# Development and Application of Basic Theory for Electron Dynamics in Chemical Reactions

Dr. Kazuo Takatsuka has made many important contributions to theoretical chemical reaction dynamics and basic theories for molecular science, along with their applications to key chemical systems. In particular, he has developed new fields of chemical dynamics beyond the Born-Oppenheimer framework and nonadiabatic electron dynamics in excited states. Below are a couple of his representative works.

**1) Nonadiabatic electron wave packet dynamics for chemical reaction dynamics**

Quantum chemistry (stationary-state electronic structure theory based on the Born-Oppenheimer fixed nuclei approximation) serves as a reliable tool for the interpretation and prediction of chemical phenomena. Nevertheless, there are many physical situations that lie out of the reach of even state-of-the-art quantum chemistry, such as chemical dynamics in highly quasi-degenerate excited states, where frequent and successive nonadiabatic transitions take place. Also, recent advances in laser technology have made it possible to generate pulses as short as tens of atto seconds, which is short enough to track real-time evolution of electron dynamics in chemical systems. Besides, intense laser sources higher than 10^{15} W/cm^{2} are not very special now. These optical interactions should also cause complicated couplings between nonadiabatic interactions and optical transitions. To appropriately describe the quantum dynamics in such situations, a theory based on time-dependent nonadiabatic electron wave packets is inevitable, and it should constitute the heart of the theory of "beyond-Born-Oppenheimer chemistry". Indeed, Dr. Takatsuka has developed a theory of path-branching representation, which explicitly describes the electron wave packet dynamics along smoothly branching non-Born-Oppenheimer paths that in turn represent the bifurcation of the nuclear wave packets. With this theory, he has evolved a chemical reaction theory to the realm far beyond the standard framework. For example he has made a nice use of the so-called electron flux, which is not generally available in the conventional quantum chemistry. The flux analysis is quite instructive for an intuitive understanding of chemistry, since it can vividly visualize the real-time flow of electrons among chemical bonds. In this way, he has established a comprehensive theory of nonadiabatic dynamics, such as electron transfers, excited state proton transfer associated with electronic-state rearrangement, mechanism of charge separation in biological and organic systems, laser induced electron dynamics, and so on.

Chemical dynamics in a dense manifold of quasi-degenerate electronic states such as those commonly found in highly excited states is another typical example that indispensably needs the theory of nonadiabatic electron dynamics. These systems are expected to undergo large fluctuation due to nonadiabatic interactions, wandering among the many electronic states involved. In these systems, nonadiabatic transitions from many-states to many-states keep taking place in the relevant manifolds of states in the time-scale of femtoseconds. Hence, the notion of isolated potential energy surface may lose the sense. This is what Dr. Takatsuka calls "chemistry without potential energy surfaces". Even in such highly quasi-degenerate electronic states, one can track those complicated nonadiabatic dynamics with the so-called "on-the-fly" method along non-Born-Oppenheimer paths. In this way, he has studied in depth chemical dynamics and the reaction fields those densely quasi-degenerate states can offer. He is also interested in the laser-control of them.

**2) Theory of direct observation of nonadiabatic transitions with time-resolved photoelectron spectroscopy**

Dr. Takatsuka and his coworkers have developed theoretical methodologies to monitor the real-time dynamics of chemical reactions by means of femto-second angle- and energy-resolved pump-probe photoelectron spectroscopy. In particular, he has shown that this method can be applied to the direct observation of nuclear wave packet bifurcation, which takes place as the molecular states pass across avoided crossings or conical intersections. This prediction has been experimentally confirmed some years later. All these studies are crucial in that they will possibly give critical information on how the key features of reaction dynamics can be modulated and/or controlled externally. For instance, Dr. Takatsuka has shown ways to shift the location of conical intersection and to control the associated nonadiabatic passage through it.

Another important work by Dr. Takatsuka is his theoretical prediction of induced photoemission from nonadiabatic electron transfer systems: Take an example from LiF↔Li^{+}F^{-},

in which electrons jump quantum mechanically due to nonadiabatic interactions. A continuous wave laser applied to this nonadiabatic system should cause accelerated motions of electrons (or dipole moments) within the molecule, leading to emission of photons, the frequencies and intensities of which turn out to be very characteristic. The emitted lights can be used as finger-prints of molecules and also new optical sources followed by high harmonic generation. These systems can be regarded as nonlinear driven oscillators, which may undergo limit cycle, frequency-locking, chaos, and so on, and will also shed a new light on "quantum nonlinear dynamics".

**3) Scattering theory of electrons by polyatomic molecules in ab initio framework**

Dr. Takatsuka has established, with Prof. V. McKoy, a stationary-state quantum scattering theory for electron collision by polyatomic molecules within the fixed nuclear approximation, with which ab initio calculations of differential cross sections not only of elastic scattering but also by polarization, Feshbach resonance, electronic-state excitation, and so on, came to become possible. These scattering phenomena are quite ubiquitous not only in the natural phenomena such as molecular evolution in cosmic space but also even in industrial applications such as those using plasma processes. This theory by Dr. Takatsuka has played a critical role to make a drastic progress in the field of electron collision phenomena.

**4) Miscellaneous contributions to fundamental theories of molecular sciences**

Dr. Takatsuka and his led group have made very fundamental contributions to the theoretical frameworks of molecular science. For instance, (a) they have found explicitly that the error in the Born-Oppenheimer approximation is proportional to the order of (*m*/*M*)^{1.5}, where *m* and *M* are the masses of electron and nuclei, respectively. The error thereby estimated is therefore expected to be very small as far as stable molecules are concerned. (b) They succeeded in identification of the quantum mechanical mechanism of quantization of classically chaotic motions in highly vibrationally excited states. (c) They developed a statistical theory of chemical reactions beyond the transition-state concept, devising new notions such as micro-canonical temperature, inter-basin mixing, and so on. (d) They have revealed significant effects of the kinematic interactions on the transition states, which arise from non-separability between rotational and vibrational motions in molecular dynamics. (e) After a long standing endeavor, they have at last established a many-body quantum theory beyond the conventional WKB theory, which is free of the spurious divergence and is followed by the discovery of a novel quantum phase emerging from an abstract rotation in intrinsically quantum (complex) space.

As described above, Dr. Takatsuka has made important and pioneering contributions to chemical dynamics and ultrafast photo-dynamics by developing basic theories and applying them to chemical systems. The Chemical Society of Japan has recognized that his achievements are worthy of the CSJ award.