Hiickel Orbitals

Hiickel orbital aray Mdbius orbital array... 

If the transition state resembles the intermediate n-complex, the structure involved is a substituted cyclohexadienyl cation. The electrophile has localized one pair of electrons to form the new a bond. The Hiickel orbitals are those shown for the pentadienyl system in Fig. 10.1. A substituent can stabilize the cation by electron donation. The LUMO is 1/13. This orbital has its highest coefficients at carbons 1, 3, and 5 of the pentadienyl system. These are the positions which are ortho and para to the position occupied by the electrophile. Electron-donor substituents at the 2- and 4-positions will stabilize the system much less because of the nodes at these carbons in the LUMO. 

Finally, we return to 2-fluoro-6-chlorotoluene (Figure 10), for which it <— it excitation and n ionization cause only minor changes in the rotor potential. In this disubstituted case, the appropriate pseudo-C2 axis would coincide with the methyl rotor axis itself. We expect the Hiickel orbitals to align with the rotor axis, which would make 0a = Ob in all three electronic states, much as in sixfold cases. Accordingly, there is little effect of electronic excitation on the barrier height, which is presumably dominated by steric repulsion in all three electronic states. In terms of ic-electron effects, 2-fluoro-6-chlorotoluene behaves much like a sixfold case. 

One of the simplest molecules in which it is customary to invoke outer d-orbital participation in a bonding is the triiodide ion. This ion has been observed with a large number of different cations and X-ray crystal studies have revealed both symmetrical and unsymmetrical species, although in both forms it is essentially linear. If the bonding involves only the valence p-orbitals then the Hiickel orbitals for the symmetric species are those shown in Fig. 12. This description is exactly equivalent to the covalent-ionic resonance formulation VII. 

Then make a transformation to an MO basis using the Hiickel orbitals ... 

The factors that control if and how these cyclization and rearrangement reactions occur in a concerted manner can be understood from the aromaticity or lack of aromaticity achieved in their cyclic transition states. For a concerted pericyclic reaction to be thermally favorable, the transition state must involve An + 2 participating electrons if it is a Hiickel orbital system, or 4 electrons if it is a Mobius orbital system. A Hiickel transition state is one in which the cyclic array of participating orbitals has no nodes (or an even number) and a Mobius transition state has an odd number of nodes. 

Figure 5 Orbital correlation diagram for the suprafacial [1,3] shift of a proton in propene. The transition-state orbitals are based on the Hiickel orbitals for cyclobutadiene...

Expansion of the Hiickel orbital (HMO) secular determinant for a PAH graph gives the characteristic polynomial P(G X) = det X1 — A where I is the identity matrix and A is the adjacency matrix for the corresponding graph [11]. The characteristic polynomial of a N carbon atom system has the following form... 

The resulting LBOs are fairly localized, one on Ci — C2 the other on C3—C4. Elowever, the delocalization tails are significant even though we used Hiickel orbitals. These large localization tails reflect the fact that butadiene has some conjugation between the n-bonds and in terms of VB theory is describable by a linear combination of the major Kekule structure and the minor long bond structure. 

The substitution also destroys the degeneracy in the frontier orbitals of benzene thus, on formation of an anion-radical from pyridine, it is i/t4 which receives the electron. As indicated in Fig. 1, the stabilized orbitals in pyridine are distorted from their symmetry in benzene. Thus, the coefficient of i//4 at the 2- and 6-positions is increased in pyridine, relative to benzene at the expense of the other positions, especially the 3- and 5-positions. The Hiickel orbital coefficients c,- are related to spin population pt by Eq. (7) thus, the simple Hiickel model of the pyridine anion-radical predicts high spin population at positions 1, 2, 4, and 6, which is in good agreement with reality (see Section III,A,1), although the McLachlan procedure gives a rather more accurate quantitative description.15,29... 

First-order perturbation uses the Hiickel orbital coefficients cJfJL of a given parent system to predict the shifts Ssj on the corresponding orbital energies sj. The shift induced by an inductive perturbation bafl is determined by the probability cj that an electron in orbital ifjj resides on atom p. (Equation 4.13). 

Apart from the hydrogenated compound,1 examples for derivatives of the fully conjugated pyridazino[3,4-c]pyridazine or the unsubstituted compound 1 itself are not known, however, 1 has been studied by AMI2 and Hiickel orbital calculations.3... 

Pyridazino[4,3-c]pyddazine (1) has been studied by AMI2 and Hiickel orbital calculations.3... 

AMI calculations have been performed on pyridazino[4,5-c]pyridazine (1) and its (V-protonated species.2 Energy levels and charge densities were calculated by Hiickel orbital calculations.3- 5... 

Two major contributions to the 7t-energy change in the ring-cleavage reaction leading to a PAHTC need to be included in the model. In a simplified Pariser-Parr-Pople (PPP) method with Hiickel orbitals as the basis [33], the PAHTC is an arylmethyl cation, with resonance energy... 

We have looked at the sum of the extended Hiickel orbital energies as a means of estimating relative stabilities of the various allotropic... 

Hiickel orbitals and to allow for the lowering of the ground state by interaction with singly excited configurations. 

The reservation against the use of was caused by the suspicion that the KS orbitals might not be normal orbitals, and should not be used in the same way as HF or extended Hiickel orbitals for qualitative rationalization of experimental trends. On the other hand, the... 

Fig. 4.7 Hiickel orbital energy spectrum of benzene as a function of index k, with allowed values 0, 1, 2,3...

FIGURE 17.7 Four sites—four electrons (L = 1). (a) Ordinary Hiickel orbitals and (b) transformed. 

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