Includes bibliographical references (p. 403-421) and index.

1. The aim of this book: where are we? 1.1. Potential energy surfaces and nonadiabatic transitions. 1.2. Necessity of nonadiabatic dynamical electron theory. 1.3. Structure of this book -- 2. Basic framework of theoretical chemistry. 2.1. Born-Huang expansion. 2.2. Born-Oppenheimer approximation. 2.3. Validity of the BO approximation. 2.4. Generalization of the adiabatic electronic states -- 3. Nuclear dynamics on adiabatic electronic potential energy surfaces. 3.1. Classical nuclear dynamics: Ab initio molecular dynamics. 3.2. Nuclear quantum dynamics on an adiabatic potential surface. 3.3. Probing the dynamics with time-resolved photoelectron spectroscopy -- 4. Breakdown of the Born-Oppenheimer approximation: classic theories of nonadiabatic transitions and ideas behind. 4.1. Theories for one-dimensional curve crossing problem. 4.2. Mixed quantum-classical formulation of electron-nucleus coupled nonadiabatic dynamics. 4.3. Surface hopping scheme and beyond. 4.4. Coherence and decoherence before and after nonadiabatic interaction. 4.5. Some specific methods recently proposed for nonadiabatic dynamics. 4.6. Hybrid methods for nonadiabatic dynamics in large molecular systems -- 5. Direct observation of the wavepacket bifurcation due to nonadiabatic transitions. 5.1. How does the Born-Oppenheimer approximation break down? 5.2. Nuclear wavepacket bifurcation as observed with time-resolved photoelectron spectroscopy. 5.3. Control of nonadiabatic chemical dynamics. 5.4. Conical intersection and wavepacket dynamics there. 5.5. High-harmonic spectroscopy to monitor nonadiabatic transition. 5.6. Electron and nucleus dynamics tracked with pulse train in time-resolved photoelectron spectroscopy. 5.7. Photoemission arising from electron transfer within a molecule -- 6. Nonadiabatic electron wavepacket dynamics in path-branching representation. 6.1. Path-branching representation for electron wavepacket propagation. 6.2. Methods of averaging and branching. 6.3. Numerical examples of branching paths and transition probability. 6.4. Highly degenerate coupled electronic states. 6.5. Electronic phase interference between different branching paths: dynamics around conical intersections. 6.6. Quantum effects manifesting in the nuclear branching paths. 6.7. Quantization of non-Born-Oppenheimer paths -- 7. Dynamical electron theory for chemical reactions. 7.1. Electron flux in chemical reactions. 7.2. Real-time dynamics of electron migration in a model water cluster anion system. 7.3. Single and relayed proton transfer in peptide. 7.4. Double proton transfer in formic acid dimer. 7.5. Excited-state proton-electron simultaneous transfer. 7.6. Chemical dynamics for systems where notion of potential energy surfaces loses sense -- 8. Molecular electron dynamics in laser fields. 8.1. Experimental progress and theoretical issues. 8.2. Dressed electronic states and nonadiabatic nuclear dynamics on them driven by laser fields. 8.3. Generalization of path-branching representation for arbitrary optical and nonadiabatic transitions. 8.4. Applications: electron jump in laser fields. 8.5. Dynamics of photoionization.

This unique volume offers a clear perspective of the relevant methodology relating to the chemical theory of the next generation beyond the Born-Oppenheimer paradigm. It bridges the gap between cutting-edge technology of attosecond laser science and the theory of chemical reactivity. The essence of this book lies in the method of nonadiabatic electron wavepacket dynamic, which will set a new foundation for theoretical chemistry. In light of the great progress of molecular electronic structure theory (quantum chemistry), the authors show a new direction towards nonadiabatic electron dynamics, in which quantum wavepackets have been theoretically and experimentally revealed to bifurcate into pieces due to the strong kinematic interactions between electrons and nuclei. The applications range from nonadiabatic chemical reactions in photochemical dynamics to chemistry in densely quasi-degenerated electronic states that largely fluctuate through their mutual nonadiabatic couplings. The latter is termed as "chemistry without the potential energy surfaces" and thereby virtually no theoretical approach has been made yet. Restarting from such a novel foundation of theoretical chemistry, the authors cast new light even on the traditional chemical notions such as the Pauling resonance theory, proton transfer, singlet biradical reactions, and so on.

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