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Molecular symmetry:

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Main Author:	Willock, David J. (Author)
Format:	Book
Language:	English
Published:	Chichester Wiley 2009
Edition:	1. publ.
Subjects:	Group theory Molecular spectroscopy Molecular structure Molecular theory Symmetry (Physics) Molekülsymmetrie Gruppentheorie Chemische Bindung Chemie Stereochemie Schwingungsspektroskopie
Online Access:	Inhaltsverzeichnis Klappentext
Physical Description:	XII, 426 S. Ill., graph. Darst
ISBN:	9780470853481 9780470853474

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adam_text	Contents Preface xi 1 Symmetry Elements and Operations 1 1.1 Introduction 1 1.2 Symmetry Elements and Operations 6 1.2.1 Proper Rotations: C„ 6 1.2.2 The Plane of Symmetry: σ 9 1.2.3 The Inversion Centre: і 13 1.3 Examples of the Impact of Geometric Symmetry on Chemistry 17 1.3. 1 Oxygen Transfer via Metal Porphyrins 17 1.3.2 Nuclear Magnetic Resonance: Chemical Equivalence 18 1.4 Summary 22 1.5 Self-Test Questions 23 Further Reading 24 2 More Symmetry Operations and Products of Operations 25 2.1 Introduction 25 2.2 Background to Point Groups 25 2.3 Closed Groups and New Operations 26 2.3.1 Products of Operations 26 2.3.2 Fixed Symmetry Elements 29 2.3.3 The Final Missing Operation, Improper Rotations: S„ 31 2.3.4 Equivalences for Improper Rotation Operations 34 2.4 Properties of Symmetry Operations 37 2.4.1 Equivalent Operations and Equivalent Atoms У1 2.4.2 The Inverse of an Operation 38 2.4.3 The Order of the Product; Operations that Commute 39 2.5 Chirality and Symmetry 41 2.6 Summary 42 2.7 Completed Multiplication Tables 43 2.8 Self-Test Questions 44 3 The Point Groups Used with Molecules 45 3.1 Introduction 45 3.2 Molecular Classification Using Symmetry Operations 45 3.3 Constructing Reference Models with Idealized Symmetry 47 vi Contents 3.4 The Nonaxial Groups: C„ Q, C, 48 3.4.1 Examples of Molecules for the Nonaxial Groups: Cs, С,, С, 49 3.5 The Cyclic Groups: Cn, Sn 50 3.5.1 Examples of Molecules for the Cyclic Groups: Cn,Sn 52 3.6 Axial Groups Containing Mirror Planes: Cnh and Cm 55 3.6.1 Examples of Molecules for Axial Groups Containing Mirror Planes: Сл and Cny 58 3.7 Axial Groups with Multiple Rotation Axes: Dn, Dni and Dnh 59 3.7.1 Examples of Axial Groups with Multiple Rotation Axes: Dn, D^andD^ 61 3.8 Special Groups for Linear Molecules: C^ and Ą^ 64 3.9 The Cubic Groups: Tă and Оъ 65 3.10 Assigning Point Groups to Molecules 69 3.11 Example Point Group Assignments 69 3.11.1 Example 1 : Conformations of Cyclohexane 69 3.11.2 Example 2: Six-Coordinate Metal Complexes 72 3.12 Self-Test Questions 73 4 Point Group Representations, Matrices and Basis Sets 75 4.1 Introduction 75 4.2 Symmetry Representations and Characters 75 4.2.1 Water, H2O, C2v 75 4.2.2 Direct Products 79 4.3 Multiplication Tables for Character Representations 81 4.4 Matrices and Symmetry Operations 82 4.5 Diagonal and Off-Diagonal Matrix Elements 85 4.5.1 Ammonia, NH3, C3v 85 4.6 The Trace of a Matrix as the Character for an Operation 87 4.7 Noninteger Characters 88 4.7.1 Boron Trifluoride, BF3, D3h 88 4.8 Reducible Representations 91 4.8.1 Water, H2O, C2v 91 4.9 Classes of Operations 93 4.9.1 [NKCNUf-, D4h 93 4.10 Degenerate Irreducible Representations 9 4.10.1 Ammonia, NHb С 3v 98 4.11 The Labelling of Irreducible Representations ^ 4.12 Summary 102 4.13 Completed Tables 102 4.14 Self-Test Questions 102 Further Reading ЮЗ Reducible and Irreducible Representations 105 5.1 Introduction 105 5.2 Irreducible Representations and Molecular Vibrations * Contents vii 5.3 Finding Reducible Representations 110 5.4 Properties of Point Groups and Irreducible Representations 112 5.5 The Reduction Formula 118 5.5.1 Applying the Reduction Formula 120 5.6 A Complete Set of Vibrational Modes for H2O 122 5.7 Choosing the Basis Set 126 5.7.1 Carbonyl Stretching Modes of ÍFe(CO)s],D3h 126 5.8 The d-Orbitals in Common Transition Metal Complex Geometries 128 5.8.1 Square Planar, D4h 132 5.8.2 Tetrahedral, Tá 137 5.8.3 Octahedral, Oh 142 5.8.4 Trigonal Bipyramidal, D3h 147 5.9 Linear Molecules: Groups of Infinite Order 154 5.10 Summary 161 5.11 Self-Test Questions 162 Applications in Vibrational Spectroscopy 163 6.1 Introduction 163 6.2 Selection Rules 165 6.2.1 Infrared Spectroscopy 165 6.2.2 Infrared Absorption and the Greenhouse Gases 173 6.2.3 Interstellar H2 177 6.2.4 Raman Spectroscopy 177 6.2.5 Comparison of Infrared and Raman Selection Rules 184 6.3 General Approach to Analysing Vibrational Spectroscopy 186 6.3.1 Example: the С—И Stretch Bands of 1 ,4-Difluorobenzene 187 6.4 Symmetry-Adapted Linear Combinations 190 6.5 Normalization 193 6.6 The Projection Operator Method 195 6.6.1 Projection Operator Applied to the С — Η Stretches of 1 ,4-Difluorobenzene 196 6.6.2 The Projection Operator and Degenerate Representations 198 6.7 Linking Results for Symmetry-Inequivalent Sets of Atoms 202 6.7.1 Sets of Atoms Differing in Mass or Chemical Bond Strength 203 6.8 Additional Examples 206 6.8.1 Benzene, D^ 206 6.8.2 The fac and rasr homers of Transition Metal Complexes 212 6.9 Summary 215 6.10 Self-Test Questions 216 Further Reading 217 Symmetry in Chemical Bonding 219 7.1 Introduction 219 7.1.1 Wave Phenomena and Interference 220 7.1.2 The Born Interpretation of the Wavefunction 222 viii Contents 7.2 Bond Energies 225 7.2.1 The Symmetry-Adapted Linear Combinations for the Molecular Orbitals of H2 + and H2 228 7.2.2 The Chemical Bond Energy from Molecular Orbitals 232 7.2.3 The Molecular Orbital Energy 236 7.2.4 Bond Order 238 7.3 The Relative Energies of Hydrogen-Like Atomic Orbitals 239 7.3.1 Radial Behaviour of Atomic Orbitals 239 7.3.2 The Relative Energies of Atomic Orbitals in Different Elements 242 7.3.3 The Relative Energies of Atomic Orbitals from Electronegativity 244 7.4 The Molecules Formed by Other Second-Row Elements with Hydrogen 252 7.4.1 BeH2, Beryllium Hydride 252 7.4.2 ВНЪ, Boron Hydride 253 7.4.3 CHA, Methane 258 7.4.4 NH3, Ammonia 264 7.4.5 H2O, Water 269 7.5 The Second-Row Diatomic Molecules 270 7.5.1 Homonuclear Diatomics 270 7.5.2 Heteronuclear Diatomics of Second-Row Elements 276 7.6 More Complex Polyatomic Molecules 278 7.6.1 Ethene 278 7.7 Metal Complexes 284 7.7.1 Complexes Containing σ -Donor Ligands 284 7.7.2 The John-Teller Effect 287 7.7.3 Complexes Containing Ligand Orbitals of π -Symmetry 291 7.8 Summary 295 7.9 Self-Test Questions 296 Further Reading 297 Appendices Appendix 1 H2O Models for Identifying the Results of Symmetry Operation Products 299 Appendix 2 Assignment of Chiral Centre Handedness using Cahn-Ingold-Prelog Rules 303 Appendix 3 Model of a Tetrahedron and the Related Cube 307 Appendix 4 Model of an Octahedron 313 Contents ix Appendix 5 Matrices and Determinants 317 A5 .1 Matrices as Representations of Symmetry Operators 317 A5.1.1 Products of Matrices 318 A5.1.2 Products of Matrices, Expressed as Summations 319 A5.2 Matrices for Solving Sets of Linear Equations 321 Further Reading 324 Appendix 6 The Mathematical Background to Infrared Selection Rules A6.1 Model Based on Classical Mechanics A6.2 Model Based on Quantum Mechanics A6.3 Excited Vibrational States A6.4 Vibrational Modes for Polyatomic Molecules A6.5 Generalization to Arbitrary Transitions A6.6 Summary of Selection Rules Further Reading Appendix 7 The Franck-Condon Principle Appendix 8 Classical Treatment of Stokes/Anti-Stokes Absorption Appendix 9 The Atomic Orbitals of Hydrogen A9. 1 Choice of Coordinate System A9.2 Separation of Variables A9.3 The Angular Equation A9.4 Physical Interpretation of the Angular Equation Solutions A9.5 Angular Momentum A9.6 The Radial Equation A9.7 The Complete Atomic Orbitals A9.8 Expectation Values A9.9 Real Combinations to Form the Familiar Atomic Orbitals A9. 10 Cartesian Forms of the Real Angular Functions A9. 11 Endnote on Imaginary Numbers Further Reading Appendix 10 The Origin of Chemical Bonding in Hj A10.1 A 10.2 A10.3 A10.4 Chemical Bond Formation H Atom and H+ Cation The Vinal Theorem H2+ Molecule A10.5 Choice of Coordinate System for HÇ: Cylindrical Polar Coordinates 325 325 328 333 335 336 337 338 339 343 345 347 348 349 354 356 359 361 364 367 369 370 373 375 376 376 379 381 383 χ Contents Α10.6 Η/: the Electron Kinetic Energy 386 A10.7 H2+: the Electronic Potential Energy 387 A10.8 The Chemical Bond Formation Energy Based on Rigid Atomic Orbitals 393 A 10.9 Optimal Radial Decay of Molecular Orbitals 396 Further Reading 399 Appendix 11 H2O Molecular Orbital Calculation in C2v Symmetry 401 Further Reading 406 Appendix 12 Character Tables 407 A12.1 Non-Axial Groups 407 A12.2 Axial Groups 407 A12.2J C„ Groups 407 A12.2.2 S„ Groups 408 A12.2.3 Cm Groups 408 A12.2.4 С„ћ Groups 409 A12.2.5 D„ Groups 410 A12.2.6 Вы Groups 411 A12.2.7 Dnh Groups 412 A12.3 Cubic Groups 413 A12.3.1 Tetrahedral, Td 413 A12.3.2 Rotational Subgroup of Td,T 413 A12.3.3 Octahedral, Oh 414 A12.3.4 Rotational Subgroup of О h, О 414 A12.4 Groups for Linear Molecules 414 Index 415 Molecular Symmetry David J. Willock School of Chemistry, Cardiff University, Cardiff, UK Symmetry and group theory provide us with a rigorous method for the description of the geometry of objects by describing the patterns in their structure. In chemistry it is a powerful concept that underlies many apparently disparate phenomena. Symmetry allows us to accurately describe the types of bonding that can occur between atoms or groups of atoms in molecules. It also governs the transitions that may occur between energy levels in molecular systems, leading to a predictive understanding of the absorption properties of molecules and hence their spectra. Molecular Symmetry lays out the formal language used in the area, with illustrative examples of particular molecules throughout. It then applies the ideas of symmetry and group theory to describe molecular structure, bonding in molecules and to consider the implications in spectroscopy. Topics covered include: Symmetry elements Symmetry operations and products of operations Point groups used with molecules Point group representations, matrices and basis sets Reducible and irreducible representations Applications in vibrational spectroscopy Molecular orbital theory of chemical bonding Molecular Symmetry is designed to introduce the subject by combining symmetry with spectroscopy and bonding in a clear and accessible manner. Each chapter ends with a summary of learning points, a selection of self-test questions, and suggestions for further reading. A set of appendices includes templates for paper models which will help students understand symmetry operations and cover key aspects of the material in depth. Molecular Symmetry is a must-have introduction to this fundamental topic for students of chemistry, and will also find a place on the bookshelves of postgraduates and researchers looking for a broad and modern introduction to the subject.
adam_txt	Contents Preface xi 1 Symmetry Elements and Operations 1 1.1 Introduction 1 1.2 Symmetry Elements and Operations 6 1.2.1 Proper Rotations: C„ 6 1.2.2 The Plane of Symmetry: σ 9 1.2.3 The Inversion Centre: і 13 1.3 Examples of the Impact of Geometric Symmetry on Chemistry 17 1.3. 1 Oxygen Transfer via Metal Porphyrins 17 1.3.2 Nuclear Magnetic Resonance: Chemical Equivalence 18 1.4 Summary 22 1.5 Self-Test Questions 23 Further Reading 24 2 More Symmetry Operations and Products of Operations 25 2.1 Introduction 25 2.2 Background to Point Groups 25 2.3 Closed Groups and New Operations 26 2.3.1 Products of Operations 26 2.3.2 Fixed Symmetry Elements 29 2.3.3 The Final Missing Operation, Improper Rotations: S„ 31 2.3.4 Equivalences for Improper Rotation Operations 34 2.4 Properties of Symmetry Operations 37 2.4.1 Equivalent Operations and Equivalent Atoms У1 2.4.2 The Inverse of an Operation 38 2.4.3 The Order of the Product; Operations that Commute 39 2.5 Chirality and Symmetry 41 2.6 Summary 42 2.7 Completed Multiplication Tables 43 2.8 Self-Test Questions 44 3 The Point Groups Used with Molecules 45 3.1 Introduction 45 3.2 Molecular Classification Using Symmetry Operations 45 3.3 Constructing Reference Models with Idealized Symmetry 47 vi Contents 3.4 The Nonaxial Groups: C„ Q, C, 48 3.4.1 Examples of Molecules for the Nonaxial Groups: Cs, С,, С, 49 3.5 The Cyclic Groups: Cn, Sn 50 3.5.1 Examples of Molecules for the Cyclic Groups: Cn,Sn 52 3.6 Axial Groups Containing Mirror Planes: Cnh and Cm 55 3.6.1 Examples of Molecules for Axial Groups Containing Mirror Planes: Сл and Cny 58 3.7 Axial Groups with Multiple Rotation Axes: Dn, Dni and Dnh 59 3.7.1 Examples of Axial Groups with Multiple Rotation Axes: Dn, D^andD^ 61 3.8 Special Groups for Linear Molecules: C^ and Ą^ 64 3.9 The Cubic Groups: Tă and Оъ 65 3.10 Assigning Point Groups to Molecules 69 3.11 Example Point Group Assignments 69 3.11.1 Example 1 : Conformations of Cyclohexane 69 3.11.2 Example 2: Six-Coordinate Metal Complexes 72 3.12 Self-Test Questions 73 4 Point Group Representations, Matrices and Basis Sets 75 4.1 Introduction 75 4.2 Symmetry Representations and Characters 75 4.2.1 Water, H2O, C2v 75 4.2.2 Direct Products 79 4.3 Multiplication Tables for Character Representations 81 4.4 Matrices and Symmetry Operations 82 4.5 Diagonal and Off-Diagonal Matrix Elements 85 4.5.1 Ammonia, NH3, C3v 85 4.6 The Trace of a Matrix as the Character for an Operation 87 4.7 Noninteger Characters 88 4.7.1 Boron Trifluoride, BF3, D3h 88 4.8 Reducible Representations 91 4.8.1 Water, H2O, C2v 91 4.9 Classes of Operations 93 4.9.1 [NKCNUf-, D4h 93 4.10 Degenerate Irreducible Representations 9" 4.10.1 Ammonia, NHb С 3v 98 4.11 The Labelling of Irreducible Representations ^ 4.12 Summary 102 4.13 Completed Tables 102 4.14 Self-Test Questions 102 Further Reading ЮЗ Reducible and Irreducible Representations 105 5.1 Introduction 105 5.2 Irreducible Representations and Molecular Vibrations *"' Contents vii 5.3 Finding Reducible Representations 110 5.4 Properties of Point Groups and Irreducible Representations 112 5.5 The Reduction Formula 118 5.5.1 Applying the Reduction Formula 120 5.6 A Complete Set of Vibrational Modes for H2O 122 5.7 Choosing the Basis Set 126 5.7.1 Carbonyl Stretching Modes of ÍFe(CO)s],D3h 126 5.8 The d-Orbitals in Common Transition Metal Complex Geometries 128 5.8.1 Square Planar, D4h 132 5.8.2 Tetrahedral, Tá 137 5.8.3 Octahedral, Oh 142 5.8.4 Trigonal Bipyramidal, D3h 147 5.9 Linear Molecules: Groups of Infinite Order 154 5.10 Summary 161 5.11 Self-Test Questions 162 Applications in Vibrational Spectroscopy 163 6.1 Introduction 163 6.2 Selection Rules 165 6.2.1 Infrared Spectroscopy 165 6.2.2 Infrared Absorption and the Greenhouse Gases 173 6.2.3 Interstellar H2 177 6.2.4 Raman Spectroscopy 177 6.2.5 Comparison of Infrared and Raman Selection Rules 184 6.3 General Approach to Analysing Vibrational Spectroscopy 186 6.3.1 Example: the С—И Stretch Bands of 1 ,4-Difluorobenzene 187 6.4 Symmetry-Adapted Linear Combinations 190 6.5 Normalization 193 6.6 The Projection Operator Method 195 6.6.1 Projection Operator Applied to the С — Η Stretches of 1 ,4-Difluorobenzene 196 6.6.2 The Projection Operator and Degenerate Representations 198 6.7 Linking Results for Symmetry-Inequivalent Sets of Atoms 202 6.7.1 Sets of Atoms Differing in Mass or Chemical Bond Strength 203 6.8 Additional Examples 206 6.8.1 Benzene, D^ 206 6.8.2 The fac and rasr homers of Transition Metal Complexes 212 6.9 Summary 215 6.10 Self-Test Questions 216 Further Reading 217 Symmetry in Chemical Bonding 219 7.1 Introduction 219 7.1.1 Wave Phenomena and Interference 220 7.1.2 The Born Interpretation of the Wavefunction 222 viii Contents 7.2 Bond Energies 225 7.2.1 The Symmetry-Adapted Linear Combinations for the Molecular Orbitals of H2 + and H2 228 7.2.2 The Chemical Bond Energy from Molecular Orbitals 232 7.2.3 The Molecular Orbital Energy 236 7.2.4 Bond Order 238 7.3 The Relative Energies of Hydrogen-Like Atomic Orbitals 239 7.3.1 Radial Behaviour of Atomic Orbitals 239 7.3.2 The Relative Energies of Atomic Orbitals in Different Elements 242 7.3.3 The Relative Energies of Atomic Orbitals from Electronegativity 244 7.4 The Molecules Formed by Other Second-Row Elements with Hydrogen 252 7.4.1 BeH2, Beryllium Hydride 252 7.4.2 ВНЪ, Boron Hydride 253 7.4.3 CHA, Methane 258 7.4.4 NH3, Ammonia 264 7.4.5 H2O, Water 269 7.5 The Second-Row Diatomic Molecules 270 7.5.1 Homonuclear Diatomics 270 7.5.2 Heteronuclear Diatomics of Second-Row Elements 276 7.6 More Complex Polyatomic Molecules 278 7.6.1 Ethene 278 7.7 Metal Complexes 284 7.7.1 Complexes Containing σ -Donor Ligands 284 7.7.2 The John-Teller Effect 287 7.7.3 Complexes Containing Ligand Orbitals of π -Symmetry 291 7.8 Summary 295 7.9 Self-Test Questions 296 Further Reading 297 Appendices Appendix 1 H2O Models for Identifying the Results of Symmetry Operation Products 299 Appendix 2 Assignment of Chiral Centre Handedness using Cahn-Ingold-Prelog Rules 303 Appendix 3 Model of a Tetrahedron and the Related Cube 307 Appendix 4 Model of an Octahedron 313 Contents ix Appendix 5 Matrices and Determinants 317 A5 .1 Matrices as Representations of Symmetry Operators 317 A5.1.1 Products of Matrices 318 A5.1.2 Products of Matrices, Expressed as Summations 319 A5.2 Matrices for Solving Sets of Linear Equations 321 Further Reading 324 Appendix 6 The Mathematical Background to Infrared Selection Rules A6.1 Model Based on Classical Mechanics A6.2 Model Based on Quantum Mechanics A6.3 Excited Vibrational States A6.4 Vibrational Modes for Polyatomic Molecules A6.5 Generalization to Arbitrary Transitions A6.6 Summary of Selection Rules Further Reading Appendix 7 The Franck-Condon Principle Appendix 8 Classical Treatment of Stokes/Anti-Stokes Absorption Appendix 9 The Atomic Orbitals of Hydrogen A9. 1 Choice of Coordinate System A9.2 Separation of Variables A9.3 The Angular Equation A9.4 Physical Interpretation of the Angular Equation Solutions A9.5 Angular Momentum A9.6 The Radial Equation A9.7 The Complete Atomic Orbitals A9.8 Expectation Values A9.9 Real Combinations to Form the Familiar Atomic Orbitals A9. 10 Cartesian Forms of the Real Angular Functions A9. 11 Endnote on Imaginary Numbers Further Reading Appendix 10 The Origin of Chemical Bonding in Hj A10.1 A 10.2 A10.3 A10.4 Chemical Bond Formation H Atom and H+ Cation The Vinal Theorem H2+ Molecule A10.5 Choice of Coordinate System for HÇ: Cylindrical Polar Coordinates 325 325 328 333 335 336 337 338 339 343 345 347 348 349 354 356 359 361 364 367 369 370 373 375 376 376 379 381 383 χ Contents Α10.6 Η/: the Electron Kinetic Energy 386 A10.7 H2+: the Electronic Potential Energy 387 A10.8 The Chemical Bond Formation Energy Based on Rigid Atomic Orbitals 393 A 10.9 Optimal Radial Decay of Molecular Orbitals 396 Further Reading 399 Appendix 11 H2O Molecular Orbital Calculation in C2v Symmetry 401 Further Reading 406 Appendix 12 Character Tables 407 A12.1 Non-Axial Groups 407 A12.2 Axial Groups 407 A12.2J C„ Groups 407 A12.2.2 S„ Groups 408 A12.2.3 Cm Groups 408 A12.2.4 С„ћ Groups 409 A12.2.5 D„ Groups 410 A12.2.6 Вы Groups 411 A12.2.7 Dnh Groups 412 A12.3 Cubic Groups 413 A12.3.1 Tetrahedral, Td 413 A12.3.2 Rotational Subgroup of Td,T 413 A12.3.3 Octahedral, Oh 414 A12.3.4 Rotational Subgroup of О h, О 414 A12.4 Groups for Linear Molecules 414 Index 415 Molecular Symmetry David J. Willock School of Chemistry, Cardiff University, Cardiff, UK Symmetry and group theory provide us with a rigorous method for the description of the geometry of objects by describing the patterns in their structure. In chemistry it is a powerful concept that underlies many apparently disparate phenomena. Symmetry allows us to accurately describe the types of bonding that can occur between atoms or groups of atoms in molecules. It also governs the transitions that may occur between energy levels in molecular systems, leading to a predictive understanding of the absorption properties of molecules and hence their spectra. Molecular Symmetry lays out the formal language used in the area, with illustrative examples of particular molecules throughout. It then applies the ideas of symmetry and group theory to describe molecular structure, bonding in molecules and to consider the implications in spectroscopy. Topics covered include: Symmetry elements Symmetry operations and products of operations Point groups used with molecules Point group representations, matrices and basis sets Reducible and irreducible representations Applications in vibrational spectroscopy Molecular orbital theory of chemical bonding Molecular Symmetry is designed to introduce the subject by combining symmetry with spectroscopy and bonding in a clear and accessible manner. Each chapter ends with a summary of learning points, a selection of self-test questions, and suggestions for further reading. A set of appendices includes templates for paper models which will help students understand symmetry operations and cover key aspects of the material in depth. Molecular Symmetry is a must-have introduction to this fundamental topic for students of chemistry, and will also find a place on the bookshelves of postgraduates and researchers looking for a broad and modern introduction to the subject.
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id	DE-604.BV023069469
illustrated	Illustrated
index_date	2024-07-02T19:32:24Z
indexdate	2024-07-09T21:10:17Z
institution	BVB
isbn	9780470853481 9780470853474
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-016272631
oclc_num	298325666
open_access_boolean
owner	DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-11 DE-355 DE-BY-UBR DE-29T DE-703 DE-20
owner_facet	DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-11 DE-355 DE-BY-UBR DE-29T DE-703 DE-20
physical	XII, 426 S. Ill., graph. Darst
publishDate	2009
publishDateSearch	2009
publishDateSort	2009
publisher	Wiley
record_format	marc
spelling	Willock, David J. Verfasser aut Molecular symmetry David J. Willock 1. publ. Chichester Wiley 2009 XII, 426 S. Ill., graph. Darst txt rdacontent n rdamedia nc rdacarrier Group theory Molecular spectroscopy Molecular structure Molecular theory Symmetry (Physics) Molekülsymmetrie (DE-588)4170385-6 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Chemische Bindung (DE-588)4009843-6 gnd rswk-swf Chemie (DE-588)4009816-3 gnd rswk-swf Stereochemie (DE-588)4129569-9 gnd rswk-swf Schwingungsspektroskopie (DE-588)4128960-2 gnd rswk-swf Stereochemie (DE-588)4129569-9 s Chemische Bindung (DE-588)4009843-6 s Molekülsymmetrie (DE-588)4170385-6 s DE-604 Schwingungsspektroskopie (DE-588)4128960-2 s 1\p DE-604 Gruppentheorie (DE-588)4072157-7 s Chemie (DE-588)4009816-3 s 2\p DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016272631&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016272631&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk
spellingShingle	Willock, David J. Molecular symmetry Group theory Molecular spectroscopy Molecular structure Molecular theory Symmetry (Physics) Molekülsymmetrie (DE-588)4170385-6 gnd Gruppentheorie (DE-588)4072157-7 gnd Chemische Bindung (DE-588)4009843-6 gnd Chemie (DE-588)4009816-3 gnd Stereochemie (DE-588)4129569-9 gnd Schwingungsspektroskopie (DE-588)4128960-2 gnd
subject_GND	(DE-588)4170385-6 (DE-588)4072157-7 (DE-588)4009843-6 (DE-588)4009816-3 (DE-588)4129569-9 (DE-588)4128960-2
title	Molecular symmetry
title_auth	Molecular symmetry
title_exact_search	Molecular symmetry
title_exact_search_txtP	Molecular symmetry
title_full	Molecular symmetry David J. Willock
title_fullStr	Molecular symmetry David J. Willock
title_full_unstemmed	Molecular symmetry David J. Willock
title_short	Molecular symmetry
title_sort	molecular symmetry
topic	Group theory Molecular spectroscopy Molecular structure Molecular theory Symmetry (Physics) Molekülsymmetrie (DE-588)4170385-6 gnd Gruppentheorie (DE-588)4072157-7 gnd Chemische Bindung (DE-588)4009843-6 gnd Chemie (DE-588)4009816-3 gnd Stereochemie (DE-588)4129569-9 gnd Schwingungsspektroskopie (DE-588)4128960-2 gnd
topic_facet	Group theory Molecular spectroscopy Molecular structure Molecular theory Symmetry (Physics) Molekülsymmetrie Gruppentheorie Chemische Bindung Chemie Stereochemie Schwingungsspektroskopie
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016272631&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016272631&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT willockdavidj molecularsymmetry

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