【作者】 迟绍明；

【导师】 李国宝； 陶建民；

【作者基本信息】 云南师范大学 ， 物理化学， 2004， 硕士

【摘要】 二十世纪最伟大的发现之一就是量子力学。1900年Plank提出了量子论，标志着量子力学的诞生。1926年薛定谔建立了著名的Schrdinger方程，求解薛定谔方程得到波函数，用波函数来描述多电子体系的性质，这是传统的处理多电子体系的基本方法，也称为波函数理论方法。然而至今波函数的物理意义不明确，波函数不能通过实验观测，并且随着电子数的增多方程求解困难较大。为此人们发展和完善许多近似方法，其中比较经典的有由Hartree提出的自洽场方法、Hartree-Forck方法、Hartree-Fock-Roothaan方法及Hartree-Fock-Slater方法等。本文第一章对此作了简述，并简要介绍了密度泛函理论及其理论基础。 就在量子化学建立的1927年，Thomas和Fermi几乎同时提出以非均匀电子气的电子密度ρ()作为变量来处理多电子原子体系的理论，得到一个以电子密度ρ()为变量的能量泛函。我们可以从势能计算电子密度，直接以电子密度作为变量来处理多电子原子体系问题，避开了用薛定谔方程难于求解的波函数，因而用TF(Thomas-Fermi)理论处理具体问题是比较方便和简单的。这种方法是一种过于简单的局域近似模型，虽然它不能正确的描述电荷密度的渐进行为，没有考虑到电子间的相关效应，但是它首先提出了以电子密度为变量的密度泛函的重要方法，是原始的密度泛函理论。目前已被广泛用来计算原子和分子的极化率、磁化率、总能量、键能等。密度泛函理论源于TF理论，但其严格的理论证明却是由Hohenberg和Kohn于1964年提出的。他们证明了多电子体系的所有性质都是电子密度ρ()的唯一泛函，即体系基态的电子密度分布可以给出体系的所有信息。电子密度是一个非常重要的可观测物理量，可以通过气态原子或分子的高能X-射线或γ-射线的Compton散射实验直接测定，在多电子体系的量子力学描述中，它起到十分重要的作用。1998年密度泛函理论的创始人美国学者Kohn获诺贝尔化学奖。 第二章阐述了信息熵与热力学熵的含义及其相互关系，还介绍了信息熵与能量的联系。熵最先于1865年由Clausius提出，以孤立体系熵增加定律的形式表述热力学第二定律。熵可以表示一个物质体系中能量衰竭程度，是用以判断自发过程的一个状态函数。热力学孤立体系由初态到终态后熵将增大，同时系统的微观状态数亦是趋向于增大。玻尔兹曼定理把体系的宏观性质和体系的微观状态联系在一起。玻尔兹曼对熵作微观解释的同时，还把熵和信息云南师范大学硕士学位论文联系起来，提出“嫡是一个系统失去了的‘信息’的度量。”。他的这一解释，为信息嫡的产生提供了思想前提。1948年Sh~on把玻耳兹曼的对嫡的解释引入信息论中，从量的方面来描述信息的传输和提取问题，并提出信息量的概念。一个系统有序程度越高，则嫡就越小，所含的信息量就越大，反之，无序程度越高，则嫡就越大，信息量就越小。信息和嫡是互补的，“信息就是负嫡”，信息量的多少可以用信息嫡来度量。信息嫡作为随机事件不确定度的量度，奠定了现代信息科学的基础。 然而在密度泛函理论的研究中，精确的能量泛函的形式还没有建立，特别是动量空间的泛函形式，而且它主要是处理基态问题。.这就要求人们不断的发展和完善它。在密度泛函理论的界限研究中我们还发现，应用信息论中最大信息嫡原t理研究界限问题也是一种有效的方法。第三章详细阐述了用信息嫡研究原子体系的进展情况。值得指出的是，我们通过Guevarn和Sargar等人建立的信息与电离能的关系，应用我们推导出的信息嫡与坐标和动量期望值的不等式关系，确定了原子体系第一电离与坐标和动量期望值的等式关系，并得到了与实验值较吻合的计算结果，这是计算第一电离能的一种新方法。 在第四章中，介绍了用信息嫡研究原子体系的一些结果应用到分子体系。数值研究表明，对只含有口一轨道的分子，因其分子轨道呈圆柱形对称，所得结果较好。事实上，Sh~on信息嫡也主要适用于密度是球形对称分布的体系。 从信息嫡本身来看，它与量子力学中的不确定关系有着本质的联系，因为信息本身就反映了系统的不确定度。应用信息论中的最大信息嫡原理研究量子化学中的多电子体系是一种很有用的方法，可以预计它的应用将有助于揭示多电子原子和分子的结构，而且它的应用具有重要的科学意义和前景。更多还原

【Abstract】 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更多还原