Atomic orbitals modem concepts

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. 

In the 1920s it was found that electrons do not behave like macroscopic objects that are governed by Newton s laws of motion rather, they obey the laws of quantum mechanics. The application of these laws to atoms and molecules gave rise to orbital-based models of chemical bonding. In Chapter 3 we discuss some of the basic ideas of quantum mechanics, particularly the Pauli principle, the Heisenberg uncertainty principle, and the concept of electronic charge distribution, and we give a brief review of orbital-based models and modem ab initio calculations based on them. 

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. 

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. 

What we called the distance of closest approach is what was already known to the ancients as the perihellion of the orbit of a planet around the Sun. Modem chemists know this concept in terms of how close the electrons get to the nucleus of the atom. For collisions under a realistic potential, if the impact parameter is quite low the molecules will get all the way in to the range of the repulsive forces. For high-impact parameters the molecules will only sample the long-range attraction and not penetrate much beyond R = b. But for any impact parameter the colliding particles will feel a mutual force. The only exceptions are potentials whose influence extends over only a finite range, such as a hard-sphere potential. 

This article provides a comprehensive review of modem approaches to analysis of electronic wavefunctions. Diverse definitions of properties such as atomic charges, energies, and valences, bond orders and energies, specialized orbitals, and similarities of atoms and molecules are presented. The merits and shortcomings of these definitions are discussed, Particular emphasis is placed on rigorous interpretive tools which produce quantities that can be regarded as tme quantum mechanical observables. Because of their lack of generality, approaches to quantification of chemical concepts that are limited to certain classes of molecules or electronic stmcture methods (such as n -electron bond orders in Hiickel theory) are not mentioned. 

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. 

The concept of a chemical bond as a localized interaction between two neighboring atoms has been a central part of chemistry for the past century and a half, yet our current description of chemical bonds is still empirical it is a collage of ill-defined and largely incompatible models that are based on assumptions that do not always correspond to physical reality. The ionic and covalent models are mutually incompatible, and both the Lewis and orbital models have serious flaws [3, 4]. They do not conform to modem views of atomic stmcture, and consequently their predictions sometimes fail. While the bond valence theory belongs to this tradition of localized bond models, it is derived from a realistic, though simplified picture of the atom, one that is compatible with more sophisticated atomic descriptions. It can be used to derive powerful and quantitative theorems about chemical stracture. The mles of both the traditional ionic and covalent models can be derived as two special cases of this model (Sects. 5 and 7.2). 

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