Positive hole density

The paramagnetic absorption of alkane radical cations is critically dependent on their conformation. In neat n-alkane crystals, alkane molecules are in the extended all-trans conformation (see Fig. 5.1) and FDMR spectroscopy unequivocally shows that alkane radical cations retain that conformation in such systems. The extended all-trans conformation is also the preferred conformation of many n-alkane radical cations in chlorofluorocarbon and perfluorocarbon matrices. In this conformation, the unpaired electron occupies the planar cr molecular orbital and delocalizes over the entire extended chain. Only two C-H bonds (both chain-end, one on each side) are in the planar ct molecular frame in the extended structure and high unpaired-electron and positive-hole density appears only on these in-plane protons. Alkane radical cations in the extended conformation (as well as in other conformations) are thus fj-delocalized paramagnetic species. The associated hyperfme interaction with the two (equivalent) in-plane chain-end protons results in a 1 2 1 three-line (triplet) EPR spectrum. The fact that the hyperfme in-... 

For n-alkane radical cations, both primary and secondary alkyl radicals may act as conjugate base, depending on the conformation of the radical cation. This is a direct consequence of the fact that the site of proton donation from alkane radical cations is strictly dependent on their electronic structure, that is, a high unpaired-electron and positive-hole density in a particular C-H bond results in proton transfer from that bond (evidence for this is given in Sections 5.7 and 5.8), whereas the electronic structure of the radical cations in turn depends on their conformation. For n-alkane radical cations in the extended conformation, in which the unpaired-electron and positive-hole delocalize over the planar C-C skeleton and two in-plane chain-end C-H bonds (one on each side), proton transfer takes place exclusively from chain-end positions and the corresponding primary alkyl radicals act as conjugate base. For n-alkane radical cations in the gauche-at-... 

For example, NH3-vapor as a reducing gas (electron donor), when contacting p-type PP film, causes a depletion of positive hole density in the near surface vicinity and therefore a corresponding reduction of its conductivity. On the other hand, NO2 as an electron acceptor increases the density of positive defects, resulting in conductivity enhancement [144]. Maximum chemical sensitivity is achieved by a polymer doping leading to the conductivity of semiconductors (ca. 10 to 10 Scm"0-... 

Figure 11-14 shows the calculated hole density (upper panel) and the electric field (lower panel) as a function of position for the three structures. For the devices with a hole barrier there is a large accumulation of holes at the interface. The spike in the hole density at the interface causes a rapid change in the electric field at the interface. The field in the hole barrier layer is significantly larger than in the hole injection layer. For the 0.5 eV hole barrier structure, almost all of the... 

Figure 11-14. Calculated hole density (upper panel) and electric field (lower panel) as a (unction of position lor the three structures of 1 ijs 11-13 at a 10 V bias.

Fig. 13 Results from the quantum calculations on the duplex sequence 5 -GAGG-3. In a, the sodium ions and their solvating water molecules are located at positions near the phosphate anions of the DNA backbone. In b, one sodium ion is moved from near a phosphate anion to N-7 of a guanine, which molecular dynamics calculations show to be a preferred site. The balloons represent the hole density on the GAGG sequences with the two different sodium ion orientations. The radical cation clearly changes its average location with movement of the sodium ion...

We define a normal system as one in which the hole density at the weakly-interacting end of the coupling-constant integration is close to that of a single Slater determinant. In such a system, the local and gradient-corrected holes, evaluated for the exact spin-densities, are nearly exact near the position of the... 

The above mentioned positivity conditions state that the 2-RDM D, the electron-hole density matrix G, and the two-hole density matrix Q must be positive semidefinite. A matrix is positive semidefinite if and only if all of its eigenvalues are nonnegative. The solution of the corresponding eigenproblems is readily carried out [73]. For D, it yields the following set of eigenvalues ... 

In most simple aldehydes and ketnoes, including benzophenone, the longest wavelength absorption is a low intensity n - iz transition. The promotion of a n-electron, localized on O-atom to a n-orbital, leaves behind a positive hole on this atom. The charge density on C-atom is increased creating a bipolar state. The dipole moment of >C = O bond is reduced. Three primary processes are commonly encountered for this electrophilic centre ... 

In this equation, Ey is the energy level of the valence band edge, Ny the effective density of states of the valence band, p the concentration of photo-generated positive holes, and pp that of Positive holes in thermal equilibrium in the dark which can be eventually ignored in a semiconductor of large band gap such as Zn°. ... 

If the density of holes Ps at the surface - or equivalently the quasi-Fermi level Ep p — are equal at the surface of an n- and p-semiconductor electrode, then the same reaction with identical rates, i.e. equal currents, takes place at both types of electrodes (Fig. 15). Since holes are majority carriers in a p-type semiconductor, the position of the quasi-Fermi level Ep,p is identical to the electrode potential (see right side of Fig. 15), and therefore-with respect to the reference electrode - directly measurable. The density of p can easily be calculated, provided that the positions of the energy bands at the surface are known. The measurements of a current-potential curve also yields automatically the relationship between current and quasi-Fermi level of holes. The basic concept implies that the position of the quasi-Fermi level Ep,p at the surface of an n-type semiconductor and the corresponding hole density Ps can be derived for a given photocurrent, since the same relationship between current and the quasi-Fermi level of holes holds. 

Because of the delocalization of electrons throughout the metallic crystal, no persistence of ionization or chemical decomposition can occur because a positive hole formed by an electron ejection is always refilled by an electron from the conduction band. On the other hand, sufficiently energetic radiations can cause atomic displacements. The production of interstitial atoms swells the lattice, thereby decreasing the density of the crystal. 

It should be borne in mind that the resemblance of a Fermi hole density to that of a localized valence orbital is obtained only when the reference electron is placed in the neighbourhood of a local maximum in the VSCC. The Fermi hole and hence the density of the reference electron are much more delocalized for general positions throughout the valence region (see Fig. E7.4(f)). Localized molecular orbitals thus overemphasize electron localiz-ability and do not provide true representations of the extent to which electrons are spatially localized. 

Fig. E7.5. Contour maps of the Fermi hole density for pyramidal (a, b) and planar (c, d) ammonia, In maps (a) and (b) the reference electron is positioned at the non-bonded and bonded maxima, respectively, in the VSCC of the nitrogen atom. Note that the Fermi density is more contracted towards the core in NH3 than it is in CH4, as are the maxima in its VSCC. Maps (c) and (d) are corresponding plots for planar ammonia. The density of the non-bonded Fermi hole, map (c), is more delocalized than that for the pyramidal geometry, map (a). In the planar geometry, contours of the non-bonded Fermi hole density encompass the N-H internuclear axis. Clearly, maps (c) and (d) overlap one another to a greater extent than do maps (a) and (b)—the electron pairs are more localized in pyramidal than in planar iunmonia.

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