First Principles Simulations: Development of New Density Functionals and Pseudopotential and Formation Mechanism of Fullerenes

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 YBa _2Cu_3O_7 high-T_{c} 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 C_{60} fullerenes formation. We also analyzed the driving force for carbon clustering and isomerization. In Chapter 7 we study the lattice properties of the YBa_2Cu _3O_7 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.