Hiickel Methods

I h c Hiickel eon stari t (k) scales Ih e in teraetiou energy between two atomic orbitals (see Kxtended Hiickel Method on page 125). HyperChem uses the defatill value of 1.75 (see the second part of th is book. Theory and Methods). You shoti Id tise th is value for m ost eases, A suggested ran ge for experimcri tal adjiistmen L of th is eon -stant is 1,6 2,0.- ... 

Note You cannot use the Hxicndcd Hiickel method or any one of th e-SCH m eth ods with theCI option being turn ed on forgeometry optim i/.ation s, m olecular dynam ics sim ulation s or vibrational cal-culations, in the ctirrcrit version ofHypcrChem. 

Unlike the Hiickel and extended Hiickel methods, the semi-empirical approaches that explicitly treat electron-electron interactions give rise to Fock matrix element... 

The Extended Hiickel method, for example, does not explicitly consider the effects of electron-electron repulsions but incorporates repulsions into a single-electron potential. This simplifies the solution of the Schrodinger equation and allows HyperChem to compute the potential energy as the sum of the energies for each electron. 

The Extended Hiickel method also allows the inclusion of d orbitals for third row elements (specifically. Si, P, S and Cl) in the basis set. Since there are more atomic orbitals, choosing this option results in a longer calculation. The major reason to include d orbitals is to improve the description of the molecular system. 

Note You cannot use the Extended Hiickel method or any one of the SCFmethods with the Cl option being turned on for geometry optimizations, molecular dynamics simulations or vibrational calculations, in the current version of HyperChem. 

Note You can not use the Extended Hiickel method, nor any of the other SCFmethods with the Cl option turned on, for geometry optimization or molecular dynamics simulations. 

The Extended Hiickel method neglects all electron-electron interactions. More accurate calculations are possible with HyperChem by using methods that neglect some, but not all, of the electron-electron interactions. These methods are called Neglect of Differential Overlap or NDO methods. In some parts of the calculation they neglect the effects of any overlap density between atomic orbitals. This reduces the number of electron-electron interaction integrals to calculate, which would otherwise be too time-consuming for all but the smallest molecules. 

The simplest approximation to the Schrodinger equation is an independent-electron approximation, such as the Hiickel method for Jt-electron systems, developed by E. Hiickel. Later, others, principally Roald Hoffmann of Cornell University, extended the Hiickel approximations to arbitrary systems having both n and a electrons—the Extended Hiickel Theory (EHT) approximation. This chapter describes some of the basics of molecular orbital theory with a view to later explaining the specifics of HyperChem EHT calculations. 

The 7i-electron wave functions in the Hiickel method are given by... 

In Section 7.3.1.3 the 71-electron MOs of benzene were obtained by the Hiickel method using only the Ip AOs on the six carbon atoms. The ground configuration is... 

One of the more useful predicative applications of the relatively crude Hiickel method has been to illustrate quantitatively the effect of benzenoid annelation on the resonance energies of furan and thiophene. The results are summarized in Figure 1. As expected, thiophenes are more stable than the corresponding furans and 3,4-fusion results in less stable compounds than 2,3-fusion (77CR(C)(285)42l). 

Although the Hiickel method has now been supplanted by more complete treatments for theoretical analysis of organic reactions, the pictures of the n orbitals of both linear and cyclic conjugated polyene systems that it provides are correct as to symmetry and the relative energy of the orbitals. In many reactions where the n system is the primary site of reactivity, these orbitals correctly describe the behavior of the systems. For that reason, the reader should develop a familiarity with the qualitative description of the n orbitals of typical linear polyenes and conjugated cyclic hydrocarbons. These orbitals will be the basis for further discussion in Chapters 9 and 11. 

The predictions of relative stability obtained by the various approaches diverge more widely when nonbenzenoid systems are considered. The simple Hiickel method using total n delocalization energies relative to an isolated double-bond reference energy (a + fi) fails. This approach predicts stabilization of the same order of magnitude for such unstable systems as pentalene and fulvalene as it does for much more stable aromatics. The HMO, RE, and SCF-MO methods, which use polyene reference energies, do much better. All show drastically reduced stabilization for such systems and, in fact, indicate destabilization of systems such as butalene and pentalene (Scheme 9.2). 

The u) parameter determines the weight of the charge on the diagonal elements. Since Ga is calculated from the results (MO coefficients, eq. (3.90)), but enters the Hiickel matrix which produces the results (by diagonalization), such schemes become iterative. Methods where the matrix elements are modified by the calculated charge are often called charge iteration or self-consistent (Hiickel) methods. 

The Hiickel method is essentially only used for educational purposes or for veiy qualitative orbital considerations. It has the ability to produce qualitatively correct MOs involving a computational effort which is within reach of doing by hand. 

For planar unsaturated and aromatic molecules, many MO calculations have been made by treating the a and n electrons separately. It is assumed that the o orbitals can be treated as localized bonds and the calculations involve only the tt electrons. The first such calculations were made by Hiickel such calculations are often called Hiickel molecular orbital (HMO) calculations Because electron-electron repulsions are either neglected or averaged out in the HMO method, another approach, the self-consistent field (SCF), or Hartree-Fock (HF), method, was devised. Although these methods give many useful results for planar unsaturated and aromatic molecules, they are often unsuccessful for other molecules it would obviously be better if all electrons, both a and it, could be included in the calculations. The development of modem computers has now made this possible. Many such calculations have been made" using a number of methods, among them an extension of the Hiickel method (EHMO) and the application of the SCF method to all valence electrons. ... 

The rule may then be stated A thermal pericyclic reaction involving a Hiickel system is allowed only if the total number of electrons is 4n + 2. A thermal pericyclic reaction involving a Mobius system is allowed only if the total number of electrons is 4n. For photochemical reactions these rules are reversed. Since both the 2 + 4 and 2 + 2 cycloadditions are Hiickel systems, the Mdbius-Hiickel method predicts that the 2 + 4 reaction, with 6 electrons, is thermally allowed, but the 2 + 2 reaction is not. One the other hand, the 2 + 2 reaction is allowed photochemically, while the 2 + 4 reaction is forbidden. 

Both the frontier-orbital and the Mobius-Hiickel methods can also be applied to the cyclohexadiene 1,3,5-triene reaction in either case the predicted result is that for the thermal process, only the disrotatory pathway is allowed, and for the... 

As expected, the Mobius-Hiickel method leads to the same predictions. Here we look at the basis set of orbitals shown in G and H for [1,3] and [1,5] rearrangements, respectively, A [1,3] shift involves four electrons, so an allowed thermal pericyclic reaction must be a Mobius system (p. 1070) with one or an odd number of sign inversions. As can be seen in G, only an antarafacial migration can achieve this. A [1,5] shift, with six electrons, is allowed thermally only when it is a Hiickel system with zero or an even number of sign inversions hence it requires a suprafacial migration. 

Molecular orbital calculations for the parent vinyl cation, Cj H3, were first reported by Hoffmann (161), who used the extended Hiickel method, and more recently by Yonezawa and co-workers (162), who used a semiempirical SCF procedure. Both treated the problem of classical, 172 (R = H), versus bridged structures, 173, but the methods suffered from their inability to account satisfactorily for bond-length changes, and neither discussed the question of linear, 172a, versus bent, 172b, structures. 

The extended Hiickel method has been used in a discussion of properties and reactivity of radicals and biradicals (75). We have found it possible to correlate the basicity constants, pKbh. of radical anions with extended Hiickel data (76). 

The definition of "concepts" must be accompanied by explicit recipes for computing them is actual cases. There is no more space in theoretical chemistty for "driving forces", "effects, etc. not accompanied by specific rules for their quantification. The impact of a new "concept will be greater if the rules of quantifications are not restricted to ad hoc methods, but related to methods of general use in molecular quantum mechanics. A concept based exclusively on some specific features of a given method, e g. the extended Hiickel method, is less robust than a concurrent concept which may be quantified also using other levels of the theory. 

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