Energy of the lowest unoccupied

The energy of the lowest unoccupied molecular indirect ELUMO 4, 8, 9... 

HOMO A [OMO 1 A,umo A.UMO+1 AHf QC Energy of the highest occupied molecular orbital Energy of the second highest occupied molecular orbital Energy of the lowest unoccupied molecular orbital Energy of the second lowest unoccupied molecular orbital Heat of formation Dipole moment... 

Thermodynamic reduction potentials of numerous aromatics were first measured by Hoijtink and van Schooten in 96% aqueous dioxane, using polarography [15, 16]. These fundamental works were decisive tests of the HMO theory, showing that the polarographic half-wave potentials vary linearly with the HMO energies of the lowest unoccupied molecular orbitals (LUMO) of the hydrocarbons [1]. Hoijtink etal. had already noticed that most aromatics can be further reduced to their respective dianions [17]. They proposed a... 

Conjugation with an electron-withdrawing group substantially lowers the energy of the lowest unoccupied molecular n-orbital, which results in less negative reduction potentials for the alkene system. The class of compounds is referred to as activated alkenes, Polarographic half-wave potentials for some activated alkenes in aprotic solvents are listed in Table 3.3... 

P). Using parameters derived from ESR data in conjunction with perturbation theory predicts no change in the energy of the lowest unoccupied molecular orbital of 1,4-naphthoquinone upon cyclobuta-annelation. This prediction results from essentially identical Hiickel coefficients at the ortho-(C2 = 0.374) and... 

Eq. 1 log A, logarithm of the percentage increase in ethylmorphine N-demethylase activity alcP, ratio of molecular area to depth-square AE, EL - Eu, difference between the energy of the lowest unoccupied to the highest occupied molecular orbital log P, logarithm of the octanol/water partition coefficient. 

Eq. 4 Induction fold induction of CYP3A4 in the presence of hGR llw, ratio of molecular length to width Mr, relative molecular mass EL, energy of the lowest unoccupied molecular orbital. 

Charge densities on individual atoms Energy of the highest occupied molecular orbital Energy of the lowest unoccupied molecular orbital Molecular dipole... 

Generally, the energy of the olefin n -level is more sensitive to substituent effects than the 7r-level (see Table IV for example). Therefore, often a simple plot of the equilibrium constant for the metal-olefin complex vs the energy of the lowest unoccupied olefin molecular orbitai gives a reasonable straight-line graph. Such a plot reported by Tolman (220) for the equilibrium... 

Fig. 13. Correlation of log K, (25°) with the energy of the lowest unoccupied orbital of the free olefin. The C2H4 F olefins are designated by crosses and C2H4 (C8H5) by squares [Reproduced from Tolman (220), by permission of the American Chemical Society.]...

In these relationships, IP and EA refer to free atoms or ions, whole molecules or radicals, rather than atoms within molecules, and so — p bears little relationship to Pauling s x- I 1 terms of molecular orbital (MO) theory, IP is the negative of the energy of the highest occupied MO (-chomo), and EA is the energy of the lowest unoccupied MO (clumo)- Thus, hard molecules... 

Thus the ionization potential corresponding to removal of the electron from occupied is just the negative of that MO s energy. This observation is known as Koopmans theorem. One can similarly show that the energy of the lowest unoccupied MO is an estimate of the electron affinity of the molecule. In fact, ionization potentials estimated by Koopmans theorem are fairly accurate, but the electron affinities calculated this way are much less so. 

Koopmans theorem can be formally applied to electron affinities (EAs) as well, i.e., the EA can be taken to be the negative of the orbital energy of the lowest unoccupied (virtual) orbital. Here, however, relaxation effects and correlation effects both favor the radical anion, so rather than canceling, the errors are additive, and Koopmans theorem estimates will almost always underestimate the EA. It is thus generally a better idea to compute EAs from a ASCF approach whenever possible. 

According to the frontier orbital theory,525 electron-withdrawing substituents lower the energies of the lowest unoccupied molecular orbital (LUMO) of the di-enophile thereby decreasing the highets occupied molecular orbital (HOMO)-LUMO energy difference and the activation energy of the reaction. 1,3-Butadiene itself is sufficiently electron-rich to participate in cycloaddition. Other frequently used dienes are methyl-substituted butadienes, cyclopentadiene, 1,3-cyclohexa-diene, and 1,2-dimethylenecyclohexane. 

The competition between these two reaction pathways depends upon both the driving forces and the intrinsic barrier factors. As proved in several cases of anion radicals, there is a rule for a reaction to proceed down the stepwise or concerted mechanism. The higher the energy of the lowest unoccupied molecular orbital and the weaker the bond strength between R and X in the starting molecule, the greater is the tendency for the concerted mechanism to prevail over the stepwise mechanism, and vice versa (Andrieux, Robert, et al. 1994) see also Section 8.2. 

In recent years, molecular descriptors such as the energy of the highest occupied molecular orbital (EHomo) ar d the energy of the lowest unoccupied molecular orbital ( IUMO) have gained in popularity for QSAR analysis, as these descriptors are readily calculated from PC-based software such as SPARTAN. Before we discuss EHomo ar d ELumo further, a brief discussion of quantum chemistry is necessary. 

To analyze the reactivity of organics in systems using zero-valent iron, AH, (standard heat of formation) and ELUMO (energy of the lowest unoccupied molecular orbital) were computed using the PM3 Hamiltonian method. Reductive dechlorination rate constants for five chlorobenzenes in the pres-... 

Energy of the lowest unoccupied molecular orbital (LUMO)... 

In superacid catalyzed reactions of hydroxyquinolines and isoquinolines, dicationic superelectrophiles were proposed as intermediates in their reactions (see Table 4).35d In order to explain differences in relative reactivities between the isomeric superelectrophiles, the energies of the lowest unoccupied molecular orbitals Ultimo ), the square of the coefficients (c2) at the reactive carbon atoms, and the NBO charges (q) on CH groups were determined by MNDO and DFT computational methods. For example, 8-hydroxyquinoline (85) is found to be more reactive than 6-hydroxyquinoline (87) in the superacid catalyzed reactions with benzene and cyclohexane (eqs 47 -8). 

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