Quantum mechanical bonding 402 Subject

Inorganic chemistry draws its strength from its great practical utility, and this book presents the subject from the standpoint of applications rather than the customary one of quantum mechanical bonding theory. Since the quintessential subject matter is the properties of the 112 known chemical elements and their compounds, we begin with a consideration of the availability of the commonest elements in the Earth s crust (Table 1.1), hydrosphere (i.e., oceans, lakes, rivers, snowfields, ice caps, and glaciers), and atmosphere, along with brief summary of the production and uses of these elements and their compounds. 

Chemistry can be divided (somewhat arbitrarily) into the study of structures, equilibria, and rates. Chemical structure is ultimately described by the methods of quantum mechanics equilibrium phenomena are studied by statistical mechanics and thermodynamics and the study of rates constitutes the subject of kinetics. Kinetics can be subdivided into physical kinetics, dealing with physical phenomena such as diffusion and viscosity, and chemical kinetics, which deals with the rates of chemical reactions (including both covalent and noncovalent bond changes). Students of thermodynamics learn that quantities such as changes in enthalpy and entropy depend only upon the initial and hnal states of a system consequently thermodynamics cannot yield any information about intervening states of the system. It is precisely these intermediate states that constitute the subject matter of chemical kinetics. A thorough study of any chemical reaction must therefore include structural, equilibrium, and kinetic investigations. 

This by no means exhaustive discussion may serve to indicate the value of the information provided by magnetic data relative to the nature of the chemical bond. The quantum-mechanical rules for electron-pair bonds are essential to the treatment. Much further information is provided when these methods of attack are combined with crystal structure data, a topic which has been almost completely neglected in this paper. It has been found that the rules for electron-pair bonds permit the formulation of a set of structural principles for non-ionic inorganic crystals similar to that for complex ionic crystals the statement of these principles and applications illustrating their use will be the subject of an article to be published in the Zeitschrift fur Kristallographie. 

The development of theoretical chemistry ceased at about 1930. The last significant contributions came from the first of the modern theoretical physicists, who have long since lost interest in the subject. It is not uncommon today, to hear prominent chemists explain how chemistry is an experimental science, adequately practiced without any need of quantum mechanics or the theories of relativity. Chemical thermodynamics is routinely rehashed in the terminology and concepts of the late nineteenth century. The formulation of chemical reaction and kinetic theories take scant account of statistical mechanics and non-equilibrium thermodynamics. Theories of molecular structure are entirely classical and molecular cohesion is commonly analyzed in terms of isolated bonds. Holistic effects and emergent properties that could... 

Quantitative estimates of E are obtained the same way as for the collision theory, from measurements, or from quantum mechanical calculations, or by comparison with known systems. Quantitative estimates of the A factor require the use of statistical mechanics, the subject that provides the link between thermodynamic properties, such as heat capacities and entropy, and molecular properties (bond lengths, vibrational frequencies, etc.). The transition state theory was originally formulated using statistical mechanics. The following treatment of this advanced subject indicates how such estimates of rate constants are made. For more detailed discussion, see Steinfeld et al. (1989). 

A simple graphical method of formula ting the independent valence-bond structures for a molecule was discovered by Rumer.1 This method has been extended to permit the secular equation for a set of resonating valence-bond structures to be written without difficulty. Quantum-mechanical treatments of aromatic and conjugated molecules have been carried out by many investigators. The subject of molecular quantum mechanics is too extensive to be reviewed in this book. 

The concepts of hybridisation and resonance are the cornerstones of VB theory. Unfortunately, they are often misunderstood and have consequently suffered from much unjust criticism. Hybridisation is not a phenomenon, nor a physical process. It is essentially a mathematical manipulation of atomic wave functions which is often necessary if we are to describe electron-pair bonds in terms of orbital overlap. This manipulation is justified by a theorem of quantum mechanics which states that, given a set of n respectable wave functions for a chemical system which turn out to be inconvenient or unsuitable, it is permissible to transform these into a new set of n functions which are linear combinations of the old ones, subject to the constraint that the functions are all mutually orthogonal, i.e. the overlap integral J p/ip dT between any pair of functions ip, and op, (i = j) is always zero. This theorem is exploited in a great many theoretical arguments it forms the basis for the construction of molecular orbitals as linear combinations of atomic orbitals (see below and Section 7.1). 

Hammett s view of the scope of the subject is summarized in the rarely mentioned sub-title of his book Reaction Rates, Equilibria, and Mechanisms . His conception of the subject still defines its core, but requires amplifying certain other topics are now usually deemed part of physical organic chemistry. Thus the rationalization of the experimental results of studies of reaction rates, equilibria, and mechanisms involves the application of the electronic theory of the structures and reactions of organic molecules, either in its early forms as developed by Robinson, Ingold, and others on the basis of the electron-pair covalent bond, or in its later forms involving quantum mechanical treatments. 

I was inspired too by Linus Pauling (1901-94), another polymath with humanistic concerns. His Nature of the Chemical Bond (1939) brought a new perspective to theories of molecular structure, and refuted the implication of a popular examination question of the time, Is inorganic chemistry a largely closed and finished subject Pauling s resonance theory, formally based on the quantum-mechanical valence-bond (VB) method for... 

But the point particles of physics ignore shape and size that are the axiomatic attributes of the subject of chemistry, be they atoms, molecules, proteins joined in a supposedly particular configuration by "chemical bonds", or transient lipid vesicles or micelles. And where one object ends and another begins is not so self-evident. The notion of a bond that emerges from a quantum mechanical theory of two interacting atoms is not so obvious if those objects are immersed in a sea of their neighbours, forming a solid or liquid. 

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