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Hierarchical Matrices to Accelerate Quantum Chemical Calculations.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Hierarchical Matrices to Accelerate Quantum Chemical Calculations./
Author:	Berard, Kenneth.
Description:	1 online resource (59 pages)
Notes:	Source: Masters Abstracts International, Volume: 84-12.
Contained By:	Masters Abstracts International84-12.
Subject:	Computational chemistry. -
Online resource:	click for full text (PQDT)
ISBN:	9798379683573

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

Hierarchical Matrices to Accelerate Quantum Chemical Calculations. - 1 online resource (59 pages)

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

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

Includes bibliographical references

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 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.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2024

Mode of access: World Wide Web

ISBN: 9798379683573Subjects--Topical Terms:

1190332
Computational chemistry.
Subjects--Index Terms:

Configuration interactionIndex Terms--Genre/Form:

554714
Electronic books.

Hierarchical Matrices to Accelerate Quantum Chemical Calculations.
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502 $a Thesis (M.S.)--State University of New York at Stony Brook, 2023.
504 $a Includes bibliographical references
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 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.
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650 4 $a Theoretical physics. $3 1180318
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653 $a Hierarchical matrices
653 $a Electronic correlation
653 $a Singular value decomposition
653 $a Storage
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