Electronic potential energy, total

The total electronic potential energy of a molecule depends on the averaged electronic charge density and the nonlocal charge-density susceptibility. The molecule is assumed to be in equilibrium with a radiation bath at temperature T, so that the probability distribution over electronic states is determined by the partition function at T. The electronic potential energy is given exactly by... 

The two physical interpretations of LSD and GGA are about equally plausible in a normal system. Buf especially in abnormal systems, these approximations may be more faithful to the alternative theory, because of the close relationship between Px=i r,r) and the electron-electron potential energy of Eq. (5). Thus, accurate total energies are expected to accompany accurate... 

This formula can be simplified. The first term on its RHS is = Vne — specifically, the total nuclear-electronic potential energy of the molecule [Eq. (4.5)] stripped of all the individual core nuclear-electronic interactions V. Next, we decompose V ... 

It is of considerable importance to note that the density-potential relationship (3) of the TF theory follows from a variational principle for the total energy. To see this, we note first that the classical electrostatic potential energy U consists of the sum of two terms in an atomic ion, the electron-nuclear potential energy Ken and the electron-electron potential energy Kee. We can write... 

Figure 4 Difference Vnn—Vee between nuclear-nuclear and electron-electron potential energy against total kinetic energy T for light molecules. Energies are in Hartree units...

From eqn (6.30) it is clear that the virial of the electronic forces, which is the electronic potential energy, is totally determined by the stress tensor a and hence by the one-electron density matrix. The atomic statement of the virial theorem provides the basis for the definition of the energy of an atom in a molecule, as is discussed in the sections following Section 6.2.2. 

Since the Hamiltonian must be invariant to all the symmetry operations of the pseudomolecule, it follows that Q and dUfdQ) have the same symmetry. Their direct product is totally symmetric. Since is S5mimetric, it follows next that d Ujd Q) is also S5mimetric. U is the nuclear-electronic and nuclear-nuclear potential energy. The kinetic energy of the electrons and electron-electron potential energy are not functions of the nuclear coordinates, to the first order. 

Another by-product of secondary electron in electron microscopic analysis is X-ray fluorescence. When an electron from the inner shell is emitted from the atom during the secondary electron emission, and another electron from the outer shell falls to its vacancy, the released energy might be emitted as X-ray to balance the total energy of the atom. Figure 5.6a and b schematically illustrates the emission processes of the K-line and L-line X-rays from a titanium atom, respectively, where Eg, 1, 2, and 3 are the electron potential energies... 

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. 

Figure Bl.26.21. Potential energy curves for an electron near a metal surface. Image potential curve no applied field. Total potential curve applied external field = -E. ...

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