Molecular Quantum Electrodynamics: Long-Range Intermolecular Interactions

411 Pages·2009·2.23 MB·English

by  Akbar Salam

MOLECULAR QUANTUM
ELECTRODYNAMICS
MOLECULAR QUANTUM
ELECTRODYNAMICS
Long-Range Intermolecular
Interactions
AKBAR SALAM
DepartmentofChemistry
Wake Forest University
Winston-Salem, NorthCarolina
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LibraryofCongressCataloging-in-PublicationData:
Salam,A.(Akbar)
Molecularquantumelectrodynamics:long-rangeintermolecular
interactions / A.Salam.
p.cm.
Includesbibliographicalreferencesandindex.
ISBN978-0-470-25930-6(cloth)
1. Quantumelectrodynamics. 2. Intermolecularforces. I. Title.
QC680.S152010
530.14033--dc22
2009035853
PrintedintheUnitedStatesofAmerica
10 9 8 7 6 5 4 3 2 1
To
C, P, and T
CONTENTS
PREFACE xi
1 MOLECULAR QUANTUM
ELECTRODYNAMICS: BASIC THEORY 1
1.1 Background 1
1.2 Quantum Description of Matter 5
1.3 Electrodynamics and Maxwell Equations 8
1.4 Quantization of the Free Electromagnetic Field 14
1.5 Interacting Particle–Radiation Field System 26
1.6 Multipolar Lagrangian 30
1.7 Multipolar Hamiltonian 37
1.8 Canonical Transformation 42
1.9 Perturbation Theory Solution 47
1.10 State Sequence Diagrams 55
2 MOLECULAR QUANTUM ELECTRODYNAMICS:
FIELD THEORETIC TREATMENT 60
2.1 Introduction 60
2.2 Nonrelativistic Quantum Field Theory 62
2.3 Quantum Canonical Transformation 71
vii
viii
CONTENTS
2.4 Multipolar Maxwell Fields 77
2.5 Minimal-Coupling Maxwell Fields 83
2.6 Multipolar Maxwell Fields in the Vicinity of a Source 90
2.7 Higher Multipole Moment Maxwell Fields 98
2.8 Maxwell Fields of a Diamagnetic Source 101
2.9 Electromagnetic Energy Density 104
2.10 Poynting’s Theorem and Poynting Vector 115
3 INTERMOLECULAR FORCES 121
3.1 Concept of Intermolecular Potential 121
3.2 Short-Range Forces 125
3.3 Long-Range Forces 127
3.4 Electrostatic Interaction 128
3.5 Induction Forces 134
3.6 Dispersion Forces 136
4 RESONANT TRANSFER OF ENERGY 139
4.1 Introduction 139
4.2 Diagrammatic Perturbation Theory 142
4.3 State Sequence Diagram Representation 149
4.4 Energy Transfer Between Chiral Systems 152
4.5 Emitter–Absorber Model 157
4.6 Response Theory Calculation 161
4.7 Time-Dependent Energy Transfer and Causality 164
4.8 Proof of Causality of Energy Transfer to all Orders
in Perturbation Theory 172
5 RETARDED DISPERSION FORCES 175
5.1 Introduction 175
5.2 Casimir–Polder Potential: Perturbation Theory 178
5.3 Near-Zone Potential: London Dispersion Energy 186
5.4 Far-Zone Dispersion Potential 189
5.5 State Sequence Diagrams for Dispersion Force 193
5.6 Dispersion Interaction Between One Ground and
One Excited Molecule: Perturbation Theory 199
ix
CONTENTS
5.7 Response Theory Calculation of Dispersion Forces 207
5.8 Dispersion Potential via the Method of Induced
Multipole Moments 216
5.9 Discriminatory Dispersion Interactions 222
5.9.1 Perturbation Theory 223
5.9.2 Response Theory 230
5.9.3 Induced Moment Approach 236
5.10 Interactions Involving Magnetically Susceptible
Molecules 243
5.11 Measurements of Casimir Effect 251
6 MANY-BODY FORCES 257
6.1 Introduction 257
6.2 Axilrod-Teller-Muto Dispersion Energy Shift 260
6.3 Retarded Triple-Dipole Dispersion Potential:
Perturbation Theory 266
6.4 Triple-Dipole Dispersion Energy Shift
via Craig–Power Hamiltonian 269
6.5 Triple-Dipole Dispersion Potential via Correlations
of the Dressed Vacuum Field 277
6.6 N-Body Dispersion Potential 283
6.7 Four-Body Retarded Dispersion Potential 292
6.8 Three-Body Dispersion Interaction Involving
One Excited Molecule 295
6.8.1 Time-Dependent Perturbation Theory 296
6.8.2 Coupling of Induced Dipoles 299
6.9 Mediation of Resonance Energy Transfer
by a Third Body 304
7 INTERMOLECULAR INTERACTIONS
IN A RADIATION FIELD 311
7.1 Introduction 311
7.2 Radiation-Induced Dispersion Force: Perturbation
Theory 313
7.3 Dynamic Mechanism 315
7.4 Static Mechanism 321
x
CONTENTS
7.5 Molecular and Pair Orientational Averaging 330
7.6 Polarization Analysis 332
7.6.1 Parallel Propagation 332
7.6.2 Perpendicular Propagation 334
7.7 Collapsed Graphs and Effective Interaction Hamiltonian 335
7.8 Radiation-Induced Intermolecular Interaction
via the Method of Induced Moments 339
7.9 Discriminatory Intermolecular Interaction in a
Radiation Field: Perturbation Theory 342
7.10 Radiation-Induced Chiral Discrimination:
Induced Moment Method 348
7.10.1 Linearly Polarized Radiation 351
7.10.2 Circularly Polarized Radiation 352
7.11 Freely Tumbling Chiral Pair in the Presence
of Circularly Polarized Light 353
7.12 Radiation-Induced Intermolecular Energy Shifts
Involving Magnetic Dipole and Electric Quadrupole
Polarizable Molecules 356
7.13 Higher Order Radiation-Induced Discriminatory
Intermolecular Interaction 361
APPENDIX A Higher Multipole-Dependent
Second-Order Maxwell
Field Operators 370
APPENDIX B Rotational Averaging of
Cartesian Tensors 378
REFERENCES 381
INDEX 389
PREFACE
Thetheoryofmolecularquantumelectrodynamicshasitsoriginsinthework
carriedoutbythefoundingfathersofquantummechanicsinthelate1920s.A
complete formulation of quantum theory applicable to nonrelativistic
particleswasquicklydeveloped,enablingafundamentaldescriptiontobe
givenof thechemicalandphysicalpropertiesofmatterattheatomicand
molecularlevels.Itwasonlynaturalthatsoonthereafterthenewmechanics
were applied to electromagnetic radiation, with the consequence that the
photon emerged as the particle associated with the quantization of the
Maxwellfield.Thiswasfollowedbytheconstructionofasingleconceptual
and calculational quantum mechanical framework for the study of the
interactionoflightwithmatter,whichprovidesameanstoprobethestructure
ofatomsandmoleculesthatmanifestinnumerousformsofspectroscopy.
Whilethenextgenerationoftheoreticalphysicistsfocusedtheirattention
onformulatingaself-consistentandfullycovarianttheoryofelectron–pho-
ton interaction, an endeavor that was ultimately successful, despite the
introductionofthemathematicallyandphysicallyunsatisfactorytechnique
of renormalization, a device that continues to be used in the present-day
calculationstoyieldresultsofphysicallyobservablequantitiesthatarenot
divergent,anegativefeaturethatbesetsallsuchfieldtheoriesandisinherent
tothem,progressinthenoncovarianttheoryofradiation–matterinteraction
continued, especially in regard to the foundations of the subject and its
applicationtoproblemsofinterestinthefieldofchemicalphysics.Detailed
expositionsmaybefoundintextssuchasPower’sIntroductoryQuantum
xi
xii
PREFACE
Electrodynamics (Longmans, London, 1964), Healy’s Non-Relativistic
Quantum Electrodynamics (Academic Press, London, 1982), Craig and
Thirunamachandran’sMolecularQuantumElectrodynamics(Dover,New
York, 1998),and Milonni’sThe QuantumVacuum(Academic Press,San
Diego,1994).Highlightsincludedtheexplanationofspontaneousemission
and the computation of its rate, the calculation of the Lamb shift—the
splittingofthe2S1=2and2P1=2levelsinatomichydrogen—andthederiva-
tionoftheformoftheretardeddispersionpotentialbyCasimirandPolder,to
namebutthreehistoricallysignificantexamples.Predictionsoftheseand
otherphenomena,suchastheanomalousmagneticmomentoftheelectron,
have been compared with measured values to unparalleled levels of
accuracy,intheprocessprovidingremarkableagreementwithexperiment
andreassuringlyhighdegreesofconfidenceinthetheory.
Atomic,molecular,andopticalphysicistsandtheoreticalchemistshave
extendedthedomainofapplicationofmolecularquantumelectrodynamics.
These include investigation of single- and multiphoton absorption and
emission and scattering of light by matter and the study of chiroptical
processessuchasopticalrotationandcirculardichroism.Withcontinuing
progress being made in the generation of coherent sources of radiation,
numerous and wide-ranging applications have been made to phenomena
occurringintheareaofnonlinearandquantumoptics.Examplesinclude,but
arebynomeanslimitedto,thelaser-inducedopticalactivity,hyper-Rayleigh
andRamanscattering,coherentanti-StokesRamanscattering,opticalKerr
effect,second-,third-,andhigh-harmonicgeneration,andfour-,five-,and
six-wavemixing,manyofwhosetheoreticalbasesmaybefoundinthebooks
byMukamel(PrinciplesofNonlinearOpticalSpectroscopy,OxfordUni-
versity Press, New York, 1995) and Andrews and Allcock (Optical Har-
monicsinMolecularSystems,Wiley-VCH,Weinheim,2002).
A topic of widespread interest and fundamental nature in which
quantumelectrodynamicshasmadesignificantcontributionisthefieldof
interatomic/intermolecular interactions. The QED formalism lends itself
naturallytoadescriptioninwhichcouplingbetweenmatteroccursviathe
exchangeofoneormorevirtualphotons.Considerableadvanceshavetaken
place in the last twenty-five years in the quantum electrodynamical
theoryofintermolecularforces,whichmainlyconstitutesthesubjectmatter
of this book. Before giving a standard presentation of the concept of an
intermolecularpotentialandasemiclassicalperturbationtheorytreatment
of short- and long-range forces, the latter decomposed into familiar
electrostatic, induction, and dispersion terms in Chapter 3, the quantum
theory of the nonrelativistic interaction of a charged particle with a
radiation field is explicated in Chapter 1. This entails construction of the