Atkins physical chemistry 9e by peter atkins and julio de paula

Atkins physical chemistry 9e by peter atkins and julio de paula Atkins physical chemistry 9e by peter atkins and julio de paula Atkins physical chemistry 9e by peter atkins and julio de paula Atkins physical chemistry 9e by peter atkins and julio de paula Atkins physical chemistry 9e by peter atkins and julio de paula Atkins physical chemistry 9e by peter atkins and julio de paula

This page intentionally left blank General data and fundamental constants Quantity Symbol Value Power of ten Units Speed of light c 2.997 925 58* 108 m s−1 Elementary charge e 1.602 176 10−19 C Faraday’s constant F = NAe 9.648 53 104 C mol−1 10 −23 J K−1 Boltzmann’s constant k 1.380 65 Gas constant R = NAk 8.314 47 8.314 47 8.205 74 6.236 37 10 10−2 10 J K−1 mol−1 dm3 bar K −1 mol−1 dm3 atm K −1 mol−1 dm3 Torr K −1 mol−1 −2 Planck’s constant h $ = h/2π 6.626 08 1.054 57 10−34 10−34 Js Js Avogadro’s constant NA 6.022 14 10 23 mol−1 Atomic mass constant mu 1.660 54 10−27 kg Mass electron proton neutron me mp mn 9.109 38 1.672 62 1.674 93 10−31 10−27 10−27 kg kg kg ε = 1/c 2μ 4πe0 μ0 8.854 19 10−12 J−1 C2 m−1 1.112 65 −10 10 J−1 C2 m−1 4π 10−7 J s2 C−2 m−1 (= T J −1 m3) μ B = e$/2me μ N = e$/2mp ge a0 = 4πε0$2/mee α = μ 0e 2c/2h α −1 c2 = hc/k σ = 2π5k 4/15h3c R = mee 4/8h3cε 02 g G 9.274 01 5.050 78 2.002 32 10−24 10−27 J T −1 J T −1 5.291 77 10−11 m Vacuum permittivity Vacuum permeability Magneton Bohr nuclear g value Bohr radius Fine-structure constant Second radiation constant Stefan–Boltzmann constant Rydberg constant Standard acceleration of free fall Gravitational constant −3 7.297 35 1.370 36 10 10 1.438 78 10−2 mK 5.670 51 10−8 W m−2 K −4 1.097 37 10 m s−2 9.806 65* 10−11 6.673 *Exact value The Greek alphabet Α, α Β, β Γ, γ Δ, δ Ε, ε Ζ, ζ alpha beta gamma delta epsilon zeta Η, η Θ, θ Ι, ι Κ, κ Λ, λ Μ, μ eta theta iota kappa lambda mu Ν, ν Ξ, ξ Π, π Ρ, ρ Σ, σ Τ, τ nu xi pi rho sigma tau Υ, υ Φ, φ Χ, χ Ψ, ψ Ω, ω cm−1 upsilon phi chi psi omega N m2 kg−2 This page intentionally left blank PHYSICAL CHEMISTRY This page intentionally left blank PHYSICAL CHEMISTRY Ninth Edition Peter Atkins Fellow of Lincoln College, University of Oxford, Oxford, UK Julio de Paula Professor of Chemistry, Lewis and Clark College, Portland, Oregon, USA W H Freeman and Company New York Physical Chemistry, Ninth Edition © 2010 by Peter Atkins and Julio de Paula All rights reserved ISBN: 1-4292-1812-6 ISBN-13: 978-1-429-21812-2 Published in Great Britain by Oxford University Press This edition has been authorized by Oxford University Press for sale in the United States and Canada only and not for export therefrom First printing W H Freeman and Company 41 Madison Avenue New York, NY 10010 www.whfreeman.com Preface We have followed our usual tradition in that this new edition of the text is yet another thorough update of the content and its presentation Our goal is to keep the book flexible to use, accessible to students, broad in scope, and authoritative, without adding bulk However, it should always be borne in mind that much of the bulk arises from the numerous pedagogical features that we include (such as Worked examples, Checklists of key equations, and the Resource section), not necessarily from density of information The text is still divided into three parts, but material has been moved between chapters and the chapters themselves have been reorganized We continue to respond to the cautious shift in emphasis away from classical thermodynamics by combining several chapters in Part (Equilibrium), bearing in mind that some of the material will already have been covered in earlier courses For example, material on phase diagrams no longer has its own chapter but is now distributed between Chapters (Physical transformation of pure substances) and (Simple mixtures) New Impact sections highlight the application of principles of thermodynamics to materials science, an area of growing interest to chemists In Part (Structure) the chapters have been updated with a discussion of contemporary techniques of materials science—including nanoscience—and spectroscopy We have also paid more attention to computational chemistry, and have revised the coverage of this topic in Chapter 10 Part has lost chapters dedicated to kinetics of complex reactions and surface processes, but not the material, which we regard as highly important in a contemporary context To make the material more readily accessible within the context of courses, descriptions of polymerization, photochemistry, and enzyme- and surface-catalysed reactions are now part of Chapters 21 (The rates of chemical reactions) and 22 (Reaction dynamics)—already familiar to readers of the text—and a new chapter, Chapter 23, on Catalysis We have discarded the Appendices of earlier editions Material on mathematics covered in the appendices is now dispersed through the text in the form of Mathematical background sections, which review and expand knowledge of mathematical techniques where they are needed in the text The review of introductory chemistry and physics, done in earlier editions in appendices, will now be found in a new Fundamentals chapter that opens the text, and particular points are developed as Brief comments or as part of Further information sections throughout the text By liberating these topics from their appendices and relaxing the style of presentation we believe they are more likely to be used and read The vigorous discussion in the physical chemistry community about the choice of a ‘quantum first’ or a ‘thermodynamics first’ approach continues In response we have paid particular attention to making the organization flexible The strategic aim of this revision is to make it possible to work through the text in a variety of orders and at the end of this Preface we once again include two suggested paths through the text For those who require a more thorough-going ‘quantum first’ approach we draw attention to our Quanta, matter, and change (with Ron Friedman) which covers similar material to this text in a similar style but, because of the different approach, adopts a different philosophy The concern expressed in previous editions about the level of mathematical ability has not evaporated, of course, and we have developed further our strategies for viii PREFACE showing the absolute centrality of mathematics to physical chemistry and to make it accessible In addition to associating Mathematical background sections with appropriate chapters, we continue to give more help with the development of equations, motivate them, justify them, and comment on the steps We have kept in mind the struggling student, and have tried to provide help at every turn We are, of course, alert to the developments in electronic resources and have made a special effort in this edition to encourage the use of the resources on our website (at www.whfreeman.com/pchem) In particular, we think it important to encourage students to use the Living graphs on the website (and their considerable extension in the electronic book and Explorations CD) To so, wherever we call out a Living graph (by an icon attached to a graph in the text), we include an interActivity in the figure legend, suggesting how to explore the consequences of changing parameters Many other revisions have been designed to make the text more efficient and helpful and the subject more enjoyable For instance, we have redrawn nearly every one of the 1000 pieces of art in a consistent style The Checklists of key equations at the end of each chapter are a useful distillation of the most important equations from the large number that necessarily appear in the exposition Another innovation is the collection of Road maps in the Resource section, which suggest how to select an appropriate expression and trace it back to its roots Overall, we have taken this opportunity to refresh the text thoroughly, to integrate applications, to encourage the use of electronic resources, and to make the text even more flexible and up-to-date Oxford Portland P.W.A J.de P 962 INDEX effect Auger 886 cage 839 centrifugal 327 Doppler 350, 366 electrophoretic 764 Joule–Thomson 80 kinetic salt 850 Meissner 731 photoelectric 256 relaxation 764 salting-in 208 salting-out 208 Stark 455, 621 effective mass 463 effective nuclear charge 344, (T) 930 effective potential energy 327 effective transverse relaxation time 544 efficiency 101 catalytic 880 effusion 745 rate of 754 Ehrenfest classification 149 Ehrenfest equations 155 eigenfunction 268 eigenvalue 268, 415 eigenvalue equation 268, 415 eigenvector 415 Einstein, A 253 Einstein coefficient 503 Einstein formula 603 Einstein formula (heat capacity) 253 Einstein relation 768 Einstein–Smoluchowski equation 773 Einstein temperature 254 elastic collision 26, 746 elastic deformation 665, 717 elastic limit 719 elastomer 665 electric conduction 745 electric dipole 4, 622 electric field 9, 250, 633 electric field strength 654 electric potential 128 electrical conductivity, temperature dependence 722 electrical double layer 673, 861 electrical heating 54 electrical power 54 electro-osmotic drag 868 electroactive species 863 electrochemical cell 227 electrochemical correlations 406 electrochemical series 236 electrode 227 counter 871 varieties 227 electrode compartment 227 electrode concentration cell 229 electrode potential 862 electrode process 861 electrode–solution interface 861 electrodialysis 672 electrokinetic potential 673 electrolysis 865 electrolyte 227, 760 electrolyte concentration cell 229 electrolytic cell 228 electromagnetic field 9, 249 electromagnetic radiation 500 electromagnetic spectrum 11, 250 electromotive force 231 electron, magnetic moment 521 electron affinity 348, (T) 931 periodicity 348 electron density 405, 703 electron diffraction 258, 709 electron gain electrical 66 enthalpy of 66, 348 electron interaction integrals 380 electron in magnetic field 521 electron microscopy 259 electron pair 342 electron pair formation 373 electron paramagnetic resonance 524, 553 electron scattering factor 738 electron spin resonance 524 electron transfer between proteins 860 reaction 822, 857 electronegativity 4, 389, (T) 933 electronic configuration 2, 342 electronic partition function 600 electronic polarizability 628 electronic structure 324 electronvolt 13 electrophoresis 680 electrophoretic effect 764 electrostatic potential surface 405 electrostatics 199 elementary reaction 802 elevation of boiling point 170 Eley–Rideal mechanism 898 elpot surface 405 emf 231 emission spectroscopy 446 Emmett, P 892 emulsification 673 emulsion 671 enantiomeric pair 426 end separation (polymer) 661 endergonic 211 endothermic process 45 energy 6, 45 conformational 668 electron in magnetic field 521 harmonic oscillator 301 multipole interaction 633 nucleus in magnetic field 522 particle in box 290 particle on ring 307 particle on sphere 312 quantization 252, 266 rotational 452 zero-point 291, 301 energy density 251, 657, 753 energy dispersal 95 energy flux 755 energy levels energy pooling 816 ensemble 579 enthalpy 56 lattice 67, 712, (T) 917 partition function 593 specific 70 variation with temperature 59 enthalpy of activation 66, 848 enthalpy of atomization 66 enthalpy of chemisorption 889, (T) 943 enthalpy of combustion 66, 68 enthalpy density 70 enthalpy of electron gain 66, 348 enthalpy of formation 66, 71 enthalpy of fusion 66, (T) 917 enthalpy of hydration 66 enthalpy of ionization 66, 347 enthalpy of mixing 66, 163 enthalpy of physisorption 889, (T) 942 enthalpy of reaction 66, 68 from enthalpy of formation 71 measurement 225 temperature dependence 73 enthalpy of solution 66 enthalpy of sublimation 66 enthalpy of transition 65, 66 enthalpy of vaporization 65, (T) 917, (T) 926 entropy Boltzmann formula 99, 577, 587 conformational 663 excess 168 from Q 582 harmonic oscillator 578 measurement 108 partial molar 112 partition function 577, 592 reaction 111 residual 111, 609 statistical definition 99, 576 thermodynamic definition 96 Third-Law 111, 577 two-level system 578 units 97 variation with temperature 107 entropy of activation 848 entropy change adiabatic process 98 heating 107 perfect gas expansion 97 phase transition 105 surroundings 98 entropy determination 108 entropy of mixing 163 entropy of transition (T) 926 entropy of vaporization 105, (T) 926 enzyme 876, 878 EPR 524, 553 EPR spectrometer 553 equation Arrhenius 799 Benesi–Hildebrand 226 Berthelot 35 Born 120, 128 Born–Mayer 713 Butler–Volmer 862, 869 Clapeyron 147 Clausius–Clapeyron 148 Clausius–Mossotti 629 Debye 629 Dieterici 35 differential 322, 796, 804 diffusion 770, 841 Ehrenfest 155 eigenvalue 268, 415 Einstein–Smoluchowski 773 Eyring 846 fundamental 121, 124, 159 generalized diffusion 771 Gibbs–Duhem 160 Gibbs–Helmholtz 125 Hartree–Fock 402 Karplus 534 Kelvin 652 Kohn–Sham 404 Margules 194 Mark–Kuhn–Houwink–Sakurada 687 material balance 843 McConnell 556 Michaelis–Menten 879 Nernst 232 partial differential 322, 323 Poisson’s 199 radial wave 326 Roothaan 402 Sackur–Tetrode 583 Scatchard 208 secular 390, 415 Stern–Volmer 819 Stokes–Einstein 769, 842 Thomson 147 transcendental 183 van der Waals 33, 35 van ’t Hoff 173, 223, 891 virial 31, 35 Wierl 737 equation of state 19 partition function 605 thermodynamic 122 equilibrium 51 approach to 796 Boltzmann distribution 220, 224 chemical see chemical equilibrium effect of compression 222 effect of temperature 223 mechanical 20 response to pressure 221 sedimentation 684 thermal 22 thermodynamic criterion 137 equilibrium bond length 372 INDEX equilibrium constant 214 contributions to 613 determination 236 molecular interpretation 220 partition function 611 relation between 218 relation to rate constant 796 standard cell potential 233 standard Gibbs energy of reaction 217 thermodynamic 216 equilibrium table 218 equipartition theorem 9, 47, 253, 601 equivalent nuclei 533, 537 ER mechanism 898 error function 319 ESR 524 essential symmetry 696 ethanol 405 ethene, MO description 396 Euler chain relation 91 Euler’s formula 286 eutectic 186 eutectic halt 186 even function 305 evolution period 546 exact differential 74, 92 criterion for 122 excess entropy 168 excess function 168 exchange–correlation energy 404 exchange–correlation potential 404 exchange current density 863, (T) 942 exchange operator 408 exchange process 539 excimer formation 816 exciplex 514 exciplex laser 514 excited-state absorption 816 excited state decay 817 exciton 724 exciton band 725 excluded volume 33 exclusion principle 342 exclusion rule 475 exercise 70 exergonic 211 exothermic process 45 exp-6 potential 642 expansion coefficient 77, (T) 926 expansion work 49 expectation value 274 exponential decay 791 exponential function 252, 741 extended Debye–Hückel law 198 extensive property 5, 47 extent of reaction 210, 786 extinction coefficient 490 extra work see additional work extrinsic semiconductor 722 eye 501 Eyring equation 846 F f block 347 face-centred cubic 710 face-centred unit cell 696 factorial 566 far-field confocal microscopy 507 far infrared region 11, 250 Faraday’s constant 199 fat 70 fcc 710 FEMO theory 411 femtochemistry 846 femtosecond spectroscopy 846 Fermi calculation 780 Fermi contact interaction 536 Fermi–Dirac distribution 721 Fermi level 721 fermion 316, 342 ferrocene 425 ferromagnetism 730 fibre 666 Fick’s first law of diffusion 756, 767 Fick’s second law of diffusion 770 FID 541, 559 field 250 electric 9, 250, 633 electromagnetic 9, 249 magnetic 9, 250 field-ionization microscopy 896 FIM 896 fine structure atomic 356 vibrational 388 fine structure (NMR) 532 finite barrier 297 first ionization energy 347 First Law of thermodynamics 48 first-order differential equation 796 first-order phase transition 150 first-order reaction 788, 791 kinetic data (T) 940 first-order spectra 538 flash desorption 888 flash photolysis 784 flocculation 674 flow method 784 fluctuations 581 fluid fluorescence 503, 815 laser-induced 851 solvent effect 505 fluorescence lifetime 818 fluorescence microscopy 507 fluorescence quantum yield 818 fluorescence resonance energy transfer 821 flux 755 foam 671 Fock, V 349 Fock operator 402 food, energy reserves 70 forbidden transition 339, 447 force 12, 281, 642 generalized 50 thermodynamic 766 force constant 282, 300, 462 force field 472 formation enthalpy of 66, 71 rate of 786 formula unit Förster theory 821, 829 four-centre integral 403 four-circle diffractometer 701 four-level laser 509 Fourier series 740 Fourier synthesis 705 Fourier transform 559, 741 Fourier-transform NMR 540 Fourier transform technique 446, 480 fractional coverage 888 fractional distillation 179 fracture 719 framework representation 902 Franck–Condon factor 496 Franck–Condon principle 495, 505, 858 Franklin, R 715 free-electron molecular orbital theory 411 free energy 117 see also Gibbs energy free expansion 51 free-induction decay 541, 559 free particle 288 freely jointed chain 661 freeze quench method 785 freezing point (T) 926 freezing-point constant 172, (T) 927 freezing temperature 138 Frenkel exciton 724 frequency 10, 250 frequency-domain signal 541 frequency doubling 727 FRET 821 Freundlich isotherm 894 frictional coefficient 684, (T) 937 Friedrich, W 700 frontier orbital 397 FT-NMR 540 fuel, thermochemical properties 70 fuel cell 867 fugacity 129 fugacity coefficient 129, (T) 927 full rotation group 425 functional 404 functional MRI 547 fundamental equation 121, 124, 159 fundamental transition 465 fusion, enthalpy of 66, (T) 917 G g subscript 382 g-value 521, 554 963 gain 727 Galileo 21 Galvani potential difference 861, 862 galvanic cell 228 working 865 γ-ray region 11, 250 gas 4, 19, 643 kinetic model 25, 745 gas constant 6, 8, 24 gas discharge lamp 479 gas laser 513 gas laws 23 gas mixture 28 gas-sensing electrode 239 gas solvation 145 gauss 521 Gaussian function 302, 741 Gaussian-type orbital 403 gel 671 general solution 322 generalized diffusion equation 771 generalized displacement 50 generalized force 50 gerade symmetry 382 Gerlach, W 314 Germer, L 258 GFP 507 Gibbs, J.W 139 Gibbs–Duhem equation 160 Gibbs energy 114 maximum non-expansion work 117 partial molar 158 partition function and 594 perfect gas 127 properties 124 surface 650 variation with pressure 126 variation with temperature 125 Gibbs energy of activation 848 electron transfer 868 Gibbs energy of formation 118, 214 Gibbs energy of mixing 162 ideal solution 167 partial miscibility 184 Gibbs energy of reaction 210, 231 standard 118, 213, 232 Gibbs energy of solvation 128 Gibbs–Helmholtz equation 125 Gibbs isotherm 651 glancing angle 702 glass electrode 239 glass transition temperature 666 global warming 474 globar 479 glucose oxidation 212 glycolysis 212 Gouy balance 729 Gouy–Chapman model 862 gradient 370 Grahame model 862 Graham’s law of effusion 754 964 INDEX grand canonical ensemble 579 graphical representation 405 graphite structure 714 gravimetry 888 gravitational potential energy green fluorescent protein 507 greenhouse effect 473 gross selection rule 447 Grotrian diagram 340 Grotthuss mechanism 762 group 2, 419 group property 420 group theory 417 GTO 403 Gunn diode 479 Gunn oscillator 553 H haemolysis 175 half-life 792 summary 795 half-reaction 228 halogen Hamilton, W 268 hamiltonian core 408 Hückel method 398 hydrogen molecule-ion 378 hamiltonian matrix 398 hamiltonian operator 267, 270 Hanes plot 906 hard sphere packing 709 hard-sphere potential 606, 642 harmonic motion 300 harmonic oscillator 301 energy 301 entropy 578 wavefunction 302 harmonic oscillator (classical) 282 harmonic wave Harned cell 233 harpoon mechanism 837 Hartree, D.R 349 Hartree–Fock equations 402 Hartree–Fock self-consistent field 349 hcp 710 heat 45 heat at constant pressure 56 heat capacity 55, 253 constant pressure 60 constant volume 54, 55 molar 60 partition function 602 phase transition 151 relation between 79, 84 relation between (perfect gas) 61 rotational transitions 603 specific 55 variation with temperature 61, (T) 916 vibrational contribution 603 heat capacity ratio 84 heat engine 94 efficiency 101 heat and work, equivalence of 48 Heisenberg uncertainty principle 276, 279 helium 342 Grotrian diagram 354 phase diagram 141 helium–neon laser 513 helix 668 helix–coil transition 615, 830 helix scattering 715 Helmholtz energy 114 molecular interpretation 116 partition function 593 Helmholtz layer model 862 Henry, W 165 Henry’s law 165 Henry’s law constant (T) 927 Hermann–Mauguin system 420 Hermite polynomial 302 hermitian operator 270 hermiticity 271 hertz 250 Hess’s law 68 heterogeneity index 679 heterogeneous catalysis 884 rate law 898 heterogeneous catalyst 876 heterogeneous reaction rate 786 heteronuclear diatomic molecule, MO description 382, 388 heteronuclear spin system 538 hexagonal unit cell 697 hexagonally close-packed 710 HF-SCF 349 high-energy phosphate bond 212 high-performance liquid chromatography 142 high-temperature superconductor 731 highest occupied molecular orbital 397 Hinshelwood, C.N 809 HOMO 397 homogeneous catalyst 876 homogenized milk 672 homonuclear diatomic molecule MO description 373 molecular orbital diagram 385 VB description 372 homonuclear spin system 538 Hooke’s law 300, 666, 719 host–guest complex 423, 640 HPLC 142 HTSC 731 Hückel, E 196, 396 Hückel approximations 396 Hückel method 396 Huggins constant 694 Hull, A 701 Humphreys series 365 Hund’s maximum multiplicity rule 345 Hush, N.S 858 hybrid orbital 375 hybridization 375 hybridization schemes 377 hydration, enthalpy of 66 hydrodynamic flow 654 hydrodynamic radius 762 hydrogen atom bound state 331 energies 328 wavefunction 328 hydrogen bond 637 hydrogen electrode 233 hydrogen fluoride, MO description 389, 394 hydrogen ion enthalpy of formation 71 Gibbs energy of formation 119 standard entropy 111 hydrogen molecule MO description 383 VB description 373 hydrogen molecule-ion 378 hydrogen/oxygen fuel cell 867 hydrogen peroxide decomposition 877 hydrogen storage 867 hydrogenation 900 hydrogenic atom 324 hydrogenic orbital, mean radius 334 hydrophilic 671 hydrophobic 638, 671 hydrophobic interaction 639 hydrophobicity constant 638 hydrostatic pressure 21 hydrostatic stress 717 hyperbola 23 hyperfine coupling constant 555, (T) 935 hyperfine structure 555 hyperpolarizability 727 hypertonic 175 hypervalent hypotonic 175 I IC 508, 816 ice 141 phase diagram 141 residual entropy 111, 610 structure 141, 715 icosahedral group 424, (T) 947 ideal-dilute solution 166 ideal gas see perfect gas ideal solution 164 Gibbs energy of mixing 167 identity operation 418 IHP 862 immiscible liquids 180 impact parameter 644 improper rotation 419 incident beam flux 655 incongruent melting 188 indefinite integral 42 independent migration of ions 760 independent molecules 582 indicator diagram 51 indistinguishable molecules 583 induced-dipole–induced-dipole interaction 636 induced dipole moment 625 induced fit model 878 induced magnetic moment 730 induction period 805 inelastic neutron scattering 758 inexact differential 75 infectious disease kinetics 907 infinite temperature 570, 571 infrared 11, 250 infrared active 464 infrared activity 477 infrared chemiluminescence 851 infrared inactive 464 infrared region 11, 250 inhibition 882 inhomogeneous broadening 544 initial condition 322 initiation step 813 inner Helmholtz plane 862 inner transition metal insulator 720 integral 42 integrated absorption coefficient 491 integrated rate law 790 summary 795 integrated signal 528 integrating factor 93 integration 42, 322 integration by parts 43 intensive property 5, 47 interference 258, 380 interferogram 481 interferometer 446, 480 intermolecular interaction 30 internal conversion 508, 816 internal energy 47 fluid 609 from Q 581 general changes in 75 heat at constant volume 54 molecular contributions 47 partition function 575, 592 properties 121 statistical 574 internal pressure 76, 122 International System (point groups) 420 International System (units) 5, 10, 20 interstellar cloud 448 interstitial impurity atom 112 intersystem crossing 505, 815 intrinsic semiconductor 722 INDEX intrinsic viscosity 686, (T) 937 inverse Fourier transform 741 inverse matrix 415 inversion, temperature 29 inversion operation 419 inversion recovery technique 544 inversion symmetry 382 inversion temperature 81, (T) 926 inverted region 861 ion activity 195 Gibbs energy of formation 119 standard entropy 111 ion channel 765 ion–ion interaction (conductivity) 763 ion mobility 761, 768 ion pump 765 ion-selective electrode 239 ionic atmosphere 196, 673, 763 ionic bond 371 ionic compound ionic mobility (T) 939 ionic radius 712, (T) 938 ionic solid 711 ionic strength 196 ionization, enthalpy of 66, 347 ionization energy periodicity 348 spectroscopic measurement 331 ionization energy 331, 347, (T) 930 irreducible representation 429 irrep 429 ISC 505, 815 isenthalpic process 80 isobar 23, 25, 29 isobaric calorimeter 57 isochore 23, 25 isodensity surface 405 isolated system 45 isolation method 789 isopleth 178 isosbestic point 518 isosteric enthalpy of adsorption 891 isotherm 23, 25, 31 isothermal compressibility 77, (T) 926 isothermal expansion 97 isothermal Joule–Thomson coefficient 81 isothermal reversible expansion 52 isotonic 175 isotope isotope abundance (T) 915 J Jablonski diagram 506 Jeans, J 251 jj-coupling 360 Joule, J.P 76 joule 6, 12, 47 Joule experiment 76 Joule–Thomson coefficient 79, (T) 926 isothermal 81 Joule–Thomson effect 80 K K-radiation 701 Karplus equation 534 Kassel, L.S 838 Kassel form 838 Keesom interaction 634 kelvin 5, 11, 22 Kelvin equation 652 Kelvin scale 5, 22 Kelvin statement 94 Kerr lens 727 Kerr medium 727 kinetic chain length 814 kinetic control 808 kinetic energy 6, 9, 26 kinetic energy density 753 kinetic energy operator 270 kinetic model of gas 25, 745 kinetic molecular theory kinetic pressure 609 kinetic theory, transport properties 757 Kirchhoff ’s law 73 klystron 479, 553 KMT see kinetic model Knipping, P 700 Knudsen method 754 Kohlrausch’s law 760 Kohn–Sham equations 404 Koopmans’ theorem 387 Krafft temperature 674 Kronecker delta 414 krypton-ion laser 513 L Lagrange method 585 Laguerre polynomial 328 Lamb formula 529 λ-line 142 λ-transition 151 Lamé constants 738 laminar flow 757 lamp 479 Landau, L 673 Langevin function 627 Langmuir, I 649 Langmuir–Blodgett film 649 Langmuir–Hinshelwood mechanism 898 Langmuir isotherm 890 lanthanoid Laplace equation 647 laplacian 199, 261, 310 Laporte selection rule 494 Larmor frequency 522, 540 laser 733 laser action 508 laser cooling 578 laser-induced fluorescence 851 laser radiation characteristics 508 lattice energy 712 lattice enthalpy 67, 712, (T) 917 lattice point 696 lattice vacancy 112 law Beer–Lambert 490 Boyle’s 23 Charles’s 23 combined gas 25 of cosines 368 Curie 729 Dalton’s 27, 176 Debye–Hückel limiting 196, 234 Debye T3 108 Dulong and Petit 253 extended Debye–Hückel 198 Fick’s first 756, 767 Fick’s second 770 First 48 gas 23 Graham’s 754 Henry’s 165 Hess’s 68 Hooke’s 300, 666, 719 independent migration of ions 760 Kirchhoff ’s 73 Kohlrausch’s 760 limiting 23, 196, 234 motion 281 Newton’s second 281 Raoult’s 164, 176 Rayleigh–Jeans 251 Second 94 Stefan–Boltzmann 284 Stokes’ 769 Third 110 Wien’s 284 Zeroth 22 LCAO-MO 378, 383, 395 symmetry considerations 439 LCAO-MO (solids) 720 Le Chatelier, H 222 Le Chatelier’s principle 222 lead–acid battery 866 LED 734 LEED 886 legendrian 261, 311 Lennard-Jones parameters (T) 936 Lennard-Jones potential 642 level atomic 355 energies 355 lever rule 178 Levich, V.G 858 levitation 731 Lewis, G.N 371 Lewis structure LH mechanism 898 965 lifetime 352 rotational state 473 lifetime broadening 352 ligand-field splitting parameter 499 ligand-to-metal transition 499 light 249, 489, (T) 934 light-emitting diode 734 light harvesting 822 light-harvesting complex 822 light scattering 681 limiting law 23, 196, 234 limiting molar conductivity 760 Linde refrigerator 82 Lindemann, F (Lord Cherwell) 809 Lindemann–Hinshelwood mechanism 809 line alternation 461 line broadening (NMR) 539 line intensity 525 line shape 351 linear combination 273 degenerate orbital 338 linear combination of atomic orbitals 378, 383, 395 linear differential equation 322 linear free energy relation 849 linear momentum 280 wavefunction 266 linear rotor 451, 454 Lineweaver–Burk plot 880 linewidth 350 lipid bilayer 764 liposome 675 liquid molecular motion 758 liquid crystal 188, 675 phase diagram 189 liquid crystal display 189 liquid junction potential 229 liquid–liquid phase diagram 181 liquid–solid phase diagram 185 liquid structure 607 liquid–vapour boundary 148 liquid viscosity 758 lithium atom 342 litre 12 LMCT 499 local contribution to shielding 528 lock-and-key model 878 logarithm 147, 200 London formula 636 London interaction 636 lone pair long-range order 607 longitudinal relaxation time 543 low energy electron diffraction 886 low overpotential limit 863 low temperature 103, 109 lower critical solution temperature 183 lowest unoccupied molecular orbital 397 LUMO 397 966 INDEX Lyman series 324 lyophilic 671 lyophobic 671 lyotropic liquid crystal 188 lyotropic mesomorph 675 M macromolecule 659 macular pigment 502 Madelung constant 713 magic-angle spinning 552 magnetic field 9, 250 magnetic flux density 728 magnetic induction 521 magnetic levitation 731 magnetic moment 521, 730 magnetic quantum number 311 magnetic resonance imaging 546 magnetic susceptibility 530, (T) 938 magnetically equivalent nuclei 537 magnetizability 729 magnetization 728 magnetization vector 540 magnetogyric ratio 521 MALDI 680 MALDI-TOF 680 manometer 21, 38 many-electron atom 324, 340 Marcus, R.A 820, 838, 858 Marcus theory 820, 858 Margules equation 194 Mark–Kuhn–Houwink–Sakurada equation 687 Mars van Krevelen mechanism 901 MAS 552 mass mass number mass spectrometry 680 material balance equation 843 matrix 414 matrix addition 414 matrix-assisted laser desorption/ionization 680 matrix diagonalization 398 matrix element 414 matrix multiplication 414 matter, nature of 316 matter flux 755 maximum multiplicity 345 maximum velocity 879 maximum work 115 Maxwell construction 35 Maxwell distribution 9, 748 Maxwell relation 122 Mayer f-function 606 MBE 724 McConnell equation 556 mean activity coefficient 195, (T) 927 mean bond enthalpy 72, (T) 932 mean cubic molar mass 678 mean displacement 304 mean distance diffused 772 mean energy 601 mean free path 752 mean molar mass 678 mean radius, hydrogenic orbital 334 mean rotational energy 601 mean speed 750 mean square displacement 304 mean square molar mass 678 mean translational energy 601 mean value theorem 43 mean value 42 mean vibrational energy 602 measurement, interpretation 274 mechanical equilibrium 20 mechanical property 717 mechanism of reaction 782 Meissner effect 731 melting, response to pressure 144 melting point (T) 914 melting temperature 138 melting temperature (polymer) 666, 670 membrane 676 transport across 772 meridional scattering 715 meso-tartaric acid 422 mesophase 188 metal metal-to-ligand transition 499 metallic conductor 720 metallic lustre 726 metalloid metarhodopsin II, 502 metastable excited state 509 metastable phase 137 methane, VB description 374 methanol cell 867 method of initial rates 789 method of undetermined multipliers 585 mho 759 micelle 674 Michaelis constant 879 Michaelis–Menten equation 879 Michaelis–Menten mechanism 879 Michelson interferometer 446, 480 microcanonical ensemble 579 microporous material 902 microstate 99 microstructure 186 microwave background radiation 447 microwave region 11, 250 Mie potential 642 milk 672 Miller indices 698 mirror plane 418 mixed inhibition 883 mixing enthalpy of 66, 163 entropy of 163 role in equilibrium 214 MLCT 499 mmHg 20 MO 378 MO theory 371, 378 mobility 761 mobility on surface 896 mode locking 511 model Bohr 366 Gouy–Chapman 862 Grahame 862 Helmholtz 862 kinetic 25, 745 RRK 838 RRKM 838 Stern 862 Zimm–Bragg 616 zipper 615 moduli 718 modulus 286 molality 160 molar absorption coefficient 490 molar concentration 160 molar conductivity 759 diffusion coefficient 769 molar heat capacity 60 molar magnetic susceptibility 728 molar mass 5, 678 molar partition function 594 molar polarization 629 molar volume critical 32 partial 157 perfect gas 25 molarity 160 mole 5, 11 mole fraction 27 molecular beam epitaxy 724 molecular beam 644, 654, 851 molecular cloud 448 molecular collision 751 molecular descriptor 640 molecular dynamics 608 molecular flow 654 molecular interaction 30 molecular interpretation equilibrium constant 220 heat and work 46 molecular modelling 72 molecular orbital 378 molecular orbital energy level diagram 383 molecular orbital theory 371, 378 molecular partition function 568, 594 molecular potential energy curve 372 hydrogen molecule-ion 281 molecular recognition 640 molecular scattering 644 molecular solid 715 molecular spectroscopy 445 molecular speed, distribution of 748 molecular vibration 462 symmetry 476 molecular weight see also molar mass molecularity 802 molecule moment of inertia 281, 306, 449 momentum flux 756 momentum operator 269 monochromatic source 479 monochromator 480 monoclinic unit cell 696, 697 monodisperse 678 monolayer 649 monomer 659 monopole 633 Monte Carlo method 608 Morse potential energy 466 most probable radius 336 most probable speed 750 MPI 851 MRI 546 Mulliken electronegativity 389, (T) 933 multi-walled nanotube 715 multinomial coefficient 566 multiphoton ionization 851 multiphoton process 508 multiplicity 358, 492 multipole 633 multipole interaction energy 633 mutual termination 814 MWNT 715 N n-fold axis of symmetry 696 n-fold rotation 418, 696 n-pole 633 n-type semiconductivity 723 NADH 212 NADP 823, 824 nanocrystal 296 nanodevice 723 nanoscience 295, 299 nanotechnology 295, 320 nanotube 714, 723 nanowire 723 natural linewidth 352 natural logarithm 147 Nd-YAG laser 733 near field 507 near-field scanning optical microscopy 507 near infrared region 11, 250 nearly free-electron approximation 720 nearly random coil 689 Néel temperature 730 negative temperature 591 neighbouring group contribution 528, 530 nematic phase 189 neodymium laser 734 neon atom 346 INDEX Nernst equation 232 Nernst filament 479 Nernst heat theorem 110 network solid 714 neutron diffraction 708 neutron magnetic scattering 709 neutron scattering 758 newton 12 Newtonian flow 756 Newton’s second law of motion 281 nicotine 183 niobium 19 nitric oxide 395 electronic partition function 600 magnetism 739 nitrogen fugacity (T) 927 VB description 374 nitrogen fixation 394 nitrogen laser 513 NMR 524 line intensity 525 spectrometer 525 noble gas nodal plane 337 node 267 NOESY 551 NOE 548 non-competitive inhibition 883 non-expansion work 50 non-primitive unit cell 696 nonlinear optical phenomena 726 nonmetal nonradiative decay 503 normal boiling point 138 normal freezing point 138 normal melting point 138 normal mode 472 group theory 478 infrared activity 477 normal transition temperature 105 normal Zeeman effect 365 normalization 263 normalization constant 263, 290 notation, orbital 436 NSOM 507 nuclear g-factor 523 nuclear magnetic resonance 524 line intensity 525 spectrometer 525 nuclear magneton 523 nuclear model nuclear Overhauser effect 548 nuclear spin 522 nuclear constitution 522 properties 523, (T) 935 nuclear spin quantum number 522 nuclear statistics 461 nucleation 653 nucleation step 616 nucleic acid 670 nucleon nucleon number nuclide abundance (T) 915 nuclide mass (T) 915 number-average molar mass 678 nylon-66 666, 812 O O branch 470 oblate 453 observable 269, 279 complementary 278 observed lifetime 818 octahedral complex 499 octahedral group 424 octet octupole 633 odd function 305 off-diagonal peaks 550 OHP 862 oil hydrogenation 901 one-component system 139 one-dimensional crystal 712 one-dimensional random walk 773 open system 44 operations, complex number 287 operator 267, 279 angular momentum 309, 314 Coulomb 408 exchange 408 Fock 402 hermitian 270 kinetic energy 270 momentum 269 position 269 potential energy 269 optical density 491 optical Kerr effect 727 optical trapping 578 optically active 426 orbital antibonding 381 atomic 1, 330 bonding 380 Gaussian type 403 orbital angular momentum 327 total 357 orbital angular momentum quantum number 311 orbital approximation 341 orbital energy variation 385 orbital notation 436 order of differential equation 322 order–disorder transition 151 order of group 431 order of reaction 788, 802 ordinary differential equation 322 orientation polarization 628 Orion nebula 448 ortho-hydrogen 462 orthogonal function 272 orthogonality 272 orthonormal 273 orthorhombic unit cell 697 osmometry 173 osmosis 173 osmotic coefficient 207 osmotic pressure 173 osmotic virial coefficient 174 Ostwald viscometer 686 Otto cycle 134 outer Helmholtz plane 862 overall order 788 overall partition function 600 Overbeek, J.T.G 673 Overhauser effect spectroscopy 551 overlap, symmetry relation 436 overlap density 379 overlap integral 379, 384 overpotential 863 overtone 466 oxidant 228 oxidation 228 oxidation number oxidation state oxidative phosphorylation 212 oxidizing agent 228 oxygen electronic states 493 molecular properties 493 ozone 41 P p band 721 P branch 468 p–n junction 723 p orbital 336 real form 337 p-type semiconductivity 722 P680 823 P700 824 packing fraction 710 para-hydrogen 462 parabolic potential 300, 462 parallel band 472 parallel β-sheet 669 parallel spins 353 paramagnetic 386, 728 paramagnetic contribution 528 paramagnetism 386 parcel (of air) 29 parity 382, 492 parity selection rule 494 partial charge 388 partial derivative 55, 91 partial differential equation 322, 323 partial fraction 43, 795 partial molar entropy 112 partial molar Gibbs energy 158 partial molar quantity 157 partial molar volume 157 partial pressure 26 partial vapour pressure 145 partially miscible 168 partially miscible liquids 181 distillation 183 967 partially rigid coil 689 particle in box 289 partition function 572 quantum number 291 particle on ring 306 particle in sphere 321 particle on sphere 310 particular solution 322 partition function canonical 581 contributions to 616 electronic 600 enthalpy 593 entropy 577, 592 equally spaced levels 570 equation of state 605 equilibrium constant 611 factorization 572 Gibbs energy 594 heat capacity 602 Helmholtz energy 593 internal energy 575, 592 molar 594 molecular 568, 594 overall 600 particle in box 572 pressure 593 rate constant 845 rotational 595, 617 second virial coefficient 606 standard molar 611 thermodynamic information 581 translational 572, 595 two-level system 569 vibrational 598 pascal 5, 12, 20 Pascal’s triangle 534 Paschen series 324 passive transport 764 patch clamp technique 765 patch electrode 765 path function 74 Patterson synthesis 706 Pauli, W 342 Pauli exclusion principle 342 Pauli principle 342, 461 Pauling electronegativity 389, (T) 933 penetration 297, 344 peptide link 615, 660, 668 peptizing agent 672 perfect elastomer 665 perfect gas 6, 8, 24 enthalpy of mixing 163 entropy change 97, 104 entropy of mixing 163 equilibria 213 Gibbs energy of mixing 162 Gibbs energy 127 internal energy 576 isothermal expansion 104 molar volume 25 statistical entropy 583 transport properties 755, 775 968 INDEX perfect-gas temperature scale 22 period periodic function 740 periodic table periodicity 346 peritectic line 187 permittivity 7, 128, 629 perpendicular band 472 persistence length 664 Petit, A.-T 253 phaeophytin 824 phase 136 phase (wave) 700 phase boundary 138, 146 phase diagram 137 carbon dioxide 141 helium 141 ice 141 liquid crystal 189 liquid–liquid 181 liquid–solid 185 sodium and potassium 187 water 141 phase encoding 546 phase gradient 547 phase problem 706 phase rule 139 phase-sensitive detection 399 phase separation 182 phase transition 136, 150 entropy of 105 phosphatidyl choline 676 phosphine decomposition 897 phospholipid 676 phosphorescence 503, 505, 815 photobleaching 518 photochemical processes 815 photochemistry 815 photodiode 482 photoelectric effect 256 photoelectron 387 photoelectron spectroscopy 387, 886 photoemission spectroscopy 886 photoisomerization 502 photomultiplier tube 482 photon 256 photophosphorylation 824 photosphere 361 photosynthesis 822 photosystem I and II, 822 photovoltaic cell detector 482 physical properties (T) 914 physical quantity 11 physical state 19 physisorption 888 π bond 374 π-bond formation energy 399 π-electron bonding energy 399 π orbital 384 π pulse 544 π-stacking interaction 640 π*←n transition 500 π*←π transition 500 π/2 pulse 541 planar bilayer 676 Planck, M 252 Planck distribution 252 Planck’s constant 252 plane polarized 10, 11, 500 plane separation 698 plasma 752 plastic 665 plastic deformation 665, 717 plastoquinone 824 PMT 482 point defect 112 point dipole 631 point group 418 point group notation 420 Poisson’s equation 199 Poisson’s ratio 718 polar bond 4, 388 polar coordinates 264, 310 polar form 286 polar molecule 426, 623 polarizability 459, 482, 624, (T) 936 frequency dependence 628 polarizability volume 624, (T) 936 polarization 475, 626 polarization (radiation) 500 polarization mechanism 536, 557 polarized light 500 polaron 667 polyacetylene 667 polyatomic molecule MO description 395 VB description 374 vibration 470 polyatomic molecule spectra 498 polychromatic source 479 polychromator 480 polydisperse 678 polydispersity index 679 polyelectrolyte 670 polyelectronic atom 324, 340 polyene 320 polymer 659 polymerization kinetics 811 polymorph 136 polynucleotide 670 polypeptide 660 helix-coil transition 830 polypeptide conformation transition 615 polypeptide melting 155 polytype 709 population 8, 565 population inversion 509 porphine 320, 444 position operator 269 positronium 365 postulates 279 potassium–bromine reaction 837 potential difference 13 potential energy 6, 30 potential energy operator 269 potential energy profile 801 potential energy surface 372, 852 powder diffraction pattern 705 powder diffractometer 701 power 12 power output (laser) 510 power series 323 pre-equilibrium 807 pre-exponential factor 799, 835 precession 522, 540 precursor state 894 predissociation 508 prefixes for units 12 pressure 5, 20 adiabatic process 64 and altitude 29 critical 32, 138 hydrostatic 21 internal 76, 122 kinetic model 746 kinetic 609 partition function 593 variation with reaction 783 pressure gauge 21 pressure jump 797 pressure units 20 primary absorption 816 primary process 815 primary quantum yield 816 primary structure 660 primitive unit cell 696 principal axis 418, 453 principal quantum number 1, 330 principle Avogadro’s 23 building-up 345 correspondence 292 equal a priori probabilities 565 equipartition 9, 47, 253, 601 exclusion 342 Franck–Condon 495, 505, 858 Le Chatelier’s 222 Pauli 342, 461 Ritz combination 325 uncertainty 276, 279 variation 390 principle of corresponding states 36 principle of equal a priori probabilities 565 probability amplitude 262 probability density 262, 267 probe 785 product rule 42 projection reconstruction 546 prolate 453 promotion 374 propagation step 616, 813 protein folding problem 668 proteomics 680 proton decoupling 548 pseudofirst-order reaction 789 psi 20 pulse technique 540 pump 784 pumping 509 pure shear 717 pyroelectric detector 482 Q Q branch 468, 470 Q-switching 510 QCM 888 QSAR 640 QSSA 805 quadrupole 633 quantitative structure–activity relationships 640 quantity calculus 23 quantization angular momentum 309 energy 252, 266 space 314 quantum defect 353 quantum dot 296 quantum mechanics 249, 260 quantum number angular momentum 311 magnetic 311 nuclear spin 522 orbital angular momentum 311 particle in box 291 principal 1, 330 spin 315 spin magnetic 315 total angular momentum 357 total orbital angular momentum 357 total spin 357 quantum oscillation 645 quantum yield 816 quartz crystal microbalance 888 quartz–tungsten–halogen lamp 479 quasi-steady-state approximation 805 quaternary structure 660 quenching 818 quenching method 785 quinoline 422 quotient rule 42 R R branch 468 radial distribution function atom 335 liquid 607 radial velocity 366 radial wave equation 326 radial wavefunction 326 radiation, black-body 251 radiation source 479 radiative decay 503 radical chain reaction 813 radio region 11, 250 INDEX radius hydrodynamic 762 most probable 336 Stokes 762 radius of gyration 662, 682, (T) 937 radius ratio 711 radius of shear 673 rainbow angle 645 rainbow scattering 645 Ramachandran plot 668 Raman activity 478 Raman spectra polyatomic molecule 475 rotational 459 vibrational 469 Raman spectroscopy 446, 482, 508 Ramsperger, H.C 838 random coil 661, 689 random walk 773 Raoult, F 164 Raoult’s law 164, 176 rate, surface process 894 rate of adsorption 888, 895 rate constant 787 diffusion controlled 842 electron transfer 857 Kassel form 838 partition function 845 state-to-state 852 rate of consumption 786 rate of desorption 895 rate-determining step 807 rate of formation 786 rate law 787 heterogeneous catalysis 898 rate of reaction 786 collision theory 801, 832 temperature dependence 799 Rayleigh, Lord 251 Rayleigh–Jeans law 251 Rayleigh radiation 446 Rayleigh ratio 681 Rayleigh scattering 681 RDS 807 reaction centre 822 reaction coordinate 801 reaction dynamics 831 reaction enthalpy 66, 68 from enthalpy of formation 71 measurement 225 temperature dependence 73 reaction entropy 111 reaction Gibbs energy 210, 231 standard 118, 213, 232 reaction mechanism 782 reaction order 788, 802 reaction product imaging 851 reaction profile 807 reaction quotient 213 reaction rate 786 collision theory 801, 832 temperature dependence 799 reactive collision 851 reactive cross-section 834, 836 read gradient 547 real gas 24, 29 real-time analysis 784 reciprocal identity, of partial derivatives 91 recursion relation 302 red shift 366, 725 redox couple 228 redox reaction 228 reduced mass 326, 463, 751 reduced representation 429 reduced variable 36 reducing agent 228 reductant 228 reduction 228 reference state 71 refinement 707 reflected wave 297 reflection 418 reflection (X-ray) 701 reflection symmetry 493 refocusing 546 reforming 901 refractive index 630, 727 refrigeration 103 regular solution 169, 181, 194 relation between Q and q 582 relative mean speed 751 relative motion 362 relative permittivity 128, 629 relativistic effect 285 relaxation effect 764 relaxation method 797 relaxation time 543, 547 REMPI 851 reorganization energy 859 representation 428 representative matrix 428 repulsion 642 repulsive surface 854 residual entropy 111, 609 resolution (microscopy) 259 resolution (spectroscopy) 551 resonance 3, 520 resonance condition 524 resonance energy transfer 821, 829 resonance integral 390 resonance Raman spectroscopy 475 resonant mode (laser) 509 resonant multiphoton ionization 851 restoring force (elastomer) 666 resultant vector 368 retinal 502, 822 retinol 503 reversible change 51 reversible expansion 51 rheology 717 rheometer 687 Rhodamine 6G 514 rhodopsin 502 rhombohedral unit cell 697 ribosome 878 ribozyme 878 Rice, O.K 838 ridge (atmospheric) 29 rigid rotor 451 ring current 531 Rice–Ramsperger–Kassel model 838 Ritz combination principles 325 RNA 670, 878 road maps 911 rock-salt structure 711 rods and cones 502 Röntgen, W 700 root mean square deviation 277 root mean square distance 773 root mean square separation 662 root mean square speed 26, 746 Roothaan equation 402 rotating frame 541 rotating rheometer 687 rotational constant 453 rotational energy level 452 rotational line intensity 458 rotational motion 306 rotational partition function 595, 617 rotational Raman spectra 459 rotational selection rule 456 rotational spectrum 457 rotational structure 497 rotational subgroup 620 rotational temperature 597 rotational term 453 rotational transitions 456 rotor 451 RRK model 838 RRKM model 838 rubber 692 ruby glass 671 rule Corey–Pauling 668 exclusion 475 gross selection 447 Hund’s 345 lever 178 phase 139 Schulze–Hardy 674 selection see selection rule specific selection 447 Trouton’s 105 Russell–Saunders coupling 359 ruthenocene 425 Rydberg, J 324 Rydberg atom 366 Rydberg constant 324, 331 Rydberg state 353 S s band 721 S branch 470 s orbital 333 Sackur–Tetrode equation 583 saddle point 853 969 SALC 437 salt bridge 227 salting-in effect 208 salting-out effect 208 SAM (scanning Auger electron microscopy) 886 SAM (self-assembled monolayer) 677 SATP 25 saw-tooth wave 740 Sayre probability relation 707 scalar coupling constant 532 scalar product 363, 369, 521 scanning Auger electron microscopy 886 scanning electron microscopy 260 scanning probe microscopy 299 scanning tunnelling microscopy 299 Scatchard equation 208 scattering factor 703 scattering theory 856 SCF 349, 402 Scherrer, P 701 Schoenflies system 420 Schrödinger equation one-dimensional 260 particle on sphere 310 three-dimensional 261 time-dependent 261 time-independent 260 vibrating molecule 463 Schulze–Hardy rule 674 Schumann–Runge band 517 screening constant (T) 930 second harmonic generation 727, 894 second ionization energy 347 Second Law of thermodynamics 94 second-order phase transition 150 second-order reaction 793 kinetic data (T) 940 second radiation constant 284 second virial coefficient (T) 915 partition function 606 secondary process 815 secondary structure 660 secular 390 secular determinant 392 secular equation 390, 415 sedimentation 684 sedimentation constant 684 sedimentation equilibrium 684 selection rule 482 atom 339, 360 diatomic molecules 494 gross 447 infrared 483 Laporte 494 many-electron atom 360 microwave transition 482 molecular vibration 464 parity 494 rotational 456 970 INDEX rotational Raman 459, 482 specific 447 symmetry considerations 439 vibrational Raman 469, 484 vibrations 482 selectivity coefficient 240 selectivity filter 765 self-assembled monolayer 677 self-assembly 671 self-consistent field 349, 402 SEM 260 semiconductor 720, 722 semi-empirical method 403 semipermeable membrane 173 separation of motion 362 separation of variables 293, 326 atom 326 sequencing 660 SFC 142 shape-selective catalyst 897 SHE 233 shear 717 shear modulus 718 sheet 668 shell 1, 332 SHG 894 shielded Coulomb potential 199 shielded nuclear charge 344 shielding 344 electronegativity 529 local contribution 528 shielding constant atom 344 NMR 526 short-range order 607 SI 5, 10, 20 side-centred unit cell 696 siemens 759 σ bond 373 σ electron 380 σ orbital 378, 383 sign convention 49 signal enhancement (NOE) 549 similarity transformation 416 simple distillation 179 simultaneous equations 415 sine function 740 single bond single-molecule spectroscopy 507 single-valued function 265 single-walled nanotube 715, 723 singlet–singlet energy transfer 816 singlet state 353 SIR model 907 Slater determinant 343, 402 slice selection 546 slip plane 719 smectic phase 189 smog 29 smoke 671 sodium D lines 356 sol 671 solar radiation 473 solder 186 solid solid hydrogen gas hydrates 643 solid–liquid boundary 147 solid-state NMR 551 solid–vapour boundary 149 soliton 667 solubility 172 solute activity 192 solution, enthalpy of 66 solvation, Gibbs energy of 128 solvent-accessible surface 405 solvent activity 191 solvent contribution 528, 531 sp hybrid 377 sp2 hybrid 376 sp3 hybrid 375 space group 418 space lattice 695 space quantization 314 spatial coherence 510 specific enthalpy 70 specific heat capacity 55 specific selection rule 447 specific volume (polymer) 667 spectral regions 250 spectrometer 446, 479, 525, 553 spectrophotometry 784 spectroscopic transition 255 spectroscopy 255, 446 spectrum 255 speed 280 distribution 748 drift 684, 761, 768 mean 750 most probable 750 relative mean 751 root mean square 26, 746 speed of light 9, 250 sphalerite 712 spherical harmonic 311 spherical polar coordinates 264, 310 spherical rotor 451 spin 315 total 357 spin correlation 345 spin decoupling 548 spin density 556 spin echo 545 spin label 558, 676 spin–lattice relaxation time 543 spin magnetic quantum number 315 spin–orbit coupling 354 spin–orbit coupling constant 355 spin packet 545 spin paired 342 spin probe 558 spin quantum number 315 spin relaxation 543 spin–spin coupling 535 spin–spin relaxation time 543 spin-1/2 nucleus 524 SPM 299 spontaneity, criteria for 113 spontaneous 94 spontaneous cooling 103 spontaneous emission 504 spontaneous nucleation centre 653 SPR 897 square modulus 286 square wave 740 square well 293 SQUID 729 stability parameter 615 standard ambient temperature and pressure 25 standard boiling point 138 standard cell potential 232 temperature coefficient 237 standard chemical potential 162 standard enthalpy change 65 standard enthalpy of combustion 68 standard enthalpy of electron gain 348 standard enthalpy of formation 71 standard enthalpy of fusion 66 standard enthalpy of ionization 347 standard enthalpy of transition 65 standard enthalpy of vaporization 65, (T) 917, (T) 926 standard entropy 111 standard freezing point 138 standard Gibbs energy of formation 118, 214 standard Gibbs energy of reaction 118, 213, 232 standard hydrogen electrode 233 standard model (stellar structure) 780 standard molar partition function 611 standard potential 233, (T) 928 combining 235 determination 233 equilibrium constant 236 standard pressure 5, 20 standard reaction enthalpy 68 standard reaction entropy 111 standard reaction Gibbs energy 118, 213, 232 standard state 65 biological 194, 220 summary 190 standard temperature and pressure 25 star 361 Stark effect 455, 621 Stark modulation 456 state function 47, 74 entropy 100 state-to-state cross-section 852 state-to-state dynamics 851 state-to-state reaction dynamics 831 statistical entropy 99, 576 perfect gas 583 statistical thermodynamics 564 steady-state approximation 805, 814 steam distillation 181 Stefan–Boltzmann law 284 stellar interior 752 stellar structure 361, 752, 780 step 885 stepwise polymerization 811 steric factor 836 steric requirement 835 Stern, O 314 Stern–Gerlach experiment 314 Stern model 862 Stern–Volmer equation 819 Stern–Volmer plot 819 steroid binding 641 sticking probability 895 stimulated absorption 503 stimulated emission 504, 816 Stirling’s approximation 567 STM 299 stoichiometric coefficient 72, 215 stoichiometric number 72, 214 Stokes–Einstein equation 769, 842 Stokes–Einstein relation 688 Stokes formula 761 Stokes’ law 769 Stokes radiation 446 Stokes radius 762 Stokes’ relation 684 stopped-flow technique 784 STP 25 strain 717 stress 717 strong electrolyte 760 strongly coupled spectra 538 structure-based design 640 structure factor (light scattering) 682 structure factor (X-ray) 704 structure refinement 707 sublimation, enthalpy of 66 sublimation vapour pressure 138 subshell 2, 332 subshell energies 345 substance substitutional impurity atom 112 substrate 878, 885 sulfur dioxide spectrum 495 Sun 752 superconducting magnet 525 superconducting quantum interference device 729 superconductor 720, 731 supercooled 653 supercritical carbon dioxide 142 supercritical fluid 32, 138 supercritical fluid chromatography 142 supercritical water 143 superfluid 142 superheated 653 superoxide ion 395 superposition 274, 373 superradiant 513 supersaturated 652 supersonic beam 655 supersonic nozzle 654 supertwist 189 INDEX supramolecular chemistry 226, 622 surface composition 651, 885 surface defect 885 surface excess 651 surface film balance 649 surface Gibbs energy 650 surface growth 885 surface plasmon resonance 897 surface pressure 649 surface tension 646, 649, (T) 937 surfactant 650, 672 surfactant accumulation 650 surfactant parameter 675 surroundings 44 entropy change 98 susceptibility 530, (T) 938 sweating 70 SWNT 715, 723 symmetric rotor 451, 453, 617 symmetric stretch 471 symmetrical exponential function 741 symmetry, and degeneracy 295 symmetry-adapted linear combination 437 symmetry axis 418 symmetry element 417, 696 symmetry number 597 symmetry operation 417, 696 symmetry species 430, 431 synchrotron radiation 479, 701 synchrotron storage ring 479 system 44 one-component 139 systematic absences 705 Système International 5, 10, 20 T T1-weighted image 547 T2-weighted image 547 T law 108 Taylor series 462 TDS 896 Teller, E 892 TEM 260 Temkin isotherm 893 temperature 5, 21 characteristic rotational 597 characteristic vibrational 599 consolute 183 critical solution 183 Curie 730 Debye 254 Einstein 254 infinite 570, 571 Krafft 674 Néel 730 negative 591 temperature–composition diagram 179 temperature conversion 22 temperature-independent paramagnetism 731 temperature jump 797 temperature programmed desorption 896 temperature scale, thermodynamic 5, 22, 102 temporal coherence 510 tensile strength 719 term, atomic 325 term symbol atom 357 diatomic molecules 492 termination step 814 terrace 885 tertiary structure 660 tesla 521 tetragonal unit cell 697 tetrahedral group 424 tetramethylsilane 527 tetraphenylmethane 424 theorem convolution 742 equipartition 9, 47, 253, 601 Koopmans’ 387 Nernst heat 110 virial 306 theoretical plate 179 theory activated complex 843 Debye–Hückel 196, 199 Debye–Hückel–Onsager 764 Förster 821, 829 Marcus 820, 858 transition state 843 thermal analysis 136, 186 thermal conduction 745 thermal conductivity 756, 757, 775 thermal de Broglie wavelength 573 thermal desorption spectroscopy 896 thermal equilibrium 22 thermal motion 46 thermal neutrons 708 thermal wavelength 573 thermochemical equation 68 thermochemistry 65 thermodynamic data elements (T) 919 inorganic (T) 919 organic (T) 918 thermodynamic equation of state 122 thermodynamic equilibrium constant 216 thermodynamic force 766 thermodynamic function, determination 237 thermodynamic limit 581 thermodynamic temperature scale 5, 22, 102 thermodynamics 44 First Law 48 Second Law 94 Third Law 110 Zeroth Law 22 thermogram 62 thermometer 22 thermotropic liquid crystal 188 Third-Law entropy 111, 577 Third Law of thermodynamics 110 Thomson equation 147 three-level laser 509 tie line 178 tight-binding approximation 720 time constant 792 time-dependent Schrödinger equation 261 time-domain signal 541 time-independent Schrödinger equation 260 time-of-flight spectrometer 680 time-resolved spectroscopy 784 TIP 731 titanium ion spectrum 499 titanium sapphire laser 734 TMS 527 TOF 680 tonne 13 torque 282 torr 20 Torricelli 21 total angular momentum 355, 357 total angular momentum quantum number 357 total energy 6, total orbital angular momentum quantum number 357 total rate of absorption 504 total spin quantum number 357 TPD 896 trajectory 281 trajectory on surface 853 trans-retinal 502 transcendental equation 183 transfer coefficient 863, (T) 942 transition 339 charge-transfer 499 cooperative 615 enthalpy of 65, 66 helix–coil 615, 830 polypeptide conformation 615 spectroscopic 255 transition dipole interaction 724 transition dipole moment 339, 447, 482, 494 symmetry considerations 439 transition metal 2, 347 transition state 801, 844, 853 transition state theory 843 transition temperature 105, 136 translational motion 288 transmission coefficient 845 transmission electron microscopy 260 transmission probability 298 transmittance 491 transmitted wave 297 transport properties 745, (T) 939 kinetic theory 757 perfect gas 755, 775 971 transpose matrix 414 transverse relaxation time 543 trial wavefunction 390 triclinic unit cell 696, 697 tridiagonal determinant 721 trigonal lattice 697 trihydrogen molecule ion 444 triple bond triple point 102, 138 triplet state 353, 506 vector diagram 353 triplet–triplet energy transfer 816 tropopause 28 troposphere 28 trough (atmospheric) 29 Trouton’s rule 105 tumbling 473 tunnelling 297, 306, 858 turnover frequency 880 two-dimensional box 293 two-dimensional NMR 550 two-level system 569, 575 Type I superconductor 731 Type II superconductor 731 U u subscript 382 ubiquitin (thermogram) 62 UHV 886 ultracentrifugation 684 ultracentrifuge 684 ultrafast techniques 846 ultrahigh vacuum technique 886 ultraviolet 11, 250 ultraviolet catastrophe 252 ultraviolet photoelectron spectroscopy 387, 886 ultraviolet radiation 41 ultraviolet region 11, 250 unbound states 331 uncertainty principle 276, 279 uncompetitive inhibition 883 undetermined multiplier 585 ungerade symmetry 382 uniaxial stress 717 unilamellar vesicle 676 unimolecular reaction 802, 809 unique rate of reaction 786 unit 5, 10 unit cell 696 unit cell volume 738 unit matrix 414 unit vector 368 upper critical solution temperature 183 UPS 387, 886 urea 70 US standard atmosphere 29 V vacuum permittivity vacuum ultraviolet region 11, 250 972 INDEX valence band 722 valence-bond theory 371, 372 valence electron 345 valence shell valence-shell electron pair repulsion theory (VSEPR theory) van der Waals, J.D 33 van der Waals coefficients 33, (T) 916 van der Waals equation 33, 35 fugacity coefficient 130 internal pressure 123 van der Waals interaction 631 van der Waals isotherms 35 van der Waals loops 35 van der Waals molecule 645 van ’t Hoff equation (equilibrium) 223, 891 van ’t Hoff equation (osmosis) 173 vanishing integral 433, 439 vaporization enthalpy of 65, (T) 917, (T) 926 entropy of 105, (T) 926 vapour composition 176 vapour pressure 32, 138 curved surface 652 decomposition 216 effect of applied pressure 145 partial 145 variation with composition 177 vapour pressure lowering 169 variance 139 variation principle 390 VB theory 371, 372 vector 368 vector addition 368 vector algebra 368 vector diagram parallel spins 353 spin paired 342 triplet state 353 vector differentiation 369 vector model, angular momentum 315 vector multiplication 369 vector product 369 vector representation, angular momentum 309 velocity 280 velocity selector 654 vertical transition 495 Verwey, E 673 vesicle 676 vibration 462 vibration–rotation spectra 467 vibrational fine structure 388 vibrational modes 470 vibrational motion 300 vibrational partition function 598 vibrational progression 495 vibrational Raman spectra 469 vibrational structure, electronic transition 490 vibrational term 464 vibrational wavenumber 473, (T) 934 vibronic laser 734 vibronic transition 494 virial 609 virial coefficient 31 virial equation of state 31, 35 virial theorem 306 viscosity 686, 745, 756, 758, 776, (T) 939 diffusion coefficient 769 viscosity-average molar mass 678 visible region 11 vision 501 vitamin C 395 void 112 volcano curve 899 volume volume magnetic susceptibility 728 von Laue, M 700 W Wannier exciton 724 water conduction in 762 entropy of vaporization 106 phase diagram 141 radial distribution function 607 residual entropy 610 supercritical 143 superfluid phase 142 triple point 102, 138 VB description 374 vibrations 471 viscosity 758 Watson, J 715 watt 12 wave wave equation 326 wave packet 276 wave–particle duality 259 wavefunction 260, 279 acceptability 265 acceptable 279 angular 326 antisymmetric 343 constraints 265 harmonic oscillator 302 hydrogen 328 interpretation 262 linear momentum 266 particle in box 290 particle on rectangular surface 294 particle on ring 307 radial 326 separation 326 trial 390 wavelength 10, 250 wavenumber 10, 250 wavepacket 847 weak acid 760 weather 28 weather map 29 weight (configuration) 566 weight-average molar mass 678 wet 649 Wien’s law 284 Wierl equation 737 Wilkins, M 715 wind 28, 29 work 45 additional 50, 118 against constant pressure 51 electrical 50 expansion 49 gas production 53 general expression 49 maximum 115 maximum non-expansion 117 non-expansion 50 surface expansion 50 varieties of 50 work function 257 wrinkle, Nature’s abhorrence of 771 X X-ray 700 X-ray crystallography 715 X-ray diffraction 700 X-ray fluorescence 886 X-ray photoelectron spectroscopy 886 X-ray region 11, 250 xanthophyll 502 xenon discharge lamp 479 XPS 886 Y yield point 665, 719 Young’s modulus 718 Z Z-average molar mass 678 Zeeman effect 365 zeolite 902 zero-order rate law 789 zero-order reaction 789 zero overlap approximation 392 zero-point energy 291, 301 Zeroth Law of thermodynamics 22 zeta potential 673 Zimm–Bragg model 616 zinc blende 712 zipper model 615 Useful relations Taylor expansions At 298.15 K RT RT/F RT ln 10/F kT/hc kT/e V m7 ƒ(x) = 2.4790 kJ mol−1 25.693 mV 59.160 mV 207.226 cm−1 25.693 meV 2.4790 × 10−2 m3 mol−1 = 24.790 dm3 mol−1 Selected units 1N Pa 1V 1T 1S kg m s−2 kg m−1 s−2 J C−1 kg s−2 A−1 Ω−1 = A V −1 ∞ A dnf D ∑ n! BC dx n EF (x − a)n n=0 a e = + x + 2x + ln x = (x − 1) − 12 (x − 1)2 + 13 (x − 1)3 − 14 (x − 1)4 + ln(1 + x) = x − 12 x + 13 x x = − x + x2 1+x Derivatives d( f + g) = df + dg d( fg) = fdg + gdf f f d = df − dg g g g kg m2 s−2 J s−1 C s−1 10−1 kg m−1 s−1 1J 1W 1A 1P df df dg = dt dg dt A ∂y D A ∂x D B E B E C ∂x F z C ∂z F y Conversion factors θ/°C = T/K − 273.15* eV 1.602 18 × 10−19 J 96.485 kJ mol−1 8065.5 cm−1 cal 4.184* J atm 101.325* kPa 760* Torr cm−1 1.9864 × 10−23 J 1D 3.335 64 × 10−30 C m 1Å 10−10 m* (*Exact values) A ∂z D B E = −1 C ∂y F x (∂y/∂x)z = 1/(∂x/∂y)z dx n = nx n−1 dx d ax e = aeax dx d ln x = dx x Integrals Ύ Ύ1x dx = ln x + constant Ύ x e dx = an! Ύsin ax dx = x − sin 2ax + constant − b)x sin(a + b)x − + constant Ύsin ax sin bx dx = sin(a 2(a − b) 2(a + b) x ndx = Mathematical relations π = 3.141 592 653 59 e = 2.718 281 828 46 ∞ x n +1 + constant n+1 n −ax n +1 Logarithms and exponentials 2 ln x + ln y + = ln xy ln x − ln y = ln(x/y) a ln x = ln x a ln x = (ln 10) log x = (2.302 585 ) log x e xe yez = e x+y+z+ x y x−y e /e = e (e x )a = eax e±ix = cos x ± i sin x 4a if a2 ≠ b2 Ύ z 2 erf z = 1/2 e−y dy π erfc z = − erf z Prefixes z zepto 10−21 a atto 10−18 f femto 10−15 p pico 10−12 n nano 10−9 m micro 10−6 m milli 10−3 c centi 10−2 d deci 10−1 da deca 101 k kilo 103 M mega 106 G giga 109 T tera 1012 P peta 1015 18 Periodic table of the elements VIII VIIA Group I II IA IIA Period Be 15 16 17 III IV V VI VII IIIA IVA VA VIA VIIA B C N O helium 4.00 1s2 F 10 Ne carbon nitrogen oxygen fluorine neon 6.94 2s1 9.01 2s2 10.81 2s22p1 12.01 2s22p2 14.01 2s22p3 16.00 2s22p4 19.00 2s22p5 20.18 2s22p6 12 Mg 13 sodium magnesium aluminium silicon phosphorus sulfur chlorine argon 22.99 3s1 24.31 3s2 26.98 3s23p1 28.09 3s23p2 30.97 3s23p3 32.06 3s23p4 35.45 3s23p5 39.95 3s23p6 Na IIIB IVB VB VIB VIIB 10 11 12 IB IIB VIIIB Cl 18 Ar 31 Ga 32 Ge titanium vanadium chromium manganese iron cobalt nickel copper zinc gallium germanium arsenic selenium bromine krypton 39.10 4s1 40.08 4s2 44.96 3d14s2 47.87 3d24s2 50.94 3d34s2 52.00 3d54s1 54.94 3d54s2 55.84 3d64s2 58.93 3d74s2 58.69 3d84s2 63.55 3d104s1 65.41 3d104s2 69.72 4s24p1 72.64 4s24p2 74.92 4s24p3 78.96 4s24p4 79.90 4s24p5 83.80 4s24p6 34 Br Kr rhodium palladium silver cadmium indium tin antimony tellurium iodine xenon 85.47 5s1 87.62 5s2 88.91 4d15s2 91.22 4d25s2 92.91 4d45s1 95.94 4d55s1 (98) 4d55s2 101.07 4d75s1 102.90 4d85s1 106.42 4d10 107.87 4d105s1 112.41 4d105s2 114.82 5s25p1 118.71 5s25p2 121.76 5s25p3 127.60 5s25p4 126.90 5s25p5 131.29 5s25p6 57 La 72 76 53 54 75 Re rhenium osmium iridium platinum gold mercury thallium lead bismuth polonium astatine radon 132.91 6s1 137.33 6s2 138.91 5d16s2 178.49 5d26s2 180.95 5d36s2 183.84 5d46s2 186.21 5d56s2 190.23 5d66s2 192.22 5d76s2 195.08 5d96s1 196.97 5d106s1 200.59 5d106s2 204.38 6s26p1 207.2 6s26p2 208.98 6s26p3 (209) 6s26p4 (210) 6s26p5 (222) 6s26p6 Fr 88 Ra 89 Ac 104 Rf 105 Db 106 Sg 107 Bh 108 Hs francium radium actinium rutherfordium dubnium seaborgium bohrium hassium (223) 7s1 (226) 7s2 (227) 6d17s2 (261) 6d27s2 (262) 6d37s2 (266) 6d47s2 (264) 6d57s2 (277) 6d67s2 Molar masses (atomic weights) quoted to the number of significant figures given here can be regarded as typical of most naturally occurring samples- 58 Ce cerium 140.12 4f15d16s2 90 Th thorium 232.04 6d27s2 59 Pr 60 Nd praseodymium neodymium 140.91 4f36s2 91 Pa protactinium 144.24 4f46s2 92 U uranium 109 Mt 78 110 Pt Ds meitnerium darmstadtium (268) 6d77s2 (271) 6d87s2 Eu 79 111 Rg 80 112 ? 81 113 82 Pb 114 83 115 84 Po 85 (272) 6d107s1 ? 6d107s2 Tb Dy Ho 68 Er Tm Yb 61 Pm 62 Sm 63 samarium europium gadolinium terbium dysprosium holmium erbium thulium ytterbium (145) 4f56s2 150.36 4f66s2 151.96 4f76s2 157.25 4f75d16s2 158.93 4f96s2 162.50 4f106s2 164.93 4f116s2 167.26 4f126s2 168.93 4f136s2 173.04 4f146s2 93 Np neptunium (237) 231.04 238.03 5f26d17s2 5f36d17s2 5f46d17s2 Rn 118 117 116 86 roentgenium copernicium promethium 64 At Xe W 77 Bi 52 tungsten Os Tl Sb tantalum 74 Hg 51 hafnium 73 Au Sn 50 lanthanum Hf Ir 49 barium 56 Ta Cd caesium Cs Ba 48 I 36 ruthenium 47 Te 35 technetium Pd In 33 molybdenum 46 Ag Zn niobium 45 Rh 30 zirconium 44 Ru Ni yttrium 43 Tc 28 38 42 Mo 27 strontium 40 41 Nb 26 rubidium 39 Zr Mn 37 Rb Sr Y 25 Se 17 22 24 As S 21 Sc V 29 Cu 16 scandium 23 Co P 15 calcium Ti Fe Si 14 20 Ca K Cr Al potassium 87 1.0079 1s1 14 boron 55 Period He 13 beryllium 19 H hydrogen lithium 11 Li Gd 65 Bk 66 67 70 94 Pu 95 Am 96 Cm 97 plutonium americium curium berkelium californium einsteinium fermium mendelevium nobelium (244) 5f67s2 (243) 5f77s2 (247) 5f76d17s2 (247) 5f97s2 (251) 5f107s2 (252) 5f117s2 (257) 5f127s2 (258) 5f137s2 (259) 5f147s2 98 Cf 99 Es 69 100 Fm 101 Md 102 No 71 Lu Lanthanoids 174.97 (lanthanides) 5d16s2 lutetium 103 Lr Actinoids (262) (actinides) 6d17s2 lawrencium 9780199543373_489_519_Ch13.qxd 502 9/25/09 14:35 Page 502 13 MOLECULAR SPECTROSCOPY 2: ELECTRONIC TRANSITIONS Photons enter the eye through the cornea, pass through the ocular fluid that fills the eye, and fall on the retina The ocular fluid is principally water, and passage of light through this medium is largely responsible for the chromatic aberration of the eye, the blurring of the image as a result of different frequencies being brought to slightly different focuses The chromatic aberration is reduced to some extent by the tinted region called the macular pigment that covers part of the retina The pigments in this region are the carotene-like xanthophylls (3), which absorb some of the blue light and hence help to sharpen the image They also protect the photoreceptor molecules from too great a flux of potentially dangerous high energy photons The xanthophylls have delocalized electrons that spread along the chain of conjugated double bonds, and the π* ← π transition lies in the visible OH HO A xanthophyll CHO 11-cis-retinal CHO All-trans-retinal Fig 13.19 The structure of the rhodopsin molecule, consisting of an opsin protein to which is attached an 11-cis-retinal molecule embedded in the space surrounded by the helical regions Only the protein is shown About 57 per cent of the photons that enter the eye reach the retina; the rest are scattered or absorbed by the ocular fluid Here the primary act of vision takes place, in which the chromophore of a rhodopsin molecule absorbs a photon in another π* ← π transition A rhodopsin molecule consists of an opsin protein molecule to which is attached a 11-cis-retinal molecule (4) The latter resembles half a carotene molecule, showing Nature’s economy in its use of available materials The attachment is by the formation of a protonated Schiff’s base, utilizing the –CHO group of the chromophore and the terminal NH2 group of the sidechain, a lysine residue from opsin The free 11-cis-retinal molecule absorbs in the ultraviolet, but attachment to the opsin protein molecule shifts the absorption into the visible region The rhodopsin molecules are situated in the membranes of special cells (the ‘rods’ and the ‘cones’) that cover the retina The opsin molecule is anchored into the cell membrane by two hydrophobic groups and largely surrounds the chromophore (Fig 13.19) Immediately after the absorption of a photon, the 11-cis-retinal molecule undergoes photoisomerization into all-trans-retinal (5) Photoisomerization takes about 200 fs and about 67 pigment molecules isomerize for every 100 photons that are absorbed The process occurs because the π* ← π excitation of an electron loosens one of the π bonds (the one indicated by the arrow in 4), its torsional rigidity is lost, and one part of the molecule swings round into its new position At that point, the molecule returns to its ground state, but is now trapped in its new conformation The straightened tail of all-trans-retinal results in the molecule taking up more space than 11-cis-retinal did, so the molecule presses against the coils of the opsin molecule that surrounds it In about 0.25–0.50 ms from the initial absorption event, the rhodopsin molecule is activated both by the isomerization of retinal and deprotonation of its Schiff’s base tether to opsin, forming an intermediate known as metarhodopsin II In a sequence of biochemical events known as the biochemical cascade, metarhodopsin II activates the protein transducin, which in turn activates a phosphodiesterase enzyme that hydrolyses cyclic guanine monophosphate (cGMP) to GMP The reduction in the concentration of cGMP causes ion channels, proteins that mediate the movement of ions across biological membranes (Impact I20.2), to close The result is an imbalance of charge that in turn creates an electrical potential across the membrane The pulse of electric potential travels through the optical nerve and into the optical cortex, where it is interpreted as a signal and incorporated into the web of events we call ‘vision’ 9780199543373_489_519_Ch13.qxd 9/25/09 14:35 Page 507 13.5 DISSOCIATION AND PREDISSOCIATION 507 IMPACT ON BIOCHEMISTRY I13.2 Fluorescence microscopy HO N O N HO NH O The chromophore of GFP Molecular potential energy, V Fluorescence is a very important technique for the study of biological molecules In fluorescence microscopy, images of biological cells at work are obtained by attaching a large number of fluorescent molecules to proteins, nucleic acids, and membranes and then measuring the distribution of fluorescence intensity within the illuminated area Apart from a small number of co-factors, such as the chlorophylls and flavins, the majority of the building blocks of proteins and nucleic acids not fluoresce strongly Four notable exceptions are the amino acids tryptophan (λ abs ≈ 280 nm and λ fluor ≈ 348 nm in water), tyrosine (λ abs ≈ 274 nm and λ fluor ≈ 303 nm in water), and phenylalanine (λ abs ≈ 257 nm and λ fluor ≈ 282 nm in water), and the oxidized form of the sequence serine–tyrosine–glycine (6) found in the green fluorescent protein (GFP) of certain jellyfish The wild type of GFP from Aequora victoria absorbs strongly at 395 nm and emits maximally at 509 nm and is commonly used as a fluorescent label Fluorescence microscopy has been used for many years to image biological cells, but the visualization of molecules requires creative strategies In a conventional light microscope, an image is constructed from a pattern of diffracted light waves that emanate from the illuminated object As a result, some information about the specimen is lost by destructive interference of scattered light waves Ultimately, this diffraction limit prevents the study of samples that are much smaller than the wavelength of light used as a probe In practice, two objects will appear as distinct images under a microscope if the distance between their centres is greater than the Airy radius, rAiry = 0.61λ /a, where λ is the wavelength of the incident beam of radiation and a is the numerical aperture of the objective lens, the lens that collects light scattered by the object The numerical aperture of the objective lens is defined as a = nr sin α, where nr is the refractive index of the lens material (the greater the refractive index, the greater the bending of a ray of light by the lens) and the angle α is the half-angle of the widest cone of scattered light that can be collected by the lens (so the lens collects light beams sweeping a cone with angle 2α) Most molecules—including biological polymers—have dimensions that are much smaller than visible wavelengths, so special techniques had to be developed to make single-molecule spectroscopy possible In near-field scanning optical microscopy (NSOM), a very thin metal-coated optical fibre is used to deliver light to a small area It is possible to construct fibres with tip diameters in the range of 50 to 100 nm, which are indeed smaller than visible wavelengths The fibre tip is placed very close to the sample, in a region known as the near field, where, according to classical physics, waves not undergo diffraction In far-field confocal microscopy, laser light focused by an objective lens is used to illuminate about µm3 of a very dilute sample placed beyond the near field This illumination scheme is limited by diffraction and, as a result, data from far-field microscopy have less structural detail than data from NSOM However, far-field microscopes are very easy to construct and the technique can be used to probe single molecules as long as there is one molecule, on average, in the illuminated area Continuum Dissociation limit 13.5 Dissociation and predissociation Key point Two further fates of an electronically excited species are dissociation and internal conversion to a dissociative state Another fate for an electronically excited molecule is dissociation, the breaking of bonds (Fig 13.26) The onset of dissociation can be detected in an absorption spectrum by seeing that the vibrational structure of a band terminates at a certain energy Absorption occurs in a continuous band above this dissociation limit because the Internuclear separation, R Fig 13.26 When absorption occurs to unbound states of the upper electronic state, the molecule dissociates and the absorption is a continuum Below the dissociation limit the electronic spectrum shows a normal vibrational structure ... Professor of Chemistry, Lewis and Clark College, Portland, Oregon, USA W H Freeman and Company New York Physical Chemistry, Ninth Edition © 2010 by Peter Atkins and Julio de Paula All rights reserved... may be used under the same conditions as the figures Other resources Explorations in Physical Chemistry by Valerie Walters, Julio de Paula, and Peter Atkins Explorations in Physical Chemistry consists... Committee on Chemistry Education of the International Union of Pure and Applied Chemistry and a member of IUPAC’s Physical and Biophysical Chemistry Division Julio de Paula is Professor of Chemistry