Electron-nuclear separations Born-Oppenheimer principle

The Born-Oppenheimer principle assumes separation of nuclear and electronic motions in a molecule. The justification in this approximation is that motion of the light electrons is much faster than that of the heavier nuclei, so that electronic and nuclear motions are separable. A formal definition of the Born-Oppenheimer principle can be made by considering the time-independent Schrodinger equation of a molecule, which is of the form... 

The time-dependent perturbation theory of the rates of radiative ET is based on the Born-Oppenheimer approximation [59] and the Franck Condon principle (i.e. on the separation of electronic and nuclear motions). The theory predicts that the ET rate constant, k i, is given by a golden rule -type equation, i.e., it is proportional to the product of the square of the donor-acceptor electronic coupling (V) and a Franck Condon weighted density of states FC) ... 

Born and Oppenheimer" showed in 1927 [9] that to a very good approximation the nuclei in a molecule are stationary with respect to the electrons. This is a qualitative expression of the principle mathematically, the approximation states that the Schrodinger equation (chapter 4) for a molecule may be separated into an electronic and a nuclear equation. One consequence of this is that all ( ) we have to do to calculate the energy of a molecule is to solve the electronic Schrodinger equation and then add the electronic energy to the internuclear repulsion (this latter quantity is trivial to calculate) to get the total internal energy (see section 4.4.1). A deeper consequence of the Born-Oppenheimer approximation is that a molecule has a shape. 

Many of the ideas that are essential to understanding polyatomic electronic spectra have already been developed in the three preceding chapters. As in diatomics, the Born-Oppenheimer separation between electronic and nuclear motions is a useful organizing principle for treating electronic transitions in polyatomics. Vibrational band intensities in polyatomic electronic spectra are frequently (but not always) governed by Franck-Condon factors in the vibrational modes. The rotational fine structure in gas-phase electronic transitions parallels that in polyatomic vibration-rotation spectra (Section 6.6), except that the rotational selection rules in symmetric and asymmetric tops now depend on the relative orientations of the electronic transition moment and the principal axes. Analyses of rotational contours in polyatomic band spectra thus provide valuable clues about the symmetry and assignment of the electronic states involved. 

In principle, it is known that the theory of quantum mechanics gives a complete description of a system at an atomic level [1]. In practice, the equations that result are impossible to solve, either analytically or numerically, except in a very few cases. It is usual, therefore, to invoke a number of simplifications. The first is the Born-Oppenheimer approximation which states that the dynamics of electrons and nuclei can be treated separately because of the large disparity in their masses. This leads to a two-step procedure in which the electronic problem is solved first and the nuclear problem is dealt with afterwards [2]. 

Since surface reconstruction under chemisorption processes is taking place [269], it is an open question how this is best accounted for. Should the atoms be allowed to relax adiabatically on an, in principle, infinite timescale, or should one use the timescale on which the collision occurs Is the Born-Oppenheimer separation meaningful under such circumstances The interplay between nuclear and electronic degrees of freedom is not fully understood in these cases. 

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