Computer Assistance in the Analysis of High-Resolution NMR Spectra

Foreword.- Notation and Symbols.- A. The Calculation of an NMR Spectrum.- A.1. Some Postulates of Quantum Mechanics.- A.2. Quantum Mechanics of a Spin System.- A.2.1. The High-Resolution NMR Hamiltonian Operator.- A.2.2. Spin Functions.- A.3. Representation of Operators.- A.3.1. Representation of an Operator Ô by a Matrix.- A.3.2. Effect of Spin Operators Î on Spin Functions.- A.3.3. Representation of the Hamiltonian Operator ?.- A.3.4. Some Properties of the Matrix ?.- A.3.5. Representation of the Lowering Operator Î_ 14.- A.3.6. Expansion of Wave Functions.- A.3.7. Basis Transformations.- A.4. Solution of the Schrödinger Equation.- A.4.1. Representation of the Schrödinger Equation by Vectors and Matrices.- A.4.2. Example: The Two-Spin System.- A.5. The Schrödinger Equation as a Basis Transformation.- A.6. Calculation of a Normal Spectrum.- A.6.1. Transition Frequencies.- A.6.2. Transition Intensities.- A.6.3. The Spectrum.- A.7. Breakdown of Hamiltonian Matrices.- A.7.1. Breakdown with Simple Product Spin Functions: Weak Coupling.- A.7.2. Breakdown with Linear Combinations of Product Spin Functions.- B. Analysis of Spectra, Unaided by a Computer.- B.1. "Hand" Methods of Analysis.- B.2. Determination of Starting Parameters for Computer-Aided Analysis.- C. Basic Computer Methods.- C.1. Simulation Programs.- C.2. Basic Iterative Programs.- C.2.1. The Swalen=Reilly Method.- C.2.2. The Hoffman Method.- C.2.3. The Granger Method.- C.2.4. The Castellano=Bothner-By/Braillon Method (Programs LAOCN3 and SUPERMAN).- C.2.5. The Arata=Shimizu=Fujiwara Method.- C. 3. Auxiliary Methods.- C.3.1. Spectral Decomposition (Program DECOMP).- C.3.2. Spectral Assignment (Program ASSIGN).- D. Developments of the Basic Computer Programs.- D.1. Developments of the Swalen=Reilly Programs.- D.1.1. Magnetic Equivalence Factoring.- D.1.2. "Missing" Energy Levels (Program NMREN2). A Unified Swalen=Reilly Method (Program NMRENIT).- D.1.3. Complete Analysis by the Lusebrink Method (Program DENOUE).- D. 2. Developments of the Castellano-Bothner-By/Braillon Method.- D.2.1. Magnetic Equivalence Factoring.- D.2.2. Weak Coupling, Symmetry Factoring. Weighting of Observables and Printout of Derivatives.- D.2.3. Analysis of Spectra of Partially Oriented Molecules.- (Programs LAOCOONOR. LAOCOONORW and LEQUOR).- E. Parameter Errors.- E.1. Description of Errors.- E.2. Significance of Covariances.- E.3. Incomplete Description of Errors.- E.4. Calculation of Errors in the Swalen=Reilly Method as Modified by FERGUSON and MARQUARDT.- E. 5. Calculation of Errors in the Castellano=Bothner-By Method and its Modifications.- F. Uniqueness of Solutions.- F.1. The Number of ELD's Derived from an Experimental Spectrum.- F.2. The Number of Parameter Sets Derived from an ELD.- F.3. The Number of Assigned Transitions Necessary for a Solution.- G. Comparison of the Iterative Methods.- G.1. Mathematical Structure and Convergence.- G.2. Computational Effort per Iteration Cycle.- G.3. Prior Knowledge of Parameters.- G.4. Conclusions.- H. Computer Assistance in NMR Studies of Rate Processes.- H.1. The Calculation of Spectra of Spin Systems Undergoing Rate Processes.- H.1.1. The Modified Bloch Equations.- H.1.2. The Density Matrix Treatment of Exchange.- H.1.3. The Unified Theory of Exchange.- H. 2. Computer Programs for Spectra of Spin Systems Undergoing Rate Processes.- H.2.1. Early Programs.- H.2.2. The Programs DNMR.- H.2.3. Computer Programs for the Study of Quadrupolar Relaxation.- I. Double Resonance.- I. 1. The Effects of Double Irradiation on NMR Spectra.- I.2. Simulation of Double Resonance Spectra (Program NMDRS).- V. Vectors and Matrices.- V.1. Vectors.- V.2. Matrices.- V.3. Operations with Matrices.- V.4. Some Rules of Matrix Algebra.- W. Diagonalization of Symmetrical Matrices.- W.1. Orthogonal Transformations.- W.2. Diagonalization of Symmetric Matrices.- W.3. The Jacobi Method.- W.4. Diagonalization via the Tridiagonal Form.- X. Least-Squares Fitting.- X.1. The Fitting Problem.- X.2. Linearization of the Fitting Problem.- X.3. The Normal Equations.- X.4. Iteration.- Y. Parameter Errors from Least-Squares Fits.- Y.1. Some Concepts from Statistics.- Y.2. The Variance-Covariance Matrix and Experimental Errors.- Y.3. Propagation of Errors.- Y.3.1. Errors of Parameters Obtained by Least-Squares Methods, Determined with Approximate Derivatives.- Y.3.2. Rigorous Calculation of the Derivatives for the Determination of Parameter Errors.- Y.4. Calculation of Linear Combinations of Parameters, Leading to Extreme Errors.- Z. The Density Matrix.- Z.1. Basic Concepts.- Z.2. Calculation of Expectation Values of an Operator.- Z.3. The Equation of Motion for ?.- Acknowledgments.- References.