Born-Oppenheimer approximation nonadiabatic dynamics

Nonadiabatic dynamics is a quantum phenomenon which occurs in systems that interact sufficiently strongly with their environments to cause a breakdown of the Born-Oppenheimer approximation. Nonadiabatic transitions play significant roles in many chemical processes such as proton and electron transfer events in solution and biological systems, and in the response of molecules to radiation fields and their subsequent relaxation. Since the bath in which the quantum dynamics of interest occurs often consists of relatively heavy molecules, its evolution can be modeled by classical mechanics to a high degree of accuracy. This observation has led to the development of mixed quantum-classical methods for nonadiabatic processes. 

Fig. 3. Vibrational population distributions of N2 formed in associative desorption of N-atoms from ruthenium, (a) Predictions of a classical trajectory based theory adhering to the Born-Oppenheimer approximation, (b) Predictions of a molecular dynamics with electron friction theory taking into account interactions of the reacting molecule with the electron bath, (c) Born—Oppenheimer potential energy surface, (d) Experimentally-observed distribution. The qualitative failure of the electronically adiabatic approach provides some of the best available evidence that chemical reactions at metal surfaces are subject to strong electronically nonadiabatic influences. (See Refs. 44 and 45.)...

In all dynamical simulations presented so far, it has been assumed that the electrons stay in their ground state throughout the whole process, i.e. the simulations have been based on the Born-Oppenheimer approximation. Still, at metal surfaces with their continuous spectrum of electronic states at the Fermi energy electron-hole (e-h) pair excitations with arbitrarily small energies are possible. However, the incorporation of electronically nonadiabatic effects in the dynamical simulation of the interaction dynamics of molecules with surface is rather difficult [2, 109, 110]. Hence the role of electron-hole pairs in the adsorption dynamics as an additional dissipation channel is still unclear [4],... 

Another area that will draw attention in the future is true quantum molecular dynamics, in which Eq. (7) or its time-dependent form describing the nuclear motion is solved quantum mechanically, without the classical approximation. This represents the ultimate limit of the Born-Oppenheimer approximation. In some cases it may be advantageous to make an additional, second-level Born-Oppenheimer separation of fast and slow nuclear motions, with inclusion of nonadiabatic transitions among nuclear quantum states. 

The Born-Oppenheimer adiabatic approximation represents one of the cornerstones of molecular physics and chemistry. The concept of adiabatic potential-energy surfaces, defined by the Born-Oppenheimer approximation, is fundamental to our thinking about molecular spectroscopy and chemical reaction djmamics. Many chemical processes can be rationalized in terms of the dynamics of the atomic nuclei on a single Born Oppenheimer potential-energy smface. Nonadiabatic processes, that is, chemical processes which involve nuclear djmamics on at least two coupled potential-energy surfaces and thus cannot be rationalized within the Born-Oppenheimer approximation, are nevertheless ubiquitous in chemistry, most notably in photochemistry and photobiology. Typical phenomena associated with a violation of the Born-Oppenheimer approximation are the radiationless relaxation of excited electronic states, photoinduced uni-molecular decay and isomerization processes of polyatomic molecules. 

Chapter 7 continues the presentation of nonadiabatic electron wavepacket d mamics as applied in various chemical reactions, mainly in electronically excited states. Quantization the branching paths (non-Born-Oppenheimer paths) will be also discussed. Likewise, in Chap. 8, the electron wavepacket dynamics is considered for molecules placed in laser fields. In addition to the ordinary nonadiabatic transitions due to the Born-Oppenheimer approximation, novel nonadiabatic transitions due to optical interactions appear to need special cares. This chapter is to be continued to future studies of laser design of electronic states and concomitant control of chemical reactions. 

It is actually very difficult to solve the entire scheme down to Eq. (6.5) for systems of chemical interest, even if a very good set of >/) is available. (Note that electronic structure theory (quantum chemistry) can handle far larger molecular systems within the Born-Oppenheimer approximation) than the nuclear dynamics based on Eq. (6.5) can do.) This is because the short wavelength natme of nuclear matter wave blocks accurate computation and brings classical nature into the nuclear dynamics, in which path (trajectory) representation is quite often convenient and useful than sticking to the wave representation. Then what do the paths of nuclear dynamics look like on the occasion of nonadiabatic transitions, for which it is known that the nuclear wavepackets bifurcate, reflecting purely quantum nature. 

Thus this book describes the recent theories of chemical dynamics beyond the Born-Oppenheimer framework from a fundamental perspective of quantum wavepacket dynamics. To formulate these issues on a clear theoretical basis and to develop the novel theories beyond the Born-Oppenheimer approximation, however, we should first learn a basic classical and quantum nuclear dynamics on an adiabatic (the Born-Oppenheimer) potential energy surface. So we learn much from the classic theories of nonadiabatic transition such as the Landau-Zener theory and its variants. 

One obvious question is whether the nuclear and electronic motion can be separated in the fashion which is done in most models for molecule surface scattering and also in the above-mentioned treatment of electron-hole pair excitation. The traditional approach is to invoke a Born-Oppenheimer approximation, i.e., one defines adiabatic potential energy surfaces on which the nuclear dynamics is solved — either quantally or classically. In the Bom-Oppenheimer picture the electrons have had enough time to readjust to the nuclear positions. Thus the nuclei are assumed to move infinitely slowly. For finite speed, nonadiabatic corrections therefore have to be introduced. Thus, before comparison with experimental data is carried out we have to consider whether nonadiabatic processes are important. Two types of nonadiabatic processes are possible—one is nonadiabatic transitions in the gas phase from the lower adiabatic to the upper surface (as discussed in Chapter 4). The other is the nonadiabatic excitation of electrons in the metal through electron-hole pair excitation. 

Based on the Born-Oppenheimer approximation, the behavior of molecules is described by the dynamics of the nuclei moving along a single potential energy surface (PES) generated by the electrons. Nonadiabatic phenomena occur when at least two potential energy surfaces approach each other and the coupling between them becomes important. The traditional... 

The goal of this review is to critically compare — from both a concep-tional and a practical point of view — various MQC strategies to describe non-Born-Oppenheimer dynamics. Owing to personal preferences, we will focus on the modeling of ultrafast bound-state processes following photoexcitation such as internal-conversion and nonadiabatic photoisomerization. To this end, Sec. 2 introduces three model problems Model I represents a three-mode description of the Si — S2 conical intersection in pyrazine. Model II accounts for the ultrafast C B X internal-conversion process in the benzene cation, and Model III represents a three-mode description of ultrafast photoisomerization triggered by a conical intersection. Allowing for exact quantum-mechanical reference calculations, all models have been used as benchmark problems to study approximate descriptions. 

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