Study On The Information Entropy Applied To Atomic Systems

It is quantum mechanics that is one of the most important discovery in 20th century. In 1900, Plank proposed the viewpoint of quantum, which is the symbol of the birth of quantum mechanics. In 1927, the Austrian physicist Erwin Schrodinger established the Schrodinger equation. The traditional approaches applied to many-electron systems are solving the Schrodinger equation and describe the properties of systems of many-electron. However, the physical significance of the wavefunction is still not clear and definite up to the present as we know and it cannot be measured directly by experiments. Moreover, it is difficult to solve the Schrodinger equation with electronical number of a system increasing. So many approaching methods have been brought forward and improved, in which more traditional methods are Hartree-Fock Method, Hartree-Fock-Roothaan Method and Hartree-Fock-Slater Method etc. In chapter one, a brief review of these is given, and an introduction is made to the density functional theory and its basis of theory.It was in 1927 , when quantum mechanics was established , Thomas and Fermi proposed a theory of dealing with many-electron atomic systems by using the electron density p(r) of heterogeneous electronical gas almost at the same time, by which an energy functional with electron density as a variable can be obtained. We can calculate the electron density with potential energy and solve the problem of many-electron atomic systems by directly using electron density as a variable to avoid the difficulty to solve the Schrodinger equation, so it is simple and convenient to deal with the problem with Thomas-Fermi (TF) theory. The method is a simple model of local approaching and can not correctly describe the asymptotic behavior of charge density because it ignores the effect of electron correlation, but it firstly puts forth the important density functional theory, which uses electron density as a unique variable and is the primitive density functional theory. Now, it has been applied to calculating atomic and molecular polarization rate, susceptibility, total energy, bond energy etc. DFT is derived from TF theory, but its rigorous theoretical proof was given by Hohenberg and Kohn in 1964. They proved that all properties ofmany-electron systems are a unique functional with electron density. Namely, electron density distribution can offer all information of systems. Electron density is a very important physical parameter that can be observed, and can be directly measured by Compton scatter experiment of high energy x-ray or r-ray of gaseous atoms and molecules. It makes an important role in describing many-electron systems. In 1988, the Nobel Prize was awarded to the American scholar Walter Kohn, who is the founder of the density functional theory.In chapter two, the relation between information entropy and thermodynamic entropy is explained and the link between information entropy and energy is also introduced. Entropy was firstly brought forward by Clausius, which explained the Second Law of thermodynamics with principle of entropy increasing in isolated system. Entropy can express the extent of the dispersal of energy and it is a state function which determines the direction of spontaneous change. Entropy of an isolated system will increase as the system changes from the initial state to the final state, and the microcosmic states number will also increase at the same time. Boltsman principle is a link between entropy and microcosmic states number. He suggested that entropy be a measure of lost information in a system. The explain for entropy was the thought premise which gave birth to information entropy. In 1948, Shannon introduced the explain into the information theory for describing the problem of information transition and for obtaining in quantity and proposed the concept of information entropy. The more ordered the system is, the smaller the entropy become and the more the information contained in the system, vice versa. Information and entropy are supplementary each other, information is ju...