LUMOs orbitals

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]. 

If the mini her of electrons, N, is even, yon can haven dosed shell (as shown ) where the occupied orbitals each contain two electron s. For an odd n nrn her of electron s, at least on e orbital rn ust be singly occupied. In the example, three orbitals are occupied by-electron s and two orbitals arc nn occupied. Th e h ighest occupied nioleciilar orbital (HOMO is t[r), and the lowest unoccupied molecular orbital (LUMO) is The example above is a singlet, a state oh total spin S=0. Exciting one electron from the HOMO to the LUMO orbital would give one ol the I ollowing excited states ... 

If yon add a single electron to the LUMO orbital above to create an anion, you obtain total spin S=l/2 (a donhlet). 

Consider now the rr-system in benzene. The MO approach will generate linear combinations of the atomic p-orbitals, producing six rr-orbitals delocalized over the whole molecule with four different orbital energies (two sets of degenerate orbitals). Figure 7.3. The stability of benzene can be attributed to the large gap between the HOMO and LUMO orbitals. 

Figure 1,4 SOMO-1IOMO and SOMO-LUMO orbital interaction diagrams.

The complexation with Lewis acids or the protonation influences both the energy and the coefficients of carbon atoms of the LUMO orbital of the dienophile. The coefficient of the carbonyl carbon orbital increases (Scheme 1.16) consequently, the stabilizing effect of the secondary orbital interaction is greatly increased and the endo addition is more favored. 

In a photochemical cycloaddition, one component is electronically excited as a consequence of the promotion of one electron from the HOMO to the LUMO. The HOMO -LUMO of the component in the excited state interact with the HOMO-LUMO orbitals of the other component in the ground state. These interactions are bonding in [2+2] cycloadditions, giving an intermediate called exciplex, but are antibonding at one end in the [,i4j + 2j] Diels-Alder reaction (Scheme 1.17) therefore this type of cycloaddition cannot be concerted and any stereospecificity can be lost. According to the Woodward-Hoffmann rules [65], a concerted Diels-Alder reaction is thermally allowed but photochemically forbidden. 

PPDs donate hydrogen atoms while QDI reacts generally by addition to the radical. Examining the LUMO orbitals of PPD and QDI rationalizes one source of the large difference in reactivity. The reaction site of the PPD will be the LUMO of the H atom attached to the N atoms. While for QDI the delocalized LUMO in the conjugated diimine ring is the reaction site. These are shown in Figure 16.1. 

Figure 7. HOMO and LUMO orbital energies for C0 2Hg, plotted vs 1/N.

The HOMO and LUMO orbital energies seem to converge towards a value of about 4 eV, which would be an estimate of the work function for single sheet graphite. This is in reasonable agreement with the work function of 4.9 eV experimentally found for bulk graphite(58). 

Fig. 6.11. Representation of transition structure and die LUMO orbitals for three stereoisomeric complexes of A-acryloyloxazolidinone with a TADDOL model, Ti[0(CH2)40]Cl2. The LUMO energies (B3LYP/6-3111+G(d)) in kcal/mol. Reproduced from J. Org. Chem., 63, 2321 (1998), by permission of the American Chemical Society.

Examination of the HOMO and LUMO orbitals in these TSs indicates that the electronic effect operates mainly through the LUMO. The EWG cyano tends to localize the LUMO on the (3-carbon, whereas ERG substituents have the opposite effect. Similar trends were found for Pd coordinated by diimine ligands.150 These results indicate that the Markovnikov rule applies with the more electrophilic Pd complexes. When steric effects become dominant, the Pd adds to the less hindered position. 

Figure 11-13. HOMO and LUMO orbitals are shown for several 2P derivatives, where X means electron-donating group (here it is amino), and Z means electron-withdrawing group (here it is nitrosyl). Orbital levels are relative and qualitative. MRCI Sj (it it ) energies are shown at bottom, in eV. (From Ref. [144])...

Pelletier and Reber315 present new luminescence and low-energy excitation spectra of Pd(SCN)42 in three different crystalline environments, K2Pd(SCN)4, [K(18-crown-6)]2Pd(SCN)4, and (2-diethylammonium A -(2,6-dimethylphcnyl)acetamide)2Pd(SCN)4, and analyze the vibronic structure of the luminescence spectra, their intensities, and lifetimes as a function of temperature. The spectroscopic results are compared to the HOMO and LUMO orbitals obtained from density functional calculations to qualitatively illustrate the importance of the bending modes in the vibronic structure of the luminescence spectra. 

Figure 10. Indicated are the HOMO and LUMO orbital energies obtained form EHT calculations for a variety of reactants. In the center are estimated orbital energies for a canonical metal cluster.

Figure 2. Frontier orbitals of D -C-is at the RFIF/6-31G level (Spartan 5.0). Both sets of HOMO and LUMO orbitals are degenerate.

In the course of investigation of reactivity of the mesoionic compound 44 (Scheme 2) the question arose if this bicyclic system participates in Diels-Alder reactions as an electron-rich or an electron-poor component <1999T13703>. The energy level of the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) orbitals were calculated by PM3 method. Comparison of these values with those of two different dienophiles (dimethyl acetylenedicarboxylate (DMAD) and 1,1-diethylamino-l-propyne) suggested that a faster cycloaddition can be expected with the electron-rich ynamine, that is, the Diels-Alder reaction of inverse electron demand is preferred. The experimental results seemed to support this assumption. 

The solvent effect on the azo-hydrazone equilibrium of 4-phenylazo-l-naphthol has been modelled using ab initio quantum-chemical calculations. The hydrazone form is more stable in water and in methylene chloride, whereas methanol and iso-octane stabilise the azo form, The calculated results were in good agreement with the experimental data in these solvents. Similar studies of l-phenylazo-2-naphthol and 2-phenylazo-l-naphthol provided confirmation. Substituent effects in the phenyl ring were rationalised in terms of the HOMO-LUMO orbital diagrams of both tautomeric forms [53]. 

The explanation of the regiospecificity of Diels-Alder reactions requires knowledge of the effect of substituents on the coefficients of the HOMO and LUMO orbitals. In the case of normal electron demand, the important orbitals are the HOMO on the diene and the LUMO on the dienophile. It has been shown that the reaction occurs in a way which bonds together the terminal atoms with the coefficients of greatest magnitude and those with the coefficients of smaller magnitude [18]. The additions are almost exclusively cis and with only a few exceptions, the relative configurations of substituents in the components is kept in the products [19]. 

The following rules were used for the determination of the LUMO orbital coefficients from the values determined for the HOMO coefficients [15]. 

Groups which add conjugation such as olefinic, acetylenic and aromatic groups lower the LUMO orbital energy one third to one half as much as the HOMO energy. 

The same equations are used to determine both the HOMO and LUMO values. This is consistent with the fact that the HOMO and LUMO orbitals are calculated from the same parent system, and that the difference between the orbital energies can be adequately covered by the two parameters 7(P) which represents the sensitivity of the parent to substitution and r(Y) which represents the electronic effect exerted by the functional group acting as a substituent. 

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