WFU Physics Colloquium

In principle, Schrödinger's equation allows us to determine the electronic properties of any material made from the elements in the first half of the Periodic Table. But solving the coupled, multi-particle differential equations we encounter in systems of practical interest is impossible. To remedy this, Hohenberg, Kohn, and Sham developed Density Functional Theory (DFT), paving the way for much of computational materials science. It describes the ground state of a non-interacting multi-electron system in the presence of an effective potential field, and is based on a theorem that an exact description of the ground state of the system based only on the electron density is possible. The theory culminates in the Kohn-Sham equations. In 1998, Walter Kohn shared the Nobel Prize for Chemistry for his work on DFT. The last few years have seen enormous improvements in computer capacity and speed. Less obvious are the even greater advancements in the algorithms used for materials simulations. In 1994, Peter Blöchl introduced the Projector Augmented Wave (PAW) method, a generalization of traditional pseudopotential methods. PAW is an ab initio all-electron method that gives accurate electronic structure and molecular dynamics calculations on the basis of DFT. The PAW method is built on projector functions, which allow one to map the complicated electronic wave functions onto more computationally convenient 'pseudo' wave functions, a la pseudopotentials. The key difference between the pseudopotential approach and the PAW method is that in the latter, the transformation is reversible, i.e., in the PAW method we can recover the original wave function. This is extremely advantageous. The research described in this thesis applies Blöchl's PAW method to the F-center in several alkali halide materials, viz., lithium fluoride, lithium bromide, lithium chloride, sodium fluoride, sodium chloride, sodium bromide, and potassium chloride, determining for each, inter alia, the lattice constant, lattice energy, and bulk modulus of the perfect crystal, the relaxed atomic configuration and cohesive energy of the defective crystal, the formation energy of the F-center, and the topology of the F-center electron, including the electron density with comparisons to ENDOR data where available, and the RMS size of the F-center electron.