The New Theory of Atoms

De Broglie s wave particle theory has been developed by Heisenberg, Schroedinger, Dirac, and others, with the object of explaining the optical and other properties of atoms. 

The new theory of atomic phenomena is known as wave mechanics or quantum mechanics. Heisenberg s theory and that of Schroedinger were based on different ideas, but they have turned out to be mathematically equivalent. This is a remarkable example of how two entirely different theories, based on quite different assumptions, may lead to identical results, and really be essentially the same. Dirac s theory is a sort of combination and generalization of those of Heisenberg and Schroedinger. — 

The table on page 71 gives some of the wave numbers or waves per centimeter of the light emitted by hydrogen atoms. It is found that these wave numbers are related to each other in a simple way. 

The constant which when multiplied by (1/n2—1/m2) gives the observed wave numbers, is equal to 109678. For example, multiplying this by 1/4—1/25 or 21/100 we get 23032, which is equal to the third number in the second column. 

A theory of these wave numbers was worked out by Bohr before the discovery of wave mechanics or the wave particle theory. Bohr s theory was based on Einstein s idea that light consists of photons and on Rutherford s nucleus theory of the atom. 

---

The topological theory of atoms in molecules <2003MI190> has been employed to calculate the conformational preference of monosubstituted 1,3-oxathianes. The preferred conformer results from an energy balance between the ring and the substituent. This method has proven to be general and is a new technique for conformational analysis. 

Despite his skepticism, Pauli learned the intricacies of matrix mathematics and applied the Heisenberg version of the new quantum mechanics to the hydrogen atom. In less than three weeks, Pauli obtained the same formula that Bohr had obtained in 1913, only this time the route to the formula was a coherent theory—the new theory of quantum mechanics. Herewith, wrote Pauli, it has been demonstrated that the Balmer terms come out directly from the new quantum mechanics. So momentous was this demonstration that the skeptic Pauli became a believer in the matrix mathematical formulation of Born, Heisenberg, and Jordan. 

With these ideas as a foundation for understanding matter, Dalton went on to publish his New System of Chemical Philosophy (vol. 1, part 1,1808, part 2, 1810 vol. 2, 1827). In it, Dalton presented his new theory of atomism. Dalton made four assumptions about atoms and the compounds built up from these ultimate particles. 

Parallel to the exciting reports about new types of hydrogen-hydrogen interactions, a paradigm shift was (and is) taking place in interpretative theoretical chemistry. Since the publication of Bader s classic monograph in 1990 [63], the quantum theory of atoms in molecules (QTAIM) has become a standard tool for the interpretation of theoretical and experimental [65-69] electron density distribution maps. The theory and its applications have been reviewed on a number of occasions by its principal author [63, 70-78] and by others [65-67, 69, 79-84]. A brief reminder of some of the basic concepts of QTAIM will be presented here with the sole purpose of keeping this chapter self-contained, but the interested reader is referred to the previously cited literature for in-depth treatments. 

J.C. Slater (1965) The Quantum Theory of Atomic Structure McGraw-Hill, New York... 

In this chapter, we present a rigorous formulation of the relativistic theory of atomic and molecular stmcture that is both simple and transparent. The resulting algorithms are fast and accurate, and require only modest computational resources, so that they constitute a new and powerful resource for quantum chemists. The formalism of QED is used to write down equations for the... 

We should note that the birth of the quantum theory came about in trying to explain the electronic structure of atoms and the properties of light. It became apparent toward the end of the nineteenth century that the classical laws of physics (classical mechanics as proposed by Isaac Newton in the seventeenth century) could not be used to describe electronic structure. The new theory of quantum mechanics, developed at the beginning of the twentieth century, was a scientific breakthrough that changed the way we view atoms. 

E. P. Wigner, Group Theory and Us Applications to the Quantum Theory of Atomic Spectra (Academic Press, Inc., New York, 1959), Chapters 9, 11, 12. 

Bader R (1994) Atoms in molecules. Oxford University Press, Oxford Matta CF, Boyd RJ (eds) (2007) The quantum theory of atoms in molecules. Wiley, Weinheim Parr RG, Yang W (1989) Density-functional theory of atoms and molecules. Oxford University Press, New York... 

A. Pullman and B. Pullman, in P. O. L6wdin (Ed.), The Quantum Theory of Atoms, Molecules and Solid State, Academic Press, New York, 1966. 

In the year 1902 (while I was attempting to explain to an elementary class in chemistry some of the ideas involved in the periodic law) becoming interested in the new theory of the electron, and combining this idea with those implied in the periodic classification, I formed an idea of the inner structure of the atom which, although it contained certain crudities, I have ever since regarded as representing essentially the arrangement of electrons in the atom. 

Lavoisier s concept of an element provided the foundation for the new version of atomism which appeared in the early years of the nineteenth century. The new theory, known as the chemical atomic theory had as its central tenet that different elements have fundamentally different atoms. In consequence, repeated division of a piece of lead would ultimately yield the last atom of lead, and similarly repeated division of a piece of gold would yield the last atom of gold. If lead and gold were genuine elements, then the atoms of lead and the atoms of gold were different. This explained the different properties of lead and gold, and the transmutation so keenly sought by the alchemists became a theoretical impossibility. 

An important feature of atomic theory is its explanation of a chemical reaction as a rearrangement of the atoms of substances. The reaction of sodium metal with chlorine gas described in the chapter opening involves the rearrangement of the atoms of sodium and chlorine to give the new combination of atoms in sodium chloride. Such a rearrangement of atoms is conveniently represented by a chemical equation, which uses chemical formulas. 

Mandado M, Gonzalez Moa MJ, Mosquera RA (2008) Aromaticity exploring basic chemical concepts with the quanmm theory of atoms in molecules. Nova Science Pubhshers, Inc., New York... 

Bader RFW (1990) Atoms in molecules a quantum theory, the inhanational stales of monographs on chemistry no. 22, Oxford University Press, New Ytnk Popelier PLA (2000) Atoms in molecules an introduction. Pearson Education, Harlow Pendas AM, Blanco MA, Francisco E (2004) Two-electron integrations in the quantum theory of atoms in molecules. J Chem Phys 120 4581-4592... 

Malta CF, Boyd RJ (2007) In the quantum theory of atoms in molecules. Wiley-VCH, New York, pp 1-34... 

Mosquera, R. A., Gonzales-Moa, M. J., Grana, A. M. (2007). Exploring Basic Chemical Concepts with the Quantum Theory of Atoms in Molecules Aromaticy In Hoffman, E. O. (Ed.)ProgrEss in Quantum Chemistry Research, Nova Science Publishers, Inc. New York, Chapter 1, pp. 1-57. 

This chapter is written as a collection of short sections, each built around a thought or an issue, or focusing on explaining one idea or fact. The number of equations in the current chapter has been deliberately suppressed unless where a verbal description alone would obfuscate the content. This decision did not apply to other chapters by the author s hand, that is, one chapter [1] containing a historical account of the development of the quantum theory of atoms in molecules (QTAIM) [2] and new didactic material, a very recent chapter [3] with refreshing and provocative philosophy, as well as an older, lengthy and dense chapter [4], written as an essay-like... 

The last part of this chapter shows that in the public sphere, the periodic system was connected to questions concerning the understanding of nature, its internal connections, and the descent theory. After 1910 the situation regarding the periodic system was changing rapidly as a result of the new understanding of atomic theory and the law of Henry Moseley (1887-1915). This time period, however, is not discussed in this chapter. 

Murrell J N and Bosanac S D 1989 introduction to the Theory of Atomic and Molecular Collisions (New York Wiley)... 

---