Defects correlation energy

Solitons are considered to be important defect states in these conjugated polymers (see Fig. 6.48). It has however been shown that correlation energy is the more important factor in giving rise to the energy gap in (CH) (Soos Ramasesha, 1983). Other polymers related to polyacetylene are polythiophene, polypyrrole, poly-phenylenesulphide, and polyparaphenylene (Section 3.3). Extensive measurements on doped polyacetylenes have been reported in the last five years and these materials, unlike other conducting polymers such as (SN), seem to have good technological potential. 

Fig. 4.3. Illustration of the one-electron and two-electron energy levels of a defect and the four possible transitions to the conduction and valence bands. The charge state is indicated when the Fermi energy lies in the different energy ranges. The defect is assumed to be neutral when singly occupied, with a positive correlation energy, U.

Another contribution to the correlation energy arises from the lattice relaxation at the defect. The previous section showed that the addition of an electron to a localized state may cause a change in the bonding, which lowers the electronic energy by the amount W given in Eq. (4.3). The total correlation energy is a combination of the Coulomb and relaxation energies. 

The second term on the right hand side raises the interesting possibility of a defect that has a negative total correlation energy. This concept was introduced by Anderson (1975) and was first observed in the defect structure of chalcogenide glasses (Street and Mott 1975). 

Lattice relaxation is an essential property of negative U defects because the Coulomb contribution to the correlation energy in Eq. 

Fig. 4.23. There has not been a similar deconvolution of the defect absorption in p-type material using the measured valence band density of states, but E fC) is estimated to be about 0.9 eV. The mobility gap is about 1.85 eV (see Fig. 3.16), so that (/—21F 0.1eV with an uncertainty of about 0.2 eV. This result is consistent with a correlation energy of 0.2 eV and a small relaxation energy. However, other investigators, with essentially the same data but different procedures for extracting the energies, have obtained negative values of the...

Although thermoluminescence studies by themselves do not contribute to the assignment of models for defects, such measurements can, when correlated to other kinds of data, yield more information about the nature of defects. Activation energies for the thermal release of trapped charge and the sign of the charge can often be determined. 

Although it is possible to obtain good estimates of the electron correlation energy by either density functional or configuration interaction methods both of these methods (for different reasons) suffer from the same defect it is not possible to obtain a clear physical and chemical interpretation of the results of the calculation. The valence bond model, in principle and in practice, puts the physical interpretation as a top priority but pays a price in the complexity of its implementation. 

Rydberg defect, eq. (1) standard oxidation potential electronic correlation energy... 

The use of finite basis sets derives in a specific defect of the quantum-chemical calculation known as the Basis Set Superposition Error (BSSE). The majority of the contribution to the energy of a system comes from the internal electrons. If the basis set of an atom is deficient in the core region, a molecular method recovers a large amount of energy correcting this deficient area with the basis set of the other atoms. The BSSE is therefore related with the improper inclusion of the correlation energy in a quantum-chemical calculation. Although present in aU... 

Simple models aside, if we choose to perform a self-consistent DFT calculation in which we explicitly treat the ionic lattice with, for example, a PP or full potential treatment, what level of accuracy can we expect to achieve As always, the answer depends on the properties we are interested in and the exchange-correlation functional we use. DFT has been used to compute a whole host of properties of metals, such as phonon dispersion curves, electronic band structures, solid-solid and solid-liquid phase transitions, defect formation energies, magnetism, superconducting transition temperatures, and so on. However, to enable a comparison between a wide range of exchange-correlation functionals, we restrict ourselves here to a discussion of only three key quantities, namely, (i) (ii) ao, the... 

---