LUMO map

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. 

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 ... 

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 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 ... 

LUMO Map. A graph that shows the absolute value of the LUMO on an Electron Density Surface corresponding to a van der Waals Surface. 

Maps of key molecular orbitals may also lead to informative models. The most popular and (to date) most important of these is the so-called LUMO map , in which the (absolute value) of the lowest-unoccupied molecular orbital (the LUMO) is mapped onto a size surface. 

This chapter illustrates the way in which graphical models, in particular, electrostatic potential maps and LUMO maps, may be employed to provide insight into molecular structure and chemical reactivity and selectivity. 

Graphical models, in particular, electrostatic potential maps and LUMO maps have proven of considerable value, not only as a means to rationalize trends in molecular structure and stability and chemical reactivity and selectivity, but also as tools with which to carry out chemical investigations. A few examples have already been provided in Chapter 4. Those which follow have been chosen to further illustrate both interpretive and predictive aspects of graphical models. 

Inspection of the LUMO map reveals that the syn proton in 2-norbomyl chloride is much more likely to undergo attack by a base than the anti proton. 

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. 

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. 

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). 

These examples clearly show the utility of LUMO maps to assign stereochemistry in nucleophilic additions to complex substrates. 

Property Map. A representation or map of a property on top of an Isosurface, typically an Isodensity Surface. Electrostatic Potential Maps, and HOMO and LUMO Maps and Spin Density Maps are useful property maps. 

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... 

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. ... 

Density-LUMO Maps Reactivities of Carbonyl Groups... 

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