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E-raamat: Molecules in Electromagnetic Fields: From Ultracold Physics to Controlled Chemistry

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Roman V. Krems

Formaat: PDF+DRM
Ilmumisaeg: 21-May-2018
Kirjastus: John Wiley & Sons Inc
Keel: eng
ISBN-13: 9781119387350

Teised raamatud teemal:

Electrochemistry & magnetochemistry

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Formaat: PDF+DRM
Ilmumisaeg: 21-May-2018
Kirjastus: John Wiley & Sons Inc
Keel: eng
ISBN-13: 9781119387350

Teised raamatud teemal:

Electrochemistry & magnetochemistry

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A tutorial for calculating the response of molecules to electric and magnetic fields with examples from research in ultracold physics, controlled chemistry, and molecular collisions in fields

Molecules in Electromagnetic Fields is intended to serve as a tutorial for students beginning research, theoretical or experimental, in an area related to molecular physics. The authora noted expert in the fieldoffers a systematic discussion of the effects of static and dynamic electric and magnetic fields on the rotational, fine, and hyperfine structure of molecules. The book illustrates how the concepts developed in ultracold physics research have led to what may be the beginning of controlled chemistry in the fully quantum regime. Offering a glimpse of the current state of the art research, this book suggests future research avenues for ultracold chemistry.

The text describes theories needed to understand recent exciting developments in the research on trapping molecules, guiding molecular beams, laser control of molecular rotations, and external field control of microscopic intermolecular interactions. In addition, the author presents the description of scattering theory for molecules in electromagnetic fields and offers practical advice for students working on various aspects of molecular interactions.

This important text:

Offers information on theeffects of electromagnetic fields on the structure of molecular energy levels Includes thorough descriptions of the most useful theories for ultracold molecule researchers Presents a wealth of illustrative examples from recent experimental and theoretical work Contains helpful exercises that help to reinforce concepts presented throughout text

Written for senior undergraduate and graduate students, professors, researchers, physicists, physical chemists, and chemical physicists, Molecules in Electromagnetic Fields is an interdisciplinary text describing theories and examples from the core of contemporary molecular physics.

List of Figures

xiii

List of Tables

xxv

Preface

xxvii

Acknowledgments

xxxi

1 Introduction to Rotational, Fine, and Hyperfine Structure of Molecular Radicals

(34)

1.1 Why Molecules are Complex

(2)

1.2 Separation of Scales

(14)

1.2.1 Electronic Energy

(5)

1.2.2 Vibrational Energy

(4)

1.2.3 Rotational and Fine Structure

(3)

1.3 Rotation of a Molecule

(4)

1.4 Hund's Cases

(2)

1.4.1 Hund's Coupling Case (a)

(1)

1.4.2 Hund's Coupling Case (b)

(1)

1.4.3 Hund's Coupling Case (c)

(1)

1.5 Parity of Molecular States

(4)

1.6 General Notation for Molecular States

(1)

1.7 Hyperfine Structure of Molecules

(7)

1.7.1 Magnetic Interactions with Nuclei

(1)

1.7.2 Fermi Contact Interaction

(1)

1.7.3 Long-Range Magnetic Dipole Interaction

(1)

1.7.4 Electric Quadrupole Hyperfine Interaction

(1)

Exercises

(4)

2 DC Stark Effect

(24)

2.1 Electric Field Perturbations

(2)

2.2 Electric Dipole Moment

(3)

2.3 Linear and Quadratic Stark Shifts

(2)

2.4 Stark Shifts of Rotational Levels

(17)

2.4.1 Molecules in 1Σ Electronic State

(4)

2.4.2 Molecules in a 2Σ Electronic State

(2)

2.4.3 Molecules in a 3Σ Electronic State

(4)

2.4.4 Molecules in a 1Π Electronic State -- Δ-Doubling

(2)

2.4.5 Molecules in a 2Π Electronic State

(2)

Exercises

(3)

3 Zeeman Effect

(22)

3.1 The Electron Spin

(4)

3.1.1 The Dirac Equation

(3)

3.2 Zeeman Energy of a Moving Electron

(1)

3.3 Magnetic Dipole Moment

(2)

3.4 Zeeman Operator in the Molecule-Fixed Frame

(1)

3.5 Zeeman Shifts of Rotational Levels

(8)

3.5.1 Molecules in a 2Σ State

(4)

3.5.2 Molecules in a 2Π Electronic State

(3)

3.5.3 Isolated Σ States

(1)

3.6 Nuclear Zeeman Effect

(6)

3.6.1 Zeeman Effect in 1Σ Molecule

(2)

Exercises

(3)

4 AC Stark Effect

(40)

4.1 Periodic Hamiltonians

(2)

4.2 The Floquet Theory

(8)

4.2.1 Floquet Matrix

(1)

4.2.2 Time Evolution Operator

(1)

4.2.3 Brief Summary of Floquet Theory Results

(2)

4.3 Two-Mode Floquet Theory

(2)

4.4 Rotating Wave Approximation

(2)

4.5 Dynamic Dipole Polarizability

(8)

4.5.1 Polarizability Tensor

(2)

4.5.2 Dipole Polarizability of a Diatomic Molecule

(2)

4.5.3 Rotational vs Vibrational vs Electronic Polarizability

101

(3)

4.6 Molecules in an Off-Resonant Laser Field

104

(3)

4.7 Molecules in a Microwave Field

107

(2)

4.8 Molecules in a Quantized Field

109

(12)

4.8.1 Field Quantization

109

(7)

4.8.2 Interaction of Molecules with Quantized Field

116

(1)

4.8.3 Quantized Field vs Floquet Theory

117

(1)

Exercises

118

(3)

5 Molecular Rotations Under Control

121

(24)

5.1 Orientation and Alignment

122

(14)

5.1.1 Orienting Molecular Axis in Laboratory Frame

123

(3)

5.1.2 Quantum Pendulum

126

(3)

5.1.3 Pendular States of Molecules

129

(2)

5.1.4 Alignment of Molecules by Intense Laser Fields

131

(5)

5.2 Molecular Centrifuge

136

(4)

5.3 Orienting Molecules Matters -- Which Side Chemistry

140

(2)

5.4 Conclusion

142

(3)

Exercises

142

(3)

6 External Field Traps

145

(30)

6.1 Deflection and Focusing of Molecular Beams

146

(5)

6.2 Electric (and Magnetic) Slowing of Molecular Beams

151

(4)

6.3 Earnshaw's Theorem

155

(3)

6.4 Electric Traps

158

(4)

6.5 Magnetic Traps

162

(3)

6.6 Optical Dipole Trap

165

(2)

6.7 Microwave Trap

167

(1)

6.8 Optical Lattices

168

(3)

6.9 Some Applications of External Field Traps

171

(4)

Exercises

173

(2)

7 Molecules in Superimposed Fields

175

(12)

7.1 Effects of Combined DC Electric and Magnetic Fields

175

(6)

7.1.1 Linear Stark Effect at Low Fields

175

(3)

7.1.2 Imaging of Radio-Frequency Fields

178

(3)

7.2 Effects of Combined DC and AC Electric Fields

181

(6)

7.2.1 Enhancement of Orientation by Laser Fields

181

(1)

7.2.2 Tug of War Between DC and Microwave Fields

182

(5)

8 Molecular Collisions in External Fields

187

(30)

8.1 Coupled-Channel Theory of Molecular Collisions

188

(20)

8.1.1 A Very General Formulation

188

(3)

8.1.2 Boundary Conditions

191

(3)

8.1.3 Scattering Amplitude

194

(3)

8.1.4 Scattering Cross Section

197

(3)

8.1.5 Scattering of Identical Molecules

200

(4)

8.1.6 Numerical Integration of Coupled-Channel Equations

204

(4)

8.2 Interactions with External Fields

208

(3)

8.2.1 Coupled-Channel Equations in Arbitrary Basis

208

(1)

8.2.2 External Field Couplings

209

(2)

8.3 The Arthurs--Dalgarno Representation

211

(3)

8.4 Scattering Rates

214

(3)

9 Matrix Elements of Collision Hamiltonians

217

(22)

9.1 Wigner--Eckart Theorem

218

(2)

9.2 Spherical Tensor Contraction

220

(1)

9.3 Collisions in a Magnetic Field

221

(8)

9.3.1 Collisions of 1S-Atoms with 2Σ-Molecules

221

(4)

9.3.2 Collisions of 1S-Atoms with 3Σ-Molecules

225

(4)

9.4 Collisions in an Electric Field

229

(3)

9.4.1 Collisions of 2Π Molecules with 1S Atoms

229

(3)

9.5 Atom-Molecule Collisions in a Microwave Field

232

(2)

9.6 Total Angular Momentum Representation for Collisions in Fields

234

(5)

10 Field-Induced Scattering Resonances

239

(18)

10.1 Feshbach vs Shape Resonances

239

(3)

10.2 The Green's Operator in Scattering Theory

242

(1)

10.3 Feshbach Projection Operators

243

(3)

10.4 Resonant Scattering

246

(3)

10.5 Calculation of Resonance Locations and Widths

249

(3)

10.5.1 Single Open Channel

249

(1)

10.5.2 Multiple Open Channels

249

(3)

10.6 Locating Field-Induced Resonances

252

(5)

11 Field Control of Molecular Collisions

257

(26)

11.1 Why to Control Molecular Collisions

257

(2)

11.2 Molecular Collisions are Difficult to Control

259

(2)

11.3 General Mechanisms for External Field Control

261

(1)

11.4 Resonant Scattering

261

(3)

11.5 Zeeman and Stark Relaxation at Zero Collision Energy

264

(5)

11.6 Effect of Parity Breaking in Combined Fields

269

(2)

11.7 Differential Scattering in Electromagnetic Fields

271

(1)

11.8 Collisions in Restricted Geometries

272

(11)

11.8.1 Threshold Scattering of Molecules in Two Dimensions

276

(4)

11.8.2 Collisions in a Quasi-Two-Dimensional Geometry

280

(3)

12 Ultracold Controlled Chemistry

283

(14)

12.1 Can Chemistry Happen at Zero Kelvin?

284

(3)

12.2 Ultracold Stereodynamics

287

(2)

12.3 Molecular Beams Under Control

289

(1)

12.4 Reactions in Magnetic Traps

289

(2)

12.5 Ultracold Chemistry -- The Why and What's Next?

291

(6)

12.5.1 Practical Importance of Ultracold Chemistry?

291

(2)

12.5.2 Fundamental Importance of Ultracold Controlled Chemistry

293

(1)

12.5.3 A Brief Outlook

294

(3)

A Unit Conversion Factors

297

(2)

B Addition of Angular Momenta

299

(8)

B.1 The Clebsch-Gordan Coefficients

301

(2)

B.2 The Wigner 3j-Symbols

303

(1)

B.3 The Raising and Lowering Operators

304

(3)

C Direction Cosine Matrix

307

(2)

D Wigner D-Functions

309

(6)

D.1 Matrix Elements Involving D-Functions

311

(4)

E Spherical Tensors

315

(6)

E.1 Scalar and Vector Products of Vectors in Spherical Basis

317

(1)

E.2 Scalar and Tensor Products of Spherical Tensors

318

(3)

References

321

(26)

Index

347

ROMAN V. KREMS is a professor of theoretical chemistry at the University of British Columbia in Vancouver, Canada. His current research focuses on understanding the effects of electromagnetic fields on dynamics of few- and many-body molecular systems, the interaction properties of molecules at extremely low temperatures, and applications of machine learning to molecular physics.

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E-raamat: Molecules in Electromagnetic Fields: From Ultracold Physics to Controlled Chemistry

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