The Simple Hiickel Method - Applications

Applications of the SHM are discussed in great detail in several books [21] here we will deal only with those applications which are needed to appreciate the utility of the method and to smooth the way for the discussion of certain topics (like bond orders and atomic charges) in later chapters. We will discuss the nodal properties of the MOs stability as indicated by energy levels and aromaticity (the An + 2 rule) resonance energies and bond orders and atomic charges. 

Hiickel s rule has been abundantly verified [17] notwithstanding the fact that the SHM, when applied without regard to considerations like the Jahn-Teller effect (see above) incorrectly predicts An species like cyclobutadiene to be triplet diradicals. The Hiickel rule also applies to ions for example, the cyclopropenyl system two n electrons, the cyclopropenyl cation, corresponds to n 0. and is strongly aromatic. Other aromatic species are the cyclopentadienyl anion (six n electrons, n = 1 Hiickel predicted the enhanced acidity of cyclopentadiene) and the cyclohep-tatrienyl cation. Only reasonably planar species can be expected to provide the AO overlap need for cyclic electron delocalization and aromaticity, and care is needed in applying the rule. Electron delocalization and aromaticity within the SHM have recently been revisited [43]. 

The SHM permits the calculation of a kind of stabilizing energy, or, more accurately, an energy that reflects the stability of molecules. This energy is calculated by comparing the total electronic energy of the molecule in question with that of a reference compound, as shown below for the propenyl systems, cyclobutadiene, and the cyclobutadiene dication. 

The propenyl cation, Fig. 4.19b cf. Fig. 4.16. If we take the total % electronic energy of a molecule to be simply the number of electrons in a n MO times the energy level of the orbital, summed over occupied orbitals (a gross approximation, as it ignores interelectronic repulsion), then for the propenyl cation 

We want to compare this energy with that of two electrons in a normal molecule with no special features (the propenyl cation has the special feature of a formally empty p orbital adjacent to the formal C/C double bond), and we choose neutral ethene for our reference energy (Fig. 4.15) 

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