Electronic nonadiabaticity

Sun X, Wang H B and Miller W H 1998 Semiclassical theory of electronically nonadiabatic dynamics Results of a linearized approximation to the initial value representation J. Chem. Phys. 109 7064... 

Quantum mechanical effects—tunneling and interference, resonances, and electronic nonadiabaticity— play important roles in many chemical reactions. Rigorous quantum dynamics studies, that is, numerically accurate solutions of either the time-independent or time-dependent Schrodinger equations, provide the most correct and detailed description of a chemical reaction. While hmited to relatively small numbers of atoms by the standards of ordinary chemistry, numerically accurate quantum dynamics provides not only detailed insight into the nature of specific reactions, but benchmark results on which to base more approximate approaches, such as transition state theory and quasiclassical trajectories, which can be applied to larger systems. 

The ZN formulas can also be utihzed to formulate a theory for the direct evaluation of thermal rate constant of electronically nonadiabatic chemical reactions based on the idea of transition state theory [27]. This formulation can be further utilized to formulate a theory of electron transfer and an improvement of the celebrated Marcus formula can be done [28]. 

INTERACTIONS OF VIBRATION ALLY-EXCITED MOLECULES AT SURFACES A PROBE FOR ELECTRONICALLY NONADIABATIC EFFECTS IN HETEROGENEOUS CHEMISTRY... 

Using this model they have tried to look at important chemical processes at metal surfaces to deduce the role of electronic nonadiabaticity. In particular, they have tried to evaluate the importance of electron-hole-pair excitation in scattering, sticking and surface mobility of CO on a Cu(100) surface.36,37 Those studies indicated that the magnitude of energy transferred by coupling to the electron bath was significantly less than that coupled to phonons. Thus the role of electron-hole-pair excitation in... 

From the point of view of associative desorption, this reaction is an early barrier reaction. That is, the transition state resembles the reactants.46 Early barrier reactions are well known to channel large amounts of the reaction exoergicity into product vibration. For example, the famous chemical-laser reaction, F + H2 — HF(u) + H, is such a reaction producing a highly inverted HF vibrational distribution.47-50 Luntz and co-workers carried out classical trajectory calculation on the Born-Oppenheimer potential energy surface of Fig. 3(c) and found indeed that the properties of this early barrier reaction do include an inverted N2 vibrational distribution that peaks near v = 6 and extends to v = 11 (see Fig. 3(a)). In marked contrast to these theoretical predictions, the experimentally observed N2 vibrational distribution shown in Fig. 3(d) is skewed towards low values of v. The authors of Ref. 44 also employed the electronic friction theory of Tully and Head-Gordon35 in an attempt to model electronically nonadiabatic influences to the reaction. The results of these calculations are shown in... 

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.)...

Fig. 3(b). The stunning agreement between experiment and theory suggests that electronically nonadiabatic effects strongly influence this reaction. 

Fig. 10. The emerging picture of electronically nonadiabatic interactions of NO molecule scattering at a metal surfaces. Transition from the ground electronic state to an anionic state which is strongly attractive to the metal surface can be accomplished by high translational energy when vibrational excitation is low (black trajectory). When vibrational motion is highly excited, even low translational energies allow transition of the anionic state (red trajectory). Recently, Monte-Carlo wavepacket calculations have been carried out which tend to support this picture.63...

We should briefly mention the electronically nonadiabatic ET situation. Here the electronic coupling is sufficiently weak that the intrinsic electronic passage from... 

It is at this stage that we should now begin to look into the details and ask just the sorts of questions that Dr. Sutin is raising — e.g., the importance of nuclear tunneling or of electronic nonadiabaticity. These are, as we might say, the fine structure of the problem. 

On the question of obtaining estimates of the electronic nonadiabaticity factor, you hinted at, but I don t think explicitly mentioned, one approximate approach. That is the method used by Dogonadze and German [German, E. D. Dogonadze, R. R. Izv. Akad. Nauk SSSR, Ser. Khim. 1973, 2155 Chem.Abstr. 1974, 80, 30998a], who compared the entropies of activation... 

In the MQC mean-field trajectory scheme introduced above, all nuclear DoF are treated classically while a quantum mechanical description is retained only for the electronic DoF. This separation is used in most implementations of the mean-field trajectory method for electronically nonadiabatic dynamics. Another possibility to separate classical and quantum DoF is to include (in addition to the electronic DoF) some of the nuclear degrees of freedom (e.g., high frequency modes) into the quantum part of the calculation. This way, typically, an improved approximation of the overall dynamics can be obtained—albeit at a higher numerical cost. This idea is the basis of the recently proposed self-consistent hybrid method [201, 202], where the separation between classical and quantum DoF is systematically varied to improve the result for the overall quantum dynamics. For systems in the condensed phase with many nuclear DoF and a relatively smooth distribution of the electronic-vibrational coupling strength (e.g.. Model V), the separation between classical and quanmm can, in fact, be optimized to obtain numerically converged results for the overall quantum dynamics [202, 203]. 

These equations enable us to compute aU the possible photofragmentation cross sections. An example of the use of these equations applied to the photodissociation of HOBr may be found in Ref. 84, and similar applications to electronically nonadiabatic photofragmentation of HF, DF, and HCl can be found in Refs. 76, 97, and 96. Time-dependent methods have been used most recently to compute vector correlations and alignment parameters [98,99]... 

A simple approach for the calculation of femtosecond pump-probe spectra for electronically nonadiabatic systems... 

If the system under consideration possesses non-adiabatic electronic couplings within the excited-state vibronic manifold, the latter approach no longer is applicable. Recently, we have developed a simple model which allows for the explicit calculation of RF s for electronically nonadiabatic systems coupled to a heat bath [2]. The model is based on a phenomenological dissipation ansatz which describes the major bath-induced relaxation processes excited-state population decay, optical dephasing, and vibrational relaxation. The model has been applied for the calculation of the time and frequency gated spontaneous emission spectra for model nonadiabatic electron-transfer systems. The predictions of the model have been tested against more accurate calculations performed within the Redfield formalism [2]. It is natural, therefore, to extend this... 

W. H. Miller In treating electronically nonadiabatic processes one often introduces (usually on physical grounds) a diabatic model, which has a nondiagonal electronic potential matrix, and then neglects any remaining derivative coupling. The total (vibronic) wave function is... 

X. Sun and W.H. Miller. Semiclassical initial value representation for electronically nonadiabatic molecular dynamics. J. Chem. Phys., 106 6346, 1997. 

Baer, M. (1985b). The theory of electronic nonadiabatic transitions in chemical reactions, in Theory of Chemical Reaction Dynamics, Vol. II, ed. M. Baer (CRC Press, Boca Raton). 

Top, Z.H. and Baer, M. (1977). Incorporation of electronically nonadiabatic effects into bimolecular reaction dynamics. II. The collinear (H2 + H+,Hj + H) systems, Chem. Phys. 25, 1. 

Our basic strategy for controlling chemical dynamics is based on the idea that there are two basic elements of wavepacket motion in chemical dynamics (i) electronic nonadiabatic transitions between adiabatic potential energy surfaces and (ii) wavepacket motion on a single adiabatic potential energy surface. If we could control these two basic motions of wavepackets, it would become possible to control various kinds of realistic chemical dynamics. 

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],... 

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