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ERNEST OR~ANDO LAWRENCE
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MagneticFieldsandDensity .
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t
LBNL-45195
MagneticFieldsandDensityFunctionalTheory
FreddieSalsbury,Jr.
Ph.D.Thesis
Departmentof Chemistry
Universityof California,Berkeley
and
MaterialsSciencesDivision
ErnestOrlandoLawrenceBerkeIeyNationalLaboratory
Universityof California
Berkeley,CA 94720
February1999
i
ThisworkwassupportebdytheDirectorO, fficeofScienceO, fficeofBasicEnergySciencesM, aterials “
SciencesDivisiono,ftheU.S.DepartmenoftEnergyunderContracNto.DE-AC03-76SFOO098.
I
I
I
I
Abstract
Magnetic Fields and Density Functional Theory
by
Freddie Salsbury, Jr.
Doctor of Philosophy in Chemistry
University of California at Berkeley
Professor Alexander Pines
and Professor Robert A. Harris
A major focus of this dissertation is the development of functional for the magnetic
susceptibility and the chemical shielding within the context of magnetic field density
functional theory (BDFT). These functional depend on the electron density in the
absence of the field, which is unlikeany other treatment of these responses.
There have been several advances made within this theory. The first of which
is the development of local density functional for chemical shielding and magnetic
susceptibilities. These are the firstsuch fimctionals everproposed. These parameters
have been studied by constructing functional for the current density and then using
the Biot-Savart equations to obtain the responses. Inorder to examine the advantages
2
and disadvantagesof the local functional, they weretested numericallyonsome small
molecules.
In order to mitigate some of the difficulties encountered with local functional,
nonlocal functional of the electron density were also developed. The consideration
of nonlocal functional led to the examination of the exchange energy inthe presence
of a constant magnetic field. In order to avoid divergences, every other treatment
of the exchange has required the screening of the exchange by correlation. The first
exchange functional in which this divergence was avoided because of the bound state
nature of the electronic system was constructed. Additionally, a conjecture was made
for the form of the full exchange-correlation energy functional. In both instances,
the functional depend on the ground state electron density in the absence of any
magnetic field.
The J, or indirect spin-spin coupling, was‘also examined. Estimates were made
of some.intermolecular xenon J couplings, which are motivating some experimental
work. This estimate was done using BDFT, but the approach was different fi-om
that used for the chemical shielding and the susceptibility as it was a direct energy
treatment, that is, the Biot-Savart integralswere not used.
An investigationwasalsomade intotherecently discovered magnetic field-dependent
quadruple splitting. The physical origin and magnitudes of both the linear and
3
quadratic dependencies on themagneticfieldwereexplained.
Pr;fessor Alexander Pines
and Professor Robert A. Harris
Thesis Committee Chairs
I
MagneticFieldsandDensityFunctionalTheory
“ Copyright@ 1999
by
Freddie Salsbury, Jr.
TheU.S.DepartmenoftEnergyhastherighttousethisdocument
foranypurposewhatsoeveinrcludintgherighttoreproduce
alloranypartthereof.
.
iv
Contents
List of Figures vi
List of Tables vii
1 Introduction to Magnetic Fields 1
l.l The Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 SpinHamiltonian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3 Nuclear Magnetic Resonance Parmeters . . . . . . . . . . . . . . . . 20
Bibliography 32
2 Electronic Structure Theory: An Introduction 34
Bibliography 52
3 Introduction to Density Functional Theory 53
Bibliography 86
4 Local Current Density Functional 88
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.2 The Current Density . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.3 The Gradient Expansion of The Current Density. . . . . . . . . . . . 95
4.4 Atomic Susceptibilities and Shielding. . . . . . . . . . . . . . . . . . 101
4.5 Susceptibilities and Shleldingsfor Hz and (He)z . . . . . . . . . . . . 11O
4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .123
Bibliography 126
5 Hydrogen Chemical Shielding 130
5.1 Introduction and Theory . . . . . . . . . . . . . . . . . . . . . . . . . 130
