Energies of lowest unoccupied molecular

Energy of lowest unoccupied molecular orbital, r) Energy gap. Ionization potential, from relationship given in ref. [8]. Ionization potential, from relationship given in ref. [9]. u) stable to distortion [10]. 

Fig. 179. Schematic energy-level diagram for an ITO/PPV/Al LED under forward bias, showing the ionization potential (Ip) and electron affinity (EyO of PPV, the work functions of ITO and Al (4>ito nd and the barriers to injection of electrons and holes (ISEe and A ,). There is a small barrier for hole injection from the ITO electrode into the valence band (of highest occupied molecular orbital, HOMO), and with aluminum as cathode, a considerably larger barrier for electron injection into the PPV conduction band states (of lowest unoccupied molecular orbital, LUMO). Reproduced by permission of Nature from R. H. Friend, R. W. Gymer, A. B. Holmes, J. H. Burroughes, R. N. Marks, C. Taliani, D. D. C. Bradley, D. A. Dos Santos, J. L. Bredas, M. Logdlund, and W. R. Salaneck, Nature 397,121 (1999).

In view of this, early quantum mechanical approximations still merit interest, as they can provide quantitative data that can be correlated with observations on chemical reactivity. One of the most successful methods for explaining the course of chemical reactions is frontier molecular orbital (FMO) theory [5]. The course of a chemical reaction is rationali2ed on the basis of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), the frontier orbitals. Both the energy and the orbital coefficients of the HOMO and LUMO of the reactants are taken into account. 

When you request an orbital, yon can use the cardinal number of the orbital (ordered by energy and starting with number=l) or an offset from either the highest occupied molecular orbital (HOMO) or the lowest unoccupied molecular orbital (LL MO). Offset from the HOMO are negative and from the LUMO are positive. Often these frontier orbitals are the ones of most chemical interest. 

LUIVIO (Section 10 13) The orbital of lowest energy that con tains none of a molecule s electrons the lowest unoccupied molecular orbital... 

Chemical Properties. The chemistry of ketenes is dominated by the strongly electrophilic j/)-hybridi2ed carbon atom and alow energy lowest unoccupied molecular orbital (LUMO). Therefore, ketenes are especially prone to nucleophilic attack at Cl and to [2 + 2] cycloadditions. Less frequent reactions are the so-called ketene iasertion, a special case of addition to substances with strongly polarized or polarizable single bonds (37), and the addition of electrophiles at C2. For a review of addition reactions of ketenes see Reference 8. 

Dinitrogen has a dissociation energy of 941 kj/mol (225 kcal/mol) and an ionisation potential of 15.6 eV. Both values indicate that it is difficult to either cleave or oxidize N2. For reduction, electrons must be added to the lowest unoccupied molecular orbital of N2 at —7 eV. This occurs only in the presence of highly electropositive metals such as lithium. However, lithium also reacts with water. Thus, such highly energetic interactions ate unlikely to occur in the aqueous environment of the natural enzymic system. Even so, highly reducing systems have achieved some success in N2 reduction even in aqueous solvents. 

It is now possible to "see" the spatial nature of molecular orbitals (10). This information has always been available in the voluminous output from quantum mechanics programs, but it can be discerned much more rapidly when presented in visual form. Chemical reactivity is often governed by the nature of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). Spectroscopic phenomena usually depend on the HOMO and higher energy unoccupied states, all of which can be displayed and examined in detail. 

The most extensive calculations of the electronic structure of fullerenes so far have been done for Ceo- Representative results for the energy levels of the free Ceo molecule are shown in Fig. 5(a) [60]. Because of the molecular nature of solid C o, the electronic structure for the solid phase is expected to be closely related to that of the free molecule [61]. An LDA calculation for the crystalline phase is shown in Fig. 5(b) for the energy bands derived from the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) for Cgo, and the band gap between the LUMO and HOMO-derived energy bands is shown on the figure. The LDA calculations are one-electron treatments which tend to underestimate the actual bandgap. Nevertheless, such calculations are widely used in the fullerene literature to provide physical insights about many of the physical properties. 

Another aspect of qualitative application of MO theory is the analysis of interactions of the orbitals in reacting molecules. As molecules approach one another and reaction proceeds, there is a mutual perturbation of the orbitals. This process continues until the reaction is complete and the new product (or intermediate in a multistep reaction) is formed. PMO theory incorporates the concept of frontier orbital control. This concept proposes that the most important interactions will be between a particular pair of orbitals. These orbitals are the highest filled oihital of one reactant (the HOMO, highest occupied molecular oihital) and the lowest unfilled (LUMO, lowest unoccupied molecular oihital) orbital of the other reactant. The basis for concentrating attention on these two orbitals is that they will be the closest in energy of the interacting orbitals. A basic postulate of PMO... 

The product of nucleophilic attack can be anticipated by examining the lowest-unoccupied molecular orbital (LUMO) on protonated cyclopentene oxide. From which direction (top or bottom) would a nucleophile be more likely to approach each epoxide carbon in order to transfer electrons into this orbital Explain. Does one carbon contribute more to the LUMO, or is the orbital evenly spread out over both epoxide carbons Assuming that LUMO shape dictates product stereochemistry, predict which stereoisomers will be obtained, and their approximate relative amounts. Is the anticipated kinetic product also the thermodynamic product (Compare energies of 1,2-cyclopentanediol stereoisomers to tell.)... 

Now, examine the orbital on cyclohexanone lithium enolate most able to donate electrons. This is the highest-occupied molecular orbital (HOMO). Identify where the best HOMO-electrophile overlap can occur. Is this also the most electron-rich site An electrophile will choose the best HOMO overlap site if it is not strongly affected by electrostatic effects, and if it contains a good electron-acceptor orbital (this is the lowest-unoccupied molecular orbital or LUMO). Examine the LUMO of methyl iodide and trimethylsilyl chloride. Is backside overlap likely to be successful for each The LUMO energies of methyl iodide and trimethylsilyl chloride are 0.11 and 0.21 au, respectively. Assuming that the lower the LUMO energy the more effective the interaction, which reaction, methylation or silylation, appears to be guided by favorable orbital interactions Explain. 

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