Born-Oppenheimer approximations adiabatic reactions

Adiabatic photoreaction Within the Born-Oppenheimer approximation , a reaction of an excited state species that occurs on a single potential-energy surface . Compare diabatic photoreaction. 

Diabatic photoreaction Within the Born-Oppenheimer approximation, a reaction beginning on one excited state potential-energy surface and ending, as a result of radiationless transition, on another surface, usually that of the ground state. Also called non-adiabatic. 

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 Chapter 4 we will learn to calculate the equilibrium constant for an exchange reaction like Equation2.15 using the Born-Oppenheimer approximation. If, in addition, the adiabatic correction is included, the equilibrium constant calculated in the Born-Oppenheimer approximation must be multiplied by a correction factor containing the energy difference AAC. 

Beam studies have until recently been largely confined to systems in which the dynamics are governed by a single potential surface. The use of classical trajectory studies and adiabatic correlation diagrams in predicting the reaction path are both implicitly founded on the Born-Oppenheimer approximation which allows us to deal with only one electronic state during... 

The adiabatic approximation for reaction dynamics assumes that motion along the reaction coordinate is slow compared to the other modes of the system and the latter adjust rapidly to changes in the potential from motion along the reaction coordinate. This approximation is the same as the Born-Oppenheimer electronically adiabatic separation of electronic and nuclear motion, except that here we... 

The modem theory of chemical reaction is based on the concept of the potential energy surface, which assumes that the Born-Oppenheimer adiabatic approximation [16] is obeyed. However, in systems subjected to the Jahn-Teller effect, adiabatic potentials have the physical meaning of the potential energy of nuclei only under the condition that non-adiabatic corrections are small [28]. In the vicinity of the locally symmetric intermediate, these corrections will be very large. The complete description of nuclear motion, i.e. of the mechanism of the chemical reaction, can be obtained only from Schroedinger s equation without applying the Born-Oppenheimer approximation in the vicinity of the locally... 

This matrix was introduced by F. T. Smith [25] for the treatment of non-adiabatic (diabatic) couplings in atomic collisions. It is now familiar also in molecular structure problems, to indicate local breakdowns of the Born-Oppenheimer approximation. Within the hyperspherical formalism, it has been introduced in the three-body Coulomb problem [20] and in chemical reactions [21-24], see also Section 3. Also, from equation (A4)... 

The concepts of energy surfaces for molecular motion, equilibrium geometries, transition structures and reaction paths depend on the Bora-Oppenheimer approximation to treat the motion of the nuclei separately from the motion of the electrons. Minima on the potential energy surface for the nuclei can then be identified with the classical picture of equilibrium structures of molecules saddle points can be related to transition states and reaction rates. If the Born-Oppenheimer approximation is not valid, for example in the vicinity of surface crossings, non-adiabatic effects are important and the meaning of classical chemical structures becomes less clear. Non-adiabatic effects are beyond the scope of this chapter and the discussion of energy surfaces and optimization will be restricted to situations where the Bom-Oppenheimer approximation is valid. 

In this thesis work. Dr. Ren also studied the non-adiabatic effect in the F -I- D2 reaction, where the F ( Pi/2) is expected to be non-reactive according to the Bom-Oppenheimer approximation. He measured accurately the population ratio of F( P3/2) and F ( Pi/2) in the beam using synchrotron radiation single photon autoionization, then determined the relative reactivity of F and F with D2. For the first time, he found that F ( Pi/2) is more reactive than F( P3/2) at low collision energy, providing a clear case of the breakdown of Born-Oppenheimer approximation. This is the first accurate experimental measurement of the non-adiabatic effects of this important system. 

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. 

The study of molecular systems using quantum mechanics is based on the Born-Oppenheimer approximation. This approximation relies on the fact that the electrons, because of their smaller mass, move much faster than the heavier nuclei, so they follow the motion of the nuclei adiabatically, whereas the latter move on the average potential of the former. The Born-Oppenheimer approximation is sufficient to describe most chemical processes. In fact, our notion of molecular structure is based on the Born-Oppenheimer approximation, because the molecular structure is formed by nuclei being placed in fixed positions. There are, however, essential nonadiabatic processes in nature that cannot be described within this approximation. Nonadiabatic processes are ubiquitous in photophysics and photochemistry, and they govern such important phenomena as photosynthesis, vision, and charge-transfer reactions. 

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