1. Introduction

With the recent energy problems and increasing seriousness of environmental problems, it is very important to develop and improve new energy sources. The role of theoretical science in this global-scale project is considerable. If we can perfectly simulate the real-time coupled electron-nuclear dynamics of the system concerned, it must be enormously helpful in the development and improvement of energy devices because the simulation can produce all physical quantities needed. Therefore, the study of the real-time coupled electron nuclear dynamics has been considered a very important subject and there have been many studies. Most of these studies have focused on how to reproduce the nuclear dynamics, not the electron dynamics. Because the study of nuclear dynamics has recently come to result in success, the main problem now has become how to simulate the electron dynamics.

Real-time electron dynamics, especially of charge-transfer reactions, is very important and accurate simulation of it is in high demand. Charge-transfer reactions are ubiquitous among reactions occurring at surfaces or interfaces in the energy devices. These systems consist of innumerable adiabatic potential energy surfaces; thus, they are nonadiabatic processes. If we can simulate the real-time electron dynamics in such nonadiabatic processes, it will produce tremendously useful knowledge to develop and improve these devices. Furthermore, considering the recent developments in intense attosecond laser technology, there is significant demand to establish simulation theory that can simulate the real-time electron dynamics in such extreme nonadiabatic processes.

Therefore, this work, entitled "Theoretical Study on Real-Time Electron Dynamics in Nonadiabatic Processes," completes a series of studies toward the establishment of an efficient simulation and control method for the real-time electron dynamics in nonadiabatic processes. For this purpose, I have devised a strategy consisting of four successive projects: (1) full inspection of the validity and limitations of previous electron dynamics simulation methods, the TDH and Ehrenfest methods, for charge-transfer reactions induced by nuclear motion, (2) practical application of the Ehrenfest method to study the real-time electron dynamics in a practical fuel cell system using TDDFT, and (3) development of the electron-nuclear correlation functional for the time-dependent multicomponent density functional theory (TDMCDFT) toward the perfect description of coupled electron-nuclear dynamics, and (4) study of the mechanism of control of real-time electron dynamics in nonadiabatic processes.

2. The Validity of Time-Dependent Hartree and Ehrenfest Methods for Real-Time Electron Dynamics Simulation of Charge Transfer Reactions Induced by Nuclear Motion

The first project is the full inspection of the previous methods of simulating real-time electron dynamics. There have been two popular methods, the TDH and Ehrenfest methods. However, their validity in reproducing the real-time electron dynamics in nonadiabatic processes has never been examined. Therefore, elucidating of their validity is extremely important. With this knowledge, we will be able to choose a method that is appropriate for the situation.

Thus, I calculated the real-time electron dynamics of charge-transfer reactions induced by nuclear motion using the TDH and Ehrenfest methods, and compared them with the numerically exact results. Employing a two-electron system, I found that, as long as nuclei move as localized wave packets, the TDH and Ehrenfest methods can reproduce the exact electron dynamics qualitatively well, even when nonadiabatic transitions occur. On the other hand, I also studied cases where the electron dynamics of the TDH and Ehrenfest methods fail by using a one-electron transfer model. I found that, when the quantum nature of nuclei is crucial neither the TDH nor the Ehrenfest method could reproduce the exact electron dynamics well.

The results of this study show the validity of the TDH and Ehrenfest methods in simulating electron transfer dynamics coupled with nuclear motion to the extent that nuclear wave packets are localized. However, it also shows their limitations for electron dynamics where splitting or broadening of nuclear wave packets occur, indicating the importance of appropriate consideration of electron-nuclear correlations in such situations.

3. Real-Time Electron Dynamics Simulation of the Adsorption of an Oxygen Molecule on Pt and Au Clusters

In the first project, it is confirmed that, as long as nuclei move as localized wave packets, the TDH and Ehrenfest methods can reproduce the real-time electron dynamics in nonadiabatic processes sufficiently well. The second project of this thesis is the application of the Ehrenfest method to study the real-time electron dynamics induced by nuclear motion in charge-transfer reactions that occur in practical energy devices. Combining real-time TDDFT, the Ehrenfest method can be applied to large systems, but so far, there have been no such studies.

Thus, as the second step of this thesis, I applied the Ehrenfest TDDFT method to simulate the real-time electron dynamics of the oxygen reduction reaction on platinum surfaces. The time correlation between electron dynamics and nuclear dynamics during dissociative adsorption of oxygen molecules on a platinum cluster was investigated. The results were compared with those on a gold cluster. It was observed that dissociative adsorption of O2 occurred on the Pt(001) surface but not on the Au(001) surface, reproducing the difference in catalytic activity between these surfaces. An analysis of the correlation between the time evolution of the O2-surface distances and the number of electrons transferred showed that electron transfer occurred more easily from the Pt(001) surface to O2 than from the Au(001) surface. It was shown that, by the time O2 approached within approximately 1.6 A of the Pt(001) surface, one electron had already finished transferring from Pt to the O2 π* antibonding orbital; thus, it could approach the surface more closely and more electrons transferred to it, which was the critical factor for dissociative adsorption.

4. Towards the Development of the Time-Dependent Effective Nuclear Potential for Time-Dependent Multicomponent Density Functional Theory

As the third project of this thesis, I attempted to develop simulation theory for real-time electron dynamics in systems where the quantum nature of nuclei is crucial. For this purpose, I aimed to establish TDMCDFT, as a suitable candidate for coupled electron-nuclear dynamics. It will provide a numerically tractable scheme that can treat both electron and nuclear dynamics quantum mechanically. However, as an electron-nuclear interaction potential functional, a key factor of this theory, had not been established, I attempted to develop one.

According to the results in the first project, I concluded that it is adequate to start with the development of time-dependent (TD) effective nuclear potentials to establish TDMCDFT and I proceeded using this strategy.

For this purpose, I focused on the concept of exact factorization of the time-dependent Schrodinger equation and the exact TDPES that was proposed recently. I found that the exactly factorized nuclear equation is nothing but the TDMCKS nuclear equation. I prepared two model systems where strong nonadiabatic transitions and splitting of the nuclear wave packets occur, and analyzed the curvature of the exact TDPES. One exact TDPES was indeed found to reproduce the nonadiabatic transition that induces splitting of the nuclear wave packet, and at that time, the discontinuous step between the two Born-Oppenheimer potential energy surfaces appears on the exact TDPES. Then, I investigated the TDPES using the time-dependent linear combination of atomic orbital (TD LCAO) ansatz approach that is considered to be a good starting point to develop the TDMCDFT. I compared this TDPES with the exact TDPES and the TDPES obtained using the TDH method, and elucidated how well this method works. Such a TDPES comparison will be very important for improving the TD LCAO approach and establishing the TDMCDFT scheme.

5. Exact time-dependent potential energy surface on electron excitation and localization in the dissociation of H2+

Finally, as the fourth project of this thesis, I addressed the ultimate application that results from the study of real-time electron dynamics in nonadiabatic processes, i.e., the control of electron localization using ultrashort pulse lasers. The control of electron dynamics and the control of chemical reactions by controlling electron dynamics should be a dream for all scientists because, if such technology exists, it will bring us a powerful tool to produce all desired reactions including the reactions of new energy devices.

To develop this technology and realize the dream, full theoretical elucidation of its mechanism is required. In particular, elucidation of the correlation between the electron motion and nuclear motion in such highly nonadiabatic processes is extremely important, because the dynamics affect each other in a very complex way and, without knowing the mechanism, arbitrary control of those dynamics will never be achieved.

Therefore, I aimed to reveal the electron-nuclear correlation in the electron excitation and localization during dissociation of H2+ by two sequential ultrashort laser pulses. I treated a one-dimensional H2+ model system and a UV pulse laser that generated electronic excitation to only the first excited state. By varying the time delay between pulses, I calculated the change of population with time for each BO state and also the exact TDPES, and evaluated the induced effect of electron localization on nuclear motion.

As a result, I revealed that the exact TDPES is a very efficient tool for analyzing the induced effect of electron localization on nuclear motion, because it produces a very clear intuitive picture of the potential the nucleus feels in real time during such a process. It can clearly explain how the dissociation dynamics is affected by the electron localization. It was found that the electron localization affects the exact TDPES in a very complex way.

In total, this work presents an important step toward the establishment of a simulation method for real-time electron dynamics in nonadiabatic processes. I conclude that the Ehrenfest TDDFT method is a very efficient method of simulating real-time electron dynamics in nonadiabatic processes as long as nuclei move as localized wave packets. Considering that TDDFT will be developed further in the future, this Ehrenfest TDDFT method will become more important and should be used more extensively. On the other hand, for the situation where the quantum nature of nuclei is crucial, such as surface reactions of small molecules or reactions in an intense laser field, the establishment of TDMCDFT is high demand. Analyzing the exact TDPES and improving the TD LCAO ansatz approach is considered a most promising direction toward this goal. Furthermore, it is considered that the exact TDPES will serve as a promising tool toward the ultimate technology of controlling real-time electron dynamics in nonadiabatic processes, and further studies are expected to be devoted to this project.

本論文は『Theoretical Study on Real-Time Electron Dynamics in Nonadiabatic Processes (非断熱過程における実時間電子ダイナミクスに関する理論的研究)』と題して、核の運動に伴う電子移動反応や強レーザー場下での電子移動反応などの、非断熱過程における実時間電子ダイナミクスのシミュレーション理論の開発と応用、さらに、非断熱的な電子ダイナミクスをコントロールする実験技術についての理論的な研究結果をまとめたものであり、全7章からなる。

第1章は序論であり、非断熱過程における実時間電子ダイナミクスに関する理論的な基礎的研究が、工業的応用からも極めて重要であり、また近年のアト秒レーザーパルス実験技術の発展に伴いますます注目されているという背景について概説している。

第2章では、本論文で研究対象とする実時間電子‐核ダイナミクス・シミュレーション手法のそれぞれの理論的な背景について記述している。

第3章では、実時間電子‐核ダイナミクスをシミュレーションするために、従来広く用いられている二つの手法、Time-Dependent Hartree(TDH)法とEhrenfest法について、それらの電子ダイナミクスの妥当性を検証している。核の運動に伴い二電子あるいは一電子が移動する一次元電荷移動モデルを用意し、それらの系の電子ダイナミクスを厳密な量子波束計算、TDH法、Ehrenfest法の3つの手法で計算し比較することにより、これら二つの近似手法の電子ダイナミクスの適用限界を精査している。その結果、核波束が局在化している限り、二つの近似手法が精度良い電子ダイナミクスを与えることが示されている。その一方で、核の量子性が顕著になり局在性が失われる時、二つの近似手法は厳密な電子ダイナミクスを再現できないことが示されている。これらの結果から、核波束の局在性に注意すれば、Ehrenfest法は効果的な電子ダイナミクス・シミュレーション理論であると結論している。

第4章では、Ehrenfest法による電子ダイナミクス・シミュレーションの実際系への応用として、時間依存密度汎関数理論(TDDFT)と組み合わせることで、白金表面の酸素分子の還元的解離吸着反応の電子ダイナミクスを計算している。白金クラスター上での電子ダイナミクスと、触媒活性をもたない金クラスター上での電子ダイナミクスを比較することで、白金表面上で解離吸着が起こるための電荷移動のダイナミクスを明らかにしている。本計算から、Ehrenfest TDDFT法が実際のエネルギーデバイスなどにおける電荷移動ダイナミクスを研究するために適していると結論している。

第5章では、核の量子性が顕著となるような非断熱過程の電子ダイナミクスを、正確かつ低コストでシミュレーションするための手法として、Time-Dependent Multicomponent DFT(TDMCDFT)法の確立を目指した研究を行っている。核波束の分裂のような量子的な現象を再現することができる時間依存有効核ポテンシャルを構築することが、その目的のための第一歩であるとし、核波束の分裂が生じるモデル系について、厳密な時間依存有効核ポテンシャル(Exact TDPES)の時間変化を示している。核波束の分裂が起こる時、Exact TDPESにボルン・オッペンハイマー断熱ポテンシャル面をつなぐ不連続なステップが見られ、その由来を明らかにしている。TDMCDFTの確立のためには、近似的手法の時間依存有効ポテンシャルをExact TDPESと比較し、その差を改善していくことが重要であると結論している。

第6章では、二つの連続したパルスレーザーにより、水素分子イオンを電子励起させ解離中の原子間の電子ダイナミクスをコントロールすることができるという実験事実に対する理論研究を行っている。厳密な量子波束計算により、二つのパルスレーザーの時間間隔を変えることで電子局在化の方向をコントロールできるという実験事実を再現し、その過程におけるExact TDPESを計算することで、電子の局在化が核のダイナミクスに与える影響を厳密かつ直観的な描像で示している。本結果から、電子ダイナミクスのコントロールを用いる核ダイナミクスのコントロールという技術を確立するのに、Exact TDPESによる解析が有効であると結論している。

第7章は総括であり、本論文の結果をまとめている。

以上要するに、本論文は、核の運動が誘起する電子移動反応やレーザー場による電子移動反応といった、非断熱過程の電子ダイナミクスを効率よくシミュレーションするための手法の構築に重要な知見を与え、さらに電子局在化がコントロールされる系における電子-核ダイナミクスの相関を理論的に明らかにしたものである。本論文で得られた理論的知見は、実時間電子ダイナミクスの研究の基礎を成すものとして理論化学及び化学システム工学に大きく貢献する。

よって本論文は博士(工学)の学位請求論文として合格と認められる。