Quantum mechanics, atomic structure hydrogen atom

The hydrogen atom, containing a single electron, has played a major role in the development of models of electronic structure. In 1913 Niels Bohr (1885-1962), a Danish physicist, offered a theoretical explanation of the atomic spectrum of hydrogen. His model was based largely on classical mechanics. In 1922 this model earned him the Nobel Prize in physics. By that time, Bohr had become director of the Institute of Theoretical Physics at Copenhagen. There he helped develop the new discipline of quantum mechanics, used by other scientists to construct a more sophisticated model for the hydrogen atom. 

In 1926 Erwin Schrodinger (1887-1961), an Austrian physicist, made a major contribution to quantum mechanics. He wrote down a rather complex differential equation to express the wave properties of an electron in an atom. This equation can be solved, at least in principle, to find the amplitude (height) of the electron wave at various points in space. The quantity ip (psi) is known as the wave function. Although we will not use the Schrodinger wave equation in any calculations, you should realize that much of our discussion of electronic structure is based on solutions to that equation for the electron in the hydrogen atom. 

This chapter builds an understanding of atomic structure in four steps. First, we review the experiments that led to our current nuclear model of the atom and see how spectroscopy reveals information about the arrangement of electrons around the nucleus. Then we describe the experiments that led to the replacement of classical mechanics by quantum mechanics, introduce some of its central features, and illustrate them by considering a very simple system. Next, we apply those ideas to the simplest atom of all, the hydrogen atom. Finally, we extend these concepts to the atoms of all the elements of the periodic table and see the origin of the periodicity of the elements. 

The initial purpose of pioneer quantum mechanics was to provide the theoretical framework to account for the structure of hydrogen and the nuclear model of atoms in general. The final result, a quantum theory of atomic structure can be discussed in terms of the time-independent Schrodinger equation, in its most general form... 

Classical electrostatic modeling based on the Coulomb equation demonstrated that the model system chosen could account for as much as 85% of the effect of the protein electric field on the reactants. Several preliminary computations were, moreover, required to establish the correct H-bond pattern of the catalytic water molecule (WAT in Fig. 2.6). Actually, in the crystal structure of Cdc42-GAP complex [60] the resolution of 2.10 A did not enable determination of the positions of the hydrogen atoms. Thus, in principle, the catalytic water molecule could establish several different H-bond patterns with the amino acids of the protein-active site. Both classical and quantum mechanical calculations showed that WAT, in its minimum-energy conformation,... 

The study of atoms and molecules in external fields is a fascinating area of research that has attracted much attention from different areas of science and engineering. Following the influential work of Loudon in 1959, in which he performed the quantum mechanical analysis of the behavior of a one-dimensional hydrogen atom in various Coulomb potentials [1], many studies have been carried out to understand the physics of excitons (hydrogen-like electron-hole pair) and some related systems [2-5]. The discovery of neutron stars and white dwarf stars further motivated rapid development of this field since it stimulated the interest of studying the variation of electronic structure and behavior of atomic and... 

An atomic unit of length used in quantum mechanical calculations of electronic wavefunctions. It is symbolized by o and is equivalent to the Bohr radius, the radius of the smallest orbit of the least energetic electron in a Bohr hydrogen atom. The bohr is equal to where a is the fine-structure constant, n is the ratio of the circumference of a circle to its diameter, and is the Rydberg constant. The parameter a includes h, as well as the electron s rest mass and elementary charge, and the permittivity of a vacuum. One bohr equals 5.29177249 x 10 meter (or, about 0.529 angstroms). 

Abstract—A quantum mechanical treatment of the hydrogen bond by the method of valence structures is described. The interaction of the group A—K and the atom B is characterized by terms which include a donor-acceptor interaction between H and B, the decrease of repulsion between the non-bonded atoms as well as the Coulomb-type attraction. The treatment yields also the explanation of some spectroscopic phenomena of the hydrogen bond. 

The discussion begins with the consideration of diatomic molecules formed by univalent elements—molecules in which there are two atoms held to one another by a single bond. The hydrogen molecule is the only molecule of this kind for which an accurate solution of the SchrSdinger wave equation has been obtained. The approximate quantum-mechanical treatment of more complex molecules has provided interesting information about their electronic structure, but work along these lines has not been sufficiently extensive to permit the... 

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