Friction electronic

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.)...

Smith, B. B. and Hynes, J. T. Electron friction and electron transferrates at metallic electrodes,... 

However, a very limited number of studies focused on the effect of solvent dynamics on electron transfer reactions at electrodes.Smith and Hynes" introduced the effect of electronic friction (arising from the interaction between the excited electron hole pairs in the metal electrode) and solvent friction (arising from the solvent dynamic [relaxation] effect) in the electron transfer rate at metallic electrodes. The consideration of electron-hole pair excitation in the metal without illumination by light seems unrealistic. 

MDEF Molecular Dynamics with Electronic Frictions... 

Including 7]xx and Fx in Langevin-type classical dynamics has been termed molecular dynamics with electronic frictions (MDEF) [70], and has now been used in several simulations of non-adiabatic dynamics. Of course, the key unknown is the magnitude of the electronic frictions (since they also determine Fx). 

Figure 3.28. N2 vibrational state distribution in associative desorption from Ru(0001). (a) Observed in experiment. From Ref. [126]. (b) From 3D (Z, R, q) first principles quasi-classical dynamics, with the solid triangles pointing upward being adiabatic dynamics and the squares from molecular dynamics with electronic frictions also from DFT. Based on the PES and frictions of Ref. [68]. The open triangles pointing downward are the results of 6D first principles adiabatic quasi-classical dynamics from Ref. [253].

Figure 3.41. Photoyield Y for H2 and D2 associative desorption from Ru(0001)(l x 1)H and Ru(0001)(lxl)D as a function of absorbed 800 nm 130fs laser pulse fluence F. (a) experimental results with circles for H2 desorption and squares for D2 desorption. Solid lines are fits to a ID friction model and dashed lines are fits to power law expressions, Y oc F28 for H2 and Y oc F3 2 for D2. From Ref. [413]. (b) Equivalent photoyields for associative desorption from 3D first principles molecular dynamics with electronic frictions. From Ref. [101].

Figure 3.43. The time dependent electronic temperature Te, lattice temperature Tq. and adsorbate temperature defined as Tads = [EH /2kB following a 130 fs laser pulse with absorbed laser fluence of 120 J/m2 centered at time t = 0. The bar graph is the rate of associative desorption dY/dt as a function of t. Te and T are from the conventional two temperature model and 7 ads and dY/dl are from 3D first principles molecular dynamics with electronic frictions. From Ref. [101].

Electron-hole pairs have already been treated on the Hartree-Fock level in otherwise classical high-dimensional molecular dynamics simulation using the molecular dynamics with electronic friction method [120]. In this approach, the energy transfer between nuclear degrees of freedom and the electron bath of the surface is also modelled with a position-dependent friction term, but additionally temperature-dependent fluctuating forces are included. 

Figure 14 Role of e-h pairs in the scattering and sticking of CO/Cu(l 11) at a surface temperature of Ts = 100 K (a) sticking probability for CO/Cu(l 1 1) under normal incidence calculated without and with electronic friction, (b) energy distribution of CO molecules scattered under normal incidence from Cu(l 11) in percent of the initial kinetic energy (after [110]).

Head-Gordon, M., TuUy, J.G. Molecular dynamics with electronic frictions, J. Chem. Phys. 1995, 103,10137. 

ASTM D5778. Standard Test Method for Electronic Friction Cone and Piezocone Penetration Testing of Soils. 

In order to evaluate the influence of phonon versus electron friction it is necessary to have models which include both aspects. Although many models for electron-hole pair excitation are available, most of these do not also consider the phonon excitation, and they are therefore not able to discriminate between the two processes. The model which is proposed by Metiu and coworkers [256] as well as Billing [262] assumes that the effective charge on the incoming molecule or adsorbate through Coulomb interaction with the metal-electrons excites these from levels below to levels above the Fermi level. Below we describe the semiclassical model proposed by Billing. This model has a collision-oriented aspect and treats the excitation processes to infinite order. 

The model used here for electronic friction can be improved by using Kohn-Sham one-particle wavefunctions instead of those based on the Bloch potential. Also the solution of the many-electron problem can be improved. Instead of using the sudden limit, we may, with present computer facilities, integrate the eqs. (11.43) for a system involving 100 to 10(X) electrons. 

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