Binding-energy

The difference between the total energy of a molecular system and the sum of the energies of its isolated components. 

An example of a continuously varying property is the binding energy (BE). This is defined for particle i and for the configuration R as follows  

This is the work required to bring a particle from an infinite distance with respect to all the other particles, to the position R,. For a system of pairwise additive potentials, (2.100) is simply the sum 

The function xB(v) is referred to as the distribution of BE. By analogy with the vector (2.97) which has discrete components, we often write xB for the whole distribution function, the components of which are xB(v). For simple spherical particles, the function xB(v) has one maximum at 2(Un)/N. For more complex liquids such as water, this function has more structure, reflecting the possibility of the different structural environments of a molecule in the liquid (for more details, see Ben-Naim 1974). 

At a given configuration / opt(tou we usually have many dissociation channels. 

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A related advantage of studying crystalline matter is that one can have synnnetry-related operations that greatly expedite the discussion of a chemical bond. For example, in an elemental crystal of diamond, all the chemical bonds are equivalent. There are no tenninating bonds and the characterization of one bond is sufficient to understand die entire system. If one were to know the binding energy or polarizability associated with one bond, then properties of the diamond crystal associated with all the bonds could be extracted. In contrast, molecular systems often contain different bonds and always have atoms at the boundary between the molecule and the vacuum. 

Figure Al.3.23. Phase diagram of silicon in various polymorphs from an ab initio pseudopotential calculation [34], The volume is nonnalized to the experimental volume. The binding energy is the total electronic energy of the valence electrons. The slope of the dashed curve gives the pressure to transfomi silicon in the diamond structure to the p-Sn structure. Otlier polymorphs listed include face-centred cubic (fee), body-centred cubic (bee), simple hexagonal (sh), simple cubic (sc) and hexagonal close-packed (licp) structures.

Figure Al.3.25. Schematic illustration of exciton binding energies in an insulator or semiconductor.

Even in semiconductors, where it might appear that the exciton binding energies would be of interest only for low temperaPire regimes, excitonic effects can strongly alter tlie line shape of excitations away from the band gap. 

Note that in core-level photoelectron spectroscopy, it is often found that the surface atoms have a different binding energy than the bulk atoms. These are called surface core-level shifts (SCLS), and should not be confiised with intrinsic surface states. Au SCLS is observed because the atom is in a chemically different enviromuent than the bulk atoms, but the core-level state that is being monitored is one that is present in all of the atoms in the material. A surface state, on the other hand, exists only at the particular surface. 

X-ray photoelectron spectroscopy (XPS), also called electron spectroscopy for chemical analysis (ESCA), is described in section Bl.25,2.1. The most connnonly employed x-rays are the Mg Ka (1253.6 eV) and the A1 Ka (1486.6 eV) lines, which are produced from a standard x-ray tube. Peaks are seen in XPS spectra that correspond to the bound core-level electrons in the material. The intensity of each peak is proportional to the abundance of the emitting atoms in the near-surface region, while the precise binding energy of each peak depends on the chemical oxidation state and local enviromnent of the emitting atoms. The Perkin-Elmer XPS handbook contains sample spectra of each element and bindmg energies for certain compounds [58]. 

NaCC) = 2.497 A, and = 0.195 cnV Finally, the position of the origin peak gives the electron binding energy (the electron affinity of NaCl, 0.727 eV) and a themiochemical cycle allows one to calculate the bond... 

The transition-state spectroscopy experiment based on negative-ion photodetachment described above is well suited to the study of the F + FI2 reaction. The experiment is carried out tln-ough measurement of the photoelectron spectrum of the anion FH,. This species is calculated to be stable with a binding energy of... 

Weak interactions are characterized by binding energies of at most a few kcal/mole and by IPSs with a very... 

XPS X-ray photoelectron spectroscopy Absorption of a photon by an atom, followed by the ejection of a core or valence electron with a characteristic binding energy. Composition, oxidation state, dispersion... 

Because a set of binding energies is characteristic for an element, XPS can analyse chemical composition. Almost all photoelectrons used in laboratory XPS have kinetic energies in the range of 0.2 to 1.5 keV, and probe the outer layers of tire sample. The mean free path of electrons in elemental solids depends on the kinetic energy. Optimum surface sensitivity is achieved with electrons at kinetic energies of 50-250 eV, where about 50% of the electrons come from the outennost layer. 

Figure Bl.25.4. C Is XPS spectrum of a polymer, illustrating that the C Is binding energy is influenced by the chemical enviromnent of the carbon. The spectrum clearly shows four different kinds of carbon, which corresponds well with the structure of the polymer (courtesy of M W G M Verhoeven, Eindhoven).

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