Symmetry Huckel method

The Huckel method and is one of the earliest and simplest semiempirical methods. A Huckel calculation models only the 7t valence electrons in a planar conjugated hydrocarbon. A parameter is used to describe the interaction between bonded atoms. There are no second atom affects. Huckel calculations do reflect orbital symmetry and qualitatively predict orbital coefficients. Huckel calculations can give crude quantitative information or qualitative insight into conjugated compounds, but are seldom used today. The primary use of Huckel calculations now is as a class exercise because it is a calculation that can be done by hand. 

As a final exercise for the reader, consider the naphthalene module (symmetry 02h) as shown in Fig. 10. Application of the HUcKel method leads to a lOx 10 secular determinant (see problem 30). However, with the application... 

We have emphasized that the Diels-Alder reaction generally takes place rapidly and conveniently. In sharp contrast, the apparently similar dimerization of olefins to cyclobutanes (5-49) gives very poor results in most cases, except when photochemically induced. Fukui, Woodward, and Hoffmann have shown that these contrasting results can be explained by the principle of conservation of orbital symmetry,895 which predicts that certain reactions are allowed and others forbidden. The orbital-symmetry rules (also called the Woodward-Hoffmann rules) apply only to concerted reactions, e.g., mechanism a, and are based on the principle that reactions take place in such a way as to maintain maximum bonding throughout the course of the reaction. There are several ways of applying the orbital-symmetry principle to cycloaddition reactions, three of which are used more frequently than others.896 Of these three we will discuss two the frontier-orbital method and the Mobius-Huckel method. The third, called the correlation diagram method,897 is less convenient to apply than the other two. 

By far, the theoretical approaches that experimental inorganic chemists are most familiar with and in fact nse to solve questions qnickly and qnalitatively are the simple Huckel method and Hoffinann s extended Hiickel theory. These approaches are nsed in concert with the application of symmetry principles in the bnUding of syimnetry adapted linear combinations (SALCs) or gronp orbitals. The ab initio and other SCF procednres ontlined above prodnce MOs that are treated by gronp theory as well, bnt that type of rigor is not usually necessary to achieve good qnahtative pictures of the character aud relative orderiugs of the molecular orbitals. 

The extended Huckel method, as simple as it is, has proven enormously successful in very many applications. Its successes depend on the fact that the Fock matrices have the correct symmetry properties and that the atomic potentials supplied through the use of experimental ionization potentials are more or less correct. Extended Huckel theory (EHT) calculations are still being performed today and yield results of interest in nearly all areas of chemistry and condensed matter theory.As this theory requires only ionization potentials and basis sets, it has been extended in one form or another to all elements of the... 

At first we would like to recall a few important conclusions from earlier studies. The electronic structure of the reactant CpML has been discussed by Hofmann and Padmanabhan [22] for various ligands L and M = Co, Rh, and Ir with the extended Huckel method. As shown in Fig. 5, the valence molecular orbitals are m, ma", n -I- l)a, (w -I- l)a", and (n + 2)a orbitals under Cj symmetry. One sees that the m and rm" orbitals are mainly d x yy and orbitals stabilized by interaction with the ir orbitals on L. At somewhat higher energy is the occupied metal-based d orbital, (n + l)a , with a weak M-L antibonding a interaction. The metal-based (m + l)fl" (dj,j) and (n -H 2)a (d y) orbitals are highest in energy, destabilized by interaction with occupied tt orbitals on the Cp ring. In addition, the (n -I- 2)a orbital destabilized by interaction with the a orbital on L. Thus, it... 

Thirdly, it has been demonstrated that shapes (Figure 1), nodal structures, momentum distributions, and symmetry properties of KS orbitals are similar to those calculated by the ab initio, semiempirical, and extended Huckel methods. ... 

The primary reason for interest in extended Huckel today is because the method is general enough to use for all the elements in the periodic table. This is not an extremely accurate or sophisticated method however, it is still used for inorganic modeling due to the scarcity of full periodic table methods with reasonable CPU time requirements. Another current use is for computing band structures, which are extremely computation-intensive calculations. Because of this, extended Huckel is often the method of choice for band structure calculations. It is also a very convenient way to view orbital symmetry. It is known to be fairly poor at predicting molecular geometries. 

In this method, the orbital symmetry rules are related to the Hiickel aromaticity rule discussed in Chapter 2. Huckel s mle, which states that a cyclic system of electrons is aromatic (hence, stable) when it consists of 4n + 2 electrons, applies of course to molecules in their ground states. In applying the orbital symmetry principle, we are not concerned with ground states, but with transition states. In the present method, we do not examine the molecular orbitals themselves but rather the p orbitals before they overlap to form the MO. Such a set of p orbitals is called a basis set (Fig. 15.5). In investigating the possibility of a concerted reaction, we put the basis sets into the position they would occupy in the transition state. Figure 15.6 shows this for both the... 

We will consider the application of the Huckel molecular orbital method to the benzene molecule and we will first see what happens when we do not make use of symmetry. The benzene molecule has a framework of six carbon atoms at the comers of a hexagon and each carbon atom contributes one w-electron. The -electron MOs will be constructed from six 2pf atomic orbitals, each located at one of the carbon atoms, thus, e... 

Following the Longuet-Higgins—Salem approach, Buck studied the tendency of aromatic monocyclic compounds to bond alternation with increasing ring size. He used the Huckel model with variable P for the 7T electrons and a Morse potential for the o electrons. His distortion energies show that the o system resists distortion and the tt system favors distortions from D h to D i2)h symmetry in C H annulenes with 77 = 6, 8, 10, 12, 14, 16. The symmetry of the HOMO and LUMO is used to predict whether the C30H30 bond alternation due to the tt electrons should occur. It was subsequently shownthat this method can also be applied to the characterization of antiaromatic polycycles. 

Another approximate scheme, MNDO, has been applied to the study of defects (10,26) in long polyenes. This self-consistent method allows the inclusion of electron interactions in an approximate way and leads to predictions similar to those of the SSH model. For example, the neutral defect is studied by exaining a 41 carbon atom polyene with a center of symmetry. This forces the defect to be centered in the middle of the chain. The MNDO results show the standard tanh structure but with t=3 (instead of t=7 from the Huckel model). The charged defects were treated in the same manner and it was found that t=5 for the positive and t<3 for the negative solitons. Note however that the tanh form was... 

In the case of ethylene the a framework is formed by the carbon sp -orbitals and the rr-bond is formed by the sideways overlap of the remaining two p-orbitals. The two 7r-orbitals have the same symmetry as the ir 2p and 7T 2p orbitals of a homonuclear diatomic molecule (Fig. 1.6), and the sequence of energy levels of these two orbitals is the same (Fig. 1.7). We need to know how such information may be deduced for ethylene and larger conjugated hydrocarbons. In most cases the information required does not provide a searching test of a molecular orbital approximation. Indeed for 7r-orbitals the information can usually be provided by the simple Huckel (1931) molecular orbital method (HMO) which uses the linear combination of atomic orbitals (LCAO), or even by the free electron model (FEM). These methods and the results they give are outlined in the remainder of this chapter. 

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