Computational methods in solid-state numerical quantum chemistry

The application of computational quantum chemistry towards the design of functional materials has been identified as one of the grand challenges in the art of high performance computing, offering substantial benefit to those who are able to make progress in the art and to those who are able to utilize the results of such techniques on a production scale economic setting.; Molecular modeling in particular is a computational technique employed to evaluate potentially interesting atomic structures and chemical processes prior to their fabrication. This technique allows the evaluation of material design properties and features at a fraction of the cost involved in real fabrication. Molecular modeling is of particular interest in connection with modern nanostructure material processing, such as semiconductor fabrication, where it permits the rapid exploration and optimization of new processing routes prior to their actual physical implementation.; In the past, efforts to obtain reasonable predictions of molecular processes at the scale of industrial technology have been obstructed by the lack of efficient numerical procedures to evaluate the electron-electron correlation energy within these structures. The choice is either to rely on empirical estimates in the form of an electron density functional, or to severely restrict the scale of structures addressable within a first principle quantum mechanical evaluation.; In the following, a novel approach to the computational evaluation of the electron-electron energy terms is discussed. The approach presents a flexible high-degree spectral expansion of the electron field in terms of a Hermite Polynomial Gaussian basis and overcomes the restrictions imposed by utilizing linear combinations of a-priori defined atomic orbitals. The flexibility gained in a Hermite Polynomial Gaussian representation is of particular interest in modeling solid-state structures where strong electronic correlation effects dominate the structure of the valence space.; An efficient numerical integration method is at the center of enabling a high degree spectral expansion of the electron field for realistic molecular calculations. A novel approach is presented here to project the adjoint components of the electron density matrix onto a local Hilbert-space representation. Subsequently, the electronic correlation integral is evaluated within this projected space. A novel kernel contraction scheme is presented to further reduce the evaluation complexity for correlation integrals with common angular momentum. The application of this contraction scheme results in a substantial new potential for the computational evaluation of molecular electron correlation integrals.