Nonadiabatic surface reaction

Bdttcher A, Imbeck R, Morgante A and ErtI G 1990 Nonadiabatic surface reaction Mechanism of electron emission in the Cs + O2 system Phys. Rev. Lett. 65 2035... 

We have shown that an accessible conical intersection forms a bottleneck that separates the excited state branch of a nonadiabatic photochemical reaction path from the ground state branch, thus connecting the excited state reactant to two or more products on the ground state surface via a branching of the... 

Fig. 12.3. Schematic representation of the potential energy surfaces of the ground (5q) and excited (i"]) state in a nonadiabatic photochemical reaction. Two reaction channels lead from the conical intersection to products Pj and 2. The trajectories entering the conical intersection determine which reaction channel is followed. Reproduced from Angew. Chem. Int. Ed. Engl, 34, 549 (1995), by permission of Wiley-VCH.

For the nonadiabatic ET reactions, the upper adiabatic PES cannot be neglected. However, recent work shows that such reactions themselves may still be described by the adiabatic Hamiltonian eqn (12.24), although the nonadiabatic tunneling elfects should be properly incorporated. The mechanism is from the surface hopping proposed by Tully and Preston. One, therefore, may extend the quantum Kramers theory to the ET process. To do so, we make the normal mode analysis in the vicinity of the barrier of the potential in eqn (12.24). The standard procedure reads ... 

The third reaction type characterized by pushing apart of nonadiabatic surfaces is associated with intersection of the frontier orbitals in the thermal reaction forbidden by the Woodward-Hoffmann rules. A typical example is given by the (2s + 2s) cycloaddition reactions. Figure 1.23b shows that the surface of the double-excited electron state intersects the PES of the ground... 

Tully J C and Preston R K 1971 Trajectory surface hopping approach to nonadiabatic molecular collisions the reaction of H" with D2 J. Chem. Phys. 55 562... 

In many instances tire adiabatic ET rate expression overestimates tire rate by a considerable amount. In some circumstances simply fonning tire tire activated state geometry in tire encounter complex does not lead to ET. This situation arises when tire donor and acceptor groups are very weakly coupled electronically, and tire reaction is said to be nonadiabatic. As tire geometry of tire system fluctuates, tire species do not move on tire lowest potential energy surface from reactants to products. That is, fluctuations into activated complex geometries can occur millions of times prior to a productive electron transfer event. 

B. H. Lengsfield and D. R. Yarkony, Nonadiabatic Interactions Between Potential Energy Surfaces Theory and Applications, in State-Selected and State to State Ion-Molecule Reaction Dynamics Part 2 Theory, M. Baer and C.-Y. Ng, eds., John Wiley Sons, Inc., New York, 1992, Vol, 82, pp. 1-71. 

In Chapter VI, Ohm and Deumens present their electron nuclear dynamics (END) time-dependent, nonadiabatic, theoretical, and computational approach to the study of molecular processes. This approach stresses the analysis of such processes in terms of dynamical, time-evolving states rather than stationary molecular states. Thus, rovibrational and scattering states are reduced to less prominent roles as is the case in most modem wavepacket treatments of molecular reaction dynamics. Unlike most theoretical methods, END also relegates electronic stationary states, potential energy surfaces, adiabatic and diabatic descriptions, and nonadiabatic coupling terms to the background in favor of a dynamic, time-evolving description of all electrons. 

Figure 6. Initial rovibrational state specified reaction probabilities. Solid line exact quantum mechanical numerical solution. Solid line with solid square generalized TSH with use of the nonadiabatic coupling vector. Solid line with open circle generalized TSH with use of Hessian. Sur= 1(2) means the ground (excited) potential energy surface. Taken from Ref. [51].

As discussed by Miller and co-workers [52,53], it is worthwhile to develop theories that enable us to evaluate thermal reaction rate constants directly and not to rely on the calculations of the most detailed scattering matrix or the state-to-state reaction probabihty. Here, our formulation of the nonadiabatic transition state theory is briefly described for the simplest case in which the transition state is created by potential surface crossing [27]. 

The total Hamiltonian is the sum of the two terms H = H + //osc- The way in which the rate constant is obtained from this Hamiltonian depends on whether the reaction is adiabatic or nonadiabatic, concepts that are explained in Fig. 2.2, which shows a simplified, one-dimensional potential energy surface for the reaction. In the absence of an electronic interaction between the reactant and the metal (i.e., all Vk = 0), there are two parabolic surfaces one for the initial state labeled A, and one for the final state B. In the presence of an electronic interaction, the two surfaces split at their intersection point. When a thermal fluctuation takes the system to the intersection, electron transfer can occur in this case, the system follows the path... 

Conical intersections are involved in other types of chemistry in addition to photochemistry. Photochemical reactions are nonadiabatic because they involve at least two potential energy surfaces, and decay from the excited state to the ground state takes place as shown, for example, in Figure 9.2a. However, there are also other types of nonadiabatic chemistry, which start on the ground state, followed by an ex-cnrsion npward onto the excited state (Fig. 9.2b). Electron transfer problems belong to this class of nonadiabatic chemistry, and we have documented conical intersection... 

Lengsfield BH, Yarkony DR (1992) Nonadiabatic interactions between potential energy surfaces theory and applications. In Baer M, Ng CY (eds) State-selected and state-to-state ion-molecule reaction dynamics part 2 theory, Vol. 82 of Advances in Chemical Physics, John Wiley and Sons, New York, p 1-71. 

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.)...

Although it falls somewhat out of the scope of this paper and has furthermore been reviewed comprehensively recently,16 it would be remiss to overlook the exciting new work on chemicurrents. As we have seen for vibrational energy transfer, it is also observed that dissipation of chemical energy released in exothermic reactions at metal surfaces may happen adiabati-cally by creation of excited phonons or nonadiabatically by excitation of... 

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