A Primer of NMR Theory with Calculations in Mathematica

ISBN-13: 9781118588994 / Angielski / Twarda / 2015 / 256 str.

Alan J. Benesi

Opis

Presents the theory of NMR enhanced with Mathematica(c) notebooks

• Provides short, focused chapters with brief explanations of well-defined topics with an emphasis on a mathematical description
• Presents essential results from quantum mechanics concisely and for easy use in predicting and simulating the results of NMR experiments
• Includes Mathematica notebooks that implement the theory in the form of text, graphics, sound, and calculations
• Based on class tested methods developed by the author over his 25 year teaching career. These notebooks show exactly how the theory works and provide useful calculation templates for NMR researchers

Spis treści

Preface viii

Chapter 1 Introduction 1

Chapter 2 Using Mathematicac; Homework Philosophy 3

Chapter 3 The NMR Spectrometer 4

Chapter 4 The NMR Experiment 7

Chapter 5 Classical Magnets and Precession 11

Chapter 6 The Bloch Equation in the Laboratory Reference Frame 16

Chapter 7 The Bloch Equation in the Rotating Frame 19

Chapter 8 The Vector Model 23

Chapter 9 Fourier Transform of the NMR Signal 29

Chapter 10 Essentials of Quantum Mechanics 31

Chapter 11 The Time ]Dependent Schrodinger Equation, Matrix Representation of Nuclear Spin Angular Momentum Operators 35

Chapter 12 The Density Operator 39

Chapter 13 The Liouville von Neumann Equation 41

Chapter 14 The Density Operator at Thermal Equilibrium 42

Chapter 15 Hamiltonians of NMR: Isotropic Liquid ]State Hamiltonians 45

Chapter 16 The Direct Product Matrix Representation of Coupling Hamiltonians HJ and HD 50

Chapter 17 Solving the Liouville Von Neumann Equation for the Time Dependence of the Density Matrix 54

Chapter 18 The Observable NMR Signal 59

Chapter 19 Commutation Relations of Spin Angular Momentum Operators 61

Chapter 20 The Product Operator Formalism 65

Chapter 21 NMR Pulse Sequences and Phase Cycling 68

Chapter 22 Analysis of Liquid ]State NMR Pulse Sequences with the Product Operator Formalism 72

Chapter 23 Analysis of the Inept Pulse Sequence with Program Shortspin and Program Poma 78

Chapter 24 The Radio Frequency Hamiltonian 82

Chapter 25 Comparison of 1D and 2D NMR 86

Chapter 26 Analysis of the HSQC, HMQC, and DQF ]COSY 2D NMR Experiments 89

Chapter 27 Selection of Coherence Order Pathways with Phase Cycling 96

Chapter 28 Selection of Coherence Order Pathways with Pulsed Magnetic Field Gradients 104

Chapter 29 Hamiltonians of NMR: Anisotropic Solid ]State Internal Hamiltonians in Rigid Solids 111

Chapter 30 Rotations of Real Space Axis Systems Cartesian Method 120

Chapter 31 Wigner Rotations of Irreducible Spherical Tensors 123

Chapter 32 Solid ]State NMR Real Space Spherical Tensors 129

Chapter 33 Time ]Independent Perturbation Theory 134

Chapter 34 Average Hamiltonian Theory 141

Chapter 35 The Powder Average 144

Chapter 36 Overview of Molecular Motion and NMR 147

Chapter 37 Slow, Intermediate, And Fast Exchange In Liquid ]State Nmr Spectra 150

Chapter 38 Exchange in Solid ]State NMR Spectra 154

Chapter 39 N MR Relaxation: What is NMR Relaxation and what Causes it? 163

Chapter 40 Practical Considerations for the Calculation of NMR Relaxation Rates 168

Chapter 41 The Master Equation for NMR Relaxation Single Spin Species I 170

Chapter 42 Heteronuclear Dipolar and J Relaxation 183

Chapter 43 Calculation of Autocorrelation Functions, Spectral Densities, and NMR Relaxation Times for Jump Motions in Solids 189

Chapter 44 Calculation of Autocorrelation Functions and Spectral Densities for Isotropic Rotational Diffusion 198

Chapter 45 Conclusion 202

Bibliography 203

INDEX 000

O autorze

Alan J. Benesi was Director of the Pennsylvania State University NMR Facility from 1987–2012. He earned his Ph.D. in Biophysics at the University of California, Berkeley, in 1975. He has published many papers related to solid state and liquid state NMR, solid state and liquid state NMR relaxation, and rotational and translational diffusion.

Blurb

Presents the theory of NMR enhanced with Mathematica© notebooks in a clear and concise manner

A Primer of NMR Theory with calculations in Mathematica© presents the theory of NMR. Enhanced with Mathematica© notebooks that show exactly how the theory is implemented, the book rigorously covers NMR theory. The Mathematica© notebooks augment the book to demonstrate the theory and applications of NMR, as well as provide calculation templates for students and researchers.

Presented in short, focused chapters the book provides a concise exposition of well–defined topics with emphasis on a mathematical description including essential results from quantum mechanics for easy use in predicting and simulating the results of NMR experiments.

A Primer of NMR Theory with calculations in Mathematica© covers:

The NMR spectrometer
The NMR experiment
Classical magnetic dipole in a magnetic field
The Bloch equation(s)
The vector model of NMR
The density operator and density matrix
The Liouville von Neumann equation
Commutation relations of nuclear spin operators
Time independent perturbation theory
Average Hamiltonian theory
The Powder Average
Effects of exchange on liquid state and solid state NMR spectra
The fundamental connection between molecular motion and NMR relaxation times

While it is not necessary to have Mathematica© to gain understanding from this book, it is highly recommend as the reader can go through the theory presented step by step by executing the Mathematica notebooks. Readers can also copy and modify the Mathematica notebooks for assigned homework or for real research problems.

The Mathematica notebooks are particularly powerful. They can be used as teaching tools and as templates for full blown research calculations. The included notebooks are extremely useful for calculation of matrix representations of nuclear spin operators and for calculation of rotations used in solid state NMR. Other notebooks provide a set of powder average angles necessary for solid state spectral simulations as well as demonstrating simulations of solid state powder patterns, effects of exchange on both liquid state and solid state NMR spectra, and for calculating explicit NMR relaxation times that can be compared to experiment.

Alan J. Benesi was Director of the Pennsylvania State University NMR Facility from 1987–2012. He earned his Ph.D. in Biophysics at the University of California, Berkeley, in 1975. He has published many papers related to solid state and liquid state NMR, solid state and liquid state NMR relaxation, and rotational and translational diffusion.