Szymanski / Bernatowicz Classical and Quantum Molecular Dynamics in NMR Spectra

1. Auflage 2018
ISBN: 978-3-319-90781-9
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 406 Seiten

The book provides a detailed account of how condensed-phase molecular dynamics are reflected in the line shapes of NMR spectra. The theories establishing connections between random, time-dependent molecular processes and lineshape effects are exposed in depth. Special emphasis is placed on the theoretical aspects, involving in particular intermolecular processes in solution, and molecular symmetry issues. The Liouville super-operator formalism is briefly introduced and used wherever it is beneficial for the transparency of presentation. The proposed formal descriptions of the discussed problems are sufficiently detailed to be implemented on a computer. Practical applications of the theory in solid- and liquid-phase studies are illustrated with appropriate experimental examples, exposing the potential of the lineshape method in elucidating molecular dynamics NMR-observable molecular phenomena where quantization of the spatial nuclear degrees of freedom is crucial are addressed in the last part of the book. As an introduction to this exciting research field, selected aspects of the quantum mechanics of isolated systems undergoing rotational tunnelling are reviewed, together with some basic information about quantum systems interacting with their condensed environment. The quantum theory of rate processes evidenced in the NMR lineshapes of molecular rotors is presented, and illustrated with appropriate experimental examples from both solid- and liquid-phase spectra. In this context, the everlasting problem of the quantum-to-classical transition is discussed at a quantitative level.  The book will be suitable for graduate students and new and practising researchers using NMR techniques.

Slawomir Szymanski is Professor at the Institute of Organic Chemistry, Warsaw, Poland.  His research centres on NMR spectroscopy, namely molecular structure and dynamics in condensed phases studied by NMR spectroscopy methods, and quantum mechanical effects in the stochastic dynamics of hindered molecular rotators.  He is a recipient of the Award of the Mathematical, Physical and Chemical Sciences Division of the Polish Academy of Sciences.   Piotr Bernatowicz is Head of the NMR Laboratory in the Institute of Physical Chemistry, Polish Academy of Sciences. 

Autoren/Hrsg.

Szymanski, Slawomir

Bernatowicz, Piotr

Inhaltsverzeichnis

1;Preface;5
2;Contents;7
3;1 Introduction;12
3.1;References;16
4;2 Principles of NMR Spectroscopy;17
4.1;2.1 Nuclear Magnetic Dipole Moment in an External Magnetic Field;17
4.2;2.2 The Statistical Operator of One-Spin System;22
4.3;2.3 A Single-Pulse Experiment of PFT NMR Spectroscopy in the Vector Model;23
4.3.1;2.3.1 The Radiofrequency Pulse in the Rotating Frame;24
4.3.2;2.3.2 The FID Signal;29
4.3.3;2.3.3 The Quadrature Detection of the FID Signal;30
4.3.4;2.3.4 The Spectrum;32
4.3.5;2.3.5 Summary;35
4.4;2.4 Coupled Spin Systems: NMR Spectra Beyond the Vector Model;36
4.4.1;2.4.1 Multi-spin Systems;36
4.4.2;2.4.2 Spin Hamiltonian of Coupled Multi-spin Systems;38
4.4.3;2.4.3 The Spectrum of Coupled Multi-spin System. Part One;41
4.4.4;2.4.4 The Notion of Quantum Coherence;44
4.4.5;2.4.5 The Spectrum of Coupled Multi-spin System. Part Two;46
4.4.6;2.4.6 Weakly Coupled Systems;50
4.4.7;2.4.7 Molecular Symmetry in Spectra;52
4.4.8;2.4.8 Magnetic Equivalence;59
4.5;2.5 Introduction to Liouville Space Formalism;62
4.5.1;2.5.1 One-Spin Systems;62
4.5.2;2.5.2 Coupled Multi-spin Systems;66
4.5.3;2.5.3 Operator Product Bases;68
4.6;2.6 Remarks on the Solid State Systems;69
4.6.1;2.6.1 Secular and Nonsecular Spin Interactions in Solids. CSA Tensor;70
4.6.2;2.6.2 Secular Part of CSA Tensor. Angular Dependence;71
4.6.3;2.6.3 Nuclei with Electric Quadrupole Moments;75
4.6.4;2.6.4 Dipole Interactions;77
4.6.5;2.6.5 Spin Systems with Different Anisotropic Interactions;79
4.6.6;2.6.6 Single-Crystal Spectra;80
4.6.7;2.6.7 Example of Bandshape Modeling in Wide-Line Spectra of Solids;81
4.6.8;2.6.8 Wide-Line Spectra of Powders;82
4.6.9;2.6.9 Magic Angle Spinning Spectra of Powders;84
4.7;2.7 Spin Echo;87
4.8;2.8 Two Dimensional Spectra;91
4.9;References;92
5;3 NMR Spectroscopy and Molecular Dynamics - An Outlook;94
5.1;3.1 Nuclear Spin Relaxation and Molecular Motion. Introductory Remarks;94
5.1.1;3.1.1 Semiclassical Approach;95
5.1.2;3.1.2 Quantum Mechanical Approach;103
5.1.3;3.1.3 Justification of the Bloch Equations;109
5.1.4;3.1.4 Explicit Evaluation of Relaxation Rates for CSA Interactions;111
5.1.5;3.1.5 Nuclear Spin Interactions Leading to Relaxation. Temperature Effects;114
5.1.6;3.1.6 More on Dipolar Relaxation. Nuclear Overhauser Effect;118
5.2;3.2 Dynamic Line Shape Effects in the Vector Model;119
5.2.1;3.2.1 Stochastic Picture;122
5.2.2;3.2.2 Heuristic Approach;126
5.2.3;3.2.3 The FID Signal and the Line Shape Equation;128
5.2.4;3.2.4 The Pulse Offset Effects;136
5.2.5;3.2.5 DNMR Spectra of Solids and the Vector Model;138
5.2.6;3.2.6 Selective Population Inversion;140
5.2.7;3.2.7 EXSY - A 2D Experiment;144
5.3;References;151
6;4 Nuclear Spin Relaxation Effects in NMR Spectra;153
6.1;4.1 Theory;153
6.1.1;4.1.1 Irreducible Spherical Tensor Description of Anisotropic Interactions;154
6.1.2;4.1.2 Derivation of BWR Relaxation Matrix;160
6.1.3;4.1.3 Heteronuclear Systems;166
6.1.4;4.1.4 General Properties of the BWR Relaxation Matrix;168
6.2;4.2 Molecular Tumbling in Isotropic Fluids;171
6.2.1;4.2.1 Angular Correlation Functions in Rotational Diffusion Model;172
6.2.2;4.2.2 BWR Relaxation Matrix in Isotropic Systems;177
6.2.3;4.2.3 Local Dynamics. Other Models of Molecular Motion;178
6.3;4.3 Nuclear Permutation and Magnetic Equivalence Symmetries;181
6.3.1;4.3.1 Permutation Symmetry in Liouville Space. Macroscopic Symmetry;182
6.3.2;4.3.2 Microscopic Symmetry;187
6.3.3;4.3.3 Violation of the Magnetic Equivalence Symmetry;191
6.4;4.4 Relaxation Effects in Spectral Line Shapes;195
6.4.1;4.4.1 A Survey of Line Shape Effects;195
6.4.2;4.4.2 Numerical Calculations of Spectra With Relaxation Effects;198
6.5;4.5 Nuclear Spin Relaxation in Solids;200
6.6;References;200
7;5 Discrete Molecular Dynamics and NMR Line Shape Effects. Intramolecular Exchange;202
7.1;5.1 Basic Notions;202
7.1.1;5.1.1 Monte Carlo Approach;204
7.1.2;5.1.2 DNMR Equation in Liouville Space;205
7.1.3;5.1.3 Degenerate Rearrangements;209
7.2;5.2 DNMR Theory for Intramolecular Rearrangements of Symmetric Molecules;211
7.2.1;5.2.1 Molecular Symmetries as Feasible Symmetries. Topomers as Cosets of Feasible Groups;213
7.2.2;5.2.2 Exchange Networks in Group Theory Language;217
7.2.3;5.2.3 Macroscopic Conservation of Symmetry in Intramolecular Dynamic Equilibria;219
7.2.4;5.2.4 DNMR Line Shape Equation for Symmetric Systems;223
7.2.5;5.2.5 DNMR Line Shape Equation in Symmetry Adapted Liouville Bases;234
7.2.6;5.2.6 Microscopic Conservation of Symmetry;236
7.2.7;5.2.7 Magnetic Equivalence and Exchange;243
7.3;5.3 Quantitative Interpretation of DNMR Spectra. Methodological Aspects;244
7.3.1;5.3.1 Proton Exchange in a Corrole Molecule. Temperature-Dependent Chemical Shifts;245
7.3.2;5.3.2 Conformational Equilibrium in [3.3]-Paracyclophane;248
7.3.3;5.3.3 Inversions of Aliphatic Bridges in [4.3]paracyclophane;250
7.3.4;5.3.4 General Remarks;253
7.4;References;254
8;6 Discrete Molecular Dynamics and NMR Line Shape Effects. General Exchange;256
8.1;6.1 Problem Outline;256
8.2;6.2 Intermolecular Rearrangements in the Vector Model;257
8.3;6.3 Density Matrix Description of Intermolecular Equilibria;261
8.3.1;6.3.1 Retrospective Picture of Intermolecular Equilibria;262
8.3.2;6.3.2 Reference Molecules and Exchange Superoperators;265
8.3.3;6.3.3 Bilinear Equations of Motion for Exchanging Systems;271
8.3.4;6.3.4 Macroscopic Symmetry in Intermolecular Processes;273
8.3.5;6.3.5 Linear Approximation;280
8.3.6;6.3.6 General Case of Exchange in Linear Approximation;283
8.4;6.4 Exchange of Fragments;284
8.4.1;6.4.1 Additional Conventions in Notation;285
8.4.2;6.4.2 Exchange Superoperators in Bilinear Equations of Motion;288
8.4.3;6.4.3 Exchange Superoperators in Linear Equations of Motion;294
8.5;6.5 Examples;295
8.5.1;6.5.1 Proton Exchange in Methanol;295
8.5.2;6.5.2 Proton Exchange in an Ammonium Salt. Symmetry-Equivalent Reactions;302
8.5.3;6.5.3 Self-Exchange with No Unique Fragmentation Pattern;308
8.5.4;6.5.4 Degenerate Exchange with No Unique Fragmentation Pattern;309
8.6;References;310
9;7 Rotational Tunneling in Stick NMR Spectra of Solids;311
9.1;7.1 Introductory Remarks;311
9.2;7.2 The Effective Spin Hamiltonian;312
9.2.1;7.2.1 Hindered Rotators in Solids;313
9.2.2;7.2.2 The Librational Hamiltonian in the Pocket Basis;316
9.2.3;7.2.3 Inclusion of Spin-Dependent Interactions;323
9.3;7.3 Tunneling Splittings of the Torsional Bands;327
9.4;7.4 A Glimpse into Temperature Effects;329
9.5;7.5 Rotational Tunneling in Experimental NMR Spectra of Solids;330
9.6;References;336
10;8 Quantum Molecular Dynamics in Liquid-Phase Stick NMR Spectra;338
10.1;8.1 The Symmetrization Postulate in Liquid-Phase NMR. Introductory Remarks;338
10.2;8.2 Transition Metal Polyhydrides;339
10.2.1;8.2.1 Experimental Evidences;339
10.2.2;8.2.2 The Effective Spin Hamiltonian for the Di- and Trihydrides;341
10.2.3;8.2.3 Temperature Effects on Exchange Couplings;348
10.3;8.3 Strongly Hindered Methyl Groups;349
10.4;References;352
11;9 Quantum Mechanical Rate Processes in NMR Spectra;354
11.1;9.1 Three-Fold Rotators in Solids;354
11.1.1;9.1.1 An Outline of the DQR Theory;355
11.1.2;9.1.2 Temperature Effects on the DQR Quantities;366
11.1.3;9.1.3 DQR Effects in Experimental Solid State DNMR Spectra;371
11.2;9.2 DQR Theory for Planar n-Fold Rotators;378
11.3;9.3 DQR Effects in Liquid Phase Spectra;382
11.3.1;9.3.1 Discrimination Between Similar Line-Shape Models;383
11.3.2;9.3.2 DQR Effects in Methyltriptycene Derivatives;385
11.4;9.4 Temperature Effects in the Spectra of the Metal Polyhydride Complexes;389
11.5;9.5 Proton-Transfer Reactions;393
11.6;References;393
12;10 Correction to: Classical and Quantum Molecular Dynamics in NMR Spectra;395
12.1;Correction to: S. Szyma?ski and P. Bernatowicz, Classical and Quantum Molecular Dynamics in NMR Spectra, https://doi.org/10.1007/978-3-319-90781-9;395
13;A Selected Properties of Matrices;396
13.1;A.1 Similarity Transformations of Matrices. Diagonalization;396
13.2;A.2 Matrix Functions of Matrices;397
13.3;A.3 Kronecker Multiplication of Matrices;398
13.4;A.4 Block Inversion of Matrices;400
14;B Derivation of a General DNMR Lineshape Equation;401
15;C Nuclear Permutation Symmetry in NMR Spectra;403
15.1;C.1 Symmetry Selection Rules for Matrix Elements of Operators;403
15.2;C.2 Decomposition of the Totally Symmetric Group Superprojector into Symmetry-Parentage Superprojectors;404
15.3;C.3 Double Cosets;405
15.4;C.4 Double Cosets and Projection Superoperators;405