Problems, 10th edition, (John Wiely & Sons, New York, 2013). [25] J. J. Sakurai and J. Napolitano, Modern Quantum Mechanics, 2nd edition, (Addison-Wesley, San Francisco, 2011). [26] D. J. Tannor, Introduction to Quantum Mechanics: a Time-Dependent Perspective, (University Science Books, Sausalito, 2007). [27] P. K. Kundu, I. M. Cohen, and D. R. Dowling, Fluid Mechanics, 6th edition, (Elsevier, San Diego, 2016). [28] H. Goldstein, C. P. P. Jr., and J. L. Safko, Classical Mechanics, 3rd edition, (Pearson, Addison-Wesley, 2001). [29] R. E. Wyatt, C. L. Lopreore, and G. Parlant, “Electronic transitions with quantum trajectories,” J. Chem. Phys. 114, 5113 (2001). [30] N. Zamstein and D. J. Tannor, “Non-adiabatic molecular dynamics with complex quantum trajectories. II. The adiabatic representation,” J. Chem. Phys. 137, 22A518 (2012). [31] C.-C. Chou, “Complex quantum Hamilton–Jacobi equation with Bohmian trajectories for wave packet dynamics,” Chem. Phys. Lett. 591, 203 (2014). [32] V. A. Rassolov and S. Garashchuk, “Semiclassical nonadiabatic dynamics with quantum trajectories,” Phys. Rev. A 71, 032511 (2005). [33] R. E. Wyatt and K. Na, “Quantum trajectory analysis of multimode subsystembath dynamics,” Phys. Rev. E 65, 016702 (2001). [34] F. S. Mayor, A. Askar, and H. A. Rabitz, “Quantum fluid dynamics in the Lagrangian representation and applications to photodissociation problems,” J. Chem. Phys. 111, 2423 (1999). [35] R. E. Wyatt and B. A. Rowland, “Computational Investigation of Wave Packet Scattering in the Complex Plane: Propagation on a Grid,” J. Chem. Theory Comput. 5, 443 (2009). [36] D. Kohena, F. H. Stillinger, and J. C. Tully, “Model studies of nonadiabatic dynamics,” J. Chem. Phys. 109, 4713 (1998). [37] J. C. Burant and J. C. Tully, “Nonadiabatic dynamics via the classical limit Schrödinger equation,” J. Chem. Phys. 112, 6097 (2000). [38] C. A. Mead and D. G. Truhlar, “On the determination of Born–Oppenheimer nuclear motion wave functions including complications due to conical intersections and identical nuclei,” J. Chem. Phys. 70, 2284 (1979). [39] C. A. Mead and D. G. Truhlar, “Conditions for the definition of a strictly diabatic electronic basis for molecular systems,” J. Chem. Phys. 77, 6090 (1982). [40] M. Baer, “Adiabatic and Diabatic Representations for Atom-Molecule Collisions: Treatment of the Collinear Arrangement,” Chem. Phys. Lett. 35, 112 (1975). [41] M. Baer, “Introduction to the theory of electronic non-adiabatic coupling terms in molecular systems,” Phys. Rep. 358, 75 (2002). [42] C. J. Ballhausen and A. E. Hansen, “Electronic Spectra,” Annu. Rev. Phys. Chem. 23, 15 (1972). [43] R. Kapral, “Progress in the Theory of Mixed Quantum-Classical Dynamics,” Annu. Rev. Phys. Chem. 57, 129 (2006). [44] T. V. Voorhis, T. Kowalczyk, B. Kaduk, L.-P. Wang, C.-L. Cheng, and Q. Wu, “The Diabatic Picture of Electron Transfer, Reaction Barriers, and Molecular Dynamics,” Annu. Rev. Phys. Chem. 61, 149 (2010). [45] A. W. Jasper, C. Zhu, S. Nangia, and D. G. Truhlar, “Introductory lecture: Nonadiabatic effects in chemical dynamics,” Faraday Discuss. 127, 1 (2004). [46] M. Baer and R. Englman, “A study of the diabatic electronic representation within the Born-Oppenheimer approximation,” Mol. Phys. 75, 293 (1992). [47] J. P. Malhado, M. J. Bearpark, and J. T. Hynes, “Non-adiabatic Dynamics Close to Conical Intersections and the Surface Hopping Perspective,” Front. Chem. 2, 1 (2014). [48] M. Born and J. R. Oppenheimer, “Zur Quantentheorie der Molekeln,” Ann. Phys. 389, 457 (1927). [49] B. T. Sutcliffe and R. G. Woolley, “On the Quantum Theory of Molecules,” J. Chem. Phys. 137, 22A544 (2012). [50] B. T. Sutcliffe and R. G. Woolley, “Comment on ”On the quantum theory of molecules”,” J. Chem. Phys. 140, 037101 (2014). [51] T. Jecko, “On the mathematical treatment of the Born-Oppenheimer approximation,” J. Math. Phys. 55, 053504 (2014). [52] C. Wittig, “The Landau-Zener Formula,” J. Phys. Chem. B 109, 8428 (2005). [53] J. R. Rubbmark, M. M. Kash, M. G. Littman, and D. Kleppner, “Dynamical effects at avoided level crossings: A study of the Landau-Zener effect using Rydberg atoms,” Phys. Rev. A 23, 3107. (1981). [54] M. Wilkinson and M. A. Morgan, “Nonadiabatic transitions in multilevel systems,” Phys. Rev. A 61, 062104 (2000). [55] C. P. Sun, X. F. Liu, D. L. Zhou, and S. X. Yu, “Quantum measurement via Born-Oppenheimer adiabatic dynamics,” Phys. Rev A 63, 012111 (2000). [56] S. H. Lin and H. Eyring, “Study of Vibronic and Born-Oppenheimer Couplings,” Proc. Natl. Acad. Sci. U.S.A. 71, 3415 (1974). [57] E. Deumens, A. Diz, R. Longo, and Y. Öhrn, “Time-dependent theoretical treatments of the dynamics of electrons and nuclei in molecular systems,” Rev. Mod. Phys. 66, 917 (1994). [58] M. V. Berry, “Quantal Phase Factors Accompanying Adiabatic Changes,” Proc. R. Soc. Lond. A Math. Phys. Sci. 392, 45 (1984). [59] A. Mostafazadeh, “Quantum adiabatic approximation and the geometric phase,” Phys. Rev. A 5, 1653 (1997). [60] V. A. Rassolov and S. Garashchuk, “Quantum adiabatic approximation, quantum action, and Berry’s phase,” Phys. Lett. A 232, 395 (1997). [61] R. Resta, “Manifestations of Berry’s phase in molecules and condensed matter,” J. Phys. Condens. Matter 12, R107 (2000). [62] C. A. Mead, “The geometric phase in molecular systems,” Rev. Mod. Phys. 64, 51 (1992). [63] A. Donoso, D. Kohen, and C. C. Martens, “Simulation of nonadiabatic wave packet interferometry using classical trajectories,” J. Chem. Phys. 112, 7345 (2000). [64] A. Donoso and C. C. Martens, “Classical Trajectory-Based Approaches to Solving the Quantum Liouville Equation,” Int. J. Quantum Chem. 90, 1348 (2002). [65] A. Donoso and C. C. Martens, “Simulation of Coherent Nonadiabatic Dynamics Using Classical Trajectories,” J. Phys. Chem. A 102, 4291 (1998). [66] A. Abedi, N. T. Maitra, and E. K. U. Gross, “Correlated electron-nuclear dynamics: Exact factorization of the molecular wavefunction,” J. Chem. Phys. 137, 22A530 (2012). [67] F. Agostini, A. Abedi, and E. K. U. Gross, “Classical nuclear motion coupled to electronic non-adiabatic transitions,” J. Chem. Phys. 141, 214101 (2014). [68] F. Agostini, A. Abedi, Y. Suzuki, S. K. Min, N. T. Maitra, and E. K. U. Gross, “The exact forces on classical nuclei in non-adiabatic charge transfer,” J. Chem. Phys. 142, 084303 (2015). [69] B. F. E. Curchod, F. Agostini, and E. K. U. Gross, “An exact factorization perspective on quantum interferences in nonadiabatic dynamics,” J. Chem. Phys. 145, 034103 (2016). [70] F. Agostini, S. K. Min, A. Abedi, and E. K. U. Gross, “Quantum-Classical Nonadiabatic Dynamics: Coupled- vs Independent-Trajectory Methods,” J. Chem. Theory Comput. 12, 2127 (2016). [71] A. Schild, F. Agostini, and E. K. U. Gross, “Electronic Flux Density beyond the Born−Oppenheimer Approximation,” J. Phys. Chem. A 120, 3316 (2016). [72] Y. Suzuki, A. Abedi, N. T. Maitra, K. Yamashita, and E. K. U. Gross, “Electronic Schr¨odinger equation with nonclassical nuclei,” Phys. Rev. A 89, 040501 (2014). [73] R. Requist, F. Tandetzky, and E. K. U. Gross, “Molecular geometric phase from the exact electron-nuclear factorization,” Phys. Rev. A 93, 042108 (2016). [74] S. K. Min, A. Abedi, K. S. Kim, and E. K. U. Gross, “Is the Molecular Berry Phase an Artifact of the Born-Oppenheimer Approximation?” Phys. Rev. Lett. 113, 123002 (2014). [75] S. K. Min, F. Agostini, and E. K. U. Gross, “Coupled-Trajectory Quantum- Classical Approach to Electronic Decoherence in Nonadiabatic Processes,” Phys. Rev. Lett. 115, 073001 (2015). [76] P. J. Mohr, D. B. Newell, and B. N. Taylor, “CODATA recommended values of the fundamental physical constants: 2014,” Rev. Mod. Phys. 88, 035009 (2016). |