A parallel implementation of the density functional method: implementation of the two-component Douglas-Kroll-Hess method and application to relativistic effects in heavy element chemistry
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| Main Author: | |
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| Format: | Thesis Book |
| Language: | English |
| Published: |
1999
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 232 S. graph. Darst. |
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MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV013112623 | ||
| 003 | DE-604 | ||
| 007 | t | ||
| 008 | 000417s1999 d||| m||| 00||| eng d | ||
| 016 | 7 | |a 958850755 |2 DE-101 | |
| 035 | |a (OCoLC)247707739 | ||
| 035 | |a (DE-599)BVBBV013112623 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-91 |a DE-29T |a DE-12 |a DE-188 | ||
| 100 | 1 | |a Mayer, Markus |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a A parallel implementation of the density functional method |b implementation of the two-component Douglas-Kroll-Hess method and application to relativistic effects in heavy element chemistry |c Markus Mayer |
| 264 | 1 | |c 1999 | |
| 300 | |a XII, 232 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 502 | |a München, Techn. Univ., Diss., 1999 | ||
| 650 | 7 | |a Dichtefunktionalformalismus |2 swd | |
| 650 | 7 | |a Parallelverarbeitung |2 swd | |
| 650 | 7 | |a Relativistischer Effekt |2 swd | |
| 655 | 7 | |0 (DE-588)4113937-9 |a Hochschulschrift |2 gnd-content | |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008933240&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-008933240 | |
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| _version_ | 1807323064861458432 |
|---|---|
| adam_text |
CONTENTS
1
INTRODUCTION
1
I
SYMMETRY ADAPTION
OF
MOLECULAR
ORBITALS
IN
POINT
GROUPS
BY
THE
EIGENFUNCTION
METHOD
7
2
BASIC
CONCEPTS
OF
THE
EIGENFUNCTION
METHOD
11
2.1
THE
CSCO
OF
A
GROUP
.
13
2.2
THE
CSCO-II
OF
G
.
18
2.3
THE
REDUCTION
OF
AN
ARBITRARY
INVARIANT
SUBSPACE
OF
G
.
20
2.4
THE
CSCO-III
OF
G
.
21
2.5
IMPLEMENTATION
.
24
2.5.1
SOLVING
THE
CSCO-III
OF
G
.
24
2.5.2
SOLVING
THE
CSCO-II
OF
G
.
29
3
SYMMETRY
ADAPTION
FOR
POINT
GROUPS
33
3.1
SUBGROUP
CHAINS
AND
MULLIKEN
LABELING
.
38
3.2
REAL
AND
PSEUDO-2D
IRREDUCIBLE
REPRESENTATIONS
.
40
3.2.1
PSEUDO-2D
IRREDUCIBLE
REPRESENTATIONS
.
41
3.2.2
-
OBTAINING
REAL
IRREDUCIBLE
REPRESENTATIONS
.
42
4
SYMMETRY
ADAPTION
IN
DOUBLE
POINT
GROUPS
49
4.1
EIGENFUNCTION
METHOD
FOR
DOUBLE
GROUPS
.
50
4.1.1
PROJECTIVE
REPRESENTATIONS
AND
DOUBLE
GROUPS
.
;
.
50
4.1.2
THE
CSCO
OF
THE
REPRESENTATION
GROUP
.
51
4.1.3
IRREDUCIBLE
REPRESENTATION
MATRICES
.
52
4.1.4
REDUCTION
OF
AN
ARBITRARY
INVARIANT
SUBSPACE
.
52
4.2
SYMMETRY
ADAPTION
OF
A
MOLECULAR
BASIS
SET
.
52
4.2.1
LEFT-HAND
PATHWAY:
ANGULAR
MOMENTUM
COUPLING
.
53
4.2.2
RIGHT-HAND
PATHWAY:
EXPLOITING
SPATIAL
SYMMETRY
(ESS)
.
56
IV
CONTENTS
II
RELATIVISTIC
DENSITY
FUNCTIONAL
THEORY
57
5
RELATIVISTIC
HOHENBERG-KOHN
THEORY
59
5.1
DERIVATION
OF
THE
HOHENBERG-KOHN
THEOREM
.
60
5.2
RELATIVISTIC
HAMILTONIANS
.
63
5.2.1
THE
DIRAC-COULOMB
HAMILTONIAN
.
63
5.2.2
THE
QED
HAMILTONIAN
.
64
5.2.3
THE
NO-PAIR
HAMILTONIAN
.
68
6
RELATIVISTIC
KOHN-SHAM-APPROACH
73
6.1
THE
KOHN-SHAM
APPROACH
.
73
6.2
DERIVING
A
TWO-COMPONENT
KOHN-SHAM
EQUATION
.
75
6.2.1
PATHWAY
VIA
A
FOUR-COMPONENT
DENSITY
FUNCTIONAL
.
77
6.2.2
PATHWAY
VIA
A
TWO-COMPONENT
DENSITY
FUNCTIONAL
.
79
6.3
SOLUTION
OF
THE
RELATIVISTIC
KOHN-SHAM
EQUATION
.
82
6.3.1
THE
HAMILTONIAN
WITH
FREE-PARTICLE
PROJECTORS
.
82
6.3.2
THE
PAULI
HAMILTONIAN
.
84
6.3.3
THE
DOUGLAS-KROLL
HAMILTONIAN
.
84
6.4
OBTAINING
A
VARIATIONAL
TOTAL
ENERGY
.
87
7
NONCOLLINEAR
SPIN-DENSITY
FUNCTIONAL
THEORY
89
7.1
ROTATIONAL
INVARIANCE
IN
SPIN
SPACE
AND
DENSITY
FUNCTIONAL
THEORY
.
.
91
7.2
SPIN
POLARIZED
KOHN-SHAM
FORMALISM
.
95
7.3
SYMMETRIES
OF
THE
SPIN
POLARIZED
KOHN-SHAM
HAMILTONIAN
.
97
7.3.1
TIME
REVERSAL
SYMMETRY
.
97
7.3.2
POINT
GROUP
SYMMETRY
.
97
7.4
ATOMIC
CALCULATIONS
.
99
8
THE
TWO-COMPONENT
RLCGTO-DF
METHOD
115
8.1
THE
RELATIVISTIC
LCGTO-DF
APPROACH
.
115
8.1.1
THE
FINITE
BASIS
SET
APPROACH
.
117
8.1.2
SOLUTION
OF
THE
KOHN-SHAM
EQUATIONS
.
120
8.2
VARIATIONAL
KOHN-SHAM
EQUATIONS
.
125
9
IMPLEMENTATION
131
9.1
THE
INTEGRAL
PART
.
131
9.1.1
SYMMETRY
ADAPTION
OF
PRIMITIVE
INTEGRALS
.
132
9.1.2
COMPUTATION
OF
RELATIVISTIC
MATRIX
ELEMENTS
.
136
9.2
THE
NUMERICAL
INTEGRATION
OF
THE
EXCHANGE-CORRELATION
POTENTIAL
.
.
.
147
CONTENTS
V
III
APPLICATIONS
151
10
SPIN-ORBIT
EFFECTS
153
10.1
SPIN-ORBIT
SPLITTINGS
OF
ONE-ELECTRON
LEVELS
.
153
10.2
DIATOMIC
MOLECULES
.
155
10.3
LOW-LYING
STATES
OF
PTH
.
166
10.4
CONCLUSIONS
.
169
11
EFFECTS
OF
RELATIVISTIC
GGA
AND
FINITE
NUCLEI
171
11.1
RELATIVISTIC
GGA
AND
FINITE
NUCLEI
.
YY.
.
.
173
11.2
CALCULATIONS
.
176
11.2.1
GOLD
ATOM
.
177
11.2.2
GOLD
DIATOMICS
.
180
11.3
CONCLUSIONS
.
184
12
BONDING
OF
TRANSITION
METALS
TO
THE
AL(100)
SURFACE
187
12.1
COMPUTATIONAL
DETAILS
.
188
12.2
RESULTS
AND
DISCUSSION
.
190
12.2.1
DIPOLE
MOMENT
CURVES
.
190
12.2.2
CHARGE
DENSITY
ANALYSIS
.
195
12.3
CONCLUSIONS
.
197
IV
SUMMARY
199
13
SUMMARY
201
A
BASIS
SETS
205
B
A
SPECIAL
FUNCTIONAL
DERIVATIVE
219
C
COLLINEARITY
OF
THE
SPIN-DENSITY
IN
THE
NONRELATIVISTIC
OASE
221 |
| any_adam_object | 1 |
| author | Mayer, Markus |
| author_facet | Mayer, Markus |
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| ctrlnum | (OCoLC)247707739 (DE-599)BVBBV013112623 |
| format | Thesis Book |
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| genre | (DE-588)4113937-9 Hochschulschrift gnd-content |
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| id | DE-604.BV013112623 |
| illustrated | Illustrated |
| indexdate | 2024-08-14T01:06:26Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008933240 |
| oclc_num | 247707739 |
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| owner | DE-91 DE-BY-TUM DE-29T DE-12 DE-188 |
| owner_facet | DE-91 DE-BY-TUM DE-29T DE-12 DE-188 |
| physical | XII, 232 S. graph. Darst. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| record_format | marc |
| spelling | Mayer, Markus Verfasser aut A parallel implementation of the density functional method implementation of the two-component Douglas-Kroll-Hess method and application to relativistic effects in heavy element chemistry Markus Mayer 1999 XII, 232 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier München, Techn. Univ., Diss., 1999 Dichtefunktionalformalismus swd Parallelverarbeitung swd Relativistischer Effekt swd (DE-588)4113937-9 Hochschulschrift gnd-content DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008933240&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mayer, Markus A parallel implementation of the density functional method implementation of the two-component Douglas-Kroll-Hess method and application to relativistic effects in heavy element chemistry Dichtefunktionalformalismus swd Parallelverarbeitung swd Relativistischer Effekt swd |
| subject_GND | (DE-588)4113937-9 |
| title | A parallel implementation of the density functional method implementation of the two-component Douglas-Kroll-Hess method and application to relativistic effects in heavy element chemistry |
| title_auth | A parallel implementation of the density functional method implementation of the two-component Douglas-Kroll-Hess method and application to relativistic effects in heavy element chemistry |
| title_exact_search | A parallel implementation of the density functional method implementation of the two-component Douglas-Kroll-Hess method and application to relativistic effects in heavy element chemistry |
| title_full | A parallel implementation of the density functional method implementation of the two-component Douglas-Kroll-Hess method and application to relativistic effects in heavy element chemistry Markus Mayer |
| title_fullStr | A parallel implementation of the density functional method implementation of the two-component Douglas-Kroll-Hess method and application to relativistic effects in heavy element chemistry Markus Mayer |
| title_full_unstemmed | A parallel implementation of the density functional method implementation of the two-component Douglas-Kroll-Hess method and application to relativistic effects in heavy element chemistry Markus Mayer |
| title_short | A parallel implementation of the density functional method |
| title_sort | a parallel implementation of the density functional method implementation of the two component douglas kroll hess method and application to relativistic effects in heavy element chemistry |
| title_sub | implementation of the two-component Douglas-Kroll-Hess method and application to relativistic effects in heavy element chemistry |
| topic | Dichtefunktionalformalismus swd Parallelverarbeitung swd Relativistischer Effekt swd |
| topic_facet | Dichtefunktionalformalismus Parallelverarbeitung Relativistischer Effekt Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008933240&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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