The Unreasonable Usefulness of Approximation by Linear Combination

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.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Chemistry

Department dc:contributor.department

Chemistry

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2018

Author dc:creator

• Lewis, Cannada Andrew

Chair dc:contributor.committeechair

• Valeyev, Eduard Faritovich

Committee members dc:contributor.committeemember

• Morris, John R.
• Crawford, T. Daniel
• Troya, Diego

• Electronic Structure
• Data-Sparsity
• Tensor
• Reduced Scaling

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

vt_gsexam:15337

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/83866