Through the exploitation of data-sparsity ---a catch all term for savings gained from a variety of approximations--- it is possible to reduce the computational cost of accurate electronic structure calculations to linear. Meaning, that the total time to solution for the calculation grows at the same rate as the number of particles that are correlated. Multiple techniques for exploiting data-sparsity are discussed, with a focus on those that can be systematically improved by tightening numerical parameters such that as the parameter approaches zero the approximation becomes exact. These techniques are first applied to Hartree-Fock theory and then we attempt to design a linear scaling massively parallel electron correlation strategy based on second order perturbation theory. / Ph. D. / The field of Quantum Chemistry is highly dependent on a vast hierarchy of approximations; all carefully balanced, so as to allow for fast calculation of electronic energies and properties to an accuracy suitable for quantitative predictions. Formally, computing these energies should have a cost that increases exponentially with the number of particles in the system, but the use of approximations based on local behavior, or nearness, of the particles reduces this scaling to low order polynomials while maintaining an acceptable amount of accuracy. In this work, we introduce several new approximations that throw away information in a specific fashion that takes advantage of the fact that the interactions between particles decays in magnitude with the distance between them (although sometimes very slowly) and also exploits the smoothness of those interactions, by factorizing their numerical representation into a linear combination of simpler items. These factorizations, while technical in nature, have benefits that are hard to obtain by merely ignoring interactions between distant particles. Through the development of new factorizations and a careful neglect of interactions between distant particles, we hope to be able to compute properties of molecules in such a way that accuracy is maintained, but that the cost of the calculations only grows at the same rate as the number of particles. It seems that very recently, circa 2015, that this goal may actually soon become a reality, potentially revolutionizing the ability of quantum chemistry to make quantitative predictions for properties of large molecules.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/83866 |
| Date | 05 July 2018 |
| Creators | Lewis, Cannada Andrew |
| Contributors | Chemistry, Valeyev, Eduard Faritovich, Morris, John R., Crawford, T. Daniel, Troya, Diego |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Detected Language | English |
| Type | Dissertation |
| Format | ETD, application/pdf, application/octet-stream, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
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