Atkins’ Physical Chemistry

Cover......Page 1
PREFACE......Page 7
USING THE BOOK......Page 8
ABOUT THE AUTHORS......Page 12
ACKNOWLEDGEMENTS......Page 13
BRIEF CONTENTS......Page 15
FULL CONTENTS......Page 17
CONVENTIONS......Page 27
LIST OF TABLES......Page 28
LIST OF THE CHEMIST’S TOOLKITS......Page 30
LIST OF MATERIAL PROVIDED AS A DEEPER LOOK......Page 31
LIST OF IMPACTS......Page 32
PROLOGUE Energy, temperature, and chemistry......Page 33
FOCUS 1 The properties of gases......Page 35
(a) Pressure......Page 36
(b) Temperature......Page 37
1A.2 Equations of state......Page 38
(a) The empirical basis......Page 39
(b) Mixtures of gases......Page 41
Checklist of equations......Page 42
1B.1 The model......Page 43
(a) Pressure and molecular speeds......Page 44
(b) The Maxwell–Boltzmann distribution of speeds......Page 45
(c) Mean values......Page 47
(a) The collision frequency......Page 49
Checklist of equations......Page 50
1C.1 Deviations from perfect behaviour......Page 51
(b) Virial coefficients......Page 52
(c) Critical constants......Page 54
(a) Formulation of the equation......Page 55
(b) The features of the equation......Page 56
(c) The principle of corresponding states......Page 58
Checklist of equations......Page 59
FOCUS 2 The First LawThe......Page 65
(a) Operational definitions......Page 66
(b) The molecular interpretation of heat and work......Page 68
(a) Molecular interpretation of internal energy......Page 69
2A.3 Expansion work......Page 70
(b) Expansion against constant pressure......Page 71
(c) Reversible expansion......Page 72
(d) Isothermal reversible expansion of a perfect gas......Page 73
(a) Calorimetry......Page 74
(b) Heat capacity......Page 75
Checklist of equations......Page 77
(a) Enthalpy change and heat transfer......Page 78
(b) Calorimetry......Page 79
(a) Heat capacity at constant pressure......Page 80
(b) The relation between heat capacities......Page 81
Checklist of equations......Page 82
(a) Enthalpies of physical change......Page 83
(b) Enthalpies of chemical change......Page 84
(c) Hess’s law......Page 85
2C.2 Standard enthalpies of formation......Page 86
2C.3 The temperature dependence of reaction enthalpies......Page 87
(a) Differential scanning calorimetry......Page 88
Checklist of concepts......Page 89
Checklist of equations......Page 90
2D.1 Exact and inexact differentials......Page 91
(a) General considerations......Page 92
(b) Changes in internal energy at constant pressure......Page 94
2D.3 Changes in enthalpy......Page 95
(a) The observation of the Joule–Thomson effect......Page 96
(b) The molecular interpretation of the Joule–Thomson effect......Page 97
Checklist of equations......Page 98
2E.1 The change in temperature......Page 99
2E.2 The change in pressure......Page 100
Checklist of equations......Page 101
FOCUS 3 The Second and Third Laws......Page 109
3A.1 The Second Law......Page 110
(a) The thermodynamic definition of entropy......Page 112
(b) The statistical definition of entropy......Page 113
(a) The Carnot cycle......Page 114
(c) The Clausius inequality......Page 117
Checklist of concepts......Page 118
Checklist of equations......Page 119
3B.1 Expansion......Page 120
3B.2 Phase transitions......Page 121
3B.4 Composite processes......Page 122
Checklist of equations......Page 123
3C.1 The calorimetric measurement of entropy......Page 124
(a) The Nernst heat theorem......Page 125
(b) Third-Law entropies......Page 126
(c) The temperature dependence of reaction entropy......Page 127
Checklist of equations......Page 128
(a) Criteria of spontaneity......Page 129
(c) Maximum work......Page 130
(d) Some remarks on the Gibbs energy......Page 131
3D.2 Standard molar Gibbs energies......Page 132
(a) Gibbs energies of formation......Page 133
(b) The Born equation......Page 134
Checklist of equations......Page 135
(a) The Maxwell relations......Page 136
(a) General considerations......Page 138
(c) The variation of the Gibbs energy with pressure......Page 140
Checklist of equations......Page 142
FOCUS 4 Physical transformations of pure substances......Page 151
(b) Phase transitions......Page 152
(c) Thermodynamic criteria of phase stability......Page 153
(a) Characteristic properties related to phase transitions......Page 154
(b) The phase rule......Page 155
(b) Water......Page 157
(c) Helium......Page 158
Checklist of equations......Page 159
(a) The temperature dependence of phase stability......Page 160
(b) The response of melting to applied pressure......Page 161
(c) The vapour pressure of a liquid subjected to pressure......Page 162
(a) The slopes of the phase boundaries......Page 163
(c) The liquid–vapour boundary......Page 164
Checklist of equations......Page 166
FOCUS 5 Simple mixtures......Page 173
(a) Partial molar volume......Page 175
(b) Partial molar Gibbs energies......Page 177
(d) The Gibbs–Duhem equation......Page 178
(a) The Gibbs energy of mixing of perfect gases......Page 179
(b) Other thermodynamic mixing functions......Page 181
(a) Ideal solutions......Page 182
(b) Ideal–dilute solutions......Page 184
Checklist of concepts......Page 185
Checklist of equations......Page 186
(a) Ideal solutions......Page 187
(b) Excess functions and regular solutions......Page 188
(a) The common features of colligative properties......Page 190
(b) The elevation of boiling point......Page 191
(d) Solubility......Page 193
(e) Osmosis......Page 194
Checklist of concepts......Page 196
Checklist of equations......Page 197
5C.1 Vapour pressure diagrams......Page 198
(a) The construction of the diagrams......Page 200
(b) The interpretation of the diagrams......Page 201
(a) Simple and fractional distillation......Page 202
(b) Azeotropes......Page 203
(a) Phase separation......Page 204
(b) Critical solution temperatures......Page 205
(c) The distillation of partially miscible liquids......Page 207
Checklist of equations......Page 208
5D.1 Eutectics......Page 209
5D.2 Reacting systems......Page 210
Checklist of concepts......Page 211
5E.1 Triangular phase diagrams......Page 212
(a) Partially miscible liquids......Page 213
Checklist of concepts......Page 214
5F.2 The solute activity......Page 215
(b) Real solutes......Page 216
5F.3 The activities of regular solutions......Page 217
(b) The Debye–Hückel limiting law......Page 219
(c) Extensions of the limiting law......Page 220
Checklist of concepts......Page 221
Checklist of equations......Page 222
FOCUS 6 Chemical equilibrium......Page 235
(a) The reaction Gibbs energy......Page 236
(a) Perfect gas equilibria......Page 237
(b) The general case of a reaction......Page 238
(c) The relation between equilibrium constants......Page 241
(d) Molecular interpretation of the equilibrium constant......Page 242
Checklist of equations......Page 243
6B.1 The response to pressure......Page 244
(a) The van ’t Hoff equation......Page 245
(b) The value of K at different temperatures......Page 247
Checklist of equations......Page 248
6C.1 Half-reactions and electrodes......Page 249
(a) Liquid junction potentials......Page 250
(a) The Nernst equation......Page 251
6C.4 The determination of thermodynamic functions......Page 253
Checklist of equations......Page 255
6D.1 Standard potentials......Page 256
(a) The measurement procedure......Page 257
(b) The determination of activity coefficients......Page 258
Checklist of concepts......Page 259
Checklist of equations......Page 260
FOCUS 7 Quantum theory......Page 267
(a) Black-body radiation......Page 269
(b) Heat capacity......Page 272
(c) Atomic and molecular spectra......Page 273
(a) The particle character of electromagnetic radiation......Page 274
(b) The wave character of particles......Page 276
Checklist of equations......Page 277
7B.1 The Schrödinger equation......Page 278
7B.2 The Born interpretation......Page 279
(a) Normalization......Page 280
(b) Constraints on the wavefunction......Page 281
Checklist of equations......Page 282
(a) Eigenvalue equations......Page 283
(b) The construction of operators......Page 284
(c) Hermitian operators......Page 285
(d) Orthogonality......Page 286
7C.2 Superpositions and expectation values......Page 287
7C.3 The uncertainty principle......Page 289
7C.4 The postulates of quantum mechanics......Page 291
Checklist of equations......Page 292
7D.1 Free motion in one dimension......Page 293
7D.2 Confined motion in one dimension......Page 294
(a) The acceptable solutions......Page 295
(b) The properties of the wavefunctions......Page 296
(c) The properties of the energy......Page 297
(a) Energy levels and wavefunctions......Page 298
(b) Degeneracy......Page 299
7D.4 Tunnelling......Page 300
Checklist of concepts......Page 303
Checklist of equations......Page 304
7E.1 The harmonic oscillator......Page 305
(a) The energy levels......Page 306
(b) The wavefunctions......Page 307
(a) Mean values......Page 309
(b) Tunnelling......Page 310
Checklist of concepts......Page 311
Checklist of equations......Page 312
7F.1 Rotation in two dimensions......Page 313
(a) The solutions of the Schrödinger equation......Page 315
(b) Quantization of angular momentum......Page 316
(a) The wavefunctions and energy levels......Page 317
(c) The vector model......Page 320
Checklist of equations......Page 322
FOCUS 8 Atomic structure and spectra......Page 335
(a) The separation of variables......Page 336
(b) The radial solutions......Page 337
(b) The energy levels......Page 340
(d) Shells and subshells......Page 341
(e) s Orbitals......Page 342
(f) Radial distribution functions......Page 343
(g) p Orbitals......Page 345
Checklist of concepts......Page 346
Checklist of equations......Page 347
8B.1 The orbital approximation......Page 348
(a) Spin......Page 349
(b) The Pauli principle......Page 350
(a) Penetration and shielding......Page 351
(b) Hund’s rules......Page 353
(c) Atomic and ionic radii......Page 355
(d) Ionization energies and electron affinities......Page 356
Checklist of concepts......Page 357
Checklist of equations......Page 358
8C.1 The spectra of hydrogenic atoms......Page 359
(a) Singlet and triplet terms......Page 360
(b) Spin–orbit coupling......Page 361
(c) Term symbols......Page 364
(e) Selection rules......Page 367
Checklist of equations......Page 368
FOCUS 9 Molecular structure......Page 373
PROLOGUE The Born–Oppenheimer approximation......Page 375
9A.1 Diatomic molecules......Page 376
9A.3 Polyatomic molecules......Page 378
(b) Hybridization......Page 379
Checklist of equations......Page 382
(a) The construction of linear combinations......Page 383
(b) Bonding orbitals......Page 385
(c) Antibonding orbitals......Page 386
Checklist of equations......Page 388
(a) σ Orbitals and π orbitals......Page 389
(b) The overlap integral......Page 391
(c) Period 2 diatomic molecules......Page 392
9C.2 Photoelectron spectroscopy......Page 394
Checklist of concepts......Page 395
Checklist of equations......Page 396
9D.1 Polar bonds and electronegativity......Page 397
9D.2 The variation principle......Page 398
(a) The procedure......Page 399
(b) The features of the solutions......Page 401
Checklist of equations......Page 402
(a) An introduction to the method......Page 403
(b) The matrix formulation of the method......Page 404
(a) π-Electron binding energy......Page 407
(b) Aromatic stability......Page 408
9E.3 Computational chemistry......Page 409
(a) Semi-empirical and ab initio methods......Page 410
(c) Graphical representations......Page 411
Checklist of equations......Page 412
FOCUS 10 Molecular symmetry......Page 419
10A.1 Symmetry operations andsymmetry elements......Page 420
10A.2 The symmetry classification of molecules......Page 422
(b) The groups Cn, Cnv, and Cnh......Page 424
(e) The cubic groups......Page 425
(a) Polarity......Page 426
Checklist of concepts......Page 427
Checklist of operations and elements......Page 428
10B.1 The elements of group theory......Page 429
(a) Representatives of operations......Page 430
(b) The representation of a group......Page 431
(c) Irreducible representations......Page 432
10B.3 Character tables......Page 433
(a) The symmetry species of atomic orbitals......Page 434
(b) The symmetry species of linear combinations of orbitals......Page 435
(c) Character tables and degeneracy......Page 436
Checklist of equations......Page 437
10C.1 Vanishing integrals......Page 438
(a) Integrals of the product of functions......Page 439
(b) Decomposition of a representation......Page 440
(b) Symmetry-adapted linear combinations......Page 441
Checklist of equations......Page 443
FOCUS 11 Molecular spectroscopy......Page 449
TOPIC 11A General features of molecular spectroscopy......Page 451
(a) Stimulated and spontaneous radiative processes......Page 452
(c) The Beer–Lambert law......Page 453
(a) Doppler broadening......Page 455
11A.3 Experimental techniques......Page 457
(b) Spectral analysis......Page 458
(d) Examples of spectrometers......Page 460
Checklist of equations......Page 461
11B.1 Rotational energy levels......Page 462
(b) Symmetric rotors......Page 464
(d) Centrifugal distortion......Page 466
(a) Selection rules......Page 467
(b) The appearance of microwave spectra......Page 468
11B.3 Rotational Raman spectroscopy......Page 469
11B.4 Nuclear statistics and rotational states......Page 471
Checklist of equations......Page 473
11C.1 Vibrational motion......Page 474
11C.2 Infrared spectroscopy......Page 475
(a) The convergence of energy levels......Page 476
(b) The Birge–Sponer plot......Page 477
11C.4 Vibration–rotation spectra......Page 478
(a) Spectral branches......Page 479
11C.5 Vibrational Raman spectra......Page 480
Checklist of concepts......Page 481
Checklist of equations......Page 482
11D.1 Normal modes......Page 483
11D.2 Infrared absorption spectra......Page 484
11D.3 Vibrational Raman spectra......Page 485
Checklist of equations......Page 486
11E.1 Classification of normal modes according to symmetry......Page 487
(a) Infrared activity of normal modes......Page 489
Checklist of concepts......Page 490
(a) Term symbols......Page 491
(b) Selection rules......Page 493
(c) Vibrational fine structure......Page 494
(d) Rotational fine structure......Page 497
11F.2 Polyatomic molecules......Page 498
(a) d-Metal complexes......Page 499
(b) π* ← π and π* ← n transitions......Page 500
Checklist of equations......Page 501
11G.1 Fluorescence and phosphorescence......Page 502
11G.2 Dissociation and predissociation......Page 504
11G.3 Lasers......Page 505
Checklist of concepts......Page 506
FOCUS 12 Magnetic resonance......Page 519
(a) The energies of nuclei in magnetic fields......Page 520
(b) The NMR spectrometer......Page 522
(a) The energies of electrons in magnetic fields......Page 523
(b) The EPR spectrometer......Page 524
Checklist of equations......Page 525
12B.1 The chemical shift......Page 526
(a) The local contribution......Page 528
(b) Neighbouring group contributions......Page 529
(c) The solvent contribution......Page 530
(a) The appearance of the spectrum......Page 531
(b) The magnitudes of coupling constants......Page 533
(c) The origin of spin–spin coupling......Page 534
(d) Equivalent nuclei......Page 535
(e) Strongly coupled nuclei......Page 536
12B.4 Exchange processes......Page 537
12B.5 Solid-state NMR......Page 538
Checklist of concepts......Page 539
Checklist of equations......Page 540
12C.1 The magnetization vector......Page 541
(a) The effect of the radiofrequency field......Page 542
(b) Time- and frequency-domain signals......Page 543
(a) The mechanism of relaxation......Page 545
(b) The measurement of T1 and T2......Page 546
12C.3 Spin decoupling......Page 547
12C.4 The nuclear Overhauser effect......Page 548
Checklist of equations......Page 550
12D.1 The g-value......Page 551
(a) The effects of nuclear spin......Page 552
(b) The McConnell equation......Page 553
(c) The origin of the hyperfine interaction......Page 554
Checklist of equations......Page 555
FOCUS 13 Statistical thermodynamics......Page 563
(a) Instantaneous configurations......Page 564
(b) The most probable distribution......Page 565
(b) The values of the constants......Page 567
Checklist of concepts......Page 568
Checklist of equations......Page 569
13B.1 The significance of the partition function......Page 570
(a) The translational contribution......Page 572
(b) The rotational contribution......Page 574
(c) The vibrational contribution......Page 578
(d) The electronic contribution......Page 579
Checklist of equations......Page 580
13C.1 The basic equations......Page 581
(b) The rotational contribution......Page 582
(c) The vibrational contribution......Page 583
(e) The spin contribution......Page 584
Checklist of equations......Page 585
13D.1 The concept of ensemble......Page 586
(b) Fluctuations from the most probable distribution......Page 587
13D.3 Independent molecules revisited......Page 588
13D.4 The variation of the energy with volume......Page 589
Checklist of equations......Page 590
(a) The calculation of internal energy......Page 591
(b) Heat capacity......Page 592
(a) Entropy and the partition function......Page 593
(c) The rotational contribution......Page 595
(d) The vibrational contribution......Page 596
(e) Residual entropies......Page 597
Checklist of equations......Page 598
13F.1 The derivations......Page 599
(b) A dissociation equilibrium......Page 602
(c) Contributions to the equilibrium constant......Page 603
Checklist of equations......Page 605
FOCUS 14 Molecular interactions......Page 615
14A.1 Electric dipole moments......Page 617
14A.2 Polarizabilities......Page 619
(a) The frequency dependence of the polarization......Page 620
(b) Molar polarization......Page 622
Checklist of equations......Page 624
(a) Charge–dipole interactions......Page 625
(b) Dipole–dipole interactions......Page 626
(d) Induced dipole–induced dipole interactions......Page 629
14B.2 Hydrogen bonding......Page 630
14B.3 The total interaction......Page 631
Checklist of equations......Page 633
(a) The radial distribution function......Page 634
(b) The calculation of g(r)......Page 635
(c) The thermodynamic properties of liquids......Page 636
(a) Surface tension......Page 637
(c) Capillary action......Page 638
(a) Surface pressure......Page 640
(b) The thermodynamics of surface layers......Page 641
14C.4 Condensation......Page 643
Checklist of equations......Page 644
14D.1 Average molar masses......Page 645
14D.2 The different levels of structure......Page 646
(a) Measures of size......Page 647
(c) Partly rigid coils......Page 650
(a) Conformational entropy......Page 651
(b) Elastomers......Page 652
14D.5 Thermal properties......Page 653
Checklist of equations......Page 654
(a) Classification and preparation......Page 655
(c) The electrical double layer......Page 656
(a) The hydrophobic interaction......Page 658
(b) Micelle formation......Page 659
(c) Bilayers, vesicles, and membranes......Page 660
Checklist of equations......Page 662
FOCUS 15 Solids......Page 671
15A.1 Periodic crystal lattices......Page 673
(a) The Miller indices......Page 675
(b) The separation of neighbouring planes......Page 676
Checklist of equations......Page 677
(a) X-ray diffraction......Page 678
(b) Bragg’s law......Page 680
(d) The electron density......Page 681
(e) The determination of structure......Page 684
15B.2 Neutron and electron diffraction......Page 686
Checklist of equations......Page 687
(a) Close packing......Page 688
(b) Electronic structure of metals......Page 690
(a) Structure......Page 692
(b) Energetics......Page 693
15C.3 Covalent and molecular solids......Page 695
Checklist of concepts......Page 696
Checklist of equations......Page 697
TOPIC 15D The mechanical properties of solids......Page 698
Checklist of concepts......Page 699
Checklist of equations......Page 700
15E.1 Metallic conductors......Page 701
15E.2 Insulators and semiconductors......Page 702
15E.3 Superconductors......Page 704
Checklist of equations......Page 705
15F.1 Magnetic susceptibility......Page 706
15F.2 Permanent and induced magnetic moments......Page 707
Checklist of concepts......Page 708
Checklist of equations......Page 709
15G.1 Excitons......Page 710
(a) Light absorption......Page 711
15G.3 Nonlinear optical phenomena......Page 712
Checklist of concepts......Page 713
FOCUS 16 Molecules in motio......Page 721
16A.1 The phenomenologicalequations......Page 722
16A.2 The transport parameters......Page 724
(a) The diffusion coefficient......Page 725
(b) Thermal conductivity......Page 726
(c) Viscosity......Page 728
Checklist of concepts......Page 729
Checklist of equations......Page 730
(a) Liquid viscosity......Page 731
(b) Electrolyte solutions......Page 732
(a) The drift speed......Page 733
(b) Mobility and conductivity......Page 735
(c) The Einstein relations......Page 736
Checklist of equations......Page 737
16C.1 The thermodynamic view......Page 738
(a) Simple diffusion......Page 740
(c) Solutions of the diffusion equation......Page 742
16C.3 The statistical view......Page 744
Checklist of concepts......Page 745
Checklist of equations......Page 746
FOCUS 17 Chemical kinetics......Page 753
(a) General considerations......Page 755
(b) Special techniques......Page 756
(a) The definition of rate......Page 757
(b) Rate laws and rate constants......Page 758
(c) Reaction order......Page 759
(d) The determination of the rate law......Page 760
Checklist of concepts......Page 761
Checklist of equations......Page 762
17B.2 First-order reactions......Page 763
17B.3 Second-order reactions......Page 765
Checklist of equations......Page 768
17C.1 First-order reactions approaching equilibrium......Page 769
17C.2 Relaxation methods......Page 770
Checklist of equations......Page 772
17D.1 The temperature dependence of reaction rates......Page 773
17D.2 The interpretation of the Arrhenius parameters......Page 774
(a) A first look at the energy requirements of reactions......Page 775
(b) The effect of a catalyst on the activation energy......Page 776
Checklist of equations......Page 777
17E.1 Elementary reactions......Page 778
17E.2 Consecutive elementary reactions......Page 779
17E.3 The steady-state approximation......Page 780
17E.4 The rate-determining step......Page 781
17E.5 Pre-equilibria......Page 782
Checklist of equations......Page 784
17F.1 Unimolecular reactions......Page 785
17F.2 Polymerization kinetics......Page 786
(a) Stepwise polymerization......Page 787
(b) Chain polymerization......Page 788
17F.3 Enzyme-catalysed reactions......Page 790
Checklist of equations......Page 793
17G.1 Photochemical processes......Page 794
17G.2 The primary quantum yield......Page 795
17G.3 Mechanism of decay of excited singlet states......Page 796
17G.4 Quenching......Page 797
17G.5 Resonance energy transfer......Page 799
Checklist of equations......Page 800
FOCUS 18 Reaction dynamics......Page 811
18A.1 Reactive encounters......Page 812
(b) The energy requirement......Page 813
(c) The steric requirement......Page 816
18A.2 The RRK model......Page 817
Checklist of equations......Page 818
(a) Classes of reaction......Page 819
(b) Diffusion and reaction......Page 820
(a) The formulation of the equation......Page 821
Checklist of concepts......Page 822
Checklist of equations......Page 823
(a) The formulation of the equation......Page 824
(c) The concentration of the activated complex......Page 825
(d) The rate constant......Page 826
(a) Activation parameters......Page 827
(b) Reactions between ions......Page 829
18C.3 The kinetic isotope effect......Page 830
Checklist of equations......Page 832
(a) Techniques......Page 833
(b) Experimental results......Page 834
(b) State-to-state reaction dynamics......Page 836
18D.3 Potential energy surfaces......Page 837
18D.4 Some results from experiments and calculations......Page 838
(a) The direction of attack and separation......Page 839
(c) Quantum mechanical scattering theory......Page 840
Checklist of equations......Page 841
18E.1 The rate law......Page 842
18E.2 The role of electron tunnelling......Page 843
18E.3 The rate constant......Page 844
18E.4 Experimental tests of the theory......Page 845
Checklist of equations......Page 847
FOCUS 19 Processes at solid surfaces......Page 855
19A.1 Surface growth......Page 856
19A.2 Physisorption and chemisorption......Page 857
19A.3 Experimental techniques......Page 858
(a) Microscopy......Page 859
(b) Ionization techniques......Page 860
(c) Diffraction techniques......Page 861
(d) Determination of the extent and rates of adsorption and desorption......Page 862
Checklist of equations......Page 863
(a) The Langmuir isotherm......Page 864
(b) The isosteric enthalpy of adsorption......Page 866
(c) The BET isotherm......Page 867
(a) The precursor state......Page 869
(b) Adsorption and desorption at the molecular level......Page 870
(c) Mobility on surfaces......Page 871
Checklist of equations......Page 872
(a) Unimolecular reactions......Page 873
(b) The Langmuir–Hinshelwood mechanismIn......Page 874
(c) The Eley–Rideal mechanism......Page 875
Checklist of equations......Page 876
19D.1 The electrode–solution interface......Page 877
(a) The Butler–Volmer equation......Page 878
19D.3 Voltammetry......Page 882
19D.4 Electrolysis......Page 884
19D.5 Working galvanic cells......Page 885
Checklist of equations......Page 886
RESOURCE SECTION......Page 893
PART 1 Common integrals......Page 894
PART 2 Units......Page 896
PART 3 Data......Page 897
PART 4 Character tables......Page 927
INDEX......Page 931