Electrons Atoms and Molecules in Inorganic Chemistry. A worked Examples Approach

748 Pages·2017·18.784 MB·english

by  Joseph J. Stephanos, Anthony W. Addison

Electrons, Atoms
and Molecules in
Inorganic Chemistry
A Worked Examples Approach
Joseph J. Stephanos
Anthony W. Addison
©2017ElsevierInc.
ISBN:978-0-12-811048-5
ForinformationonallAcademicPresspublicationsvisitour
websiteathttps://www.elsevier.com/books-and-journals
Contents
Preface XIII 2.5 The Angular Equation 47
2.6 The <!>-Equation 48
2.7 The 8-Equation 51
1. Particle Wave Duality
2.8 The Radial Equation 57
1.1 Cathode and Anode Rays 2.9 The Final Solution for the Full Wave
1.2 Charge of the Electron 4 Function, 111n tm(r, 0, (/J) 66
1.3 Mass of Electron and Proton 6 2.10 The Orthonormal Properties of the
1.4 Rutherford's Atomic Model 9 Real Wave Functions 71
1.5 Quantum of Energy 10 2.11 The Quantum Numbers: n, I, and m 76
1
1.6 Hydrogen Atom Line-Emission Spectra; The Principle Quantum Number, n 76
Electrons in Atoms Exist Only in Very The Quantum Numbers I and Angular
Specific Energy States 13 Momentum 76
1.7 Bohr's Quantum Theory of the The Angular Momentum Quantum
Hydrogen Atom 15 Numbers, I and m 78
1.8 The Bohr-Sommerfeld Model 18 Picture and Represent Precisely m
1
1.9 The Corpuscular Nature of Electrons, Vectors of p- and d-Orbitals 78
Photons, and Particles of Very Small Mass 18 2.12 The Spin Quantum Number, s 84
1.10 Relativity Theory: Mass and Energy, 2.13 The Boundary Surface of s-Orbital 85
Momentum, and Wavelength 2.14 The Boundary Surface of p-Orbitals 87
Interdependence 21 2.15 The Boundary Surface of d-Orbitals 91
1.11 The Corpuscular Nature of 2.16 Calculating the Most Probable Radius 99
Electromagnetic Waves 21 2.17 Calculating the Mean Radius
The Photoelectric Effect 22 of an Orbital 100
The Compton Effect 25 2.18 The Structure of Many-Electron Atoms 108
1.12 de Broglie's Considerations 26 2.19 The Pauli Exclusion Principle 109
1.13 Werner Heisenberg's Uncertainty 2.20 Slater Determinant 111
Principle, or the Principle of 2.21 Penetration and Shielding 113
Indeterminacy 27 2.22 The Building-Up Principle 11 7
1.14 The Probability of Finding an Electron 2.23 Term Structure for Polyelectron
and the Wave Function 28 Atoms 121
1.15 Atomic and Subatomic Particles 29 2.24 Term Wave Functions and Single
Elementary Particles 29 Electron Wave Functions 129
Suggestions for Further Reading 32 2.25 Spin-Orbital Coupling 131
2.26 Spin-Orbital Coupling in External
2. Electrons in Atoms Magnetic Field 133
Suggestions for Further Reading 144
2.1 The Wave Function (the Schri:idinger
Equation) 37
3. Chemical Bonding
2.2 Properties of the Wave Function 39
2.3 Schri:idinger Equation of the 3.1 Electronegativity and Electropositivity 149
Hydrogen Atom 40 3.2 Electronegativity and Electropositivity
2.4 Transformation of the Schri:idinger Trends 150
Equation From Cartesians to Spherical 3.3 Molecular and Nonmolecular
Polar Coordinates 41 Compounds 151
vii
viii Contents
3.4 Types of Bonds 152 Macrocyclic Effect 193
3.5 Metallic Bonding and General Solvation Enthalpy Differences 196
Properties of Metals 152 Donor Atom Basicity 196
Conductivity and Mobility of Electrons 153 Cavity Size 197
Luster and Free Electron Irradiation 154 Solvent Competition 197
Malleability, Cohesive Force, Number Steric Effect 198
of Valence Electrons 154 Stability and Metal Oxidation State 198
Theories of Bonding in Metals 155 Stability and Metal Ionization Potential 201
Free Electron Theory 155 3.9 Intermolecular Interactions 204
Bond Lengths 156 van der Waals Forces 204
Crystal Structures of Metals (Metallic ion-Induced Dipole Forces,
Structures) 156 ion-Dipole Forces, and Hydrogen
Alloy and Metallic Compounds 158 Bonding 206
3.6 Ionic Bonding 159 3.10 Covalent Networks and
Lattice Energy and Cohesion Giant Molecules 212
of Atomic Lattice 159 Graphite, Fullerenes, Graphene, Carbon
Born-Haber Cycle and Heat of Formation 163 Nanotubes, and Asbestos 214
Ionic Crystal Structures and the Radius Suggestions for Further Reading 225
Ratio 164
Stoichiometric and Nonstoichiometric 4. Molecular Symmetry
Defects 169
Ionic Character and Covalency 4.1 Molecular Symmetry 228
Interference 170 4.2 The Symmetry Elements 230
Ionic Character and Melting Point 1 71 Identity, E 230
Solubility of the Ionic Salts 171 Proper Rotation Axis, Cn 230
3.7 Covalent Bonding 173 Plane of Symmetry, a 233
The Lewis Structures and Octet Rule 173 (Pntpr of Symmetry, i 2.15
Exceptions to the Octet Rule 173 Sn: Improper Rotation Axis 236
Bonding and Polarity 174 4.3 The Symmetry and Point Group 238
3.8 Coordinate Covalent Bond 4.4 Some Immediate Applications 239
(Dative Bonding) 175 Dipole Moments and Polarity 239
Coordination Number and the Chirality 244
"18-Eiectron Rule" 176 Equivalent Atoms: (Or Group of Atoms) 244
Ligand Denticity 176 Crystal Symmetry 245
Nomenclature of Complexes 176 4.5 Group Theory: Properties of the
Complex Formation 178 Groups and Their Elements 250
Coordinative Comproportionation 4.6 Similarity Transforms, Conjugation,
Reaction 181 and Classes 252
Complexation Equilibrium 182 4.7 Matrix Representation 254
Multiligand Complexation 183 Matrices and Vectors 254
Stepwise Formation Constants and the Matrix Representation of Symmetry
Sequential Analysis 184 Operation 255
Complex Stability 186 Matrix Representation of Point Group 258
Hard and Soft Interactions, HSAB 186 Irreducible Representations 260
Chemical Features of Hard and Soft Ions, Irreducible and Degenerate
and Classification 189 Representations 261
Rule of Interactions 190 4.8 Motion Representations of the
Hard-Hard and Soft-Soft Interactions 190 Groups 262
Hard-Soft Interaction and Anion Translation Motion 262
Polarizabi I ity 190 Rotational Motion 264
Chelate Effect 191 4.9 Symmetry Properties of Atomic
Entropy and Chelate Formation 192 Orbitals 266
Stability and the Geometry of the Mullikan Notation 266
Chelate Ring 193 Atomic Orbital Representation 267
Contents ix
4.10 Character Tables 269 6.5 Heterodiatomic Molecules 347
Properties of the Characters of 6.6 Polyatomic Molecules 349
Representations 270 6.7 Molecular Orbitals for a Centric Molecule 351
4.11 Relation Between any Reducible and 6.8 Properties Derived From Molecular
Irreducible Representations 272 Wave Function 366
The Direct Product 274 6.9 Band Theory: Molecule Orbital Theory
4.12 Group Theory and Quantum and Metallic Bonding Orbit 394
Mechanics: Irreducible Representations 6.10 Conductors, Insulators, and
and Wave Function 275 Semiconductors 397
Suggestions for Further Reading 280 Suggestions for Further Reading 401
7. Crystal Field Theory
5. Valence Bond Theory and Orbital
Hybridization
7.1 The Advantages and Disadvantages of
Valence Bond Theory 405
5.1 Valence Bond Theory 282
7.2 Bases of Crystal Field Theory 405
5.2 VSEPR Theory and Molecular
d-Orbitals in Cubic Crystal Field 405
Geometry 283
f-Orbitals in Cubic Crystal Field 406
5.3 lsoelectronic Species 284
7.3 The Crystal Field Potential 407
5.4 Procedures to Diagram Molecular
Octahedral Crystal field Potential, Voct. 407
Structure 284
Square Planar Crystal Field Potential, Vsq.PI. 412
5.5 Valence Bond Theory and Metallic
Tetragonal Crystal Field Potential, VTetrag. 415
Bonds 288
Tetrahedral Crystal Field Potential, Vrd 417
5.6 Orbital Hybridization 290
7.4 Zero-Order Perturbation Theory 419
5.7 Rehybridization and Complex Formation 291
The Linear Combination of Atomic
5.8 Hybridization and o--/rr-Bonding 294
Orbitals, LCAO-MO, and Energy
5.9 Orbital Hybridization and Molecular
Cillc:uliltion 419
Symmetry 296
The Perturbation Theory for Degenerate
Trigonal Planar Hybridization 296
Systems 421
The Extend of d-Orbital Participation in
The Splitting of d-Orbitals in Octahedral
Molecular Bonding 301
Crystal Field, Voct. 423
Trigonal Bipyramidal Hybridization 301
The Splitting of d-Orbitals in Tetrahedral
Tetragonal Pyramidal Hybridization 303
Crystal Field, Vrd 430
Square Planar Hybridization 304
The Splitting of d-Orbitals in Tetragonal
Tetrahedral Hybridization 306
Crystal Field, Vo.h 435
Octahedral Hybridization 308
7.5 Types of Interactions That Affect the
5.10 Hybrid Orbitals as Symmetry
Crystal Field Treatment 442
Adapted Linear Combination of Atomic
7.6 Free Jon in Weak Crystal Fields 442
Orbitals (SALC) 311
Problems and the Required
5.11 Molecular Wave Function as Symmetry
Approximations 442
Adapted Linear Combination of Atomic
The Effect of the Crystal Field on S Term 442
Orbitals (SALC) 322
The Effect of the Cubic Crystal Field on
Suggestions for Further Reading 330
P Term 442
The Effect of a Cubic Crystal Field on
6. Molecular Orbital Theory
D Term 44f)
6.1 Molecular Orbital Theory Versus The Effect of a Cubic Crystal Field
Valence Bond Theory 332 on F Term 447
6.2 Molecular Orbital Wave Function and The Effect of a Cubic Crystal Field on G,
Symmetry 333 H, and I 455
6.3 The Linear Combination of Atomic 7.7 Strong Field Approach 457
Orbitals-Molecular Orbital (LCAO-MO) Determinantal Wave Functions 457
and Hi.ickel Approximations 333 The Determinantal Wave Functions of d2
6.4 Atomic Orbitals Combinations for the in Strong Field of Tetragonal Structure,
Second Row Diatomic Molecules 338 Trans-ML Z 457
4 2
X Contents
The Symmetry and the Energy of 9.8 Vibrations of Polyatomic Molecules 532
Determinant Wave Functions of D2 in 9.9 Polyatomic Molecular Motions and
a Strong Field of Trans-ML Z 458 Degrees of Freedom 532
4 2
The Appropriate Hamiltonian in Strong 9.10 Normal Modes of Vibration, Normal
Field 459 Coordinates, and Polyatomic
The Diagonal Interelectronic Repulsion 460 Molecules 533
The Nondiagonal Interelectronic Repulsion 9.11 Vibrational Energy of Polyatomic
and the Energy of Each Level of the d2 Molecules 536
Configuration in Strong Field of Trans- 9.12 Vibrational Displacements 536
ML Z 463 9.13 Vibrational Energy and Normal
4 2
Suggestions for Further Reading 470 Coordinates 537
9.14 Stretching Vibrations of Linear
8. Ligand Field Theory
Molecules 543
9.15 Symmetry and Normal Modes of
8.1 The Advantages and Disadvantages of
Vibration 545
Crystal Field Theory 472
9.16 Assigning the Normal Modes of
8.2 Symmetry and Orbital Splitting by
Vibration 549
Ligand Field 473
Normal Modes of Vibration for
8.3 Correlation Table 478
Linear Triatomic Molecule 552
Orbital Correlation Table 478
9.17 Force Constants and the GF-Matrix
Term Correlation Tables 480
Method 555
8.4 Correlation Diagrams of Strong and
Lagrange's Equation in Terms of
Weak Fields 481
Symmetry Coordinates 565
Correlation Diagram of Strong and
9.18 Selection Rules 568
Weak Field States of Oh 481
IR-Selection Rules 568
Method of Descending Symmetry
Raman Selection Rules 571
(Descending Multiplicities of the
9.19 Center of Symmetry and the Mutual
Orbital States) 485
Exclusion Rule 575
Correlation Diagram of Weak and Strong
9.20 Isolation of a Particular Type of
Field States of Td 486
Motion 576
8.5 Orgel Diagram 488
9.21 Detecting the Changes of Symmetry
Orgel Diagram of D Term Configuration 488
Through Reaction 581
Orgel Diagram ofF Term 489
Suggestions for Further Reading 582
Configuration and Term Interactions 493
8.6 Tanabe-Sugano Diagrams 498
The Advantages 498
dn and d10- n Diagrams 499 10. Electronic Spectroscopy
d5 Diagram 502
10.1 Beer-Lambert Law 587
Suggestions for Further Reading 503
Molar Extinction Coefficient,
9. Vibrational Rotational Spectroscopy Oscillator Strength, and Dipole
Strength 587
9.1 Infrared and Raman Spectroscopy 507 10.2 Allowed Electronic Transition 589
9.2 Permanent Dipole and Polarizability 509 The Transition Moment and Electronic
9.3 The Classical Explanation of Infrared Transitions 589
and RAMAN Spectroscopy 509 The Born-Oppenheimer Approximation 590
9.4 Rotation of Diatomic Molecules 511 Even and Odd Functions and the
Rigid and Nonrigid Models 514 Symmetry Considerations 590
9.5 Vibration of Diatomic Molecules 515 Symmetry Representations and the
Vibrational Energy Levels 516 Allowed Transitions 591
Anharmonic Oscillation 521 10.3 Basis of the Selection Rules 592
9.6 The Quantum Mechanics of the 10.4 Selection Rules 593
Translation, Vibration, and Spin, Orbital, and Vibrational
Rotation Motions 523 Constraints 593
9.7 Vibration-Rotation Energies of Diatomic 10.5 Unexpected Weak Absorbance 595
Molecules (Vibrational-Rotational State) 529 10.6 Spectroscopy of Electronic Excitations 597
Contents xi
10.7 Electronic Spectra of Selected Examples 601 11. Magnetism
Jahn-Teller Theorem and Vibronic
Coupling: d1 Configuration 601 11.1 Magnetic Susceptibility 648
11.2 Types of Magnetic Behaviors 649
The Expected Position of Absorption
Peaks: d2 Configuration 603 11.3 Diamagnetic Behavior 652
Configuration Interaction: d3 11.4 Spin-Only Magnetic Susceptibility,
Magnetic Moment, and Thermal
Configuration 605
Spreading 654
Temperature and Absorption Spectra 607
11.5 Orbital Magnetic Moment 659
Spectrochemical Series 607
Configuration: Cr(H20)6 2+ Versus 11.6 Second-Order Zeeman Effect and
Cr(H20)63+ 609 Van Vleck Equation 662
Octahedral Versus Tetrahedral: d5 11.7 Spin-Orbital Coupling and
Magnetic Susceptibility 664
Configuration 609
11.8 Spin-Orbital Coupling: In A and E
Simultaneous Pair Excitations: Bridged
Ground Terms 671
Dinuclear Metal Centers 612
11.9 Spin-Orbital Coupling: In T Ground
Bandwidth in the Electronic Spectra 614
The Low-Spin Versus High-Spin: d6 Terms 672
11.10 Curie Law, Deviation, and Data
Configuration 615
Representations 678
The Effect of Low Symmetry 618
Band Intensity and Ligand-Field: d7 11.11 The Magnetic Behaviors of
Compounds Contain a Unique
Configuration 621
dB Configuration: d2 Versus dB Magnetic Center 681
Spin Crossover Compounds 681
Complexes 623
11.12 Structure-Linked Crossover, Thermal
Calculation of Oq and fJ for
Isomerization 688
Octahedral Ni(ll) Complexes 624
d9 Configuration: rc-Binding 626 11.13 Interactions Between Magnetic
Centers 691
Intensely Colored Metal Complexes 630
Homobinuclear Interaction 691
Donor-Acceptor Complexes 631
Heterobinuclear Interaction 696
10.8 Spectroscopy of Porphyrins 632
Coupling Mechanisms in Binuclear
Configuration Interaction, Absorption
Compounds 700
of the Unpolarized Light 632
11.14 Measurement of the Magnetic
The Vibronic Excitation of Ov-Band (/})
Susceptibility 701
in Electronic-Spectra of Hemoproteins 635
Gouy's Method 702
10.9 The Magnetic Dipole Moment and
Faraday's Method 705
the Absorbance Intensity 635
Quincke's Method 706
Circular Dichroism Spectroscopy 636
NMR Method 708
The Effects of Lower Symmetry 639
Suggestions for Further Reading 709
Absolute Configuration 640
Kuhn anisotropy Factor and Deducing
the Energy Levels Within the Mathematics Supplement 711
Molecule 641 Character Tables 729
Suggestions for Further Reading 644 Index 739
Preface
This book presents the chemical concepts that govern the chemistry of molecular construction. The emphasis is on the
building up of an understanding of essential principles and on familiarization with basic inorganic concepts. Necessary
backgroundinformationisintroducedtocomprehendthefieldfrombothchemicalandpracticalareas.Thebookexplains
anddetailsthefundamentalsthatserveasasourceofnumerousbasicconceptsofmethodsandapplications.Thecombi-
nationofthebasicconcepts,methodsandapplicationswithexampleexercisesyieldsamorepositiveoutcomeforstudents
andteachers.
Manyinorganictextbooksthatareavailablecovertoomuchmaterialanddonotgointothedepthneededforfunda-
mentalprinciples.Mostoftheseareseemtobeeitherfairlyelementaryorveryadvanced.Studentsmightbedispleasedby
thecurrentselectionavailable,andthereisagreatneedforaninorganicprinciplesofchemicalbondingtext.Inourbook,
webridgeandintegratebothelementaryandmoreadvancedprinciples.Astudentshouldbeabletobecomefamiliarwith
thetopicspresentedwiththisonebook,ratherthanlearnthebasicsinoneanduseanotherforthemoreadvancedaspectsof
the material.
Giventhecomplexandabstractnatureofthesubject,thebookiseasytofollow.Thetextiscarefullythoughtthrough
andlaidout.Theapproachofdevelopingthematerialbyansweringquestionsandproblemsrelevanttoinorganicchemistry
in extensive mathematical detail is unique and makes the book attractive especially for university students, as a study
materialsourceforexaminations.Everymathematicalstepinthebookiselaboratedwithcloseattentiontoeverydetail.
Thatnecessarymathematicalfoundationisfoundinaseparatesupplement,asanentirelynon-mathematicalapproachwill
beoflittlevalueforthepurpose.Thebulletpointapproachofansweringcommonquestionsratherwritinganarrativeand
startingeachchapterwiththecircleschemedescribingthesectionstobediscussedareintendedtobeattention-catchingand
could attract certainstudents andaid themas they study.
Thecontentandthestyleofthebookshouldcapturereadersfrombothtraditionalandmodernschools.Itisusefulasa
referenceandtextforspecializedandgraduatecoursesinphysicalinorganicoradvancedorganicchemistry.Thebookis
intendedforadvancedundergraduatesandforpostgraduatestakingcoursesinchemistry,studentsstudyingatomicstructure
andmoleculeformationinchemicalengineeringandmaterialscience.Itshouldalsobeofvaluetoresearchworkersinother
fields,whomightneedanintroductiontoessentialinorganicprinciples.Thisbookisverysuitableforself-study;therange
coveredissoextensivethatthisbookcanbestudent’scompanionthroughouthisorheruniversitycareer.Atthesametime,
teachers can turnto itfor ideasand inspiration.
Thisbookisdividedinto11chapters,andcoversafullrangeoftopicsininorganicchemistry:wave-particleduality,
electrons in atoms, chemical bonding, molecular symmetry, theories of bonding, valence bond theory, VSEPR theory,
orbital hybridization, molecular orbital theory, crystal field theory, ligand field theory, vibrational, rotational, and elec-
tronic spectroscopy, magnetism and finally, a mathematics supplement outlining the necessary methods.
Inthebeginningofthisbookwedevelopandprovideanunderstandingofthedualwave-particlenatureofelectrons,
photons, andotherparticles ofsmallmass.
Schr€odinger’smethodislinkedforexploringthemoderntheoryofatomicstructure,andtoestablishtheformalmath-
ematical framework. This framework is employed to set up the final real solution for the full orbital wave function and
identify the four quantum numbers n, l, m, and s, also to compute the most probable radius, mean radius of an orbital,
andtheboundarysurfacesofs,panddorbitals.Theorbitalwaveequationsareusedasthekeyfeatureinordertoexplain
theorbitalandspinangularmomenta,aswelltheelectronicconfigurationsofmany-electronatoms,andspin-orbitalcou-
pling.Weexaminehowtoidentifythetermsymbolsofthegroundstateandthedifferenttermsoftheexcitedmicrostatesof
polyelectronicatoms,andhowmanysubtermsarisewhenspin-orbitcouplingistakenintoconsideration.Thesplittingof
Russell–Saunders terms into microstates in an external magnetic field and their energies are identified. The term wave
functions and the corresponding single electron wave functions are described in order to understand the effect of the
ligand field.
Thenwebeginwithareviewofbasicelectronaccountingproceduresfordifferenttypesofbondformationandproceed
toamodelforpredictingthree-dimensionalmolecularstructure.Thebasicconceptsofmetallicstructurethatdescribethe
bonding,definetheroleofthefreevalenceelectrons,andrelatethephysicalpropertiesandtheoriesofmetallicbondingare
explored.Emphasisisalsoplacedonionicbondingandtherelationshipsamongthelatticeenergy,thermodynamicparam-
etersandcovalency.We reviewthegroundsoftheioniccrystal structure,inwhich radiusratios governthegeometrical
arrangements,andreviewthefactorsthatinfluencethesolubilities.Thefoundationandbasicsofcoordinationchemistryare
laid out: firstly, characterization, formulation, formation and stability including hard and soft acid/base interactions, the
chelate and macrocycle effects, cavity size, solvation enthalpy, donor atom basicity, solvent competition, steric effects,
metaloxidationstate,andmetalionizationpotential.Anextensivediscussionisgivenofintermolecularforces,exploring
theirr^oles,consequencesandsignificances.Considerationsaregiventothestructuralandchemicalnatureofthecovalent
networksin giantmolecules such diamond,graphite, fullerenes,graphene, nanotubes andasbestos.
In order to deal with molecular structures, where many energy levels of atoms are involved, symmetry concepts are
extensivelyinvoked.Thus,itisappropriatetoexplain howtoestablishapropersystemfor sortingmolecules according
totheirstructures.Onepurposeofthissortingistointroducesomeideasandmathematicaltechniquesthatareessentialfor
understandingthestructureandpropertiesofmoleculesandcrystals.Matrixrepresentationsofsymmetryoperations,point
group,translation,rotationmotions,andatomicorbitalarethoroughlyexamined.Thisleadstopresentationofthecharacter
tables,andfinallyshowshowthatthesymmetryrepresentationsfortheatomicorbitalsformbasesforthemolecularwave
functions.
Thevalencebondtheoryconceptisexplained,thenweinvestigatehowtopredicttheshapesandgeometriesofsimple
molecules using the valence shell electron-pair repulsion method. The process of predicting the molecule’s structure is
reviewed.Aswell,therelationshipsbetweenthechemicalbondsinmoleculesanditsgeometryusingorbitalhybridization
theoryareaddressed.Specialattentionisdevotedtotheanglesbetweenthebondsformedbyagivenatom,alsotomultiple
bonding and σ/π hybridization of atomic orbitals. Symmetry-adapted linear combination of atomic wave functions
(SALC’s)arecomposedanddetailed,thenusedtocomputethecontributionofeachatomicorbitaltothehybridorbitals.
A brief representation of molecular orbital theory is elaborated. Understanding the electronic distribution of some
electedsmallmolecules,andapproachestotherelativeenergiesofthemolecularorbitalsarereviewed.Wethenexplain
howtheelectrondistributionchangesupongoingtosomelow-lyingexcitedelectronicstates.Thetheoryisemployedto
estimateenergychangesinchemicalreactions,tostudystability&reactivity,tofindthedelocalizationenergy,electron
density,formalcharge,bondorder,ionizationenergy,equilibriumconstant,andconfigurationinteraction.Theorbital
combination introduces the band theory concept that makes it possible to rationalize conductivity, insulation and
semiconductivity.
Havingnowavailablethevalenceorbital’swavefunctionsofthecentralionintheirrealforms,itispossibletoexplore
theimpactofvariousdistributionsofligandatomsaroundthecentralionuponitsvalenceorbitals.Aquantitativebasisof
thiseffectinthecaseofapurelyionicmodelofcoordination,andotherdegreesofmixingareaddressed.Inthispart,we
indicatewhythereisaneedforbothcrystalfieldtheoryandligandfieldtheory.Theeffectofacubiccrystalfieldond-and
f-electronsisintroduced,thentheexpressionsoftheHamiltoniantofindthecrystalfieldpotentialexperiencedbyelectrons
inoctahedral,squareplanar,tetragonallydistortedoctahedral,andtetrahedralligandarrangementsarecomputed.Theper-
turbationtheoryfordegeneratesystemsisusedtoexplainhowthecrystalfieldpotentialofthesurroundingligandsperturbs
thedegeneracyofdorbitalsofthecentralion.Theenergiesoftheperturbedd-orbitalsarecalculatedbysolvingthesecular
determinant.Theobtainedenergiesarefedbackintosecularequationsthatarederivedfromtheseculardeterminanttoyield
wavefunctionsappropriateforthepresenceofthepotential.Thevariationinthepotentialenergyofeachdelectrondueto
the crystal field isdetermined and the splitting of d-orbitals so deduced inoctahedral, tetrahedral, tetragonallydistorted
D geometriesintermsofD ,D,andD.Problemsandtherequiredapproximationsarediscussedforthefreeioninweak
4h q t s
crystal field. Then, we study the influence of weak field on polyelectronic configuration of free ion terms, and find the
splitting in each term and the wave function for each state. In the strong field situation, the first concern was how the
strong field differs from the weak field approach; define the determinant, symmetry and the energy of each state. We
compute the appropriate Hamiltonian and the diagonal and off-diagonal interelectronic repulsion in terms of the Racah
parametersA, B, and C.
Wefirstlyexaminehowitispossibletousesymmetryandgrouptheorytofindwhatstateswillbeobtainedwhenanion
isplacedintoacrystallineenvironmentofdefinitesymmetry.Secondly,therelativeenergiesofthesestateswillbeinves-
tigated.Thirdly,weshowhowtheenergiesofthevariousstatesintowhichthefreeiontermaresplitdependonthestrength
of the interaction of the ion with its environment. The relationship between the energy of the excited states and D are
q
discussed using correlation, Orgel, andTanabe-Sugano diagrams.
Thevibrationalspectraofdiatomicmoleculesestablishmostoftheessentialprinciplesthatareusedforcomplicated
polyatomicmolecules.Sinceinfraredradiationwillexcitenotonlymolecularvibrationbutalsorotation,thereisaneedto
comprehendbothrotationandvibrationofdiatomicmoleculesinordertoanalyzetheirspectra.Molecularvibrationsare
explainedbyclassicalmechanicsusingasimpleballandspringmodel,whereasvibrationalenergylevelsandtransitions
between them are concepts taken from quantum mechanics. The quantum mechanics of the translation, vibration and
rotation motions are explored in detail. As well, the expression for the vibration-rotation energies of diatomic molecule
for the harmonic and anharmonic oscillator models is introduced. Then, we identify the Schr€odinger equation for the
vibrationsystemofn-atommolecules.Weelucidatehowtoobtain,monitor,andexplainthevibrational–rotationalexci-
tations,findthequantummechanicalexpressionforthevibrationalandrotationalenergylevels,predictthefrequencyofthe
bands,andcompareharmonicvs.anharmonicoscillatorsandbetweenrigidandnonrigidrotormodelsforthepossibleexci-
tations.Lagrange’sequationisusedtoshowthechangeintheamplitudeofdisplacementwithtime.Weexaminealsohow
tocalculatetherelativeamplitudesofmotionandthekineticandpotentialenergiesforthevibrationalmotionsofann-atom
molecule.CalculationoftheforceconstantsusingtheGF-matrixmethodarediscussed.Thegeneralstepstodeterminethe
normalmodesofvibration,andthesymmetryrepresentationofthesemodesareoutlined.Weexaminetherelationshipand
thedifferencesamongthecartesian,internal,andnormalcoordinatesusedtocharacterizethestretchingvibrations.Then
weshowwhythenormalcoordinatesareusedtocalculatethevibrationalenergyofpolyatomicmolecules.Inthispartwe
alsofocusonhowthemoleculesinteractwiththeradiationandthechemicalinformationobtainablebymeasurementofthe
infrared and Raman spectra. Only the radiation electric field interacts significantly with molecules and is important in
explaininginfraredabsorptionandRamanscattering.Therequirementsandtheselectionrulesfortheallowedvibrational
and rotational excitations are explored. We investigate the relationship between the center of symmetry and the mutual
exclusion rule, how todistinguish among isomersand ligand bindingmodes,and define the forms ofthe normal modes
ofvibrationand which of these modes are infrared and/or Raman active.
Wethenfocusonthechemicalinformationobtainedfromelectronicspectrainthevisibleandultravioletregions.We
examinetherelationshipbetweenthesoluteconcentrationandlightabsorbance,aswellthecorrelationamongthemolar
extinctioncoefficient,integratedintensityanddipolestrength.ThesignificanceoftheBorn-Oppenheimerapproximationis
considered,andsymmetryconsiderationsareelaboratedwithrespecttoallowednessofelectronictransitions.Theconse-
quences of spin, orbital and vibrational constraints are investigated to explore the basis of the electronic absorption
selectionrules.Theelectronicexcitationoffunctionalgroups,donor–acceptorcomplexes,andporphyrinsarespectroscop-
icallycharacterized.Thestudyoutlinestheroles ofvibroniccoupling,configurationinteraction,andπ-bonding.Factors
that affect the bandwidth, band intensity, and intense colors of certain metal complexes are also identified. The text
addresses the effects of Jahn–Teller distortion, temperature, and reduced symmetry, and elaborates the spectrochemical
series.Comparativestudiesofoctahedralversustetrahedral,low-spinversushigh-spin,anddnversusd10-nconfiguration
areconducted.WeillustratehowtoevaluateD andβ fromthepositionsoftheabsorptionpeaks,anddiscusstheunex-
q
pectedlyweakabsorbances,simultaneouspairexcitations,andtheabsorptionofunpolarizedlightingeneral.Theroleofthe
magneticdipolemomentontheabsorbanceintensityisinvestigated,usingcirculardichroismspectroscopyandtheKuhn
anisotropy factor to examine the effects of lower symmetry, absolute configuration, and the energy levels within the
molecule
Finallyweinvestigatethetypesofmagneticbehaviors,givingkeydefinitionsandconceptsleadingtotherelationships
relevanttomagnetochemistry.Theseprovideabridgetounderstandspinandorbitalcontributionstomagneticmoments.
Then,thermalspreadingusingtheBoltzmanndistributionisemployedtoinvestigateandestimatethemagneticmoments
andsusceptibilities.ThesubsequentsectiondealswiththevanVlecktreatmentandthesecondorderZeemanEffecttolink
thespinandorbitalcontributionstothemagneticsusceptibility.Requirementsandconditionsfornonzeroorbitalcontri-
butionarediscussed.Thefollowingsectionisdevotedtotheeffectofimpositionofaligandfieldonspin-orbitalcouplingin
A,E,andTgroundterms.TheCurielaw,deviations,anddatapresentationmodesareshown.Spin-crossoverandtheeffects
ofthermaldistortionarediscussed,followedbythebehaviorofdinuclearsystemswithexchangecoupling.Finally,Gouy’s,
Faraday’s,Quincke’s, andNMRmethods for susceptibility are described.
Joseph J. Stephanos
Anthony W. Addison