Molecular orbital theory development

To further illuminate the LCAO variational process, we will carry out the steps outlined above for a specific example. To keep things simple (and conceptual), we consider a flavor of molecular orbital theory developed in the 1930s by Erich Huckel to explain some of the unique properties of unsaluralcd and aromatic hydrocarbons (Huckel 1931 for historical... 

Orbitals) (CO) are expressed as a linear combination of atomic orbitals (LCAO) or similar local functions. There is an obvious parallelism with the traditional Molecular Orbital Theory see Molecular Orbital Theory) developed by chemists, in which the wavefimctions describing the motion of an electron in the molecule (i.e. the Molecular Orbitals) (MO) are also expressed as a LCAOs. As a matter of fact, the first orbital describing the motion of an electron in a polyatomic system was written by Bloch in 1928 and it was a CO. Hence, MO theory finds its roots in solid-state physics. 

This sequence was also observed for the long wavelength maxima of the corresponding species of 2-hydroxypyrazine (821) and was in accord with a molecular-orbital theory developed by Mason (1480). Cullen and Harrison (905) have found a broad maximum in the 380-400 nm region for a series of C-methyl 2-mercaptopyrazines and 3-mercaptopyrazine 1-oxides. This was shifted to shorter wavelengths by about 40 nm in the spectrum of the anion. 

In the molecular orbital theory, developed by Mulliken, Hund and Huckel, a molecule is considered to be quite different from the constituent atoms. MO theory describes covalent bonds in terms of molecular orbitals, which are formed from orbitals of the bonding atoms and are spread over the atoms of the entire molecule. 

In this section, the conceptual framework of molecular orbital theory is developed. Applications are presented and problems are given and solved within qualitative and semi-empirical models of electronic structure. Ab Initio approaches to these same matters, whose solutions require the use of digital computers, are treated later in Section 6. Semi-empirical methods, most of which also require access to a computer, are treated in this section and in Appendix F. 

The electronic theory of organic chemistry, and other developments such as resonance theory, and parallel developments in molecular orbital theory relating to aromatic reactivity have been described frequently. A general discussion here would be superfluous at the appropriate point a brief summary of the ideas used in this book will be given ( 7- )-... 

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. 

Both the language of valence bond theory and of molecular orbital theory are used in discussing structural effects on reactivity and mechanism. Our intent is to illustrate both approaches to interpretation. A decade has passed since the publication of the Third Edition. That decade has seen significant developments in areas covered by the text. Perhaps most noteworthy has been the application of computational methods to a much wider range of problems of structure and mechanism. We have updated the description of computational methods and have included examples throughout the text of application of computational methods to specific reactions. 

For a molecule as simple as Fl2, it is hard to see much difference between the valence bond and molecular orbital methods. The most important differences appear- in molecules with more than two atoms. In those cases, the valence bond method continues to view a molecule as a collection of bonds between connected atoms. The molecular- orbital method, however, leads to a picture in which the sane electron can be associated with many, or even all, of the atoms in a molecule. We ll have more to say about the similarities and differences in valence bond and molecular- orbital theory as we continue to develop their principles, beginning with the simplest alkanes methane, ethane, and propane. 

How does electron sharing lead to bonding between atoms Two models have been developed to describe covalent bonding valence bond theory and molecular orbital theory. Each model has its strengths and weaknesses, and chemists tend... 

Viewed from the standpoint of molecular orbital theory, as it has developed during the last decade or so3, the above simple pictures of the sulfur bonding in a dialkyl sulfide are somewhat naive but they serve to introduce the subject and act as a basis for discussing the bonding in sulfoxides and sulfones. It will be convenient to use the second of the two pictures as the basis for further discussion, i.e. that involving the use of 3sp3 hybridized orbitals on sulfur. 

The development of molecular orbital theory (MO theory) in the late 1920s overcame these difficulties. It explains why the electron pair is so important for bond formation and predicts that oxygen is paramagnetic. It accommodates electron-deficient compounds such as the boranes just as naturally as it deals with methane and water. Furthermore, molecular orbital theory can be extended to account for the structures and properties of metals and semiconductors. It can also be used to account for the electronic spectra of molecules, which arise when an electron makes a transition from an occupied molecular orbital to a vacant molecular orbital. 

The VB and MO theories are both procedures for constructing approximations to the wavefunctions of electrons, but they construct these approximations in different ways. The language of valence-bond theory, in which the focus is on bonds between pairs of atoms, pervades the whole of organic chemistry, where chemists speak of o- and TT-bonds between particular pairs of atoms, hybridization, and resonance. However, molecular orbital theory, in which the focus is on electrons that spread throughout the nuclear framework and bind the entire collection of atoms together, has been developed far more extensively than valence-bond... 

As their names suggest, molecular orbitals can span an entire molecule, while localized bonds cover just two nuclei. Because diatomic molecules contain just two nuclei, the localized view gives the same general result as molecular orbital theoiy. The importance of molecular orbitals and delocalized electrons becomes apparent as we move beyond diatomic molecules in the follow-ing sections of this chapter. Meanwhile, diatomic molecules offer the simplest way to develop the ideas of molecular orbital theory. 

The limitation of the above analysis to the case of homonuclear diatomic molecules was made by imposing the relation Haa = Hbb> as in this case the two nuclei are identical. More generally, Haa and for heteronuclear diatomic molecules Eq. (134) cannot be simplified (see problem 25). However, the polarity of the bond can be estimated in this case. The reader is referred to specialized texts on molecular orbital theory for a development of this application. 

Molecular Beams, Reactive Scattering in (Herschbach) Molecular Orbital Theory, Recent Developments in (Longuet-Higgins). ... 

Recent Advances in Polymer Chemistry (Szwarc). Recent Developments in Molecular Orbital Theory 2 147... 

Having learnt about the concerted reactions, we can now undertake the theory of these reactions. The development of the theory of concerted reactions has been due chiefly to the work of R.B. Woodward and R. Hoffmann. They have taken the basic ideas of molecular orbital theory and used them, mainly in a qualitative way, to derive selection rules which predict the stereochemical course of various types of concerted reactions. These rules are best understood in terms of symmetries of interacting molecular orbitals. Here are will see some of the most important theoretical approaches and see how they are interrelated. 

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