若干新材料的B3LYP杂化密度泛函理论研究
摘要
随着计算方法和计算机技术的飞速发展，计算化学在化学研究中已经占有越来越重要的地位。其中，密度泛函方法由于计算量适中、计算精度较高，已成为计算化学领域中最重要的理论方法之一。杂化密度泛函B3LYP在处理团簇小分子体系已经相当准确，尤其受到了化学家们的普遍公认。本论文将B3LYP推广到较复杂的固体、表面等体系的计算当中去。我们研究了一系列不同维度的新型材料(从简单的团簇小分子，纳米管，到固体和固体表面)，研究涉及的材料物性包括几何构型、电子结构、磁学性质和压电性质等方面。
在第一章中，我们简要介绍了密度泛函理论的基本框架和其发展过程。量子化学的发展是密度泛函理论产生的历史背景，我们首先对其进行了简单的回顾。接着，介缁了密度泛函理论的发展过程，从Thomas-Fermi模型，到Hohenberg-Kohn定理，再到Kohn-Sham方程，直到最近的对密度泛函理论的各种修正和扩充。我们介绍了各种常用的交换相关泛函，特别是杂化密度泛函。然后介绍了含时密度泛函理论。最后介绍了一些基于密度泛函理论的常用软件包。
在第二章中，我们研究了两类团簇—V_2O_6和WO_4。团簇的尺寸处于原子和宏观体系之间，本身性质具有多样性和奇异性，是实验和理论研究的一个重要对象。我们用杂化密度泛函B3LYP的方法，研究了团簇V_2O_6，WO_4的一价阴离子和中性分子的几何结构和电子性质。我们用理论计算光电子能谱的两种方案，分别研究了这俩个团簇体系的光电子能谱。我们用M~0方法对V_2O_6~-的光电子能谱做了指认。对于WO_4~-的光电子能谱，我们用M~+方法，即用密度泛函和含时密度泛函方法，对光电子能谱上得到的信息，一一进行了分析，包括绝热电子亲和能和垂直电离能、光电子能谱中的振动结构和激发态性质。所有的计算结果都与实验符合得很好。
Along with the rapid development of computational methods and computer technology, computational chemistry has become more and more important in modern chemistry. Due to its moderate computational consume and high precision, density functional theory (DFT) has become one of the most important methods in computational chemistry. The hybrid density functional B3LYP has been widely applied to calculate molecules and clusters. The great success has been acknowledged especially by chemists. In this dissertation, the B3LYP functional is extended to calculate some other complicated systems such as solid and surface. We study a variety of materials with different dimensions, from simple cluster, nanotube, to solid and surface. The concerned properties include geometry, electronic structure, magnetic order and piezoelectric properties.
In Chapter 1, we introduce the basic concept and progress of DFT. Development of quantum chemistry promotes the establishment of DFT. Thomas-Fermi model is the first theory using density of electrons as the main variable. Theorem of Hohenberg-Kohn is the fundament of DFT and is developed to Kohn-Sham equation, which can be used to perform real calculations. Now, new corrections and extensions, together with developed exchange-correlation functionals, especially the hybrid density functional, have made DFT more accurate and suitable for more systems. We also introduce the basic concept and progress of time-dependent DFT. At the end of this chapter, we introduce some widely used simulation packages.
In Chapter 2, we study two kinds of clusters —V_2O_6 and WO_4. With a size between those of atoms and macroscopical systems, clusters have many
在第一章中，我们简要介绍了密度泛函理论的基本框架和其发展过程。量子化学的发展是密度泛函理论产生的历史背景，我们首先对其进行了简单的回顾。接着，介缁了密度泛函理论的发展过程，从Thomas-Fermi模型，到Hohenberg-Kohn定理，再到Kohn-Sham方程，直到最近的对密度泛函理论的各种修正和扩充。我们介绍了各种常用的交换相关泛函，特别是杂化密度泛函。然后介绍了含时密度泛函理论。最后介绍了一些基于密度泛函理论的常用软件包。
在第二章中，我们研究了两类团簇—V_2O_6和WO_4。团簇的尺寸处于原子和宏观体系之间，本身性质具有多样性和奇异性，是实验和理论研究的一个重要对象。我们用杂化密度泛函B3LYP的方法，研究了团簇V_2O_6，WO_4的一价阴离子和中性分子的几何结构和电子性质。我们用理论计算光电子能谱的两种方案，分别研究了这俩个团簇体系的光电子能谱。我们用M~0方法对V_2O_6~-的光电子能谱做了指认。对于WO_4~-的光电子能谱，我们用M~+方法，即用密度泛函和含时密度泛函方法，对光电子能谱上得到的信息，一一进行了分析，包括绝热电子亲和能和垂直电离能、光电子能谱中的振动结构和激发态性质。所有的计算结果都与实验符合得很好。
Along with the rapid development of computational methods and computer technology, computational chemistry has become more and more important in modern chemistry. Due to its moderate computational consume and high precision, density functional theory (DFT) has become one of the most important methods in computational chemistry. The hybrid density functional B3LYP has been widely applied to calculate molecules and clusters. The great success has been acknowledged especially by chemists. In this dissertation, the B3LYP functional is extended to calculate some other complicated systems such as solid and surface. We study a variety of materials with different dimensions, from simple cluster, nanotube, to solid and surface. The concerned properties include geometry, electronic structure, magnetic order and piezoelectric properties.
In Chapter 1, we introduce the basic concept and progress of DFT. Development of quantum chemistry promotes the establishment of DFT. Thomas-Fermi model is the first theory using density of electrons as the main variable. Theorem of Hohenberg-Kohn is the fundament of DFT and is developed to Kohn-Sham equation, which can be used to perform real calculations. Now, new corrections and extensions, together with developed exchange-correlation functionals, especially the hybrid density functional, have made DFT more accurate and suitable for more systems. We also introduce the basic concept and progress of time-dependent DFT. At the end of this chapter, we introduce some widely used simulation packages.
In Chapter 2, we study two kinds of clusters —V_2O_6 and WO_4. With a size between those of atoms and macroscopical systems, clusters have many
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