Molecules and atoms

The names and symbols recommended here are in agreement with those recommended by IUPAP [4] and ISO [5.j]. Additional quantities and symbols used in atomic, nuclear and plasma physics can be found in [4 and 5.k]. 

2nd hyper-polarizability y Vabcd = d3Pa/dEbdEcdEd C4m4J 3 14 

To understand the chanical nature of pyrotechnics and other energetic mixtures, one must begin at the atomic level. Two hundred years of elegant experiments and complex calculations have led to our present picture of the atom as the fundamental 

Particle Location Charge Mass, amu Mass, grams 

Symbols, Atomic Weights, and Atomic Numbers of the Elements 

Element Symbol Atomic Number Atomic Weight, amu  

Element Compound No. of hydrogen atoms No. of bonds No. of unpaired electrons Valency of element 

These electronic interpretations of valency allow us to interpret the phenomenon of variable valency exhibited by many of the transition metal elements. As shown in Fig. 10.5 (Chapter 10), the transition metals exist because the energy of the outer d orbitals lies between the 5 and p energy levels of the next lowest orbitals, and thus are filled up in preference to the p orbitals. Copper, for example (1 s22s22p63s23p63dl04sl), has a single outer s electron available for bonding, giving rise to Cu(I) compounds, but it can also lose one of the 3d electrons, giving rise to Cu(II) compounds. 

Electronegativity (x) is an empirical measure of the tendency of an atom in a molecule to attract electrons. The noble gases, therefore, do not have electronegativity values because they do not easily form molecules. The electronegativity value depends primarily on the element, but also on the oxidation state, i.e., the electronegativity of elements with variable valency can be different for each valency thus that of Fe2+ is different from that of 

There are several ways of defining electronegativity, the simplest being that of Allred and Rochow (1958), which calculates the force experienced by the outer electron from the nucleus using Coulomb s law of electrical attraction  

Upon the heterogeneity imparted to science by its multiple and fortuitous origins is thus superimposed another resembling that of a picture whose various parts are painted by artists of different schools. Judgements may often differ as to which of two conceptions is the more fundamental, so that related theories may sometimes start from very varying premisses. The unaesthetic element of 

It is in this spirit that we shall examine the scope and achievements of physical chemistry, and see what views about the nature of things it refiects. We shall attempt to show the subject in a continuous development which reveals its structure and displays the relation of its parts. We shall therefore not pay much attention to the accidents of history, but we shall be very much concerned with the methods by which an inquiring mind can penetrate the secrets of nature. In this sense the treatment may reasonably be called humanistic. 

We shall find it necessary to keep before us what is meant by a scientific explanation it is in effect the representation of the unknown in terms of the known, but we shall find that the idiom in which the representation is expressible has to suffer some remarkable transformations as we proceed. In the early stages, to employ yet 

Chemistry rests largely upon the theory of atoms and molecules. The idea of an atomic constitution of things was arrived at by the ancients, though the basis of their speculations differed considerably from that of modern chemistry. They thought that there must be a limit to the divisibility of matter, that living creatures must be reproduced from Tiltimate primordial bodies of the appropriate kind, that various natural phenomena such as the penetration of heat and cold depend upon the hidden motions of tiny particles, and so on. It is hardly conceivable that chemistry as we know it could have arisen directly in this way. 

The theory, however, that the sensible qualities of objects could be interpreted in terms of the motion of minute particles of specific kinds was a very great achievement, and itself must have depended upon a long evolution of ideas. We need not enter into this history, but it is important to realize that it must have existed. To distin guish between the material substratum and the qualities for which it is responsible required enlightenment and profound thinking. As far as chemistry is concerned, the process cannot be said really to have been completed until the phlogiston theory disappeared. 

The study of the atom began in the 5th century BC itself. Democritus of Greece, described the atom as that which cannot r be cut up further . Kanada of India defined H the atom as eternal and indestructible and which cannot exist in the free state . 

However, it was more than a thousand years later, that a better understanding of the atom became possible. 

Chemicals are composed of atoms, discrete particles of matter incapable of further subdivision in the course of a chemical reaction. They are the smallest units of an element. Atoms of the same element are identical and equal in weight. All specimens of gold have the same melting point, the same density, and the same resistance to attack by mineral acids. Similarly, all samples of iron of the same history will have the same magnetism. Atoms of different elements have different properties and differ in weight. 

Chemicals are classed as either elements or compounds. The former are substances which cannot be split into simpler chemicals, e.g. copper. There are 90 naturally-occuiTing elements and 17 artificially produced. In nature the atoms of some elements can exist on their own, e.g. gold, whilst in others they link with other atoms of the same element to form molecules, e.g. two hydrogen atoms combine to form a molecule of hydrogen. Atoms of different elements can combine in simple numerical proportions 1 1, 1 2, 1 3, etc. to produce compounds, e.g. copper and oxygen combine to produce copper oxide hydrogen and oxygen combine to produce water. Compounds are therefore chemical substances which may be broken down to produce more than one element. Molecules are the smallest unit of a compound. 

Substances such as brass, wood, sea water, and detergent formulations are mixtures of chemicals. Two samples of brass may differ in composition, colour and density. Different pieces of wood of the same species may differ in hardness and colour. One sample of sea water may contain more salt and different proportions of trace compounds than another. Detergent formulations differ 

Element Symbol Atomic No. electrons No. electrons No. electrons No. electrons in 

Element Symbol Atomic (proton) number No. electrons No. electrons in 1st shell in 2nd shell No. electrons in 3rd shell No. electrons in 4th shell 

The particulate perspective provides a more detailed look at the distinction between chemical and physical changes. Because atoms and molecules are far too small to observe directly or to photograph, typically we will use simplified, schematic drawings to depict them in this book. Often, atoms and molecules will be drawn as circles to depict them and consider their changes. 

The word atom comes from the Creek word atomos meaning indivisible. 

To correctly depict the relative densities of a gas and a liquid, much more space would need to be shown between particles in a gas than can be shown in a drawing like Rgpre 1.3. 

If we observe these two reactions macroscopically, what would we see and how would we know the difference In both cases, we would see bubbles forming, only in one case the bubbles will contain water vapor (gas) and in the other they contain hydrogen. Despite this similarity, we can make observations at the macroscopic level to distinguish between these two possibilities. Example Problem 1.1 poses an experiment that could be set up to make such observation. 

Consider the experimental apparatus shown in the photo to the right. This equipment could be used to test a hypothesis about the chemical composition of the gas in the bubbles that rise from boiling water. What would the observation be if the bubbles were composed of (a) water, (b) hydrogen, or (c) oxygen  

The model of a molecule derived from the circle of research (Fig. 4) must be critically evaluated as to whether it contains the information associated with the emergent behaviour of the molecule. In other words, the question must be asked whether information from the atom level exceeds the logical depth necessary to understand the emergent properties of molecules as they relate to drug research (Kier and Hall, 1992). 

Courtesy of the Royal Swedish Academy of Sciences, Stockholm, Sweden. 

Humphry Davy was not only an exceptionally gifted scientist, he also had remarkable social talents, and it is typical of him that already as a young man his career was sponsored by such luminaries in British science as Sir Joseph Banks, Henry Cavendish and Benjamin Thompson (Count von Rumford). He was also a great communicator, who from an early age made a name for himself in the popularization of science. At the same time, he had an intuition in scientific matters that allowed him to select problems that would prove to be fruitful and important. His work on electrolysis using Alessandro Volta s newly invented pile is a good example of this. He was convinced that in electrolysis the current induced the separation of compounds into their elementary components rather than the synthesis of new substances, as many scientists believed at the time. 

In 1807, Davy made an important discovery when he subjected slightly moistened potash (potassium carbonate) to electrolysis. He noticed that a silvery matter was deposited at the negative pole, while at the positive pole oxygen was liberated. Davy surmised that the silvery matter observed at the negative pole was of a metallic nature and called it potassium. In similar experiments with sodium hydroxide he also characterized the metal sodium. He then went on to electrolyze the so-called alkaline earths, which led to the isolation of magnesium, calcium, strontium and barium. Davy announced his remarkable discoveries in a series of Bakerian Lectures (he gave all in all no less than five such lectures) and his fame 

Root mean square deviation relative to experiment. 

The 5y and 5y6d manifolds of in solid hosts are the object of basic and applied interests. They are made of hundreds of energy levels whose identification requires the knowledge of the corresponding energy levels of the free ion. However, in this case, as in the case of many other actinide ions, no experimental data on the free ion levels are available in the literature. Nor 

Calculated energy levels of the 5f configuration of free Note that all states are 

Term Energy Level Main character Energy double-group levels  

Relative to the 5f - ground term. The values of J are indicated. Relative to the 5f J-9/2 ( l) ground level. Bethe notation is used for these Kramer s doublets. 

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We have two interaction potential energies between uncharged molecules that vary with distance to the minus sixth power as found in the Lennard-Jones potential. Thus far, none of these interactions accounts for the general attraction between atoms and molecules that are neither charged nor possess a dipole moment. After all, CO and Nj are similarly sized, and have roughly comparable heats of vaporization and hence molecular attraction, although only the former has a dipole moment. 

Finally, in the case of solids, there is the difficulty that surface atoms and molecules differ in their properties from one location to another. The discussion in Section VII-4 made clear the variety of surface heterogeneities possible in the case of a solid. Those measurements that depend on the state of surface atoms or molecules will generally be influenced differently by such heterogeneities. Different methods of measuring surface area will thus often not only give different absolute values, but may also give different relative values for a series of solids. 

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. 

Applications of quantum mechanics to chemistry invariably deal with systems (atoms and molecules) that contain more than one particle. Apart from the hydrogen atom, the stationary-state energies caimot be calculated exactly, and compromises must be made in order to estimate them. Perhaps the most useful and widely used approximation in chemistry is the independent-particle approximation, which can take several fomis. Conuiion to all of these is the assumption that the Hamiltonian operator for a system consisting of n particles is approximated by tlie sum... 

At this point, it is appropriate to make some conmrents on the construction of approximate wavefiinctions for the many-electron problems associated with atoms and molecules. The Hamiltonian operator for a molecule is given by the general fonn... 

For many-electron systems such as atoms and molecules, it is obviously important that approximate wavefiinctions obey the same boundary conditions and symmetry properties as the exact solutions. Therefore, they should be antisynnnetric with respect to interchange of each pair of electrons. Such states can always be constmcted as linear combinations of products such as... 

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. 

Karplus M and Porter R N 1970 Atoms and Molecules an Introduction for Students of Physical Chemistry (Reading, MA Addison-Wesley)... 

Parr R G and Yang W 1994 Density-Functional Theory of Atoms and Molecules (New York Oxford)... 

Gordon R J and Rice S A 1997 Active control of the dynamics of atoms and molecules Annu. Rev. Phys. Chem. 48 601... 

Note that the van der Waals forces tliat hold a physisorbed molecule to a surface exist for all atoms and molecules interacting with a surface. The physisorption energy is usually insignificant if the particle is attached to the surface by a much stronger chemisorption bond, as discussed below. Often, however, just before a molecule fonus a strong chemical bond to a surface, it exists in a physisorbed precursor state for a short period of time, as discussed below in section AL7.3.3. 

Adsorbed atoms and molecules can also diflfiise across terraces from one adsorption site to another [33]. On a perfect terrace, adatom diflfiision could be considered as a random walk between adsorption sites, with a diflfiisivity that depends on the barrier height between neighbouring sites and the surface temperature [29]. The diflfiision of adsorbates has been studied with FIM [14], STM [34, 35] and laser-mduced themial desorption [36]. 

The structure of a fluid is characterized by the spatial and orientational correlations between atoms and molecules detemiiued through x-ray and neutron diffraction experiments. Examples are the atomic pair correlation fiinctions (g, g. . ) in liquid water. An important feature of these correlation functions is that... 

We discuss classical non-ideal liquids before treating solids. The strongly interacting fluid systems of interest are hard spheres characterized by their harsh repulsions, atoms and molecules with dispersion interactions responsible for the liquid-vapour transitions of the rare gases, ionic systems including strong and weak electrolytes, simple and not quite so simple polar fluids like water. The solid phase systems discussed are ferroniagnets and alloys. 

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. 

Other atoms and molecules also show similar series of lines, often in the vacuum ultraviolet region, which fit approximately a similar fonuula ... 

Bethe provided the theoretical basis for understanding the scattering of fast electrons by atoms and molecules [3, 4]. We give below an outline of the quantum-mechanical approach to calculating the scattermg cross section. 

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