Perspectives in electronic structure theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2012
|
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | XIX, 718 S. graph. Darst. |
| ISBN: | 3642201792 9783642201790 9783642201806 |
Internformat
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| 245 | 1 | 0 | |a Perspectives in electronic structure theory |c Roman F. Nalewajski |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2012 | |
| 300 | |a XIX, 718 S. |b graph. Darst. | ||
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| 650 | 4 | |a Quantum chemistry | |
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IMAGE 1
CONTENTS
PART I FOUNDATIONS O F Q U A N T U M MECHANICS
1 SOURCES 3
1.1 EXPERIMENTAL ORIGINS AND OLD QUANTUM THEORY 3
1.2 CLASSICAL-MECHANICAL DESCRIPTION AND A N E E D FOR ITS REVISION IN
GENERALIZED MECHANICS 9
1.3 IMPLICATIONS FROM THE PARTICLE DIFFRACTION EXPERIMENT 12
1.4 PARTICLE SPIN 16
1.5 BIRTH O F MODERN QUANTUM MECHANICS 17
REFERENCES 18
2 MATHEMATICAL APPARATUS 21
2.1 GEOMETRICAL ANALOGIES 2 2
2.2 DIRAC'S VECTOR NOTATION AND DELTA FUNCTION 2 5
2.3 LINEAR OPERATORS AND THEIR ADJOINTS 2 9
2.4 BASIS SET REPRESENTATIONS O F VECTORS AND OPERATORS 3 2
2.5 EIGENVALUE PROBLEM O F LINEAR HERMITIAN OPERATORS 35
2.6 POSITION AND M O M E N T U M REPRESENTATIONS 3 9
2.7 ENERGY REPRESENTATION AND UNITARY TRANSFORMATIONS 4 2
2.8 FUNCTIONAL DERIVATIVES 4 6
REFERENCES 5 0
3 BASIC CONCEPTS AND A X I O M S 51
3.1 /V-ELECTRON W A V E FUNCTIONS AND T H E I R PROBABILISTIC
INTERPRETATION 5 2
3.2 SUPERPOSITION PRINCIPLE, EXPECTATION VALUES, AND
INDISTINGUISHABILITY O F IDENTICAL PARTICLES 5 9
3.3 RESULTS O F PHYSICAL MEASUREMENTS 6 4
3.3.1 CLASSICAL OBSERVABLES IN POSITION AND M O M E N T U M
REPRESENTATIONS 6 4
IX
HTTP://D-NB.INFO/1010389548
IMAGE 2
X CONTENTS
3.3.2 POSSIBLE OUTCOMES O F A SINGLE MEASUREMENT 6 6
3.3.3 EXPECTATION VALUE O F REPEATED MEASUREMENTS AND HEISENBERG
UNCERTAINTY PRINCIPLE 6 8
3.3.4 ENSEMBLE AVERAGES IN M I X E D STATES 71
3.4 ANGULAR M O M E N T U M AND SPIN OPERATORS 7 5
3.5 PICTURES O F T I M E EVOLUTION 7 8
3.6 SCHRODINGER PICTURE: DYNAMICS O F W A V E FUNCTIONS AND DENSITY
OPERATORS 8 0
3.6.1 ENERGY REPRESENTATION AND STATIONARY STATES 8 2
3.6.2 T I M E DEPENDENCE O F EXPECTATION VALUES AND EHRENFEST PRINCIPLE
8 5
3.6.3 PROBABILITY CURRENT AND CONTINUITY EQUATION 8 6
3.7 HEISENBERG AND INTERACTION PICTURES O F QUANTUM DYNAMICS 8 8
REFERENCES 9 1
4 HYDROGEN-LIKE A T O M 9 3
4.1 SEPARATION O F HAMILTONIAN AND CENTER-OF-MASS MOTION 9 3
4.2 FREE MOTION IN SPHERICAL COORDINATES 9 5
4.3 EIGENFUNCTIONS O F ANGULAR M O M E N T U M OPERATORS 9 8
4.4 RADIAL EIGENFUNCTIONS AND ENERGY LEVELS 101
4.5 ORBITAL DEGENERACY AND ELECTRON DISTRIBUTION 104
4.6 ATOMIC UNITS 109
PART II THEORIES O F ELECTRONIC STRUCTURE
5 APPROXIMATING MOLECULAR SCHRODINGER EQUATION 113
5.1 RUDIMENTS O F PERTURBATIONAL AND VARIATIONAL APPROACHES 113
5.1.1 PERTURBATION THEORY 114
5.1.2 VARIATIONAL METHOD 118
5.2 ADIABATIC SEPARATION O F ELECTRONIC AND NUCLEAR MOTIONS 125
5.3 ORBITAL APPROXIMATION O F ELECTRONIC W A V E FUNCTIONS 130
5.4 MATRIX ELEMENTS O F ELECTRONIC HAMILTONIAN IN ORBITAL APPROXIMATION
134
5.5 EXAMPLE: HELIUM ATOM 141
5.5.1 PERTURBATION APPROXIMATION 141
5.5.2 VARIATIONAL ESTIMATES 143
5.6 IDEA O F A PSEUDOPOTENTIAL 144
REFERENCES 147
6 W A V E FUNCTION METHODS 149
6.1 SELF-CONSISTENT FIELD THEORIES 151
6.1.1 HARTREE METHOD 151
6.1.2 HARTREE-FOCK THEORY 155
6.1.3 TRANSITION-STATE CONCEPT 160
IMAGE 3
CONTENTS XI
6.1.4 ANALYTICAL REALIZATION O F HALL AND ROOTHAAN 163
6.1.5 LOCAL PSEUDOPOTENTIAL 166
6.2 BEYOND H F THEORY: ELECTRON C O U L O M B CORRELATION 167
6.2.1 ERRORS IN S C F M O CALCULATIONS 171
6.2.2 STATIC AND DYNAMIC CORRELATION 174
6.2.3 CORRELATION HOLES 180
6.3 CONFIGURATION INTERACTION TECHNIQUES 187
6.3.1 SPECIAL VARIANTS O F LIMITED C I 190
6.3.2 PERTURBATIONAL THEORY O F M0LLER AND PLESSET 193
6.3.3 DENSITY MATRICES AND NATURAL ORBITALS 197
6.4 ELECTRON PAIR THEORIES 2 0 3
6.4.1 ELECTRON PAIRS ON STRONGLY ORTHOGONAL GEMINALS 2 0 5
6.4.2 INDEPENDENT ELECTRON PAIR APPROXIMATION 2 0 8
6.4.3 COUPLED ELECTRON PAIR APPROXIMATIONS 2 1 2
6.5 SECOND-QUANTIZATION REPRESENTATION 2 1 8
6.5.1 FOCK SPACE AND CREATION/ANNIHILATION OPERATORS 2 1 9
6.5.2 CLUSTER EXPANSION O F ELECTRONIC STATES 2 2 8
6.5.3 COUPLED CLUSTER METHOD 2 3 0
6.6 ELEMENTS O F VALENCE B O N D APPROACH 2 3 1
6.6.1 ORIGINS O F V B THEORY 2 3 3
6.6.2 B O N D ENERGIES AND IONIC STRUCTURES 2 3 7
6.6.3 COMPARISON WITH M O THEORY AND A O EXPANSION THEOREM 2 3 9
6.6.4 SEMILOCALIZED A O AND EXTENSION TO POLYATOMIC SYSTEMS 2 4 2
6.6.5 A B INITIO V B CALCULATIONS 2 4 5
REFERENCES 2 5 0
7 DENSITY FUNCTIONAL THEORY 2 5 5
7.1 H O H E N B E R G - K O H N THEORY 2 5 7
7.1.1 FIRST H K THEOREM 2 6 0
7.1.2 SECOND H K THEOREM 2 6 2
7.1.3 REFINEMENTS 2 6 6
7.1.4 FINITE TEMPERATURE AND OPEN SYSTEM EXTENSIONS 2 6 9
7.2 FUNCTIONALS FROM THE UNIFORM SCALING O F THE ELECTRON DENSITY 2 7 7
7.3 K O H N - S H A M THEORY 2 8 0
7.3.1 ORBITAL APPROXIMATION AND ENERGY EXPRESSION 2 8 0
7.3.2 ADIABATIC CONNECTION 2 8 4
7.3.3 K O H N - S H A M - M E R M I N THEORY 2 8 9
7.3.4 D O N O R - A C C E P T O R COMPLEXES 2 9 2
7.3.5 ZERO-TEMPERATURE LIMIT 3 0 0
7.3.6 PHYSICAL INTERPRETATION O F K S EIGENVALUES 3 0 4
7.3.7 CHEMICAL REACTIVITY CONCEPTS 307
7.4 LOCAL DENSITY AND GRADIENT APPROXIMATIONS 3 1 2
IMAGE 4
XII CONTENTS
7.5 ORBITAL-DEPENDENT FUNCTIONALS 3 1 9
7.5.1 OPTIMIZED POTENTIAL METHOD 320
7.5.2 DENSITY-FUNCTIONAL PERTURBATION THEORY 323
7.5.3 A B INITIO D F T 3 2 6
7.6 RUDIMENTS O F ENSEMBLE THEORY FOR EXCITED STATES 328
7.7 DENSITY-MATRIX FUNCTIONAL THEORY 3 3 3
7.8 W E A K MOLECULAR INTERACTIONS IN D F T 338
7.9 TIME-DEPENDENT D F T 348
7.9.1 EXTENSIONS O F H K THEOREMS INTO T I M E DOMAIN 348
7.9.2 LINEAR-RESPONSE FUNCTIONS 3 5 2
7.9.3 EXCITATION ENERGIES 355
7.9.4 VAN DER WAALS INTERACTIONS REVISITED 358
7.10 CONCLUSION 3 6 0
REFERENCES 361
PART III INSIGHTS FROM INFORMATION THEORY
8 ELEMENTS O F INFORMATION THEORY 371
8.1 INTRODUCTION 371
8.2 SHANNON AND FISHER MEASURES O F INFORMATION 375
8.3 ENTROPY DEFICIENCY 377
8.4 DEPENDENT PROBABILITY DISTRIBUTIONS 378
8.5 INFORMATION PROPAGATION IN COMMUNICATION SYSTEMS 3 8 2
8.6 SEVERAL PROBABILITY SCHEMES 385
8.7 VARIATIONAL PRINCIPLES 391
REFERENCES 3 9 2
9 SCHRODINGER EQUATIONS FROM INFORMATION PRINCIPLES 397
9.1 FISHER-INFORMATION DENSITY AND ITS CURRENT 397
9.2 CONTINUITY EQUATIONS AND INFORMATION SOURCE 4 0 0
9.3 PHYSICAL INFORMATION PRINCIPLES GENERATING SCHRODINGER EQUATIONS 4 0
4
9.4 INFORMATION PRINCIPLE FOR ADIABATIC APPROXIMATION 4 0 7
9.5 K O H N - S H A M EQUATIONS FROM INFORMATION RULE 411
REFERENCES 4 1 4
10 ELECTRON DENSITY AS CARRIER O F INFORMATION 4 1 5
10.1 LOCAL ENTROPY-DEFICIENCY (SURPRISAL) ANALYSIS 4 1 5
10.2 DISPLACEMENTS IN ENTROPY DENSITY 4 2 1
10.3 ILLUSTRATIVE APPLICATION TO PROPELLANES 4 2 4
10.4 NONADDITIVE INFORMATION MEASURES 4 2 8
10.5 ELECTRON LOCALIZATION FUNCTION 4 3 0
10.6 CONTRA-GRADIENCE CRITERION FOR LOCATING BONDING REGIONS IN
MOLECULES 4 3 4
10.7 ILLUSTRATIVE APPLICATIONS O F C G PROBE 4 3 9
REFERENCES 4 5 0
IMAGE 5
CONTENTS XLLL
11 BONDED A T O M S F R O M INFORMATION THEORY 4 5 3
11.1 CHEMICAL CONCEPTS 4 5 3
11.2 STOCKHOLDER A T O M S IN MOLECULES 4 5 5
11.3 INFORMATION THEORETIC JUSTIFICATION 4 6 0
11.4 REPRESENTATIVE INFORMATION DENSITIES 4 6 4
11.5 CHARGE SENSITIVITIES O F STOCKHOLDER A I M 4 6 9
REFERENCES 4 7 8
12 ORBITAL COMMUNICATION T H E O R Y O F THE CHEMICAL BOND 481
12.1 MOLECULAR COMMUNICATION SYSTEMS 4 8 2
12.2 INFORMATION CHANNELS IN ATOMIC ORBITAL RESOLUTION 4 8 4
12.3 ENTROPY/INFORMATION DESCRIPTORS O F B O N D COMPONENTS 4 8 8
12.4 TWO-ORBITAL MODEL O F CHEMICAL B O N D 4 9 0
12.5 ADDITIVE AND NONADDITIVE COMPONENTS O F INFORMATION CHANNELS 4 9 1
12.6 QUANTUM CONDITIONING O F ORBITAL SUBSPACES AND CONDITIONAL A O
EVENTS 4 9 4
12.7 FLEXIBLE INPUT APPROACH 5 0 0
12.8 LOCALIZED BONDS IN DIATOMIC FRAGMENTS 5 0 2
12.9 MANY- ORBITAL EFFECTS 5 0 9
12.10 THROUGH-SPACE AND THROUGH-BRIDGE B O N D COMPONENTS 5 1 4
12.10.1 BOND PROJECTIONS AND DENSITY MATRIX 5 1 5
12.10.2 THROUGH-SPACE AND THROUGH-BRIDGE B O N D ORDERS 517
12.10.3 CONDITIONAL PROBABILITIES FOR INFORMATION PROPAGATION 5 2 3
12.10.4 ILLUSTRATIVE APPLICATION TO 7T-ELECTRON SYSTEMS IN BENZENE AND
BUTADIENE 5 2 7
12.10.5 INDIRECT ORBITAL COMMUNICATIONS 531
12.10.6 QUALITATIVE MODEL O F BONDS IN PROPELLANES 5 3 6
12.11 AMPLITUDE CHANNELS AND INTERFERENCE OF ORBITAL COMMUNICATIONS 5 3
8
12.11.1 PROBABILITY SCATTERING STATES AND STATIONARY COMMUNICATION MODES
5 3 9
12.11.2 CASCADE PROBABILITY SCATTERINGS AND THEIR INTERFERENCE 541
12.11.3 IMPLICIT DEPENDENCY ORIGINS O F THROUGH-BRIDGE INTERACTIONS 5 4
3
12.12 CONCLUSION 5 4 9
REFERENCES 5 5 3
PART IV CHEMICAL CONCEPTS FOR MOLECULAR STRUCTURE AND REACTIVITY
13 ALTERNATIVE PERSPECTIVES IN CHEMICAL THEORIES 5 5 7
13.1 SURVEY O F REACTIVITY PHENOMENA AND N E E D FOR CONCEPTUAL
APPROACHES 5 5 8
13.2 CHEMICAL UNDERSTANDING O F MOLECULAR PROCESSES 5 6 4
IMAGE 6
X I V
CONTENTS
13.3 HORIZONTAL AND VERTICAL DISPLACEMENTS O F MOLECULAR
ELECTRONIC STRUCTURE 5 7 2
13.4 CONSTRAINED EQUILIBRIA IN MOLECULAR SUBSYSTEMS AND CHARGE
SENSITIVITIES O F REACTANTS 5 7 6
13.5 TRANSFORMATIONS O F PERTURBATIONS INTO RESPONSES 5 8 2
13.6 ILLUSTRATIVE DESCRIPTION O F BIMOLECULAR REACTIVE SYSTEMS 5 8 5
13.6.1 EQUILIBRIA AND CHARGE SENSITIVITIES O F REACTANTS 5 8 5
13.6.2 IN SITU QUANTITIES IN D O N O R - A C C E P T O R SYSTEMS 5 9 4
13.6.3 IMPLICATIONS O F EQUILIBRIUM AND STABILITY CRITERIA 5 9 7
REFERENCES 6 0 0
14 COUPLING BETWEEN ELECTRONIC AND GEOMETRICAL STRUCTURES 6 0 5
14.1 ELECTRONIC-GEOMETRIC REPRESENTATIONS O F MOLECULAR STATES 6 0 6
14.2 PERTURBATION-RESPONSE RELATIONS IN GEOMETRIC REPRESENTATIONS 6 0 9
14.3 DESCRIPTORS O F ELECTRONIC-GEOMETRIC INTERACTION 6 1 5
14.4 COMPLIANCE FORMALISM AND MINIMUM-ENERGY COORDINATES 617
14.5 ILLUSTRATIVE APPLICATION TO CONFORMATIONAL CHANGES 621
14.6 USE O F COMPLIANT CONSTANTS AS REACTIVITY INDICES 6 2 5
14.7 MODELING COUPLINGS IN COLLINEAR A T O M - D I A T O M COLLISIONS 6
2 8
14.7.1 DERIVATIVE DESCRIPTORS O F COLLINEAR REACTIVE SYSTEM - 6 2 9
14.7.2 MODELING ELECTRONIC AND NUCLEAR FUKUI FUNCTIONS 6 3 2
14.7.3 SENSITIVITIES FOR COLLECTIVE CHARGE DISPLACEMENTS 637
14.7.4 COUPLINGS ALONG THE MINIMUM-ENERGY PATH 641
14.8 CONCLUSION 6 4 5
REFERENCES 647
15 QUALITATIVE APPROACHES TO REACTIVITY P H E N O M E N A 6 4 9
15.1 INTRODUCTION 6 5 0
15.2 INFORMATION PROBES O F ELEMENTARY REACTION MECHANISMS 6 5 4
15.3 CHEMICAL REACTIVITY INDICES 6 5 6
15.4 INTERNAL AND EXTERNAL EIGENVALUE PROBLEMS 6 6 0
15.5 COMPLEMENTARY DECOUPLING SCHEMES O F MOLECULAR HARDNESS TENSOR 6 6
6
15.6 HARDNESS/SOFTNESS PRINCIPLES IN CHEMISTRY 6 6 8
15.7 CONCLUSION 6 6 9
REFERENCES 671
REFERENCES 675
INDEX 6 9 5 |
| any_adam_object | 1 |
| author | Nalewajski, Roman F. |
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| indexdate | 2024-08-21T00:21:26Z |
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| isbn | 3642201792 9783642201790 9783642201806 |
| language | English |
| lccn | 2011934249 |
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| spelling | Nalewajski, Roman F. Verfasser aut Perspectives in electronic structure theory Roman F. Nalewajski Berlin [u.a.] Springer 2012 XIX, 718 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Quantum chemistry Molecular structure Quantenchemie (DE-588)4047979-1 gnd rswk-swf Quantenchemie (DE-588)4047979-1 s DE-604 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3681255&prov=M&dok_var=1&dok_ext=htm Inhaltstext DE-601 pdf/application http://www.gbv.de/dms/tib-ub-hannover/653822634.pdf Inhaltsverzeichnis DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025416534&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nalewajski, Roman F. Perspectives in electronic structure theory Quantum chemistry Molecular structure Quantenchemie (DE-588)4047979-1 gnd |
| subject_GND | (DE-588)4047979-1 |
| title | Perspectives in electronic structure theory |
| title_auth | Perspectives in electronic structure theory |
| title_exact_search | Perspectives in electronic structure theory |
| title_full | Perspectives in electronic structure theory Roman F. Nalewajski |
| title_fullStr | Perspectives in electronic structure theory Roman F. Nalewajski |
| title_full_unstemmed | Perspectives in electronic structure theory Roman F. Nalewajski |
| title_short | Perspectives in electronic structure theory |
| title_sort | perspectives in electronic structure theory |
| topic | Quantum chemistry Molecular structure Quantenchemie (DE-588)4047979-1 gnd |
| topic_facet | Quantum chemistry Molecular structure Quantenchemie |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3681255&prov=M&dok_var=1&dok_ext=htm http://www.gbv.de/dms/tib-ub-hannover/653822634.pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025416534&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT nalewajskiromanf perspectivesinelectronicstructuretheory |