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Fast Algorithms for Exact Exchange.

Manzer, Samuel Fenton.

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Fast Algorithms for Exact Exchange.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Fast Algorithms for Exact Exchange./
Author:	Manzer, Samuel Fenton.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2016,
Description:	112 p.
Notes:	Source: Dissertation Abstracts International, Volume: 78-03(E), Section: B.
Contained By:	Dissertation Abstracts International78-03B(E).
Subject:	Quantum physics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10150778
ISBN:	9781369055436

Fast Algorithms for Exact Exchange.
Manzer, Samuel Fenton.

Fast Algorithms for Exact Exchange. - Ann Arbor : ProQuest Dissertations & Theses, 2016 - 112 p.

Source: Dissertation Abstracts International, Volume: 78-03(E), Section: B.

Thesis (Ph.D.)--University of California, Berkeley, 2016.

This thesis describes several new theoretical developments that facilitate the computation of the exact exchange energy, a vital component of accurate molecular simulations. The primary technique on which these developments are based is the resolution of the identity approximation, particularly the pair atomic resolution of the identity approximation (PARI). We prove that computation of exact exchange using the PARI approximation is variationally stable, and provide benchmarks of the performance and accuracy of our implementation. We then show that the most commonly used SCF convergence acceleration algorithm, DIIS, enables the design of a new fast exchange algorithm that we designate as occ-RI-K. Next, we combine the preceding occ-RI-K algorithm with the PARI approximation to create a linear-scaling exact exchange algorithm for the specific case of large weakly-interacting systems. Finally, we discuss our development of a high-level, object-oriented software library for block-sparse tensor operations. This library provides the underlying implementation for all of the algorithms discussed in this thesis.

ISBN: 9781369055436Subjects--Topical Terms:

726746
Quantum physics.

Fast Algorithms for Exact Exchange.
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500 $a Source: Dissertation Abstracts International, Volume: 78-03(E), Section: B.
500 $a Adviser: Martin Head-Gordon.
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520 $a This thesis describes several new theoretical developments that facilitate the computation of the exact exchange energy, a vital component of accurate molecular simulations. The primary technique on which these developments are based is the resolution of the identity approximation, particularly the pair atomic resolution of the identity approximation (PARI). We prove that computation of exact exchange using the PARI approximation is variationally stable, and provide benchmarks of the performance and accuracy of our implementation. We then show that the most commonly used SCF convergence acceleration algorithm, DIIS, enables the design of a new fast exchange algorithm that we designate as occ-RI-K. Next, we combine the preceding occ-RI-K algorithm with the PARI approximation to create a linear-scaling exact exchange algorithm for the specific case of large weakly-interacting systems. Finally, we discuss our development of a high-level, object-oriented software library for block-sparse tensor operations. This library provides the underlying implementation for all of the algorithms discussed in this thesis.
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