2D NMR: Density matrix and product operator treatment

2D NMR......Page 1
Dedication......Page 2
Table of Contents......Page 3
Forward......Page 6
Preface......Page 7
Acknowledgments......Page 9
1.2 The Density Matrix......Page 10
1.3.1 Calculation Steps......Page 13
1.3.2 Equilibrium Population......Page 14
1.3.3 The First Pulse......Page 16
1.3.4 Evolution from t(1) to t(2)......Page 18
1.3.5 The Second Pulse......Page 19
1.3.7 The Role of Delta-1......Page 20
1.3.8 Third and Fourth Pulses......Page 22
1.3.9 The Role of Delta-2......Page 23
1.3.10 Detection......Page 25
1.3.11 Comparison of DM Treatment with Vector Representation......Page 30
1.4 The Density Matrix Description of a Double-Quantum Coherence Experiment (INADEQUATE)......Page 40
1.4.1 Equlibrium Populations......Page 41
1.4.2 The First Pulse......Page 43
1.4.3 Evolution from t (1) to t (2)......Page 44
1.4.4 The Second Pulse......Page 46
1.4.5 Evolution from t (3) to t (4)......Page 47
1.4.7 Evolution from t (5) to t (6)......Page 48
1.4.8 The Fourth Pulse......Page 49
1.4.9 Detection......Page 51
1.4.10 Carbon-Carbon Connectivity......Page 52
1.5.1 Equilibrium Populations......Page 54
1.5.2 The First Pulse......Page 55
1.5.5 Detection......Page 58
1.7 Conclusion of Part I......Page 68
1.6.1 Comparison with the Previous Sequence......Page 61
1.6.2 The Second Pulse......Page 62
1.6.3 Detection......Page 66
2.2 Expressing the Density Matrix in Terms of Angular Momentum Components......Page 69
2.3 Describing the Effect of a Pulse in Terms of Angular Momenta......Page 71
2.4 An Unsuccessful Attempt to Describe a Coupled Evolution in Terms of Angular Momenta......Page 74
2.5 Product Operators (PO)......Page 76
2.6 Pulse Effects (Rotations) in the Product Operator Formalism......Page 79
2.7 Treatment of Evolutions in the Product Operator Formalism......Page 83
2.8 Refocusing Routines......Page 86
2.9 PO Treatment of 2DHETCOR: Two Spins (CH)......Page 89
2.10 PO Treatment of 2HETCOR: CH2 AND CH3......Page 92
2.11 PO Treatment of Polarization Transfer Sequence: INEPT (Insensitive Nuclei Enhancement by Polarization Transfer) with Decoupling......Page 96
2.12 Coupled INEPT......Page 98
2.13 PO Treatment of Dept (Distortionless Enhancement Polarization Transfer)......Page 103
2.14 PO Treatment of APT (Attached Proton Test)......Page 111
Appendix A: Math Reminder......Page 114
Appendix B: Density Matrix Formalism......Page 129
Appendix C: Angular Momentum and Rotation Operators......Page 146
Appendix D: Properties of Product Operators......Page 156
Appendix E: Demonstration of the Rotation Rules......Page 168
Appendix F: Demonstration of the Coupled Evolution Rules......Page 172
Appendix G: PO Evolution Tables......Page 178
Appendix H: Demonstration of the Refocusing Rules......Page 180
Appendix I: Supplementary Discussions......Page 183
Appendix J: Product Operators and Magnetization Components......Page 189
Appendix K: When to Drop Nonobservable Terms (NOT)......Page 192
Appendix L: Magnetic Equivalence, the Multiplet Formalism......Page 193
Appendix M: Rotations About Nontrivial Axes......Page 197
Suggested Readings......Page 201
Index......Page 202