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First principles simulations: Development of new density functionals and pseudopotential and formation mechanism of fullerenes.

机译：第一性原理模拟：开发新的密度泛函和富勒烯的假电势及形成机理。

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This thesis consists of two parts. Part I deals with the development of first principles methodologies. Part II deals with applications on materials. Part I includes two topics, one is the new density functionals for density functional theory (DFT) calculations and the other is first principles pseudopotentials (PP). Part II also includes two topics, one is the fullerenes formation mechanism and the other is the lattice properties for the {dollar}YBasb2Cusb3Osb7{dollar} high-T{dollar}rmsb{lcub}c{rcub}{dollar} superconductor.; In Chapter 1 we summarize the hierarchy models for materials simulations and review the state-of-the-art tools at various levels of that hierarchy. In Chapter 2, after analyzing the nature of gradient corrected functional for DFT, we propose a new exchange energy functional. The new functional is tested on several atoms and molecules and is found to reproduce the Hartree-Fock eigenvalues to a good accuracy. With the incorporation of correlation energy, the new functionals show promise to be the first theoretical prediction of the energy band gaps from first principles. Chapter 3 and 4 describe a new way of implementing the first principle PP (i.e. ECP). The method was tested on most of the atoms in the periodic table, on molecules and crystals, for both DFT and ab initio theories. The results showed excellent agreement with the standard method at a cost of about 1/16 as much as the latter. In Chapter 5 we study the thermodynamical properties of carbon clusters by DFT and MD simulations. Chapter 6 we described a model of fullerene formation mechanism. Using a combined DFT and MD approach we provided the energetics for a complete pathway of the {dollar}Csb{lcub}60{rcub}{dollar} fullerenes formation. We also analyzed the driving force for carbon clustering and isomerization. In Chapter 7 we study the lattice properties of the {dollar}YBasb2Cusb3Osb7{dollar} superconductor using MD. We derived a ionic-covalent force field from fitting the experimental data. Our FF is able to reproduce the structure and Raman modes accurately. The FF predictions of isotope shifts of Raman frequencies, phonon dispersion spectra, phonon density of states, elastic stiffness constants, and volume thermal expansion are all in fairly good agreement with experiments.
机译：本文分为两部分。第一部分论述第一性原理方法论的发展。第二部分涉及材料的应用。第一部分包括两个主题，一个是用于密度泛函理论（DFT）计算的新密度泛函，另一个是第一原理伪势能（PP）。第二部分还包括两个主题，一个是富勒烯的形成机理，另一个是{Basul} YBasb2Cusb3Osb7 {dollar}高T {dollar} rmsb {lcub} c {rcub} {dollar}超导体的晶格性质。在第1章中，我们总结了用于材料模拟的层次模型，并回顾了该层次的各个级别上的最新工具。在第二章中，在分析了DFT的梯度校正函数的性质之后，我们提出了一种新的交换能量函数。该新功能已在多个原子和分子上进行了测试，并被发现可以很好地重现Hartree-Fock特征值。随着相关能量的结合，新功能显示出有望成为从第一性原理对能带隙的第一个理论预测。第3章和第4章介绍了实现第一个原理PP（即ECP）的新方法。对于DFT和从头算论，该方法已在元素周期表中的大多数原子，分子和晶体上进行了测试。结果表明，与标准方法的一致性很好，成本约为后者的1/16。在第五章中，我们通过DFT和MD模拟研究了碳簇的热力学性质。第6章介绍了富勒烯形成机理的模型。使用DFT和MD的组合方法，我们为{Csb {lcub} 60 {rcub} {dol}}富勒烯形成的完整途径提供了能量学。我们还分析了碳簇化和异构化的驱动力。在第七章中，我们使用MD研究了{Basic} YBasb2Cusb3Osb7 {dollar}超导体的晶格性质。我们通过拟合实验数据得出了一个离子共价力场。我们的FF能够准确再现结构和拉曼模式。拉曼频率，声子弥散谱，声子态密度，弹性刚度常数和体积热膨胀的同位素位移的FF预测与实验相当吻合。

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