Electron potential energy

Bohr also realized that the opposite is true when a high-potential-energy electron in an atom loses some of its energy, the electron moves closer to the nucleus and the energy lost from the electron is emitted from the atom as a photon of light. Both absorption and emission are illustrated in Figure 5-12. 

In our subsequent development we shall take the origin of coordinates to be at the centre of mass of the two nuclei, although we could equally well have chosen the molecular centre of mass as origin. Setting aside the translational motion of the molecule, we use equation (2.28) to represent the kinetic energy of the electrons and nuclei. To this we add terms representing the potential energy, electron spin interactions, and nuclear spin interactions. We subdivide the total Hamiltonian Xx into electronic and nuclear Hamiltonians,... 

A second surface effect is due to the high kinetic energy and small mass of the free electrons (see Section 4.3). Electrons impinging on the surface wall may penetrate this wall this decreases their kinetic energy and increases their potential energy. Electrons spill over the surface plane, which corresponds to the center of the core ions. A time-averaged sketch of the distribution of the electrons and ions near the surface of a metal is presented in Figure 13(a). 

A FIGURE 18.3 An Analogy for ectrical Current Just as water flows downhiU in response to a difference in gravitational potential energy, electrons flow through a conductor in response to an electrical potential difference, creating an electrical current. 

Fig. VIII-5. Schematic potential energy diagram for electrons in a metal with and without an applied field , work function Ep, depth of the Fermi level. (From Ref. 62.)...

The result is that, to a very good approxunation, as treated elsewhere in this Encyclopedia, the nuclei move in a mechanical potential created by the much more rapid motion of the electrons. The electron cloud itself is described by the quantum mechanical theory of electronic structure. Since the electronic and nuclear motion are approximately separable, the electron cloud can be described mathematically by the quantum mechanical theory of electronic structure, in a framework where the nuclei are fixed. The resulting Bom-Oppenlieimer potential energy surface (PES) created by the electrons is the mechanical potential in which the nuclei move. Wlien we speak of the internal motion of molecules, we therefore mean essentially the motion of the nuclei, which contain most of the mass, on the molecular potential energy surface, with the electron cloud rapidly adjusting to the relatively slow nuclear motion. 

Note the stnicPiral similarity between equation (A1.6.72) and equation (Al.6.41). witii and E being replaced by and the BO Hamiltonians governing the quanPim mechanical evolution in electronic states a and b, respectively. These Hamiltonians consist of a nuclear kinetic energy part and a potential energy part which derives from nuclear-electron attraction and nuclear-nuclear repulsion, which differs in the two electronic states. 

Figure Al.6.13. (a) Potential energy curves for two electronic states. The vibrational wavefunctions of the excited electronic state and for the lowest level of the ground electronic state are shown superimposed, (b) Stick spectrum representing the Franck-Condon factors (the square of overlap integral) between the vibrational wavefiinction of the ground electronic state and the vibrational wavefiinctions of the excited electronic state (adapted from [3]).

The fimctiong(ri is central to the modem theory of liquids, since it can be measured experimentally using neutron or x-ray diffraction and can be related to the interparticle potential energy. Experimental data [1] for two liquids, water and argon (iso-electronic with water) are shown in figure A2.4.1 plotted as a fiinction ofR = R /a, where a is the effective diameter of the species, and is roughly the position of the first maximum in g (R). For water, a = 2.82 A,... 

The potential energy of the electrons, V, which is a negative quantity that can be partitioned into bulk and surface contributions, as shown. 

There are significant differences between tliese two types of reactions as far as how they are treated experimentally and theoretically. Photodissociation typically involves excitation to an excited electronic state, whereas bimolecular reactions often occur on the ground-state potential energy surface for a reaction. In addition, the initial conditions are very different. In bimolecular collisions one has no control over the reactant orbital angular momentum (impact parameter), whereas m photodissociation one can start with cold molecules with total angular momentum 0. Nonetheless, many theoretical constructs and experimental methods can be applied to both types of reactions, and from the point of view of this chapter their similarities are more important than their differences. 

Many potential energy surfaces have been proposed for the F + FI2 reaction. It is one of the first reactions for which a surface was generated by a high-level ab initio calculation including electron correlation [47]. The... 

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