Hiickel diagram

Note This simple orbital interaction picture is useful for interpreting results, but neglects many aspects of a calculation, such as electron-electron interactions. These diagrams are closely related to the results from Extended Hiickel calculations. 

We have now considered three viewpoints from which thermal electrocyclic processes can be analyzed symmetry characteristics of the frontier orbitals, orbital correlation diagrams, and transition-state aromaticity. All arrive at the same conclusions about stereochemistiy of electrocyclic reactions. Reactions involving 4n + 2 electrons will be disrotatory and involve a Hiickel-type transition state, whereas those involving 4n electrons will be conrotatory and the orbital array will be of the Mobius type. These general principles serve to explain and correlate many specific experimental observations made both before and after the orbital symmetry mles were formulated. We will discuss a few representative examples in the following paragraphs. 

Draw an energy diagram for the three molecular orbitals of the cyclopropenyl system (C l I3). How ate these three molecular orbitals occupied in the cyclopropenyl anion, cation, and radical Which of the three substances is aromatic according to Hiickel s rule ... 

Chapters 7 to 9 apply the thermodynamic relationships to mixtures, to phase equilibria, and to chemical equilibrium. In Chapter 7, both nonelectrolyte and electrolyte solutions are described, including the properties of ideal mixtures. The Debye-Hiickel theory is developed and applied to the electrolyte solutions. Thermal properties and osmotic pressure are also described. In Chapter 8, the principles of phase equilibria of pure substances and of mixtures are presented. The phase rule, Clapeyron equation, and phase diagrams are used extensively in the description of representative systems. Chapter 9 uses thermodynamics to describe chemical equilibrium. The equilibrium constant and its relationship to pressure, temperature, and activity is developed, as are the basic equations that apply to electrochemical cells. Examples are given that demonstrate the use of thermodynamics in predicting equilibrium conditions and cell voltages. 

Thus, the frontier-orbital and Hiickel-Mobius methods (and the correlation-diagram method as well) lead to the same conclusions thermal 2 + 4 cycloadditions and photochemical 2 + 2 cycloadditions (and the reverse ring openings) are allowed, while photochemical 2 + 4 and thermal 2 + 2 ring closings (and openings) are forbidden. 

In the Mobius-Hiickel approach, diagrams similar to Figure 18.4 can be drawn for this case. Here too, the disrotatory pathway is a Hiickel system and the conrotatory pathway a Mobius system, but since six electrons are now involved, the thermal reaction follows the Hiickel pathway and the photochemical reaction the Mobius pathway. 

Figure 1. Hiickel n-MO correlation diagrams for planar- perp twisting of pcntamethine cyanine about the 2-3 and 3-4 bonds (a), and simultaneous twisting about 2-3 and 4-5 bonds (b). For the perp forms the orbitals belonging to the different n fragments are indicated and the CT nature of the HOMO-LUMO excitation is emphasized.

Fig. 7.15 is constructed from reactivity diagrams of aromatic hydrocarbons already published. The reactivity of fluoranthene has often been investigated in detail from both, the experimental and theoretical aspects 116>. The values of /rE> calculated by the Pariser-Parr method (SCF) 117> as well as by the Hiickel MO (HMO) modified by considering... 

Construct a diagram like Figure 9.18 for (a) the Hiickel closure of butadiene to cyclobutene and (b) the Hiickel and Mobius cycloadditions of butadiene and ethylene. 

A Hiickel molecular orbital calculation for the cyclopentadiene system can be carried out as illustrated in Chapter 5. As is shown in Figure 5.20, the Frost-Musulin diagram places the five molecular orbitals at energies of a + 2/3, a + 0.618/3 (2), and a — 1.618/3 (2). Because the cyclopentadienyl anion has six electrons, only the three lowest energy levels are populated and are the orbitals interacting with those on the iron. Figure 21.15 shows the orbitals of the cyclopentadienyl anion. 

Fig. 9 Hiickel MO diagrams of diphenykarbene [15 m = 1], m-phenylenebis(phenylcarbene) [15 m = 2] and poly( i-phenylene-carbenes) [15],...

Fig. 6. Orbital correlation diagram for the DHP-cis-stilbene conrotatory path. R is the C(4a) — C(4b) separation. The dotted line indicates the ground state occupancy limit. The molecular orbitals were computed by the Extended Hiickel method )...

Calculations and Experiments on the Stereomutation of Cyclopropane. In 1965, Hoffmann published a seminal paper on trimethylene, another name for propane-1,3-diyl (8). He used extended hiickel (EH) calculations and an orbital interaction diagram to show that hyperconjugative electron donation from the central methylene group destabilizes the symmetric combination of 2p-n AOs on the terminal carbons in the (0,0) conformation of this diradical. Hoffmann s calculations predicted that the resulting occupancy of the antisymmetric combination of 2p-n AOs in 8 should favor conrotatory opening of cyclopropane (7), as depicted in Figure 22.8. 

Diagrams AS, ISA, and 2SA (S = MO symmetric with respect to the plane, A = MO asymmetric with respect to the C2 axis) represent the symmetries of three lowest unoccupied molecular orbitals of a phenoxy radical. The order of increasing energy AS < ISA < 2SA is chosen according to an extended Hiickel calculation. Consideration of the symmetry properties of these MO s led Sandner, Hedaya, and Trecker34 to the following conclusions ... 

X is NR R2. The substituent is converted to a Z substituent via the low-lying a orbital, and the ring is deactivated toward further electrophilic attack. The ortho and para channels lead to products. The interaction diagram for an X -substituted pentadienyl cation, substituted in the 1-, 2-, and 3-positions, as models of the transition states for the ortho, meta, and para channels, are too complex to draw simple conclusions. The HOMO and LUMO of the three pentadienyl cations with an amino substituent are shown in Figure 11.3. Notice that the LUMO of each is suitable to activate the C—H bond at the saturated site toward abstraction by the base. Curiously, the meta cation has the lowest LUMO and should most readily eliminate the proton. The stabilities of the transition states should be in the order of the Hiickel n energies. These are 6a — 8.7621/ , 6a — 8.499 / , and 6a — 8.718 / , respectively. Thus the ortho and para channels are favored over the meta channel, and the ortho route is slightly preferred over the para route. Experimentally, para substitution products are often the major ones in spite of there being two ortho pathways. The predominance of para products is usually attributed to steric effects. 

Figure 11.14 shows a molecular orbital diagram for cycloheptatrienyl cation. There are seven tt MOs, three of which are bonding and contain the six tt electrons of the cation. Cycloheptatrienyl cation is a Hiickel (4n + 2) system and is an aromatic ion. 

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