Manual Atoms in Molecules: A Quantum Theory

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Given sufficient information about the present state of part of the Universe, it should be possible, at least in principle, to predict its future behavior as well as its complete history. This capability is known as determinism. For example, solar and lunar eclipses can be predicted centuries ahead, within an accuracy of several seconds.

But interestingly, we can't predict even a couple of days in advance if the weather will be clear enough to view the eclipse!


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The other great pillar of classical physics is Maxwell's theory of electromagnetism. The origin of quantum theory can be marked by three diverse phenomena involving electromagnetic radiation, which could not be adequately explained by the methods of classical physics.

First among these was blackbody radiation, which led to the contribution of Max Planck in Next was the photoelectric effect, treated by Albert Einstein in Third was the origin of line spectra, the hero being Neils Bohr in The remainder of this Chapter will describe the early contributions to the quantum theory by Planck, Einstein and Bohr. It is a matter of experience that a hot object can emit radiation. A piece of metal stuck into a flame can become "red hot. Josiah Wedgwood, the famous pottery designer, noted as far back as that different materials become red hot at the same temperature.

The quantitative relation between color and temperature is described by the blackbody radiation law. Consistent with our experience, the maximum in the distribution, which determines the predominant color, increases with temperature.

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This relation is given by Wien's displacement law, which can be expressed. Intensity distributions of blackbody radiation at three different temperatures.

The origin of blackbody radiation was a major challenge to 19 th Century physics. Lord Rayleigh proposed that the electromagnetic field could be represented by a collection of oscillators of all possible frequencies. By simple geometry, the higher-frequency lower wavelength modes of oscillation are increasingly numerous since it it possible to fit their waves into an enclosure in a larger number of arrangements.

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Rayleigh assumed that every oscillator contributed equally to the radiation the equipartition principle. This agrees fairly well with experiment at low frequencies. But if ultraviolet rays and higher frequencies were really produced in increasing number, we would get roasted like marshmallows by sitting in front of a fireplace! Fortunately, this doesn't happen, and the incorrect theory is said to suffer from an "ultraviolet catastrophe. Max Planck in derived the correct form of the blackbody radiation law by introducing a bold postulate.

He proposed that energies involved in absorption and emission of electromagnetic radiation did not belong to a continuum, as implied by Maxwell's theory, but were actually made up of discrete bundles which he called "quanta. For our development of the quantum theory of atoms and molecules, we need only this simple result and do not have to follow the remainder of Planck's derivation. If you insist, however, the details are given in Supplement 1B. A familiar device in modern technology is the photocell or "electric eye," which runs a variety of useful gadgets, including automatic door openers.

The principle involved in these devices is the photoelectric effect, which was first observed by Heinrich Hertz in the same laboratory in which he discovered electromagnetic waves. Visible or ultraviolet radiation impinging on clean metal surfaces can cause electrons to be ejected from the metal. Such an effect is not, in itself, inconsistent with classical theory since electromagnetic waves are known to carry energy and momentum.

But the detailed behavior as a function of radiation frequency and intensity can not be explained classically. This corresponds to the energy which an electron picks up when accelerated across a potential difference of 1 volt.

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The classical expectation would be that radiation of sufficient intensity should cause ejection of electrons from a metal surface, with their kinetic energies increasing with the radiation intensity. Moreover, a time delay would be expected between the absorption of radiation and the ejection of electrons. The experimental facts are quite different. Photoelectric data for sodium Millikan, The kinetic energy increases linearly with frequency above the threshold but is independent of the radiation intensity.

Increased intensity does, however, increase the number of photoelectrons. Einstein's explanation of the photoelectric effect in appears trivially simple once stated.

Einstein believed that the radiation field actually did consist of quantized particles, which he named photons. Although Planck himself never believed that quanta were real, Einstein's success with the photoelectric effect greatly advanced the concept of energy quantization. Most of what is known about atomic and molecular structure and mechanics has been deduced from spectroscopy.

A continuous spectrum can be produced by an incandescent solid or gas at high pressure. Blackbody radiation, for example, is a continuum.

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An emission spectrum can be produced by a gas at low pressure excited by heat or by collisions with electrons. An absorption spectrum results when light from a continuous source passes through a cooler gas, consisting of a series of dark lines characteristic of the composition of the gas. Frauenhofer between and discovered nearly dark lines in the solar spectrum viewed at high resolution.

It is now understood that these lines are caused by absorption by the outer layers of the Sun. Figure 6. In the solar emission spectrum in the visible range from nm to nm, Fraunhofer lines are observed as vertical black lines at specific spectral positions in the continuous spectrum. Highly sensitive modern instruments observe thousands of such lines. The book is designed for all those who would like to know more about the mathematics and physics of relativistic atomic and molecular theory and who wish to use the computational machinery now available to solve problems in atomic and molecular physics and their applications.

Atoms in Molecules: A Quantum Theory by Richard F.W. Bader - scutrosuppdow.ga

Written by a master of the field, it contains a wealth of information about relativistic atomic and molecular structures. Although the book is particularly tailored towards applications within atomic and molecular theory, several chapters may also be useful for readers whose interests embrace more general aspects of relativistic quantum mechanics.

The Quantum Theory that Connects the Entire Universe

Hogreve, Mathematical Reviews, Issue c. JavaScript is currently disabled, this site works much better if you enable JavaScript in your browser. Physics Quantum Physics. Buy eBook. Buy Hardcover. Buy Softcover.


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FAQ Policy. About this book This book presents a unified approach to modern relativistic theory of the electronic structure of atoms and molecules which will provide experimental and theoretical scientists and graduate students with a range of powerful computational tools for a growing range of physical, chemical, technological and biochemical applications. Show all. From the reviews: "Relativistic Quantum Theory of Atoms and Molecules is a book that should be on the desk of every atomic-physics student and research scientist.

Table of contents 13 chapters Table of contents 13 chapters Relativity in atomic and molecular physics Pages Relativistic wave equations for free particles Pages The Dirac Equation Pages Quantum electrodynamics Pages Analysis and approximation of Dirac Hamiltonians Pages Complex atoms Pages Computation of atomic structures Pages