LUMO map, for

LUMO map for cyclohexanone axial face (left) and equatorial face (right)... 

LUMO map for equatorial methylcyclohexanone shows (in blue) where the LUMO is most-heavily concentrated. 

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 map for 2-methylcyclohexanone reveals (in blue) acidic protons, susceptible to H/D exchange. 

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 ... 

In accord with experimental data, LUMO maps for both cyclohexanone and 1,3-dioxan-5-one clearly anticipate preferential nucleophilic attack onto the axial carbonyl face,... 

The LUMO map for the axial-axial conformer shows very strong distinction between the axial and equatorial faces. Attack onto the axial face is preferred, consistent with the experimentally observed product. 

Thermodynamic properties such as heats of reaction and heats of formation can be computed mote rehably by ab initio theory than by semiempirical MO methods (55). However, the Hterature of the method appropriate to the study should be carefully checked before a technique is selected. Finally, the role of computer graphics in evaluating quantum mechanical properties should not be overlooked. As seen in Figures 2—6, significant information can be conveyed with stick models or various surfaces with charge properties mapped onto them. Additionally, information about orbitals, such as the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), which ate important sites of reactivity in electrophilic and nucleophilic reactions, can be plotted readily. Figure 7 shows representations of the HOMO and LUMO, respectively, for the antiulcer dmg Zantac. 

Finally, select acetone from the molecules on screen. Here, both the LUMO and the LUMO map are available under the Surfaces menu. First, select LUMO and display it as a Solid. It describes a 7U-type antibonding ( i ) orbital concentrated primarily on the earbonyl carbon and oxygen. Next, turn off this surface (select None under the LUMO sub-menu), and then seleet LUMO Map under the Surfaces menu. Display the map as a transpareni solid. Note the blue spot (maximum value of the LUMO) directly over the carbonyl carbon. This reveah the most likely site for nucleophilic attack. 

Compare atomic charges and electrostatic potential maps for the three cations. For each, is the charge localized or delocalized Is it associated with an empty a-type or Tt-type orbital Examine the lowest-unoccupied molecular orbital (LUMO) of each cation. Draw all of the resonance contributors needed for a complete description of each cation. Assign the hybridization of the C" atom, and describe how each orbital on this atom is utilized (o bond, n bond, empty). How do you explain the benzene ring effects that you observe ... 

Methylcyclohexanone, pK 20, is typical of a weak acid that undergo H/D exchange. Identify the acidic protons of 2-methylcyclohexanone, i.e., those most susceptible to attack by base, as positions for which the value of the lowest-unoccupied molecular orbital (LUMO) is large. Use a LUMO map (the value of the LUMO mapped onto the electron density surface). Does this analysis correctly anticipate which of the anions obtained by deprotonation of 2-methylcyclohexanone is actually most stable Are any of the other ions of comparable stability, or are they aU much less stable ... 

LUMO maps, which reveal the most electron deficient sites on a molecule, that is, those which are most susceptible to attack by a nucleophile, should be able to account for differences in direction of nucleophilic attack among closely-related systems. They will be employed here first to verify the above-mentioned preferences and then to explore stereochemical preferences in a number of related systems. 

The LUMO map shows a strong preference for nucleophilic attack onto the 7-membered ring carbonyl as opposed to the 5-membered ring carbonyl (in accord with experiment), and a much weaker preference for attack ofsyn to the adjacent methyl group as opposed to anti to methyl (also in accord with experiment). 

Fig. 5.49 (a) Norcamphor, with the LUMO mapped onto the van der Waals surface. The LUMO as seen on the surface is most prominent at the carbonyl carbon, on the "top" of the molecule (the exo face), as shown by the blue area. Viewed from the bottom of the molecule (not shown here), the LUMO still lies at the C=0 carbon, but is less prominent (the blue is less intense). We can thus predict that nucleophiles will attack the C=0 carbon, from the exo direction, (b) Camphor (norcamphor with three methyl groups) the carbonyl carbon is shielded from exo attack by a methyl group, so for steric reasons nucleophiles tend to attack this carbon from the endo direction, despite exo attack being electronically favored... 

Fig. 12.2 Fukui contour maps for H2CO (a) /+(r) wp(r) (LUMO) contours on the plane perpendicular to the nuclear plane (b) / (r) r) (HOMO) contours on the nuclear plane. (Adapted with permission from ref. 77 copyri t 1989, Oxford University Press.)...

Turning to non-transition-metal catalysis, transition-state structures for the reduction of 2-methyl- and 2-isopropyl-cyclohexanone by LAH have been identified by DFT, and LUMO maps and NBO analysis have been used to examine the uneven distribution of the molecular orbital about the carbonyl r-plane, in order to explain the product ratio " substituent effects, the conformational ratio in the reactant, and... 

The reduction of 2-methylcyclohexanone and 2-isopropylcyclohexanone by LiAlH was subjected to DFT analysis (B3LYP/6-31G(d,p)) to optimize the TSS. Four TSSs were located for each ketone for the axial and equatorial attacks by LiAlH4. Electronic potential maps were used to investigate the electronic effect of the substituents on TSS stabilization. The lowest unoccupied molecular orbital (LUMO) maps and natural bond orbital (NBO) analysis helped in elucidating the uneven distribution of molecular orbital around the carbonyl tt-plane, and the preference for the hydride attack in terms of tensional and electronic properties. ... 

The second common type of mapping plots values of one of the frontier orbitals (either the HOMO or the LUMO) in color on the density surface. The color values plotted correspond to the value of the orbital where it intersects the surface. For a density-LUMO plot, for instance, the "hot spot" would be where the LUMO has its largest lobe. Because the LUMO is empty, this would be a bright blue area. In a density-HOMO plot, a bright red area would be the "hot spot."... 

Part Three. The benzyl (and allyl) halides are a special case they have resonance. To see how the charge is delocalized in the benzyl carbocation, request two plots the electrostatic potential mapped onto a density surface and the LUMO mapped onto a density surface. Submit these for calculation at the AMI semiempirical level. On a piece of paper, draw the resonance-contributing structures for the benzyl cation. Do the computational results agree with the conclusions you draw from your resonance hybrid ... 

Figure 20.20 Density contour maps for orbitals in the conduction band, (a) Density map for 63, the LUMO level. Both 4p(+4s) and Ga 4s(+4p) AOs are included, (b) Density map for orbital 64. Major electron density is on Zn atoms, (c) Density map for orbital 65. Major electron density is on Ga atoms, (d) Density map for orbital 69. Electron is localized on Zn 4p AO and Ga 4p AOs...

Although the most important, the electrostatic potential is not only the quantity which when mapped onto an electron density surface may provide useful chemical information. Maps of certain key molecular orbitals, in particular, the HOMO and LUMO, may also lead to informative models. Consider, for example, a map of the (absolute) value of the lowest-unoccupied molecular orbital (LUMO) in cyclohexanone, two views of which are shown below. 

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