Highest occupied molecular orbital oxidation-reduction potentials

Figure 8-1 shows the potential energy barrier for the transfer reaction of redox electrons across the interface of metal electrode. On the side of metal electrode, an allowed electron energy band is occupied by electrons up to the Fermi level and vacant for electrons above the Fermi level. On the side of hydrated redox particles, the reductant particle RED is occupied by electrons in its highest occupied molecular orbital (HOMO) and the oxidant particle OX, is vacant for electrons in its lowest imoccupied molecular orbital (LUMO). As is described in Sec. 2.10, the highest occupied electron level (HOMO) of reductants and the lowest unoccupied electron level (LUMO) of oxidants are formed by the Franck-Condon level sphtting of the same frontier oihital of the redox particles... 

Commonly used descriptor variables for QSARs involving redox reactions include substituent constants (o), ionization potential, electron affinity, energy of the highest occupied molecular orbital (EHOMO)or lowest unoccupied molecular orbital (ELUMO), one-electron reduction or oxidation potential (E1), and half-wave potential (E1/2)- One descriptor variable (D), fit to a log-linear model, is usually sufficient to describe a redox property of P. Such a QSAR will have the form... 

The potentials of reversible one-electron oxidations (reductions) of alternant aromatic hydrocarbons have been found to give good straight lines when plotted against the calculated energies of the highest occupied molecular orbitals (HOMOs lowest unoccupied molecular orbitals = LUMOs) [Heilbronner (91)]. The results indicate two important trends ... 

To illustrate the tuning aspects of the MLCT transitions in ruthenium polypyridyl complexes, the well known [RuLs] (L = 4,4 dicarboxylic acid-2,2 -bi-pyridine) type of complex can be considered. This complex shows strong visible band at 466 nm, because of CT transition from metal t2g highest occupied molecular orbitals (HOMO) to jr -lowest unoccupied molecular orbitals (LUMO) of the ligand (Fig. 3). The Ru(II)/(III) oxidation potential is at 1.3 V, and the ligand based reduction potential is at —1.5V... 

Another definition of aromaticity that does not depend explicitly on either experimental results or on comparison with reference compounds is derived from the concept of absolute hardness, 17, which is defined as one-half of the energy difference between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of a system (equation 4.70). According to Koopmans theorem, Ehomo is related to the ionization potential of the species, while Elumo is related to its electron affinity. A large gap between these two orbitals implies resistance to both oxidation and reduction, and low chemical reactivity is one of the defining characteristics of aromaticity. 

Fig. 15 Schematic overview of artificial photosynthesis employing water as electron source and producing hydrogen as fuel product. The valence band (VB, for a semiconducting material) or the highest occupied molecular orbital (HOMO, for a molecular photosensitizer) must have a reduction potential more positive than the water oxidation catalyst to promote efficient electron transfer. Likewise, the hydrogen evolution catalyst must have a reduction potential more positive than the conduction band (CB, for a semiconducting material) or the lowest unoccupied molecular mbital (LUMO, for a molecular photosensitizer, since this molecular orbital is the most likely to be occupied by an electron upon excitation) for electron transfer to be thermodynamically favorable. Water, a coordinating ligand, can have a significant impact on catalysts with an opcm coordination site. Thus the RHE scale has been included...

The two electrode materials are in direct contact with the liquid electrolyte, an environment made up of molecular species, characterized by their highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energy levels. Adding an electron to the electrolyte s LUMO results in the reduction of the latter, whereas removing an electron from its HOMO results in its oxidation. So long as the positive electrode material s Fermi level is situated above the electroljde s HOMO level, no electron transfer will occur from the electrolyte to the positive electrode, and the electrolyte remains electrochemically stable since it does not oxidize continually on contact with the electrode. This remains theoretically true for positive electrode materials whose potential does not exceed approximately 4.5 V versus Li /Li, which is the case for the usual materials, such as LiCo02. 

Table 2.3 Highest occupied molecular orbitals (HOMO), lowest unoccupied molecular orbitals (LUMO), oxidation potentials (OP), reduction potentials (RP), and BE F binding affinity values in eV.

Electrochemistry is an analytical tool that can be used to determine redox potentials of an analyte as well as the fate of a molecule upon addition or removal of electrons. Of particular importance to photochemists is the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). Cyclic voltammetry is one of the most commonly used electrochemical techniques and is based on the change in potential as a linear function of time. An electrochemical reaction is reversible if = 1 and AEp = 59/n mV, where ip is the anodic peak current, ip is the cathodic peak current, and A p (AE), = A p — Ep ") is the potential peak separation for the anodic ( ), ) and cathodic Ep ) peaks. The oxidation or reduction potential for a reversible electrochemical process is given by 1/2 = Ep + Ep jl and is recorded vs. a reference electrode. All electrochemical data provided herein are converted to V vs. saturated calomel electrode (SCE) to make the comparison more facile. A reversible redox couple implies that the complex undergoes facile electron transfer with the electrode and that no chemical reaction follows the electrochemical step. 

The reduction potential of a compound depends on the energy of the lowest vacant molecular orbital, whereas the oxidation potential is dependent on the energy of the highest occupied orbital. If the electron-transfer reaction is fast, i.e., a reversible reaction, the reduction potentials of a series of compounds may be evaluated theoretically with some success when complicating factors, such as solvation energy, are constant or absent. Quantum mechanical calculation of polaro-graphic half-wave potentials of azaheteroaromatic compounds have been performed using different approximations.17-19... 

In aprotic nonaqueous media, the organic electrochemistry of anodic and cathodic reactions is concerned predominantly with radical-ion chemistry in many cases involving aromatic substances, the radicals are of sufficient stability for them to be characterized spectroscopically by conventional absorption spectrophotometry and by esr spectroscopy. Linear relations are found between the cathodic and anodic half-wave potentials and the ionization potentials or electron affinities determined in the gas phase. The oxidation and reduction potentials can also be related to the theoretically calculated energies of the highest occupied (anodic process) or lowest vacant (cathodic process) molecular orbitals. 

---