Computational methods for understanding the role of electric fields in quantum confined materials
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The invention of pseudopotential-density functional theory to solve for the electronic structure of materials is one of the major successes of modern computational physics. A code based on this formalism was used to solve for the electronic structure of systems with limited dimensionality. The code solves for the electronic structure problem on a real-space grid without the use of an explicit basis. This scheme is particularly well suited for studying molecules, clusters, and nanostructures. The code was applied to assess how an applied electric field changes the properties of two different systems: the change of vibrational modes with the field in molecules or clusters and tuning the electronic gap with the field in 2D materials. Three approaches were employed to study the effect of electric fields on the vibrations of small molecules. The approaches used perturbation theory, a finite field method, and an ab initio molecular dynamics approach. This work provides a better understanding of experimental techniques to probe the local electric field in complex materials as in photovoltaics and biomolecules. The second part of this thesis leverages mixed boundary conditions to study the effects of finite electric fields on two-dimensional materials such as phosphorene. These results demonstrate the ability to tune the band gap and drive semiconductor to metallic transitions in novel two-dimensional materials. This property may enable the creation of nanoscale transistors and sensors to power the next generation of electronic devices.