Potential energy surface , concept

Both the BO dynamics and Gaussian wavepacket methods described above in Section n separate the nuclear and electronic motion at the outset, and use the concept of potential energy surfaces. In what is generally known as the Ehrenfest dynamics method, the picture is still of semiclassical nuclei and quantum mechanical electrons, but in a fundamentally different approach the electronic wave function is propagated at the same time as the pseudoparticles. These are driven by standard classical equations of motion, with the force provided by an instantaneous potential energy function... 

The BO picture is what gives rise to the concept of a manifold of potential energy surfaces on which vibrational/rotational motions occur. 

The low-temperature chemistry evolved from the macroscopic description of a variety of chemical conversions in the condensed phase to microscopic models, merging with the general trend of present-day rate theory to include quantum effects and to work out a consistent quantal description of chemical reactions. Even though for unbound reactant and product states, i.e., for a gas-phase situation, the use of scattering theory allows one to introduce a formally exact concept of the rate constant as expressed via the flux-flux or related correlation functions, the applicability of this formulation to bound potential energy surfaces still remains an open question. 

The concept of a potential energy surface has appeared in several chapters. Just to remind you, we make use of the Born-Oppenheimer approximation to separate the total (electron plus nuclear) wavefunction into a nuclear wavefunction and an electronic wavefunction. To calculate the electronic wavefunction, we regard the nuclei as being clamped in position. To calculate the nuclear wavefunction, we have to solve the relevant nuclear Schrddinger equation. The nuclei vibrate in the potential generated by the electrons. Don t confuse the nuclear Schrddinger equation (a quantum-mechanical treatment) with molecular mechanics (a classical treatment). 

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... 

Ethylene electronic isomerism is introduced as a new concept and examined from the perspective of the generalized electronic diabatic (GED) scheme. In chemistry isomerism is related to distributions in space of atomic nucleus in one and the same adiabatic potential energy surface. Therefore, in this case cis and trans isomers would be indistinguishable when the four hydrogen atoms are identical. Nevertheless, in this paper we show that isomerism is an electronic... 

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