LUMO, for

I he electron density distribution of individual molecular orbitals may also be determined and plotted. The highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) are often of particular interest as these are the orbitals most cimimonly involved in chemical reactions. As an illustration, the HOMO and LUMO for Jonnamide are displayed in Figures 2.12 and 2.13 (colour plate section) as surface pictures. 

Fig. 7. Graphical representations of (a) the Highest Occupied Molecular Orbital (HOMO) and (b) the Lowest Unoccupied Molecular Orbital (LUMO) for ranitidine. It is possible, in the ordinarily visible color-coded data not shown here, to distinguish the strong localization (a) of the HOMO to the sulfur atom and adjacent nitroethyleneamine fragment and the contrasting localization (b) of the LUMO to the nitroethylenearnine fragment. Neither the LUMO not HOMO appear to have contributions from the dimethylaminomethyl-suhstitiited furan.

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. 

Here are the HOMO and LUMO for ethylene (some non-significant lines have been removed from the output) ... 

Next, examine the lowest-unoccupied molecular orbital (LUMO) for the cation. The components of the LUMO (its lobes ) identify locations where the cation might bond to a water molecule. How many lobes are associated with C 7 For each lobe, draw the alcohol that will be produced (show stereochemistry). How many alcohol enantiomers will form If more than one is expected, decide which wiU form more rapidly based on the relative sizes of the lobes. 

Display the lowest-unoccupied molecular orbital (LUMO) for cyclohexyl bromonium ion. From which side will the Br attack Will this lead to formation of cis-1,2-dibromo-cyclohexane or 1,2-dibromocyclohexane Is this... 

LUMO for endoO endoCHjBr shows likely site for intramolecular nucleophilic attack. 

LUMO for equatorial methylcyclohexanone reveals likely site of nucleophilic attack. 

Display the lowest-unoccupied molecular orbital (LUMO) for equatorial methylcyclohexanone. This is the orbital into which the nucleophile s pair of electrons will go. Is it larger on the axial or equatorial face A clearer picture follows from the LUMO map, which gives the value of the LUMO on the electron density surface, that is, the accessible surface of the molecule. Display the LUMO map for equatorial methylcyclohexanone. Which face of the carbonyl group is more likely to be attacked by a nucleophile Which alcohol will result ... 

LUMO for cyclohexenone reveals the likely sites of nucleophilic attack. 

One way to investigate the electrophilic properties of these molecules is to examine the orbital that each uses to accept electrons from a nucleophile. This orbital is the lowest-unoccupied molecular orbital (LUMO). Examine the LUMO for methyl acetate (Z=OCH3), acetaldehyde (Z=H), N,N-dimethylacetamide (Z=N(CH3)2) and acetyl chloride (Z=C1) (acetaldehyde is not a carboxylic acid derivative, but is included here for comparison). What is the shape of the LUMO in the region of the carbonyl group Is it a o or 7U orbital Is it bonding or antibonding What other atoms contribute to the LUMO Which bonds, if any, would be weakened when a nucleophile transfers its electrons into the LUMO ... 

LUMO for protonated methyl acetate reveals likely site of attack by water. 

Examine the lowest-unoccupied molecular orbital (LUMO) for the most stable conjugate acid of each compound (inchideprotonated acetonitrile). Which atom makes the largest contribution to this orbital Is this the site of H2O attack Will adding electrons to the LUMO strengthen or weaken die C=0 (C=N) 7U bond Explain. 

Woodward and Hoffmann pointed out that the Diels-Alder reaction involved bonding overlap of the highest-occupied molecular orbital (HOMO) on the diene and the lowest-unoccupied molecular orbital (LUMO) on the dienophile. Display the HOMO for 2-methoxybutadiene. Where is it localized Display the LUMO for acrylonitrile. Where is it localized Orient the two fragments such that the HOMO and LUMO best overlap (A clearer picture is provided by examining-the HOMO map for 2-methoxybutadiene and the LUMO map for acrylonitrile.) Which product should result ... 

LUMO for acrylonitrile receives electrons in a Diels-Alder addition. 

The ratio of the two diastereomeric products 190 and 191 was found to depend on the reaction temperature and reaction time. The addition of acrolein or methyl vinyl ketone proceeded smoothly, but in the case of methylacrylate or acrylonitrile the reaction did not proceed under the same conditions (EtsN THF 30°C). An accompanying AMI calculation of these Q ,/3-unsaturated compounds [LUMOs for acrolein, -0.13877 for methyl vinyl ketone, -0.06805 (s-trans) for methyl acrylate, -0.01413 (s-tmns) for acrylonitrile, 0.04971] suggested the low reactivity of methyl acrylate and acrylonitrile toward the Michael reaction (99H1321). 

Problem 30.1 Look at Figure 30.1, and tell which molecular orbital is the HOMO and which is the LUMO for both ground and excited states of ethylene and 1,3-butadiene. 

FIGURE 19. Trends in HOMO and LUMO for the molecules considered. 

For tables of experimentally determined HOMOs and LUMOs for dienes and dienophiles, see Smith, M.B. Organic Synthesis, McGraw-Hill, NY, 1994, p. 1104 and 1109. 

The HOMO and LUMO for anthracene are shown in Figure 2.4.u> The i734 -> 7t33 anthracene transition is allowed in the direction of the short axis of the molecule. The square of the coefficients provides a measure of the probability of finding an electron at a particular carbon atom. Note that for both 33 the greatest electron density is at the 9,10 carbon atoms. This suggests that any chemical reaction involving these electrons will likely occur at these positions. This is indeed the case, as we shall see later when we consider the photochemistry of anthracene. 

The regioselectivity in radical addition reactions to alkenes in general has successfully been interpreted by a combination of steric and electronic effects1815,47. In the absence of steric effects, regiochemical preferences can readily be explained with FMO theory. The most relevant polyene orbital for the addition of nucleophilic radicals to polyenes will be the LUMO for the addition of electrophilic orbitals it will be the HOMO. Table 10 lists the HOMO and LUMO coefficients (without the phase sign) for the first three members of the polyene family together with those for ethylene as calculated from Hiickel theory and with the AMI semiempirical method48. 

We have studied the FCl results for the ground, Xg, state of the linear, D i,BeH2 molecule with a minimal basis set. The orbitals 1, 2, and 3 are of the a type 4 and 5 area and 6 and 7 are degenerate The HF corresponds to a double occupancy of orbitals 1, 2 and 4. A bar over the orbital label indicates that its spin is p. It is important to note that 2 and 4 may be considered the homo of the Og and a symmetry-shells respectively. Similarly, 3 and 5 are the respective lumo for the same symmetry-shells. In the following analysis we will denote genetically the homos by hi and the lumos by U. 

We now turn to the gas-phase 1,3-dipolar cycloaddition of fulminic acid to ethyne. The concerted, almost synchronous nature of this reaction might create the impression that the electronic mechanism of this process should be very similar to that of the Diels-Alder reaction. Such an expectation is reinforced by frontier orbital theory, which treats both reactions in very much the same way (see Ref. 32). The only significant differences are related to the fact that the lowest unoccupied MO (LUMO) for a linear 1,3-dipole... 

Frontier molecular orbital calculations have been employed successfully to predict reactions by examining the LUMO for nucleophihc substitution reactions and the HOMO for electrophilic reactions. Although these calculations have become quite routine, they unfortunately have not been applied to 1,2,3-thiadiazoles. 

So far, the changes described apply to orbitals which are all occupied in the molecules under discussion, and therefore do not alter the overall stability of the molecules substantially. This is not the case for the anti-bonding 2nu orbitals, which in N02 and NO, represent the HOMOs. They lose their degeneracy by bending, to give the orbitals labelled as 2b, and 6a,. The former remains as an anti-bonding rc-type orbital, and the latter is approximately non-bonding and initially derives some stabilization as a result. The 5a + orbital is the LUMO for NO, and... 

The lowest unoccupied molecular orbital (LUMO) for trans-peroxynitrous acid and for putative hydroxyl radical-like intermediates. The LUMO is the orbital that electrons must enter when per-... 

L in Scheme 11.3) departs. Nucleophilic addition to the intermediate benzyne (step D) is readily explained by perturbative MO arguments. The extra and orbitals of benzyne are compared to those of ethylene in Figure 11.7. The aromatic n system is not involved in the special properties of benzyne. The third benzyne n bond is due to the overlap in fashion of the two sp2 hybrid orbitals which lie in the nodal plane of the intact 6 electron system. Two factors contribute to a very low LUMO for benzyne. First, the sp2 hybrid orbitals are lower in energy than the 2p orbitals from which the ethylene orbitals are constructed. Second, the intrinsic interaction between the two sp2 orbitals is less than the normal / cc since the orbitals have less p character and are tipped away from each other. The low LUMO of benzyne makes the molecule a strong Lewis acid, susceptible to attack by bases, and a reactive dienophile in Diels-Alder reactions, as we shall see later. 

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