Huckel Molecular Orbital HMO Theory

Aromaticity is usually described in MO terminology. Cyclic structures that have a particularly stable arrangement of occupied 7t molecular orbitals are called aromatic. A simple expression of the relationship between an MO description of stmcture and aromaticity is known as the Hiickel rule. It is derived from Huckel molecular orbital (HMO) theory and states that planar monocyclic completely conjugated hydrocarbons will be aromatic when the ring contains 4n + 2 n electrons. HMO calculations assign the n-orbital energies of the cyclic unsaturated systems of ring size 3-9 as shown in Fig. 9.1. (See Chapter 1, Section 1.4, p. 31, to review HMO theory.)... 

Equations (3.3) define the essence of the Huckel molecular orbital (HMO) theory. Notice that the total energy is just the sum of the energies of the individual electrons. Simple Huckel molecular orbital (SHMO) theory requires further approximations that we will discuss in due course. 

Aromaticity and Bandgap. Since most of the conducting polymers contain aromatic ring systems, it is worthwhile to look closer into a possible correlation among resonance (or ir delocalization in terms of the VB theory), aromaticity, and bandgap. The following discussion will be pursued within the framework of the Huckel molecular orbital (HMO) theory [1050,1073-1082]. 

HTS transmission cables, 23 852-854 HTU values, 15 696 Huang-Minlon reaction, 13 569-570 Huckel molecular orbital theory (HMO), 16 736 Hue, 7 305... 

We start with some biographical notes on Erich Huckel, in the context of which we also mention the merits of Otto Schmidt, the inventor of the free-electron model. The basic assumptions behind the HMO (Huckel Molecular Orbital) model are discussed, and those aspects of this model are reviewed that make it still a powerful tool in Theoretical Chemistry. We ask whether HMO should be regarded as semiempirical or parameter-free. We present closed solutions for special classes of molecules, review the important concept of alternant hydrocarbons and point out how useful perturbation theory within the HMO model is. We then come to bond alternation and the question whether the pi or the sigma bonds are responsible for bond delocalization in benzene and related molecules. Mobius hydrocarbons and diamagnetic ring currents are other topics. We come to optimistic conclusions as to the further role of the HMO model, not as an approximation for the solution of the Schrodinger equation, but as a way towards the understanding of some aspects of the Chemical Bond. 

HMO theory (Huckel Molecular Orbital theory) A simple molecular orbital theory applied to planar 7i-conjugated systems. A key simplification involves treatment of the n-system independently from the cr-system. The HMO molecular orbital energies are in terms of a and p, where a is equated with the energy of an isolated orbital, and P is the resonance integral, equated to the energy associated with having electrons shared by atoms. As reference, benzene is 4P more stable than an isolated orbital. 

The fundamental assumption of HMO theory is that we may calculate molecular orbitals through a process known as LCAO the linear combination of atomic orbitals. That is, we use some combination of the wave functions of the atomic orbitals to produce a set of molecular orbitals. In the Huckel method, we combine a set of atomic p orbitals to produce a set of n molecular orbitals. For a set of n parallel p orbitals, the Huckel molecular orbitals have the form shown in equation 4.1. In this equation is the wave function... 

HMO theory is named after its developer, Erich Huckel (1896-1980), who published his theory in 1930 [9] partly in order to explain the unusual stability of benzene and other aromatic compounds. Given that digital computers had not yet been invented and that all Hiickel s calculations had to be done by hand, HMO theory necessarily includes many approximations. The first is that only the jr-molecular orbitals of the molecule are considered. This implies that the entire molecular structure is planar (because then a plane of symmetry separates the r-orbitals, which are antisymmetric with respect to this plane, from all others). It also means that only one atomic orbital must be considered for each atom in the r-system (the p-orbital that is antisymmetric with respect to the plane of the molecule) and none at all for atoms (such as hydrogen) that are not involved in the r-system. Huckel then used the technique known as linear combination of atomic orbitals (LCAO) to build these atomic orbitals up into molecular orbitals. This is illustrated in Figure 7-18 for ethylene. 

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