LUMO energy

Quantum chemical descriptors such as atomic charges, HOMO and LUMO energies, HOMO and LUMO orbital energy differences, atom-atom polarizabilities, super-delocalizabilities, molecular polarizabilities, dipole moments, and energies sucb as the beat of formation, ionization potential, electron affinity, and energy of protonation are applicable in QSAR/QSPR studies. A review is given by Karelson et al. [45]. 

Quantum mechanical descriptors (e.g. HOMO-LUMO energy gap) 3D structure See Section 2.7.4... 

HOMO and LUMO energies FMO reactivity indices Refractivity Total energy Ionization potential Electron affinity Energy of protonation Orbital populations Frontier orbital densities Superdelocalizabilities... 

Some researchers use molecule computations to estimate the band gap from the HOMO-LUMO energy separation. This energy separation becomes smaller as the molecule grows larger. Thus, it is possible to perform quantum mechanical calculations on several molecules of increasing size and then extrapolate the energy gap to predict a band gap for the inhnite system. This can be useful for polymers, which are often not crystalline. One-dimensional band structures are... 

Many organic compounds such as lycopene are colored because their HOMO-LUMO energy gap is small enough that appears m the visible range of the spec trum All that is required for a compound to be colored however is that it possess some absorption m the visible range It often happens that a compound will have its k m the UV region but that the peak is broad and extends into the visible Absorption of the blue to violet components of visible light occurs and the compound appears yellow... 

HOMO-LUMO energy difference in ethylene is greater than that of cis trans 1 3 cyclooctadiene... 

Electron Level Position. One essential condition of spectral sensitization by electron transfer is that the LUMO of the dye be positioned above the bottom of the conduction band, eg, > —3.23 eV in AgBr or > —4.25 eV in ZnO (108). To provide the desired frontier level position respectively to the valence and conduction bands of the semiconductor, it is necessary to use a polymethine with suitable electron-donor abiHty (Pq. Increasing the parameter (Pq leads to the frontier level shift up, and vice versa. Chain lengthening is known to be accompanied by a decrease of LUMO energy and hence by a decrease of sensitization properties. As a result, it is necessary to use dyes with high electron-donor abiHty for sensitization in the near-ir. The desired value of (Pq can be provided by end groups with the needed topological index Oq or suitable substituents (112). 

Since 1,3-dipolar cycloadditions of diazomethane are HOMO (diazomethane)-LUMO (dipolarophile) controlled, enamines and ynamines with their high LUMO energies do not react (79JA3647). However, introduction of carbonyl functions into diazomethane makes the reaction feasible in these cases. Thus methyl diazoacetate and 1-diethylaminopropyne furnished the aminopyrazole (620) in high yield. 

A molecule with a low energy LUMO can accept electrons more readily than a molecule with a higher energy LUMO. The LUMO energies (in au) for the above molecules ai e 0.192 (methyl acetate), 0.161 (acetaldehyde), 0.212 (N,N-dimethylacetamide), and 0.132 (acetyl chloride). Order these molecules from most electrophilic to least electrophilic. 

A molecule with a lower energy LUMO will generally react more rapidly. The LUMO energies of acetic anhydride and ethyl acetate are 0.143 and 0.193 au, respectively. Which reagent is a better aeylating agent in the kinetic sense ... 

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. 

Repeat your analysis for the LUMO of ethene, 1,3-butadiene, 1,3,5-hexatriene and -carotene, except now focus on each orbital s net antibonding character. (Assume that LUMO energy rises as net antibonding character increases.) What effect does conjugation have on LUMO shape and energy Are your predictions for the HOMO-LUMO energy gap consistent with the experimental data ... 

Lewis acids catalyze Diels-Alder reactions. Do they enhance overlap between diene and dienophile orbitals and/ or do they reduce the HOMO/LUMO energy difference ... 

LUMO energies for free and complexed acrylonitrile are. 103 and. 089 au (65 and 56 kcal/mol), respectively. On the basis of orbital energies, would you expect BF3 to enhance, retard, or leave unchanged the rate of Diels-Alder cycloaddition ... 

These concepts play an important role in the Hard and Soft Acid and Base (HSAB) principle, which states that hard acids prefer to react with hard bases, and vice versa. By means of Koopmann s theorem (Section 3.4) the hardness is related to the HOMO-LUMO energy difference, i.e. a small gap indicates a soft molecule. From second-order perturbation theory it also follows that a small gap between occupied and unoccupied orbitals will give a large contribution to the polarizability (Section 10.6), i.e. softness is a measure of how easily the electron density can be distorted by external fields, for example those generated by another molecule. In terms of the perturbation equation (15.1), a hard-hard interaction is primarily charge controlled, while a soft-soft interaction is orbital controlled. Both FMO and HSAB theories may be considered as being limiting cases of chemical reactivity described by the Fukui ftinction. 

LUMO energy of the diene is lowered. However, for the eyeloaddition to oeeur, the dienophile is now the nueleophile and the diene is now the eleetrophile. Sinee the nature of the reaeting partners is inverted relative to the elassical ease, it is ealled an inverse eleetron demand Diels-Alder reaetion. Thus the Diels-Alder reaetion ean proeeed, in praetieal terms, in one of two eleetronie modes a) the normal mode whieh is HOMOdiene-eontrolled or b) the inverse eleetron demand or LUMOdiene-controlled process. 

The transition state for the BH3-catalyzed reaction was also found. The favored regioisomer and the influence of the Lewis acid on the reactivity was accounted for by a FMO-way of reasoning using as outlined in Fig. 8.11 to the left. The coordination of BH3 to formaldehyde was calculated to lower the LUMO energy by... 

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