Nonadiabatic reaction

Adiabatic reactions, occurring on a single-sheet PES correspond to B = 1, and the adiabatic barrier height occurs instead of E. The low-temperature limit of a nonadiabatic-reaction rate constant equals... 

The physical picture of the transition is different here from that for nonadiabatic reaction. Equation (34.34) shows that the probability of electron transfer becomes equal to 1 when the acceptor energy level passes a small energy interval Ae 1/(2jiYlzP) near the Fermi level. However, unUke the nonadiabatic case,... 

The height of the potential barrier is lower than that for nonadiabatic reactions and depends on the interaction between the acceptor and the metal. However, at not too large values of the effective eiectrochemical Landau-Zener parameter the difference in the activation barriers is insignihcant. Taking into account the fact that the effective eiectron transmission coefficient is 1 here, one concludes that the rate of the adiabatic outer-sphere electron transfer reaction is practically independent of the electronic properties of the metal electrode. 

Approximate calculation of the integral over 8 in Eq. (34.27) shows that the ejfective electron transmission coefficient for nonadiabatic reactions is equal to... 

Figure 9.2. Reaction profiles involving a conical intersection (a) a photochemical reaction (b) an upwards excursion via a conical intersection in a nonadiabatic reaction (c) a chemiluminescent reaction.

Figure 9.17. Adiabatic and nonadiabatic reaction profiles for the TICT process.

However, if the PES are multidimensional, as is the case for reactions in the condensed phase, the adiabatic approach is inconvenient for practical calculations, especially for nonadiabatic reactions. 

Another approach widely used for nonadiabatic reactions is the diabatic one. The channel Hamiltonians Hex and H determining the zeroth-order Born-Oppenheimer electron states of the donor A and acceptor B and the perturbations Vt and Vf leading to the forward and reverse electron transitions, respectively, are separated... 

The activation energy for the nonadiabatic reaction, "ad, is determined by the point of minimum energy on the intersection surface of PES Ut and Uf9 and the transmission coefficient k is determined by the electron resonance integral... 

In calculating the transition probability for the nonadiabatic reactions, it is sufficient to use the lowest order of quantum mechanical perturbation theory in the operator V d. For the adiabatic reactions, we must perform the summation of the whole series of the perturbation theory.5 (It is insufficient to retain only the first term of the series that appeared in the quantum mechanical perturbation theory.) Correct calculations in both adiabatic and diabatic approaches lead to the same results, which is evidence of the equivalence of the two approaches. 

The diabatic approach will be mainly used below, since it is more convenient for nonadiabatic reactions. However, in Section VI adiabatic reactions will be also considered using the adiabatic approach. 

A New Approach to the Interaction of the Electron with the Polarization of the Medium in Nonadiabatic Reactions... 

For nonadiabatic reactions, the higher lability of the transferable electrons or atoms leads to the following effects ... 

Recently, much attention has been paid to the investigation of the role of this interaction in relation to the calculations for adiabatic reactions. For steady-state nonadiabatic reactions where the initial thermal equilibrium is not disturbed by the reaction, the coupling constants describing the interaction with the thermal bath do not enter explicitly into the expressions for the transition probabilities. The role of the thermal bath in this case is reduced to that the activation factor is determined by the free energy in the transitional configuration, and for the calculation of the transition probabilities, it is sufficient to know the free energy surfaces of the system as functions of the coordinates of the reactive modes. 

Marcus uses the Born-Oppenheimer approximation to separate electronic and nuclear motions, the only exception being at S in the case of nonadiabatic reactions. Classical equilibrium statistical mechanics is used to calculate the probability of arriving at the activated complex only vibrational quantum effects are treated approximately. The result is... 

Both the initial- and the final-state wavefunctions are stationary solutions of their respective Hamiltonians. A transition between these states must be effected by a perturbation, an interaction that is not accounted for in these Hamiltonians. In our case this is the electronic interaction between the reactant and the electrode. We assume that this interaction is so small that the transition probability can be calculated from first-order perturbation theory. This limits our treatment to nonadiabatic reactions, which is a severe restriction. At present there is no satisfactory, fully quantum-mechanical theory for adiabatic electrochemical electron-transfer reactions. 

We now turn to the electronically adiabatic ET reaction problem (cf. Sec. 2.2). There has been a spate oftheoretical papers [8,11 28,33,35,36,50] dealing with the possible role of solvent dynamics in causing departures from the standard Marcus TST rate theory [27,28] (although many of these deal with nonadiabatic reactions). The ET reaction considered is a simplified symmetric model, A1 2 A1/2 A1/2 A1/2, in a model solvent similar to CH3C1. The technical and computational... 

The reason for the absence of the nuclear frequency from eq 17 is that the slowest process in a nonadiabatic reaction is, by definition, the electron transfer that is, ve v n for a nonadiabatic reaction. 

The local permutational symmetry [Aa ] [AB ] is restricted such that the total permutational symmetry [A] is contained in T a 1 [V . When [Aa] [Ab] and [Aa ] [AB ] are not equal the corresponding separated molecule energies are different. Then for [Aa] [AB] / [Aa ] [AB ], the [Aa] [Ab] and [Aa ] [AB ] states are on different potential surfaces, and the process (5-9) is nonadiabatic. Thus the nonadiabatic reaction (5-9) might be expected to be most probably when the spin-free adiabatic potentials approach close to one another, since this is just the condition for the breakdown of the adiabatic approximation (see Sect. IV). 

Understanding the mechanism of this nonadiabatic radiationless decay is central to explaining excited state processes. There are two possible mechanisms (see nonadiabatic reactions in Figure 1). When real surface crossings exist (conical intersection, see left side of Figure 1) and are accessible, the Landau-... 

H. Kim, G. Hanna, and R. Kapral. Analysis of kinetic isotope effects for nonadiabatic reactions. J. Chem. Phys., 125 084509, 2006. 

The concept of adiabacity in e.t. processes has gained importance in recent years, and the question does arise to what extent it may influence the observation of the M.I.R. In principle, the occurence of the M.I.R. is related only to the quadratic form of the activation energy, not to the form of the pre-exponential factor. The M.I.R. should therefore be observed for both adiabatic and nonadiabatic reactions. However, if the observable rate of an adiabatic process is controlled by the solvent relaxation time, the influence of the exponential factor may be negligible [18]. 

Understanding the theoretical principles of light induced nonadiabatic reactions is therefore crucial for the comprehension of the photo-driven processes that lead to photoinduced charge transfer and energy transfer reactions which will be discussed later on in this thesis. 

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