MO theory Huckel

Calculate die energy levels and coefScients for 1,3-butadiene using Huckel MO theory. 

The Longuet-Higgins theory based on Huckel MO theory and Hund s rule was pioneering work in the area of molecular design of high-spin alternant hydrocarbons and has been appreciated for its predictability. 

Bicyclo[3.3.0]octa-l,3,5,7-tetraene (2), trivially called pentalene [26, 27], is the second member in the series of fully unsaturated oligoquinanes. Huckel MO theory predicts that this planar hydrocarbon with its 8 r-electron system should be an antiaromatic species [25]. 2-Methylpentalene (37) has been generated by a retro-Diels-Alder reaction and deposited as a film at —196 °C on a NaCl or quartz plate for its spectroscopic characterization. It rapidly dimerized upon warming the cold plates to temperatures above —140 °C [26]. Only two stable derivatives of pentalene not complexed to a metal [29], the hexaphenyl- (38) [30] and 2,4,7-tri-tert-butylpentalene (39) [31], have hitherto been reported (Figure 4). 

Nitrenium ions are isoelectronic to carbenes [177]. They contain a dicoordinated nitrogen atom formally with two valence electrons. The possible electronic structures of the parent nitrenium ion NHj are shown in Figure 7.9. On the basis of Huckel MO theory one would expect that the lowest energy configuration, that is, the electronic ground... 

The reactivity and regioselectivity of 1,3-dipolar cycloadditions have been discussed in terms of the frontier orbitals [271]. Most of the features may be understood on the basis of simple Huckel MO theory. The HOMO and LUMO n orbitals and n orbital energies for all 18 combinations of the parent dipoles are shown in Figure 12.8. The frontier orbitals of many of the 1,3-dipoles have previously been derived by CNDO/2 and extended Huckel theory [272]. The first six structures, all of 16-electron type, are shown in greater detail ... 

Hofmann rearrangement, 118 Homotopic groups, 9 Homotropenylium, 152 Huckel array, 85 Huckel MO theory, 35, 86 Huckel 4n + 2 rule, 150, 151 Hund s rule, 114 Hunsdiecker reaction, 305-307 Hybridization, 15, 16... 

The orbital energies, e, also have been calculated by methods of quite variable sophistication and accuracy. Yet the results always seem to support the concept that molecules tend to be as hard as possible . Even a method as primitive as Huckel MO theory can be used with good results. 

This picture can be made more quantitative, at least at the level of simple Huckel MO theory. Take a linear chain of H atoms, or a linear chain of CH units, with a constant spacing, a, between the units. The energy of the levels in such a case is given by... 

Despite their increasing use, theoretical calculations have not been widely carried out on dioxazines, oxathiazines or dithiazines. Extended Huckel MO theory explained the short (1.84-2.68 A) nonbonded S" 0 interaction found in 3-(acylimino)-l,2,4-oxathiazines (11). The calculations indicated coupling between the O lone-pair to the S atom of an adjacent molecule by way of the... 

In addition, Tsuda and Oikawa carried out molecular orbital calculations of the electronic structures in the excited states of poly(vinyl cinnamate) [131, 132], They based their calculations on the reaction of intermolecular concerted cycloaddition that take place according to the Woodward-Hoffmann s rule. This means that the cyclobutane ring formation takes place if a nodal plane exists at the central double bond in the lowest unoccupied MO(LLUMO) and not in the highest occupied MO (HOMO) of the grotmd state cinnamoyloxy group. This is within the picture of Huckel MO or Extended Huckel MO theory. The conclusion is that the cmicerted cycloadditions occur favorably in the lowest triplet state Ti and in the second excited singlet state S2 [132]. 

Various aromatic and conjugated polyunsaturated hydrocarbons undergo one-electron reduction by alkali metals." Benzene and naphthalene are examples. The EPR spectrum of the benzene radical anion was shown in Fig. 12.2a (p. 657). These reductions must be carried out in aprotic solvents, and ethers are usually used. The ease of formation of the radical anion increases as the number of fused rings increases. The electrochemical reduction potentials of some representitive compounds are given in Table 12.1. The potentials correlate with the energy of the LUMO as calculated by simple Huckel MO theory." A correlation that includes a more extensive series of compounds can be observed with the use of somewhat more sophisticated molecular orbital methods." ... 

In most practical applications, PMO theory is implemented with the integral approximations of Huckel MO theory. For early formulation and application, see Dewar, M.J.S. "The Molecular Orbital Theory of Organic Chemistry" McGraw-Hill New York, 1969. 

For pedagogical presentation and application of Huckel MO theory, see, inter alia ... 

Hg is more stable as 3H2 than as hexagonal Hg. This means that electron pair bonds repel each other regardless of whether 4N or 4N + 2 electrons are involved, in contrast to commonly held beliefs fostered by Huckel MO theory. 

Indeed, in a previous chapter we advanced the argument that benzene is pi destabilized and explained why Huckel MO theory fails to show this pi destabilization. Now, imagine six carbons with one electron per valence AO coming together to form a six membered benzene ring of Dg symmetry in conjunction with a Dg cyclic array of six hydrogens with one electron per valence AO. 

At a simple level, Huckel MO theory (proposed in the 1930s by Erich Huckel) works well for dealing with the 7r-systems of unsaturated organic molecules. By extending the basis set and including overlap and all interactions (a and tt), Roald Hoffmann showed that extended Huckel theory could be applied to most hydrocarbons. This theory has since been developed further and continues to be a useful method to determine the relative energies of different conformers of an organic molecule. 

For the vinyl substituent we can analyze the stabilization in terms of simple Huckel MO theory. The interaction of a p orbital with an adjacent vinyl group creates the allyl radical. In Huckel calculations the resulting orbitals have energies of a -h 1.4, a, and a - 1.4/3. Thus the interaction of the p orbital with both the tt and 7T C=C orbitals leaves it unchanged but the tt and tt become ip] and of an allyl radical. There is a net stabilization of 0.4. ... 

---