First principles simulations : development of new density functionals and pseudopotentials and formation mechanism of fullerenes

Citation

Hua, Xinlei (1996) First principles simulations : development of new density functionals and pseudopotentials and formation mechanism of fullerenes. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/r7qa-wt76. https://resolver.caltech.edu/CaltechETD:etd-01072008-115130

Abstract

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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 of atomistic simulations, i.e. quantum mechanics and molecular dynamics simulations.

Part I includes two topics. One is generalized gradient correction for the density functional theory which constitutes Chapter 2. The other is first principle pseudopotentials which is covered in Chapter 3 and 4. Chapter 3 develops the density functional theory version used mostly in solid state physics, while Chapter 4 develops the Ab initio version used mostly in chemistry. Part II also includes two topics. One is the fullerenes formation mechanism which is covered in Chapter 5 and 6. Chapter 5 deals with their thermodynamical properties and Chapter 6 discusses their formation processes. The other is the lattice properties for the [...], superconductor which is covered by Chapter 7. Also, 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.

Predicting the band gap from first principles has been hindered by the complexity of the systems and the flaws in the simplified theories. The most successful first principle theory, i.e. DFT, gives a value about the 2/3 of the measured one. [...] This is partly due to the approximate nature of the functionals used in DFT calculations. It has long been known that HOMOs calculated with LDA, the most commonly used DFT, is far from ionization potential. [...] In Chapter 2, after analyzing the nature of gradient corrected functional for DFT, we proposed a new exchange energy functional. The new functional is tested on several atoms and molecules and found to reproduce the Hartree-Fock eigenvalues to a good accuracy. With the incorporation of correlation energy in DFT, we can hope that the new functional would lead to a new and efficient way of predicting energy band gaps for all the materials from first principles.

All chemistries involve mainly valence electrons. The effect of inner shells, shielding the nucleus Coulomb potential and providing Pauli repulsions to support the valence electrons, can be implemented by a potential called effective core potential (ECP). Since valence electrons of different angular momentum would experience different Pauli repulsion of the core electrons, this ECP is angular momentum dependent. This leads to a nonlocal potential and requires three-center integrals, which scales quadratically with the size of the system. On the other hand, the wave nature of electrons allows us to lower the resolution in describing the potential. By using a set of Gaussian functions to replace real-space grid in representing the ECP, we factorized the three-center integral into a sum of products of two-center integrals. We have found a set of Gaussian functions that gives accuracy of better than [...] for all the elements in the periodic table, sufficient for all ECP calculations. The new method scales linearly with the system size. At 128 atoms, the cost is 1/15 of the old ECP method. This cleared a bottleneck for first principle programs that use ECP to study heavy elements.

Why [...] fullerenes are so stable and how this highly symmetric molecule is formed in the super-heated vapor is the two most fundamental questions in fullerene research. Prompted by the recent observations of the monocyclic ring and bycyclic rings as intermediates, we performed DFT calculations on the ring isomers and fullerene isomers of carbon clusters of various sizes. From it we extracted a force field (FF) for molecular dynamics simulations. This FF is used to calculate the free-energies at different temperatures. Based on our analysis of the physical forces that drive the carbon clustering and isomerization, we describe an evolution process for fullerene formation that is consistent with all the observations so far. With a combined DFT/MD method we are able to provide the energetics for a complete path of fullerene formation. Hint for synthesis improvement are suggested.

High-Tc superconductors are ceramics. To improve their mechanical and electrical properties, we conducted a molecular dynamics simulation for the [...] superconductor. 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.

Thesis Files