Filled molecular orbitals

Although the reduction process is not always a reversible one, oxidation and reduction potential values can be sometimes related to the Hiickel energies of the highest and lowest filled molecular orbital of the dye (108). 

The TT-electron density refers to the electron density at a given carbon atom obtained by summing the contributions from all the filled molecular orbitals. Electrophilic attack occurs where this density is highest, and nucleophilic attack where it is lowest tt-electron densities are not dominant in determining the orientation of homolytic substitution. 

The filled molecular orbitals beyond the crg and au that arise from combining the 2s atomic functions are (tcJ2 (-,J2 (.-r,]2. However, there is an empty antibonding orbital (designated as 7r or zr, ) on CN that can be shown as... 

CCI2 possesses both a high-energy filled molecular orbital in the o plane and a low-energy unfilled molecular orbital perpendicular to that plane (see discussion in the previous chapter). To interact optimally with the n electrons of an olefin, the carbene must orient itself in the following manner,... 

Molecular-orbital theory treats molecule formation from the separated atoms as arising from the interaction of the separate atomic orbitals to form new orbitals (molecular orbitals) which embrace the complete framework of the molecule. The ground state of the molecule is then one in which the electrons are assigned to the orbitals of lowest energy and are subject to the Pauli exclusion principle. Excited states are obtained by promoting an electron from a filled molecular orbital to an orbital which is normally empty in the ground state. The form of the molecular orbitals depends upon our model of molecule formation, but we shall describe (and use in detail in Sec. IV) only the most common, viz., the linear combination of atomic orbitals approximation. 

Intensification of the 7F0 - 5D0j 7F0 - sDi and 7Fo bLi bands in the somewhat unstable Eu3+-diethyldithiocarbamate has been reported by J0RGENSEN 592. He has also observed genuine electron transfer bands from the highest filled molecular orbital to the partly filled 4/ shell in the bromo complexes of Nd3+, Sm3+, Eu3+, Tm3+ and Yb3+. In the case of Eu3+ the electron transfer bands occur [592] at 3200, 2660 and 2300 A corresponding to 31250, 37594 and 43478 cm-1 respectively. 

In order to understand this process, the nature of the Fermi level must be considered. Within the nomenclature of physics, the Fermi level is defined as the energy at which there is a 50% probability of finding an electron in a metal— what a chemist would call the highest filled molecular orbital (i.e., the top of the valence band). In an intrinsic semiconductor, a material having a completely filled valence band and a completely empty conduction band, this energy level... 

No detailed evaluation of the different factors contributing to this binding has been made yet. One quantitative relationship relevant to the binding has nevertheless been obtained. Thus we have been able to show that the solvent power of a series of purines toward, say, a given hydrocarbon runs parallel to the electron donor properties of the purines, as measured by the value of the energy coefficient of their highest filled molecular orbital. These values are reproduced in Table I for the essential biochemical purines and... 

It is more difficult to find a good analogy between an electrochemical oxidation process and a chemical one. Certain metal ion oxidations, e.g. by Mn (III) 421 and Co (III) 43 are known to be of the electron transfer type, one electron being transferred from the highest filled molecular orbital of the organic molecule to an orbital of the metal ion. The oxidizing power of a particular metal ion towards a substrate is dependent on the energy difference between these orbitals. 

So the eight pairs of electrons of this molecule occupy delocalized molecular orbitals lag to 1 3U, while the first vacant orbital is l g- Note that the names of these orbitals are simply the symmetry species of theZ)2h point group. In other words, molecular orbitals are labeled by the irreducible representations of the point group to which the molecule belongs. So for ethylene there are three filled orbitals with Ag symmetry the one with the lowest energy is called lag, the next one is 2ag, etc. Similarly, there are two orbitals with Z iu symmetry and they are called lb u and 2bi . All the molecular orbitals listed above, except the first two, are illustrated pictorially in Fig. 6.4.2. By checking the >2h character table with reference to the chosen coordinate system shown in Fig. 6.4.2, it can be readily confirmed that these orbitals do have the labeled symmetry. In passing, it is noted that the two filled molecular orbitals of ethylene not displayed in Fig. 6.4.2, lag and l iu, are simply the sum and difference, respectively, of the two carbon Is orbitals. 

The photoluminescence of lattice oxide ions of transition-metal oxides mixed or supported on conventional carriers has also been reported (160b). The luminescence is shown to occur from oxo complexes (M04)" (M = V, Mo, W, Cr) in which the transition-metal ion exists in a high oxidation state with a d° electronic configuration. Since the d orbitals of the transition-metal ion are not occupied and therefore the d-d transitions impossible, S0 -)-S charge-transfer electronic transitions occur in the oxo complexes upon absorption of light. The result is that an electron is transferred from a filled molecular orbital localized mainly on the O2 anions to a d orbital of the transition-metal ion. This leads to the formation of an excited singlet electronic state S, with two unpaired electrons, in which the total electron spin,... 

As with all molecules, it is the energy of the electrons in the molecular orbitals of the radical that dictate its stability. Any interaction that can decrease the energy levels of the filled molecular orbitals increases the stability of the radical (in other words, decreases its reactivity). Before we use this energy level diagram of the methyl radical to explain the stability of radicals, we need to look at some experimental data that allow us to judge just how stable different radicals are. 

Many metal chalcogenides and oxides are known to be semiconductors. These materials can act as sensitizers for light-induced redox processes due to their electronic structure consisting of a valence band with filled molecular orbitals (MO s) and a conduction band with empty MO s. Absorption of a photon with an energy above the bandgap energy Eg generally leads to the formation of an electron/hole pair in the semiconductor particle (18). ... 

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