Potential energy surfaces, adiabatic Born-Oppenheimer

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.)...

The idea of a classical treatment of the nuclear motion within the molecular dynamics (MD) scheme with ab initio determined, quantum-mechanical forces acing on nuclei is as old as quantum mechanics.11,12 The commonly used Born-Oppenheimer approximation12 introduces the concept of potential energy surface (PES). Different time-scales for nuclear and electronic motion allows for the adiabatic separation of the nuclear and electronic wave-function. In the Born-Oppenheimer molecular dynamics (BO-MD) the nuclei move according to Newton laws, while the quantum mechanics is required to determine the potential for this motion ... 

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. 

Within the Born-Oppenheimer approximation—that is, after separating off the nuclear motion—adiabatic potential energy surfaces are obtained by... 

The Born-Oppenheimer approximation states that the electrons are able to adjust themselves instantaneously to tlie motions of the nuclei. The motions of the nuclei are in this approximation therefore not able to induce electronic transitions, an assumption that is also known as tire adiabatic approximation. The electrons thus create an effective electronic potential in which the nuclei move, and for a given electronic state tire valuation in the electronic energy with respect to the nuclear configuration defines a potential energy surface for the electronic state. The electronic Schrodinger equation can be written as... 

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... 

---