HOMO, LUMO

After this, Martinez and Ben-Nun applied the method to the photoexcitation of ethylene [88,247]. The lowest energy excitation is the HOMO-LUMO n n transition. These states are labeled A and Close in energy to... 

Figure 2-125. Different isovalue-based surfaces of phenylalanine a) isoelectronic density b) molecular orbitals (HOMO-LUMO) c) isopotential surface and d) isosurface of the electron cryo-microscopic volume of the ribosome of Escherichia coii.

FMO theory requires that a HOMO of one reactant has to be correlated with the LUMO of the other reactant. The decision between the two alternatives - i.e., from which reactant the HOMO should be taken - is made on the basis of which is the smaller energy difference in our case the HOMO of the electron rich diene, 3.1, has to be correlated with the LUMO of the electron-poor dienophile, 3.2. The smaller this HOMO-LUMO gap, the higher the reactivity will be. With the HOMO and LUMO fixed, the orbital coefficients of these two orbitals can explain the regios-electivity of the reaction, which strongly favors the formation of 3.3 over 3.4. 

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

Dimethyl-2-butene and 2,5-dimethylhexadiene have absorption peaks at 192 and 243 nm in the ultraviolet. Which peak corresponds to which compound What are the approximate HOMO-LUMO separations in electron volts ... 

Hydrogen bonding of water to the activating group of (for normal-electron demand Diels-Alder reactions) the dienophile constitutes the second important effect". Hydrogen bonds strengthen the electron-withdrawing capacity of this functionality and thereby decrease the HOMO-LUMO gap... 

Most of the semiempirical methods are not designed to correctly predict the electronic excited state. Although excited-state calculations are possible, particularly using a CIS formulation, the energetics are not very accurate. However, the HOMO-LUMO gap is reasonably reproduced by some of the methods. 

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... 

Lithium aluminum hydride reduction of 2,3,4-triphenylisoxazolin-5-one yielded 1,2,3-triphenylaziridine and dibenzylaniline. The reaction was considered to proceed by a concerted [l,3]-sigmatropic migration of the N to a C atom. HOMO-LUMO calculations show this type of concerted reaction is possible (Scheme 68) (80JA1372). 

Calculations for Ceo in the LDA approximation [62, 60] yield a narrow band (- 0.4 0.6 eV bandwidth) solid, with a HOMO-LUMO-derived direct band gap of - 1.5 eV at the X point of the fee Brillouin zone. The narrow energy bands and the molecular nature of the electronic structure of fullerenes are indicative of a highly correlated electron system. Since the HOMO and LUMO levels both have the same odd parity, electric dipole transitions between these levels are symmetry forbidden in the free Ceo moleeule. In the crystalline solid, transitions between the direct bandgap states at the T and X points in the cubic Brillouin zone arc also forbidden, but are allowed at the lower symmetry points in the Brillouin zone. The allowed electric dipole... 

Since the optical transitions near the HOMO-LUMO gap are symmetry-forbidden for electric dipole transitions, and their absorption strengths are consequently very low, study of the absorption edge in Ceo is difficult from both an experimental and theoretical standpoint. To add to this difficulty, Ceo is strongly photosensitive, so that unless measurements arc made under low light intensities, photo-induced chemical reactions take place, in some cases giving rise to irreversible structural changes and polymerization of the... 

For C70, molecular orbital calculations [60] reveal a large number of closely-spaced orbitals both above and below the HOMO-LUMO gap [60]. The large number of orbitals makes it difficult to assign particular groups of transitions to structure observed in the solution spectra of C70. UV-visible solution spectra for higher fullerenes (C n = 76,78,82,84,90,96) have also been reported [37, 39, 72]. 

As shown in Fig. 7, a large increase in optical absorption occurs at higher photon energies above the HOMO-LUMO gap where electric dipole transitions become allowed. Transmission spectra taken in this range (see Fig. 7) confirm the similarity of the optical spectra for solid Ceo and Ceo in solution (decalin) [78], as well as a similarity to electron energy loss spectra shown as the inset to this figure. The optical properties of solid Ceo and C70 have been studied over a wide frequency range [78, 79, 80] and yield the complex refractive index n(cj) = n(cj) + and the optical dielectric function... 

Another characteristic of aromatic compounds is a relatively large HOMO-LUMO gap, which can be expressed in terms of hardness, t] (see p. 21 for the definition of hardness) ... 

The numerical value of hardness obtained by MNDO-level calculations correlates with the stability of aromatic compounds. The correlation can be extended to a wider range of compounds, including heterocyclic compounds, when hardness is determined experimentally on the basis of molar reffactivity. The relatively large HOMO-LUMO gap also indicates the absence of relatively high-energy, reactive electrons, in agreement with the reduced reactivity of aromatic compounds toward electrophilic reagents. 

When both the 1,3-dipoIe and the dipolarophile are unsymmetrical, there are two possible orientations for addition. Both steric and electronic factors play a role in determining the regioselectivity of the addition. The most generally satisfactory interpretation of the regiochemistry of dipolar cycloadditions is based on frontier orbital concepts. As with the Diels-Alder reaction, the most favorable orientation is that which involves complementary interaction between the frontier orbitals of the 1,3-dipole and the dipolarophile. Although most dipolar cycloadditions are of the type in which the LUMO of the dipolarophile interacts with the HOMO of the 1,3-dipole, there are a significant number of systems in which the relationship is reversed. There are also some in which the two possible HOMO-LUMO interactions are of comparable magnitude. 

Consideration of the HOMO-LUMO interactions also indicates that the [2n + 2ti] additions would be allowed photochemically. The HOMO in this case is the excited alkene 71 orbital. The LUMO is the ti of the ground-state alkene, and a bonding interaction is present between the carbons where new bonds must be formed ... 

In a few instances the technique of magnetic circular dichroism (MCD) spectroscopy has been used to corroborate assignments based on UV-visible spectroscopy. For example, the assignment of the intense 360 nm band for [S,N,Y to a r (2e") r (2a2") (HOMO LUMO) excitation has been confirmed by the measurement of the MCD spectrum of The MCD spectrum of [S4N3] indicates that each of the... 

We will perform an AMI calculation on tetraphenylporphin (TPP), pictured at right, in order to examine the four important molecular orbitals for this molecule the second-highest and highest occupied MO s and the lowest and second-lowest unoccupied MO s (which we denote HOMO-1, HOMO, LUMO and LUMO-ll, respectively). 

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