UCLA

We discuss the formulation and use of computational first principles-based methods to study the electronic structure and quantum properties of novel nanomaterials and biomolecules. A helical symmetry-adapted spectral framework, HelicES, is developed for the electronic structure calculation of quasi-one-dimensional structures with imposed or intrinsic twists. Such structures, including nanotubes and nanoribbons, have the potential to exhibit fascinating electronic, optical, and transport properties. We explore the convergence properties of our method, and assess its accuracy by comparison against reference finite difference, transfer matrix method and plane-wave results. Next, we introduce a pseudo-spectral representation of the Laplacian in helical coordinates, which lays down the path towards incorporating self consistency within HelicES by enabling an efficient evaluation of the electrostatic potential. Here too, we provide a comparison between our method and other conventional methods used for the evaluation of this Newtonian potential, such as Ewald summations. Then, in a slightly different line of work involving quantum properties of biomolecules, we present a detailed and comprehensive study on calcium phosphate clusters, most notably, the calcium phosphate trimer (Posner molecule). First, we use ab initio methods to examine the structural ensemble of these clusters. This is essential to then calculate the phosphorus nuclear spin state lifetimes in these molecules, in light of the claim that these spin states in pairs of Posner molecules might be extremely long-lived. Our work, however, conclusively proves that the Posner molecule does not maintain long-lived spin states. Lastly, realizing that many of the frameworks developed and discussed in this work have poor (cubic) scaling with respect to the system size, we also discuss the development of a generalised machine learning framework to overcome this intrinsic limitation of density functional theory (DFT) calculations. We showcase the utility of the uncertainty quantification-enabled method to systems beyond the reach of conventional DFT calculations, i.e. those with millions of atoms. We end with a brief discussion on the ongoing and future applications of our work which may find uses in the study and discovery of novel nanomaterials.