Molecular orbitals modem concepts

Pauling always favored the Valence Bond (VB) theory over the Molecular Orbital (MO) theory for the description of the electronic structure of molecules, because the VB model resembles more the pre-quantum theoretical models of chemical bonding. However, modem quantum chemistry is dominated by MO theory, which has clearly prevailed in the computational applications. Nevertheless, a number of terms and concepts of VB theory still play an important role when it comes to the interpretation of the results of a quantum chemical calculation. 

This sets the context of this book. The power of the modem spreadsheet is applied to make familiar fundamental concepts of Basis Set theory, which is at the heart of modem Molecular Orbital theory. There are over 100 fully interactive EXCEL files on the CD supplied with this book. You can treat the CD as a learning aid and simply open and consult each file during your study of the various topics discussed in the text. There is a separate folder for each chapter and the corresponding figure numbers of the illustrations in the text identify the spreadsheets. 

Werner s coordination theory, with its concept of secondary valence, provides an adequate explanation for the existence of such complexes as [Co(NH3)6]Cl3-Some properties and the stereochemistry of these complexes are also explained by the theory, which remains the real foundation of coordination chemistry. Since Werner s work predated by about twenty years our present electronic concept of the atom, his theory does not describe in modem terms the nature of the secondary valence or, as it is now called, the coordinate bond. Three theories currently used to describe the nature of bonding in metal complexes are (1) valence bond theory (VBT), (2) crystal field theory (CFT), and (3) molecular orbital theory (MOT). We shall first describe the contributions of G. N. Lewis and N. V. Sidgwick to the theory of chemical bonding. 

One of the most important types of chemical reactions is the acid-base reaction. However, the definition of which species constitute acids or bases has evolved over the years as the breadth of known chemical reactions has continued to proliferate. For this reason, it is necessary to first introduce the more common historical definitions of acids and bases so that we may better understand how they each fit into the lexicon of chemical reactivity. Just as there were several complimentary models to facilitate our understanding of chemical bonding, so too there are numerous definitions of what it means to be an acid or a base. Which of these definitions we choose will depend on the complexity of the specific acid-base interaction at hand. Ultimately, however, every acid-base reaction entails a change in the way that the valence electrons are arranged in the atomic or molecular orbitals of the participating species. Therefore, the most modem definition of acid-base chemistry builds upon the MO concepts developed in previous chapters and provides the context for a natural continuation of that discussion. 

The theories of bonding in coordination compounds [3] have evolved subsequent to Werner s coordination theory (1893). Werner introduced the concept of primary and secondary valency, explaining the formation of the coordination compounds. The 18-electron rule, stating that the stable complexes with low formal oxidation states of metal ions should have 18 bonding electrons around the metal ion, became an important beginning point toward the study of the stabihty of the complexes. The 18-electron rule is significant in modem coordination chemistry as it is also supported by the molecular orbital theory. However, a smaller number of complexes with metals in low oxidation states restrict its wide applicability. An important advance in the theories of bonding in coordination compounds was the introduction of... 

Indeed, chemists think of atoms as the building blocks of molecules (and their assemblies), whereas the physically rooted Schrodinger equation thinks of molecules in terms of electrons and nuclei. Another example of such dislocation is the computationally convenient molecular orbital theory versus the chemically more intuitive valence bond theory. In this chapter we will introduce QCT, starting with QTAIM [2, 17, 18]. This theory will serve as a tool to bridge the gap between the numerical emptiness of modem wave functions and the wealth of chemical concepts. In an ideal world, chemical insight can indeed be safely extracted from modem wave functions. If this extraction persistently fails for a chemical concept such as aromaticity, for example, then the concept should be modified or abandoned. 

Several methods of quantitative description of molecular structure based on the concepts of valence bond theory have been developed. These methods employ orbitals similar to localized valence bond orbitals, but permitting modest delocalization. These orbitals allow many fewer structures to be considered and remove the need for incorporating many ionic structures, in agreement with chemical intuition. To date, these methods have not been as widely applied in organic chemistry as MO calculations. They have, however, been successfully applied to fundamental structural issues. For example, successful quantitative treatments of the structure and energy of benzene and its heterocyclic analogs have been developed. It remains to be seen whether computations based on DFT and modem valence bond theory will come to rival the widely used MO programs in analysis and interpretation of stmcture and reactivity. 

The availability, only, of numerical data for the electron distributions in atoms other than hydrogen and the increasing complexity of that data with the atomic number of the atom, would be a serious limitation on our comprehension of atomic and molecular theory. In Chemistry the orbital is fundamental to the understanding of all the body of data that can be catalogued using the modem Periodic Table. It is an essential concept, too, in modem bonding theory, because general mles can be established, based on orbital interactions. 

The concept that substances are composed of molecules, and molecules are composed of atoms, can be traced back to chemical antiquity. Nevertheless, in modem molecular electronic stmcture theory, the atomic constituents differ appreciably from the immutable, indivisible particles envisioned by the ancients. Of course, the signature properties of an atom are only indirectly linked to the positively charged nucleus, which carries virtually the entire atomic mass but occupies only an infinitesimally small portion of the apparent atomic volume. We now understand the atom to be composed of the surrounding quantum mechanical distribution of electrons that occupy the characteristic set of orbitals associated with the nucleus in question. Finding the atom in a molecular wavefunction therefore reduces (as in Chapter 2) to the problem of finding the atomic orbitals and the associated electronic configuration (number of electrons occupying each available atomic orbital) around each nuclear center. 

However, a localized adaptation of the natural orbital algorithm allows one to similarly describe/civ-center molecular subregions in optimal fashion, corresponding to the localized lone pairs (one-center) and bonds (two-center) of the chemist s Lewis structure picture. The Natural Bond Orbitals (NBOs) that emerge from this algorithm are intrinsic to, uniquely determined by, and optimally adapted to localized description of, the system wavefunction. The compositional descriptors of NBOs map directly onto bond hybridization, polarization, and other freshman-level bonding concepts that underlie the modem electronic theory of valency and bonding. 

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