Date of Degree

9-2021

Document Type

Dissertation

Degree Name

Ph.D.

Program

Chemistry

Advisor

Edward G. Hohenstein

Committee Members

Glen R. Kowach

Louis Massa

Thomas Kurtzman

Subject Categories

Physical Chemistry

Keywords

Coupled Cluster, Low-rank approximation, Algorithms

Abstract

The ultimate goal of electronic structure theory is solving the electronic Schr¨odinger Equation. However, even accurate approximations of solving Schr¨odinger Equation, such as high order coupled cluster theories, require computational efforts that are too demanding to be applied on large chemical systems. This thesis tackles the problem of curse of dimensionality: how to reduce the time complexity of high-accuracy coupled cluster methods in order to accelerate computations of molecular energy. On one hand, we believe that low-rank approximation (i.e. Tensor HyperContraction) of high-order tensors appearing in coupled cluster theory is a promising way to achieve rank-reduced coupled cluster theory. On the other hand, we think that the work of deriving, optimizing and implementing low-rank approximated coupled cluster theory is both tedious and repetitious, and shall be performed by an automatic code engine other than chemists.

In this thesis, we introduce our chemistry equation compiler, Autom: a code engine that is designed for automatically deriving, optimizing and implementing low-rank approximated coupled cluster theories. With Autom, the development of electronic theories is greatly simplified. Autom can easily generate runnable codes in minutes for tensor-algebra based chemistry equations with customized low-rank approximation rules; conventionally, such procedure may take an expert weeks or even months to manually program.

This thesis roughly consists of two parts. In the first part, we aim to cover the lowrank approximation techniques for high-accuracy coupled cluster theories, emphasizing on two new factorization techniques we developed especially for several coupled cluster theories including triple contributions. In the second part, we demonstrate the algorithms of our automatic code engine. We also summarize recent advances of domain specific compilers in Machine Learning community and discuss future directions for compute graph optimization. We believe that this new software infrastructure holds great promise for future chemistry package designs.

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