Equilibrium Molecular Structures: From Spectroscopy to Quantum Chemistry

✍ Scribed by Jean Demaison, James E. Boggs, Attila G. Császár, Editors

• Publisher: CRC Press
• Year: 2010
• Tongue: English
• Leaves: 280
• Edition: Har/Cdr
• Category: Library

✦ Synopsis

Molecular structure is the most basic information about a substance, determining most of its properties. Determination of accurate structures is hampered in that every method applies its own definition of "structure" and thus results from different sources can yield significantly different results. Sophisticated protocols exist to account for these differences, but until now, no textbook has been written to discuss such topics in a widely accessible manner.Balancing quantum theory with practical experiments, Equilibrium Molecular Structures focuses on the theory involved in determining and converting measured and computed data sets into accurate and well-defined equilibrium structures.This textbook begins with a discussion of quantum chemistry and the concept of potential energy surfaces, quantum chemical computation of structures and anharmonic force fields. The reader is next introduced to the method of least squares and the problem of ill-conditioning, leverage points, perturbation theory, computational aspects of determining semi-experimental equilibrium structures, the determination of moments of inertia from spectra, and the treatment of resonances. The textbook also examines the determination of diatomic molecular potentials using semiclassical and quantum mechanical methods as well as position and distance averages.From basic elements to the latest advances and current best practices, Equilibrium Molecular Structures contains abundant references, examples, and exercises and includes a CD with additional examples. These features make the book ideal for class instruction but also user-friendly for self-instruction. It is recommended for newcomers to the field and also for experienced spectroscopists who want to expand their area of knowledge.

✦ Table of Contents

Cover
......Page 1
Equilibrium Molecular Structures: From Spectroscopy To Quantum Chemistry......Page 2
Equilibrium Molecular Structures: From Spectroscopy To Quantum Chemistry......Page 3
Contents......Page 5
Foreword......Page 7
References......Page 10
Editors......Page 11
Contributors......Page 12
Introduction......Page 13
References......Page 15
Principal Structures......Page 16
1.1 Concept of the Potential Energy Surface......Page 18
1.2 Interplay of Electronic and Nuclear Contributions to the Potential Energy Surface......Page 22
1.3 Optimization Algorithms......Page 28
1.4 Anharmonic Molecular Force Fields......Page 31
1.5 A Hierarchy of Electronic Structure Methods......Page 34
1.5.1 Physically Correct Wave Functions......Page 37
1.5.2 One-Particle Basis Sets......Page 39
1.6 Pursuit of the Ab Initio Limit......Page 42
REFERENCES AND SUGGESTED READING......Page 45
2.1 Introduction......Page 46
2.2.1 Principle of the Method......Page 47
2.2.2.1 Solution......Page 49
2.2.2.2 Ill-Conditioning......Page 50
2.2.3.1 Leverage......Page 54
2.2.3.2 Analysis of Residuals......Page 56
2.3 Nonlinear Least Squares......Page 57
2.4.1 Method......Page 58
2.4.2 Iteratively Reweighted Least Squares......Page 60
2.5 Correlated Least Squares......Page 61
2.6.1 Method of Predicate Observations......Page 62
2.6.2 Constrained Least Squares......Page 64
2.7.2 Autocorrelation of the Errors......Page 65
References......Page 68
Contents of Appendix II ( on CD- ROM)......Page 69
3.1 Introduction......Page 70
3.2.1 Rigid Rotators......Page 71
3.2.2 Real Molecules: Vibration-Rotation Interaction Constants......Page 74
3.2.3.1 Vibrational Corrections and “Alphas”: Not the Same Thing......Page 76
3.2.3.2 Centrifugal Distortion......Page 78
3.2.3.3 Electronic Contribution to Rotational Constants......Page 79
3.3 Semiexperimental Equilibrium Structures......Page 80
3.3.1 Calculation of Vibrational Contributions......Page 82
3.3.2 Outline of Procedure for Obtaining Semiexperimental Equilibrium Structures......Page 85
3.4.1 Studies of Isocyanic Acid, Ketene, and Glycine......Page 86
3.4.2 Selected Other Studies: Small- and Medium-Sized Molecules Containing First-Row Atoms......Page 90
3.4.3 Selected Other Studies: Small and Medium Molecules Containing Second-Row Atoms and Beyond......Page 97
References......Page 101
Contents......Page 105
4.2.1 C onstruction of the Hamiltonian......Page 106
4.2.2 T ransformations of the Hamiltonian......Page 112
4.2.3.1 Reduction of the Hamiltonian......Page 116
4.2.3.2 Choice of Reduction and Representation......Page 117
4.2.5 T he Symm etric-Top Molecule......Page 118
4.3.1 Vibrational Correction......Page 119
4.3.2 Electronic Correction......Page 120
4.3.3 Centrifugal Distortion Correction......Page 122
4.4.1 Coriolis Interaction......Page 124
4.4.2 Anharmonic Resonances......Page 127
4.5.1 Ground-State Rotational Constants......Page 129
4.6.1 Case of Weakly Perturbed States......Page 130
4.6.2 Case of Significantly Perturbed States......Page 131
4.6.3.1 v6 = 1 State of Trans-HCOOH......Page 133
4.7 Nonorthorhombic Rotational Hamiltonian......Page 135
4.8 Conclusions......Page 137
References......Page 138
Contents of Appendix IV ( on CD- ROM)......Page 140
Contents......Page 141
5.2.1 Structural Data to Be Determined......Page 142
5.2.2 Basic Model......Page 143
5.2.3 Observables......Page 146
5.2.4 Classes of Molecules......Page 148
5.2.5 Methods......Page 149
5.3.1 Principle of the Method......Page 150
5.3.2 Variants Using Differences of Moments of Inertia......Page 151
5.3.4 Accuracy......Page 153
5.4.1 Kraitchman’s General Equations......Page 156
5.4.2 Further Aspects......Page 160
5.4.4 Accuracy......Page 162
5.5.1 The rm Structure......Page 165
5.5.2 The rc Structure......Page 166
5.5.3 rmρ Structure......Page 167
5.5.4.1 Principle of the Method......Page 168
5.5.4.2 Laurie Correction......Page 169
5.5.4.3 Accuracy......Page 170
5.7 Conclusion for Empirical Structures......Page 171
References......Page 172
Contents of Appendix V ( On CD Rom): Determination of the Structural Parameters from the Iner tial Moments......Page 173
Contents of Appendix Va ( On CD ROM): Determination of the Structural Parameters from the Inertial Moments: Practical Calculation of the Moments of Inertia and the Jacobian Matrix......Page 174
Contents......Page 175
6.1 Quantum Mechanics of Vibration and Rotation......Page 176
6.2.1 The Semiclassical Quantization Condition......Page 180
6.2.2 The Rydberg–Klein–Rees Inversion Procedure......Page 184
6.2.3 Near-Dissociation Theory......Page 190
6.2.4 Conclusions Regarding Semiclassical Methods......Page 199
6.3.1 Overview and Background......Page 200
6.3.2 Potential Function Forms......Page 201
6.3.2.1 Polynomial Potential Function Forms......Page 202
6.3.2.2 The Expanded Morse Oscillator Potential Form and theImportance of the Definition of the Expansion Variable......Page 204
6.3.2.3 The Morse/Long-Range (MLR) Potential Form......Page 206
6.3.2.4 The Spline-Pointwise Potential Form......Page 209
6.3.3 Initial Trial Parameters for Direct Potential Fits......Page 210
6.4 Born – Oppenheimer Breakdown Effects......Page 211
6.5 Conclusion......Page 214
Appendix: What Terms Contribute to a Long- Range Potential?......Page 215
Exercises......Page 216
References......Page 217
Contents......Page 220
7.2 Nuclear Spin Statistical Weights......Page 221
7.3 Electric Dipole Moments......Page 225
7.4.1 Definition......Page 228
7.4.2 Approximate Methods......Page 229
7.4.3 Applications......Page 231
7.4.4 Planar Moments of Inertia......Page 232
7.5 Torsional Potential Function......Page 233
7.6.1 Nuclear Quadrupole Interaction......Page 235
7.6.2 Spin-Rotation Interaction......Page 236
7.6.3 Spin–Spin Interaction......Page 237
7.6.4 Use of the Off -Diagonal Elements of theQuadrupole Coupling Tensor......Page 238
7.6.5.1 Principle of the Method......Page 239
7.6.5.2 Variation of the Electric Field Gradient upon Complexation......Page 240
7.6.5.3 Determination of the Bond Lengthening fromthe Nuclear Quadrupole Coupling......Page 241
7.7 Isolated Stretching Frequencies......Page 242
References......Page 245
Contents of Appendix VII ( On CD ROM)......Page 246
8.1 Position versus Distance Averages......Page 247
8.2.1 A Short Treatise on Probability Theory......Page 252
8.2.2 The Linear Harmonic Oscillator Model......Page 254
8.2.3 The Morse Potential......Page 257
8.2.4 Probability Distribution Function of Internuclear Distances and Related Moments......Page 260
8.3 The Perturbational Route......Page 262
8.4 Variational Route......Page 266
8.4.1 Eckart–Watson Hamiltonian......Page 267
8.4.2 Rovibrational Hamiltonians in Internal Coordinates......Page 269
8.4.3 Variational Averaging of Distances......Page 270
8.4.4 Vibrationally Averaged Rotational Constants......Page 271
Major Texts on Molecular Vibrations......Page 275
Major Reviews on Nuclear Averaging......Page 276
Appendix A: Bibliographies of Equilibrium Structures......Page 277
B.1 Fundamental Constants......Page 279
B.3 Nuclear Masses......Page 280

✦ Subjects

Химия и химическая промышленность;Квантовая химия;