Qualitative molecular orbital theory

Frontier molecular orbital theory is closely related to various schemes of qualitative orbital theory where interactions between fragment MOs are considered. Ligand field theory, as commonly used in systems involving coordination to metal atoms, can be considered as a special case where only the d-orbitals on the metal and selected orbitals of the ligands are considered. 

There are two important features. The change in orbital energies is dependent on the magnitude of the overlap, and inversely proportional to the energy difference of 

It is important to realize that whenever qualitative or frontier molecular orbital theory is invoked, the description is within the orbital (Hartree-Fock or density functional) model for the electronic wave function. In other words, rationalizing a trend in computational results by qualitative MO theory is only valid if the effect is present at the HF or DFT level. If the majority of the variation is due to electron correlation, an explanation in terms of interacting orbitals is not appropriate. 

The interacting fragment orbital analysis can be put on more quantitative terms by performing explicit energy decomposition analysis of FIF or DFT wave functions. The extended transition state (ETS) approach decomposes the energy change into four 

An alternative decomposition, due to K. Morokuma, partitions the interaction energy into five terms.  

Besides the already mentioned Fukui function, there are a couple of other commonly used concepts which can be connected with Density Functional Theory (Chapter 6). The electronic chemical potential p is given as the first derivative of the energy with respect to the number of electrons, which in a finite difference version is given as half the sum of the ionization potential and the electron affinity. Except for a difference in sign, this is exactly the Mulliken definition of electronegativity.  

The second derivative of the energy with respect to the number of electrons is the hardness r) (the inverse quantity is called the softness), which again may be approximated in term of the ionization potential and electron affinity. 

These concepts play an important role in the Hard and Soft Acid and Base (HSAB) principle, which states that hard acids prefer to react with hard bases, and vice versa. By means of Koopmann s theorem (Section 3.4) the hardness is related to the HOMO-LUMO energy difference, i.e. a small gap indicates a soft molecule. From second-order perturbation theory it also follows that a small gap between occupied and unoccupied orbitals will give a large contribution to the polarizability (Section 10.6), i.e. softness is a measure of how easily the electron density can be distorted by external fields, for example those generated by another molecule. In terms of the perturbation equation (15.1), a hard-hard interaction is primarily charge controlled, while a soft-soft interaction is orbital controlled. Both FMO and HSAB theories may be considered as being limiting cases of chemical reactivity described by the Fukui ftinction. 

There are two important features. The change in orbital energies is dependent on the 

These concepts play an important role in the Hard and Soft Acid and Base (HSAB) principle, which states that hard acids prefer to react with hard bases, and vice versa. 

By means of Koopmann s theorem (Section 3.4j the hardness is related to the HQMQ- LUMO energy difference, i.e. a small gap indicates a soft molecule. From second-order perturbation theory it also follows that a small gap between occupied and unoccupied orbitals will give a large, mntribnrinn to the pol.nriznhility (Section 10.6) i softness is a measure of how easily the electron density can he distorted by extemal- 

If the two initial orbitals contain one, two or three electrons, the interaction will lead to a lower energy, with the stabilization being largest for the case o  

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The first pair of examples we would like to discuss occurs in a field which lends itself naturally to be conquered by theory. Indeed, the past three decades have seen the exploration of mechanistic details of pericyclic reactions as one of the major success stories of computational chemistry. Rooted in qualitative molecular orbital theory, the key concept of... 

In the case of tt complexes of substituted cyclopentadienones, such as the iron tricarbonyl derivatives prepared by Weiss and H libel (30), qualitative molecular-orbital theory (20) predicted a considerable reduction of the ketonic carbonyl bond order. It was observed that the ketonic carbonyl frequency dropped by as much as 65 cm-1, in agreement with theory. A similar explanation can also be provided in terms of valence bond theory (Fig. 14). It has been suggested that n complexing of arenes such as benzene results in loss of aromaticity of the ring in contrast to the dicyclopentadienyl... 

Qualitative molecular-orbital theory approaches (and related qualitative treatments) are discussed throughout the text (particularly in Chapters 4 and 6), and a more detailed discussion of the contributions of such approaches presented in Chapter 8. As with the experimental methods discussed in Chapter 2, the topics presented in the present chapter are associated with numerous abbreviations and acronyms (and alternative titles). Both to serve as a key to these abbreviations, and as a source of reference to the numerous theoretical approaches now available, they are listed along with brief descriptions and references to further information in Appendix C. 

Qualitative Theories 15.1 Frontier Molecular Orbital Theory 15.2 Concepts from Density Functional Theory 15.3 Qualitative Molecular Orbital Theory 34, 347 351 353 ... 

The manuscript, also, has provided an opportunity to summarize our distinct methodology, which allows the direct identification of the appropriate linear combinations of atomic orbitals needed for the Qualitative Molecular Orbital theory analyses, so useful in modem Chemistry. This approach fits very namrally with the orbit-by-orbit procedure for performing the group theory, and which is at the heart of the construction of the calculator files on the CDROM. 

QUALITATIVE MOLECULAR ORBITAL THEORY AND PERICYCLIC REACTIONS... 

Chapter 12 Qualitative Molecular Orbital Theory Pericyclic Reactions... 

This chapter is an introduction to qualitative molecular orbital theory and pericyclic reactions. Pericyclic reactions have cyclic transition states and electron flow paths that appear to go around in a loop. The regiochemistry and stereochemistry of these reactions are usually predictable by HOMO-LUMO interactions, so to understand them we need to understand molecular orbital theory, at least on a qualitative basis. 

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