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Hierarchical Matrices to Accelerate ...

Berard, Kenneth.

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Hierarchical Matrices to Accelerate Quantum Chemical Calculations.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Hierarchical Matrices to Accelerate Quantum Chemical Calculations./
Author:	Berard, Kenneth.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2023,
Description:	59 p.
Notes:	Source: Masters Abstracts International, Volume: 84-12.
Contained By:	Masters Abstracts International84-12.
Subject:	Computational chemistry. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30425157
ISBN:	9798379683573

Hierarchical Matrices to Accelerate Quantum Chemical Calculations.
Berard, Kenneth.

Hierarchical Matrices to Accelerate Quantum Chemical Calculations. - Ann Arbor : ProQuest Dissertations & Theses, 2023 - 59 p.

Source: Masters Abstracts International, Volume: 84-12.

Thesis (M.S.)--State University of New York at Stony Brook, 2023.

This item must not be sold to any third party vendors.

Configuration interaction (CI) is a powerful numerical method capable of accurately describing electronic correlation, however the computational cost remains too expensive for most chemical systems. In this work, we present a concept to reduce the computational cost of CI calculations by compressing the CI matrix using hierarchical matrices. We studied how compression affects the singlet ground state and lowest energy triplet state's spin, and singlettriplet gap errors for 9 and 12-acene which represent systems with strong electronic correlation. The systems are studied using complete active space CI (CASCI) in 10-10, 12-12, 14-14, and 16- 16 active spaces. All methods in this study were compared to a truncated singular value decomposition (SVD) of the CI matrix as a function of the total storage required for a given accuracy. We propose a hierarchical data structure we call reordered increasing rank leading quarter hierarchical matrices (Reordered IR-LQH-Mat). For a given amount of storage, compression using Reordered IR-LQH-Mat provides more accurate energy and spin expectation values for 9 and 12-acene compared to truncated SVD. Applying this method without permuting{A0}the matrix elements resulted in errors in the triplet wavefunctions compared to truncated SVD. By using the same rank for every block in the hierarchical data structure (not increasing the rank) increased spin contamination for the triplet state wavefunction was seen as compared to truncated SVD. Applying a permutation to the static rank leading quarter hierarchy to achieve better compression resulted in increased singlet and triplet wavefunction spin contamination along with increased triplet energy error. A diagonal dominant hierarchy was assessed, however the method required significantly more storage than SVD to produce accurate results in all metrics. Finally, we present a method of a truncated singular value decomposition of the CI matrix with the replacement of the true diagonal which improves singlet energy and spin errors for an insignificant increase in storage cost.

ISBN: 9798379683573Subjects--Topical Terms:

3350019
Computational chemistry.
Subjects--Index Terms:

Configuration interaction

Hierarchical Matrices to Accelerate Quantum Chemical Calculations.
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035 $a (MiAaPQ)AAI30425157
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100 1 $a Berard, Kenneth. $3 3764336
245 1 0 $a Hierarchical Matrices to Accelerate Quantum Chemical Calculations.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2023
300 $a 59 p.
500 $a Source: Masters Abstracts International, Volume: 84-12.
500 $a Advisor: Levine, Benjamin G.;Simmerling, Carlos.
502 $a Thesis (M.S.)--State University of New York at Stony Brook, 2023.
506 $a This item must not be sold to any third party vendors.
520 $a Configuration interaction (CI) is a powerful numerical method capable of accurately describing electronic correlation, however the computational cost remains too expensive for most chemical systems. In this work, we present a concept to reduce the computational cost of CI calculations by compressing the CI matrix using hierarchical matrices. We studied how compression affects the singlet ground state and lowest energy triplet state's spin, and singlettriplet gap errors for 9 and 12-acene which represent systems with strong electronic correlation. The systems are studied using complete active space CI (CASCI) in 10-10, 12-12, 14-14, and 16- 16 active spaces. All methods in this study were compared to a truncated singular value decomposition (SVD) of the CI matrix as a function of the total storage required for a given accuracy. We propose a hierarchical data structure we call reordered increasing rank leading quarter hierarchical matrices (Reordered IR-LQH-Mat). For a given amount of storage, compression using Reordered IR-LQH-Mat provides more accurate energy and spin expectation values for 9 and 12-acene compared to truncated SVD. Applying this method without permuting{A0}the matrix elements resulted in errors in the triplet wavefunctions compared to truncated SVD. By using the same rank for every block in the hierarchical data structure (not increasing the rank) increased spin contamination for the triplet state wavefunction was seen as compared to truncated SVD. Applying a permutation to the static rank leading quarter hierarchy to achieve better compression resulted in increased singlet and triplet wavefunction spin contamination along with increased triplet energy error. A diagonal dominant hierarchy was assessed, however the method required significantly more storage than SVD to produce accurate results in all metrics. Finally, we present a method of a truncated singular value decomposition of the CI matrix with the replacement of the true diagonal which improves singlet energy and spin errors for an insignificant increase in storage cost.
590 $a School code: 0771.
650 4 $a Computational chemistry. $3 3350019
650 4 $a Theoretical physics. $3 2144760
650 4 $a Chemistry. $3 516420
653 $a Configuration interaction
653 $a Hierarchical matrices
653 $a Electronic correlation
653 $a Singular value decomposition
653 $a Storage
690 $a 0219
690 $a 0753
690 $a 0485
710 2 $a State University of New York at Stony Brook. $b Chemistry. $3 2094227
773 0 $t Masters Abstracts International $g 84-12.
790 $a 0771
791 $a M.S.
792 $a 2023
793 $a English
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30425157