Chemical Theory Beyond The Born-oppenheimer Paradigm: Nonadiabatic Electronic And Nuclear Dynamics In Chemical Reactions

Nonadiabatic Electronic and Nuclear Dynamics in Chemical Reactions

Kazuo Takatsuka, Takehiro Yonehara, Kota Hanasaki, Yasuki Arasaki

• Publisher: WSPC
• Year: 2014
• eBook ISBN: 9789814619660
• Topic: Biological Sciences
• Subtopic: Science General
• Index: Biological Sciences

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.

Contents:

• The Aim of This Book: Where are We?
• Basic Framework of Theoretical Chemistry
• Nuclear Dynamics on Adiabatic Electronic Potential Energy Surfaces
• Breakdown of the Born–Oppenheimer Approximation: Classic Theories of Nonadiabatic Transitions and Ideas Behind
• Direct Observation of the Wavepacket Bifurcation Due to Nonadiabatic Transitions
• Nonadiabatic Electron Wavepacket Dynamics in Path-branching Representation
• Dynamical Electron Theory for Chemical Reactions
• Molecular Electron Dynamics in Laser Fields

Readership: Graduate students, professional scientists in theoretical chemistry, quantum chemistry, chemical dynamics, nonadiabatic transition, molecular physics, electron dynamics, and experimentalists in laser chemistry (including ultrafast chemical dynamics), photochemistry, laser control of chemical reactions, and scientists working in physical chemistry and chemical physics in general.
Key Features:

• Presents a new framework of theory for ultrafast chemical reactions based on the nonadiabatic electron wavepacket dynamics
• Offers a very powerful yet futuristic methodology to handle the attosecond electron-wavepacket quantum dynamics associated with non-Born-Oppenheimer nuclear paths
• Describes the original and powerful practices to cope with actual molecular systems that have been attained through authors' long-standing studies

Chapter 1

The Aim of This Book:
Where Are We?

1.1 Potential energy surfaces and nonadiabatic transitions

1.1.1 Electronic state theory

In the stationary molecular electronic state theory, alias quantum chemistry, a great success has been achieved historically, and still active studies are going on mainly towards very accurate calculations of molecular properties and/or for the development of methodology to treat large molecules. The theoretical framework that basically supports quantum chemistry is the so-called Born–Oppenheimer approximation, in which time variable is eliminated by freezing the nuclear motions (molecular geometry). Quantum chemistry can now provide an extremely useful method to study rather mild chemical reactions by identifying the molecular structures not only of stable configurations but also those at transitions states, which are usually invisible experimentally. Various static molecular properties are also estimated accurately, in particular, energetics reflecting the global feature of potential energy surfaces is extremely useful to understand and even predict chemical reactions under study.

The electronic energy thus computed at each molecular shape serves as a potential function working on nuclei, called (adiabatic) potential energy surface (PES), which drives nuclear wavepackets on it, and only in this stage time-variable is retrieved, to the time scale of nuclear dynamics mostly of the order of femtosecond. This is the standard theoretical framework for the study of the dynamics of molecules [59]. Very well structured and fast computer codes for quantum chemistry are now available, which can serve even as an alternative for experimental apparatus.

1.1.2 Nonadiabatic transitions—A brief overview

It is well-known however that in case two or more adiabatic potential energy surfaces come close to each other in energy, the Born–Oppenheimer approximation breaks down and nonadiabatic transition takes place as an important quantum effect (see [28, 84, 85, 117, 198, 291] for extensive reviews). The theory of nonadiabatic transition was first proposed in 1932 by Landau [229], Zener [505], Stueckelberg [395], and London [246], to study phenomena including electron transfer between two atoms. Since then, nonadiabatic dynamics has been found in many other phenomena mostly in chemical reactions. Among these the dynamics across conical intersections is one of the most important subjects in current chemistry. These classic theories, however, suffer from severe limitations and/or drawbacks from their theoretical structures. For instance, the Landau–Zener formula assumes linearly crossed diabatic (one-dimensional) energy curves with a constant nonadiabatic transition coupling, thereby allowing a transition only at the crossing point. However, these assumptions are far from the reality in many systems. To overcome these difficulties, many theories have been proposed in the literature. For example, the Zhu–Nakamura theory [513] is regarded as an ultimate theory within the Landau–Zener type dynamics.

Another basic theory of nonadiabatic transitions is the semiclassical Ehrenfest theory (SET). Although it can cope with multidimensional nonadiabatic electronic-state mixing, it inevitably produces a nuclear path that runs on an averaged potential energy surface after having passed across the nonadiabatic region, which is totally unphysical. Unfortunately, since SET seems intuitively correct, a naive and conventional derivation of this theory obscures how this critical difficulty arises.

Surface Hopping Model (SHM) first proposed by Tully and Preston [444] is a practical method to cope with nonadiabatic transition. It is actually not a theory but an intuitive prescription to take account of “quantum coherent jump” by replacing with a classical hop from one potential energy surface to another with a transition probability that is borrowed from other theories of semiclassical (or full quantum mechanical) nonadiabatic transitions state theory such as Zhu–Nakamura method. The fewest switch surface hopping method [445] and the theory of natural decay of mixing [197, 452, 509, 515] are among the most advanced methodologies so far proposed to practically resolve the critical difficulty of SET and the primitive version of SHM.

Recognizing that these classic standard theories have made and will continue to make great contributions to the progress of chemical dynamics, we on the other hand faithfully admit that there are many situations that are not even considered by such state-of-the-art theories. For instance, recent advances in laser technology enables drastic modification in the molecular electronic states, which in turn can induce novel nonadiabatic coupling in addition to the native nonadiabatic transition. Besides, the ultrashort laser pulses currently available (shorter than 100 attoseconds (1 as = 10^–18 s)) is faster the typical motions of valence electrons in molecules. Such nonadiabatic chemistry in intense laser fields and ultrafast electron dynamics make the current situation in science totally different from that of traditional theories of nonadiabatic transition. Another new perspective of excited state chemistry is in the study of the properties and chemical dynamics of molecules having densely quasi-degenerate electronic states. In those systems the continuous nonadiabatic couplings induce a large fluctuation of electronic states, which should be described as electron wavepacket dynamics beyond the Born–Oppenheimer framework of chemistry. It seems therefore obvious that we should reconsider the theory of nonadiabatic transitions from a deeper point of view rather than try to technically augment the classic theories that rest on sometimes naive assumptions.

1.2 Necessity of nonadiabatic dynamical electron theory

Let us look into a little more detailed aspects of the current and future perspective for chemical dynamics. As noted above, the foundations of theoretical chemistry were already established in the 1920’s (both the papers of Born–Oppenheimer and Heitler London were published in 1927) and 1930’s (Landau and Zener published in 1932, and the transition state theory of Eyring and Evans–Polanyi was almost simultaneously launched in 1935), and even today the basic framework remains essentially the same. However, there are many reasons we need to promote the electronic-state theory into the realm of dynamical electron theory by taking explicit account of time t in it. Below are listed some of the current attempts to achieve this goal.

1.2.1 Progress in laser chemistry

1.2.1.1 Tracking attosecond electron dynamics

The most powerful driving force to demand for the advancement of the dynamical theory of electronic states comes from the progress being made in laser technology of which there are two aspects. The first is in the rapid advances of ultra-short pulse lasers, whose width is shorter than 100 attoseconds. This is comparable with or shorter than the time scale of the valence electrons in a molecule [30, 72, 97, 179, 212, 222, 254, 282, 300, 323, 345]. For many years, nothing that could be experimentally generated was faster than the time scale of electrons. But that has changed and now the exploration of electron wavepacket dynamics in chemical reactions of polyatomic molecules becomes more and more realistic using such ultrafast laser pulse technology. To date most of the full quantal numerical studies on electronic–nuclear entire dynamics are made for the hydrogen molecule or its cation. Those relevant works include Ref. [33, 79, 80, 88, 89, 169, 170, 194, 204, 205, 216, 258, 264, 300, 313, 314, 344, 390, 440].

However, to achieve further progress, more general ab initio methods need to be developed for the treatment of multi-electronic and polyatomic molecules.

1.2.1.2 Modulating electronic states and control of chemical reactions

Intense lasers have brought about a revolutionary change in modern molecular spectroscopy. In the past, in the field of photochemistry only a weak and/or almost resonant perturbation was applied to a molecule to observe its response. This meant that only the static states were characterized. On the other hand, a laser field which is more intense than 10¹⁶ W cm^–2 can apply as strong forces to nuclei and electrons as their original interactions do. The result therefore is that it can readily modulate the electronic states directly by creating a new wavepacket state. It can also induce nonadiabatic interactions in addition to the original ones. For instance, an efficient way of inducing an electronic excitation can be possible through the use of vibrational excitation using IR lasers [425]. One of the ultimate aims in this context would be to create new electronic states, through which the control of chemical reactions could be achieved.

1.2.1.3 Dynamics of internal and external electrons

Similarly, intense lasers make it possible to study the early stages in the multiphoton ionization of molecules through multiply excited states. Above-threshold ionization gives rise to a quasi-free electronic wavepacket state, and the recombination (collision) of such an electronic wavepacket with the remaining cation species results in the high harmonic generation [96, 114, 193, 237, 303, 317, 375]. These issues give rise an extremely interesting challenge on how to describe the electronic wavepacket states.

1.2.1.4 Secondary effects of an induced electromagnetic field by a molecular electron current in external laser fields

The electron current within a molecule driven by an intense laser field should generate ...

Table of contents

• Cover
• Half Title
• Title
• Copyright
• Contents
• Preface
• Acknowledgments
• 1. The Aim of This Book: Where Are We?
• 2. Basic Framework of Theoretical Chemistry
• 3. Nuclear Dynamics on Adiabatic Electronic Potential Energy Surfaces
• 4. Breakdown of the Born–Oppenheimer Approximation: Classic Theories of Nonadiabatic Transitions and Ideas behind
• 5. Direct Observation of the Wavepacket Bifurcation due to Nonadiabatic Transitions
• 6. Nonadiabatic Electron Wavepacket Dynamics in Path-branching Representation
• 7. Dynamical Electron Theory for Chemical Reactions
• 8. Molecular Electron Dynamics in Laser Fields
• Epilogue
• Bibliography
• Index