Principles Atoms and Molecules

There are a number of fundamental concepts that are essential to know about in order to understand any account of modern chemistiy. This chapter desaibes, in very general terms, the nature of atoms and how they bond together in characteristic arrangements to form mdecuks and other fundamental types of compound. 

Central to any discussion of chemistry is the Periodic Table, that masterpiece of organization formulated in the 19th century principally by Dmitri Mendeleev (1834-1907) and its basis understood in the 20th century once the structures of atoms had been explained. That the table is important is confirmed by its ubiquity it hangs on laboratory and lecture room walls and is printed in every introductory chemistry textbook. There is a version towards the end of this book. Its importance, though, should not be overstated. Working chemists do not gaze 

The Periodic Table portrays an extraordinary feature of matter that the elements are related to one another. We are now so familiar with the table that that feature is easily forgotten. But imagine yourself in an era before the table had been formulated. Then you would have known of the gas oxygen and the yellow solid sulfur, and would almost certainly not have dreamt that there could be any relation between them. You would have known of the largely inert gas nitrogen and the incandescent solid phosphorus, and would not have conceived that they were related. And what about red copper, grey zinc, and liquid mercury A family Surely not How, indeed, is it even possible for different forms of matter to be brothers or cousins Even the concept of family relationships between different substances was hardly conceivable. 

The Periodic Table, though, reveals that the elements are indeed related to one another. Oxygen and sulfur are cousins and stand next to each other in the table so are nitrogen and phosphorus copper, zinc, and mercury are members of the same family and lie together. Their very different appearances 

It was perhaps a little disconcerting for me to mention in Chapter 1 that to understand the structures of atoms it would be necessary to turn to quantum mechanics and all its incomprehensibilities. However, I did also mention that I would distil from that extraordinary theory only concepts and information that concern us. With that restriction in mind, it turns out that atoms have a rather simple structure and that it is quite easy to understand relationships between the elements and to understand, as this account unfolds, why some combinations of atoms are allowed and others not. 

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The purpose of this chapter is to provide an introduction to tlie basic framework of quantum mechanics, with an emphasis on aspects that are most relevant for the study of atoms and molecules. After siumnarizing the basic principles of the subject that represent required knowledge for all students of physical chemistry, the independent-particle approximation so important in molecular quantum mechanics is introduced. A significant effort is made to describe this approach in detail and to coimnunicate how it is used as a foundation for qualitative understanding and as a basis for more accurate treatments. Following this, the basic teclmiques used in accurate calculations that go beyond the independent-particle picture (variational method and perturbation theory) are described, with some attention given to how they are actually used in practical calculations. 

The representation of trial fiinctions as linear combinations of fixed basis fiinctions is perhaps the most connnon approach used in variational calculations optimization of the coefficients is often said to be an application of tire linear variational principle. Altliough some very accurate work on small atoms (notably helium and lithium) has been based on complicated trial functions with several nonlinear parameters, attempts to extend tliese calculations to larger atoms and molecules quickly runs into fonnidable difficulties (not the least of which is how to choose the fomi of the trial fiinction). Basis set expansions like that given by equation (A1.1.113) are much simpler to design, and the procedures required to obtain the coefficients that minimize are all easily carried out by computers. 

In the quantum mechanics of atoms and molecules, both perturbation theory and the variational principle are widely used. For some problems, one of the two classes of approach is clearly best suited to the task, and is thus an established choice. Flowever, in many others, the situation is less clear cut, and calculations can be done with either of the methods or a combination of both. 

Themiodynamic stability requires a repulsive core m the interatomic potential of atoms and molecules, which is a manifestation of the Pauli exclusion principle operating at short distances. This means that the Coulomb and dipole interaction potentials between charged and uncharged real atoms or molecules must be supplemented by a hard core or other repulsive interactions. Examples are as follows. 

The Goeppert-Mayer two- (or multi-) photon absorption, mechanism (ii), may look similar, but it involves intennediate levels far from resonance with one-photon absorption. A third, quasi-resonant stepwise mechanism (iii), proceeds via smgle- photon excitation steps involvmg near-resonant intennediate levels. Finally, in mechanism (iv), there is the stepwise multiphoton absorption of incoherent radiation from themial light sources or broad-band statistical multimode lasers. In principle, all of these processes and their combinations play a role in the multiphoton excitation of atoms and molecules, but one can broadly... 

First-principles models of solid surfaces and adsorption and reaction of atoms and molecules on those surfaces range from ab initio quantum chemistry (HF configuration interaction (Cl), perturbation theory (PT), etc for details see chapter B3.1 ) on small, finite clusters of atoms to HF or DFT on two-dimensionally infinite slabs. In between these... 

In principle, emission spectroscopy can be applied to both atoms and molecules. Molecular infrared emission, or blackbody radiation played an important role in the early development of quantum mechanics and has been used for the analysis of hot gases generated by flames and rocket exhausts. Although the availability of FT-IR instrumentation extended the application of IR emission spectroscopy to a wider array of samples, its applications remain limited. For this reason IR emission is not considered further in this text. Molecular UV/Vis emission spectroscopy is of little importance since the thermal energies needed for excitation generally result in the sample s decomposition. 

Nobel-laureate Richard Feynman once said that the principles of physics do not preclude the possibility of maneuvering things atom by atom (260). Recent developments in the fields of physics, chemistry, and biology (briefly described in the previous sections) bear those words out. The invention and development of scanning probe microscopy has enabled the isolation and manipulation of individual atoms and molecules. Research in protein and nucleic acid stmcture have given rise to powerful tools in the estabUshment of rational synthetic protocols for the production of new medicinal dmgs, sensing elements, catalysts, and electronic materials. 

In 1923. Lewis published a classic book (later reprinted by Dover Publications) titled Valence and the Structure of Atoms and Molecules. Here, in Lewis s characteristically lucid style, we find many of the basic principles of covalent bonding discussed in this chapter. Included are electron-dot structures, the octet rule, and the concept of electronegativity. Here too is the Lewis definition of acids and bases (Chapter 15). That same year, Lewis published with Merle Randall a text called Thermodynamics and the Free Energy of Chemical Substances. Today, a revised edition of that text is still used in graduate courses in chemistry. 

Brickstock, A., and Pople, J. A., Phil. Mag. 44, 705, The spatial correlation of electrons in atoms and molecules. IV. The correlation of electrons on a spherical surface." Two examples—four electrons of the same spin and eight paired electrons—have been studied to compare the effects of the exclusion principle and the interelectronic repulsion. 

Chemical Principles presents the concepts of chemistry in a logical sequence that enhances student understanding. The atoms-first sequence starts with the behavior of atoms and molecules and builds up to more complex properties and interactions. 

Whi comk to chemistry You are about to embark on an extraordinary voyage that will take you to the center of science. Looking in one direction, toward physics, you will see how the principles of chemistry are based on the behavior of atoms and molecules. Looking in another direction, toward biology, you will see how chemists contribute to an understanding of that most awesome property of matter, life. You will be able to look at an everyday object, see in your mind s eye its composition in terms of atoms, and understand how that composition determines its properties. 

Avogadro s principle rather than law, because it is based not on observation alone but also on a model of matter—namely that matter consists of molecules. Even though there is no longer any doubt that matter consists of atoms and molecules, it remains a principle rather than a law. 

Heisenberg, Z. Physik, 33, 879 (1925). Bom and Jordan, ibid., 34, 858 (1925). Born, Heisenberg and Jordan, ibid., 35, 557 (1926) etc. Heisenberg based his theory on the thesis that it should not contain reference to quantities which are in principle unobservable. It is of interest that G. N. Lewis, in 1923, suggested this idea, writing. "we should look for no effects which depend upon the momentary position of any electron in its orbit ("Valence and the Structure of Atoms and Molecules, Chemical Catalog Co., New York, 1923, p. 52). 

In this chapter we give a brief review of some of the basic concepts of quantum mechanics with emphasis on salient points of this theory relevant to the central theme of the book. We focus particularly on the electron density because it is the basis of the theory of atoms in molecules (AIM), which is discussed in Chapter 6. The Pauli exclusion principle is also given special attention in view of its role in the VSEPR and LCP models (Chapters 4 and 5). We first revisit the perhaps most characteristic feature of quantum mechanics, which differentiates it from classical mechanics its probabilistic character. For that purpose we go back to the origins of quantum mechanics, a theory that has its roots in attempts to explain the nature of light and its interactions with atoms and molecules. References to more complete and more advanced treatments of quantum mechanics are given at the end of the chapter. 

The magnetic forces between electrons are negligibly small compared to the electrostatic forces, and they are of no importance in determining the distribution of the electrons in a molecule and therefore in the formation of chemical bonds. The only forces that are important in determining the distribution of electrons in atoms and molecules, and therefore in determining their properties, are the electrostatic forces between electrons and nuclei. Nevertheless electron spin plays a very important role in chemical bonding through the Pauli principle, which we discuss next. It provides the fundamental reason why electrons in molecules appear to be found in pairs as Lewis realized but could not explain. 

Exchanging the coordinates of the two electrons changes the wave function to tlf(x2, yi, z2) Pa(x, yi, Zi), which is the same as before. Since the wave function does not change sign, it is forbidden by the Pauli principle. Hence two electrons with the same spin cannot be described by the same wave function, or, in other words, an orbital cannot contain two electrons with the same spin. As we shall see, this form of the Pauli principle is used in describing atoms and molecules in terms of orbitals. 

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 conclusion that the local hardness is given entirely by the variable parts of the kinetic energy is very logical. It is the kinetic energy increase which limits the distribution of electron density in all systems with fixed nuclei. Since the equilibrium state of atoms and molecules is characterized by minimum energy, they will also be marked by maximum kinetic energy because of the virial theorem. This will put them in agreement with the principles of maximum hardness, for which much evidence exists. 

Photoelectron spectroscopy (PES, a non-mass spectral technique) [87] has proven to be very useful in providing information not only about ionization potentials, but also about the electronic and vibrational structure of atoms and molecules. Energy resolutions reported from PES are in the order of 10-15 meV. The resolution of PES still prevents the observation of rotational transitions, [79] and to overcome these limitations, PES has been further improved. In brief, the principle of zero kinetic energy photoelectron spectroscopy (ZEKE-PES or just ZEKE, also a nonmass spectral technique) [89-91] is based on distinguishing excited ions from ground state ions. 

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