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Current-Constrained Reduced-Density-...

Raeber, Alexandra Elizabeth.

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Current-Constrained Reduced-Density-Matrix Theory for Molecular Conductivity.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Current-Constrained Reduced-Density-Matrix Theory for Molecular Conductivity./
Author:	Raeber, Alexandra Elizabeth.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2020,
Description:	87 p.
Notes:	Source: Dissertations Abstracts International, Volume: 82-04, Section: B.
Contained By:	Dissertations Abstracts International82-04B.
Subject:	Chemistry. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28031531
ISBN:	9798672127873

Current-Constrained Reduced-Density-Matrix Theory for Molecular Conductivity.
Raeber, Alexandra Elizabeth.

Current-Constrained Reduced-Density-Matrix Theory for Molecular Conductivity. - Ann Arbor : ProQuest Dissertations & Theses, 2020 - 87 p.

Source: Dissertations Abstracts International, Volume: 82-04, Section: B.

Thesis (Ph.D.)--The University of Chicago, 2020.

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

In this work, I study a variety of problems in electronic structure from a reduced density matrix perspective. In Chapter 2, I describe an extension of the current-constrained density matrix theory from its two-electron reduced density-matrix (2-RDM) formulation to a one-electron reduced density matrix (1-RDM) formulation. I demonstrate the current-constrained 1-RDM method through the computation of the theoretical, intrinsic resistance of acenes and phenacenes. In Chapter 3, I use reduced density matrix theory to study the electronic structure and conductivity of cyclo[18]carbon and its boron nitride analogue. I use the current-constrained matrix (1-RDM) theory to compute the molecular conductance in two cases: (1) conductance in the plane of the molecule and (2) conductance around the molecular ring as potentially driven by a magnetic field through the molecule's center. Off-diagonal long-range order (ODLRO) in the two-electron reduced density matrix (2-RDM) has long been recognized as a mathematical characteristic of conventional superconductors. The large eigenvalue of the 2-RDM has been shown to be a useful measure of this long-range order. In Chapter 4, I show that the cumulant 2-RDM also has a large eigenvalue in the limit of ODLRO. The largest eigenvalue of the cumulant 2-RDM is bounded from above by N. The large eigenvalue of the cumulant 2-RDM implies the large eigenvalue of the 2-RDM, and hence, is a natural measure of ODLRO that vanishes in the mean-field limit. In Chapter 5, I propose and implement a universal signature of the van der Waals interactions based on the cumulant part of the two-electron reduced density matrix (2-RDM). Due to the connected property of the cumulant, it can be used to detect the van der Waals interactions between two molecular moieties. In particular, I use the squared Frobenius norm of the cumulant of the 2-RDM, which has been previously shown to provide a size-extensive measure of the electron correlation. I study this signature of van der Waals forces in a collection of small molecules of varying geometries.

ISBN: 9798672127873Subjects--Topical Terms:

516420
Chemistry.
Subjects--Index Terms:

Cumulant density matrix

Current-Constrained Reduced-Density-Matrix Theory for Molecular Conductivity.
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260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2020
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500 $a Source: Dissertations Abstracts International, Volume: 82-04, Section: B.
500 $a Advisor: Mazziotti, David.
502 $a Thesis (Ph.D.)--The University of Chicago, 2020.
506 $a This item must not be sold to any third party vendors.
520 $a In this work, I study a variety of problems in electronic structure from a reduced density matrix perspective. In Chapter 2, I describe an extension of the current-constrained density matrix theory from its two-electron reduced density-matrix (2-RDM) formulation to a one-electron reduced density matrix (1-RDM) formulation. I demonstrate the current-constrained 1-RDM method through the computation of the theoretical, intrinsic resistance of acenes and phenacenes. In Chapter 3, I use reduced density matrix theory to study the electronic structure and conductivity of cyclo[18]carbon and its boron nitride analogue. I use the current-constrained matrix (1-RDM) theory to compute the molecular conductance in two cases: (1) conductance in the plane of the molecule and (2) conductance around the molecular ring as potentially driven by a magnetic field through the molecule's center. Off-diagonal long-range order (ODLRO) in the two-electron reduced density matrix (2-RDM) has long been recognized as a mathematical characteristic of conventional superconductors. The large eigenvalue of the 2-RDM has been shown to be a useful measure of this long-range order. In Chapter 4, I show that the cumulant 2-RDM also has a large eigenvalue in the limit of ODLRO. The largest eigenvalue of the cumulant 2-RDM is bounded from above by N. The large eigenvalue of the cumulant 2-RDM implies the large eigenvalue of the 2-RDM, and hence, is a natural measure of ODLRO that vanishes in the mean-field limit. In Chapter 5, I propose and implement a universal signature of the van der Waals interactions based on the cumulant part of the two-electron reduced density matrix (2-RDM). Due to the connected property of the cumulant, it can be used to detect the van der Waals interactions between two molecular moieties. In particular, I use the squared Frobenius norm of the cumulant of the 2-RDM, which has been previously shown to provide a size-extensive measure of the electron correlation. I study this signature of van der Waals forces in a collection of small molecules of varying geometries.
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650 4 $a Computational chemistry. $3 3350019
650 4 $a Molecular chemistry. $3 1071612
653 $a Cumulant density matrix
653 $a Molecular conductivity
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