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Journal of the Chemical Society, Faraday Transactions I1 SUBJECT INDEX-VOLUME70, 1974 PAGE 11, 1Kinetic Spectroscopy (see also 11, 5) Atomic Resonance Fluorescence and Mass Spectrometry for Measurements of the Rate Constants for Elementary Reactions: 03Pj+N02 -+ N0+02 and NO+03+N0+02. (Bemand, Clyne and Watson) . .... . . . . 564 Determination of Atomic Oscillator Strengtlk using Resonance Absorption with a Doppler Line Source: Transitions of Br and I(n+ l)s--np5. (Clyne and Townsend) 1863 Excited Mercury-Ammonia System. Part 1 : Kinetics of the Attachment of NH3 and ND;to Hg(63Po), and Measurements of the Emission Rates. (Callear, Connor and Kos- kikallio) . .. 1542 Excited Mercury-Ammonia System. Part 21 Attachment of NH3 Clusteis to Hg(63p0) and Estimates of the Bond Energies.(Callear and Connor) . 1667 Isotope Effects in the Quenching of Electronically Excited Atoms. Par; 3: Quenching of I(52P+)by HD. (Butcher, Donovan and Strain) . . . . 1837 Kinetic Behaviour of OH X211 and A2C+using Molecular Resonance Fluorescence Spec- trometry. (Clyne and Down) 253 Kinetic Study of Electronically Excited Nitrogen Atoms, N(2"Dj, 2zP*),'by akenuakon oi Atomic Resonance Radiation in the Vacuum Ultra-Violet. (Husain, Mitra and Young) . ... 1721 Rate Measurements of Reactions of OH by 'Resonance'Absorption. Part 3 : Reactions of OH with HI, Dz and Hydrogen and Deuterium Halides. (Smith and Zellner) . . 1045 Vibrational Excitation in Atom Exchange Reactions. (Simons and Tasker) . . . 1496 11, 2 Photophysics (fluorescence, phosphorescence, luminescence, dispersion, dichroism, etc.) Absolute Measurement of the Quantum Yield of Quinine Bisulphate.(Gelernt, Findeisen, Stein and Poole) 939 Carrier Traps in Ultra-High Puiity Single Crystals of 'Anthracene: (Owen, Sworkowski', Thomas, Williams and Williams) . . 853 Cryogenic Photolysis Studies. Part 1: Iodoalkanes. iBarnes, Hallam and Howelis) * 1682 Effect of Concentration on the Absorption and Fluorescence Spectra of Pyrene in a Solid Solution of Poly(methy1 methacrylate). (Avis and Porter) 1057 Electroluminescence and Enhanced Double-injection in Crystals of Ant&acene. (Swora-kowski, Thomas, Williams and Williams) . 676 Exchange Coupling and Triplet Exciton Migration in Semiconducting (h;"-D'ibenzyl-4,4'- bipyridylium)2+(7,7,8,8-tetracyanoquinodimeth~e)~-Crystals. (Shields) 1372 Fluorescence Emission from the First- and Second-excited r-Singlet States of Arbmati; Hydrocarbons in Solutions, and their Temperature Dependences. (Easterly and Christophorou) ... ... .. 267 Inter- and Intra-molecular Quenching of hthracene Fluorescence by Pyridihium Ion in Solution. (Hann, Rosseinsky and White) . . . . . . . 1522 Interaction between Oxygen and Aromatic Molecules. (Gijzeman) 1153 Intramolecular Energy Transfer in the Lysozyme-Eosin Complex. (Bau'gher, Grossweinei andLewis) . .... 1389 Laser-stimulated Fluorescence of Diamond.* (Adams and Payne) 1959 Laser Study of the Protonation Equilibrium of Triplet Benzophenone. (Rayner and Wyatt) .. ..945 Luminescence During Charge Recombination in Luminescent Matices. ' Part' 1 : Benzene. (Houben, Monti, Berti and Boustead) . 121 1 Mechanism of the Direct trans-cis Photoisome;ization of 'Stilbene. Part -1 : Potential Energy Surfaces of the Lowest Excited States. (Momicchioli, Bruni, Baraldi and Corradini) ..... 1325 Mercury Photosensiti&d Luminescence of Water Vapour. (Callear and Connor) 1 1767 Orientation Effects in Triplet-Triplet Energy Transfer from Benzophenone to Phenanthrene by Photoselection Studies. (Adamczyk and Phillips) 537 Photophysical Processes in the Vapour-phase measured by the' Optic-aco&tic Effec;.Part 1 : The Model and Apparatus for the study of Radiationless Processes. (Hunter,Rumbles and Stock) .. 1010 Photophysical Processes in the Vapour-phase measuied by the Optic-acoustic 'Effect'. Part 2: Triplet State Yield and Lifetime in High Pressure Biacetyl Vapour. (Hunterand Stock) . . 1022 17 SUBJECT INDEX-VOLUME 70, 1974 PAGE Photophysical Processes in the Vapour-phase measured by the Optic-acoustic Effect. Part 3: Radiationless Processes from the Lowest Singlet and Triplet States of [lH6]-Benzene and [2H6]Benzene. (Hunter and Stock) . . . 1028 Quenching of the First Excited Singlet State of Substituted Benzenes by Molecular Oxygen. (Brown and Phillips) . .. 630 Quenching of the First Excited' Singiet State of Subs'tituted Benzenes by Nitric Oxide. (Brown and Phillips) . .. 1435 Quantum Mechanical Tunnelling in ;he Radiatibnless Transitions of 'Large Moiecules.(Formosinho) 605 Singlet -+ Triplet Absorption Spectra'of Substituted Benzenes. (Metcalfe, Rockley and Phillips) 1660 Spin State Equiiibria .and Localized veisus Collect'ive &Election Behaviour in Neodymium and Gadolinium Trioxocobaltate(Ir1). (Rajoria, Bhide, Rao and Rao) 512 Switching and Other High Field Effects in Organic Films. (Garrett, Pethig and Soni) : 1732 Theory of Intramolecular Vibrational Relaxation in Large Systems. (Fleming, Gijzeman and Lin) . . . 37 Time Dependent Fluorescence Polarization Studies using Isotropic and Liquid Crystal Media. (Cehelnik, Cundall, Lockwood and Palmer) 244 Time Resolved Absorption Spectra. (Fleming, Gijzeman and Linj 1074 Triplet State of a-Nitronaphthalene.(Capellos and Porter) . .. 1159 II,3 Quantum and General Theory (including valence theory, ab initio calculations, computer simulation, etc.) Ab Initio Calculations for the Reactions CH2+Hz and CHz+CH2. (Cremaschi and Simonetta) . 1801 Ab Initio Calculations on Some Aspects of Structure, Bonding and Reactivity 'of Pyridine; Phosphabenzene and Arsabenzene. (Clarke and Scanlan) . 1222 Ab Initio Calculations on Valence-shell Molecular Orbitals. (Horn and 'Murrell) : 769 Ab Initio Unrestricted Hartree-Fock Calculations. Part 9 : Hyperfine Coupling Constants in the Ethyl Radical. (Claxton and Overill) 1005 Applications of a Simple Molecular Wavefunction. Part 1:'Floating Spheridal Gaussian Orbital Calculations for Propylene and Propane.(Blustin and Linnett) 274 Applications of a Simple Molecular Wavefunction. Part 2: The Torsionai Bariier in Ethane. (Blustin and Linnett) 290 Applications of a Simple Molecular Wavefunction. Part 3 : Ethyl 'and Propyi Carbonium Ions. (Blustin and Linnett) 297 Applications of a Simple Molecular Wave Funciion. 'Part 4: The Force Fields of BH,CH4 and NH4. (Easterfield and Linnett) . .. 317 Applications of a Simple Molecular Wave Function. Part 5 :Floating Spherical Gaussian Orbital Open-shell Calculations : Introduction. (Blustin and Linnett) . 327 Applications of a Simple Molecular Wavefunction. Part 6 : FSGO Open-shell Calcu: lations on First-row Diatomic Molecular Systems. (Blustin and Linnett) 826 Approximate Non-paired Spatial Orbital Approach to a Regular One-dimensional iattice Structure.(Duke) . 3 39 Bonding in Krypton Difluoride. ' (Coilins, Cruickshank and'Breeze) 393 Calculation of Atomic Polarizabilities by Finite-difference Methods. Part 2: Study'of the Beryllium Isoelectronic Sequence. (Stewart and Webster) 524 Calculation of Spin-Spin Interaction between Nickel Ions in Halide' Bridged Dimers. (Barraclough, Brookes) .. 1364 Calculation of the Geometries of Binaiy Transition Meial Carbonyl and Diniirogen' Corn: plexes. (Burdett) . 1599 Computer Simulation of some' Reactions ' of Energetic Tiitium' and 'Fluoiine Atoms'. (Malcolme-Lawes) .. 1942 Computational Study of Verticai Ioni&tion'Potentials using 'the A1NDO-t FOCI Method. (Chong, Herring and McWilliams) .193 Continuum Model for Solvated Electrons. (Carmichael and'webster) 1 1570 Electronic Structure of Boron Hydrides. Ab inirio Study of B1OH14, Bl,H& and BIOH:;. (Guest and Hillier) 2004 Gaussian Cell Model for Molecular Oibitals'. (Hains, Murrell, Ralston .and Woodnutt) 1794 Graphical Method for Factorizing Secular Determinants of Huckel Molecular Orbital Theory. (McClelland) .. 1453 Ground and Excited State Dipoie Moments and Energies for'n-.rr* Transitions 'in Caibonyl Compounds: INDO Configuration Interaction Calculations. (Davies and Elvin) 727 Ionization Potentials of Cycloalkenes. (Ciary, Lewis, Morland, Murrell and Heilbronner) 1889 Molecular Calculations using Spherical Gaussian Orbitals. Part 1: Optimization of the Atomic Parameters for the First-row Atoms.(Archibald, Armstrong and Perkins) . 1557 Multipole Expansion of Molecular Charge Distribution. (Dovesi, Pisani, Ricca and Roetti) . .. .. 1381 SUBJECT INDEX-VOLUME 70, 1974 19 PAGE New Analytic Form for the Potential Energy Curves of Stable Diatomic States. (Murrelland Sorbie) . . . .... 1552 Operator Formulation of the Diatomic Partition Function. iWitslhe1) . 1441 Simulated ab initiu Molecular Orbital Technique. Part 3 :Open-shell Radicals in the Spin Unrestricted Formalism. (Duke, Eiliers and O'Leary) 386 Simulation of SCF Perturbation Theory by a Simple Model Potential Met'hod. 'Polar: isabilities of Divalent Atomic Species. (Stewart) . . .. 85 Theoretical and Experimental Study of the Low Energy Ionic States 'of n-Cyclopenta- dienylnickel Nitrosyl.(Evans, Guest, Hillier and Orchard) . 41 7 Theoretical Study of the Electronic Structure of the Diboron and Tetrahedron 'Tetra: halides. (Guest and Hillier) .... 398 Theoretical Study of the Structure of Some Tiigonal Radicals. (Aarons, Hillier and Guest) . . ....... 167 Time-dependent Orientation Distribution Function Calculated from Time-correlation Functions by Use of Information Theory. (Clarkson and Williams) 1705 Uncoupled and Coupled Hartree-Fock Calculations of Dipole Polarizabilit'ies or Con: densed Hydrocarbons. (Lazzeretti and Taddei) . ..... 1153 Wavefunction for "4-Electron, 3-Centre" Bonding Units. (Harcourt and Harcourt) . 743 11, 4 Relaxation Phenomena (dielectric, magnetic, ultrasonic, etc.) Acoustic Studies of Solutions of Narrow Molecular Weight Polystyrene in Toluene.(Cochran, Dunbar, North and Pethrick) . .. 21 5 Acoustic Studies of Styrene- and-ar-Me th yls t yrene-Alkane Copolymers. ' (Noith ,Pet hr ick and Rhoney) ... 223 Anomolous Electric Polarizations of 1 ;4-Benzoqu&one and Related Compounds. (Haigh,Jinks, Leach, Milligan, Sutton and Waddington) .. 779 Comparison of Dielectric Relaxation and Viscoelast'ic Retardation in Three Viscous Liquids. (Shears, Williams, Barlow and Lamb) .. 1783 Comparison of the Viscoelastic, Dielectric and Light Scaitering Properties of &my1Benzoate. (Barlow and Erginsav) ... 885 Dielectric Measurements of N-(p-Methoxybenzy1idene)-p-butylanilinein the Frequency Range 1 kHz to 120 MHz.(Agarwal and Price) . .. 188 Dielectric a Relaxation in Siloxane Oligomer +Diluent Systems. (Baird and Sengupta) . 1741 Dielectric Relaxation in Clathrates of Dianin's Compound. (Cook, Heydon and Welsh) 1591 Dielectric Relaxation in Non-aqueous Solutions. Part 5:Propylene Carbonate (4-Methyl- 1,3-dioxolan-2-0ne). (Cavell) 78 Dielectric Relaxation Studies in some Monomer Acrylaies. &aka and Sobhanadri) 344 Dielectric Relaxation Time, a Non-linear Function of Solvent Viscosity. (Magee) . . 929 Dielectric Studies of Non-electrolyte Solutions. Part 2: Non-linear Behaviour of Associ- ated Liquids. Application to the Study of PyridineChloroform Interactions. (Rivailand Thiebaut) .. . . . . . 430 Dipole Moments of Halogenogermanes &om "on-resonant Absorption of Vapours.(Bellama, Wandiga and Maryott) ..... .. 719 Interaction of Lithium Salts with Amides. Part 1 : Ultrasonic Relaxation. (Adams;Baddiel, Jones and Matheson) . 1114 Kinetics of Micellization from Ultrasonic Relaxation Studies'. (Rasing ,Sams and Wyn: Jones) .... .. 1247 Multiple Reflktion Time 'Domain Spectrokopy. Application to Dielectric Relaxation Properties of Aqueous Systems in the Time Range 10-lo to lW4s. (Clark, Quickenden and Suggett) . ... ... 1847 Non-linear Dielectric Mea'surements in Conducting Media using a Frequency Sampling Technique. (Jones and Krupkowski) . . 862 Permittivity Increments in Non-dipolar Solvents due to High Electrid Fields. (Lpkowski',Parry Jones and Davies) .. 1348 Ultrasonic Relaxation in Aqueous Solutions of Lithium Salts and Sodium'Poly(a,L-glutamicacid). (Adams, Baddiel and Matheson) .. 1756 Ultrasonic Studies of Perfluoro-n-alkanes. (Cochran, North and Pethri'ck) . .. 1274 Viscoelastic and Ultrasonic Relaxation in DL(Zethylhexy1) Phthalate. (Barlow, Erginsav, McLachlan and Singh) . .. 1288 11, 5 Spectroscopy (a) Microwave, infra-red, Raman Application of a Laser Self-beat Spectroscopic Technique to the Study of Solutions of Human Plasma Lipoproteins. (Davi) .. .. . 700 Concentrated Potassium Zincate Solutions studied using Laser Raman Spectroscopy and Potentiometry. (Briggs, Hampson and Marshall) ....... 1978 SUBJECT INDEX-VOLUME 70, 1974 PAGE Effect of Temperature on the Hydrogen Bond US Band. Part 3: Liquid Phase.(Zdzienskiand Wood) . 409 Evidence for Short-range Orientation Effect, in Dipolar Aprotic Liquids. from' Vibrational Spectroscopy. Part 2: Carbonyl Compounds. (Fini and Mirone) . . 1776 "Hot" Transitions in the Infra-red spectra of Iodoacetylene. (Rogstad) . . 1412 Hydrogen Bonding in the Gas Phase. Part 1 : Infra-red Spectroscopic Investigation of Amine-Alcohol Systems. (Hussein and Millen) . 685 Hydrogen Bonding. in the Gas Phase. Part 2: Determination of Thermodynamic. Para: meters for Amine-Methanol Systems from Pressure, Volume, Temperature Measure- ments. (Millen and Mines) 693 Infra-red Spectroscopic Studies of the Bending Modes of Waier. Detectibn of'1:l and 1 :2 Complexes in Organic Solutions.(Gentric, Le Navor and Saumagne) . 1191 Infra-red Spectrum and Conformations of 2,2,2-Trifluorethyl Vinyl Ether. (Charles;Cullen and Owen) . 483 Interpretation of the Infra-red 'Spectra of' CO Adsoibed on Evaporated Alkali 'Metai Halides. (Rao and Dignam) . 492 Interpretation of the Microwave and Far Infra-red absorption of some Dipolar Liquids in Terms of Vibrational and Relaxational Motion. (Larkin and Evans) . 477 Microwave and Infra-red Spectra and Conformation of Methyl Trifluoroacetate. (Jones,Summers and Owen) . .. 100 Microwave Spectrum, Torsional Frequency and Barrier to Inteinal Rotation in Phenyiboron Difluoride. (Christen, Lister and Sheridan) 1953 A New Route to Matrix Isolated Iron Atoms. (Poliakoff and Turner) 93 Preparation and Infra-red Spectrum of [2,3,6,6-2H4]Biphenylene.(Lunelli and Peciie) : 1186 Rayleigh (Strutt) Method of Making an Approximate Correction to Spectra for Finite Slit Widths.(Hill and Steele) . . 1233 Rotational Isomerism, Barrier to Internal Rotation and'E1ect;ic Dipole Momeht of AcrylicAcid by Microwave Spectroscopy. (Bolton, Lister and Sheridan) 113 Rotational Velocity Correlation Function for assessing Molecular Models for Gas and Liquid Phase Studies. (Evans) 1620 Simple Models of the Far Infra-red Absorphon of Pola; Molecule; in Liquid and Rotato; Phases. Part 2: Application to Systems of Non-spherical Molecules. (Larkin) 1457 Single-crystal Raman Spectrum of Strontium Dichloride Hexahydrate and some Related Materials.(Adams and Trumbel) .... 1967 Spectroscopic Studies of Hydrogen Bonded Aromatic 'Complexes at Low Temperatures: External Deuterium Isotope Effects. (Simons and Smith) 53 Spectroscopic Studies. Part 10: Infra-red Studies of Solute-Solven't Interactions of Phenol in Fluorinated and Mixed "Inert" Solvents. (Szczepianak and Orville-Thomas) . 1175 Study of the Rotational Ranian Spectra of 14N15N2, using a Fabry-Perot Etalon. (Butcherand Jones) . 560 Vapour Phase Infra-red Studies of * Alcohols. * Par; 2: Hetero-association. (Barnes,Hallani and Jones) . 422 Vibrational Spectra, Barriers to Internal Rotation' and Conformatibn of 'Propargyl Methyl Ether and Methoxyacetonitrile. (Charles, Cullen, Jones and Owen) . .. 758 Vibrational Spectra of Octafluoronaphthalene.(Girlando, Tamburini andiPecile) . . 6 Vibrational Spectrum of the ReH;- Ion. (Creighton and Sinclair) . . . . 548 (b)electronic (visible, ultra-violet, absorption and emission) Assignment of the Charge-transfer Bands in some Metal Phthalocyanines. Evidence for me S = 1 state of Iron(I1) Phthalocyanine in Solution. (Stillman and Thomson) . 790 Density and Refractive Index of Solid Layers of Noble Gases and Sulphur Hexafluoride. (Schulze and Kolb) 1098 Derivation and Interpretation of the Spectra of Aggregates. 'Part 3: Prediction Analytical Study of the Spectrum of Pyronine Y in Aqueous Solution. (Gianneschi and Kuruscev) . 1334 Electronic Absorption, Luminescence, Infra-red and Raman Spectra of the Cr(NCS)i- Ion. (Flint and Matthews) .. .. 1301 Electronic Spectroscopy of Mercury(1;) Halides in some Non-aromatic Organic Solvents'. (Eliezer and Avinur) . . .. Fluorescence and Absorption Spectra . of Anthracene Crystais at 4 K Doped *with i-and 1316 2-Aminoanthracene: Effects of Guest Orientation. (Bridge and Vincent) . 30 Luminescence Spectrum of the Cr(CN):- Ion. (Flint and Greenough) 815 Magneto Optical Rotatory Dispersion Studies of Simple Electrolyte Solutions: (Dawber) 597 Magneto Optical Rotatory Dispersion Studies of Simple Electrolyte Solutions. Part 2 : Measurements on Solutions of NaBr, KBr, NaI and KI. (Dawber) . 1748 Orbital Reduction Factors in the Lowest Excited State of the Phthalocyanine Ring and their Measurement by Magnetic Circular Dichroism Spectroscopy.(Stillman and Thomson) . .......... 805 SUBJECT INDEX-VOLUME 70,1974 21 PIG# Spectra of some d2 and d8Transition Metal Ions. (Stewart) . 1882 Spectral Analysis of the Light Scattered by a Ternary Mixture. (Lekkeikerker and Laidlaw) . .. 1088 Structural Aspects of Noniinear Optics: Optical 'Properties of KZH(I0&Cl bd Related Compounds. (Tofield, Crane and Bergman) . ..... 1488 t 3, Transitions of the trans-Difluorobis(ethylenediamine)chromium(m) Ion. Vibronic Analyses and Crystal Field Calculations. (Flint and Matthews) 1307 Vapour Phase Electronic Absorption Spectrum of Nitrosobenzene in the 750nm Region. (Bhujle, Rao and Wild) . . . . . , . . . . 1761 (c) photoelectron Covalent Character of Lithium Compounds Studies by X-Ray Photoelectron Spectroscopy.(PoveyandSherwood) . . . 1240 Electronic Structure of Diazocyclopentadiene. A Study using Low and High Energy Photoelectron Spectroscopy and ab initio Molecular Orbital Calculations. (Aarons,Connor, Hillier, Schwarz and Lloyd) . .. 1106 Electronic Structure of some Oxyanions studied *by X-Ray 'Emission and Photoeiectron Spectroscopy. (Connor, Hillier, Wood and Barber) . 1040 Electronic Structures of Metal Complexes containing the n-Cyclopentadienyl and Related Ligands. Part 2 :He-I Photoelectron Spectra of the Open-shell Metallocenes. (Evans,Green, Jewitt, King and Orchard) . .. 356 He-I Photoelectron Spectra of some do Transition 'Metai Compounds. (Burroughs, Evans; Hamnett, Orchard and Richardson) .1895 High Energy Photoelectron Spectroscopy of Transition Metai Complexes. Part 4.: Bis(arene) and related Complexes of Chromium, Manganese and Iron. (Connor,Derrick and Hillier) . . . ... 941 Ionisation Energies of Pyridine N-Oxides determined by Photoelectron Spectroscopy. (Maier and Muller) . 1991 Photoelectron Spectra of Inner Valende Sheils. Part 1.: Saturated'Hydrocarbons. '(Potts and Streets) . 875 Photoelectron Spectra of * Inn& Valence Shells: Pait 2 : 'Unsa&ate'd Hydrocarbons.(Streets and Potts) ... 1505 Photoelectron Spectra of t'he Trimethyl Compounds of: the Group V Elements. Constant Ionisation Potentials of the Lone Pair Orbital Electrons. (Elbel, Bergmann and EnBlin) 555 Photoelectron Studies of 'Metai Carbonyls.Part 4:' Mono-substituted Complexes of Chromium and Tungsten Carbonyls. (Higginson, Lloyd, Connor and Hillier) . . 1418 Vacuum Ultraviolet Photoelectron Spectroscopy of Transient Species. Part 2: The use of Phase-sensitive Detection for Investigating the Electronic States of 0:. (Jonathan,Morris, Okuda, Ross and Smith) . 1810 Vacuum Ultraviolet Photoelectron Spectroscopy of 'Transient Species. Part 3: The SO(3C-) Radical. (Dyke, Golob, Jonathan, Morris, Okuda and Smith) . 1818 Vacuum Ultraviolet Photoelectron Spectroscopy of Transient Species. Part 4:Difluoro: methylene and Ozone. (Dyke, Golob, Jonathan, Morris and Okuda) . . . 1828 (d) electron spin resonance Electron Paramagnetic Resonance Study of Ce3+, Dy3+ and Yb3+ in CszNaYC16. A crystal with Sites of Perfect Octahedral Symmetry.(Schwartz and Hill) .. 124 Electron Spin Resonance of Alkali Metal o-Dimesitoylbenzene Radical Complexes: (Pasimeni, Brustolon and Corvaja) 734 Electron Spin Resonance and CND0/2 Study of the Radicals produced during Fas; Electron Irradiation of Substances containing Nitrogen. Part 3 : Piperidine. (Helckeand Fantechi) . 1912 Electron Spin Resonance Spectra and Conformations of Radicals' Produced from Cyclo: alkanols. (Corvaja, Giacometti and Sartori) .. 709 Electron Spin Resonance Study of Copper(r1) Bis(diseienocaibamate) in Liquid Crystals.. (Agostini, Nordio, Pasimeni and Segre) .. 621 Electron Spin Resonance Study of Paramagnetic Ion Pair Systems with Non-parallei Alignment of Their Axes.(Carr, Smith and Pillbrow) . . 497 Electron Spin Resonance Study of the Super-oxide Ion in Melt-recrystallized Strontium Chloride. (H. N. Ng (Ng Hok Nam) and Harrison) . . .. 45 Electron Spin Resonance Studies of Spin-labelled polymers. Part 7: Dependence of Ro-tational Correlation Times on Solvent Properties and Polymer Concentration. (Bul-lock, Cameron and Smith) . 1202 Hyperfine Coupling Constants and Angles of Twist 'of Phenyl 'and Pentafluorophenyl substituted Methyl Radicals. (Hudson, Kent, Jackson and Treweek) 892 Long-range Electron Spin Resonance Coupling Constants in Radical Adducis of Malei; Acid. (Dixon, Foxall and Williams) . . . . . . . . 1614 SUBJECT INDEX-VOLUME 70, 1974 PAGE Proton Hypefine Structure in the Electron Spin Resonance Spectrum of the Acetonitrile Dimer Radical Anion.(Gillbro, Takeda and Williams) 465 Single Crystal Electron Spin Resonance Spectrum of the p-Toiyl Radical: Hypefine Tensors of ortho Protons. (Barigalletti, Poggi and Breccia) . 1198 Substituent Effects in the Electron Spin Resonance Spectra of Phenoxyl Radicais. (Dixon;Moghimi and Murphy) 1713 Unstable Intermediates. Part I37 : a-Bromoalkyl Radicals in Irradi’ated Organic Bromides’: an Electron Spin Resonance Study. (Mishra, Neilson and Symons) . 1165 Unstable Intermediates. Part 146: Electron Spin Resonance Spectra for Linear BrCNL and BrzCN Radicals in Irradiated Cyanogen Bromide Crystals. (Mishra, Neilson and Symons) . .. 1280 (e) nuclear magnetic resonance, quadruple resonance Bromine Nuclear Magnetic Resonance Study of the Reorientation of Bromomercurio-N- acetyl-L-phenylalanine, Bromomercuriocinnamic Acid, Bromomercuriobenzoic Acid and Bromomercuriomethane in Water.(Garnett and Halstead) . 1920 Deuteron Magnetic Resonance Studies. Part 5 : Interpretation of Deuteron Quadrupole Coupling Constants using a Localized Orbital Model. (Bearfield, Robb and Smith) 920 Electron-coupled “Through-space” Nuclear Spin-Spin Interaction. (Buckingham and Cordle) 994 Measurement of the ‘Sign and Magniiude of J(XX’) in AnAn’XX’ Nuclear Spin Systems.: Examples from Organophosphorus Chemistry. (McFarlane and Rycroft) . 377 Molecular Motion in Solid Complexes. Part 1: T-T Molecular Complexes of Pyrene studied by Nuclear Magnetic Resonance Spectroscopy.(Fyfe) . 1633 Molecular Motion in Solid Complexes. Part 2: T-n Molecular Complexes of Naphthalenestudied by Nuclear Magnetic Resonance Spectroscopy. (Fyfe) 1642 Proton Magnetic Resonance Spectra of Partially Oriented Samples of’ Cyclopentadienyl Compounds. (Beattie, Einsley and Sabine) . 1356 Proton Magnetic Resonance Study of Molecular Moiion in Trimethyiamine-Trimethyl:aluminium and Trimethylamine-Trimethylgallium. (Ang and Dunell) . 17 Spin-lattice Relaxation Time of 3C Satellites in Proton Nuclear Magnetic Resonanc; Spectra and their use in Determining Molecular Rotational Diffusion Constants. (Heatley) 148 Wide Line Nuclear Magnetic Resonance Study of Molkcula; Motions in Solid Sulpholan. (Gilson and Saviotti) ...... 1 (f)neutron scattering Segmental Diffusion in Rubbers Studied by Neutron Quasielastic Incoherent Scattering. (Allen, Higgins and Wright) . 348 (g)ion cyclotron resonance, mass spectrometry etc. Collision Cross-sections for Low-energy Electrons in some Simple Hydrocarbons. (Duncanand Walker) 577 Gas Phase Electron biffradtion Study of Six F1uo;oethylenes: (Carlos, Karl and Bauer) ; 177 Gas Phase Structure of Tetramethylethylene. (Carlos and Bauer) . 171 High-resolution Electron-microscopic Studies of Structural Faults in Layered Siiicates. (Jefferson and Thomas) .. 1691 Mass Spectrometric Evidence for the Very High Stability‘ of Diatomic Cerium Com- pounds with Some Platinum Metals and Predicated Dissociation Energies of Selected Diatomic Intermetallic Compounds with Multiple Bonds.(Gingerich) . 471 Mass Spectrometric Studies of the Fragmentation of the Methanethiol Ion Induced by Charge Exchange. (Jonsson and Lind) . . .. 1399 Threshold Electron Energy-loss Spectra for Some Simple Alkynes. (Dance and Walker) 1426 11, 6 Statistical ?Aechanics Anliarmsnicity Correction for Kinetic Isotope Effect Calculations involving Hydrogen Isotopes. (Bron) . 240 Application of the Density Matrix Meihod in the ‘Quantum Mechanical Calcuiation’ of the Bridgc-assisted Electron Transfer Probability in Polar Media. (Kharkats, Madumarov and Vorotyntsev) . .. .. 1578 Attractive and “Repulsive” Forces between Neuiral Particles in Ionic ’Solution. ‘(Rich- mond) 1650 Calculation of ;he Solvation Enet-gy of Dipolar Molecuies.(Kharkats) . : 1345 Dispersion Forces in Physical Adsorption. (Mahanty and Ninham) 637 Distribution of Occupied Sequences in One-dimensional Arrays. Models for t‘he Reaction of Polymer Substituents. (Barron, Bawden and Boucher) 65 1 Electrical Forces between Particles with Arbitrary Fixed Surface Charge Disjributions in Ionic Solution. (Richmond) . ... .... 1066 SUBJECT INDEX-VOLUME 70, 1974 23 PAGE Electrokinetic Effects in Charged Capillary Tubes. (Ssrensen and Koefoed) . . . 665 Interaction of Alkanes with Graphite. (La1 and Spencer) .. .. 910 Interionic Pair Potentials in the Alkali Metal Halides. (Woodcock) . 1405 Isotope Effects on Partition Functions and Thermodynamic Quantities of the 'Stable Diatomic Hydrides.@ron and Paul) .. .. 1294 Non-retarded van der Waals Energies between a Finite Rod and a Plana; Substrate'. (Richmond) . .. 229 Phase Transitions in Polymer Solutions and the Prediction' of 0' Temperatures. '(Chan andNinham) . 586 Polar Solvent Structure in fhe Theory of Ionic Soivatioh. (Dogonadze and Kornyshev) 1 1121 Quantum Theory of Concerted Proton Transfer Reactions in Polar Media. Linear Electronic Terms. (Dogonadze, Kharkats and Ulstrup) . 64 Stability of Colloidal Dispersions. Theory for the Interaction between Particles Dis'persed in a Regular Mixture. (Ash) . .... 895 Zero-point Energy of Linear Triatomic Molecules. (Bron) ... 871 11, 7 Thermodynamics (reversible and irreversible) Excess Thermodynamic Functions of Binary Mixtures of Normal and Isomeric Alkanes (Ce5 and C6).(Chen and Zwolinski) . 1133 Extension of a Model for Solutions of Non-metals in Liquid 'Alkali-metals: Calculakon of the Enthalpy of Solution. (Gellings, van der Scheer and Caspers) . 531 Generalized Treatment of Alkanes. Part 3 : Triatomic Additivity. (Somayajuiu and Zwolinski). . 967 Generalized Treatment of 'Alkanes. Part 4: Triatomic Additiviiy Applications to Sub- stituted Alkanes. (Somayajulu and Zwolinski) . . 973 Generalized Treatment of Aromatic Hydrocarbons. Part 1 : Triatornic' Additivity 'Appli- cation to Parent Aromatic Hydrocarbons. (Somayajulu and Zwolinski) 1928 Quantitative Interpretation of Excess Properties of n-Alkane Mixtures Through Prigogine's Solution Theory.(Janini and Martire) . 837 Spontaneous Rupture of Thin Liquid Films. (Ruckenstein and Jain) . 132 Thermodynamic Effects of Orientational Order in Chain-molecule iixtures. Part Heats of Mixing of Globular and Normal Alkanes. (Lam, Picker, Patterson and Tancrede) . . 1465 Thermodynamic Effects of Orientational Order' in Chain-molecule Mixtures. Part 2': Temperative dependence of Heats of Mixing of Branched and Normal Alkane Mixtures. (Croucher and Patterson) . 1479 Thermodynamics of Solutions of Interacting Aghegatks by' Methods Similar to Surfack Thermodynamics. Part 2 : Solutions of Non-associating Marcromolecules. (Hall) . 1526 Thermodynamic Properties of Organic Oxygen Compounds. Part 34: Chemical Thermo- dynamic Properties of Propanal. (Frankiss) .. . .. 1516 11, 8 Transport Phenomena (see also I 6) Diffusion of Polystyrene in Solution Studied by Photon Correlation Spectroscopy. (Pusey,Vaughan and Williams) . . 1696 Formation and Migration of Vacancies in Rubidium Halide;. (Shukla'and Rao) : . 1628 Influence of Imbedded Particles on Steady-state Diffusion. (Bell and Crank) . 1259 Kirkwood-Rice-Allnatt Kinetic Theory of Transport in Liquids. (Smedley and Wood-cock) . 955 Mossbauer Studies of Mairix-isolated' Sn, §nz and Higher Polymers and their Diffusion Behaviour in Solid Nitrogen. (Bos and Howe) . 451 Mossbauer Studies of Matrix-isolated SnO, SnzO2 and Higher Polymers. iBos, Howe,Dale and Becker) . .. ... . 440 *:1 Faraday I1 AUTHOR INDEX-VOLUME70, 1974 PAGE PAGE Aarons, L.J. . .. . 167, 1106 Carmichael, I. ... . 1570 Adamczyk, A. . .. 537 Carr, S. G.. .. . 497 Adams,D.M. . .. .. 1959, 1967 Caspers, W. J. . . 531 Adams, M. J. . . 1114, 1756 Cavell, E. A. S. . . 78 Agarwal, V. K. . . 188 Cehelnik, E. D. .. . 244 Agostini, G. . .. . 621 Chan,D. .. 586 Allen, G. . . 348 Charles, S. W. .. 483, 758 Ang, T. T. . . 17 Chen, S. S. . .. . 1133 Archibald, R. M. . . 1557 Chong, D. P. .. . 193 Armstrong, D. R. . 1557 Christen, D. . 1953 Ash, S. G. .. . 895 Christophorou, L.G. . . 267 Avinur, P. . . 1316 Clark, A. H. .. . 1847 Avis, P. .. . 1057 Clark, D. T. .. . 1222 Clarkson, T. S. . . 17051Baddiel, C. B. . .. . 1114, 1756 Clary, D. C. . . 18891Baird, M. E. . . 1741 Claxton, T.A. . 10051Baraldi, I. . .. . 1325 Clyne, M. A. A. . 253, 564, 1863 1Barber, M. . . 1040 Cochran, M. A. . . 215, 1274 1Barigelletti, F. . .. 1 198 Collins, G. A. D. . 3931Barlow, A. J. . . 885; 1288, 1783 Connor, J. A. . 94i,1040, 1106, 1418 1Barnes, A. J. . 422, 1682 Connor, J. H. .. 1542, 1667, 1767 13arraclough, C. G. . 1364 Cook, J. S. . 15911Barron, T. H. K. . 651 Cordle, J. E. .. . 994 1Bauer, S. H. . : 1'71, 177 Corradini, G. R. . 132513augher, J. F. . . 1389 Corvaja, C. .. : 709,734I3awden, R. J. . . 651 Crane, G. R. . . 148813earfield, D. W. . . 920 Crank, J. . 125913eattie, I. R. . . 1356 Creighton, J. A. . 54813ecker, L. W. . . 440 Cremaschi, P. . . 1801I3el1, G. E. . . 1259 Croucher, M. D. .. . 14791%llama, J. M. . .719 Cruickshank, D. W. J. . .. 39313emand, P. P. . . 564 Cullen, F. C. .... 483, 758 13ergman, J. G. . . 1488 Cundall, R. B. ..... 244 13ergmann, H. . . 555 13erti, C. . . 1211 Dale, B. W. . . 440 13hide, V. G. . ... . 512 Dance, D. F. . . 1426 13hujle, V. V. . 1761 Davi, S. K. . . 700 13lustin, P. H. . 274, 290,'297, 327, 826 Davies, D. W. : . 727 13olton, K. .. 11 3 Davies, M. .. 1348 1~OS,A. 440, 451 Dawber, J. G. .. : 597, 1748 13oucher, E. A. . 651 Derrick, L. M. R. . . 941 I3oustead, I. . 1211 Dignam, M. J. . 492 13reccia, A. . . 1198 Dixon, W. T. . : I&, 1713 I3reeze, A. . 393 Dogonadze,R. R. .. . 64, 1121 13ridge, N. J. .. . 30 Donovan, R. J. . . 1837 13riggs, A. G. . . 1978 Doskikallio, J. . . 1542 13rinton, R. K. . -.203 Dovesi, R. . .. . 1381 13ron, J. . 253 I3rookes, R.'W. : . 240, 871, 1294 Down, S. . .. . . 13481364 Drupkowski, T. 13rown, R. G. . 630, 1435 Duke,B. J. .. : 339, 386 1Bruni, M. C. . . 1325 Dunbar, J. H. . . 215 13rustolon, M. 734 Duncan, C. W. . . 577 I3uckingham, A. b. . . 994 Dunell, B. A. . 17 13ullock, A. T. . . 1202 Dyke, J. M. .. : isis, 1828 13urdett, J. K. . . 1599 I3u~roughs,P. . 1895 Easterfield, J. R. . . 317 13utcher, R. J. . 560, 1837 Easterly, C. E. . . 267 Eiliers, J. E. . . 386 Callear, A. B. . . 203, 1542, 1667, 1767 Elbel, S. . . 555 Cameron, G. G. . . 1202 Eliezer, I. . . 1316 Capelos, C. 1159 Elvin, R. . . 727 Carlos, J. L., Jr. . i71, 177 Emsley, J. M'. : .. . 1356 24 AUTHOR INDEX-VOLUME 70, 1974 25 PAGE PAGE EnBlin, W... 555 Jewitt, B. ... . . 356 Erginsav, A. . 885, 1288 Jinks, K. M. .. 779 Evans, M. . 477, 1620 Jonathan, N. .. 181'0, isi8,1828 Evans, S. .. : 356,417, 1895 Jones, D. ... 422 Jones, G. I. L. .. ioo, 758 Fantechi,R. . .. . 1912 Jones, G. P. .. . 862, 1348 Findeisen, A. . .. . 939 Jones,R. G. .. . . 1114 Fini, G. Fleming, G.R. : .. 1776 Jones, W. J. .. . 560 37, 1074 Jonsson, B.-0. .. . . 1399 Flint, C. D. 81'5, 1301, 1307 Formosinho, S. J. . 605 Karl, R. R., Jr. .. . . 177 Foxall, J. ... 1614 Kent, H. J. .. . . 892 Frankiss, S. 'G. .. 1516 Khanna,R. K. .. 344 Fyfe, C. A.. . . . 1633, 1642 Kharkats, YuI. .. 64, 1345, 1578 King, G. H. .. . 356 Garnett, M. W. . ... 1920 Koefoed,J.. .. . 665 Garrett, S.G. E. . .. . 1732 Kolb, D. M. .. . 1098 Gelernt, B. ... 939 Kornyshev, A. A. .. . 1121 Gellings, P. J. . ... 531 Koskikallio, J. .. 1542 Gentric, E. . . ... 1191 Jhpkowski, T. .. 862,1348 Giacometti, G. . ... 709 Kurucsev, T. .. . 1334 Gianneschi, L. P. 1334 Gijzeman, 0.L. J. : 37, 1074, 1143 Laidlaw, W. G. .. . 1088 Gillbro, T. .. . . 465 La1,M. ... . 910 Gilson, D. F. R. . ... 1 Lam,V.T.. .. . 1465 Gingerich, K. A. . .. . 471 Lamb, J. ... , 1783 Girlando, A. . 6 Larkin, I. . 477 Giwekksm, H. D. R. 1682 Larkin, I. W. . 1457 Golob, L. : isis, 1828 Lazzeretti, P. . . 1153 Green, M. L. H. : .. . 356 Leach, A. G. . 779 Greenough, P. . .. . 815 Lekkerkerker, H. 'N. W: . 1088 Grossweiner, L. I. 1389 LeNarvor, A. .. . 1191 Guest, M.F. . i67,398,4i7,2004 Lewis, A. A. . . 1889 Lewis, C. ... 1389 Haigh, J. . 779 Lin, S. H. . .. 37, 1074 Haines, L. M. : . 1794 Lind. J. ... . 1399 Hall, D. G. 1526 Linnett, J. W. . 274,290, 297, 317, 327, 826 Hallam, H. E. . 422, 1682 Lister, D. G. .. . 113. 1953 Halstead, T. K. . . 1920 Lloyd, D. R. . . 1106,1418Hamnett, A. . . 1895 Lockwood, J. R. . , . 244 Hampson, N. A. . . 1978 Lunelli, B. ... . . 1186 Hann,R.A. . . 1522 Harcourt, A. . . 743 McClelland, B. J. . . 1453 Harcourt, R. D. . . 743 McFarlane, W. .. . . 377 Harrison, L. G. . . 45 McLachlan, R. J. . . . 1288 Heatley, F. .. . 148 McWilliams, D. .. . . 193 Heilbronner, E. . . 1889 Madumarov, A. K. . . . 1578 Helcke, G. A. . . 1912 Magee, M. D. .. . . 929 Herring, F. G. .. 193 Mahanty, J. . . . 637 Heydon, R. G. . . 1591 Maier, J. P. . . 1991 Higgins, J. S. . . 348 Malcolme-Lawes, D. J. ' . . 1942 Higginson, B. R. . . 1418 Marshall, A. . . . 1978 Hill. I. R. . . 1233 Martire, D. E. . . 837 Hri11; N. J. .. . 124 Maryott, A. A. 719 H[illier,I. H. 167, 398, 417, 941, 1040, 1106, Matheson, A. J. : iii4,1756 1418,2004 Matthews, A. P. . 1301, 1307 orn, M. .. ... 769 Metcalfe, J. 1660 ouben, J. L. .. .. 1211 Millen, D. J. : 685, 693 'owe, A. T. .... 440,451 Milligan, B. D. . . 779 owells, J. D. R. . 1682 Mines, G. W. . . 693 udson, A. . . .. 892 Mirone, P. 1776 unter, T. F. .. . ioio, 1022,1028 Mishra, S. P. 1165, 1280 usain, D. . .. 1721 Mitra, S. K. . . 1721 ussein, M. A. : . . 685, 929 Moghimi, M. . . 1713 Momicchioli, F.. . 1325 Jackson, R. A. . . 892 Monti, S. . . . 1211 Jain, R. K. .. ... . 132 Morland, D. 1889 Janini, G. M. . .... 837 Morris, A. . i8io. isi8.1828 Jefferson, D. A. ..... 1691 Muller, J.-F. ... 1991 26 AUTHOR INDEX-VOLUME 70, 1974 PAGE PAGE Murphy, D. . 1713 Murrell, J. N. . 769, 1552, 1794, 1889 Neilson, G. W. Ng, H. N. (Ng Hok Nam) Nierzwicki, W. . . Ninham,B. W. . . Nordio, P. L. . North,A.M. . Okuda,M. . . . O’Leary, B. . Orchard, A. F. Orville-Thomas, W. J. : Overill. R. E. . Owen,&. P. . Owen, N. L. . Palmer, T. F. Pasimeni, L. Patterson, D. Paul, S. 0. . Payne, S. J. Pecile, C. Perkins, P. G. Pethig, R. . Pethrick, R. A. Phillips, D. . Picker, P. Pilbrow, J. R. Pisani, C. , Poggi, G. Poliakoff, M. Poole, A.. Porter, G. . Potts, A. W. Povey, A. F. Price, A. H. Pusey, P. N. Quickenden, P. A. R R R R R R R R R R R R R R R R R R R R R hjoria, D. S. . !alston, B. J. . Lao, B. . Lao, C.N.R. . Lao, G. R. :assing, J. !ayner, D. M. . !honey, I. . . :im, F. . . Lichardson, N. V. Lichmond, P. . :hail, J. L. . :obb,M.A. . Lockley, M. G. . Loetti, C. . Logstad, A. . !oss, K. J. . . :osseinsky, D. R. Luckenstein, E. . lumbles, D. . Lycroft, D. S. . . 1165, 1280 . 45 10571 586,637621: 215, 223, 1274 . 1810, 1818, 1828 . 386 . 356,417, 1895 . 1175 . 1005 853 ’100,483,758 244 . 1465,1479 . 1294 . 1959 . 6, 1186 . 1557 1732 * 215,223, 1274 537, 630, 1435,1660 : 621,734 .~ . . 1465 . 497 . 1381 . 1198 . 93 939: 1057, 1159 . 875,1505 . . 1240 . 188 . 1696 . 1847 . . 512 . . 1794 .. 492 512, 1761,1628 . 512 . . 1247 . . 945 . 223 . 1381 1895 229, 1066, 1650 . 430 . . 920 . 1660 . . 1381 . 1412 . 1810 . . 1522 . 132 . 1010 . 377 Scanlan, I. W. . Schulze, W. . Schwarz, M. . Schwartz, R. W. . Segre, U. Sengupta, C: R. Shears, M. F. . Sheridan, J. Sherwood, P. M. A. Shields, L. . Shukla, A. K. . Simonetta, M. . Simons, J. P. . Sinclair, T. J. . Singh, R. P. . Smedley, S. I. . Smith, A. L. . Smith, D. J. . Smith, I. W. M. . Smith, J. A. S. . Smith, P. M. . Smith, T. D. . Sobhanadri,J. . Somayajulu, 6.R. Soni, V. Sorbie, K. S: 1 Sprensen, T. S. . Spencer, D. . Steele, D. . Stein, A. Stewart, J. J. P. : Stewart, R. F. . Stillman, M. J. . Stock, M. G. . Strain, R. H. . Streets, D. G. . Suggett, A. . . Summers, T. D. . Sutton, L.E. . Sworakowski, J.. Symons, M. C.R. Szczepianak, K. . Taddei, F. . Takeda,K. . Tamburini, B. . Tancrede, P. . Tasker, P.W. . Thiebaut, J. M. . Thomas, J. M. . Thomson, A. J. . Tofield, B. C. . Townsend, L. W. . Treweek, R. F. . Trumble, W. R. . Turner, J. J. . Ulstrup, J. . van der Scheer, A. Vaughan, J. M. . Vincent, D. Vorotyntser, M. A. . 1222 . 1098 . 1106 . 124 . 621 . 1741 1783 . 1240 . 1372 . 1628 1801 53,1496 . 548 . 1288 . 955 53 . 1045 . 920 . 1202 . 497 ii3,1953 isio,1818 . . 344 967, 973, 1928 . . 1732 . 1552 . 665 . . 910 . 1233 . 939 . 1882 . 85, 524 790, 805 lOlb,1022, 1028 18371 8j5, 1505 . . 1847 . . 100 779 676,853 . 1165, 1280 . 1175 . 1153 . 465 . 6 . 1465 . 1496 430 676, 853, 1691 . 790. 805 . 1488 . 1863 . 892 . 1967 . 93 . 64 . 531 . 1696 . 30 . 1578 Sabine, R.M. Sams, P. J. Sartori, G. . Saumagne,P.Saviotti, P. P. . . . . . . . . . . . . 1356 1247 709 1191 I1 Waddington, D. Walker, I. C. Wandiga, S. 0. Watson, R. T. Webster, B. . . . . 779 5j7, 1426 . 719 . 564 . 1570 AUTHOR INDEX- VOLUME 70, 1974 27 PAQE PAGE Webster, B. C. Welsh, H. K. White, T. P. Wild, U. P. Williams, D. F. Williams, F. Williams, G. Williams, G. H. Williams, J. 0. Witschel, W. Wood, J. L. Wood, M. H. . . . . . . . 1 . . . 524 . 1591 . 1522 1761: 676, 853 465 1696, 1705, 1783 I 1614 . 676, 853 . 1441 . 409 . 1040 Woodcock, L. V. . Woodnutt, D. J. . Wright, C. J. . Wyatt, P. A. H. . Wyn-Jones, E. . Young,A. N. . Zdzienski, H. K. . Zellner, R. . . Zwolinski, B. J. . . . . . . 955, 1405 . 1794 . 348 . 945 .1247 . . . 1721 . . 409 . . . 1045 967,973, 1133, 1928 THE THIRD ANNUAL GENERAL MEETING OF THE FARADAY DIVISION of the Chemical Society was held at 9.00 a.m., on 11th September 1974, in the Physical Chemistry Lecture Theatre, The University of Cambridge, with Professor T. M. Sugden, M.A., Sc.D., F.R.S., in the Chair. 1 Minutes The Minutes of the Second Annual General Meeting of the Faraday Division, which had been circulated previously, were taken as read and confirmed. 2 Election of Council The Members of Council of the Faraday Division of The Chemical Society elected to take office from 9 April 1975 were as follows: President Prof. T. M. Sugden, M.A., Sc.D., F.R.S. Vice-Presidents who have held the ofice of President SIR FREDERICK DAINTON, M.A., D.PHIL., F.R.S.MA., SCD., F.R.S. PROF.J. W. LINNETT, PROF. C. E. H. BAWN, C.B.E., PH.D., F.R.S. PROF. SIR GEORGE PORTER M.A., Sc.D., PROF.G. GEE, C.B.E., M.Sc.,Sc.D.,F.R.S. F.R.I.C., F.R.S. Vice-presidents M.B.E., M.A., D.Sc. PROF.J. S. ROWLINSON,PROF.D. H. EVERETT, M.A., D.PHIL., F.R.I.C., PROF.P. GRAY, M.A., Sc.D. F.R.S. PH.D. DR.H. A. SKINNER, PROF.J. N. MURRELL, B.A., B.Sc., D.PHIL. D.Sc., F.R.I.C., F.R.S. PROF.W. C. PRICE, Sc.D., F.INsT.P., F.R.S. PROF.F. C. TOMPKINS, Ordinary Members of Council M.A., PH.D., PROF. M. MAGAT, PROF. A. D. BUCKINGHAM, D.Sc., D.PHIL. F.R.I.C., F.R.A.C.I. PROF.I. M. MILLS, D.PHIL. PROF.MANSEL Sc.D. PROF. A. M. NORTH, D.Sc., F.R.S.E., F.R.T.C. DAVIES, D.Sc., F.R.I.C. DR.D. N. HAGUE, M.A., PHD. DR. R. PARSONS, PH.D. DR. B. A. PETHICA,PROF.N. B. H. JONATHAN, D.Sc. PROF.DR. J. LYKLEMA Honorary Treasurer PROF. P. GRAY, M.A., Sc.D. Honorary Secretary PROF.F. C. TOMPKINS, D.Sc., F.R.I.C., F.R.S. The President thanked Professor Allen and Professor Caldin, the retiring members of Council, for their services. 3 Annual Report During 1973 the Faraday Division was very active both in continuing the traditional Faraday Discussions and Symposia and also representing physical chemistry and chemical physics interests in the activities of The Chemical Society as a whole. Two General Discussions were held, “ Molecular Beam Scattering ” at University College, London and ‘‘ Intermediates in Electro- chemical Reactions ” at Oxford; the proceedings being published as Faraday Discussions of The Chemical Society Nos.55 and 56. Two Symposia were also held during the year; the first, “Fogs and Smokes ”, which formed part of the Annual Congress of The Chemical Society at Swansea, and the second, “ High Temperature Studies in Chemistry ” at the Royal Institution, London :both will appear in print as Symposia Nos. 7 and 8 respectively. In addition, two informal discussions took place, one on “ Physical Methods of Studying Surface Adsorbed Molecules ” arranged in 28 ANNUAL GENERAL MEETING association with the Surface Reactivity and Catalysis Group during the Autumn Meeting of The Chemical Society at the University of East Anglia and the other on “ The Role of Surface Charge in Reactions at Interfaces ” at University College, Cork.The seven subject groups affiliated to the Division continued to make a valuable contribution by arranging a programme of group discussion meetings during the year. The 1973 Bourke Lecturer was Professor B. Baranowski (Polish Academy of Sciences, Warsaw) who delivered the following lectures; “Physical Chemistry in the High Pressure Region ”, “Metal Hydrogen Systems in the Region of High Pressure of Gaseous Hydrogen ” and “Irreversible Thermodynamics in Physical Chemistry”. During theyear three half day symposia arranged round an endowed lecture of The Chemical Society were allocated to the Faraday Division and incor- porated the Centenary Lecture by Professor J. P. Toennies on “ Measurements of Differential Inelastic Scattering Cross Sections ”, the Liversidge Lecture by Professor R. P. Bell on “ Recent Developments in the Study of Kinetic Hydrogen Isotope Effects ” and the Tilden Lecture by Professor J. M. Thomas on “ Role of Linear and Planar Defects in Solid State Chemistry ”. The Marlow Medal for 1973 was awarded to Professor K. F. Freed of the University of Chicago for theoretical contributions on molecular structure and the problem of electron correlation. PRINTED IN GREAT BRITAIN AT 'XTE UNIVERSITY PRESS ABI?RDEEN

ISSN:0300-9238    

DOI:10.1039/F297470BA001

出版商:RSC    

年代:1974

数据来源: RSC

摘要:

Vibrational Spectra of Octafluoronaphthalene t BY ALBERTO BRUNO TAMBURINI PECILEGIRLANDO, AND CESARE * Institute of Physical Chemistry, Via Loredan, 2, 35100 Padova, Italy Received 14th May, 1973 The vibrational spectra of octafluoronaphthalene have been investigated by using Raman spectra of the powder and the solution, and infra-red absorption measurements of the vapour, the solution, and of (100) and (010) crystal planes. The overall assignment of fundamentals is discussed ; that of the in-plane modes is assisted by a 25 parameter Valence Force Field which reproduces the observed frequencies with an average error of less than 10cm-l. The vibrational behaviour of aromatic perfluorocarbons has been studied only with hexafluorobenzene '* and a few other fluorinated benzene^.^^ No attempts have been made to extend the investigation to the members of the catacondensed aromatic perfluorocarbons, as has widely been done with the corresponding aromatic hydrocarbons because of their structural and spectroscopic relevance.The interest of a systematic comparison between these two families of compounds is enhanced by the specific electronic effects associated with the substitution of hydrogen by fluorine atom^.^ It is also worthwhile in this connection to undertake the vibrational study of octafluoronaphthalene, whose infra-red and Raman spectra have not, as far as we know, been previously reported. In the present work, the vapour, solution and single crystal infra-red spectra and the powder and solution Raman spectra of octafluoronaphthalene (hereafter designated OFN) are reported.The interpretation of single crystal spectra takes advantage of recently reported preliminary X-ray data 6* and offers some insight into the crystal field effects. EXPERIMENTAL The octafluoronaphthalene used, purchased from the Imperial Smelting Co. Ltd., was recrystallized as colourless needles from light petroleum ether. Single crystals were easily grown by Bridgman's method as cylindrical rods whose growing direction was identified as the a crystal axis by X-ray methods using a precession camera. Samples suitable for infra-red measurements were obtained by cutting the single crystal rod along the ac plane and the bc cleavage plane. Thinner samples with the bc plane developed were also obtained by slow cooling of the melt between KBr plates. Beckman IR 9 and IR 11 spectrometers were used for the infra-red measurements, and the Raman spectra were recorded on a Jarrel-Ash 25-300 spectrophotometer. The exciting laser light was 632.8 nm (He-Ne Spectra Physics 125 A), and at 514.5 nm (Ar-Kr Coherent Radiation 52G-MG).The experimental procedures for infra-red and Ramaii measure-ments are the same as previously reported. t This work was supported in part by the National Research Council of Italy through its Centro Studi sugli Stati Molecolari Radicalici ed Eccitati. 6 A. GIRLANDO, B. TAMBURINI AND C. PECILE RESULTS The polarized absorption spectra (from 400 to 1750 cm-') of the bc and of the ac crystal planes are shown in fig.1 and 2 respectively, while fig. 3 shows the powder Ramaii spectrum of OFN. Since it was not possible conveniently to reduce the thickness of the ac sample, its absorptions are very strong (fig. 2). The qualitative dichroic behaviour can, however, be evaluated. Table 1 collects the observed frequencies and relative intensities in the infra-red for vapour, solutions and crystal samples. Table 2 collects the Raman shifts of powder and solution samples, also giving the measured depolarization ratios. i1cm-l FIG.1 .-Polarized infra-red spectra of octafluoronaphthalene,(100) crystal plane. Solid line, electric vector parallel to b axis ; dashed line, electric vector perpendicular to b axis. I600 1400 1200 1000 800 600 ;/cm-' FIG.2.-Polarized infra-red spectra of octafluoronaphthalene, (010) crystal plane. Solid line, electric vector at 120"from a axis ; dashed line, electric vector at 30" from a axis (see footnote of table 1). 1600 1200 800 400 too ilcrn-' FIG.3.-Raman spectrum of octafluoronaphthalene powder. 8 VIBRATIONAL SPECTRA OF OCTAFLUORONAPHTHALENE TABLE1 .--CN~:RA-RED SPECTRA OF OCTAFLUORONAPHTHALENE single crystal solution vapour ~~ ____~~___ bc plane ac planeE Oo(lj) and E 30°(1)and Vlcrn-1 90"(1)from b lZO"(ll) from n Vlcin-1 intensity b Flcm-1 191 sh 195 br I92 87 276 300 317 II, I 315 (250) 316 sh 318 (250) 321 w 328 sh 390 sh 405 I 404 174 397 s 425 w 447 I 533 II, I II 53 1 10 555 597 I I 596 673 II /I 670 5 692 I I 690 690 vw 704 I,II i 705 730 I I 727 749 I I 752 790 I 11, L 784 (445) 782 m, sh 802 I I 795 (248) 795 s 847 sh 847 sh 851 I, I, 852 14 856 w11 /I867 I I 907 II II 906 926 I, I!, I 929 14II I 930 vw {E972 ;;;} ;;;} n', €3 w,B II 953 1500II str II II 970 sh 991 II II 992 18 1005 -1 I 1026 II II 1019 17 1017 vw 1047 1069 It I II -.L 1040 1071 14 1040 vw 1075 vw II Lstr L 1126 620 1132 m 1144 1162 I,II II I II 1143 1157 15 10 1188sh 1180 sh {E1250 sh llstr I II 1201 1248 545 1205 m 1258 1273 I I I I 1257 1268 1253 vw, sh 1265 vw 1286 I 1285 24 1286 vw 1291 1333 119 I I II 1 1324 32 1337 sh 1340 5 1337 vw 1391 w, sh A.GIRLANDO, B. TAMBURINI AND C. PECILE 9 TABLE1 .-continued single crystal a solution vapour B/cm-1{tt:!1431 bc planeEoOo(ll)and90 (I)from b I lbtr II ac planeE 30"(1)and 120"(11) from a II II i/cm-1 1415f 1428 intensity 1750 160 i/cm-' 1421 s 1455 sh 1479 1- _I- 1479 1810 1484 vs 1483 1492 I/I ll I 1515 1531 -L I I I_- 1517 1528 88 61 1519 m 1545 I I 1545 34 1546 m, sh 1555 1577 1,I I I 1556 1578 17 34 1580 w 1590 I I1 1652 sh 1650 sh 1653 sh 1662 II I1 1660 875 1663 s 1687 II II 1685 1710 II I1 1702 1705 vw 1729 -1 I 1724 1813 I I 1812 1839 I I 1855 1 I 1862 1870 1919 1952 IIY I II L 11, I II I 1871 1919 1947 1966 I I 1957 1985 I I 1981 Symbols used : sh, shoulder ; br, broad ; str, stronger component of the doublet.In the spectral region 300-40cm-', the spectra were recorded with unpolarized light only. In the ac plane, the angles are measured counterclockwise, i.e., the sense of rotation which transforms the c into the a axis through the obtuse angle. b intensity expressed as peak extinction coefficient (rnol-' 1. cm-I), not corrected for band overlap. Values in parentheses refer to cases in which the overlapping is quite strong. C Vapour spectrum has not been measured below 250 cm-'. Relative intensities are indicated as vs, very strong ; s, strong ; m, medium ; w, weak ;vw, very weak. d Solution in benzene; e solution in carbon disulphide : f solution in carbon tetrachloride. DISCUSSION PRELIMINARY ASSIGNMENT The OFN molecular crystal is monoclinic,6 space group P2,/c(C:,) and the unit cell contains two molecular units on Ci sites.The reported X-ray investigation is only preliminary and gives no definitive information on the molecular symmetry. However, it is reasonable to assume that the OFN molecule, like hexafl~orobenzene,~*~~ is planar and belongs to the DZhpoint group. The selection rules for the isolated molecule, for the molecule in the crystal and for the unit cell are those reported in table 3. The OFN molecular plane is approximately parallel to the (T12) crystallographic plane,6 and this allows us to predict the dichroic behaviour of the bJuout-of-plane modes in the infra-red polarized spectra.Within the limits of the oriented gas model," these modes should be polarized parallel to the b axis and perpendicular to VIBRATIONAL SPECTRA OF OCTAFLUORONAPHTHALENE the extinction direction a' (a' lying in the ac plane, at 30" counterclockwise from a) respectively, when the bc and ac planes are examined. Since the orientation of the y and z molecular axes relative to the crystal axes is not known, the dichroic behaviour of the in-plane modes cannot be predicted. TABLE2.--RAMANSPECTRA OF OCTAFLUORONAPHTHALENE powder a ii/CXll-1 B/cm-1 solution * P assignment 28 sh,br 58 s, br 70 sh, br 130 mw 164 w, br 282 sh 280 sh 286 ms 284 0.77 290 sh 286 sh 296 ms 297 0.09 335 s 334 0.78 372 s 370 0.79 391 ms 391 0.26 508 vs 507 0.04 525 vw 572 vw,br 568 P 598 m 598 0.75 756 mw 756 0.83 1070 mw 1068 0.41 1082 w 1078 0.74 1238 sh 1238 w, br 1246 1270 0.6 a,, v4 1332 vw 1327 P 1348 vw 1344 P 1363 sh 1371 s 1372 0.13 1492 vw 1515 sh 1510 sh 0.24 1520 mw 1518 0.30 1619 w 1624 br P 1625 w a Relative intensities of the powder spectra are indicated by vs, very strong; s, strong ; ms, medium strong ; m, medium ; mw, medium weak ; w, weak ; vw, very weak ; shy shoulder ; br, broad.b Frequency values and depolarization ratios (p) measured in benzene solution (m 0.5 M) ; dichloromethane was used for the lines at 598 and 1624 cm-'.To overcome this limitation, the band envelopes of the vapour absorption spec- trum, which are predicted to be of the same type of naphthalene, may be helpful. The infra-red vapour spectrum gives little information but the clear B-type envelope of the bands at 957 and 997 cm-' allows the identification of their bl, symmetry species. Examination of the bc and ac polarized infra-red spectra (fig. 1 and 2), on the other hand, leads one to group the absorption bands into two sets according to the polarization pattern. The spectral predictions for the out-of-plane modes and the information from the vapour spectrum indicate that the set of bands parallel to b in the bc spectrum are of bl, or bJu type; perpendicular bands are then of b2,, type. An analogous distinction is retained in the ac spectrum where the b,, and b3, A.GIRLANDO, R. TAMBURINI AND C. PECILE bands are stronger when the electric vector is at 120" counterclockwise from a, and the b2, ones are stronger when the electric vector is at 30" from a. The number of strong bands in the absorption spectra is lower than that of the infra-red active fundamentals, when, considering their polarization, the following direct assignment is possible : bl, : 1660, 1415, 1201, 953 cm-l bzu: 1479, 1126, 784,404 cm-l. Below 900cm-l the choice of the bl, modes interferes with assignment of the b3umodes ; below 300 cm-l no good polarization data could be obtained. TABLE3.-sYMMETRY CLASSES AND SELECTION RULES FOR THE MOLECULE AND THE UNIT CELL OF OCTAFLUORONAPHTHAIBNE molecular group D2h site group Ci factor group C2R degrees of freedom species and activity a species and activity a degrees of freedom 9 27 3+ R, 4+ Ry8+R, bc) 27 (3 tors.) (3 tors.) 4 26 (2 transl.)+ T', 8+ TI au 8+ Ty 4+ Tx a Factor group symmetry species are distinguished by the use of capital letters.Powder and solution Raman spectra of OFN (fig. 3 and table 2) are not rich in lines. The depolarization ratios in solution lead to the assignment of seven out of nine totally symmetric modes, namely : a, : 1624, 1518, 1372, 1068, 507, 391, 297 cm-l. Other Raman active modes are not recognizable from solution data, and repeated attempts to take advantage of single crystal Raman spectra were not successful, probably owing to the depolarization of the exciting light by unavoidable imper- fections of the sample.The use of the calculated frequencies as a guide in the identification of the un- attributed in-plane fundamentals of OFN appears to be the more logical approach for the extension of the preceding assignment. NORMAL COORDINATE ANALYSIS The molecular constants of the OFN ring were assumed to be the same as in naphthalene l2 and the CF bond length was taken as the standard value l3 of 1.33A. The G matrix was constructed using these parameters and the internal coordinates sketched in fig.4. The force field was derived from a widely tested and applied model used for naphthalene.12 This choice seemed to be more advantageous than an extension of the hexafluorobenzene force field by a somewhat arbitrary introduction of additional force constants relative to the conjugated rings.As regards the CF stretch and bend force constants, values in the range 6.8-7.4 N m-1 x and 0.56-0.83 N m rad-2 x VIBRATIONAL SPECTRA OF OCTAFLUORONAPHTHALENE 10IR,respectively, were adopted.2. l4 All the other force constants were initially given the same values as in naphthalene ;only the interactions CF stretch-CC stretch in ortho and CF stretch-CCF bend were added. I I FIG.4.-Internal co-ordinates of octafluoronaphthalene. The numerical calculations were carried out with a CDC 6600 computer, using a modified version of a program written by Schachtschneider. The zero order calculation of the in-plane modes led to an encouraging agreement with the partial assignment discussed above ; therefore, the calculated frequencies could be used with some confidence as a guide in extending the initial attributions.A standard refinement process was carried out to improve the fitting between calcu- lated and observed frequencies, and eventually an assignment as complete as possible was made. The final force constants are collected in table 4, and the observed and calculated frequencies are given in table 5, together with the approximate potential energy distribution. TABLE4.-vALENCE FORCE CONSTANTS FOR OCTAFLUORONAPHTHALENE forcc const. a force const." coordinates involved mi symbol coordinates involved Or a Stretch constants are in units of N m-* x ; stretch-bend, N rad-' x 10' ; bend, N m x 10l8.A. GIRLANDO, B. TAMBURINI AND C. PECILE TABLEj.-OBSERVED ' AND CALCULATED IN-PLANE FUNDAMENTALS OF OCTAFLUORO-NAPHTHALENE B/cm-I sym. species obs. calc. potential energy distribution (%) 0 a,v 1 1624 1606 v2 1518 1509 v3 1372 1369 v4 1246 1247 vs 1068 1061 v6 507 496 v7 391 378 V8 297 301 V9 -234 b3gV37 -1654 v38 1492 * 1486 v39 (1344) 1335 v40 1078 1056 v41 756 755 v42 525 * 532 v43 334 3 30 v44 284 275 blUV17 1660 1659 v18 1415 141 6 v19 1201 121 1 v20 953 962 v2 1 795 802 v2 2 531 526 vz 3 315 295 v24 -149 b2uv29 1578 1572 v30 1479 1484 v3 1 1324 1320 V3 2 1126 1137 v33 784 779 v34 404 434 v35 318 314 v3 6 276 * 293 a Wavenumber values marked with asterisk(*) refer to bands observed in the powder spectra ody, the others to lines observed in the solution spectra.Contributions less than 15 % are not in-cluded. Coordinates involved in potential energy distribution: K1to &, ring CC stretch; K.,CF stretch ; HI to H,, ring CCC bend ; H,, a-CFbend ; H5,p-CF bend. FINAL ASSIGNMENT A detailed re-examination of OFN spectra is possible on the basis of the calculated frequencies in table 5. The bzumodes ~29and ~31,calculated at 1572 and 1320 cm-I, are recognized as the correctly polarized bands at 1578, and 1324 cm-'. The choice of the former is less direct, due to the interference of numerous combination tones of the same polarization.The strong b2"band at 784 cm-' presumably masks the polarization of the bl, mode calculated at 802 cm-'. Its reasonable location at 795 cm-I is sup-ported by the presence of two strong bands in the solution and vapour spectra. The bl, VIBRATIONAL SPECTRA OF OCTAFLUORONAPHTHALENE polarized band at 531 cm-l is attributed to the v22 mode calculated to be at 526 cm-l. Correlative criteria (see below) lead us to exclude the presence of b3u modes, which would display the same polarization, near this frequency. Analogously, the out-of- ' plane modes should not interfere in the sorting out of the bluv23 and b2uV35 and vS6, all calculated to lie in the restricted range 320-280 cm-l (table 5). Accordingly, the three bands observed in the powder and solution spectra at 315, 318 and 276 cm-l, are assigned respectively to the latter modes.The lacking bluv24 mode is discussed together with the out-of-plane fundamentals (see below). On the basis of the calculation, the a,v4 mode is recognized as the weak line at 1246 cm-l. Its measured depolarization ratio is clearly influenced by the presence of an overlapping combination tone at 1238 cm-l. No Raman line is observed from 280 to 170 cm-l in correspondence with the lowest frequency agmode, which is calcu- lated to be at 234 cm-' and whose approximate description corresponds to an a-CF bend. The introduction of a bend-bend force constant between the peri fluorine atoms, interaction which could be of relevance considering the molecular geometry, did not modify the calculated frequency to support a reasonable attribution.The b,, modes located by means of the calculation, the assignment of which does not interfere with that of the out-of-plane fundamentals, are at 1492, 1078 and 525 cm-l (table 5). Among them, the 1078 cm-l line is depolarized in solution, whereas the 1492 and 525 cm-l lines could be detected in the powder spectrum only. The b3g~37mode (calculated at 1654 cm-l) is probably too weak to be detected, and the b3g~39must be considered to be overlapped by an a, combination tone at 1344 cm-l. The three lacking b,, frequencies are calculated to be at 755, 330 and 275cm-l. Although the interference of out-of-plane modes near these frequencies cannot be ignored (see below), the choice of the depolarized lines at 756, 334 and 284 cm-l as the b3g~41,v43 and v44 is, however, completely acceptable.As regards the out-of-plane modes, the sorting out of the fundamentals can be based on a correlative comparison between OFN and hexafluorobenzene 2*'9 assisted by the parallel comparison between benzene l6 and na~htha1ene.l~ The number of bands or lines detected, which can be considered as candidates for the assignment of the out-of-plane modes, is rather low. This fact may well be connected with accidental frequency coincidences and is to be expected especially for the CCFC bendings, as suggested by correlative criteria. The two infra-red active CCFC out-of-plane modes should be located 1v 2* in the spectral region 220-120 cm-l, where the presence of a third b3,,mode connected with the 176 cm-l butterfly deformation of naphthalene l7 and of the b1,,~24mode (see above) must also be considered.In the far infra-red spectra from 100 to 270 cm-l only a strong and wide absorption at 192 cm-l is observed. One b3u out-of- plane CCFC deformation is safely attributable to this frequency (194 cm-l for 1,2,4,5-tetrafluorobenzene4). The association with the same frequency of other modes of the same symmetry (b3J seems improbable since that of the bluv24 should lie near 150cm-1. The b,,,~~~ should be a ring deformation analogous to the 595 cm-l mode of hexafluorobenzene.l* 2* Such a inode can be roughly related to the 404cm-l absorption of benzene l6 and the 476 cm-l absorption of naphthalene.' This correlative scheme upholds our attribution of the 670 cm-l parallel absorption.Arguments analogous to those applied for the assignment of the b3u~45allow us to locate the highest frequency b,, ring deformation at 756 cm-l, which is then assumed to coincide by accidental degeneracy with the b3gV41. The two Raman active b2, CCFC bendings are expected 1* 2* at about 250 and 370 cm-l and one of the b,, again at 370 cm-l. Accordingly, the b2g~27 and the bl9~15are both assigned to the strong depolarized line at 370cm-l, and the b2g~28is tentatively attributed to the A. GIRLANDO, B. TAMBURINI AND C. PECILE shoulder at 286 cm-l. No reasonable assignment is found for the second CCFC deformation of b,, type, presumably lying in the spectral region 300-200 cm-I, and for the third b,, fundamental, which probably corresponds to the skeletal deformation of naphthalene l7 at 392 cm-l.The b,, symmetry block is completed by assigning to the b2,vZ6the depolarized line at 598 cm-1 which cannot be related with b,, or b,, modes. The previous discussion gives us acceptable attributions for eight out of eleven optically active out-of-plane fundamentals. Table 6 collects these assignments. TABLE6.-vIBRATIONAL ASSIGNMENT OF THE OUT-OF-PLANE FUNDAMENTALS (Cm-') OF OCTA-FLUORONAPHTHALENE b1gv14 - b2gv25 756 b3uV45 670 V15 370 v2 6 59s v4 6 - v16 - v2 7 v2s 370 286 v47 v48 192 - Although the desirability of a sound discussion on lattice modes, related to the OFN continuous diffuse scattering,6 is recognized, the need for further spectroscopic work and more detailed structural data keeps us from undertaking it in the present paper.It is worthwhile to add a few comments on crystal field splittings and shifts of OFN. The infra-red bands at 1415, 1201, 1126 and 953 cm-I display in the bc spectrum a doublet structure, typical of crystal field splittings. The crystal field origin of these doublets is partially confirmed by the inspection of the ac spectrum, although an accurate comparison between bc and ac spectra is limited by the difficulty of obtaining the latter for thin samples. No corresponding splittings could be detected in the powder Raman spectrum with the experimental conditions used.The frequency separation of the few doublets observed in absorption spectra is of about 5 cm-l, and the frequency shifts between solid and fluid phases are not greater than 10 cm-l both in Raman and infra-red. These characteristics are indicative of rela- tively weak intermolecular interactions and comparable with those of naphthalene * which crystallizes in the same space group. CONCLUSIONS The present investigation makes a reliable and almost complete assignment of octafluoronaphthalene vibrational fundamentals available for the first time. The results are particularly satisfactory if one considers the difficulties deriving from a more complex spectrum in respect to aromatic hydrocarbons. These difficulties are increased by the evident occurrence of some accidental degeneracies which can largely be related to the perfluoro substitution. The assignment of the in-plane fundamental frequencies has taken advantage of a normal coordinate analysis based on a naphtha- lene Valence Force Field.12 This force field, well tested for aromatic hydrocarbons, can be transferred to octafluoronaphthalene and so it should also be applicable to other aromatic perfluorocarbons.The technical aid of Mrs. F. Marzola is gratefully acknowledged. The authors are also grateful to Prof. G. Zerbi for the use of an Argon ion laser Raman instrument at the Istituto Nazionale delle Macromolecole, C.N.R., Milan. VIBRATIONAL SPECTRA OF OCTAFLUORONAPHTHALENE D. Steele and D. H. Whiffen, Trans.Faraday Soc., 1959, 55, 369 ; S. Abramowitz and I. W. Levin, Spectrochim. Acta, 1970, %A, 2261 ; P. Delorme, F. Denisselle and V. Lorenzelli, J. Chim. phys., 1967, 64, 591 ; D. Steele and W. Wheatley, J. Mol. Spectr., 1969, 32, 265 and references to previous work therein. D. Steele and D. H. Whiffen, Trans. Faraduy Soc., 1960,56, 5. D. A. Long and D. Steele, Spectrochim. Acta, 1963, 19, 1955 ; D. Steele and D. H. Whiffen, Spectrochini. Acta, 1960,16, 368 ; I. J. Hyams, E. R. Lippincott and R. T. Bailey, Spectrochim. Acta, 1966, 22, 695 ; H. F. Shurvell, A. S. Blair and R. J. Jakobsen, Spectrochim. Acta, 1968, 'I>. MA, 1257. A. Long and D. Steele, Spectrochirn. Ada, 1963, 19, 1947 ; R. A. R. Pearce, D. Steele and K. Radcliffe,J. Mol.Struct., 1973, 15,409. See for instance: C. R. Brundle, M. B. Robin and N. A. Kuebler, J. Attier. Chettt. Suc., 1972, 94, 1466 and references therein. 'A. Del Pra, Acta Cryst., 1972, B28,3438. 'The only crystal structure of aromatic perfluorocarbons known in detail is that very recently reported of hexafluorobenzene: N. Boden, P. P. Davis, C. H. Stam and G. A. Wesselink, Mol. Phys., 1973, 25, 81. C. Pecile and B. Lunelli, J. Cheni. Phys., 1968, 48, 1336. A. Girlando and C. Pecile, J.C.S. Favaday 11, 1973, 69, 818. lo A. Almenningen, 0. Bastiansen, R. Seip and H. M. Seip, Acta Cheni. Sccitid., 1964, 18, 2115. G. C. Pimentel and A. L. McClellan, J. Chem. Phys., 1952, 20, 270. l2 N. Neto, M. Scrocco and S. Califano, Spectrochim. Acta, 1966, 22, 1981. l3 L. E. Sutton, Tables of Znteratotiric Distances (Chem. SOC. Spec. Publ. no. 18, 1965). G. De Alti, V. Galasso and G. Costa, Spectrochim. Acta, 1965, 21, 649. l5 J. H. Schachtschneider, Tech. Rep. No. 57-65, Shell Development Co., California, U.S.A. l6 G. Varsanyi, Vibrational Spectra of Benzene Derivatives (Academic Press, New York, 1969), p. 70. H. Yamada and K. Suzuki, Spectrochitn. Acta, 1967,23A, 1735 ; M. Suzuki, T. Yokoyania and M. Ito, Spectrochim. Actu, 1968, 24A, 1091 ; D. M. Hanson and A. R. Gee, J. Chem. Phys., 1969, 51, 5052. lS G. C. Pimentel, A. L. McClellan, W. B. Person and 0.Schnepp, J. Chern. Phys., 1955,23,234.

ISSN:0300-9238    

DOI:10.1039/F29747000006

出版商:RSC    

年代:1974

数据来源: RSC

摘要:

Proton Magnetic Resonance Study of Molecular Motion in Trimethylamine-Trimethylaluminiumand Trimethylamine-Trimethylgallium BY T. T. ANGt AND B. A. DUNELL* Chemistry Department, The University of British Colunibia, Vancouver 8, British Columbia Received 4th June, 1973 Proton magnetic resonance second moments and spin-lattice relaxation times of trimethylamine- trimethylaluminium and trimethylamine-trimethylgalliumhave been measured between liquid nitrogen temperature and their melting points. The second moments show that the methyl groups attached to Al or Ga are reorientating fast enough to narrow the n.m.r. line at the lowest observed temperatures. Reorientation of the N-methyl groups about their C,axes and of the whole molecule about the N-A1 or N-Ga bond at n.m.r.line width frequencies can be distinguished from the second moment curves as separate processes occurring at higher temperatures. The variation with temper- ature of the spin-lattice relaxation time has been interpreted for each compound in terms of reorient- ation with one correlation time of methyl groups on A1 or Ga, reorientation with a longer correlation time (at given temperature) of methyl groups on N, and reorientations with yet longer correlation times about the central bond. Separate motions are distinguished for reorientation of the two moieties in the gallium complex. Phase transitions are found in both solids, and in the highest temperature phase of each solid the spin-lattice relaxation results, augmented by values of the spin- lattice relaxation time in the rotating frame, have been interpreted as showing a combined motion of isotropic rotation and self-diffusion.Activation energies have been found for the several motional processes. The investigation which is reported here is a continuation of a study of the re-orientation of methyl groups and larger moieties in a series of addition complexes of di- and tri-methylamine and trimethylphosphine with trimethylborane, trimethyl- a1umi nium, and trime t hylgallium. The work on trimethy lamine- trimeth ylborane was published recently. EXPERIMENTAL The addition complex trimethylamine-trimethylaluminium (TMA-TMAI) was prepared by introducing an excess of anhydrous trimethylamine (Eastman Kodak) to trimethyl- aluminium (Alfa Inorganics) at liquid nitrogen temperature.The transfer was made in a vacuum system, the mixture of compounds warmed slowly from 77 K to room temperature, and the excess trimethylamine pumped off at room temperature. The product which re- mained was sublimed into a vacuum and collected on a cold finger which was at about 10°C. The cold finger was then warmed slowly to room temperature and the product kept under vacuum overnight. Finally the product was transferred in a dry box to sample tubes for CW and puked n.m.r. measurements. The same procedure was used for the preparation of the trimethylamine-trimethylgallium complex (TMA-TMGa) from anhydrous trimethylamine and trimethylgallium (Alfa Inorganics). The procedures for measuring second moments and spin-lattice relaxation times were the same as those used previously.' The use of thin walled sample tubes and a Bruker B-KR 300215 box-car integrator with a digital voltmeter has, by improving the signal to noise ratio, increased the precision of TI to within about a 3 % uncertainty.The spin-lattice t present address : School of Chemical Sciences, Universiti Sains Malaysia, Penang, Malaysia. 17 P.M.R. STUDY OF MOLECULAR MOTION relaxation time in the rotating frame, Tlp,was measured by spin-locking the nuclear magnet- ization by applying a 90"pulse followed immediately by a pulse of variable duration whose r.f. phase was shifted by 90" from that of the first pulse. The phase shift was established by using a modified Carr-Purcell sequence with a water sample.The intensity HI of the r.f. field was determined by measuring the length of a 180" pulse applied to a water sample, and was 15 G in all the Tlpexperiments reported here. We note that there was a small drift in HI within the duration of the pulse when the pulse length was greater than 3 ms. The error in Tlpis estimated to be about 20 %. RESULTS AND DISCUSSION LINE WIDTH AND SECOND MOMENT The variations of line width and second moment with temperature are very similar for the two compounds and are illustrated in fig. 1. The common features to be explained are the plateau in second moment at about 20 G2 near liquid nitrogen temperatures, a brief halt in the decrease of second moment with increasing temper- ature at about 10 G2 near 120 K, a constant second moment of 2 G2 for some tens of degrees about 260 K, and an abrupt transition to essentially zero line width and second moment at 313 K for the aluminium complex and at about 290 K for the gallium complex.With the gallium complex there is hysteresis in the behaviour of both the line width and second moment at this transition. These parameters both decrease suddently at 290 K with increasing temperature. As temperature is de- creased, the parameters begin to increase slowly at about 300 K and finally complete the transition to their lower temperature values at about 275 to 280 K. Times of 20 NP l5 NY 0\Yi 810E m.P2 20-E s I I a $ I 55H a 15-8 2 10-.B-5-.e3 M I I I f :I m.p. I I 0 9 9 a 5z3 .3I i 1 0- I150Pi I250 I I350 I TIK FIG.1.-Line width and second moment of TMA-TMAI and TMA-TMGa as functions of temper- ature : open circles, second moment of TMA-TMGa ; filled circles, line width of TMA-TMGa ;open triangles, second moment of TMA-TMAI ; filled triangles, line width of TMA-TMAl. The left hand ordinate scale applies to TMA-TMGa. The right hand ordinate scale applies to TMA-TMAI. TABLE SECONDMOMENTS FOR TMA-TMAl AND TMA-TMGa (IN G2)AND THE COMPARISON WITH EXPERIMENTAL VALUES1 .-THEORETICAL group motion* theoretical second moment contribution experimentaltMe A1 or inter-CH3 but proton to N second temperature? Me3N dqGa intra-CH3 intramolecular and A1 or Ga intermolecular total moment T/K S S 21.3 2.5 0.3 64 1 30.1f 1 S c3 13.3 2.3 0.1 4.3f 0.5 20.0f0.5 20.34 0.5 65-80 20.4f 0.5 65-88 9 2: c3 S 13.3 2.2 0.3 4.340.5 20.1+0.5 0 9c3 c3 5.3 2.2 0.1 2.440.5 lO.O+O.S 9.8k0.3 120-130 2:10.340.5 120-1 34 U Ix'c,+ c; c3 } 3.0 1.2 0 1.7f0.5 5.9k0.5 9 c3 c3+c; c3+ci c,+ c; 0.6 0.3 0 1.O+ 0.3 1.9+ 0.3 2.0+ 0.3 220-313 U 2.0+ 0.I 240-280 c diffusion 0 0 0 0 0 -0 3 13-m.p.-0 300-m.p. * S = stationary ; C, = methyl groups reorienting ; C;= reorientation about N-A1 axis or N-Ga axis f-italicised values are for TMA-TMGa. P.M.R. STUDY OF MOLECULAR MOTION about 30 min were allowed for "equilibration " of the sample at any temperature before a spectrum was recorded and then duplicate spectra were normally taken over a period of about an hour.It is quite possible that the effect is a failure to reach equilibrium in a slow transition. Above these transition temperatures the line widths are determined by the amplitude of the modulation field and the field inhomo- geneity of the magnet. Using the methods for estimating the theoretical second moment which werc described in detail in our earlier paper,' we have obtained theoretical second moments for rigid lattice conditions and for various types of molecular motion for these two compounds, whose detailed crystal structures are unreported. These values are listed in table 1 together with the experimental values of second moment at the various plateaus. In addition to assuming all bond angles to be tetrahedral, we have used the following interatomic distances 4* in the calculation of theoretical second mom- ents: C-H, 1.lOA; C-N, 1.47A; C-Al, 2.00A; N-A1, 1.93A; C-Gay 2.03 A ; and N-Gay 1.96A. It is clear from the table that even at the lowest observed temperature the rigid lattice second moment is reached by neither compound.The experimental second moments of both complexes at the low temperature plateaus agree well with the theoretical values obtained on the assumption that three of the six methyl groups in the molecule are reorienting rapidly. Since the C-A1 and the C-Ga bonds are each much longer than the C-N bond, it seems highly probable that the rapidly reorienting methyl groups are those attached to aluminium in the one compound or to gallium in the other.This conclusion is supported by the fact that the methyl groups in hexamethyldisilane rotate essentially freely at liquid nitrogen tempera- ture,6p 'whereas the methyl groups in hexamethylethane are severely limited in their rotational freedom at 85 K7*One notes that the bond lengths are in the order C-Ga-C-A1-C-Si >C-C N C-N. A similar result and interpretation was found for trimethylamine-trimethylborane, in which the difference in bond lengths, C-B>C-N, is less pronounced. The second moment of approximately 10 G2 at the brief halt in the decrease of second moment with increasing temperature between 120 and 130K corresponds very well with the theoretical value calculated on the basis of all six methyl groups rotating rapidly.The further gradual decrease in line width and second moment is attributed to reorientation of the whole molecule about its C; rotation axis, namely, the N-A1 or N-Ga bond direction. The observed second moment of 2.0k0.3 G2 agrees with the theoretical value for combined C3and C; rotations of all methyl groups and the whole molecule. For the gallium complex there is some indication that the decreases in line width and second moment between 130 and 240 K take place in two overlapping stages. We tentatively attribute this to more rapid reorientation of one of the two moieties, GaMe, or NMe,, than of the other. This will be discussed again in a later section. The second moment for both compounds above their respective sharp transitions in line width and second moment corresponds to self diffusion in the crystal lattice at rates sufficient to affect these n.m.r.parameters. SPIN-LATTICE RELAXATION TRIMETHYLAMINE-TRIMETHYLALUMINIUM The variation of TI and TIPwith reciprocal temperature for TMA-TMA1 is shown in fig. 2. Large sudden changes in T,are observed at 290 and 313 K and at the melting point, 375 K,which is 3 K lower than the melting point given by Davidson and Brown.2 The abrupt changes below the melting point are attributed to phase transi- T. T. ANG AND B. A. DUNELL tions in the solid. We designate the solid between the melting point and 313 K as phase I, between 313 and 290 K as phase 11, and below 290 K as phase 111. We believe that the increase in Tl as the temperature increases from the lowest observed point corresponds to progressively more rapid reorientation of the least hindered methyl groups, those attached to aluminium, in the region ooze+ 1.In the temper- ature range 77 to 88 K the contribution to the overall rate of spin-lattice relaxation made by the mechanism which produces a T, minimum at higher temperature lies within the experimental uncertainty in T1 and will be ignored. A least squares determination of the dope of the best straight line between 77 and 88 K gives an activation energy of 2.9k0.4 kJ mol-l for reorientation of the methyl groups attached to aluminium. This value is smaller than that reported for methyl groups attached to silicon,6 6.53 k0.33 kJ mol-' (1.56+0.08 kcal mol-'), and is essentially the same as the value, uncorrected for any temperature dependence of the pre-exponential factor in z, of 2.73 kO.12kJ mol-' (653 +29 cal mol-') given by Smith for tetra- methylgermane, in which the C-Ge bond length of about 1.99 A is close to the C-A1 bond length in trimethylaluminium. c t IlO-Iv7--r-------;j/ 1 I I I1 13 11 9 7 5 3 I 103 KIT FIG.2.--Spin-lattice relaxation time in the fixed (open circles) and rotating frames (filled circles) as functions of temperature for TMA-TMAI. The solid lines represent calculated values based on eqn (5), (8)+(9), and (11)+(12). The work of Dunn and McDowel1,'O which is an extension of work by Woessner ' and Stejskal and Gutowsky,' is particularly useful for interpreting the spin-lattice relaxation times above 100 K.For an angle of 70.5" between the C3and Cj axes, Dunn and McDowell's eqn (1) may be written where z, is the correlation time for isotropic rotation ; T;? = zG1cz; l, z, being the correlation time for C3rotation of a methyl group ; T;~~= zFI1+z,z', zC2being the P.M.R. STUDY OF MOLECULAR MOTION correlation time for C;rotation of the whole molecule ; 2r51= z;ll +2; +z;; ; and r is the interproton distance in the methyl group ; f(COOT) = COOT/(14-w;z2)4-4m0z/(1+4#zz2). Below 313 K isotropic tumbling does not affect the second moment of TMA-TMAl, and, for the Larmor frequency of 30 MHz used here, we can say moz,l-+oo below 313 K and write where zC51 = 2; +&.If one assumes that the distinct separation of the two minima indicates that 2, <zC2,one can obtain values of z, from the depth of the lower temper- ature minimum and experimental values of Tl on the lower temperature side of that minimum. The assumption that z, is an Arrhenius function of temperature then allows one to resolve Tl into contributions from each relaxation process and obtain values for zC2. When those values of z, and zC2were reinserted into eqn (2), the curve obtained for Tlover the temperature range 125 to 290 K was not significantly different from that obtained from the reduced equation T; = (9y4h2/80w0r6)[(108/27)f(co~~,)+(32/27)f (moz,,)] (3) which results from putting z,<z,, in eqn (2). When zc-+O, the contribution of the dipolar interactions between different methyl groups within the same molecule to the rate of spin lattice relaxation may be approxi- mated l3 by (Tl-'linter CH3 = 3(9Y4h2/20m~r:)f(#ozc2) (4) where r* is the distance between the centres of the three-spin sets. Combining eqn (3) and (4)we get : Tl- = Af (wad+Bf (QwCZ) (5) where, theoretically, A = 9y4h2/20m0r6 nd B = 2y4h2/15m,r6 +27y4h2/20m0rz. (7) The correlation times are assumed to be of the form z, = 7: exp(E/RT) and zC2= z& exp(E,/RT).Eqn (5) was fitted to the experimental points between 125 and 290 K by a non-linear least squares program,14 which we have used before l5 and which determines the best parameters A, B,z:, 2E2, E and E2. These are listed in table 2 and the fit obtained is shown by the solid line in fig.2. Since the program does the least squares fit of T;l, a weight of T: was assigned to each value T; to reduce the relative importance of errors in Ti when Tlis small. The minimum at about 180 K is assigned to reorientation about their C3axes of the methyl groups attached to the nitrogen atom. The decrease in second moment that is centred on M2 = 15 G2 at 105 K has also been attributed to this motion. For M2 = 15 G2,zc-(yJT2)-l = 9.6 ps, and the parameters for the Tlminimum at 180 K predict that Z, has this value at 95_+ 2 K, which agrees reasonably well with the mid-temperature of the second moment decrease. The minimum in Tlat 280 K has been assigned to rotation of the whole molecule about its N-A1 axis.For this mechanism a correlation time of 15 ps, corresponding to the mid point of the second step of the observed second moment decrease, is predicted to occur between 125 and 167 K, with 150 K as the best value. The mid point (6 G2)in the change of second moment is observed at 160 K, again in satisfactory agreement with the prediction from the relaxation results. T. T. ANG AND B. A. DUNELL Comparison of the best-fit values of the coefficients A and B with their theoretical values calculated from eqn (6) and (7) also provides a good check on the correctness of the assignment of the relaxation mechanisms. Since we believe that the methyl 4 1 for these groups on aluminium are reorienting so rapidly above 125 K that ~t)~z, groups, they must be relaxed principally by spin diffusion l6 to the methyl groups on nitrogen for which ~l)~z,-1.We should therefore expect A to be half the value calculated by eqn (6)for the relaxation of a single methyl group rotating about its C3 axis. For the interproton distance in a methyl group, r = 1.79A, and for a Larmor frequency of 30 MHz, and introducing a factor of 0.5 to account for relaxation of other methyl groups by spin diffusion, we obtain a theoretical value of A = 20.6s-' compared with the best-fit value of 19.2k0.9s-l. The value of B calculated from eqn (7) for C; rotation of an X(CH3)3moiety is 17.4s-' for the group N(CH3)3, in which r* = 3.02 A (C-N, 1.47A), and 13.4s-l for the group Al(CH3)3, in which r* = 3.88w (C-Al, 2.00A).The evidence of the second moment suggests that both moieties reorient at about the same frequency. We therefore take the average of the above values for B, 15.4 s-l. This agrees with the best-fit value of 14.8f.0.4 s-l. Although one would expect the values of A and Bobtained from eqn (6) and (7) to be smaller than the experimental values because of the neglect of intermolecular contri- butions to the relaxation rate, the agreement we obtain is sufficient to support the assignments that we have made for the relaxation mechanisms. The predicted values of A and B are also shown in table 2. TABLE2.-EXF'ERIMENTAL AND THEORETICAL PARAMETERS FOR SPIN-LATTICE RELAXATION STUDIES ON TMA-TMAl c3 c3 Cj isotropic rotation diffusion Me3Al Me3N whole molecule whole molecule parameter observed TI TI Ti TIand TIP TIand TIP activation energy E/kJ mol-1 2.9f0.4 13.3&0.2 22.6& 1.8 25 75 P/S (4.54&0.64)x 10-13 (1.93Zl.6)X 1 x 10-10 4x 10-18 *A or B expt./s-1 19.23Z0.9 (A) 14.8&0.4 (B) tA or B theor./s-1 20.6 (A) 15.4 (B) * to make eqn (5) fit data, t calculated from eqn (6)or (7).The sudden change in TI at 290 K is taken to indicate the existence at that temper- ature of a phase transition which allows a sudden change in the correlation fre- quencies of the relaxation processes. One can see from the position of the TI mini-mum at 280 K that the correlation frequency for C; motion is very close to the Larmor frequency just below the transition temperature. Since this is much larger than the motional frequency which would affect the line width and second moment, no change in these parameters is observed at the transition between phases I1 and 111.Although the (log TI,T-l) curve can be fitted between 291 and 313 K by a straight line whose slope corresponds to an apparent activation energy of 16+2 kJ mol-l, it is not possible to say that this value corresponds to the Ci motion in phase I1 since the effect of the transition on the correlation frequency of the C3motion relative to that on the C; motion is unknown. There is also a sudden change in TI at 3 13 K correspondingto the rapid changes in linewidth and second moment which were observed at this temperature. We propose that a phase transition occurs at this temperature, allowing self-diffusion to occur in the higher temperature phase (I) with sufficient frequency to reduce line width and second moment effectively to zero.Since the second moment was 2 G2just below 3 13 K, it is reasonable to suggest that the correlation frequency for diffusional motion P.M.R. STUDY OF MOLECULAR MOTION just above 3 I3 K is given by q,<(y Jn/J2)-' = (y ,/2)-' = 2.6 x lo-' s. For a diffus- ional frequency of this order, w()Td+ 1, the contribution to T; is very small, and relaxation between 313 and 340 K must be attributed mainly to another mechanism. A consideration of both T1and T,, (see below) measurements shows that a single mechanism, either diffusion or isotropic rotation, will not serve to explain both sets of results, for the activation energy that one would obtain from the TI, curve is inconsistent with that required to fit the dependence of T, on temperature. We conclude that the relaxation is mainly due to C; reorientation of the whole molecule in the region between 31 3 and 340 K, where TIincreases with increasing temperature, and that the more efficient relaxation past the maximum in T, at 350 K is to be attrib- uted to the increasingly important contributions of isotropic reorientation and diffusion.The contribution to the rate of spin-lattice relaxation made by isotropic reorient- ation superimposed on very fast C, and C;motions may be written as Following Albert el aL7and Chezeau et aZ.,* who have applied the diffusion theory of Torrey l7 to relaxation in substances similar to ours, we write for the contribution to the relaxation rate made by random diffusional jumps between nearest neighbour sites in a solid lattice.Here AM2is the decrease in second moment produced by diffusion, zd is the time between diffusional jumps, and the functions G are given in numerical tabulation by Resing and Torrey.18 Numerical values of AM2,z;, Ed, rc;,and El, where zd = 7: exp(Ed/RT) and zC1 = zE1exp(E,/RT), were chosen for the calculation of (Ti + (T; l)d by eqn (8) and (9). To be worth further consideration, the values chosen had to give reasonable values for = (Ti')obs-(T-l1)iS"-(r-l1)d between 313 and 375 K. These numerical values were also required to give a reasonable shape for the (log Tlp,T-l) curve calculated from them.Accept-able values for AM2were considered to lie between 2.0 G2(the value of second moment reduced by C3and C; motions) and 0.55 G2(the lowest estimate of second moment reduced by C3, C;, and isotropic reorientation^).^. Values of z,, and zd were required to be less than 2.5 x s at 313 K. In eqn (S), r was put equal to 1.79 A and a mean value of r>6 was taken from r* = 3.02A for the TMA moiety and 3.88 A for the TMAl moiety. The solid line in fig. 2 between 313 and 375 K is the calculated value of T, for AM2 = 0.55 G2, z; = 4.0x s, Ed = 75 kJ mol-', zEl = 1.0x IO-lO s, El= 25 kJ mol-', (Trl)ci= 3.1 s at 313 K, and E2 = 22 kJ mol-l. The value of Ed may be compared with 36 kJ mol-' for diffusion in hexamethyldisilane and 80 kJ mol-1 for diffusion in he~arnethylethane,~.and the value of El with 8 kJ mol-l for isotropic tumbling in hexamethylethane and hexamethyldisilane.'* The value for isotropic tumbling ranges, however, from 38 to 54 kJ mol-' in tetra- methylsilane and tetramethylammonium halides. ' s The activation energy for the Cj motion in phase I, E2 = 22 kJ mol-l, is the same as the value for the same motion in the lower temperature phase 111, 23 f2 kJ mol-'. Even though one might expect this activation energy to be lower in the higher temperature phase, the agreement is regarded as supporting the general validity of the resolution and parameters in phase I. TIp MEASUREMENTS FOR TMA-TMAI Spin-lattice relaxation times in the rotating frame have been measured for TMA- TMAl in a temperature range (phase I) in which H, = I5 G%6H or HL, where 6H T.T. ANG AND B. A. DUNELL is the linewidth and HL= JM,/~ is the local field. A theoretical expression for Tlpwhich has been obtained by Look and Lowe 2o and Jones 21 and has been used by other workers 79 is the same as that for TI except that f(o,z) must be modified. Near a minimum in Tlp,where ooz % mlz -1, replacef(moz) by where m1 = yH1. The minimum in TIPat 333 K is considered to be due to both isotropic rotation and self-diffusion. The Ci rotation mechanism will not contribute since m1zc2<m0zc2< 1 above 313 K. To a good approximation the contribution to relaxation rate in the rotating frame by isotropic rotation is and that made by self-diffusion is 7* (TT:)d = (3y2AM2/2)7dG(k,mlzd).(12) The values of AM2,z;, Ed,z; and El given in the previous section were used to calculate (by eqn (11) and (12)) the relaxation time [(T;:)iso+(Tik)d]-l, which is shown as the solid line in the Tlppart of fig. 2. It can be seen that the shape of the calculated Tlpcurve agrees fairly well with the experimental curve even though there is a rather large discrepancy in the absolute values of the calculated and experimental relaxation times in the rotating frame. TRIMETHYLAMINE-TRIMETHYLGALLIUM The observed values for TI for trimethylamine-trimethylgalliumare shown as the open points in fig. 3. The very rapid change in TI between 284 and 292 K corresponds to the abrupt change in line width and second moment at about the same temperature, and suggests the existence of a phase transition in the solid.As with the line width and second moment in this temperature range, the TI values are not reproducible between 284 and 292 K, but depend on the manner in which the sample has been heated or cooled. Between 77 and 200 K the (log TI,T-l) curve for this compound is very similar to that for the aluminium complex, and the interpretation of its features parallels that made for the aluminium complex. Above 200 K, the analysis is a little more compli- cated than that for TMA-TMAI. Most of the results of the analysis are summarized in table 3. The activation energy of 13.010.3 kJ mol-1 for C3reorientation of the N-methyl groups (Tl minimum at 196 K) is the same as that found for the aluminium complex (13.3 +0.2), and in general agreement with the value of 15.150.4 W mol-1 (3.6 50.1 kcal mol-l) found for trimethylamine-trirnethy1borane.l A unique value for this energy should not be expected from studies on solids because of the possibility of considerable variation in the packing of molecules in the crystal.Experimental and predicted (with consideration of spin diffusion) values of the TIminimum for a C3 motion agree satisfactorily, as do experimental (105 K) and predicted (97+4 K) values of the temperature at which the mid point (15 G2) of the change in second moment occurs for the reorientation of the N-methyl groups. One may be confident, then, that the assignment of this relaxation mechanism is correct.Between 200 and 284 K we have subtracted from the observed relaxation rate the contribution made by the reorientation of the N-methyl groups to the relaxation rate. The net relaxation times thus obtained are shown by the filled circles of curve (a). P.M.R. STUDY OF MOLECULAR MOTION This resolved curve appears to have two minima, and we suggest that these minima correspond to Cj rotation of the trimethylamine moiety at the lower tcmperature and of the trimethylgallium moiety at the higher temperature. The motions of the two moieties are considered to be quite independent of each other. Coupling between the C3 motion of the N-methyl groups and the C;motion of the trimethylamine portion of the molecule will be considered later.An attempt to fit curve (a) to two independent BPP terms by the non-linear least squares program l4 mentioned earlier gave a satisfactory refinement of parameters for the mechanism producing the first minimum but not for that producing the second minimum, whose complete definition is interrupted by the phase transition. These parameters may, however, be obtained from the following analysis of the T,, results, which are illustrated in fig. 4. a E107 Y 1013 11 9 7 5 3 1 103 KIT FIG.3.-Spin-lattice relaxation time as a function of temperature for TMA-TMGa. The solid lines represent calculated values based on eqn (15) and (8)+(9). Curve (a) is a resolved contribution made to the relaxation by C; motions of the moieties.The dotted line represents eqn (14). The Tlppoints below 284 K were fitted to a three term expression Tlpl = A,g(vc) +~pg(WlG2N)+%I(WlZ,2Ga) (13) where g(co,z) = (3/2)co,z/(l+4co~22). The parameters listed in table 3 give the solid curve that passes through the TIPpoints. From expressioiis comparable to (6) and (7), but with cooreplaced by ul,we can calculate values for A,, B,, and B;, and, by putting g(co,z) = 3for a minimum in TIP,we can also calculate values on the assump- tion that at each minimum only one relaxation mechanism is effective. In each case, it is considered that half the methyl groups relax by spin diffusion and the calculated values of A,, B,, and B; as well as the predicted depths of the Tlpminima have been adjusted accordingly.It can be seen from table 3 that the Tlpmiilima agree with C3 motion of 3 methyl groups at the lowest temperature, Ci motion of the (CH3)3N moiety (distinguishable from the (CH,),Ga moiety by its smaller value of r* and TABLE3 .-EXPERIMENTAL AND THEORETICAL PARAMETERS FOR SPIN-LATTICE RELAXATION STUDIES ON TMA-TMGa ? motion c3 c3 c3 c; c; c; isotropic diffusion r' rotation > '1 group Me3Ga Me3N Me3N Me3N Me,N Me,Ga whole Qmolecule > parameter observed Tl Tl TIP Tl TIP TI and TIP T1 and TIP 2: activation energy U E/kJ mo1-1 2.9k0.4 13.020.3 14 21 22 30 31 63 F ZO/S (9.3k2.8)~10-13 6.9~ 10-11 2.1x 10-l6 p10-13 1.1 x 10-13 LOX 10-13 3.1 x 10-14 1.2~ ex~t.(TI or Tlp)min/mS 37 0.3 0.6 0.8 theor.(Tl or TIP)min/mS 35 0.28 0.65 0.85 U *AP,BP,or Bi expt./rns--l 9.0 (Ap) 4.1 (BPI 3.1 (Bh) zA,, BP,or Bi theor./ms-l 9.5 (Ap) 4.1 (BPI 3.15 (Bh) r r * to make eqn (13) fit data P.M.R. STUDY OF MOLECULAR MOTION hence its lower minimum) at about 150 K, and Cj motion of the (CH,),Ga group at about 210 K. The activation energy of 21 kJ mol-' and z"value of 1.1 x 10-13 s for the mechanism corresponding to the Tip.minimum at 150 K agree with the vzlues of 22 kJ mol-' and (9.9 &I .l) x s which fit the resolved T, curve (a) in its lower temperature range. 0 0 0 00 1 10" 9 I I I I I I 7 5 3 103 KIT FIG.4.-Spin-lattice relaxation time in the rotating frame as a function of temperature for TMA-TMGa. The solid lines represent calculated values based on eqn (1 3) and (1 1)+ (12).Returning now to the T, values, we may note that the dotted line of curve (a) is the theoretical curve TFal =7-99f (00,7cZN)+6-3 f(OO, Tc2Gs) s-' (14) where zc2N= 1.O x lo-' exp(2.2 x 104/RT)is the correlation time for C$ motion of the (CH3)3Nmoiety, and T~~~~ = 3.1 x 10-14 exp(3.0 x 104/RT)is the correlation time, taken directly from the TlPanalysis, for C;motion of the (CH,),Ga moiety.* Using eqn (7) and taking account of spin diffusion we can calculate the theoretical values of the coefficients in eqn (14) to be 8.8 and 6.7 s-l. The C3and C;motions of the methyl groups in the trimethylamine portion of the molecule can be expected to couple. Nevertheless the resolution of the relaxation parameters that has already been achieved near the T, minimum is satisfactory, as can be shown by the agreement between the experimental points in fig.3 and the solid line, which is the curve for the equation T;' = 5.66 f(oo.t,)f7.99 f(W0Tc2~)f13.4 f(Wo.t,5~)+6.3 ~(OJOZ,~G~)S-' (15) where the f(o,z) functions and the z, values are those that have already been estab- lished. The first 3 terms of eqn (15) correspond to eqn (2) with modification of the coefficients of each term to give the best fit. Coupling between C3and C;motions has thus been considered. The fourth term of eqn (15) accounts for the C;motion *where R =4.18 J K-*mol-' T. T. ANG AND B. A. DUNELL of the (CH,),Ga group, which is assumed to reorient independently of the other moiety.The analysis of the T1 and T,pcurves in the high temperature phase of TMA-TMGa is similar to that for phase I of TMA-TMAI. The following choice of parameters yields the solid lines shown in fig. 3 and 4close to the experimental TI and TI,points in the temperature range 305 to 365 K : AMz = 0.55 G2,28 = 2.1 x s, Ed = 63 kJ mol-I, z,"~= 1.2x 10-l1 s, and El = 31 kJ mol-I. With this set of parameters the activation energy for C; rotation in the high temperature phase is found to be 16 kJ mol-I. We are grateful to thc National Research Council of Canada for a Grant-in-Aid of this research and to the Committee on Research of the University of British Col- uiu bia for other financial assistance. T. T. Ang and B. A. Dunell, J.C.S.Farahy ZI, 1972, 68, 1331. N. Davidson and H. C. Brown, J. Amer. Chem. Soc., 1942,64, 316. G. E. Coates, J. Chem. Soc., 1951, 2003. 'Iiiteratomic Distances, Chem. SOC., Spec. Publ., no. 11, 1958, and no. 18, 1965. L. Pauling, TIre Nature ofthe Chemical Bond (Cornell University Press, 3rd edn., 1960), p. 228. ti T. Yukitoshi, H. Suga, S. Seki and J. Itoh, J. Phys. Soc. Japan., 1957, 12, 506.'S. Albert, H. S. Gutowsky and J. A. Ripmeester,J. Chem. Phys., 1972, 56, 1332. J. M. Chezeau, J. Dufourcq and J. H. Strange, Mol. Phys., 1971, 20, 305. G. W. Smith, J. Chem. Phys., 1965,42,4229. lo M. B. Dunn and C. A. McDowell, Mol. Phys., 1972, 24,969. ''D. E. Woessner, J. Chem. Phys., 1962, 36, 1. E. 0.Stejskal and H. S. Gutowsky, J. Chem. Phys., 1958,28, 388. l3 S. Albert, H. S. Gutowsky and J. A. Ripmeester,J. Chem. Phys., 1972, 56,3672. l4 The programme was written by P.Sampson,Health Sciences Computing Facility,The University of California at Los Angeles. l5 B. A. Dunell, M. Pachal and S. E. Ulrich, Canad. J. Chem., 1973,51, 1107. l6 J. E. Anderson and W. P. Slichter, J. Phys. Chem., 1965, 69, 3099. H. C. Torrey, Phys. Reo., 1953,92,962 ; 1954, %, 690. H. A. Resing and H. C. Torrey, Phys. Reo., 1963, 131, 1102. "S. Albert and J. A. Ripmeester, J. Chem. Phys., 1972,57,2641. 'O D. C. Look and I. J. Lowe, J. Chem. Phys., 1966,44,2995.'' G. P. Jones, Phys. Rev., 1966, 148, 332.

ISSN:0300-9238    

DOI:10.1039/F29747000017

出版商:RSC    

年代:1974

数据来源: RSC

摘要:

Fluoresceiice and Absorption Spectra of Anthracene Crystals at 4 K Doped with 1-and 2-Aminoanthracene: Effects of Guest Orientation BY N. JAMESBRIDGE'::AND DAVIDVtNCENT The Chemistry Laboratory, The University, Canterbury, Kent, CT2 7NH Ruceiimi 13th Jurrc, 1913 Anthracene crystals doped with 2-aminoanthracene give low temperature guest absorption and cmission spectra which show the presence of two distinct types of trap, corresponding to different orientations of the guest in the host lattice. 1-Aminoanthracene gives similar results. Steric strain, exciton polarization, exciton-phonon coupling and host-to-guest energy transfer all depend strongly on guest orientation, but in different ways. If crystalline anthracene is doped with an anthracene derivative having a small substituent at the I-or 2-position, one expects that each guest molecule will replace one host molecule.The site symmetry being Cl,I at least two distinct orientations of the guest are possible, related by a half turn about the long axis of the anthraceiie re~idue.~-~At 4 K, these should give rise to resolvable electronic spectra, since the excitation energy depends on the coupling of host and guest states and thus on the orientation of the transition dipole of the guest.5 Such effects may be expected to be particularly noticeable for the amhoanthracenes, in which the first excited state has some charge-transfer character, so that the transition dipole is rotated away from the short in-plane axis of the anthracene residue.6 In this case a half turn about the long axis changes the direction of the transition dipole, not inerely its sign.The effect on the excitation energy of the guest should then be substantially larger than that due to a small change of alignment of the guest within the lattice, such as observed for phen-anthrene in biphenyl,' but comparable to that associated with substitution in crystal-lographically inequivalent sites.4 In anthracene, guest spectra arising from allowed transitions typically exhibit strong phonon side-bands,* which could be confused with multiplet structure due to site effects. However, only pure electronic transitions can appear in both absorption and emission at 4K, since at this temperature the initial state is not vibrationally excited.Traps associated with interacting pairs of guest molecules are not expected to be significant at guest mole fractions of or less and in any case are easily recognised by comparing spectra obtained with varied dopant levels.8 The most serious difficulty, perhaps, is to rule out spectra due to unwanted inipurities ; to this end we have deliberately run the spectra of many crystals, prepared in different ways and with variously purified dopants. EXPERIMENTAL 2-aminoanthracene is a potent carcinogen and must be handled with care. It is also susceptible to atmospheric oxidation, particularly in solution. One sample (Koch-Light) was purified by two successive gradient sublimations under helium. Another was chromato-30 N.J. BRIDGE AND D. VINCENT graphed over a low activity silica gel column, using toluene as solvent, recrystallised and sublimed twice, first in vucuo and then under helium. The yellow crystals melted with slight decomposition at 242-3°C. Doped anthracene crystals were grown by cosublimation, using anthracene purified as previously described.8 Dopant mole fractions were 2x to the lower levels being produced by stepwise dilution. 1-aminoanthracene is rather more sensitive to oxidation and to thermal decomposition. Starting with 90 % pure material (R. N. Emanuel), gradient sublimation gave a poor yield of yellow powder. Chromatography over alumina (Brockman activity 111) in toluene gave a clear yellow solution, about 0.002 M, with the expected visible and near ultra-violet absorp- tion This was used as solvent to recrystallise previously purified anthracene, giving well-formed flakes containing 0.7 % dopant (estimated from the single crystal absorp- tion).Some of these crystals were examined directly and some used to prepare vapour grown crystals with dopant levels to Fluorescence is excited by 366 nm radiation from a mercury arc lamp. The cryostat and spectrometer are as described in our earlier paper but a tungsten lamp has been added and the crystal mount modified so that polarised absorption and fluorescence spectra can be recorded for the same crystal at 4 K. Crystal thickness ranged from 5 to 50 pm, as measured (k20 %) from the interference fringes seen under a microscope in the conoscopic mode.The extended face is the ab plane ; spectra are recorded for emergent light polarised parallel to a or b axes of the crystal. The Raman spectrum of pure crystalline 2-aminoanthracene was run on a Coderg PH1 spectrometer with 633 nm excitation. The Raman scattering of our crystalline sample of 1-aminoanthracene was obscured by continuous emission. RESULTS Chroniatographed 1 -and 2-aminoanthracene each gave two distinct guest fluor- escence spectra. 2-aminoanthracene gave two absorption series, the origins of which coincide with those of the emission spectra; 1-aminoanthracene gave only one, corresponding to the deeper trap. We refer to the four types of guest as lA, lB, 2A and 2B, A indicating the deeper trap of a pair. The frequency and polarization data are given in table 1 and representative spectra reproduced in fig.1-4. Dopants prepared by sublimation produced additional fluorescence bands but there was no sign that the method of growth or purification affected the distribution of intensity between the A and B bands, for either dopant. The vibrational analysis of the 2A and 2B spectra, both in absorption and in emission, and the agreement between the fluorescence data and the wavenumbers of the corresponding lines in the Raman spectrum of the pure crystalline dopant, show clearly that 2-aminoanthracene is responsible for both traps. The 1A and 1B spectra are not so easily interpreted and of the two frequencies which can be compared one shows a small but significant shift, 385 to 394cm-l.2-aminoanthracene shows a similar but smaller shift, 1413 to 1420 cm-I ; both cases may be attributed to site effects. The polarization ratios (PR) given in table 1 are emission intensity ratios (&/Ia) or absorbance ratios, as appropriate. The emission data refer to bands other than the origin line itself; this is the only transition common to emission and absorption and would show the same PR in both, were reabsorption negligible. The difference between 2A absorption and fluorescence is striking and shows that the oriented gas model is completely inappropriate. (We have obtained similar results for tetracene in anthracene,1° for which the PR in absorption is 5.5 +0.5, the PR of the fluorescence origin is 5.9 0.6, while the other fluorescence bands give 3 PR of 2.8 f0.4.) Thus estimates of dopant concentration from the absorbance are necessarily rough, though in the aminoanthracene case they agree acceptably well with estimzltes based on the composition of the material from which the crystals were grown.SPECTRA OF DOPED ANTHRACENE 0.-rn' rn-g 22000 21500 21000 20500 20000 wavenumber/cm-* FIG.1.-b-polarised fluorescence of 2-aminoanthracene guest in an thracene. Dopant mole fractions are about for upper trace and lo-' for lower trace. The emission features to the left are host combination bands. Guest origins, inolecular vibrational lines and phonon peaks are indicated respcctively by long, niedium and short markers. J 21500 22000 22500 25000 23500 24000 wavenumber/cm-FIG.2.--Absorption of 2-aminoanthracene in anthracene ; dopant level is about 1O-j.The trans- mitted light is polarised parallel to crystallographic h axis (upper trace) and a axis (lower trace). N. J. BRIDGE AND D. VINCENT c .-v)'G 1 I I I 21500 2Ooo 20500 2oooo wavenumber /cm- ' FIG.3.-b-polarised fluorescenceof 1-aminoanthracene in anthracene ( mole fraction of guest). I 2mo 21500 22000 22500 wavenumber/cm-' FIG.4.--6-polarised absorption of 1-aminoanthracene in anthracene mole fraction of guest). The 1A absorption spectrum (fig. 4) shows clearly how overlapping progressions of phonon bands produce intense diffuse bands. Similar effects are seen in 2A absorption and also account for the broadness of the fluorescence bands, which persists even at very low dopant levels.At high concentrations, guest-guest interactions may be expected to produce a further broadening of the fluorescence bands, but the effect is not obvious in our spectra. Instead we find that emission from the deeper traps is enhanced relative to that from the shallower. (See fig. 1 ; 1-aminoanthracene behaves similarly.) It could be that the proportion of A to B traps changes, but a neater explanation is that the average rate of energy exchange between guest molecules becomes fast compared with the lifetime of the excited state. Taking this to be about 20 ns," the average coupling between neighbouring guest molecules must be of the order of 0.005 cm-' for a dopant mole fraction of Thermal detrapping is, of course, insignificant at 4 K.11-2 34 SPECTRA OF DOPED ANTHRACENE TABLE1.-SPECTRA 1 -aminoanthracene 2-aminoan thracene guest 1A 18 2A 2B origins (V/cm-' in uacno) 21 176 21 332 21 807 22086 Raman (1 molecular vibrations active in 385 394 333 -333 fluorescence (V/crn-l, f3 cm-l) I 400 1 403 371 374 375 503 504 505 1413 1420 1411 ditto, in absorption 345 335 333 378 382 370 406 452 460 498 496 928 phonon peaks in origin band in 51 25 40 40 fluorescence (Vlcm-', f5 cm-l) 93 56 93 93 130 ditto, in absorption 47 42 54 99 110 138 163 polarization ratios in fluorescenceb (b :a, _+ 10 %) 3 3.1 1.9 1.6 ditto, in absorption 3,l -25 2.2 0 Recorded for pure crystalline dopant, with 633 nm excitation ; b for bands other than the electronics origin line.See text. We have not attempted a quantitative study of the rates of host-to-guest energy transfer. However, comparing fluorescence spectra for single crystals which give measurable absorption for the deeper traps, we find that whereas with l-amino- anthracene the guest and host emission are of comparable intensity, 2-aminoanthra- cene quenches the host emission almost entirely. The ratio of guest to host fluo-rescence quantum yield is equal to the product of the mole fraction of the guest and the "energy transfer coefficient " l2 ; estimating the guest concentrations from their absorption it appears that the energy transfer coefficient for 1A traps is at least fifty times lower than for 2A.One cannot avoid this conclusion by supposing that the 1A fluorescence (but not the absorption) arises from a transition polarised normal to the crystal face, since the fluorescence origin is as weak as the other bands. Nor is it possible that the energy is transferred to the 1A traps and then quenched, since this would imply a fiftyfold reduction in the intensity of emission from heavily doped samples; no such change occurs. Comparing the spectra with those we have obtained for tetracene in anthracene, it seems that the energy transfer coefficient for 1A traps is abnormally low, rather than the 2A value very high. Integrating over the band and averaging over a and b polarization, the ratio of 2A to 2B absorbance is similar to the intensity ratio for the fluorescence of lightly doped crystals; however, the latter is hard to measure accurately since the spectra N.J. BRIDGE AND D. VINCENT overlap. It follows that 2A and 2B are comparably efficient exciton traps and the intensity ratio shows that about 13 % of the guests take up the B orientation. The complete obscuration of 1B absorption by 1A implies that the 1B absorbance is 110 greater than 2 % of that of IA, since otherwise the sharp origin line would at least be visible. However the strong phonon bands in 1B fluorescence indicate a high electronic oscillator strength, as for 1A and as expected for I-aminoanthracene. We therefore assume that the concentrations of 1A and 1B traps are in rough pro- portion to their absorption.At low dopant levels, 1B emission equals or outweighs 1A (the spectra overlap so badly that one cannot be precise); the energy transfer coefficient for 1B thus appears to be as great as for 2A and 2B sites. Taking it to be the sanie, the proportion of 1-aminoanthracene molecules taking up the B orientation will be about 2 %. The smallness of this number shows that this orientation produces a bad fit of the guest in the lattice, presumably because the amino group is crowded. The steric hindrance is expected to stiffen the molecule against vibration and could well account for the site effect noted above. 2 -I3 YD R OXYA NT HRA CENE In our earlier paper,* we assigned the impurity origin appearing at 24 159 cm-' in the fluorescence of anthracene crystals to 2-hydroxyanthracene and noted also that this spectrum always appeared in conjunction with another having its origin at 25 348 cm-I.These spectra have very similar vibrational structure, with prominent bands corresponding to a molecular vibration at 504 cm-l. We have not found this band in the fluorescence of any other substituted anthracene, excepting only 2-aminoanthracene. Despite our previous reservations, we now believe that 2-hydroxy- anthracene creates two distinct typss of trap in the anthracene crystal. Hydroxy-and amino-anthracenes are very similar in molecular shape and in the nature of the first electronic transiticm6 There are many points of similarity between the fluo- rescence of 2-hydroxy- and 2-amino-anthracene : separation of A and B origins ; intensity distribution between A and B bands ; molecular vibrational structure ; structure of the phonon bands, which are more strongly developed for the deeper traps. Finally, heavy doping with 2-hydroxyanthracene enhances the fluorescence of the deeper traps, an effect which initially led us to suppose that we were "purifying " the guest producing the deep traps.DISCUSSION We coiiclude that each of the four aminoanthracene trays corresponds to a differ-ent orientation of the transition dipole of the guest molecule with respect to the lattice. The electronically excited guest is stabilised by second order energy exchange with neighbouring host molecules to produce a partially delocalised "trapped exciton ".By a pretty coincidence, each type of trap has some particular distinguishing feature : 1A has a very low host-to-guest energy transfer coefficient ; I B gives appreciable steric strain ; 2A gives exceptionally pure b-polarised absorption ; and 2B spectra show relatively weak phonon side-bands, indicating rather weak excito n-pho t on coupling. Evidently steric hindrance, exciton polarization, exciton-phonon coupling and energy transfer from the host all depend differently on the orientation of the guest. How-ever, we do expect a correlation between the guest-host exchange energy and exciton- plionon coupling, which will be slight for that orientation of the guest which minimises SPECTRA OF DOPED ANTHRACENE exchange, and hence also mininlises the change in exchange energy produccd by any possible deformation of the lattice.The 2B guests, for 2-hydroxyanthracene as well as for 2-aminoanthracene, apparently approxiniate to this orientation, giving high energy traps and spectra with weak phonon side-bands. A possible complication is the variation of conformation of the guest with orient- ation. Inspection of a model of the lattice shows that tlie amino group will be held nearly in the plane of the molecule in all four cases but since the excitation energy of the free guest must depend strongly on the angle of twist about the CN bond, even small variations between sites might be important. We plan to investigate this point further, both by experiments on chloro- and cyano-anthracenes and by perturbational calculations of the exchange energy. The observed differences in excitation energy between A and B sites seem rather large to be due entirely to coupling between the guest and the first exciton band of the host, itself only 680 cm-' wide,I3 but contri- butions from the second exciton band may well be important since the mismatch of energy is largely offset by the much greater oscillator strength.We thank Mr J. Archard for assistance in the laboratory. V. M. Robertson, A. M. Mathieson and V. C. Sinclair, Actu Cryst., 1950, 3,245. J. S. Vincent and A, H. Maki, f. Chem. Phys., 1965, 42, 865. G. Fischer, Mol. Cryst. Liquid Cryst., 1970, 11, 85. R.G. Bray and D. P. Craig, Chem. Phys. Letters, 1972, 13, 577. D. P. Craig and S. H. Walmsley, Excirons in Molecular Crystals (Benjamin, N.Y., 1968), Chap. 6. M. Tichy and R. Zahradnik, J. Phys. Chem., 1969,73, 534. 'R. M. Hochstrasser and G. J. Small, Cliem. Comm., 1965, 87.* N. J. Bridge and D. Vincent, J.C.S. Faraday 11, 1972, 68, 1522. S. Suzuki and H. Babi, Biill. Client. Soc. Japan, 1964, 37, 519. lo D. Vincent, Ph.D. Thesis (University of Kent at Canterbury, 1972). The radiative lifetime measured for 2-aminoanthracene in cyclohexane solution is 40 ns (1. B. Berlman, Handbook of Fluorescence Spectra of Aromatic Molecules (Academic Press, N.Y., 1965)). This is halved to allow for the greater refractive index of the host crystal (see Chap. 4 of ref. (12)). l2 J. B. Birks, Photophysics of Aromatic Molecules (Wiley, N.Y., 1970), Chap. 11. l3 M. R. Philpott, J. Chem. Phys., 1971, 54, 111.

ISSN:0300-9238    

DOI:10.1039/F29747000030

出版商:RSC    

年代:1974

数据来源: RSC

摘要:

Theory of Intramolecular Vibrational Relaxation in Large Systems R. FLEMING,* AND SHENGBY GRAHAM ONNOL. J. GIJZEMAN H. LINT Davy Faraday Research Laboratory of the Royal Institution, 21 Albemarle Street, London W1X 4BS Received 21st June, 1973 A general theory for intramolecular vibrational relaxation is proposed. The theory provides a master equation, analogous to the Pauli master equation in nonequilibrium statistical mechanics, for this process. The master equation contains a completely general time independent perturbation operator, which causes the system to relax to equilibrium. The choice of the three-phonon interaction operator as a perturbation is treated in detail, and a comparison with experimental data is made. Until some years ago it had always been assumed that electronically excited molecules in dense media radiate only from the lowest vibrational level of the lowest excited electronic state.However, recent, more sensitive, experimental techniques have shown that this is not always the ca~e.~'~ The vibrational energy content of a molecule can be altered in two ways. If a molecule in a dense medium is vibrationally excited, it will usually transfer its excess energy to the surroundings. The medium can either be a solvent or a high pressure of inert gas. This collisional vibrational energy transfer process is commody called vibrational relaxation. A different situation may occur when a large isolated mole- cule is vibrationally excited. Provided that the molecule is large enough, i.e., it has a large number of vibrational degrees of freedom, the excess energy will be distri- buted over all available vibrations, assuming that there is some sort of coupling between the various vibrational modes.This latter process is usually referred to as vibrational redistribution. The effect of vibrational relaxation on the observed rates of electronic relaxation has rscently been ~tudied.~-~ On the other hand, there has been some argument in the literature '9 * as to whether intramolecular vibrational redistribution takes place at all in polyatomic molecules following optical excitation. One sensitive experimental probe is that of resonance fluorescence spectroscopy, which has recently been reviewed by Parmenter ; he finds no evidence for intramolecular vibrational redistribution in benzene single vibronic level fluorescence spectra.Although diffuseness is observed as higher single vibronic levels are populated in toluene and naphthalene, in both cases this can be plausibly attributed to spectral overcrowding rather than vibrational redi~tribution.~ However, the non-exponential fluorescence decay of isolated pyrene molecules has been explained as being due to incomplete vibrational redistribution,'* and there seems no doubt that rapid energy migration between normal modes occurs in some unimolecular decompositions. For instance, the rate of intramolecular t John Simon Guggenheim Fellow, permanent address : Department of Chemistry, Arizona State University, Tempe, Arizona 85281.37 VIBRATIONAL RELAXATION IN LARGE SYSTEMS vibrational redistribution in vibrationally excited hexafluorobicyclopropyl-d, has been measured by Rynbrandt and Rabinovitch.12 They find that the rate of vibra-tional redistribution is 1.1 x 10l2s-' in this case. It would thus seem desirable to derive some theory which may help to clarify these different observations. Although the above definitions of vibrational redistribution and vibrational relaxation are different, it is possible to adopt a slightly more general viewpoint, which will enable us to treat these two processes by the same theoretical methods. To this end, we treat a vibrationally excited molecule plus its surroundings as one isolated "supermolecule ",where vibrational energy is transferred from one or more particular vibrational degrees of freedom to all others. We show that, under certain circumstances, the same type of master equation can be used to describe both vibra- tional redistribution and collisional vibrational relaxation.The problem we want to solve can now be stated as follows. If we consider a large molecule (or a "supermolecule "as defined above) consisting of Nnormal modes, then the state (or wavefunction) of the system will be completely specified at any time t by the set of vibrational quantum numbers vl(t), v2(t),.. .vN(t)or {~(t)]in a convenient shorthand notation. It should be noted that this notation does not assume that we are dealing with harmonic oscillators. It only assumes that the coupling between the different normal modes is sufficiently weak to ensure that each oscillator retains its own identity.Since spectroscopy has amply shown the usefulness of the concept of normal modes, this assumption seems entirely reasonable. Let us now suppose that at t = 0 the system is prepared in some state (~(0)).If the system is large, it will undergo a spontaneous irreversible change under the influence of the small perturbation, caused by the interaction between the various normal modes. This can be written : where we expect {~(m)}to correspond to the normal Boltzmann distribution of a set of oscillators. It should be noted that, since we are dealing with an isolated system, energy must be conserved ; in other words, for all t, &YOi(,,) = ~EOi(tl,where 1 I E,,,denotes the energy of mode i with quantum number ut.This condition can be easily met for large systems. In the following section, we give the quantum mechanical rate equation for the process shown in eqn (1). This equation has been derived previously,l and is in fact a general equation for time dependent processes under the influence of a stationary perturbation. We will then apply this result to the problem of vibrational relaxation in large systems. THE MASTER EQUATION In this section we are concerned with the form of a master equation for relaxation phenomena in isolated systems. One way of deriving such a formula would be to start with a giyen wavefunction (u(O)), assumed to be the solution of a zero orcer Hamiltonian H,, and to introduce a tims-independent perturbation operator H', representing the coupling between the various normal modes.The standard methods of time dependent perturbation theory l4 can then be used to calculate the wave-function (~(t)).This approach has the disadvantage that the final formula will only be applicable to the specific choice of (~(0)),and the calculation has to be repeated for every other (~(o)].There exists, however, an alternative mathematical technique which circumvents this difficulty. This technique is known as the density matrix l6 We G. R. FLEMING, 0. L. J. GIJZEMAN AND S. H. LIN now digress briefly to clarify the physical meaning of this formalism. The discussion closely follows that given by Messiah.Let us first change the notation and write {u(t)> as one symbol, In), ; thus stands for a particular set of vibrational quantum numbers, different In), (In'),, In"), etc.) corresponding to different sejs of ds. The functions In), are the eigen- functions of a zero order Hamiltonian (Ho)and can thus be regarded as orthonormal. We will now define the density operator p(t) as : where the pn are the statistical weights of the states In)t; clearly, cpn = 1. It n follows from eqn (2) that (nlp(0)ln) = p(O),, = pn. Thus, at t = 0, the diagonal matrix elements of the density operator represent the probability of finding the system in the state In). From our assumption that the functions In) are orthonormal we infer that at t = 0 the density matrix is diagonal.It can be shown by consideringJhe time development of the states In) under the influence of the total Hamiltonian H of the system that at later times p(t),.,. represents the probability of finding the system in the state In'). Thus a solution of the equation of motion for p(t), combined with a given initial distribution p(0) would provide us with the time development of every possible state In). Or, returning to our old notation, given any (~(0))we would know (~(t)]and we would have solved our problem stated in the introduction once and for all. In general, the equation of motion for p is l5 where fi represents the total Hamiltonian of the system. This equation is rigorously equivalent to the time dependent Schrodinger equation.The approximate solution of eqn (3) has been discussed by several authors (see for example ref. (13)), using a perturbation method approach. Here the Hamiltonian is written : ii = &+;UzI (4) where fi0 is the zero order Hamiltonian (with eigenfunctions In)) and H represents a time independent perturbation (in our case the coupling between the various normal modes). The parameter ;Z is introduced for convenience to separate the different orders of approximation. After a straightforward calculation the first order solution of eqn (3) is given by the Pauli master equation l3 where It is seen from these equations that to the lowest order of approximation we obtain the master equation with the detailed rate constants (knn-)expressed in the "golden rule" form.At equilibrium eqn (5) reduces to pnn = pnttnt.for E,, = Ent.,which expresses the familiar postulate of equal apriori probabilities in statistical mechanics. VIBRATIONAL RELAXATION IN LARGE SYSTEMS APPLICATION To show some application of eqn (5)let us try to find an explicit expression for the master equation, applicable to the vibrational relaxation of a large system. We will assume that the zero order wavefunctions of the system are simple harmonic oscillator functions. Then, the coupling between the various normal modes can be expressed in the three-phonon approximation as l7 where U represents the nuclear potential energy and Q labels the normal coordinates of the total system. Since we will only be interested in the diagonal matrix elements of p, we will drop the second subscript of p in the following ;thus pnn= pn.Substituting eqn (7)and (6) into eqn (5) we obtain vi(vi-1)(uj+f)(pui-2,uj+ 1 -~u,,vj)>* (8) In this equation pustands for the probability of finding the system in the state specified by the quantum numbers vl, u2, . . . vi, vj, uk, . . . vN. Symbols like pui-~,u,+~,vk+l denote the probability of finding the system in the state ul, u2, . ..uf-1, vj+ 1, uk+ 1, . ..vN. Sijk(or Sij)stands for the cyclic permutation of i,jand k (or i and j) and the k’s are defined by The factors in front of the density matrix elements in eqn (8) arise from the well known properties of the matrix elements for harmonic oscillator wavefunctions,’ e.g., I(uil Qilui +1)12 = (vi + 1)/(2Pi).Let us now consider some particular cases of eqn (8).If we are concerned with the relaxation of one mode i, and the other modes are assumed to be in thermal equilibrium, eqn (8) can be simplified to : G. R. FLEMING, 0. L. J. GIJZEMAN AND S. H. LIN where ki(fl) = cck$b(l-exp(-flhoj)}-'(l-exp(-flhok)}-' ik k,(P), = kii,{l-exp (-flhuj)}-' j ki(fl)2= 2 kijj{l-exp (-ptt~~))-~i where B = l/kT. In most cases the contribution from kill (or k,,,) is smaller than that from k$, since energy matching will be more difficult and the number of terms like k,,,will be less than that of the type k& (cf. eqn (7)). If we ignore the contributions from terms with two equal indices, eqn (9) becomes It should be noted that the physical meaning of the density matrix elements has now changed somewhat; pul now denotes the probability of finding the system with u quanta in mode i, all the other modes being in thermal equilibrium. Eqn (10) seems to be a natural starting point for a discussion of vibrational relaxation, since many cases of practical interest correspond to this equation.For instance, electronic excitation of an isolated molecule frequently prepares the molecule with vquanta in a specific vibration, all other modes remaining unaffected by this process and thus remaining in thermal equillibrium. Similar considerations apply to molecules, embedded in a dense medium. Eqn (10) has the same form as the master equation used in collisional vibrational relaxation based on the Landau-Teller theory.Ig The only difference is in the factor k,@, which, however, has no influence on the form of the solution.The common assumption in our description of intramolecular vibrational relaxation and the Landau-Teller theory is the fact that in both cases the normal mode under consideration is coupled linearly to the vibrations of the heat bath. Whereas this assumption could in principle be relaxed in our case (e.g., by the explicit inclusion of the terms neglected in eqn (9), or by choosing a different perturbation Hamiltonian), a modification of the Landau-Teller scheme seems more difficult. However, adopting the approximations made so far, the mathemetical formula for the description of intramolecular vibrational relaxation is identical to that used to describe collisional deactivation.The general solution of eqn (10) has been obtained by Montroll and Shuler for various initial conditions.lg If the system is initially in the state ui, i.e., at t = 0 the oscillator under consideration is excited with ulquanta, the solution is given by where el. = hul/(kT),z = k,(B)t(l-eAt), at = sinh(Oi/2)/sinh(~/2),and F(-vi, -ui, 1 ;u2)represents the hypergeometric function. When T+O, eqn (1 1) becomes particularly simple Ui! { 1 -exp (-ki(m)t)}U1-Ufexp (-viki(m)t).PU,(O = Vi!(Ui -VJ! This result implies that the initial state uf decays exponentially with rate constant VIBRATIONAL RELAXATION IN LARGE SYSTEMS u,k,(co) and that the lower states ui dccay exponentially only at longer times, each with a different rate constant viki(co).Eqn (12) is illustrated in fig. 1. Another simple case that can be considered is ui = 0, i.e., the heating of the ith mode by the heat bath. In this case eqn (1 1) becomes When t+oo we obtain the equilibrium distribution p,,(W) = (eei 1)e-ei(Oi+1)I The particular results of eqn (12) and (13) have also been obtained by Nitzan and Jortner, using an entirely different approach.20 7 FIG.1.-Population, at T = 0, of the first five vibrational levels of a mode, initially in v = 4, as a function of reduced time T. The numbers refer to the vibrational quantum numbers. It should be noted at this point that the detailed rate constants k$i are generally not equal to the observed decay constants.In principle one must solve the master equation (eqn (5) or (8)) with the proper initial conditions, corresponding to the experiment under investigation. Let us now make a preliminary comparison of the theory, outlined in this section, with some experimental data. A possible example of slow vibrational redistribution that has been reported is the anomalous temperature dependence of the hot band (Sf) and S2 emission in 3,4-benzpyrene and other aromatic compounds in glassy matrices. It has been found that the intensity ratios $(S2)/f(Sl) and $(Sf)/ $(SJ as a function of temperature followed the normal Boltzmann behaviour when the system was excited into the lowest level, S1.After excitation into S, a deviation from Boltzmann behaviour was observed. G. R. FLEMING, 0. L. J. GIJZEMAN AND S. H. LIN As a simple model for this system we will consider three levels (corresponding to S2,STand S1respectively) and determine the population of the middle level STas a function of time and temperature, if either the lower level (S,)or the upper level (SJ is excited initially. From the eqn (11) and (13) we then obtain the graphs, shown in fig. 2. The Boltzmann equilibrium value at different temperatures is indicated by a straight line. The curve, approaching this limit from above corresponds to excitation of thc S, upper state, the one approaching the equilibrium value from below corre- sponds to excitation into the lower level, S,.It is seen that in allcases equilibrium is reached at later times, when the excitation is into S,. This time-lag becomes larger at lower temperatures. It should be noted that according to the definition of z the time scales for the curves belonging to different temperatures are not strictly the same. This will lead to an even larger increase in the time-lag at lower temperatures. 0=5 Io-~ 7 Fic. 2.-Population, at different reduced temperatures 0 (= @w), of the first vibrational level of a mode, initially in u = 2 (downward curves) or u = 0 (upward curves) as a function of reduced time 7. The straight lines indicate the Boltzmann equilibrium values at the particular temperature. Note that the time scale is different for different temperatures and increases with decreasing temperature. This model implies that the STlevel is temporarily "overpopulated " when excit- ation is into S,; thus, if emission takes place before equilibrium is reached, an anomalously large emission intensity from Sf can be expected.This effect will be more pronounced, the lower the temperature of the system. When excitation is into S1,equilibrium is reached relatively quickly, and no anomalous behaviour is expected(except possibly at very low temperatures). Similar plots for the population of S2 show an even greater time-lag, i.e., it takes longer to reach equilibrium "from above " than "from below ". It is thus expected that the ratio #(S2)/#(S1)will begin to deviate from Boltzmann behaviour at higher temperatures than $(S;F)/f(S,) ; this is confirmed by experiments.l* VIBRATIONAL RELAXATION IN LARGE SYSTEMS The conclusions obtained in this section are based on the use of the three-phonon interaction operator as a perturbation in the master equation (eqn (5)) However, any other type of perturbation can be used ; for example, if we choose we can study multiphonon decay with the present formalism It thus seems that this approach constitutes a general scheme for the study of vibrational relaxation in large systems One of us (S.H. L.) thanks Prof. G. Porter and A. D. Buckingham for their hospitality. We also thank the S.R.C. for the award of a Studentship to G. R. F., and the Royal Society European Exchange Programme for the award of a Fellow-ship to 0.L.J. G. P.A. M. van den Boogaardt, R. P. H. Rettschnick and J. D. W. van Voorst, Client. Plij?~. Letters, 1973, 18, 351. F. Hirayama, T. A. Gregory and S. Lipsky, J. Client. Phys., 1973, 58, 4696. C. E. Easterly, L. G. Christophorou and J. G. Carter, J.C.S. Faraduy II, 1973, 69, 471. S. H. Lin, J. Chem. Phys., 1972, 56, 4155. ’D. F. Heller and K. F. Freed, J. Chern. Phys., 1973, in press. A. Nitzan and J. Jortner, J. Chem. Phys., 1973, 58,2412. ’S. F. Fisher, J. Chem. Phys., 1972, 56, 5199; A. Nitzan and J. Jortner, J. Cheni. Pli?:~...1972, 56, 5200. D. F. Heller and K. F. Freed, Intern. J. Quantum Chem., 1972, 6, 267. C. S. Parmenter, in M.T.P. International Review of Science, Physical Chemistry, vol.III (Butter-worth, London, 1972). lo C. J. Werkhoven, T. Deinum, J. Langelaar, R. P. H. Rettschnick and J. D. W. van Voorst, Chem. Phys. Letters, 1973, 18, 171. l1 L. D. Spier and B. S. Rabinovitch, Ann. Rev. Plzys. Chem., 1970, 21, 349. l2 J. D. Rynbrandt and B. S. Rabinovitch, J. Cheni. Phys., 1971, 54, 2257; J. Phys. Cltem., 1971, 75,2164. I. Prigogine, Non-Equilibrium Statistical Mechanics (Wiley-Interscience, New York, 1961), p. 257; R. Zwanzig, Pltysica, 1964, 30, 1109; W. M. Gelbart, S. A. Rice and K. F. Freed, f. Chem. Phys., 1972, 57, 4699. l4 D. Bohm, Quuntutn Theory (Prentice-Hall, N.J., 1951), p. 407. A. Messiah, Quuntutn Mechanics (North-Holland Publishing Company, Amsterdam, 1965),!p. 331. l6 R. C. Tolman, The Principles of Statistical Mechanics (Clarendon Press, Oxford, 1938), p. 325. l7 R. E. Peierls, Quantum Theory of Solids (Oxford University Press, Oxford, 1955), p. 40. E. B. Wilson, J. C. Decius and P. C. Cross, Molecular Vibrations (McGraw-Hill, New York, 1955), p. 289. E. W. Montroll and K. E. Shuler, J. Chem. Phys., 1957,26,454 ; Adu. Chem. Phys., 1958,1,361. 2o A. Nitzan and J. Jortner, Mol. Phys., 1973, 25, 713.

ISSN:0300-9238    

DOI:10.1039/F29747000037

出版商:RSC    

年代:1974

数据来源: RSC

摘要:

Electron Spin Resonance Study of the Superoxide Ion in Me1 t-recr yst allized Strontium Chloride BY€3. N. NG (NGHOKNAM)~ G. HARRISON*AND LIONEL Department of Chemistry, The University of British Columbia, Vancouver 8, B.C., Canada Received 29th June, 1973 An e.s.r. spectrum in melt-recrystallized SrCI2 single crystals has a fully anisotropic g-tensor with principal values 2.0028,2.0093 and 2.053 in directions oriented in the crystal as [llo], [110]and [Ool].The spectrum is ascribed to 0;in a site of Dzh symmetry between two anion vacancies, and inter- acting with two Sr2+ions so that the unpaired electron resides in a Bzg orbital localized mainly on the Oi. The crystal field splitting A between BZgand B3g(OZrg(x)and rrg(y) mixed with Sr 4d) is about 40 times the spin-orbit coupling constant, i.e.about 0.9 eV. When A is so large, the orbital angular momentum reduction parameter cannot be estimated accurately from the g-tensor. Oxygen-containing impurities, including such species with unpaired electrons as 0-and O;, are common in metal halides. 0; can be formed without the aid of ionizing radiation. Kanzig estimated that commercial preparations of KCl, KBr and KI contain from IOl4 to 10l6 0; ions per cm3. The discovery of 0; in melt-recrystallized SrC1, reported in this paper is therefore not very surprising. This ion is, however, interesting to study in any new environ- ment. In common with some other oxygen ions (0-,Of, Oi), the superoxide ion has an orbitally degenerate ground state, and normally locates itself in an environment of such symmetry as to lift the degeneracy. The details of this interaction with the environment of the 0; provide the main interest in studies of this ion.In the present case, the crystal field sphtting seems to be as large as in MgO, ZnO and zeolite hosts, and much larger than in alkali halides. EXPERIMENTAL SAMPLE PREPARATION Baker Analytical Reagent Grade SrC12-6H20 was dehydrated at 200°C for 12 h in air, ground to a fine powder and melted in a graphite boat in an atmosphere of dry oxygen. After melting it was kept just below the melting point (about 850°C) for 24 h in an oxygen atmosphere and cooled to room temperature over a period of 12 h. Such samples always gave an e.s.r. signal, but the radical concentration was not reproducible.Melting the powder in a platinum crucible in air would sometimes, but not always, give the same e.s.r. signal. The material recrystallized in a graphite boat contained reasonably large single crystals. Pieces with dimensions larger than about 5 mm which appeared to be single crystals were often found to consist of two or three slightly misoriented crystals. Crystals were found to have two types of cleavage plane, the most prominent being (111) and the other (100). Crystallographic data, including the nature of cleavage planes, were obtained by X-ray diffraction with a STOE precession camera with the precession axis perpendicular to the cleavage. For e.s.r. work crystals about 3 x 3 x 1mm were used, a smaller fragment from the crystal being used for X-ray diffraction determination of its orientation. t present address : Department of Chemistry, McMaster University, Hamilton, Ontario, Canada.45 0;IN MELT-RECRYSTALLIZED SrCl, E.S.R. SPECTROMETER, AND MOUNTING OF SAMPLE The e.s.r. spectrometer was a Varian E3 model employing X-band microwaves, 100 KHz modulation, cavity of TElozmode capable of accepting sample tubes up to 11.5 mm diameter, and 4-inch magnet with maximum field of 6 kG. Line positions were measured (with varying magnetic field) relative to that of a standard sample of diphenylpicrylhydrazyl in poly- crystalline KCl (g = 2.0036). Accuracy of estimation of the g-value of a line was normally rt 0.0005. The sample, with its cleavage plane horizontal, was cemented with Pliobond adhesive to a vertical Teflon rod which could be rotated through known angles with the aid of a pointer and protractor. Accuracy of crystal orientation was 5", and of changes in that orientation by rotation +lo.Crystal and rod were immersed in liquid nitrogen in a double-walled dewar in the spectrometer cavity. RESULTS At room temperature only weak and unidentifiable e.s.r. absorption was observed. At 77 K, well-resolved spectra were recorded with both powder and single crystals. A crystal could be stored for months at room temperature without measurable decay of the signal; slight decay was observable after annealing for 24 h at 200°C. Single crystal spectra are shown in fig. 1. ni V 10gauss 3bO 3213 3230 3250 3270, field/G FIG.1.-E.s.r.single crystal spectra of melt-recrystallized SrCI, at 77 K. (a)Magnetic field parallel to crystal Czaxis ; (b)field parallel to crystal C4 axis. These data (together with plots of magnetic field at resonance against angle of rotation about C3 and C4 axes) indicate a species of spin S = +, with no hyperfine interactions, and with a completely anisotropic g-tensor having the following principal values and directions : g,, = 2.0028+0.0005 x (or y)11[110] g,,,, = 2.0093+0.0005 y (or ~)II[li0] gzz = 2.053+0.001 ~ll[0011. (The [1lo] and [IT01 directions are crystallographically indistinguishable, but are distinguishable in the point symmetry of most locations displaced from a lattice site.) H.N. NG AND L. G. HARRISON The g-values obtained were the same, to well within limits of error, for both powder and single crystal samples. For single crystals, a general orientation of the crystal to the field should present the species in six different orientations. Six reso- nance lines were in general observed as the crystal was rotated about a C3axis. These reduced to four or three lines for the special orientations, field 11[211] and fieldll[llO] type directions respectively. In the latter case, two of the lines give g,, and gyy directly (fig. l(a)). When the crystal was rotated about a C4 axis, four lines were observed, the maximum for a species of hue symmetry mmm3 in a crystal of sym- metry m3m when the field lies in a (ZmO)type plane.2 These reduced to two lines for field)l[lOO] type directions, and one of the lines then gives gzzdirectly (fig. I@)).DISCUSSION IDENTIFICATION OF THE RADICAL AS 0, The following oxygen-containing species will be considered as possibly responsible for the observed spectrum: OH, H02, 0+,Oi, 0-, 0;and 0;.The hydrogen- containing species may be eliminated on the basis that hyperfine splitting by the proton spin should have been readily observable. The splitting is normally about 43 G for OH and 13 G for H02, easily resolvable at the present linewidth of 2 G. (The g-values are quite possible ones for either OH or HO,. For example, OH in ice has principal g-values 2.0050,2.0090,2.0585, while HO, in hydrated SrC1,-6H20 has g-values 2.003, 2.008, 2.0355.HO, is in fact very closely related to the species 0;to which we finally ascribe this spectrum.) Both Of and 0;should have coupling to an orbital above that of the unpaired electron, giving one negative g-shift. In the case of O;, the orbitals thus interacting are the degenerate pair in the isolated ion. Their small splitting in a crystal field should give a large negative g-shift. Compare the isoelectronic N; : in KC1.KNO3, g-values 1.908, 1.998, 2.000; in KN3,61.983, 2.0008, 2.0027. (Jaccard identified a radical in KN0,-doped KC1 and KBr as Oi, although all three g-shifts were positive : g-values 2.003, 2.010, 2.042. This identification seems very doubtful ; the dioxygen cation is in any case a most unlikely species to be formed in the absence of either ionizing radiation or a very powerful oxidizing agent.8) O+ has not been positively identified by e.s.r. in any system.All the g-shifts in the present spectrum are positive, Asxx being close to zero. To first-order approximation, this is the expected direction of the shifts for spin-orbit coupling of the oribital of the unpaired electron to orbitals lying below it, and hence is expected in all the negatively-charged species. (In a more accurate approximation, the small shifts Agxx and Ag,, can be negative, as discussed in more detail below.) We shall consider the possible species 0-, 0;and 0;. For 0-in a site of orthorhombic symmetry, the degeneracy of the 2p orbitals should be lifted completely, and the g-shifts should be qualitatively as observed.But in known examples of 0-,the splittings are small and the g-shifts are hence much larger than those observed here (e.g., in KC1,9 g-values of about 2.22, 2.45 and 1.95 ; for some axially-symmetric cases,10'12 g1 ranges from 2.0516 to 2.2931). 0; is a Czvmolecule; the unpaired electron occupies a bl orbital constructed mainly from out-of-plane oxygen 2p orbita1s.l The g-shift in the out-of-plane direction should be roughly zero, and those in the in-plane directions positive but very small (typically l4 : out-of-plane 2.0025 ; in-plane 2.0174 and 2.01 13 ; see also values observed 15* l6 for 0;in Sr(N03)2 and values for the closely similar mole- cule C102 179 la). 0;has the ground state ,lI3of the configuration (2p7~~(y))~(2p7r~(x))~.Agxx is 0; IN MELT-RECRYSTALLIZED SrCI, thus expected to be close to zero. In a crystal field which splits the degeneracy of ng(x)and ng(y),spin-orbit coupling across the small gap between them (by L,) should give a large positive ASzz. Coupling through L,, to 2pag should be much smaller, giving a small positive Ag,,,,. These predictions fit the present g-values. These are similar to those of 0;in some other hosts 19-24 (table 1). The tabulated values show, however, that Agxxand Asyy are sometimes negative; this is accounted for by the equations of Kanzig and Cohen l9 (eqn (1) to (5) below). TABLETYPICAL &VALUES OF 0, IN VARIOUS HOST CRYSTALS host lattice gzz gull Srz ref. KCI* 1.9512 1.9551 2.4360 19,30 NaI 1.99% 2.0004 2.1859 30 NaO, 1.99 1.99 2.175 20 H202 *CO(NHz)2 2.001 2.008 2.049 24 MgO 2.0011 2.0073 2.077 21 ZnO 2.0020 2.0082 2.051 21 Na-Y zeolite 2.002 2.007 2.074 23 Sr-Y zeolite 2.0017 2.011 2.049 23 Ba-Y zeolite 2.0046 2.0093 2.057 22 SrC12 2.0028 2.0093 2.053 this work zis the internuclear axis and x chosen such that ng(x) is the orbital of the unpaired electron.* typical of alkali halides (except NaI) listed in ref.(30). LOCATION OF THE 0, RADICAL-ION The 0;ion must lie in the SrCl, lattice with the internuclear axis z in a [Ool]type direction and x and y in [!lo] type directions. But [110] and [lTO] are equivalent in cubic symmetry, while x and y are inequivalent for this species. Hence the centre of the ion cannot lie on a lattice site, where the site symmetry would fail to split the degeneracy of the 0;ground state.The most probable way in which 0;might achieve a lower site symmetry appears to be by displacement from an anion site along the [Ool] internuclear axis, cf. the displacement of 0-in CaF,.25 The most probable extent of displacement is that ........ '. .........: .*.. i. ci-:i ; c1-*i............i ............. .... . I.... .; (-1-.j ......... @.*.. a.i. cr ...;.. ............ .......... -. I Oo= 6.977A I-3.488ii----i FIG.2.-Proposed location of Oi in SrCl, lattice, shown as a projection on a (110) plane. Each broken circle represents two ions, lying ())2-faoabove and below the plane.Squares represent anion vacancies. H. N. NG AND L. G. HARRISON 49 which places the 0; symmetrically between two anion sites. The distance between two anion sites is 3.49 A. The ionic radius of C1- is 1.81 8, and the internuclear distance of 0; is 1.32-1.358,(interpolation in the series Oi, O2and 0~~~).Hence for this model to be satisfactory sterically the two anion sites adjacent to the ends of the 0; must be vacant. A referee has suggested that the charge imbalance in this model might be compensated by the presence of a monovalent cationic impurity such as Naf. The model is shown as a projection on a (110)plane in fig. 2. The reason for the assignments of x and y in this diagram is discussed in the next section. BONDING SCHEME OF 0, TO ITS ENVIRONMENT The 0; ion and its immediate environment may be regarded as a “complex” C1,Sr-02-SrC1, ; the symmetry is D2h.For the present purpose, we need discuss only n-and 8-bonding utilizing O2ng2p(x and y) and Sr M(yz and zx) orbitals. The ways in which these combine to form B3, and B,, molecular orbitals are shown pictorially in fig. 3. The relative energies of these orbitals are unknown, but it is Y t, i X (4 (b) FIG.3.-Sketch of the 0;2p7rg and Sr 4d orbitals which combine to form (a)the BJgand (6)the BZgmolecular orbital . reasonable to suppose that the overlap of atomic orbitals shown in fig. 3(a) should stabilize this m.0. relative to that shown in fig. 3(b). Hence the unpaired electron should be forced into the latter, the B2, orbital, and localized mainly on the 0; group.This leads to the identification of the Sr-Sr direction as the y axis. The bonding scheme envisaged for this system is essentially the same as that discussed in detail by VlEek 27 for p-peroxo-dicobalt complexes. THE 9-VALUES AND LIGAND FIELD INTERACTIONS Kanzig and Cohen l9 developed the following equations for the g-values of 0; when the degeneracy of the ng orbitals has been lifted to give a splitting A between 0; IN MELT-RECRYSTALLIZED SrCl, 7~J.x) and nTts(y).E is the larger splitting between ng(x)and a,, and A is the spin-orbit coupling constant : gzz = ge+2IQ ; Syy = 9e Q’-(A/E)(Q-Q’-1) ; gxx = 9e Q’-(A/E)(I-Q -Q’). Here Q and Q’ are functions of the splitting A as follows : Q = [1+ (A2/A2)]-* ; Q’ = [1+ (12/A2)]-*.The value of the parameter I in eqn (1) is a measure of “ orbital angular momentum reduction ” by molecular orbital formation between the orbitals of the 0; ion and orbitals on neighbouring atoms. It is closely related to the orbital reduction factor k devised by Stevens 28 to explain the low g-values for NiC1;- and IrCli-. The topic has been reviewed by Gerloch and Miller.29 In the isolated ion, I would have the value 1. Molecular orbital formation (in the present case, chiefly the mixing of Sr dyzwith oxygen n,(y) in the Bfgorbital) could cause I to assume values less than unity. Zeller and Kan~ig,~~ using forms of eqn (1)-(3) further refined to allow for different values of I and A in x,y and z directions, find values of Zz between 0.932 and 1.021 from experimental g-values for eight out of nine cases of 0;in alkali halides.Error limits on Zz range from +0.001 to Jr0.03 in the various examples. The re- maining case (0; in NaI) gives the unusual value 1.8k0.2, which Zeller and Kan~ig,~* following Ham,31 attribute to a dynamical Jahn-Teller effect, i.e. vibronic interaction of the electronic states and lattice vibrations. The values of the three parameters A/A, A/E and I are found by first using the experimental gxxand gyy values and solving eqn (2) and (3) iteratively for A/A and A/E, and then substituting the value of A/A in eqn (1) to find I from experimental gzz. In the first stage of this process, A/A and A/E can be determined very accurately when the g,, and g,,,,values are appreciably less than ge,e.g.in the range 1.92-1.96. Asthe g-values rise, however, the accuracy of determination of these parameters rapidly diminishes : error limits become about 3 % for g-values around 1.98 and k10 % for values very close to 2.00 (as in the NaI case). This means, in effect, that as the splitting A becomes larger, the accuracy of its determination from g-values rapidly diminishes. This may be seen by examining the approximate form of eqn (1) to (3) for large A : 9zz = ge +2l(A/A>; (6) gyy = 9e +2(A/E) -(A/E>(A/A>; (7) gxx = 9e +(AlE)(A/A)-(8) In this approximation, if we use the notation Agqq = gqq-ge = gqq -2.0023, the three parameters are obtained as : (WE)= (A9xx +A9J2 ; (9) = A9xx/(~lE); (10) I = A9zz/(2A/A)* (1 1) The experimental data in the present work are : Agzz = 0.0507+_0.001 ‘gyy = 0.0070+ 0*0005Agxx+Agyy= 0.0075 0.00 1.Agxx = 0.0005 5O.OOO5) H.N. NG AND L. G. HARRISON 51 From these data, the three parameters and their error limits are : (A/E)= 0.003 75+0.0005 (A/A) = 0.133 3k0.133 3 and I has a range of possible values from 0.09 to infinity. Hence I cannot be found from the present data. For the splitting A, the best that can be done is to take I = 1 in eqn (I 1) and hence obtain : (A/A) = 0.025 35+_0.0005, i.e. A = (39.4+_0.8)A. The error limits here do not include the uncertainty in the assumption Z = 1. Molecular orbital formation introduces a possible error of only a few percent from this cause ; but if there is a dynamical Jahn-Teller effect like that in NaI, we have may underestimated A by something approaching a factor of 2.Our best value for A, as given above, is much larger than that found in most alkali halides (generally A = 4A to 7A; but for NaI, A = 191) but comparable to values for 0; in MgO, ZnO and zeolites (table 2). In all these cases, error limits are large for any procedure which treats Z as an unknown. In some cases, eqn (9) to (11) give infinite error limits on Z, while use of eqn (1) to (3) even gives imaginary values. TABLE2.-PARAMETERS OF ORBITAL SPLITTING AND ANGULAR MOMENTUM REDUCTION FROM g-VALUES OF 0, IN VARIOUS HOST CRYSTALS method of host lattice WA 104.41~ I calculation ref.KCI" NaI MgO 0.2315+0.1 % 0.052410 % 0.036+20 % 0.037 25.18k0.05 % 4.2240.5 % 32.2+1 % 19 0.961k0.1 % 1.8410 % 1.0'';g5 eqn (1)-(3) eqn (1)-(3) eqn (043)ford: I= 1, 30 30 21 ZnO {0:02+5,qi%t 0 024 0.022 2; i"Na-Y zeolite {o.036 (0yt ;g 5Sr-Y zeolite 0234 SrClz {&I254 31.62:% 28 25.5?/% 22 47.8212 40.5 i 37.5 1.3f?& 1 1.9+,md% 0.9+100%-20% eqn (1)-(3) 21 eqn (11) ;for E, eqn (9) A: I= 1, (11); E: eqn (9) A: I= 1,(11) E: eqn (9) A: I= 1, (11) E: eqn (9) eqn (1)-(3) this work A: I= 1, (11) eqn (1)-(3) 23 eqn (1)-(3) 23 E: eqn (9) * typical of alkali halides (except NaI) listed in ref. (30) ; the notation i signifies imaginary values ; " + co,i " is to be read " error limits of g-values allow calculation of values going through + 00 to imaginary ".If following Zeller and Kan~ig,~O we assume R = I80 cm-1 = 0.0223eV, then the most probable values for the splittings of the 0; 2pn orbitals in SrC1, become A = 0.88 eV and E = 5.95 eV. The latter is to be compared with about 5 eV from the U.V. absorption spectrum of O;.30 We thank the National Research Council of Canada for an Operating Grant. One of us (H. N. N.) thanks the University of British Columbia for a Graduate Fellowship. 0; IN MELT-RECRYSTALLIZED SrC1, W. Kanzig, J. Phys. Chem. Solids, 1962, 23, 479. A. D. Rae, J. Chem. Phys., 1968,50,2672. G. H. Dibdin, Trans. Faraday SOC.,1967, 63, 2098. R. C. Catton and M. C. R. Symons,J. Chem. SOC.A, 1969, 1393. D. Schoemaker and E. Boesman, Phys. Stat.Solid., 1963, 3, 1695. M. C. R. Symons, J. Chem. Soc., 1963, 570. C. Jaccard, Phys. Rev., 1961, 124, 60. * N. Bartlett and D. H. Lohmann, J. Chem. SOC.,1962, 5253. J. R. Brailsford and J. R. Morton, J. Chern. Phys., 1969, 51, 4794. lo B. Segall, G. W. Ludwig, H. H. Woodbury and P. D. Johnson,Phys. Reo., 1962, 128, 76. l1 J. R. Brailsford, J. R. Morton and L. E. Vannotti, J. Chem. Phys., 1968, 49, 2237. l2 M. J. Blandamer, L. Shields and M. C. R. Symons,J. Chem. Soc., 1964,4352. l3 M. M. Cosgrove and M. A. Collins, J. Chem. Phys., 1970,52,989. l4 P. W. Atkins, J. A. Brivati, N. Keen, M. C. R. Symons and P. A. Trevalion, J. Chem. SOC.,1962, 4785. l5 H. N. Ng and L. G. yarrison, J.C.S. Faraday I, 1973, 69, 1432. l6 2.Sroubek and K. 2ddnsk9, Czech.J.Phys. B, 1964,14, 121. l7 R. S. Eachus, P. R. Edwards, S. Subramanian and M. C. R. Symons, J.Chem.SOC.A, 1968,1704. l8 T. M. Pietrzak and D. E. Wood, J. Chem. Phys., 1970,53,2454. W. Kanzig and M. H. Cohen, Phys. Rev. Letters, 1959, 3, 509. 2o J. E. Bennett, D. J. E. Ingram and D. Schonland, Proc. Phys. SOC.A, 1956, 69, 556. 21 J. H. Lunsford and J. P. Jayne, J. Chem. Phys., 1966,44, 1487. 22 P. H. Kaisai, J. Chem. Phys., 1965, 43, 3322. 23 K. M. Wong and J, H. Lunsford, J. Phys. Chem., 1970, 74, 1512. 24 T. Ichikawa, M. Iwasaki and K. Kuwata, J. Chem. Plzys., 1966,44,2979. 25 H. Bill and R. Lacroix, Phys. Letters, 1966, 21,257. 26 F. Halverson, J.Phys. Chem. Solids, 1962, 23, 207. 27 A. A. Vlhk, Trans, Faraday SOC.,1960,56,1137. 28 K. W. H. Stevens, Proc. Roy. SOC.A, 1953,219,542. 29 M. Gerloch and J. R. Miller, Puogr. horg. Chem., 1968, 10, 1. 30 H. R. Zeller and W. Kanzig, Helu. Phys. Acta, 1967, 40, 845. 31 F. S. Ham, Phys. Reo. A, 1965,138,1727.

ISSN:0300-9238    

DOI:10.1039/F29747000045

出版商:RSC    

年代:1974

数据来源: RSC

摘要:

Spectroscopic Studies of Hydrogen Bonded Aromatic Complexes at Low Temperatures:External Deuterium Isotope Effects BYJOHNP. SIMONS* L. SMITHAND ANDREW Chemistry Dept., The University, Birmingham B15 2TT Receiued 2nd July, 1973 Association complexes of benzene and its alkyl homologues with weakly acidic halogeno-alkanes and -alkenes have been studied spectroscopically in frozen 3-methylpentme solutions at 77 K. Investigation of steric, and external deuterium isotope effects on their absorption and luminescence spectra and phosphorescence decay indicate that (i) photoexcitation into the lowest singlet or triplet state alters the equilibrium conformation of the complexes from one in which the C-H bond lies perpendicular to the plane of the benzene ring to one in which the bond is tilted with respect to the perpendicular axis, (ii) intermolecular vibronic coupling in the triplet state with the acidic proton only occurs when the proton lies off the central axis, and (iii) the coupling vanishes when bulky groups prevent the excited complex from relaxing into a tilted conformation.While association with CHCI3 or CHCl2CCI3promotes the molecular distortion of the triplet state in benzene, the effect rapidly decreases when alkyl groups are substituted into the aromatic ring. In complexes with the di- or trichloroethylenes, the phosphorescence of the aromatic hydrocarbon is quenched by triplet-triplet energy transfer. Photosensitised&-trans isomerisation has been demon- strated in dilute solution in frozen 3-methylpentane at 254 nm.At low temperatures and in dilute solution, benzene and its alkyl homologues form weak but specifically oriented complexes with chloroform and other weakly acidic halogeno-alkanes and -alkenes. 1-3 The perturbations introduced by complex- ing alter both the spectroscopic and photochemical behaviour of the aromatic mole- cule ; for example, the radiationless decay of the triplet state in complexes of benzene and [2H,]benzene with CHC13 includes a contribution from intermolecular vibronic coupling since substitution of CDCl, for CHCIJ reduces the rate of decay of the phosphorescence and also suppresses the photochemical formation of he~atrienes.~ Further detailed spectroscopic studies of the complexes and of the effects of external deuterium isotope substitution have provided new data from which inferences have been drawn concerning, (i) their equilibrium molecular conformations both in the ground state and the first excited singlet and triplet states, (ii) the effects of steric crowding, (iii) the contributions made by intermolecular vibronic coupling to the decay of the triplet state and (iv) its dependence on the reIative orientation of the halogenoalkane molecule with respect to the benzene ring.The observations can be understood if the vibronic coupling vanishes when the acidic proton lies on the central axis directed perpendicular to the aromatic ring. EXPERIMENTAL U.V. absorption spectra were recorded on a Pye Unicam spectrophotometer (SPSOO) at 77 K, using a locally constructed stainless steel cryostat.The cylindrical absorption cell assembly fitted snugly into a horizontal tube let into the inner portion of the Dewar vessel : this allowed the refrigerant to surround the cell but excluded it from the optical path. Emis-sion spectra were recorded photoelectrically as described ear lie^,^ using a Rank precision 53 HYDROGEN BONDED AROMATIC COMPLEXES grating monochromator, type D330, equipped with E.M.I. photomultipliers (types 9783 or 9558Q). The entry and exit slits were set to provide a band-pass of 1 nm. The phosphorescence lifetimes of the frozen glassy solutions were measured in 5 mm square Spectrosil cells immersed in liquid nitrogen. For convenience, the output from the photomultiplier/d.c. amplifier system was compressed by an additional logarithmic amplifier (Kane Engineering Laboratories, type KEL 601), before being displayed on a Tektronix storage oscilloscope (type 549).While the decay of the phosphorescence of some of the complexes with CHC1, was found to be non-exponential the phosphorescence of solutions containing only benzene or its alkyl homologues decayed exponentially over at least four natural lifetimes. Prolonged U.V. irradiation, infra-red annealing of the frozen solutions or reduction in the phosphorescence cell dimensions did not alter the decay rates. This excluded the possibility of non-exponential decay being associated with inadequate freezing or the non-attainment of equilibrium conditions.The CHCI, (Hopkin and Williams, A.R.) and CDCI, (Nuclear Magnetic Resonance) samples were found to contain small quantities of CzH50H and CC14, respectively (ca. 2 % by volume), but neither the chromatographic removal of the ethanol nor the addition of 2 % of ethanol or carbon tetrachloride to the CDCl, and CHCl, samples affected the experimental observations. The photosensitised cis-trans isomerisation of 1,2-dichloroethylene was followed gas chromatographically using a 10 ft SE30 silicone gum column and an electron capture detec- tion system (Pye 104/74). This had the advantage of very high sensitivity to trace amounts of the dichloroethylene and insensitivity to the hydrocarbon solvent. All materials were used as supplied apart from 3-methylpentane, which was purified on an activated silica gel column under dry nitrogen, and cis-l,2-dichloroethylene,which was fractionally distilled.RESULTS AND DISCUSSION For convenience the principal observations will be reviewed briefly and the results of ancillary experiments deferred until the appropriate point in the subsequent discussion. (1) On complexing with protic halogeno-alkanes or -alkenes at low temperatures, the absorption spectra associated with the So-+S1 transition in the aromatic mole- cules, suffer discrete shifts -200 to 400-450cm-l to higher frequencies ; these corres- pond to formation of complexes incorporating one or two molecules of the halogeno- alkane (or -alkene), respectively. Their oscillator strengths and vibronic structures remain unaltered, though in benzene particularly, there is an increase in the spectral line widths. Substitution of alkyl groups into the ring increases the stability of the complexes provided there is no steric crowding and also reduces the level of line broadening.In complexes of hexaethylbenzene or 1,2,4,5-tetraisopropylbenzene with CHC13 (or CDC13) there was no perceptible increase in line width. (2) The fluorescence spectra also shift to higher energies but the shifts were smaller than those observed in absorption, see fig. 1 ; however, the discrepancy steadily decreased as bulkier groups were introduced into the ring or the halogeno- alkane and in the hexaethylbenzene-CHCI, complex the shifts were almost identical (see fig.2). The frequency shifts observed in the phosphorescence spectra showed similar trends, see fig. 1. (3) In the phosphorescence spectra of complexes with benzene or [2H,]benzene the spectral origin and the progressions in the totally symmetric ring-breathing mode based upon it, become but in the alkyl substituted benzene complexes there was little change in vibronic structure apart from a moderate intensification in the spectral origin in the mono-substituted derivatives, see fig. 3. As with the absorption spectra the increased line widths apparent in the vibronic structures of the luminesc- ence spectra, decreased with increasing alkyl substitution or replacement of CHCI, by the bulkier CHCI2CCl3 molecule. J. P. SIMONS AND A.L. SMITH 55 5001400t <I/ B loop?---'6 0 obt!i&~t2~Anb+ 1 :1 complexes 1 :2 complexes FIG.1.-Fluorescence (---) and phosphorescence (-) spectral shifts. 0,CHCl3; 0,C2HC15. a 1 :1 complexes 1 :2 complexes FIG.2.-Discrepancies between spectral shifts measured in absorption and emission. 0,CHCI, ; 0,CzHC15. (4) Complexing with CHC13 or CHC12CC13 quenched the fluorescence and in- creased the phosphorescence :fluorescence ratio, see fig. 3, though with mesitylene- CHC13 the increase was negligible. Complexing also accelerated the phosphorescence decay ; the acceleration was invariably smaller in complexes with CHCI2CCl3 than with CHC13, see table 1 and fig. 4. (5) The phosphorescence was completely quenched in complexes with the di- and HYDROGEN BONDED AROMATIC COMPLEXES tri-chloroethylenes.Photochemical experiments with frozen solutions of cis-1,2-dichloroethylene (8 mmol dm-,) and benzene (0.1 mol dm-3) or hexaethylbenzene (8 mol dm-,), established the occurrence of photosensitised cis-trans isomerisation at 254 nm, consistent with quenching via triplet-triplet energy transfer within the association complex. 260 300 340 380 420 260 300 340 380 420 260 300 340 380 420 4 wavelength/nm FIG. 3.-Fluorescence and phosphorescence spectra of benzene hydrocarbon-halogenoalkane complexes, measured in 3-methylpentane at 77 K. -, pure hydrocarbon, ---,+ CHC13, _._.-,+ C2HCI5(fluorescence bands for mesitylene have been displaced). I0 20 so40 024 6 --024 6 0 02468 0 4 8 12 I6 tls FIG.4.-Phosphorescence decay of aromatic complexes at 77 K in 3-methylpentane.-,Pure hydrocarbon solute ; ---,+ CHC13; ----, + C2HC15. (6) The phosphorescence of glassy solutions of uncomplexed aromatic hydro- carbons decayed exponentially but in many of the complexes with CHC1, the decay was markedly non-exponential ; this was particularly evident with [2H,]benzene and mesitylene, see fig. 4 and 5. On the other hand when bulky groups were introduced into the benzene ring or when CHC12CC1, replaced CHCl, the decay became more and more closely exponential. For example, the phosphorescence of the hexa- ethylbenzene-CHCI, complex decays exponentially over at least five natural lifetimes, see fig. 4. J. P.SlMONS AND A. L. SMITH TABLE1 .--PHOSPHORESCENCE LIFETIMES IN 3-METHYLPENTANE AT 77 K TpCHC13 rPCDCl3 T~CHCI~CC~~TO benzene 5.3 0.9** I .7 2.0* [’H Jxnzene 9.9 1.1*** 3.2 3.2* 1 : 1 ttoluene 7.5 1.3** 2.4 2.8 t-butyl benzene 2.7 0.8** 1.7 1.5 I o-xylene 8.O 1.8** 3.5 2.0 rn-xylene 8.5 1.5** 3.5 2.7 p-xylene 8.8 1.8** 3.8 3.O mesitylene 7.6 0.8*** 3.4 2.3 2:l. octahydroanthracene 10.2 1.1* 2.0 3.2 octahydrophenanthrene 5.9 1.4* 2.2 3 .O 1,2,4,5-tetraisopropyI benzene 4.1 2.0 1.8 3.1 hexamethylbenzene 5.3 1.6 1.8 2.7 hexaethy Ibenzene 8.6 2.9 2.9 -non-exponential decay : *** strong, ** moderate, * slight.Fii0 4 8 12 16 \\ @IF b ‘. a:02 4 6 8 0246802468 tls FIG.5.-External deuterium isotope effect on phosphorescence decay in 3-methylpentane at 77 K.Complexes with CHC13,-; with CDCI3,---. (7) Substitution of CDCl, for CHC13 increased the phosphorescence intensities of the benzene and [2H,]benzene complexes by factors of two and three, respectively, but had no effect on their absorption or fluorescence ~pectra.~ The phosphorescence lifetimes increased in approximately the same ratio (though they were still shorter than those of the uncomplexed benzene), and in complete contrast to CHC1, the decay became accurately exponential again, see fig. 5. Similar behaviour was observed with the lower alkyl substituted benzene derivatives. In complexes with more sterically crowded molecules the external deuterium isotope effect was less marked and it disappeared entirely in the complexes with 1,2,4,5-tetraisopropyl-, hexamethyl- and hexaethyl-benzene, see table 1 and fig.5 and 6. (8) Complexing with CHC13 or CHC12CC13 suppresses the formation of the benzylic radicals 1* and 3-methylpentyl “solvent ”radicals (observed through their u.v.~and e.~.r.~spectra, respectively), and also the “solvent-substituted” hexatrienes l* that are formed through U.V. irradiation of the frozen glassy solutions. There is instead, a HYDROGEN BONDED AROMATIC COMPLEXES photochemical reaction with the associated halogenoalkane which produces a lialogen-substituted hexatriene.l Substitution of CDCl, for CHC1, and/or the introduction of bulky side groups suppressed even this reaction. h 260 300 340 380 420 250 300 340 380 420 460 wavelength/nm FIG.6.-External deuterium isotope effect on the fluorescence and phosphorescence spectra of complexes with CHC13.-,CHC13; ---,CDC13. FLUORESCENCE AND PHOSPHORESCENCE SPECTRA Examples of the total luminescence spectra of a range of alkyl substituted benzene derivatives complexed with CHC1, or CHC1,CCl3 were shown in fig. 3. The general observation that the fluorescence efficiency decreases on complexing with chloro- alkanes while in most cases, the phosphorescence :fluorescence intensity ratio increases, parallels the behaviour observed in systems where external spin-orbit coupling enhances the rates of intersystem cro~sing.~ Consistent with this, com- plexing hexaethylbenzene with CHF, hardly altered the phosphorescence :fluoresc-ence ratio or the phosphorescence lifetime but complexing with CHC1,Br reduced the total luminescence intensity to a level below the limit of detection. The fluorescence was partially quenched in complexes with chloroalkenes but unlike the chloroalkanes, the phosphorescence disappeared entirely. As discussed earlier, this is due to the intervention of triplet-triplet energy transfer which can lead to cis-trans isomerisation of the acceptor.Since the quantum efficiencies of isomerisation in the 1,2-dichloro- ethylenes are known from other measurements ** the photo-sensitisation would provide a method of estimating the quantum efficiency of intersystem crossing in this particular case, i.e. modified by the presence of the external C1 atoms.The vibronic structure of the fluorescence spectra was not altered by complexing FIG.8.-Molecular conformation of the hexaethylben~ene-CHCl~ complex. To face page 591 J. P. SIMONS AND A. L. SMITH and, with the cxception of benzene and to a much lesser degree, its iiionoalkyl substi- tutsd derivatives, it had little effect on that of the phosphorescence spectra either. The dominant vibrational progressions, which have wavenumbers -1000 cm-l (fluorescence) and -1600 cm-1 (phosphorescence), probably correspond to the ring breathing and quinoidal stretching modes, v,(alg) and v,(e,& of benzene. In the benzene complex itself, the progressions in v1 dominate both the fluorescence and the phosphorescence spectra.The fluorescence spectral origins remained very weak in all cases ; there was some intensification of the spectral origin in the phosphorescence of the mono-alkyl substituted benzene complexes and of the progression in v1 based upon it but in comparison with the changes observed with benzene the increases were small and the effect rapidly disappeared with further alkylation of the ring. The ,Blu state in benzene is uniquely sensitive to an external perturbation lo such as that introduced by complexing, because of its susceptibility to a "pseudo Jahn- Teller '' distortion when the intramolecular vibronic coupling acts in conjunction with an external field.ll Nieman l2 has suggested that the changes in vibronic structure caused by substituting alkyl groups into the ring could be understood if they act as "particularly intimate solvent molecules " providing an internal field which stabilises the distortion in the triplet state. Since complexing does not affect the vibronic structure in the phosphorescence of poly-substituted alkylbenzenes, the imposition of an external perturbation does not seem to promote any further dis- tortion when the internal perturbation is sufficiently strong.MOLECULAR CONFORMATIONS Fig. 7 shows the near U.V. absorption spectrum of hexaethylbenzene in solution in 3-methylpentane at 77 K, before and after U.V. irradiation, alone and complexed with CHC13. As with all the other benzene hydrocarbons, complexing has shifted the absorption spectrum to the higher frequencies : it has also suppressed all photochem- ical activity.The hexaethylbenzene-CHCl, complex was the most stable of all those studied : discrete spectral shifts were recorded at temperatures as high as 230 K (cf. 130 K with benzene). Despite this stability no evidence for complexing could be obtained when the bulkier molecule CHCl,CCl,, was substituted for CHC1,. For example, fig. 7 shows that pentachloroethane promotes no spectral shift nor does it suppress the formation of benzylic radicals on irradiation. It has no effect on the fluorescence or phosphorescence spectra either and does not alter the phosphorescence lifetime. However, CHC12CC13 does form 1 :1 and 1 :2 complexes with all the methyl substituted benzenes, including hexamethylbenzene, where the steric crowding is less severe.There is much evidence, particularly from n.m.r. studies,13 that in complexes of CHC1, with benzene and its alkyl homologues in fluid bulk solution, the C1,C-H bond tends to be perpendicular to the plane of the aromatic ring. With CHC12CC13 the extra bulk of the CCl, group would prevent alignment along the symmetry axis and preclude close association but fig. 8 shows how CHC13 and hexaethylbenzene can form a compact structure with this conformation. The increased spectral line widths apparent in absorption and emission in the less heavily substituted complexes probably reflect the spread in conformations that can exist when there are no bulky groups to keep the C-H bond aligned along the central axis perpendicular to the ring.Subse-quent discussion will show that this interpretation is consistent with many other observations. The S,-+S, absorption bands of the aromatic molecule were shifted towards HYDROGEN BONDED AROMATIC COMPLEXES higher frequencies in all the complexes studied but while the direction of the frequency shifts was retained in the emission spectra their magnitudes differed from those measured in absorption. The discrepancy decreased with the level of substitution both in the aromatic ring and in the halogenoalkane. Relevant data are presented graphically in fig. 1 and 2. 2 t d 0 I 0 (a)250 275 300 325 350 375 common in hydrogen bonded systems l4 and also in fluid media where there are changes in solvation following photo-excitation.The present observations can be understood if the excited complexes relax into a more stable codormation within the lifetime of the excited state, even though the medium is a rigid glass, frozen at 77 K. Relaxation in the excited state will promote a complementary destabilisation of the ground state and the spectral shifts measured in emission will be less than those in absorption, see fig. 9. The data in fig. 1 and 2 imply that structural changes occur in both excited singlet and triplet states provided the changes are not further restricted by the presence of bulky substituents. When this proviso is not met, as for example in the hexaethylbenzene-CHC1, complex, the spectral shifts observed in absorption and emission are almost equal.Similarly when CHC13 is replaced by CHC1,CCl3, the disparity between the spectral shifts measured in absorption is always reduced. The questions now arise as to the nature of the intermolecular interaction and of the changes in conformation which accompany excitation into the first excited singlet and triplet states. For interaction to occur, the presence of the H atom in the halo- J. P. SIMONS AND A. L. SMITH geno-alkane or -alkene is essential. Hexaethylbenzene forms specifically oriented complexes with CHF, and CHBr, as well as CHCl,, but not with the fully substituted methanes ; benzene forms complexes with CHC13, CHC12CC13 and CHC1=CC12 but not CC14, C2Cl, or C2C14.1 Thus association probably involves interaction of electrons in the n-system of the ring with the weakly acidic proton on the halogeno- alkane or -alkene.This would help to account for the intermolecular vibronic coupling in the triplet state revealed through the external deuterium isotope effect ; electrons circulating in the aromatic ring would then be sensitive to the motion of the H atom in the halogeno-alkane, (see later discussion). It is also consistent with the increase in stability with increasing alkyl substitution in the ring. uncomplexed cornpIexed SO \ +“dy’riI ’ \ \ / FIG.9.-Origin of spectral shifts in benzene-halogenoalkane complexes. Seq and SFC indicate singlet states with equilibrium and Franck-Condon conformations, respectively.The following observations show that the changes of conformation are rather more subtle. (1) The substitution of bulky groups either in the aromatic ring or in the halogeno- alkane, restricts the ability of the excited complexes to relax into more stable con-formations. (2) In each complex the spectral shift was toward higher frequencies both in absorption and emission; this can only arise if the intermolecular interaction is weaker in the excited complex than in the ground state. If relaxation involved attraction of the halogeno-alkane toward the plane of the ring, e.g. because of an increase in the polarisability of the aromatic hydrocarbon in the excited state, a stronger interaction would be implied. While this could account for the steric hindrance it could not account for the shift of the emission spectra to higher frequencies relative to the uncomplexed hydrocarbons.Repulsion would account for the shifts to higher frequencies but not the steric hindrance. Thus the HYDROGEN BONDED AROMATIC COMPLEXES relaxation process cannot be ascribed simply to a change in the equilibrium inter- molecular distance perpendicular to the ring ; the polarizability cannot be an import- ant parameter in determining the stabilities of the complexes. Two alternatives may be considered : either the halogeno-alkane molecule twists about the C-H bond axis or it tilts at an angle to the plane of the ring so that the C--H bond is no longer directed toward the centre of the ring. Although both changes would be restricted by steric hindrance the occurrence of tilting can also account for the phosphorescence behaviour discussed below.PHOSPHORESCENCE DECAY; STERIC AND EXTERNAL DEUTERIUM ISOTOPE EFFECTS Measurement of the phosphorescence decay revealed the following major trends, see fig. 4 to 6. (1) In lightly substituted benzenes the phosphorescence of complexes with CHC13 decayed non-exponentially. When CHC1,CC13 was substituted for CHC1, the rate of decay was slower and much more nearly exponential. Substitution of CDCl, for CHC13 reduced the rate still further ; the kinetics became accurately exponential and the triplet lifetimes (7,) and phosphorescence efficiencies (+,) always increased in the same ratio, T:/T;-#:/@.Since deuterium substitution had no effect on the fluorescence efficiencies or integrated absorptions the external deuterium isotope effect can be ascribed solely to a reduction in the rate of radiationless decay of the triplet ~tate.~ (2) In complexes with heavily substituted benzenes the phosphorescence decay was exponential in all cases and the external deuterium isotope effect disappeared completely. The recovery of an exponential decay law with increasing substitution can be understood if steric crowding forces the complexes to adopt a unique conformation. Fig. 8 shows that this would be one which funnels the halogeno-alkane down the central axis lying perpendicular to the aromatic ring. When such a conformation is achieved there is no deuterium isotope effect on the rate of decay of the triplet state.This is not surprising because the three nodal surfaces of the B1, electronic wave function intersect along the central perpendicular axis and with the external acidic proton lying on this axis, intermolecular vibronic coupling could not occur. On the other hand, if the halogeno-alkane molecules could tilt so that the proton were moved away from the central axis some vibronic interaction would be possible. Its strength would depend on the angle of orientation and in the absence of steric hindrance the spread of orientations would lead to non-exponential decay of the triplet state. In complexes with CHC1,CCl3 the extra bulk of the CCl, group would make tilted conformations much less likely, particularly when alkyl groups are substituted into the benzene ring.This would reduce the strength of the vibronic interaction as well as its angular variation and permit the slower, near exponential decay observed experiment- ally. In summary it is proposed that non-exponential decay of the triplet state is associzted with a radiationless decay path introduced by intermolecular vibronic coupling. Its contribution effectively disappears when bulky substituents force the halogeno-alkane molecule to remain in a conformation in which the acidic proton lies on the central axis perpendicular to the aromatic ring, or when the proton is replaced by deuterium. The residual acceleration in the decay of the triplet state can be ascribed to heavy atom perturbation by the C1 atoms.Inspection of table 1 shows that the intermolecular vi bronic coupling is actually very weak since the ratio TF/T,W 64 ; J. P. SIMONS AND A. L. SMITH indeed it can only be detected in the triplet state because the competing decay pro- cesses are so slow. Processes ocurring in the much shorter lived, excited singlet state are unaffected by external deuterium isotope substitution. The authors are grateful to Mr. S. Travers and Mr. R.Dackus for assistance in the design and construction of metal and silica cryostats and thank the S.R.C. for a grant and also a research studentship (to A. L. S.). N. C. Perrins and J. P. Simons, Trans. Faraday SOC., 1969, 65, 390. N. C. Perrins, J. P. Simons and A.L. Smith, Trans. Faraduy Soc., 1971, 67, 3415. J. P. Simons and A. L. Smith, Chem. Phys. Letters, 1972, 16, 536. I. Norman and G. Porter, Proc. Roy. Soc. A, 1955,230,399. B. Brocklehurst, W. Gibbons, F. T. Lang, G. Porter and M. Savadatti, Trans. Faraday Soc., 1966,62,1793 ; B.N. Shelimov, N. V. Fok and V. V. Voevodskii, Doklady Akad. Nauk S.S.S.R., 1962, 144, 596. E. Migirdicyan, J. Chim. phys., 1966, 63, 520. S. P. McGlynn, T. Azumi and M. Kinoshita, Molecular Spectroscopy of the Triplet Stuk (Prentice Hall, Englewood Cliffs, N.J., 1969), p. 316.* Z. R. Grabowski and A. Bylina, Trum. Faraduy SOC., 1964, 60,1131. G. R. DeMare, M.-C. Fontaine, G. Huybrechts and M. Termonia, J. Photochem., 1973, I, 289. lo G. W. Robinson, J. Mol. Spectr., 1961, 6, 58. l1 J. Van Egmond, D. M. Burland and J. H. Van der Waals, Chem. Phys. Letters, 1971, 12, 206. G. C. Nieman, J. Chem. Phys., 1969, 50,1674. l3 C. J. Cresswell and A. L. Allred, J. Clzern. SOC.B, 1967, 540; A. A. Bothner-By and R. E. Glick, J. Chem. Phys., 1957, 26, 1657. l4 N. Mataga and T. Kubota, Moleculur Interactions arid Electronic Spectru (Marcel Dekkcr, New York, 1970), p. 342. l5 E. G. McRea, J.Phys. Chern., 1957, 61, 562.

ISSN:0300-9238    

DOI:10.1039/F29747000053

出版商:RSC    

年代:1974

数据来源: RSC

摘要:

Quaiiturn Theory of Concerted Protoii Transfer Reactioiis in Polar Media Linear Electronic Terms BY REVAZR. DOGONADZEAND YURIJI. KHARKATS Institute of Electrochemistry of the Academy of Sciences of the U.S.S.R., Leninskij Project 31, Moscow V-71, U.S.S.R. AND JENSULSTRUP" Chemistry Department A, Building 207, The Technical University of Denmark, 2800 Lyngby, Denmark Received 9th May, 1973 A quantum mechanical theory has been developed for concerted two-proton transfer reactions in polar media. The formulation is based on second order quantum mechanical perturbation theory ; this assumes that the intermediate state, i.e., the state prevailing after the transfer of the first proton, is short-lived compared with the uncertainty time of the system. The energy of activation Ea of the overall process is determined by the value of Ea for either the first or the second proton transfer, and it is shown how, at least in principle, a distinction from a one-proton and a consecutive two-proton transfer reaction can be made.Important qualitative and semiquantitative correlations between energy of activation and overall energy of reaction are predicted, and the Brransted coefficient and pre- exponential Arrhenius factor are discussed. 1. INTRODUCTION The concept of general acid base catalysis of proton transfer reactions in aqueous and other polar media has been accepted for a long time in physical organic chem- istry.l* For most cases of such reactions the Brarnsted relationship (eqn (1.1)) log k = const.+aApK (1.1) is applied for a quantitative phenomenological description. k is here the rate con- stant, ApK the difference in pK values between the acid and base, and a the Brarnsted coefficient. In general, a changes from zero to unity over a ApK range which can be related to various important kinetic parameters, such as the energy of reorganization of the solvent and of the internal degrees of freedom. The usual application of the Brarnsted relationship implies that the rate determining step is a one-proton transfer (or-for high values of ApK-diffusion of the reactants to form a reactive collision complex 4). However, in chemical and enzymatic proton transfer reactions, two or more protons are commonly transferred, and the highest energy barrier may be connected with several of these, if the ApK interval is wide enough. This may in some cases require a reinterpretation of the Brarnsted plots. Several formulations of a quantum mechanical theory of one-proton transfer 64 R.R. DOGONADZE, YU. I. KHARKATS AND J. ULSTRUP reactions in polar media have been A complete theory should, however, take into account all proton transfers and predict the conditions under which one particular transfer becomes rate determining. In this respect the problem arises whether the proton transfers occur consecutively, i.e., in such a way that all the degrees of freedom of the system relax into their equilibrium configurations after each step, or whether they occur " simultaneously ",i.e., so that the intermediate states are very short-lived compared with the relaxation times of the system.It is obvious that consecutive proton transfers would not present any new theoretical features, and the overall rate constant can immediately be deduced from the rate constants of the individual proton transfers. On the other hand, concerted reactions require that account be taken of some special features of quantum mechanical virtual states ; a partial reformulation of the theory of one-proton transfer reactions is therefore required. In a previous communication,'* a semi-quantitative theory of concerted two- proton transfers in a polar medium was formulated. Parabolic electronic terms '' were used, which resulted in a Gaussian dependence of the overall probability of proton transfer on the quantum numbers of the protons in the various states.The summation over these numbers could therefore not be carried out, and the final result was obtained from an estimate of the contribution from each proton quantum state. For linear electronic terms the dependence becomes exponential. The present work shows that an exact summation then becomes possible, and that the final result has the same physical meaning as for parabolic terms. 2. MODELS FOR THE REACTING SYSTEM Two mechanisms for a double proton transfer can be distinguished, corresponding to general base and general acid catalysis A-H + B-H + C+ A + H-B-H + C+A + H-B + H-C (2.1) A-H + B-H + C+A-H + B+ H-C+A + H-B + H-C. The elementary reaction steps are to be conceived as proton transfers, but for the sake of clarity the chsuges have been omitted.The initial and final states of the two mechanisms are the same, whereas the intermediate states are clearly different and have different values of the total potential energy. In the following we shall consider only the base catalysis (eqn (2.1)). The calculztions for the acid catalysis are quite analogous.For the sake of simplicity we neglect reorganization of the internal degrees of freedom of the reacting molecules ; these reorganizations could be appropriately accounted for in terms of a general theory of electron transfer.12 The total system can then be divided into three subsystems, i.e., the electrons, the protons and the solvent, with each of which is associated a set of characteristic frequencies.In the dielectric continuum approximation (which is adopted here) the solvent frequencies c1) are those of the polarization fluctuation, and from measurements of absorption of electromagnetic radiation in the Debye range these frequencies are found to be of the order lo1' s-l. Since the corresponding energy hco<kT at room temperature, the solvent frequencies can be considered classical. The characteristic proton vibration frequencies i2 are usually of the order 5 x 1014 s-l, which is one or two orders of magnitude higher than kT at room temperature. The proton movements must therefore apriori be treated quantum mechanically. This is also true for the electrons, the characteristic frequencies of which are of the order 1015-1016s-l.11-3 THEORY OF CONCERTED PROTON TRANSFERS 3. WAVE FUNCTIONS AND TERMS The large differences in the characteristic frequencies of the three subsystems allow application of the double adiabatic approximation.6 The total wave functions of the initial (i), intermediate(k)and final (f)state are written as products of the wave: functions of each of the three subsystems Yi(x, 51, 529 4) = $i(x; 51,523 4)4i(51,52 ;q)x(q-qio) yk(x, 51 -510, 52, 4) = $k(x ;51-510, 527 q)4k(51-510, 52 ;q)x(q-qkO) (3.1) 'u,(x, 51 -510,52-520, 4) = $f(X;51 -510, 52 -520,4)4f(51 -5107 52 -520 ;q)x(4-4.f0). Y is the approximated total wave function, while $, 4 and x are the electron, the proton, and the solvent wave functions respectively. x represents the set of electron coordinates, q a generalized dimensionless solvent coordinate (for the sake of sim- plicity a 0n.e-d.imensiona1 solvent description is used), the qo's represent the equilib- rium values of this coordinate, el and c2the dimensionless coordinate of the first and second proton (equilibrium value zero), and Cl0 and 520the equilibrium valuesofc, and C2 after the transfer of the appropriate proton.We assume that the proton movements are adequately described in the harmonic approximation, i.e., for the 4's we shall use wave functions of the form 4:; and 47; are the wave functions for the first and second proton respectively, n1 and n2the vibrational quantum numbers of these protons, and H,, and H,,the Hermitc polynomials of order n1and n2.Analogous expressions can be written for cjkand 4f. For x a similar expression could be used. However, since the solvent at room temg- erature exists in a highly excited state, we shall make use of the quasiclassical approxi- mation 9* 14* l5 for the solvent. In the region of classical movement we shall, therefore, for x use functions of the form x(q-qi0) = Cp-' cos {k-l p dq -~/4 (3.3)S' I where C is a normalization constant, p the nzomentum, and a the left hand turning point. This allows us to apply a result obtained previously for concerted electron transfer reactions in polar media. l4 In the general case, the values of the proton frequencies differ from each other in the various states.However, since the difference is usually small, and since a full account of the differences complicates the calculations considerably, we shall in the following assume that all the proton frequencies have the same values. The total potential energy of the system in the various states as functions of the proton and solvent coordinates (the electronic terms) can be written The 1,'s are the equilibrium energies of the system, including that arising from the interaction among the reactants and the solvent, and the e's characterize the slopes of the electronic terms. Since the E'S mainly depend on the solvent frequencies, and since the latter can be considered constant in the various states, we shall put E~ = R.R. DOGONADZE, YU. I. KHARKATS AND J. ULSTRUP &k = Ef = E in the following. In the harmonic approximation the electron-proton terms become Ui = Jio +hQn, +hQn2 +Elq-qiol Uk = Jko+hnm +hQn, +E 1q-qkoI (3.5) uf= Jfo +hml+ tihz +Elq-qfOl where mland m, are the proton quantum numbers in the final state, and the Zo’s include the zero-point energies of the protons. The electron-proton terms corresponding to the ground states of the protons are plotted in fig. 1. For higher proton states the terms are shifted vertically upwards by integral multiples of kSZ. It will be assumed that no change in the solvent equilibrium coordinates occurs when the protons are excited. u 4io 4ko 4fo 4 FIG.1.-Linear electron-proton terms for the initial (i), intermediate (k)and final (f)states, corres- ponding to Eg >E;.Ground states of the protons. 4. EXPRESSION FOR THE OVERALL PROTON TRANSFER PROBABILITY The overall probability per unit time Wfiof the concerted double proton transfer is calculated by second order quantum mechanical perturbation the01-y.~ It is given by wfi = 2n/hAvi 6(Ei-Ef)1 (yfl vfklyk)(ykl vkilyi)/(Ei-Ek+ir)l (4*1)f k where Avi indicates a thermal averaging over all initial states, Zkand Zfare summa- tions over all intermediate and final states, and 6(E,-E,) indicates that the total energy is conserved in the overall process. r is an infinitesimally small positive number, and i = J-1. V,, and Vfkare the interaction operators between the initial and intermediate, and the intermediate and final state respectively.Averaging over initial proton and solvent states and using the double adiabatic approximation,6 Wfi can be written ‘Q; ’ exp { -hQ(n, +n2)/kT)Xwfi= 2n/hl i/fkI21vkil2Q; vnln2 exp { -tzul(v+~)*/kT] IM,,J26(E,-E,). (4.2)Pnllwz 68 THEORY OF CONCERTED PROTON TRANSFERS v and p are the solvent quantum numbers of the initial and final state respectively, Ql and Q2the statistical sums of the solvent and protons, i.e., aJ Q, = exp {-hw(v+f)*/kT) (4.3) v=o 03m Q2= 1 exp(-fiR(n,+rz2)/li7') = [l-exp(-tlR/kT)]-~ = I. nl=0 nz=O and I Vk,12I VfkI2 are the electronic matrix elements at the values of 5 and q, which give a maximum contribution to W',. Furthermore where I, and I2 are the proton, and A the solvent quantum numbers of the intermediate state.Using the harmonic approximation for the proton wave functions, it is found that in the summation over I, and I, only those terms differ from zero for which I, = m,, and n2 = 12. Also, since ho-gkT,the solvent energy levels are so closely spaced, that the summations over ,u and iz can be replaced by integrations over the correspond- ing energy levels. This gives for Wfi where pi exp (-Ei/kT)dEi.Jn I n2 i0 The p's are the densities of the solvent states, and the values of the lower integration limits include the proton energies. Use of the results of previous calculations l4 for Z finally gives Wfi= &r3ft-8~-i(kT)-1 V,,I2 xI VJkI21 Elk and Ekfare the energies of the intersection points between the intermediate and either the final or the initial term, respectively.They are clearly functions of the proton quantum numbers. For the linear terms it is found that IEki-Jrdn2= $(Eki+AJ;;) +$hQ(~n-rt ) (4.8) E/k -Jn'n2 = $(Er d-AJ&)++hQ(WI2 -122) +AJzi +hR(I~Z -11 1) (4.9);O R. R. DOGONADZE, YU. 1. KHARKATS AND J. ULSTRUP 69 and E,, -Eki = f(Eik+AJ;,) -+(Ef'+AJ&)+$hn(m,-n, +m2-n,) +AJii. (4.10) E, is the energy of reorganization of the solvent for the step indicated by the superscript (approximately independent of the proton quantum numbers), and A.7' the heat of reaction corresponding to the ground states of the protons. Introducing the harmonic approximation for the proton wave functions and calculating the matrix elements l6 we can write for Wfl Wsi = ~713h-30-"kT)-1(IEfk-El;il)-~exp {-(Epl +E,,)/hQ) x S, (4.1 1) where S = S, +Sz 3) The L's represent Laguerre polynomials.ED,and ED2are the respective energies of reorganization of the two protons (Epl = 4hQc:o, and Ep2= &FIQ[$~). The factor (IEfk -Ekll)-*has been taken outside the summation signs, since, in contrast to the other factors, it depends slowly on the proton quantum numbers. As opposed to the case for parabolic terms,1° the exponents here depend linearly on the proton quantum numbers, and it is therefore possible to carry out the summations. 5. SUMMATION WITH RESPECT TO PROTON STATES From eqn (2.5) it is seen that for given values of n, and m2an increase in n2 or in1 will shift the initial and intermediate terms, or the intermediate and final tams respectively, upwards by the Same amount relative to the remaining term.However, an increase in n, or m2for given values of n2 or m,will only shift the initial (n,) or final (m,)term upwards with respect to the other terms. The summation over all the quantum numbers is therefore complicated by the change in the relative values of Efk and &i with increasing values of n,, 1z2, In, and m2,and both eqn (4.12) and (4.13) must be applied. From fig. 1 can be obtained an illustration of the necessary number of proton states to be considered. Since the slopes are (numerically) uniform and in order that the intersection points can be defined, it is necessary that (Ef'+AJ,Oi)/frQ> H 1 -1711 > (AJ,Oi-E:')/hR (5.1) and (ESk+AJ;k)/hn > n2-in2 > (AJ&-E:k)/hQ.(5.2) Also, Efk2Eklfor nl-~n,+n2-nz, 5 2(E;,-EE,o) = E{k-E:i+AJ;k+AJLi. (5.3) THEORY OF CONCERTED PROTON TRANSFERS Plotting (n,-m,)against (n, -m,) according to eqn (5.3) (fig.2a and 2b) the area in the (nl -m1)/(n2-m2) plane over which the summations should be carried out, can be defined. Only the unshaded areas give contributions to the sums, and it is shown for which corresponding values of (n,-ml) and (n,-m,) Efk)<Eki.For Efk>Ekieqn (4.13) should be used, for Efk<Ekieqn (4.12). In the following we shall consider the case for which Ekl>Efk (fig. 1) which is illustrated in fig.2a. The first summation (eqn (4.12)) can be written S; = c m2!/n2!(Ep2/hQ)"2-n'2[L~2-m2~(Ep2/hQ)]2exp (-hQn2/kT)x S'i (5.4a) n2m2 where Sl; = c ml!/nl!(Epl/h~).1~~"1[~~~~"1~(Epl/hS2)]2exp (-tlQ(n, +m1)/2kT). (5.4b) nlml The summation should here be carried out over the area in fig. 2a where Ekl>Efk. However, instead of estimating this area we sum over all values from zero to infinity with respect to the proton quantum numbers nl, m,and n2. This gives a sum which is bigger than that required. On the other hand, the extended summation allows us to express the Laguerre polynomials in terms of Bessel functions and to make use of the asymptotic approximation for the latter, since the arguments are l6 Carrying out this summation in the same way as previously, and using the fact that hQ$ kT,we find that the total summation gives mf S1= exp { -(Eii-Jl;)/kT) mz=O (rn2!)-1(Ep2/f2R)mz.(5.5) This shows that only the value zero for n,, n2 and m,gives a significant contribution to S1.mz is here the upper limit of m2for which Egi>Ejk, when n1 = n2 = m, = 0. The effective number of proton states giving finite contributions to S, is illustrated by the thick line in fig. 2a ; they are all seen to be situated within the area where Eki>Efk, which justifies the extension of the summation with respect to n,, n2 and ml to the interval 0-co. The second summation (eqn (4.13)) can be written S; = c n2!/m2 x!(Ep2/hn>m2-n2[L~:-n2(Ep2/hQ)]2 nm2 exp { -hR(n2 +m2)/2kT)S! (5.6a) where Sli = c m,!In,!(E,,/hn~1-m1[L~~-m1(Epl/hn)]2exp (-hRrn,/kT).(5.6b) nlm Calculating at first Sg, extending formally the summation with respect to (n,-m,) to the interval 0-co, we find msx where n;"axis the maximum value of n, for which Efk>Eki,when m, = 0. Eqn (5.7) shows that m, = 0 gives the main contribution to Sg. Inserting this result into eqn (5.6a), changing the order of summation, and extending formally the summation range with respect to n2-rn, to the interval 0-m we find nYax Q, S; = (n2!)-1(Epl/hfi)"1 (m2!)-1(Ep2/hQ)m2exp (-hQrn2/2kT) (5.8) n1=0 m2 =myin which shows that the main contribution to Siis obtained for n2 = 0. The summation range for m,-for a given value of n,-is from m2 = myin = n,+mz+ 1 to infinity, R.R. DOGONADZE, YU. I. KHARKATS AND J. ULSTRUP where nzz is the highest integer lower than 2(E,"i-E3/fiQ. This is seen from the inequalities of eqn (5.1)-(5.3) and from fig. 2a. The extra term + 1 arises from the fact that the points in the (n,-m,)/(n,-m,) plane corresponding to proton vibra- tional states form a discrete set, and that only in special cases can the condition Eki = Efkbe fulfilled for integral values of m2. Carrying out the summations with respect to m2 and n, it is seen that the main contribution to the sum is given by the lowest values of n1 and m2,or S$ = [(m~+l)!]-'(E,,/A~)":+lexp (-hR(rn;+1)/2kT). (5.9j This gives again S2 = [(m;+ l)!]-1(E,2/hQ)m:+ exp (-E,/kT) (5.10a) where E, = E;lk-J:o + hQ(rn; + 1)/2.(5.1Ob) The main contribution to S2is thus represented by the first point in the " S,-region " of the (nl-m,)/(n,-m,) plane along the thick line of fig. 2a, and corresponding to the value of mz = m, + 1. This point is situated in the region where Efk>Eki. Since the main contributions to the sum with respect to n,, n2 and m,is given by the value zero, the extension of the summations with respect to these proton quantum numbers, to the interval 0-00 is thus justified. Higher quantum states are formally included, but their contribution is negligible. t a (4 (6) FIG.2.-Plots of the inequalities (5.1)-(5.3) in the (nl -ml)/(nz-m2)plane. The closed rectangular areas indicate the summation areas for the proton vibrational quantum numbers, and the thick lines the main contributions to the sums.a, E,&> E;k ; b, < E& The total sum S was equal to S,+ S2. From the definition of m; it is seen how- ever, that in general hhz <2(Eii-E2k)<hn(rn;+ l). Since =7 kcal mol-l, and kTx0.6 kcal mol-1 at room temperature, the exponential factor of eqn (5.10a) will normally be considerably smaller than that of eqn (5.5). If, for example, the condition Eii = Efk correspondedto a value of m2halfway between two integers, the ratio between the two exponential factors would be about e3x33. In the pre- exponential factors the quantity EJhQ is about 5 (see below), and although in eqn (5.100) its exponent is higher than the highest one in eqn (5.5) by unity (thus causing a THEORY OF CONCERTED PROTON TRANSFERS factor 5 in the oppositc direction) this will not in general compensate for the difference in the exponential factors.The final result for Wfiwhen Eii>E;h can thus be written -1wJ~ ”(/~T)-’IvJL~~~Y,~~~= -,-~~X~~I-’CU exp [--(E,, i-~p~)/~~Q}(E~i-~’~~-~ iIf12 exp { -(E;i --,~jo)/k~j1(It72 !>-I(~~~/hR>)nl.(5.11) l!lL = 0 For Eii<E;, an expression analogous to cqn (5.1 1) can be derived. It can be shown that in this case Wfiis W’i= j3gx31h-’(!>-’(kT)-’ I V,,l I K,,+l exp { -(E,, + Ep2)/hQ](EJ,-Ekj)-x n: exp {-(E;,~-J,;)/~T) C (ill !)-‘(~~,/hR)”1 (5.12) 11, =o where, as before, nT is defined by the condition E;k =. Ehi. For concerted proton transfer reactions excited proton states are thus always involved for sufficiently large values of IEii-E;kI.However, because of the relatively large value of hQ, normally only one or a few terms would have to be included in the summations (see also below). 6. DISCUSSION AND COMPARISON WITH EXPERIMENT Expressions for the overall probability per unit time of two concerted proton transfers have been derived (eqn (5.1 1) and (5.12)). For the sake of simplicity only the “ normal ”range l1 of AJ has been considered, i.e., we have assumed that IAJI <E,. The expressions are formally equivalent to the ones obtained previously lo for para- bolic terms, i.e., the energy of activation is determined by the highest intersection point of the intermediate term with the initial or final term, corresponding to the ground states of all the protons.The pre-exponential factors contain factors expres- sing the effective numbers of participating proton energy levels, weighted by the factors (m,!)-1(Ep,/hC2)mzand (n,!)-l (EP1 respectively (actudly the squares of /hQ).l, the overlap integrals of the proton wave functions). This result is also formally equivalent to the result for electron transfer between two ions via a bridge with several participating electronic energy levels. The value of Efh(m2)in the pre-exponential factor of eqn (5.1 1) and E,,(n,) in eqn (5.12) depend on iii2 and n,,respectively. The dependence is weak however, and the values giving the maximum contribution to WfI (m;and n: respectively) should be inserted.Using values of 0.5 8, for the shift of the proton equilibrium coordinates and 5 x IOl4 s-’ for C2it is found that EJhRz 5. For relatively small n, and m2 it is therefore clear that the highest possible values of these quantum numbers give the main contribution to the sum. This is again due to the increased overlap of the proton wave functions with increasing quantum numbers. If-for the general base catalysis-we consider a series of closely related rcoctions with various bases for which E, and Ep cm be considered zpproximately constant, only the final term is shifted vertically relative to the initial and intermediate terms, while the latter two terms maintain their relative position. The only parameter varying is therefore dJ7k(and AJ;i). If the left hand intersection point is the higher, the energy of activation E, is determined by this point, and the observed E, should then show no dependence on the overall heat of reaction.If, by changing the base, the right hand intersection point becomes the higher, E, will be determined by this point and therefore increases with increasing AJ;i. For linear terms R. R. DOGONADZE, YU. I. KHARKATS AND J. ULSTRUP Since Eik and AJG are constants, application of linear terms thus predicts a straight line of slope 0.5 in the whole AJ;i range, when the right hand intersection point becomes the higher. The linear terms do not allow quantitative predictions about the detailed depend.ence of E, on AJ>i; thus, in most cases a smooth change in a is observed experimentally over AJ;i ranges comparable to E,.This behaviour would be described satisfactorily by parabolic terms which give expressions of the form 6*l1 E, = (E,+AJ)2/4Es (6.2) for the exponents of the activational factors of the elementary proton transfer steps. Although the characteristic "sudden " changes in a axe predicted by both sets of terms, the smooth changes are better described by the parabolic terms, and the following discussion will therefore refer to the latter. The total dependence of E, on AJ;i in general base catalysis is plotted in fig. 3a ; the transition region from a = 0 to a = 0.5 is of the order of a few multiples of kT (one or two pK units), whereas the change from a = 0.5 to unity occurs gradually (Le., within an approximate energy range of E,M 20 kcal mol-l).FIG.3.-Qualitative dependence of Ea on AJin general base catalysis for variable base (a)and variable acid (b). Same energy scale on the two axes. When the acid is varied, the initial term is shifted with respect to the intermediate and final term, while the relative position of the latter terms stays constant. When E, is plotted against AJ;i, and the left hand intersection point is the higher, a straight line of slope zero (the " activationless " region 11) is at first found. This value gradually changes into 0.5 within anapproximate range of Ef =20 kcal mol-l. When the right hand point becomes the higher, the slope changes from 0.5 to unity within a few multiples of kT. This behaviour is qualitatively illustrated in fig.3b. If, finally, the catalyst is varied, the intermediate term is shifkd with respect to the initial and final terms. In this case E, will change, while AJ:i remains constant. In the case of general acid catalysis the order of the proton transfers is reversed. The anticipated experimental behaviour is again illustrated by fig. 3a and 3b, except that now fig. 3a corresponds to a changing acid, and fig. 3b to a changing base. The foregoing discussion was based on a one-dimensional description of the solvent. Recently a theory of coupled electron transfix reactions via a virtual inter- mediate state was formulated using a many-dimensional description. 's It can be shown that also in this formulation changes in a are expected when the highest inter- section point (or minimum point on an intersection surface) is shifted from the right hand one to the left hand one, although in some cases less abruptly than for the one- dimensional description.The equations derived are based on the assumption of concerted proton transfer steps, as opposed to consecutive steps. In the latter case the two proton transfer THEORY OF CONCERTED PROTON TRANSFERS steps are independent of each other, and energy conservation factors referring to each step are introduced explicitly. On the other hand, although it turns out that the energy is effectively conserved also for concerted react ions, no energy conset vation factor involving the energy of the intermediate state is a priori taken into account.This means that a kind of " memory "effect works between the first and the second proton transfer step. The presence of concerted proton transfers is implied in various chemical reactions, and the possible distinction between consecutive and concerted mechanisms discussed at various places in the literature. Thus, the Grotthus mechanism of proton mobility requires the cooperating movement of many protons 19* 2o and is most conveniently envisaged as concerted proton transfers. A similar mechanism may work in the reaction between Hf and OH-, which possibly occurs via intermediate water mole- cule~.~ Reactions undergoing general acid base catalysis (keto-enol tautomerisni, hydra- tion-dehydration reactions, etc., as well as acid base enzyme reactions) must also involve the transfer of at least two protons and possibly several, as first suggested by Eigen.21 Bell deduced that rate terms containing the product of the concentrations of an acid and its corresponding base were indicative of a concerted rather than a step-wise mechanism.On this basis, kinetic investigations suggested that the former seldom occurs in hydroxylic, but more frequently in other solvents. However, analysis of more recent based mainly on phenomenological "extrathermo-dynamic " arguments,21*26 suggests that the concerted mechanism may also occur commonly in hydroxylic solvents. Very recently, simple theoretical calculations have been made 279 28 in order to distinguish between the two mechanisms. Thus, kinetic data show that in dioxan solutions the hydration of carbonyl compounds involves altogether three water molecules in the activated state, and that a cyclic configuration most conveniently explains the large negative entropy of activation observed.29 This would require the transfer of three protons. On the basis of a simple electro- static model it was found that the concerted mechanism requires an energy of activa- tion about twice as high as a consecutive mechanism, which is therefore the more probable. A similar conclusion would be reached for a two-proton transfer. This result is in pronounced disagreement with the one reached in the present and previous work.l0 It was realized, 28 that the electrostatic model is much too simple to provide conclusive evidence for one possibility or the other (e.g.,the specific nature of the reactants is only reflected in the partial charge on the oxygen atoms, the proton moves like a classical charged sphere, no account is taken of the solvent).Therefore, although the experimental data are extremely interesting, they leave open the question of cooperative movement. The theory developed in the present work at least in principle, although hardly in practice, provides an opportunity to distinguish between the two mechanisms. For consecutive reactions the observed rate constants are for eqn (2.l)'k kobs%kl for k-,<k, (6.3~) k,,,~k2Kfor k-l>k2 (K = kl/k-l). (6.3b) kl and k2 are the rate constants for the first and second step respectively, and k-, the rate constant of the back reaction of the first step.If the pre-exponential factors are not widely different the conditions (6.3~)and (6.3b) correspond to Eki>Efk,and Eki<Efk, respectively. For step-wise reactions kobs is, therefore, equal to a rate * For the sake of simplicity we omit additional diffusion and hydrogen bond formation steps. This does not represent a limitation of the considerations in the text. R. R. DOGONADZE, YU. I. KHARKATS AND J. ULSTRUP constant of one elementary step, as opposed to a concerted mechanism. Since the activational factor is the same in the two cases, the ratio between the observed rate constants equals the ratio between the pre-exponential factors. This ratio has somewhat different values for linear and for parabolic terms, but inserting reasonable values for the parameters of the system (E, = 1 ev, I vl = kT, IEki-EfkI = 0.1 eV, and o = 10 lls-l), it is found that k,,,, is higher than k,,,, by at least an order of magnitude, and the concerted mechanism is thus the more probable.This is compat- ible with a higher positive entropy of activation for the concerted mechanism, corres- ponding to the delocalization of two, rather than one proton in the activated state. Although for concrete models of the system a distinction is thus possible in principle, the estimate is rough, and the conclusion might well be reversed, if more accurate values of the parameters were available. The Bronsted coefficient a originally introduced as a coefficient in the Brnrnsted equation, expresses a relation between the energy of activation and the overall free energy or enthalpy of the reaction a = aE,la(AJ). (6.5) The variation of a with AJ (ApK) has been discussed in detail previously 49 6*29 for a number of systems, under the assumption that one particular proton transfer is rate determining throughout the whole ApK range.The present theory would predict the same correlations, even though parabolic terms are required for a quantitative agree- ment with the experimental data. Smooth Bromted plots are obtained when a plot of log k against ApK expresses the plot of E, against AJ, i.e., when E, and Ep are constant throughout a series of related reactants. Since E, and Ep are to a large extent determined by the dimensions of the reactants and by the steric conditions at the site of the proton transfer, the Bramsted plots are meaningful only when these factors are constant.Corrections for variable E, and Ep,as well as for reorganization of the internal degrees of freedom and the electronic structure can be made however, provided that suitable models for the reacting molecules in the polar solvent are available. Although many acid base catalyzed proton transfer reactions are known, a quantitative comparison with the present theory, with due account taken of the fact that different proton transfer steps may become rate determining in a series of reac- tions, is very difficult. Either more than two protons are transferred (e.g., hydration reactions), or the proton transfers are accompanied by the breaking of other chemical bonds (e.g., decomposition of diazocompounds).In any case, for two-proton transfer reactions, variation of either the catalyst or one of the substrates throughout a series implies that all the three electron-proton terms may move independently of each other, which leads to a complicated relationship between E, and AJ, not presenting a possibility of a straightforward test of the theory. Only if A differs from C in eqn (2.1) and (2.2) can a relatively sharp change in a, such as pictured in fig. 3a and 3b, be expected. This might happen in apparently simple acid base reactions in which a water molecule may serve as a bridge, but the literature only presents a few experimental data in favour of such a mechan-ism 1,2.4,22-25,30,31, .more data are needed in order to elucidate the composition of the activated complex of such reactions, in particular as to the number of water molecules involved. Consideration of a number of acid base catalyzed reac- tions 2*4*30*31 in general seems to reveal no abrupt changes in a, and although a concerted mechanism may well prevail in some cases, one particular proton transfer must therefore be rate determining throughout the series investigated. In one case however, i.e., the water-catalyzed enolization of the experimental points THEORY OF CONCERTED PROTON TRANSFERS give a distinct, relatively sharp (i.e,, a pK unit) change in a from 0 to about 0.5, followed by a gradual slight increase (fig.4). If this effect does not reflect experimental scatter or changes in E, and Ep,it may be explained by the participation of an extra bridge water molecule in the first, rate determining proton transfer step. The mechanism of this step could then be the following (the pull-push mechanism) /\CH=O + OH2+ OH2 -+ \CH=O + OH-+ HOH; /)CH=O+OH-+HOH; /-+ \C-O+HOH+HOH;. The horizontal part of fig. 4 represents the situation where the first step is the rate determining one (independent of the actual carbonyl compound) the line of slope 0.5 that where the second step has become rate determining (this step obviously depends on the nature of the carbonyl compound). The push-pull mechanism would predict a smooth change of a from zero (the activationless region 11) to 0.5 (the normal region l).The rate constant of the horizontal part corresponds to a proton transfer between two water molecules in the activated complex (e.g., of a cyclic configuration). Its value will in general differ from that corresponding to reaction between two free water molecules. FIG.4.-Plot of log k against pK for the water-catalyzed enolization of a series of ketones (from the compilation of ref. (32)). The solid line was drawn in order to indicate a smooth change of a. The broken line indicates an alternative correlation in agreement with a two-proton transfer mechanism, in which both the individual proton transfers may be come rate determining.R. P. Bell, The Proton in Chemistry (Methuen, London, 1959). M. L. Bender, Mechanisms of Homogeneous Catalysis fromProtons to Proteins (Wiley-Inter-science, New York, London, Sidney, Toronto, 1971).J. N. Bransted and K. J. Pedersen, 2.phys. Chem., 1924, 108, 185. M. Eigen, Angew. Chem., 1963,75,489. S. A. Bernhard, The Structure and Function of Enzymes (Benjamin, New York, Amsterdam, 1968).6V.G. Levich, R. R. Dogonadze, E. D. German, A. M. Kuznetsov and Yu. I. Kharkats, Electrochim. Acta, 1970, 15, 353.’R. R. Dogonadze, A. M. Kuznetsov and V. G. Levich, Electrochim. Acta, 1968,13,1025. R. A. Marcus, J. Phys. Chem., 1968,72, 891. L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Pergamon, Oxford, 1965). lo R. R. Dogonadze, J. Ulstrup and Yu.I. Kharkats, Doklady Akad, Nauk S.S.S.R., Ser. Phys.Chem., 1972, 207, 640. R. R. DOGONADZE, YU. I. KHARKATS AND J. ULSTRUP l1 R. R. Dogonadze, Reactionsof Molecules at Electrodes, ed. N. S. Hush (McGraw-Hill, London, New York, Sidney, 1971). l2 M. A. Vorotyntsev and A. M. Kuznetsov, Vestn. Moskov. Univ. Ser. Phys., 1970,2, 146. l3 J. A. Saxton, Proc. Roy. SOC. A, 1952,213,473. 14M. V. Volkenstein, R. R. Dogonadze, A. K. Madumarov and Yu. I. Kharkats, Doklady Akad. Nauk S.S.S.R. Ser. Phys. Chem., 1971,199, 124. l5 Yu. I. Kharkats, Elektrokhim., 1972, 8, 1300. l6 I. S. Gradstein and I. M. Ryjik, Tablesof Integrals, Sums,Series andproducts (Nauka, Moscow, 1971). l7 R. R. Dogonadze, J. Ulstrup and Yu. I. Kharkats, J. Theor. Biol., in press.l8 P. P. Schmidt, Austral. J. Chem., 1969, 22, 673. l9 M. Sheinblatt, J. Chem. Phys., 1962, 36, 3103. 'O B. Silver and Z. Luz, J. Amer. Chem. Soc., 1961, 83, 786.'' M. Eigen, Disc. Furaday SOC., 1965, 39, 7. 22 E. Grunwald, C. F. Jumper and S. Meiboom, J. Amer. Chem. Soc., 1963, 85, 522. 23 E. Grunwald and S.Meiboom, J. Amer. Chem. SOC., 1963, 85,2047. 24 E. Grunwald and C. F. Jumper, J. Amer. Chem. SOC.,1963, 85,2051. 25 Z. Luz and S. Meiboom, J. Amer. Chem. SOC., 1963, 85,2060. 26 W. J. Albery, Progr. Reaction Kinetics, 1967, 4, 353. 27 R. P. Bell, J. P. Millington and J. M. Pink, Proc. Roy. SOC.A, 1968, 303, 1. 28 R. P. Bell and J. E. Critchlow, Proc. Roy. SOC. A, 1971, 325, 35. 29 R. P. Bell and P. E. Ssrensen, J.C.S. Perkin II, 1972, 1740. 30 A. 0.Cohen and R. A. Marcus, J. Phys. Chem., 1968,72,4249. 31 E. D. German, R. R. Dogonadze, A. M. Kuznetsov, V. G. Levich and Yu. I. Kharkats, J. Hokkaido Res. Insf. Catalysis, 1971, 19, 115. 32 R. G.Pearson and R. L. Dillon, J. Amer. Chern. Soc., 1953,75, 2439.

ISSN:0300-9238    

DOI:10.1039/F29747000064

出版商:RSC    

年代:1974

数据来源: RSC

摘要:

Dielectric Relaxation in Non-aqueous Solutions Part 5.-Propylene Carbonate (4-Methyl-l,3-dioxolan-2-one) BY EDMUNDA. S. CAVELL Department of Chemistry, The University, Southampton SO9 5NH Received 6th July, 1973 The permittivity (E’) and loss (E”) of propylene carbonate (4-methyl-l,3-dioxolan-2-one)have been measured at several temperatures between 0” and 50°C in the frequency range 0.5 to 35 GHz. The overall frequency response of the complex permittivity is unsymmetrical but can be satisfactorily represented by the equation d(w)-id’(~) = +(E~-E~)/(~+iw7,,)5. The temperature dependence of the relative static permittivity (E~)is accurately described by the empirical relation, E~ = A exp(-LT), with A = 195.6 and L = 3.681 x K-l, although the dielectric relaxation times (T,,) do not fit the usual Arrhenius expression.The distribution parameter (0and high frequency limiting permittivity (E~)both vary in an irregular manner with increasing temperature. Propylene carbonate also absorbs in the far infra-red between 20 and 170 cm-1 with a maximum absorption at about 70 cm-‘. Values of the Kirkwood correlation parameter (9)calculated from cS indicate that short range order is not signscant in liquid propylene carbonate. The unsymmetrical frequency response of (c’-id’) has been discussed in terms of current molecular theories. Aprotic solvents of high dielectric constant are of considerable interest as media for electrochemical studies and propylene carbonate is becoming increasingly import- ant in this respect.’ Partly for this reason, no doubt, several determinations of its static permittivity (E,) have been undertaken.2 In addition, the temperature depend- ence of the permittivity (8’) and loss (&”) of the supercooled liquid has been investigated at a fixed frequency of 1 kHz in the vicinity of its glass transition ternperat~re.~ The present investigation is principally concerned with the frequency dependence of E’ and E” in the temperature range 0 to 50°C and measurements have been made at a number of frequencies between 0.5 and 35 GHz.EXPERIMENTAL Measurements of permittivity and loss in the frequency range 0.5 to 3.0 GHz were made by a travelling wave method using the coaxial line apparatus described in an earlier paper.4 The experimental arrangement employed at 10 GHz is shown schematically in fig.1. The cell used to hold the liquid under investigation was constructed from a length of WG 15 rectangular waveguide (internal cross-section 2.850 cm x 1.262cm) to the lower end of which was soldered a standard choke flange and a kovar-glass window to retain the liquid within the guide. A taper transformer provided the necessary transition to waveguide size 16, from which the commercially available components used in the bridge were manu- factured. The upper part of the cell consisted of a length of waveguide 16, closed at its lower end by a window and machined so that it could move freely within the larger lower section of waveguide 15. The liquid, which was accommodated between the two windows, entered through a small hole in the narrow wall of the lower guide from an external reservoir.The length of the column of liquid could be varied by adjusting the position of the smaller upper section of guide, the displacement of which was measured by a dial gauge. The larger lower section of guide and the liquid reservoir were enclosed in a cylindrical outer casing, 78 E. A. S. CAVELL through which water from a thermostat could be pumped. Temperatures were controlled to +-O.I"C. The attenuation constant (a2)and phase constant (p2)of the electromagnetic radiation within the liquid were measured by adjusting the phase and amplitude of the signals travelling along the two arms of the bridge to produce a null reading at the output meter for at least two different depths of liquid as described previously. A similar experimental arrangement to that shown in fig.1 was also used at 35 GHz except that a precision rotary vane attenuator was substituted for the piston attenuator and an E-H plane tuner was used as an input matching device for the cell. L As+&J DGX K I C A T FIG.1.-Block diagram of apparatus used for measurement of permittivity and loss at 10 GHz: K klystron oscillator, I isolator, H hybrid tee, P piston attenuator, S phase shifter, A variable atten- uator, C liquid cell, T three screw stub tuner, M matched load, D directional coupler, X crystal mixer, G amplifier, W wavemeter. The far infra-red absorption spectrum of liquid propylene carbonate was recorded between 20 and 200 cm-I by means of an R.I.I.C.FS720 interferometer in association with a Fourier transform computer 100-7. The optical cell employed to hold the sample had windows of pure silicon separated by a 300 pm spacer. MATERIALS Laboratory grade propylene carbonate was dried by allowing it to stand for several days over a molecular sieve type 5A. It was then repeatedly fractionally distilled in uacuo until the refractive index and electrical conductivity of the distillate showed no perceptible change in value, i.e., Q (20°C)= 1.4~ ohmb1m-l , n~(20"C)= 1.421 66. Four successive distillations were usually required for this purpose. The final product was analyzed at three temperatures (150,170 and 200°C) using a Pye 104vapour phase chromatograph with a 5ft column filled with 10 % SE 30 on Diatomite " C "(60-72 mesh), which had been acid washed and treated with hexamethyldichlorosilazane. There was no indication of any impurities of any kind in the samples of propylene carbonate studied.RESULTS Permittivity and loss (relative to free space) were calculated from the measured attenuation constant (a,) and phase constant (p2 = 2n/A2) of the electromagnetic wave within the liquid by means of the equation,6 E' -id' = [(1/3Lc)2 -(a, +ip,)2/4n2]/[(1 +(1 /A1)2], (1) DIELECTRIC RELAXATION IN SOLUTIONS in which A, is the wavelength of the radiation in the air-filled guide, A, is the wavelength in the liquid-filled section and i is J-1.For the method of operation employed here, the cut-off wavelength (A,) of a rectangular guide is twice its longer dimension and is related to the free-space wavelength (Ao) of the electromagnetic wave by the expression For measurements with coaxial line apparatus, the propagation mode is such that the cut-off wavelength is infinity.6 Within a given experiment, the mean deviations of individual measurements of a2 and p2 from their mean values were usually better than f0.5 % and & 1 % respect-ively, while for replicate determinations, values of E’ and E” generally agreed to within 2 % and 5 % respectively. Mean values of permittivity and loss for various fre- quencies and temperatures are summarised in table 1. As a check on the absolute accuracy of the experimental techniques employed, several measurements of the permittivity and loss of pure water at 20°C have also been made.The results obtained at 3.00 GHz for E’ and E” were 77.6 and 13.3 respectively compared with literature values of 77.2 and 13.1. At 9.99 GHz, the permittivity of water was found to be 60.2 and its dielectric loss 33.6. Corresponding values obtained by calculation from the dielectric dispersion parameters reported by Grant, Buchanan and Cook were 60.5 and 32.2 for E’ and E” respectively. It appears therefore that the present measurements on propylene carbonate are free from any significant systematic error. TABLE1.-VARIATIONOF RELATIVE PERMITTIVITY (E’) AND LOSS (E”) OF PROPYLENE CARBONATE WITH FREQUENCY FOR VARIOUS TEMPERATURES fIGHz &I El’ E’ &I’ 2°C 20°C 0.50 67.7 12.5 64.2 8.04 1.oo 60.9 22.5 61.6 15.3 1.50 52.5 28.3 56.4 21.4 3.oo --41.2 29.7 9.997 11.42 16.0 13.8 21.5 33.88 --5.74 7.51 40°C ooc 1.oo 58.7 10.06 57.0 8.44 1.50 --55.2 12.25 3.00 --48.1 20.3 9.997 19.8 23.9 21.1 25.2 33.88 8.40 10.40 9.47 11.67 Of the empirical functions available for describing the frequency dependence of the complex permittivity of a dielectric, that proposed by Cole and Davidson * (eqn (3)) provides the best fit for the present experimental data.Values of the parameters E,, E,, zo and 5 appearing in eqn (3) which give the best repre- sentations of the experimental data are summarised in table 2. They were computed employing a numerical procedure which involved minimizing the square of the devia- tion (6) defined in eqn (4), in which N is the number of frequencies at which measure- ments were made for a particular temperature ; &Lalc and && are the values obtained after appropriate substitution into eqn (3).The values of zo quoted in table 2 are E. A. S. CAVELL probably accurate to f5 % while the uncertainty in the magnitude of the distribution parameter has been estimated as kO.04. a2 = (~/N)(C[(E'-E~,~~)/E']~ (4)+C[(E"-E~~~~)/E"]~}. From the literature data available,2 it has been found by a non-linear least squares procedure that the temperature dependence of the relative static permittivity (8,) of liquid propylene carbonate between 213.2 K and 323.2 K can be expressed by means of the relation? E, = A exp(-LT), (5) in which A = 195.6 and L = 3.681 x K-l.The values of E, obtained from the present measurements by the use of eqn (3) agree with those calculated from eqn (5) to within k0.5 %. On the other hand the temperature dependence of the dielectric relaxation times (7,) cannot be represented by the usual Arrhenius expression. Plots of log zo against 1/T show a pronounced curvature? which suggests that the experi- mental relaxation times are composite quantities. TABLE2.-DIELECTRIC RELAXATION TIME (TO), DISTIUBUTION PARAMETER (t)LOW AND HIGH FREQUENCY LIMITING RELATIVE PERMITTIVITIES (Es AND Em) OF PROPYLENE CARBONATE AT VARIOUS TEMPERATURES AND DEVIATION (6) DEFINED BY EQN (4) temp/"C 6s Em 10122& r 6 2 70.75 4.45 74.7 0.85 0.0122 20 66.4 3.9 46.2 0.91 0.0297 40 62.7 4.55 33.4 0.86 0.0417 50 59.7 3.4 31.8 0.78 0.0649 Liquid propylene carbonate also absorbs in the far infra-red between 20 and 170 cm-l with a maximum absorption at about 70 cm-l.In addition? some indica- tion of a further absorption beyond 200 cm-1 was also noted. DISCUSSION According to Harris and Alder,g the static permittivity of a polar liquid containing N inolecular dipoles per unit volume is given by the relation (8, -ng) = [NE,(ng +2)IE0(2E, + I)] (gp2/3kT)? (6) in which c0 is the permittivity of free space, no is the low frequency limiting refractive index and g is the Kirkwood correlation parameter.1° The effective molecular electric moment (p) within a polar liquid is related to the dipole moment (pv) of the isolated molecule in the vapour phase by the expression,'l p = p,(n: + 2)(2~,+ 1)/3(2~,+ n:).(7) The low frequency limit of the refractive index should in principle correspond to the square root of the high frequency limiting permittivity. For reasons considered below, the absorption observed between 20 and 17Ocm-l is thought to contribute to the relaxation of the total mean square dipole moment, so that to equate n; with values of e, given in table 2 is unjustified. Instead no has been represented by the commonly used but arbitrary approximation, no = 1.1 ytD, for the appropriate temperatures being calculated from the linear expression,2 n, = A-BT (8) with A = 1.5314 and B = 3.752~ K-l.DIELECTRIC RELAXATION IN SOLUTIONS There is also some uncertainty regarding the magnitude of the vapour phase moment of propylene carbonate, since the only experimental data available refer to benzene as solvent. Apparent dipole moments in benzene solution are frequently less than the vapour phase value although several instances are known where the reverse is true. If pvis taken to be 5.1 D (1 C m = 3 x D), i.e.,about 3% greater than the value reported for benzene so1ution,l2 then estimates for g obtained by substitution into eqn (6)range from 0.80at 2°C to 0.86at 50°C. The precise magnitude of g is, in any case, strongly dependent on no,being smaller the larger the value of no assumed. In spite of these uncertainties, the numerical results obtained here for g do indicate that specific short range forces capable of generating a degree of local structure are not a significant feature of liquid propylene carbonate in the tem- perature range studied.As for the unsymmetrical frequency response of the complex permittivity, several models have been proposed which could be used to provide a molecular interpretation for the behaviour observed. Of these, the rotational diffusion model of Nee and Zwanzig,13 which also makes provision for the effect of dielectric friction, seems the least likely to apply to propylene carbonate, since this model requires the molecular dipoles to be constrained to move on the surface of a cone in those cases where the dielectric dispersion is asymmetric with respect to the frequency of maximum loss.In an alternative proposal,14 molecular reorientation is assumed to be influenced by a time-dependent fluctuation in some environmental parameter. In these cir- cumstances, the time correlation function for the dipole reorientation (y(t) = (p(t)*p(0))/p2) has been represented as the product of an exponential term and a second factor determined by the probability p(t) of the occurrence of a favourable fluctuation in the environmental parameter at time t, i.e. y(t) = (1 -p(t)) exp(-I/$). The frequency response of (cf -id'), which is related to the Laplace transform of (-dy(t)/dt), could thus be regarded as the result of a superposition of an exponential and a non-exponential decay process.A complex plane plot of E' against E'~ similar in form to that generated by eqn (3) is obtained when the time constant governing the environmental fluctuations and the relaxation time zf are of comparable magnitudes. For those systems in which cooperative motions are considered to determine the dielectric relaxational behaviour, the experimental data can often be interpreted in terms of the empirical decay function, exp -(t/z,)@,with 0 </?< 1. In this case, a complex plane plot of E' against E" although unsymmetrical in character, differs significantly, particularly at higher frequencies, from that required by eqn (3). A non-exponential decay function of this form cannot therefore apply to the present experimental data.On the other hand, an asymmetrical top molecule such as propylene carbonate might be expected to exhibit three distinct molecular relaxation times corresponding to reorientation about its three principal inertial axes. X-ray diffraction studies and gas phase microwave absorption measurements l7 on ethylene carbonate show that in its equilibrium configuration the five membered ring is "bent " with the bond joining the two methylene carbon atoms making an angle of 20" with the plane con- taining the carbonate group. The infra-red spectra, n.m.r. chemical shifts and coupling constants of ethylene and propylene carbonates indicate that their molecules have similar structures. * In both molecules the resultant electric moment vector is expected to be parallel to the direction of the carbonyl group.lg The component of the molecular moment perpendicular to one of the principal inertial axes of propyl- ene carbonate may therefore be too small for it to make an appreciable contribution to the relaxation of the total mean square dipole moment.At first sight, it would appear that the dielectric relaxational behaviour of propylene E. A. S. CAVELL carbonate might approximate to that produced by the superposition of two exponen- tial decay processes. However, propylene carbonate cannot be regarded as a rigid molecule, since in general molecules containing saturated five membered rings have two skeletal vibrations. In particular cases, these vibrations can interact in such a way as to cause the phase of the resultant puckering to rotate around the ring and a series of absorption maxima observed in the vapour phase absorption spectrum of 1,3-dioxolan between 20 and 95 cm-l has been interpreted in terms of changes in the energy of this pseudorotation.20 For rings containing hetero atoms and/or substit- uents other than hydrogen, pseudorotation is usually subject to hindrance from a potential energy barrier, which in the case of ethylene carbonate is said to be quite large.Nevertheless the absorption band at 217cm-I noted in the spectrum of solutions of ethylene carbonate in benzene has been assigned to an out-of-plane bending vibration of the ring,21 so that it seems reasonable to suggest that the puck- ering and/or bending motions of the propylene carbonate ring contribute to the absorption between 20 and 170 cm-l reported here, although other processes could also be involved.22 The skeletal vibrations of propylene carbonate about its most stable configuration will also result in periodic fluctuations in the magnitude of the molecular moment. They will thus contribute to its overall relaxation, so that the limiting high frequency values of the permittivity will of necessity be smaller than those of E summarised in table 2.The influence of these vibrations should also be reflected in the experimental microwave values of E' and E", although the exact extent to which th eseare affected will presumably depend on temperature and the size of any energy barriers involved.In any quantitative representation of the present limited experimental data as the weighted sum of a series of Debye dispersions, therefore, the theoretical significance to be attached to the individual relaxation times must be subject to some uncertainty. TABLE3.-PARAMETERS Es, Em, Ti,72 AND c1 REQUIRED BY EQN (9) FOR VARIOUS TEMPERATURES AND DEVIATION (6) DEFINED BY EQN (4) t emp/"C & &W 101Ztl/s 10'24s c1 6 2 71.25 6.5 76.7 37.3 0.72 0.0197 20 66.5 4.6 49.3 22.5 0.76 0.0287 50 59.7 3.0 27.4 2.9 0.88 0.0524 The experimental data can, of course, be represented empirically by the equation, and an acceptable numerical fit is obtained with the values of the appropriate para- meters shown in table 3.The results for E, are in good agreement with those predicted by eqn (5) and the temperature dependence of the parameter z1is accurately described by the equation, z1 = zy exp (HJRT) (10) with 7; = 7.58 x 10-14 s and H1 = 15.82 kJ/mol, although the variation of x2 with temperature cannot be so represented. It is possible that the values of r1 given in table 3 do provide an indication of the relaxation times associated with the principal molecular reorientation mechanism, but in view of the reservations noted above such an identification must necessarily be tentative. A grant from the Science Research Council towards the cost of apparatus is gratefully acknowledged. DIELECTRIC RELAXATION IN SOLUTIONS R.J. Jasinski, Advances in Electrochemistry and Electrochemical Engineering, Vol.8, ed. C. W. Tobias (Wiley-Interscience, N.Y. 1971), p. 253. L. Simeral and R.L. hey, J. Phys. Chem., 1970,74, 1443 and op cit. G. P. Johari and M. Goldstein, .I.Chem. Phys., 1970,53,2372. E. A. S. Cavell, J. Sci. Instr., 1967, 44, 401. E. A. S. Cavell, Trans. Faraday SOC.,1965, 61, 1578. S. Roberts and A. von Hippel, J. Appl. Plrys., 1946, 17, 610. ' E. H. Grant, T. J. Buchanan and H. F. Cook,J. Chem. Phys., 1957, 26, 156. R.H. Cole and D. W. Davidson, J. Chem. Phys., 1951, 18, 1417. F. E. Harris and B. J. Alder, J. Chem. Phys., 1953, 21, 1031. lo J. G. Kirkwood, J. Chem. Phys., 1939,7,911. L. Onsager, J. Amer. Chem. Soc., 1936,58, 1486. l2 R.F. Kempa and W. H. Lee, J. Chem. SOC.,1961, 100 and op cir. l3 Tsu-Wei Nee and R. Zwanzig, J. Chem. Phys., 1970, 52,6353. l4 S. H. Glarum, J. Chem. Phys., 1960,33,369 ; J. E. Anderson and R. Ullmann, J. Chem. Phys., 1967,47,2178. Is G. Williams, M.Cook and P. J. Hains, J.C.S. Faraday 11, 1972, 68, 1045 ; G. Williams, D. C. Watts, S. B. Dev and A. M. North, Trans. Faraday SOC., 1971, 67, 1323. l6 C. Brown, Acta Cryst., 1954, 7,92. B. Arbuzov, Bull. SOC.Chim., France, 1960, 1813. l8 R.A. Pethrick, E. Wyn-Jones,P. C. Hamblin and R. F. M. White,J. Chem. SOC.A, 1969,1852. l9 R. J. W. Le Fevre, A. Sundaram and R.K. Pierens, J. Chem. SOC.,1963,479. 2o J. A. Greenhouse and H. L. Strauss, J. Chem. Phys., 1969,50, 124. 21 J. R. Durig, G. L. Coulter and D. W. Wertz, J. Mol. Spectr., 1968, 27, 285. 22 N. E. Hill, Dielectric Properties and Molecular Behauiour, ed. M. Davies (van Nostrand Reinhold, London 1969), p. 88.

ISSN:0300-9238    

DOI:10.1039/F29747000078

出版商:RSC    

年代:1974

数据来源: RSC

摘要:

Simulation of SCF Perturbation Theory by a Simple Model Potential Method Polarisabilities of Divalent Atomic Species BY RONALDF. STEWART* Department of Chemistry, University of Glasgow, Glasgow G12 SQQ, Scotland Received 11th July, 1973 A simple model potential approach is described for the calculation of static and dynamic polar-isabilities of atomic species containing an s2 valence pair. Results differ considerably depending on whether coupling between the perturbed orbitals is neglected, values derived with the inclusion of intra-shell selfconsistency being in good agreement with polarisabilities found by allelectron Coupled Hartree-Fock methods. Polarisabilities are given for a number of systems for which accurate, non-empirical results are not yet available.The calculation of atomic polarisibilities remains an area of considerable research activity owing to both the theoretical and experimental importance of these quantities. With the exception of very small systems, for which one may contemplate the use of more refined approaches, these properties are generally computed within an SCF framework, frequently by perturbation theory. However, as the number of electrons involved increases, the computational labour inherent in such calculations rises rapidly, exceptionally so for the Coupled Hartree-Fock method which is usually considered the most accurate.' It is thus the object of this paper to demonstrate that, for the evaluation of the polarisabilities of certain atomic species, the salient features of SCF perturbation theory can be accurately simulated by a simple model potential approach.The manner in which the problem can be reduced to one involving solely the valence electrons will first be demonstrated, the "field " and "exclusion " effects of the core being reproduced by a suitable model potential of a type commonly used in many areas of chemical physic^.^-^ For the systems studied in this work, divalent species such as Mg which have an s2 valence pair, the pseudopotential method yields a series of He-like problems and hence the perturbation equations may be solved rapidly. For this purpose efficient, but flexible, finite-difference methods are em- ployed.Finally the computed static and dynamic polarisabilities will be discussed against a background of such theoretical and experimental data as are available. DERIVATION OF THE MODEL POTBNTIAL EQUATIONS Following Weeks and Rice,2 and Weeks, Hazi and Rice we consider a mono-valent atom the valence orbital of which is given by the model potential eqn (1).(-+v: +V(1)-E0)40( 1) = 0. (1) In the above, Vis an I-dependent potential (2) (IZ)(Z[ being a projection operator * present address : Harvard College Observatory, Cambridge, Massachusetts 02138, U.S.A. 85 ATOMIC POLARISABILITY involving the appropriate angular variables) which is adj usted so that the eigenvalues of the Hamiltonian correspond to the experimental spectrum of the valence electron. V(1) = c ll>WI)<ll-(2) It may be noted that for the present study the lowest eigenvector of each angular symmetry (with, of course, a nodeless radial part) is assumed to simulate the appro- priate valence orbital of the system.This is in contrast to the usual situation in which the valence orbitals display oscillations near the nucleus to give orthogonality to the core functions. However to take account of the Pauli principle it is necessary to include a repulsive component in the model potential for the I for which the valence functions have precursors in the core (a very brief and lucid account of this aspect of pseudo-potentials is given by Gombas 6). Thus here the V, contain terms which represent both the “field ” and “ exclusion ’’ effects of the care. For an atom containing a doubly occupied orbital in the valence shell it appears reasonable to assume that the core potentials for such a system are little different from those corresponding to the monovalent species.Hence, developing an effective SCF equation for the valence orbitals, for an s2pair the homogeneous eqn (3) is obtained (cf. Kutzelnigg, Koch and Binge1 ’). This may be reduced to the radial eqn (4)for the distribution function P&. (-3v:+W>+p#M 2)r-1: 4SOCF (2)dz2-E&F)4&F(1) = (3) where J(rl) = p&F(r2)r ‘ps”cF(r2> dr2. (5) Now consider the system to be perturbed by a static electric field, representable as a sum of one-electron operators (6) : HI = c2 -rp,(cos ei). (6)i=1 Expanding the Hamiltonian, valence orbitals and energies as in (7) this yields the eqn (8) for the perturbed orbital, PI2being a permutation operator.H= Ho+AH1+.. . 4 = . . . & = &O+A&’+ ... (7)(-+G+v(1)+<4sOcFIr1;1(1 +~P~~)I~:CF)--E~CF)~~(~) = (rl,P,(cos m&cF(1)-(8) In turn, the above furnishes (9) if the coupling terms are neglected or alternatively (10) provided intra-shell self-consistency is retained. or R. F. STEWART where J(r,) is defined as in (5) and K(r,) as below : Possibly the most notable feature of the above is that, if an I-dependent potential of the type (2) is employed, V, appears in the radial equations rather than V,: a property also included by Adelman and Szabo in their modification of the Coulomb approximation and by Kutzelnigg in his study of dispersion forces.A pseudo SCF approximation may also be developed for a dynamic as well as a static perturbation, the radial equations being (12) and (13) for the uncoupled and coupled schemes respectively. At this point it must be observed that the validity of the above approximations rests critically on a number of assumptions : that the polarisability of the core is small in comparison to that of the valence shell ; that the effect of the core can be simulated by a pseudopotential; that the charge distribution due to the valence shell is accur- ately represented by the pseudowavefunction. These have been examined elsewhere for the model potential calculation of a number of properties of monovalent atoms, it being shown that, indeed, for such systems the various suppositions do appear to hold.g On physical considerations it is also expected to be the case for the divalent species studied here.This is supported by the results of numerical calculations, which follow. CHOICE OF PSEUDOPOTENTIAL AND METHOD OF CALCULATION For the present calculations a choice was made of the Hellmann potential (14), Z,,, being the net charge on the core, and A, and K, being parameters which are varied so that the eigenvalues of the model eqn (1) correspond to spectral data. V,(r)= Alr1exp(-2.0 K,r)--&r-l. (14) The above type of potential has been employed successfully for many applications, including the evaluation of polarisabilities and van der Waals coefficients by the a~thor.~In the latter work it was demonstrated that these properties, computed using a wide variety of model potential schemes, are relatively independent of the choice of pseudopotential provided that the model Hamiltonian yields a fairly good representation of the experimental spectrum.Here the pre-exponential factors were based on those used previously in another context by Schwartz,lo the exponents being adjusted until the lowest eigenvalues of the eqn (l), numerically determined as described below, agreed with the requisite empirical quantities. Generally the K,were found to differ only marginally from Schwartz's listed values. As implied above, the precise form of the potential (14) is not expected to be particularly important since the correct asymptotic behaviour is reproduced with, where necessary, the effect of the Pauli principle being simulated in the model by a repulsive first term (the latter may be very weakly attractive for angular symmetries 88 ATOMIC POLARISABILITY which do not have precursors in the core).This conjecture is supported by a com- parison of the computed E&-with the all-electron, Hartree-Fock calculations of Clementi (table I), agreement being surprisingly close despite the apparent naivety of the model potential approach. TABLE1.-A COMPARISON OF VALENCE ORBITAL ENERGIES AS DERIVED USING THE MODEL POTENTIAL APPROACH WITH THOSE FROM THE HARTREE-FOCK lCALCULATIONS OF CLEMENTI. ATOMICUNITS ARE EMPLOYED IN THIS TABLE THROUGHOUT THIS WORK UNLESS OTHERWISE INDICATED model potential Clement i Li--0.014 54 -0.014 53 Be -0.310 0 -0.30927 B+ -0.875 9 -0.873 86 C2+ -1.698 -1.694 05 Na--0.013 76 -0.01255 Mg -0.256 7 -0.253 04 Al+ -0.659 3 -0.652 61 Si2+ -1.192 -1.182 09 K--0.01 1 14 -0.01021 Ca -0.203 6 -0.195 50 -1-atomic unit of energy = hartreew4.3598 aJ.To solve the above eigenvalue problem and the other homogeneous and inhomo- geneous differential equations arising in this work finite-difference techniques were utilised. These are extremely simple in concept but prove accurate in practice. To determine the solution to (4) a method similar to that already employed in one-centre molecular studies l2 was used, 150(50)300 strips on a "square root " grid being sufficient to furnish at least five to six digit accuracy on application of the Richardson extrapolation process.For the perturbation equations, comparable techniques were used with mainten- ance of uniform accuracy for both uncoupled and coupled equations. For the latter no convergence difficulties were found, even for the solution of (13) close to a reson-ance, the Aitken S2 process giving satisfactory stabilisation for this He-like problem (cf. Alexander and Gordon 13). RESULTS AND DISCUSSION In table 2 the present results for the dipole polarisabilities of the alkaline earth atoms are collated with other theoretical and experimental values of these properties. From the physical considerations on which the model potential method is constructed, it would be expected that the coupled polarisabilities should be more accurate than the uncoupled results and that the former should be close to non-empirical, Coupled Hartree-Fock polarisabilities.This apparently is so. Nevertheles, despite the satisfactory simulation of the Coupled Hartree-Fock method, owing to the neglect of zeroth s-p mixing it must be asked whether the present approach does give polar- isabilities which are in the region of the correct values. The accurate results of Kelly for Be and Stwalley for Mg suggest that this deficiency is not serious, this being sup- ported by the work of Drake and Cohen.l8. 19* 25 However evidence to the contrary has been produced by Kolker and Michels 26 in a CI study, a result recently con- firmed by R~bb.~~ R.F.STEWART TABLE2.-A COMPARISON OF VALUES OF THE DIPOLE POLARISABILITIES OF THE ALKALINE EARTH METAL ATOMS (1 a.u.-0.148 18 x m3) this work Be Mg Ca Sr Ba uncoupled value coupled value uncoupled Hartree- Fock l4 81.64 44.84 52.4 131.0 76.76 95.2 291.8 158.6 228.0 357.9 195.9 225.0 492.2 263.3 335.0 coupled Hartree- Fock 15, l6 45.5 81.0 Coulomb approximation other a 40.6 46.8 b 70.9 74.9+ 3.4 C 165.0 128.0-142.0d 206.0 157.0-177.0d 294.0 207.0-234.0 169.0& 20.0 e 215.0-300.0d 506.0+ 101.0-f Various other results-for a full compilation of polarisability calculations on these systems see Teachout and Pack.” b Many-body perturbation theory calculation of ‘Kelly.ls C Accurate semi- empirical calculation of Stwalley.l9 d Oscillator strength calculations of Altick 2o and Cohen.21 e Experimental lower limit of Hall, Holberling and Zorn.22 f Experimental estimate of Drechsler and Muller,23 and Liepack and Dre~chler.~~ For the heavier systems, because of the absence of sufficiently accurate data, it is more difficult to assess the validity of the model potential method : it would seem likely that the various approximations would hold less well as 2 increases.None-theless, the coupled polarisabilities broadly appear to be in harmony with the results of other workers, notably with those from the Coulomb approximation scheme of Adelman and Szabo which is in the same spirit as the present approach.8 TABLE3.-THE DIPOLE POLARISABILITIES OF THE Be ISOELECTRONIC SEQUENCE AS COMPUTED USING THE MODEL POTENTIAL APPROACH DESCRIBED IN THE TEXT AND BY COUPLED HARTREE-FOCKMETHODS uncoupled coupledresult result coupled HartreeFock a* Li-2043.O 1188.0 (1050.0) Be 88.64 44.84 45.61 45.5 B+ 20.26 11.17 11.38 11.35 C2+ 7.99 4.42 4.508 4.49 N3i 3.96 2.20 2.237 2.22 04+ 2.25 1.25 1.271 1.27 F5+ 1.40 0.775 0.7903 0.784 a,b Non-empirical results of Lahiri and Mukheiji l5 and Cohen 28 respectively ; c this value determined with less certainty owing to convergence difficulties.It might reasonably be expected that a simple pseudopotential approach would break down far ions, especially those bearing a substantial positive charge. In tables 3 and 4, though, dipole and quadrupole polarisabilities for the Be isoelectronic sequence (Li- -F5+)are compared with available highly accurate Coupled Hartree- Fock calculations.With the possible exception of Li-, in no case do the coupled values differ from the ab initio polarisabilities by more than 2 %. Interestingly, the very material effect on the computed dipole polarisabilities of including the intra-shell self-consistency correction may be noted. The Li- polarisabilities, judging from Adelman’s study of the hydride are probably severely in error owing to the poor representation of the charge density by an SCF wavefunction. One may observe, though, the general agreement with the ab ATOMIC POLARISABILITY initio value of Cohen '* and also with polarisabilitics recently by it non-empirical procedure which includes only intrashell coupling 31 (method b in the notation of Langhoff, Karplus and Hurst I).The latter are 1183.0 and 1.098x 105a.u. for the dipole and quadrupole polarisabilities, respectiveljj, which may be compxed with the pseudopotential values of 1188.0and 1.147 x lo5a.u. TABLE4.-THE QUADRUPOLE POLARISABILITIES OF THE Be ISOELECTRONIC SEQUENCE (1 a.u.wO.414 96x m5) uncoupled coupledresult result coupled Hartree-Fock 29 Li-1.225 x SO5 1.147~lo5 Be 356.4 335.1 342.5 B+ 29.06 27.66 28.27 C2+ 5.32 5.11 5.225 N3+ 1.45 1.40 1.433 04+ 0.504 0.489 0.4996 F5+ 0.206 0.201 0.2048 a Many-body perturbation theory calculation (Kelly Is) yields 340 a.u. For the other systems, it is again not easy to estimate the accuracy of the computed polarisabilities but, from such data as are available, the dipole polarisabilities for the Mg series reported in table 5 should give at least " order of magnitude " values of these quant,ities.TABLE5.-THE DIPOLE POLARISABILITIES OF THE MEMBERS OF THE Mg ISOELECTRONTC SEQUENCE AS COMPUTED BY THE AUTHOR AND BY OTHERS uncoupledresult coupledresult other Na- 2261.O 1340.0 1690.0 Mg 131.0 76.76 95.2 70.9 b 74.9 Al+ 41.56 25.22 27.1 27.0 Si2+ s9.54 12.14 P3+ 11.01 6.963 S4+ 6.897 4.420 c15+ 4.627 2.996 a Uncoupled SCF calculations of Thorhallson, Fisk and Fraga l4 ; b modified Coulomb approxi- mation results of Adelman and Szabo ; C St~a1ley.l~ Finally, turning to the frequency-dependent problem, uncoupled and coupled dynamic polarisabilities are reported for Be in table 6 together with the Coupled Perturbed Hartree-Fock calculations of Kaveeshwar, Chung and Hurst.As before, the coupled model potential computations accurately simulate the much more complicated non-empirical approach, though the uncoupled approximation furnishes an inadequate dipole spectrum. Even close to the resonance the ab initio and pseudopotential studies do not differ greatly, the resonance wavelengths being estimated at 2592 and 2565 A for the two methods (cf. experimental value of Moore 33 of 2349 A). For other systems satisfactory dynamic polarisabilities also appear to be obtained with, for example, in the figure the results for Mg being compared with those for Be.However, again, an SCF scheme results in a resonance wavelength which differs somewhat from experiment, the relevant values being 2995A from this work and 2853 A from Moore.33 R. F. STEWART TABLE6.-A COMPARISON OF THE PRESENT RESULTS FOR THE DYNAMIC POLARISABILITY OF Be WITH THE FULLY COUPLED, NON-EMPIRICAL CALCULATIONS OF KAVEESHWAR,CHUNGAND HURST32 uncoupled coupled Lo 18, result result Kaveeshwar et al. co 81.64 44.84 45.624 9071.O 95.88 48.66 49.538 8063.O 100.5 49.79 50.694 7257.0 106.3 51.11 52.053 6047.0 122.8 54.47 55.500 5183.0 150.3 59.07 60.21 6 4535.0 203.O 65.46 66.770 4032.0 337.7 74.62 76.191 3628.O 1344.0 88.58 90.479 3456.0 -2223.0 98.49 100.679 3299.0 -584.3 111.7 114.196 3155.0 -328.5 130.0 132.888 3024.0 -225.7 156.8 160.330 2903.0 -169.8 200.0 204.394 2791.O -134.7 281.2 286.436 2688.0 -110.9 485.6 491.938 2592.0 -93.61 2 027.0 1933.777 2560.0 -88.62 -15 992.0 -2502.0 -80.39 -868.9 -946.774 350 -1 I I \ I \I I \25C \ \\ \P \ \ / .nc(.-\ '\.* ISC \ .n2-0 a 5c I I I I I 25 i0 3500 4500 5500 6500 7500 XlA FIG.1.-A comparison of the dynamic dipole polarisabilities of Mg and Be (A and B respectively) as computed using the coupled model potential scheme. The wavelength of the incident radiation is in A while the polarisability is in a.u. CONCLUSIONS It may be concluded that, for the determination of the polarisabilities of certain systems, SCF perturbation may be simulated to a substantial degree by a simple model potential scheme.This results, of course, in appreciable savings in computa-tional labour especially as the number of electrons increases. Thus, here it has been ATOMIC POLARTSABILITY possible to give estimates for the polarisabilities of a number of atoms for which more refined calculations are, at present, impractical. There would appear to be no reason why the model potential method, perhaps within a statistical formulation for general usage,6* 34 cannot be extended to further systems and states, especially to those which are now inaccessible to accurate theor- etical treatment. Alternatively a refinement of the present study to examine the effect of zeroth s2-p2 near-degeneracy seem quite possible although the forinulation of the calculations will be rather more complicated.However, as here, this will be much simpler than the corresponding all-electron investigation since, by the use of model potentials, the problem can effectively be reduced to one involving only two electrons. I thank the Carnegie Trust for the Universities of Scotland for generous fin- ancial support, and both referees for their constructive criticisms. ' P. W. Langhoff, M. Karplus and R. P. Hurst, J. Chem. Php., 1966, 44, 505.'J. D. Weeks and S. A. Rice, J. Chem. Pliys., 1968,49, 2741. J. D. Weeks, A. Hazi and S. A. Rice, Ado. Chem. Phys., 1969, 16,283. W. Kutzelnigg, Chem. Phys. Letters, 1969, 4,435. R. L. Smith and R. W. Labahn, Phys. Rev.A, 1970,2,2317. P. Gombas, Phys. Letters, 1965, 14, 30. W. Kutzelnigg, R. J. Koch and W. A. Bingel, Chem. Pliys. Letters, 1968, 2, 197. S. A. Adelman and A. Szabo, Phys. Rev. Letters, 1972,28, 1427 ; J. Chcmi. Phys., 1973,58, 687. R. F. Stewart, Theor.Chim. Acta, submitted for publication. lo W. H. E. Schwartz, Theor. Chim. Ac/a, 1968, 11, 377. E. Clementi, Supplement to IBMJ. Res. DcP.,1965, 9, 2.'' R. F. Stewart, Mol. Phys., 1972, 24, 879 ; Mol. Phys., 1973, 25, 1451. l3 M. H. Alexandcr and R. G. Gordon, J. Chem. Phys., 1972, 56, 3823. l4 J. Thorhallson, C. Fisk, and S. Fraga, Thcor. Chim. Acra, 1968, 10, 388 ; J. Chem. Phys., 1968, 49, 1987. l5 J. Lahiri and A. Mukherji, J. Phys. SOC.Japan, 1966, 21, 1178. l6 S. Kaneko and S.Arai, J. Phys. Sac. Japan, 1969, 26, 170. R. R.Teachout and R.T. Pack, At. Data, 1971, 3, 195. "H. P. Kelly, Phys. Rev., 1964, 136, B896. 19W. C. Stwalley, J. Chem. Phys., 1971,54,4517. 2o P. L. Altick, J. Chem. Phys., 1964, 40, 238. 21 M. Cohen, Canad. J. Phys., 1967, 45, 3387. 22 W. D. Hall, R.E. Holberling and J. C. Zorn, Bull. Amer. Fli.i*.v.Soc., 1965, 13, 21. 23 M. Drechsler and E. W. Miiller, 2.Phys., 1952, 132, 195. 25 H. Liepack and M. Drechsler, Nutiirwiss., 1956, 43, 52. 25 G. W. F. Drake and M. Cohen, J. Cliem. Phys., 1968, 48, 1168. 26 H. J. Kolker and H. H. Michels, J. Chem. Phys., 1965, 43, 1027. 27 W. D. Robb, J. Phys. B, 1973, 6, 945. ?' H. D. Cohen, J. Chem. Phys., 1965,43, 3558. 29 J. Lahiri and A. Mukherji, Phys. Rev., 1966, 141, 428. 30 S. A. Adelman, Phys. Rev. A, 1972, 5, 508. 31 R. F. Stewart and B. C. Webster, J.C.S. Fnruday II, 1973, 69, 1685. 32 V. G. Kaveeshwar, K. T. Chung and R. P. Hurst, Phys. Rev., 1968, 172, 35. 33 C. E. Moore, Atomic Energy Lecels, National Bureau of Standards, 1959, 1. 34 W. H. E. Schwartz, Thcor. Chim. Acta, 1972, 24, 29.

ISSN:0300-9238    

DOI:10.1039/F29747000085

出版商:RSC    

年代:1974

数据来源: RSC