Ionization potentials reorganization energy

The individual terms, e , in Eq. (2.27) are termed one-electron orbital energies and correspond to the ionization potential (-e ) of an electron in MO i r assuming that no reorganization of the core nuclei, or the other (2N — 1) electrons, takes place during ionization. The total energy of the system [Eq. (2.27)] is clearly not the sum of the one-electron energies because electron-electron interaction terms are included twice. 

The photoelectron spectrum is frequently discussed in terms of Koopmans theorem, which states that the ionization potentials (IPs) are approximately related to the energies of the canonical orbital found in molecular orbital calculations.106. The relationship is approximate because two factors are neglected the change in the correlation energy, and the reorganization energy, which is a consequence of the movement of electrons in response to the formation of a cation. The two quantities are approximately equal and opposite. 

The difference between Eph and the ionization potential /g in the gaseous phase equals the energy required for reorganizing the medium after one of the molecules has been replaced by a positive ion.193 194 (Approximately, we can take this energy to be the polarization energy P+... 

At 25°C, the cyclohexane molecules mainly have the chair form. The equilibrium concentration of the isomeric twist form is 10-4 mol-dm-3. On ionization, the solvent cation radicals in chair form are predominant. Electron transfer between the chair form of the cyclohexane cation radicals and the chair-shaped surrounding cyclohexane molecules is very fast, since it requires minimum reorganization energy. However, the chair-form cation radical sometimes approaches a minor part of the neutral molecules in twist form. Because the twist cyclohexane has lower ionization potential, the twist-shaped molecules scavenge the cation radicals in chair form. 

TTie solution phase ionization potentials of Br in 16 solvents have been determined by photoeiectron emission spectroscopic technique. The values obtained as the threshold energy E for Br" in various solvents are found to be correlated well with the Mayer-Gutmann acceptor number of solvent. The reorganization energy AC, of solvent after the photoionization of Br" has been obtained from the E value. The AG, values are well reproduced by using a simple model which incorporates the dipole-dipole repulsion and the hydrogen-bond formation in the first solvation layer. The solvation structures of Br" determined by EXAFS are used for the AG, calculation. 

Metallocenes are useful electron donors as judged by their low (vertical) ionization potentials in the gas phase and oxidation potentials in solution (see Table 2). In fact, the electron-rich (19 e ) cobaltocene with an oxidation potential of E°ox = -0.9 V relative to the SCE [45] is commonly employed as a very powerful reducing agent in solution. Unlike the alkylmetals (vide supra), the HOMOs of metallocenes reside at the metal center [46] which accounts for two effects (i) Removal of an electron from the HOMO requires minimal reorganization energy which explains the facile oxidative conversion from metallocene to metallocenium. (ii) The metal-carbon bonding orbitals are little affected by the redox process, and thus the resulting metallocenium ions are very stable and can be isolated as salts. 

A quasi-linear correlation of log/c or AG with the ionization potentials of the electron donors as observed in the FeL3 - + reactions is predicted by Marcus theory for outer-sphere electron transfers. Accordingly, the free-energy dependence of AG can be satisfactorily simulated with the Marcus equation (Eq. 90), taking a (constant) value of A = 41 kcal mol as reorganization energy for all tetraalkyltin compounds (see Figure 19A) [32]. 

It has been reported that the direct substitution of the benzene ring of ben-zothiophene in such compounds can be used as a tool for modification of electronic and photophysical properties of Tt-conjugated materials. In particular, the substituent effect on HOMO/LUMO energies, ionization potentials, electron affinities, and reorganization energies have been described for 4,6-di(thiophen-2-yl)pyrimidine derivatives (Scheme 36(b) 2014CTC(1031)76). 

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