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Journal of the Chemical Society, Faraday Transactions I1 Journal of the Chemical Society, Faraday Transactions I1 SUBJECT INDEX-VOLUME69, 1973 11, 1 Kinetic Spectroscopy (see also 11, 5) Atomic Resonance Fluorescence Spectrometry for Rate Constants of Rapid Bimolecular Reactions. Part 3: Oxygen Atom Resonance 03S1-3P2.1,0.(Bemand &Clyne) .1643 Flash Spectroscopy with Mercury Resonance Radiation. Part 5 :Formation and Relaxa- tion of Hg(63P,). (Callear &McGurk) . . . . . . 97 Kinetic Investigation of Electronically Excited Oxygen Atoms, 0(2'D2), by Time-resolved Attenuation of Atomic Resonance Radiation in the Vacuum Ultra-violet. Part 2: Collisional Quenching by the Atmospheric Gases N2,02,C02,HzOand 03. (Heidner,Husain &Wiesenfeld) .. . . . . . . . . . 927 Kinetic and Spectroscopic Studies of Oz(a'Ag)by Time-resolved Absorption Spectroscopy in the Vacuum Ultra-violet. (Collins &Husain). . . . . . . 145 Kinetic Study of the Collisonal Quenching of Electronically Excited Phosphorus Atoms, P(32Dj32Pj),by Polyatomic Molecules, (Acuna &Husain) . . . . . 585 Kinetic Study of Electronically Excited Lead Atoms, Pb(6'So), by Time-resolved Absorp- tion Spectroscopy using Attenuation of Atomic Resonance Radiation. (Husain & Littler) . . . . . . . 842 Laser Emission from CO Formed in the Flash-initiated Reactions of 0(3P)Atoms with CS and CSe. (Rosenwaks &Smith) . . . . . . . . . 1416 Oscillator Strength of the C; B2C-XzC Transition:A Shock-tube Determination. (Cathro &Mackie) .. . . . . . . . . 237 Phase-shift Studies of Hg(3P0) Reactions. Part 4: Observations of the Hg, Emission Bands at 335 and 485 nm. (Ladd, Freeman, McEwan, Claridge &Phillips) . .849 Rate Measurements of Reactions of OH by Resonance Absorption. Part 2: Reactions of OH with CO, C2H4 and CzHz. (Smith &Zellner) . . . . . . 1617 Recombination of Ground State Halogen Atoms. Part 4: Kinetics of Recombination of Bromine Atoms. (Clyne &Woon-Fat) . . . . . . . 412 11, 2 Photophysics (fluorescence, phosphorescence, luminescence, dispersion, dichroism, etc.) B3110,+--XIXiSystem of lz7I2:Rotational Analysis and Long-range Potential in the BZno,+ State. (Barrow &Yee) . . . . . . . . . . . 684 Fluorescence from the Second Excited x Singlet State of Aromatic Hydrocarbons in Solution (Easterly, Christophorou &Carter) .. . . . . . . 47 1 Intermolecular Energy Transfer and Fluorescence in Solid BenzoyltrifluoroacetylacetonateLanthanide Complexes. (Curran &Shepherd) , . . . . . . 126 Intramolecular Heavy-atom Effect and Intersystem-crossing in Monohalogenated Pyrenes. (Barradas, Ferreira &Thomaz) . . . . . . . . . . 388 Oxygen Quenching of Aromatic Triplet States in Solution. Part 1. (Gijzeman, Kaufman &Porter) . . . . . . . . . . . . . 708 Oxygen Quenching of Aromatic Triplet States in Solution. Part 2. (Gijzeman & Kaufman). . . . . . . . . . . . 721 Photochromism of Spiropyrans. Part 1 :Mechanism of Photocolouration.(Reeves & Wilkinson) . . . . . . . . . . . . 1381 Photoinjection of Holes into Anthracene Crystals using Aqueous 13 Solutions:MagneticField Effects. (Vogel, Geacintov &Pope) . . . . . . . . 1208 Photophysical Decay Processes of Toluene in Dilute Solution. (Cundall, Pereira & Robinson) . . . . . . . . . . . . 701 Priniary Photochemical and Photophysical Processes in Chloro- and Bromo-acetylene. (Evans, Scheps, Rice and Heller) . . . . . . . . . 856 Quenching of Aromatic Triplet States in Solution by Nitric Oxide and Other Free Radicals. (Gijzeman, Kaufman &Porter) . . . . . . . . . . 727 Quenching by Dimethylmercury of 1,2-Benzanthracene FIuorescence via an Exciplex. (Donckt, Lietaer &Matagne) ..........322 19 SUBJECT INDEX-VOLUME 69, 1973 PAGE Spin-orbit Relaxation of Te(53P1)and Te(53P0).(Donovan &Little) . 952 Vibrational Energy Transfer in Carbon Monoxide at Low Temperatures. (Smith & Wittig) ... .. .. . . .. 939 11, 3 Quantum and General Theory (including valence theory, ab initiu calculations, computer simulation etc.) ab initio Molecular Orbital Study of the Geometry of the Interhalogens. (Guest, Hall & Hillier) . 1829 ab initio Study of Electronic Structures' and Heats of Foimation of Sorne'Adducts of Boron Trifluoride. (Archibald, Armstrong &Perkins) . ... 1793 Additivity of Contributions to the Stabilization Energy of 'Donor-Acceptor Complexes: (Hancock &Murrell) . . 115 Anisotropic Pseudo-potential for a Vanadyl Cheiate Dissolved in'a Nematic' Mesophase.(Humphries &Luckhurst) . ..... 1491 Calculation of Atomic Polarisabilities by Finite-difference Methods. Part 1 :Static Polarisabilities for the Helium Sequence. (Stewart &Webster) . 1685 Classical and Quanta1 Contributions to the Mechanisms of Ion-Molecule Reactions. Chemistry of 0;.(Hollebone &Bohme) ... .. .. 1569 CNDO :Problems in Electron Population Analysis. (Grabenstetter &Whitehead) .962 Determination of Ionization Potentials. Part 1 :The Use of Theoretical Expressions which Incorporate the Effects of Maxwellian Inhomogeneity. (Pitt &Rosenthal) . 332 Effects of Induction and Resonance in the Calculation of Ionization Potentials of Substituted Benzenes by Perturbation Molecular Orbital Theory.(Johnstone &Mellon) . 36 Equivalent Cores Method of Computing Core Electron Binding Energies. (Aarons & Hillier) .. ... .. 1510 Energy Band Structure of Silica. (Breeze &Perkins) . ...... 1237 Group Function Analysis of the Barriers to Internal Rotation in Propargyl Alcohol and Hydroxyacetonitrile. (Bendazzoli &Bernardi) . .. ..579 Hybridization and Prediction of Equilibrium Geometries in Alkanes, Alkylarnines, Alkanols and Ethers. (Pozzoli, Rastelli &Tedeschi) . .. . . 256 INDO Calculations on FZ,Clz, Br, and I2 using the Deb-Coulson Parameters. (Spurling .I.&Snook) . . . ... . ... 1183 Ionic Solvation in Formic Acid. Part 3: Molecular Orbital Studies of the Reaction Path- ways for the Solvation of Atomic Ions.(Rode) .... .. 1439 Lifting of Vibrational Degeneracies in a Crystal Field. (Waddington &Salthouse)..262 Ligand Geometries and Excited States of Allene. (Albinati, Maraschini &Zocchi) . .798 Non-empirical Valence-electron Calculations on Small Molecules containing Phosphorus or Sulphur. (Hyde, Peel, &Terauds) .. .... .. 1563 Potential Energy Surfaces for the Reaction CH2 +H2+CH4. (Murrell, Pedley &Durmaz) 1370 SCF-MO Calculations of some Molecular Properties of the Isoelectronic Series FCI, HOCI, NH,Cl and CH3Cl. (Bendazzoli, Lister &Palmieri) .. .. 791 Semi-empirical LCAO MO Theory for Infinite Systems. Part 3 :Regular Boron-Nitrogen Polymers. (Armstrong, McAloon &Perkins) .... .. 968 Some Helium Autoionization States and the Stabilization Method. (Eliezer &Moualem) 1835 Spin Density Calculations by Modified INDO and MZDO Methods.Part 1: Organic Radicals. (Casey, Craig &Scarlett) . . . . .. 132 Theoretical Study of the Geometry of PH3, PF3 and their Ground Ionic States. (Aarons, Guest, Hall &Hillier) . . . 634 Theoretical Studies of Nitrile Systems. Calculation of some One Electron Properties of CN-and HCN. (Dixon &Doggett) . 298 Valence Orbital Behaviour During Changes in Intermolecular Separation. Comparison of Models based on the Empirical United Atom Theory and on the Semi-empirical CNDO/BW Theory. (Hollebone &Whitehead) . .. 648 II,4 Relaxation Phenomena (dielectric, magnetic, ultrasonic, etc.) Dielectric Absorption in Pentachlorobenzene Compounds.(Hall &Horsfall).. 1071 Dielectric Investigation of Hydrogen-bonding in Hydroxynitrotoluenes and Nitroresorcinols. (Hall &Horsfall) . .. ... .. 1078 Dielectric Properties of Cyclic Nitramines and Related Compounds. Part 2: Solid State Measurements on Cyclic Nitramines, Cyclic Nitrosamines, Cyclic Thianes and Penta- fluorobenzene Compounds. (Hall &Horsfall) . .. .. 1515 SUBJECT INDEX-VOLUME 69, 1973 21 PAGE Dielectric Properties of Electrolyte Solutions. Lithium Perchlorate Solutions in Tetra- hydrofuran+Benzene Mixtures. (Badiali, Cachet, Cyrot &Lestrade) . . 1339 Dielectric Relaxation in Non-Aqueous Solutions. Part 4: Solutions of Tri-(n-buty1)am- monium Picrate in Benzene.(Cave11 &Sheikh) . ...... 315 Dielectric Relaxation of Rigid Solute Molecules in Benzene+ Paraffin Solutions. (Balogun &Cumper) . ... ........ 1172 Dipole Moment of N-(p-Methoxy1idene)-p-butylaniline. (Maurel &Price) . .. 1486 Molecular Dynamics of the Supercooled Liquid State A Dielectric Study of the Low Fre- quency Motions of Fluorenone in a-Terphenyl and Mixed Solvents and of Di-n-butyl Phthalate in o-Terphenyl. (Shears &Williams) ....... 608 Molecular Dynamics of the Supercooled Liquid State. Low Frequency Dielectric Relaxa- tion of Benzophenone, Cyclohexanone and Fenchone in o-Terphenyl. (Shears & Williams) . ... . ....... .. 1050 Molecular Motion and Molecular Interaction in the Nematic and Isotropic Phases of a Liquid Crystal Compound.(Evans, Davies &Larkin) ..... 1011 Molecular Motion in the Supercooled Liquid State: Ion Pairs in Slow Motion. (Davies,Hains &Williams) . . . ... ... 1785 Molecular Organisation within the Smectic C Mesophase of the Liquid Crystal 4,4'-Di-n- heptyloxyazoxybenzene. (Luckhurst, Ptak &Sanson) ...... 1752 Pressure Dependence of the Viscoelastic Properties of Castor Oil. (Barlow, Harrison Kim&Lamb) . .. ... 1446 Proton Transfer in some Amino-acids Studied by the. Ultrasonic Method. (Grimshaw,Heywood &Wyn-Jones) . .. ...... 756 Proton Transfer in some Model Equilibria Studied by the Ultrasonic Method. (Grimshaw &Wyn-Jones) ....... ... 168 Relaxation of an Alkali-metal Halide Aerosol in a Shock Wave. (Evans &Mackie) .224 Solute-Solvent Interactions from Relaxation Data by a Novel Procedure.(Magee & Walker) . ... .. ..... ... 161 Temperature Dependence of the Rate of Micellization Determined from Ultrasonic Re- laxation Data. (Rasing, Sams &Wyn-Jones) . . ..... 180 Viscoelastic Behaviour of some Viscous Liquids. (Davies, Matheson &Glover) ..305 Viscoelastic Retardation of Liquid Mixtures. (Barlow &Erginsav) .... 1200 11, 5 Spectroscopy (a)Microwave, infra-red, Raman Absorption Spectra of Molecules Adsorbed within Porous Media and the Effect of Molecular Orientation. (Dignam, Rao &Roth) ... ...... 804 Calculated Frequencies and Intensities Associated with Coupling of the Proton Motion with the Hydrogen Bond Stretching Vibration in a Double Minimum Potential Surface.(Janoschek, Weidemann &Zundel) .. ....... 505 CND0/2 Calculation of the Absolute Infra-red Intensities of a Series of Monosubstituted Ethylenes. (Brownlee, Munday, Topsom &Katritzky) ...... 349 Collision Induced Absorption in Compressed Gaseous Cyanogen and Comparison with the Liquid Phase Absorption in the region 20-120 cm-l. (Evans). .... 763 Dihedral Angle of Bipehnyl in Solution and the Molecular Force Field. (Eaton &Steele) 1601 Effect of Temperature on the Hydrogen Bond vs Band. Part 1 :Experimental. (Rice & Wood) .. ........ a7 Effect of Temperature on the Hydrogen Bond vs Band. Part 2: Theory. (Rice &Wood) 91 Evidence for Short-range Orientation Effects in Dipolar Aprotic Liquids from Vibrational Spectroscopy.Part 1:Ethylene and Propylene Carbonates. (Fini, Mirone & Fortunato) ......... .... 1243 Far Infra-red Absorptions of Non-dipolar Liquids. Part 1 :Experimental Measurements, Quadrupole Interpretation and Model Calculations. (Davies, Chamberlain &Davies) 1223 Far Infra-red Absorptions of Non-dipolar Liquids. Part 2: Temperature and Dielectric Studies. (Davies &Chamberlain) . .. .. .. 1739 Influence of Surface Roughness on the Transmissi'on and Reflectance Spectra of Adsorbed Species. (Dignam &Moskovits)........ .. 65 Infra-red Cryogenic Studies. Part 11 :Hydrogen Iodide and HI Complexes. (Barnes,Davies, Hallam &Howells). . ......... 246 Infra-red Cryogenic Studies.Part 12: Alkenes in Argon Matrices. (Barnes &Howells). 532 SUBJECT INDEX-VOLUME 69,1973 Infra-red Cryogenic Studies. Part 13:Halogenoalkanes in Argon Matrices. (Barncs, Hallam, Howells &Scrimshaw) . .. Infra-red Emission from Shock-heated Mixtures of Carbon Monoxide and Neon. Examina-tion of the Landau-Teller Model for Vibrational Relaxation. (Borrell &Millward) . Infra-red Spectra of the Hydrates of Hydrogen Chloride and Hydrogen Bromide. Absorp-tion Bands of the M50iSpecies. (Gilbert &Sheppard) . . Infra-red Spectrum and Structure of Collagen. (Roberts) .... Microwave Spectrum, Barrier to Internal Rotation of the Methyl Group, Chlorine-35 Nuclear Coupling Constants and Molecular Conformation of Methyl Chloroformate.(Lister &Owen) . Microwave Spectrum and Molecular Conformation of p-Fluoroanisole. (Lister &Owen)Microwave Spectrum of Tellurium Pentafluoride Chloride. (Legon) . Nitrogen Quadrupole Hyperfine Splitting in the Microwave Spectrum of Dinitrogen Trioxide. (Cox &Finnigan) . Optical Properties of Sub-monolayer Molecular Films. (Dignam &Moskovits) . Pulsed Matrix Isolation. A Comparative Study. (Perutz &Turner) . Resonance Raman Spectra of Vitamin B12 and Some Cobalt Corrinoid Derivatives. (Mayer, Gardiner &Hester) . Rotational Isomerism and Barriers to Internal Rotation in Hydroxyacetonitrile from Microwave Spectroscopy. (Cazzoli, Lister &Mirri) . . Rotational Isomerism in Propargyl Amine studied by Raman Spectroscopy.(Verma & Bernstein) . . . . . Rotational and Vibrational Spectra of 2-Fluoropropane. (Griffiths, Owen &Sheridan) . Simple Models of the Far Infra-red Absorption of Polar Molecules in Liquid and Rotator Phases. (Larkin) ... Single Crystal Vibrational Spectra of Chloranil (2,3,5,6-Tetrachloro-p-benzoquinone).(Girlando &Pecile) ...... Splitting of the 2E(t2)State of Cr(NH3)5XZ+ Ions. Significance of the Coulombic Parameter B. (Flint &Matthews) . . .. Structure of the Amine Group in rn-Fluoroaniline by Microwave Spectroscopy. (Cazzoli, Damiani &Lister) ... . . Structure and Potential Energy Function of Cyclopent-3-enone. Part I :Microwave Spect- rum Ring Planarity, r,-structure, and Dipole Moment. (Bevan &Legon) .Structure and Potential Energy Function of Cyclopent-3-enone. Part 2: Out-of-plane Ring Modes from Far Infra-red, Raman and Microwave Spectra: Ring Bending Potential Function. (Bevan &Legon). . . . Submillimetre Absorption of Rod-like Polar Molecules in Liquids. (Higasi, Minami, Takahashi &Ohno) .. . .. Vapour Phase Roman Spectra of Mercury(I1) Chloride, Mercury(I1) Bromide and Mer- cury(I1) Iodide. v1 (C;)band Contours and the Mercury-Halogen Bond Polarisability Derivatives. (Clark &Rippon) . .... Very Polarisable Hydrogen Bonds in Solutions of Bases having Infra-red Absorption Con- tinua. (Schioberg &Zundel) . .... Vibrationla Spectra of Biphenylene. In-plane Normal Modes of Biphenylene, [2,3,6,7-’H4]- Biphenylene and [2H8]Biphenylene.(Girlando &Pecile) . Vibrational Spectra and Rotational Isomerism of Methyl and Ethyl Cyanoacetate. (Charles, Jones &Owen) ......... . (6)electronic (visible, ultra-violet absorption and emission) Bonding Studies from Charge-transfer Absorption and Magnetic Circular Dichroism Spectra. Part 3: Meridonal Complexes of Osmium(II1). (McCaffery &Rowe) . Bonding Studies from Charge-transfer Absorption and Magnetic Circular Dichroism Spectra. Part 4: Facial Isomers of MC13L3. (McCaffery &Rowe) . Derivation and Interpretation of the Spectra of Aggregates. Part 2: Dimer of Rhodamine B in Aqueous Solutions. (Gal, Kelly &Kurucsev) . ... 2E_t4A Transition of the Hexa-amminechromium(II1) Ion in Non-cubic Environments. (Flint, Greenough &Matthews) .... Luminescence Spectra of Binuclear Chromium(I1) Compounds. (Flint &Greenough) . Magnetic Circular Dichroism Spectrum of the Tetraiodonickelate(I1) Ion. (Collingwood,Day &Denning) . .. Near Ultra-violet Absorption Spectrum of Biphenylene. (Zanon) . . PAGE 738 1060 1628 1084 1036 1304 29 49 56 452 1350 5 69 1586 1359 1278 1291 419 119 902 916 1579 1496 771 818 1454 1767 1779 395 23 1469 591 1164 SUBJECT INDEX-VOLUME 69, 1973 23 ?MI Optical and Spectroscopic Study of the Phase Transition at 116 K in Hexamethylbenzene. (Bertinelli &Stremmenos) ... .. .... .889 Polarization, Temperature Dependence and Absorption Mechanism of the Electronic Transitions in Some Linear Antiferromagnets.(Day &Dubicki) ... 363 Theory of Pressure-induced Absorption by Symmetric Top Molecules. (Frost) . . 1142 Zero Field Splitting in Tetragonal Di-iodotetrakis(pyrazole)manganese(II). (Reedijk and Klaaijsen &Witteveen) ...........1537 (c) photoelectronBonding in some Donor-Acceptor Complexes involving Boron Trifluoride Study by means of ESCA and Molecular Orbital Calculation. (Barber, Connor, Guest, Hillier, Schwartz &Stacey) ....... 551 He-(I) Photoelectron Spectra of some Metal Complexes Containing the Ligands Tri- methylsilylmethyl and Neopentyl. (Evans, Green &Jackson) .. 191 High Energy Photoelectron Spectroscopy of Transition Metal Complexes.Part 2: Metal-locenes. (Elarber, Connor, Derrick, Hall &Hillier) . . .. 559 High Energy Photoelectron Spectroscopy of Transition Metal Complexes. Part 3 :Direct Measurement and Interpretation of the Core Level Shifts between Free and Complexed CO, and the Bonding in some Substituted Manganese Pentacarbonyls. (Connor, Hall, Hillier, Meredith, Barber &Herd) . . . ... 1677 Photoelectron Spectra of Zinc and Cadmium Halides. icocksey, EIand &Danby) . . 1558 Photoelectron Spectroscopy of Sulphur-containing Heteroaromatics and Molecular Orbital Calculations. (Johnstone &Mellon) . .. ..... 1155 Photoelectron Studies of Metal Carbonyls. Part 2: The Valence Region Photoelectron Spectra of the Group VIA Hexacarbonyls. (Higginson, Lloyd, Burroughs, Gibson & Orchard) ........... . . 1659 Satellite Phenomena in the High Energy Photoelectron Spectra of Tetramethyl-p-phenylene-diamine (TMPD), Tetracyanoquinodimethane (TCNQ), and their Derivatives. (Aarons, Barber, Connor, Guest, Hillier, Ikemoto, Thomas &Kuroda) .. 270 Steric Inhibition of Resonance Studied by Molecular Photoelectron Spectroscopy. Part 2: Phenylethylenes. (Maier &Turner) ......... 196 Steric Inhibition of Resonance Studied by Molecular Photoelectron Spectroscopy. Part 3 : Anilines, Phenols and Related Compounds. (Maier &Turner) .... 521 Use of Koopmans' Theorem to Interpret Core Electron Ionization Potentials. (Aarons, Guest, Hall &Hillier) ... ....... 563 (d)electron spin resonance Alkali Metal Hyperfine Coupling Constant in Biphenylene Alkali Metal Ion Pairs. (Corvaja &Pasimeni) ......... ... 623 Electron Nuclear Double Resonance of the Lithium and Sodium Complexes of Di-o-mesi- toylbenzene. (Atherton &Day) ... .. .. 1801 Electron Paramagnetic Resonance Studies of Metal-Ketal Interactions in Manganese(I1) Complexes. The 10/3 Effect. (Pleau &Kokosza) . . . ... 355 Electron Spin Resonance Flash Photolysis and Chemically Induced Nuclear Polarisation Study of the Photolysis of Benzaldehyde in Solution. (Atkins, Frimston, Frith, Gurd &McLauchlan). . .. 1542 Electron Spin Resonance Investigation on cis and trans Semidone Alkali Metal Ion Pairs. (Brustolon, Corvaja &Pasimeni) . . .. . . 403 Electron Spin Resonance for Trapped Hydrogen Atoms in Aqueous Media.Comments and Calculations on the Radicals H302'and H30. (Claxton, Ginns, Godfrey, Rao & Symons) ... .. .... 21 7 Electron Spin Resonance Spectra of Fluoroalkyl Radicals in Polycrystalline Matrices. Part 3: Photolysis of Lead(1V) Fluoroalkanoates. (Ayscough, Machova &Mach) .750 Electron Spin Resonance Spectra of Secondary Alkylperoxy Radicals. (Bennett & Summers) .. .. .. 1043 Electron Spin Resonance Studies' of Reduction by Solvated Electrons in Liquid Ammonia: Part 6: @-Unsaturated Ketones. (Elson, Kemp, Greatorex &Jenkins) .. 665 Electron Spin Resonance Studies of Reduction by Solvated Electrons in Liquid Ammonia. Part 7: a$-Unsaturated Carboxylic Acids, Esters and Nitriles.(Elson, Kemp, Greatorex &Jenkins) ...........1402 24 SUBJECT INDEX-VOLUME 69, 1973 PA8B Equilibria of Copper(I1) Acetate with Acetylacetone in Acetic Acid and Methanol Solutions from Optical and Electron Spin Resonance Measurements. (Grasdalen) . . . Formation and Structure of Penta- and Hexa-coordinate Cobalt(I1)-Methyl Isocyanide 462 Complexes in Y-type Zeolites. (Lunsford &Vansant) . . . . Unstable Intermediates. Part 122 :Electron Spin Resonance Studies of Radicals from 1028 Irradiated Trimethylphosphine Oxide: the Me2P0 Radical. (Begum &Symons) . 43 Unstable Intermediates. Part 123 :Electron Spin Resonance Studies of 1-Monochloro and 1,l-Dichloro Radicals formed from Irradiated Alkyl Chlorides and a-Chlorocarboxylic Acids. (Mishra, Neilson &Symons) .. . . .1425 (e) nuclear magnetic resonance, quadrupole resonance Deuteron Magnetic Resonance Studies. Part 4: Dependence of some One Electron Pro- perties of the Ammonium Ion on Internuclear Distance. (Claxton, Dixon &Smith). 186 Double Resonance Nuclear Magnetic Resonance Spectra of Partially Aligned Molecules. (Emsley, Lindon &Tabony) . 10 Interpretation of Deutron Magnetic Resonance Spectroscopic Studies of the Hydration of Macromolecules. (Finer) . ... .... 1590 Magnetic Resonance Studies in Aqueous Systems. Part 2: Chemical Shift and Relaxation Time Studies of Hydroxylic Protons in Dilute Alcohol+ Water Mixtures. (Oakes) .1311 Magnetic Resonance Studies in Aqueous Systems.Part 3: Electron Spin and Nuclear Magnetic Relaxation Study of Interactions between Manganese Ions and Micelles. (Oakes) .... . ...... 1321 Measurement of Nuclear Magnetic Spin-lattice Relaxation Times by the use of Repetitive Sweep Techniques. (Heatley) . .... 83 1 Molecular Motion in cis-and trans-Dichlorotetra-amminecobalt(II1) Chloride by Proton Magnetic Resonance. (Ulrich &Dunell) . 1609 Nuclear Magnetic Resonance and Quadrupole Resonance Studies of Triethylamine Di- hydrochloride. (Cousseau, Gouin, Jones, Jugie &Smith) . . 1821 Nuclear Magnetic Resonance Study of Crystalline Bis(cyc1ooctatetraene)iron. (Chierico &Mognaschi) .. ... 433 Proton Magnetic Resonance Study of Molecular Motion'in Triphenyltin Fluoride, Chioride, Bromide and Hydroxide.(Dunell &Ulrich) . 377 Solid Phases of 2,3-Dimethylbutane. (Anderton &Llewellyn) . 1249 Solvation Spectra. Part 44: Nuclear Magnetic Resonance Study of Binary Solvent Mix- tures: Water Structural Effects. (Kingston &Symons) . . 978 Theory of Nuclear Magnetic Resonance Paramagnetic Shifts in Liquid Crystalline Solvents. (Giacometti, Nordio, Rigatti &Segre) . . . . . 1815 (f)neutron scattering Characterisation of the Torsion Potential for Ethylene Ligands using Inelastic Neutron Scattering. (Ghosh, Waddington &Wright) . .275 Librational Motion in Sodium and Lithium Aluminium Hydrides, studied 'by IneIastic Neutron Scattering. (Temme &Waddington) ... .783 Neutron Inelastic Scattering Studies on the Hydrogen Dihalides.(Smith; Temme, Ludman &Waddington). . .1477 Proton Motions in Hydrogen-bonded Ferroelectric and Antiferroelectric Solids. Part 2 : Neutron Incoherent Scattering in Polycrystalline Ag2H3L06 and Ag4H2I2OI0.(Temme, Smith &Waddington) . .1 (g)ion cyclotron resonance, mass spectrometry etc. Fragmentation Reactions in the Mass Spectrometer for C2-C5 Alkanes. (Flesch &Svec) .1187 Gas Phase Proton Affinities of Carbonyl Compounds by Ion Cyclotron Resonance Spectro- scopy. (Isolani, Riveros &Tiedemann) . .1023 Long-lived Parent Negative Ions Formed via Nuclear-excited Feshbach Resonances. Part 1:Benzene Derivatives. (Hadjiantoniou, Christophorou &Carter) . .1691 Long-lived Parent Negative Ions Formed via Nuclear-excited Feshbach Resonances.Part 2 :Aromatic Molecules other than Benzene Derivatives and Non-aromatic Organic Structures. (Hadjiantoniou, Christophorou &Carter) . .1704 Long-lived Parent Negative Ions Formed via Nuclear-excited Feshbach Resonances. Part 3 :Variation of the Autodetachment Lifetime with Incident Electron Energy. (Christophorou, Hadjiantoniou &Carter) .. .1713 SUBJECT INDEX-VOLUME 69, 1973 25 PAW Mass Spectra, Ionisation Potentials and Related Properties of Metal-free and Transition Metal Phthalocyanines. (Eley, Hazeldine &Palmer) ...... 1808 11, 6 Statistical Mechanics Chemical Combinatorics. Part 3: Stereochemical Invariance Law and the Statistical Mechanics of Flexible Molecules. (Gordon &Temple) ..... . 282 Free Energy of Small Face Centred Cubic Clusters of Atoms. (Burton). ... 540 Graph-like State of Matter. Part 2:LCGI Schemes for the Thermodynamics of Alkanes and the Theory of Inductive Inference. (Gordon &Kennedy) .... .484 Intrinsic and Extrinsic Defect Pairs in Caesium Halides. (Shulka, Ramdas &Rao). .207 Kinetics and Statistics of Random Cooperative and Anti-cooperative Occupation of Linear Arrays. (Boucher) . .... . . . .1839 Molecular Optical Anisotropy of n-Alkanes and Polyoxyethylene Oiigomers by Depolarized Rayleigh Scattering. (Bothorel &Fourche) . . .... .441 Monte Carlo Computer Simulation of Chain Molecules. Part 6: Interactions Between n-Alkane Molecules. (La1 &Spencer) .. . .... 1502 Point Defects in the Adsorption of Rare Gas Atoms on a Xenon Crystal. (Dovesi, Pisani &Ricca) .......... .1330 Problems in the Estimation of Entropy from Monte Carlo Acceptance Ratios. (Valleau & Whittington) . .. ........ .1004 Stereochemical Equilibrium in 2,4,6-Trichloro-n-heptanewith Applications to Poly(viny1 chloride). (Flory &Pickles) ........ .632 Surface Relaxation Effects in the Adsorption of Neon on Xenon Crystals. (Dovesi, Pisani &Ricca) .............. 79 11, 7 Thermodynamics (reversible and irreversible) An Attempt to Define Generally Isothermal Differences in the Chemical Potentials of Individual Ionic Species in Solution. (Hall) ....... . 1391 Approximate Expression for the Interaction of Diffuse Electrical Double Layers at Constant Charge.(Gregory) ............ 1723 Contribution of Ionic Effects to Electron Transfer Reactions. (Schmidt) ... 1132 Equivalence of Two Alternative Expressions for the Primary Medium Effect. (Hall) .975 Multimolecular Adsorption on Cell Surfaces under the Influence of van der Waals Forces. (Ninham &Richmond) . ........ 658 Osmotic Pressure of Polystyrene in Toiuene Solutions, measured over Wide Ranges ofCon-centration and Degree of Polymerization of the Polymer. (Hansen &Hvidt) ..881 Rate of Decomposition of Brownian Particles under the Action of London and Double- Layer Forces. (Ruckenstein &Prieve) ........ 1522 Structure of the Double Layer at the Oxide/Water Interface. (Perram) .. 993 Theory of Simple Electron Transfer Reactions in Solution.(Schmidt) .... 1104 Theory of Simple Electron Transfer Reactions in a Damped Dielectric Continuum Solvent. (Schmidt) . . ... ... ..... 1122 Thermodynamics of the Effects of Adsorption on Interparticle Forces. (Ash, Everett & Radke) ... ... .. 1256 van der Waals Dispersion Force‘ Cont;ibution to ‘Works of Adhesion and Contact Angles on the Basis of Macroscopic Theory, (Israelachvili) ... .. 1729 LI,8 Transport Phenomena (see also I, 6) Anomalous Diffusion-controlled Evaporation. (Nooney) . . . . . . 330 Close Collision Cross Sections for Ions and Symetric Top Molecules. (Hyatt &Stanton) .340 Electrical and Mass Transport in Salt-free Polyelectrolyte Solutions. (Schmitt &Varoqui) 1087 Zeolite Exchangers.Thermodynamic Treatment when Not All Ions are Exchangeable. (Barrer, Klinowski &Sherry) . . . . . ..... 1669 AUTHOR INDEX-VOLUME69, 1973 PAGE PAGE Aarons, L. J. . 270, 563, 643, 1510 Connor, J. A. . 270, 551, 559, 1677 Acuna, A. U. . . . 585 Corvaja, C. 403, 623 Albinati, A.. .798 Cousseau, J. . .1821 Anderton, K. J. . . .1249 Cox, A. P. .. .49 Archibald, R. M. . .1793 Craig, R. A. . .132 Armstrong, D. R.. .968, 1793 Cumper, C. W. N. .1172 Ash, S. G. . .1256 Cundall, R. B. . .701 Atherton, N. M. . .1801 Curran, J. S. . . . .126 Atkins, P. W. . .. .1542 Cyrot, A. . * 1339 Ayscough, P. B. . . . . 750 Damiani, D. . .119 Badiali, J. P. . .1339 Danby, C. J. . . . .1558 Balogun, G. A. ..1172 Davies, D. B. . .305 . .1223, 1739Barber, M. . 270, 551, 559, 1677 Davies, G. J. Barlow, A. J. . .1200,1446 Davies, J. B. . .. .246 .1011, 1223, 1785 Barnes, A. J. . .246, 532, 738 Davies, &I. Barradas, I.. . .388 Day,B. .. .1881 .. .361, 591 Barrer, R. M. . .1669 Day,P. Barrow, R. F. . .684 Denning, T. G. . .591 A? .. .559Begum,A. . .43 Derrick 56, 64, 804 Bendazzoli, G. L.. .. 579, 791 Dignam, M. J. . 186, 298Bennett, J. E. . .. .1043 Dixon,M. . .298Bemand, P. P. . .1643 Doggett, G. .952Bernardi, F. . .579 Donovan, R. J. .79, 1330 Bernstein, H. J. . .1586 Dovesi,R. . .363Bertinelli, F. . .889 Dubicki, L. . Bevan, J. W. . 902,916 Dunell, B. A. .377, 1609 .1370Bohme,D.K. . .1569 Durmaz, S. . Bothorel, P.. .. .441 Easterly, C. E. .471 Borrell, P. . .1060 Eaton, V. J. .1601 Boucher, E. A. . .1839 Eland, J. H. D. .1558 Breeze, A. . .1237 Eley, D. D.. .1808 Brownlee, R. T. C. .349 Eliezer, I. . .1835 BrustoIon, M. . 403, 622 Elson, I. H. .665, 1402 Burroughs, P. . .1659 Emsley, J. W. .10 Burton, J. J. . .540 Erginsav, A. .1200 Evans, K. . .856 Cachet, H. . .1339 Evans, M. . .763, 1011 Callear, A. B. . . 97 Evans, P. J. .224 Carter, J. G. . 471, 1691, 1704, 1713 Evans, S. .. .191 Casey, A. T. . .132 Everett, D. H. . .1256 Cathro, W. S. . .237 Cavell, E. A. S. . .315 Ferreira, J. A. . . 388 Cazzoli, G. . .119, 569 Finer, E. G. . .1590 Chamberlain, J. . .1223, 1739 Fini, G. . .1243 Charles,S. W. . .1454 Finnigan, D. J. . . 49 Christophorou, L.G. .471, 1691, 1704, 1713 Flesch, G. D. . .1187 Chierico, A. . .433 Flint, C. D. 23, 419, 1469 Claridge, R. F. C. . . 849 Flory, P. J. . .632 Clark, R. J. H. . .1496 Fortunato, B. . .1243 Claxton, T. A. . .186,217 Fourche, G. .441 Clyne, M. A. A. . .412, 1643 Freeman, C. G. . .849 Cocksey, B. G. . . .1558 Frimston, J. M. . .1542 Collingwood, J. C. .591 Frith, P.G. .1542 Collins, R. J. . .145 Frost, B. S.. .1142 26 AUTHOR INDEX-VOLUME 69, 1973 27 PAGE emt Gal, &I. E. . .395 Jones, G. I. L. ... .1455 Gardiner, D. J. . .. 1350 Jones, L. V. . . .1821 Geacintov, N. E. . .1208 Johnstone, R. A. W. . .36, 1155 Ghosh, R.E. . .275 Jugie, G. . ... ..1821 Giacometti, G. . .1815 Gibson, D. M. . .1659 Katritzky, A. R. ..349 Gijzeman, 0. L. J. $08, 721, 727 Kaufman, 708, 721, 727 Gilbert, A. S. . .1628 Kelly, G. R. . . . .395 Ginns, I. S. . ..217 Kemp,T. J. . .665, 1402 Girlando, A. . .818, 1291 Kenndy7J.W. . .484 Glover, G. M. . Kim, M. G. .1446 * iy; Kingston, B. : . .978Godfrey M. J. . .&2, 484 Klaaijsen, F. W. . . . .1537Gordon, M. .1821 Klinowski, J. . .1669Gouin, L. . Grabenstetter, J. E. 962 Kokoszka, G. ... . .355 * 462 Kuroda, H. . . . . .270Grasdalen, H. . ' 665, 1402 Kurucsev, T. . . . .395Greatorex, D. . Green, J. C. . .191 Ladd, A. G. ..... 849Greenough, P. . .23, 1469 Lal, M. . . . .1502 Gregory, J. . . .1723 Lamb, J. . .1446 Griffiths, J. H. . .1359 Larkin, I. W. ... .1278Grimshaw, D. . .168, 756 Larkin, L. . .. .1011 Guest, $1.F. . 270, 551, 563, 643, 1829 L.egon,A. C. . . . 29,902, 916 Gurd, R. C.. . .1542 Lestrade, J. C. . . . .1339 Liktaer, D. .. .. . 322 ieatley, F. . . . . 831 Lindon, J. C. ..... 10[eidner,R. F., I11 .927 Lister, D. G. . 119, 569, 791, 1036, 1304 [eller,D. . ... 856 Little, D. J. ..... 952[erd, Q. . .... 1677 Littler, J. G. F. . .. ..842 [ester,R. E. . ....1350 Llewellyn, J. P. ..... 1249[eywood,P. J. ..... 756 Lloyd, D. R. . . ... 1659[igasi,K. .. .. .1579 Luckhurst, G. R. .... 1491, 1752[igginson, B. R. ..... 1659 Ludman, C. J. ..... 1477[illier,I. H. . 270, 551, 559, 563, 643, Lunsford, J. H. . .... 10281510, 1677, 1829 Hollebone, B. R. .... 648, 1569 McAloon, B. J. ..... 968 Horsfall, G. S. . .1071, 1078, 1515 McCaffery, A.J. ....1767, 1779 Howells, J. D. R. .. 246, 532, 738 McEwan, M. J. . . .849 Humphries, R. L.. ... .1491 McGurk, J. C. . .... 97 Husain, D. . . . 145, 585, 842,927 Mach, K. . . . . . .750 Hvidt, A. . .881 Machova, J. ..... 750 Hyatt, D. .. .. .340 Mackie, J. C. .... 224, 237 Hyde, R. G. . .1563 McLaughlan, K. A. .... 1542 Hadjiantoniou, A.. .1691, 1704, 1713 Magee, M. D. .. ... 161 Hains, P. J. . .1785 Maier, J. P. ..... 521 Hall, D. G.. . . . .975, 1391 Maraschini, F. ... .798 Hall, M. B. 559, 563, 643, 1677, 1829 Matange, &I. . . ... 322 Hall, P. G. . . .1071, 1078, 1515 Matheson, A. J. . . . . 305 Hallman, H. E. . .. .246, 738 Matthews, A. P. . . 23, 419 Hancock, F. E. . ... .115 Maier, J. P. . .... 196 Hansen, J. . .881 Maurel, P.. . . .1486f.. Harrison, G. . .1446 Mayer, E. . .1350 Hazeldine, D. J. . .1808 Mellon, F. A. . ... 36, 1/55 Meredith, W. N. E. .... 1677 Ikemoto, I. . .270 Millward, G. E. ..... 1060 Isolani, P. C. . .1023 Minami, R.. . .1579 Psraelachvili, J. N. ... .1729 Mirone, P. . ... .1243 Mirri, A. M. . .569 Jackson, S. E. . . .191 Mishra, S. P. . . . . .1425 Janoschek, R. . .... 505 Mognaschi,. ..... 433 Jenkins, PI. D. B.. .665, 1402 Moskovits, M. .... 56, 65 28 AUTHOR INDEX-VOLUME 69, 1973 PAen PADE Moualem, A. ..... 1835 Salthouse, J. A. .. . .262 Munday, J.. .....349 Sarns,P. J. .180 Murrell, J. N. ..115, 1370 Sanson, A. . .. . .1752 Scarlett, M. J. . . .132 Neilson, G. W. .. 'z:; Scheps, R. . . . .856 Ninham, B. W... .. Schioberg, D. . . .771 Nooney, G. C. ' 330 Schmitt, A. . .1087 Nordio, P. L. :1815 Schmidt, P. P. . .1104, 1122, 1132 Schwarz M. .. .551 Scrimshaw, G. F.. . .738 Oakes, J. . .1311, 1321 Segre,U. . .. .1815 Ohno, A. ... .1579 Shears, M. F. .. .608, 1050 Orchard, A. F. .1659 Sheikh, M. A. . .315 Owen, N. L. 1036, 1304, 1359, 1454 Shepherd, T. NJ. . .126 Sheppard, N. . . .1628 Palmer, T. F. .1808 Sheridan, J. . .1359 Palmieri, P. 579, 791 Sherry, H. S. .1669 Pasimeni, L. 403, 622, 623 Shuk1a9 A. K. * .207 Pecile, C. . 818, 1291 Smith, I. W. M. . . .939, 1416, 1617 Pedley, J. B. .1370 Smith, J. A. S. . . .I, 186, 1477, 1821 Peel, J. B. . .1563 Snook,I. K. . .1183 Pereira, L. C. 701 Spencer, D.. . .1502 .1183Perkins, P. G. :968, 1237, 1793 T.-Perram, J. W. . . .. 993 Stacey M. ... .551 Perutz, R. N. . . Stanton, L. . .. .340 Phillips, L. F. ti; Steele, D. . .1601 I. Pickles, C.J. .. * 632 Stewart, R. F. . .1685 Pisani, C. . Stremmenos, C. . .889 Pitt, C. G. . . 79, Summers, R. . .1043 Pleau, E. . . . 355 Svec, H. J. . .1187 Pope, M. . 1208 Symons, M. C. R. , .43, 217, 978, 1425 Porter, G. . . 708, 727 Pozzoli, S. A. .256 Tabony, J. M. . . 10 Price, A. H. .1486 Takahashi,H. . .1579 Prieve, D. C. .1522 Tedeschi, M. . .256 Ptak, M. . .1752 Temme, F. P. . 1, 783, 1477 Temple, W. B. . .282 Radke, C. J. .1256 Terauds, K. .1563 Ramdas, S. . Thomas, J. M. . .270 Rao, B. . * i:i Thomaz, M. F. . .388 Rao, C. N. R. * 207 Tiedemann, P. W. . .1023 Rao, K. V. S.Topsom, R. D. . .349 Rassing, J. . ' :ii Turner, D. W. . .196, 521 Rastelli, A. . * 256 Turner, J. J. . .452 Reedijk, J. . .1537 Reeves, D. A. .1381 Ulrich, S. E. .. .377, 1609 Ricca, F. . . 79, 1330 Rice, S. A. . 87, 91, 856 Valleau, J. P. . .1004Richmond, P. .658 Vander Donckt, E. .322Rigatti, G. . .1815 Vansant, E. F. . .1028Rippon, D. M. .1496 Riveros, J. M. .1023 Varoqui, R.. . .1087 Roberts, N. K. .1084 Verma, A. L. . .1586 .1208Robinson, D. A. .701 Vogel, F. . Rode, B. M. .1439 Rosenthal, D. .332 Waddington, T. C. 1, 262, 275, 783, 1477 Rosenwaks, S. .1416 Walker, S. . .161 Roth, J. . ..804 Webster, B. C. . .1685 Rowe, M. D. .1767, 1779 Weidemann, E. G. .505 Ruckenstein, E. .1522 Whitehead, M. A. . 648, 962 AUTHOR INDEX-VOLUME 69.1973 29 PAGE PAGE Whittington. S.G.. . . . 1004 Wright. C.J......275 Wiesenfeld. J.R.. . . . 927 Wyn.Jones. E....168. 180. 756 Wilkinson. F.. . . . . 1381 Yee. K.K.......684Williams. G.. . . 608. 1050. 1785 Witteveen. H.T.. . . . . 1537 Zanon. I.......1164 Wittig. C... .939 Zellner. R .......1617 Wood. J.L. . . . . 87. 91 Zocchi. M.. . . . . . 798 Woon.Fat. A.R .. . . .412 Zundel. G...... 505. !771 THE SECOND ANNUAL GENERAL MEETING of the Faraday Division of The Chemical Society was held at 9.00a.m., on 19th September, 1973, in the Physiology Lecture Theatre, The University of Oxford, with Professor Sir George Porter, M.A., Ph.D., Sc.D., F.R.S., in the Chair. 1 The Minutes of the First 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 3 April 1974 were as follows: President PROF. T. M. SWGDEN,M.A., Sc.D., F.R.S. Vice-presidents who have held the ofice of President SIRFREDERICK M.A., Sc.D., F.R.S. PROF. J. W. LINNETT,DAINTON, M.A., D.Phil., F.R.S. 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 DAVIES, M.Sc., Ph.D., Sc.D. DR. B. A. PETHICA, PROF. MANSEL Ph.D., D.Sc. PROF.D. H. EVERETT, M.B.E., M.A., D.Sc. PROF.W. C. PRICE, Sc.D., F.Inst.P., F.R.S. PROF.P. GRAY, M.A., Ph.D., Sc.D. PROF. F. C. TOMPKINS,D.Sc., F.R.I.C., PROF.J. N. MWRRELL,B.Sc., Ph.D. F.R.S. Ordinary Members of Council PROF.G. ALLEN, B.Sc., Ph.D. ,F.Inst .P. PROF.I. M. MILLS, B.Sc., D.Phi1. PROF.E. F. CALDIN,M.A., D.Phi1. DR. R. PARSONS, D.Sc., A.R.C.S., F.R.I.C. DR. A. KELLY, B.Sc.,Ph.D., S.D., F.R.S. PROF.J. S.ROWLINSON,M.A., D.Phil., PROF.N. B. H. JONATHAN,BSc., Ph.D. F.R.I.C., F.R.S. PROF. M. MAGAT, D.Sc., D.Phi1. DR.H. A. SKINNER, B.A., B.Sc., D.Phil. PROF.DR.J. LYKLEMA Honorary Treasurer PROF. P. GRAY, M.A., Ph.D., Sc.D. Honorary Secretary PROF.F. C. TOMPKINS,DSc., F.R.I.C., F.R.S. The President thanked Professor Ubbelohde and Professor Coulson for their services as Vice- Presidents and Professor Dr. Franck, Professor Hills and Professor PurnelI as the retiring Ordinary Members of Council.3 Annual Report In his report for the year 1972-3,The President said that during the first year of amalgamation, the Faraday Division had been increasingly active. Two traditional General Discussions, ‘Reactions of Small Molecules in Excited States’ and ‘Photoelectron Spectroscopy of Molecules’ were held, the proceedings being published as Faraday Discussions of The Chemical Society, No. 53 and 54, and Special Discussion No. 2 on ‘Solid Solid Interfaces’ took place. A Sym-posium on ‘Molecular Motions in Amorphous Solids and Liquids’ formed part of the first Annual Congress of the amalgamated bodies and appeared in print as Faraday Symposium of The Chemical Society No.6. In addition, informal discussions on ‘Ordered Structure in Liquids’, ‘Solvation Effects’ and ‘Chemical and Electrical Effects from the Mechanical Treat- ment of Polymers’ took place. There were also a considerable number of Group discussion meetings arranged by the Subject Groups affiliated to the Faraday Division. The following lectures, associated with the Faraday Division, were delivered :The Faraday Division Presidential Address by the President, Professor J. W. Linnett; a Plenary Lecture at the Autumn Meeting by Professor H. L, Friedman (State University of New York); the Chemical Society Cen- tenary Lecture by Professor J. A. Pople (Carnegie-Mellon University); the Bourke Lectures by 30 ANNUAL GENERAL MEETING Professor I. Prigogine (Free University of Brussels) and the Spiers Memorial Lecture by Professor G.G.Hall (University of Nottingham). The Marlow Medal for 1972 was awarded to Dr. W. G. Richards (University of Oxford). Publications in the Transactions, now published as two journals relating to Physical Chemistry and Chemical Physics respectively, increased during the year by about 25 %. The President concluded that the Faraday Division had successfully maintained and extended the traditional activities of the old Society during its first year as part of The Chemical Society. CORRIGENDA Molecular Complexes of Substituted Thiophens with c and nAcceptors by GIAN GAETANO PIGNATAROALOISI and SALVATORE J.C.S. Faraday I, 1973, 69, 534 Page 535, 13th line from the bottom of the page : for lower wavelength read longer wave- length. Far Infra-red Absorptions of Non-dipolar Liquids. Part 1.-Experimental Measure-ments, Quadrupole Interpretation and Model Calculations. BY GRAHAM JOHN CHAMBERLAINJ. DAVIES, AND MANSELDAVIES J.C.S. Faraday 11,1973,69, 1223 Although the numerical values of the moments given are correct in both e.s.u. and SI units, some of the equations were incorrectly converted from c.g.s. to SI representation. Eqn (64 and (6b) should read Eqn (9) should read Eqn (10) should read Eqn (14) should read 1 CSeiSeju(r) = --.4n~, r Eqn (16) should read We are grateful to Dr. A. M. Price for helpful comments. 32

ISSN:0300-9238    

DOI:10.1039/F297369BA001

出版商:RSC    

年代:1973

数据来源: RSC

摘要:

Double Resoiiance Nuclear Magnetic Resonance Spectra of Partially Aligned Molecules BY J. W. EMSLEY,J. C. LINDONAND J. M. TABONY Chemistry Dept., University of Southampton, Southampton SO9 5NH Received 3rd July, 1972 The theory of Anderson and Freeman for double resonance has been extended to the case of partially aligned systems. A computer programme has been written to calculate such spectra and the results are given for a number of spin systems. Some examples are given showing decoupling of interactions between hydrogen and deuterium by coherent double resonance. The theory of phase modulated double resonance is presented and it is shown experimentally to give improved decoupling. It has been widespread practice for some time to use strong double irradiation to simplify the high resolution n.m.r.spectra of isotropic liquids ; the theory of such an experiment is well understood.l* The use of spin decoupling for anisotropic liquids has not been extensively applied, but the potential usefulness of this technique is probably greater than for isotropic liquids since, without resorting to some means of spectral simplification, the spectrum often defies analysis or is not observed at all. Two accounts of spin decoupling for anisotropic solutions have been rep~rted,~. showing that the experiment is practicable in some cases. We present here a dis-cussion of the theory of spin decoupling for anisotropic liquids, together with com- puted spectra, and some practical examples of the technique.THEORETICAL We assume that the effects of relaxation on the spectra can be neglected provided the observed nuclear spins are not saturated, when we employ the method developed by Anderson and Freeman to derive an appropriate hamiltonian. Three magnetic fields are applied to the sample. A static field B, in the z direction separates the nuclear magnetic energy levels. A field B, applied in the x direction oscillates with a frequency m2, which is in the region of the Larmor frequency of the S spins. We use the symbol S for the nuclear spin angular momentum of the irradiated spins, and Ifor the observed spins. A second oscillating magnetic field B, is applied in the x-direction, but its frequency o1is in the region of the Larmor frequency of the I spins.The hainiltonian for such a system, neglecting relaxation, can be written as 2r = %c+ A?:+ &+ H:”+%A+ 3r; +%AS+ H6+%; +%l(t) +X2(t) (1) where the individual terms are as follows. and is the Zeeman interaction between the applied field Bo and the Z and S spins. Thus alland cuk3are the resonance frequencies of the I and S spins in the field B,. 10 J. W. EMSLEY, J. C. LINDON AND J. M. TABONY I X: = 271C JiJi ' Ij i< j and is the scalar part of the electron coupled spin-spin interaction between non- equivalent I spins. Similarly is the same interaction between non-equivalent S spins, and I.S A?:' = 271C JJi ' Sk iik is between S and Z spins. The term magnetic equivalence must be used in the appro- priate sense for anisotropic system^.^ The terms J'?; and 2l'g represent the nuclear dipole-dipole interaction, and also include any anisotropic electron coupled interactions, although we will not un-necessarily complicate matters by separating these two interactions.In the usual high-field approximation these termshave the forms, *S, = 271C 2Drt(SzrSzt -3s+ rs-t -ts-r S + t) r<t where the summations are over all pairs of nuclei. Similarly XLsis the dipolar interaction between Z and S spins, The two terms X'&and 2:refer to the interaction between the electric quadrupole moments of nuclei Z and S with the electric field gradients at the nuclei. Assuming that the Z and S spins are effectively aligned along the field (2) direction, then the quadrupole terms are, T where qrr= e2 V,,, QIand qks = e2 VkzzQs.The terms Vtzzand VkzZ referring to the zz components of the electric field gradient tensor at nucleus i and k, and QI and Qsare the nuclear quadrupole moments of spins I and S. The last two terms in the hamiltonian of eqn (1) represent the interaction between I spins and the oscillating field B1,and the S spins and the oscillating field BZ. X,(t)= -yIBl(Ix cos wlt-Zy sin colt) S2(t)= -ysB2(Sx cos 02t-S, sin w2t). The hamiltonian of eqn (1) represents a system in which the nuclear spins are either observed or irradiated. We will not treat explicitly the general system which would include groups neither observed or irradiated, since to do so simply complicates the algebra; the general principles of double resonance behaviour can be illustrated on the simpler 1-5' system.The computer programme for double resonance spectra does include the general case, DOUBLE RESONANCE SPECTRA The method of Anderson and Freeman is to remove the w2 time-dependencefrom eqn (1) by a transformation to a coordinate system rotating about the z axis with frequency co2. The appropriate operator is which produces a transformed hamiltonian YfT according to the relationship JfT = TA?T-l+iTT-l. The terms %:, Jff, 2?,S;,%';, XL', X;, X: are all unchanged by this trans- formation, and the remaining terms become, S 1 X2T = -YsB2Sx %'(I) = -yIB,(Ixcos (w,-w2)t-I, sin (a1-w&). Thus in this new frame of reference the hamiltonian contains only %(t) as a time- dependent term, and is like a single resonance hamiltonian, in which X(t)induces transitions between stationary state energy levels at frequencies (q1-0,).A computer programme has been written, based on that of Govil and Whiffen,6 to compute double resonance spectra of anisotropic systems, and for which I and S may be + or 1.Theoretical spectra have been computed for some spin systems to illustrate the general features of anisotropic systems, and to assess the practicality of spin decoupling for the spectra of solutes dissolved in ordered fluids, such as nematic liquid crystals. EXAMPLES OF COMPUTED SPECTRA For examples of spin systems we will use the accepted nomenclature, thus A-(XIrefers to an AX system with A observed and X irradiated.The angular momentum operators for the observed spins, A, will be denoted by the symbol 1, and for the irradiated spins by S. A-(X) SYSTEM WITH BOTH NUCLEAR SPINS 3 In this case the time-independent part of the transformed hamiltonian is simply, ZT= -[(WA-WZ)I~+ (O~-~O,)S,-~.~DA,Z,S,-~~J,~Z~S~+Y~B~S,]. This hamiltonian differs from that of the isotropic case only by the replacement of JAX by (JAX+IZDAX), and this does not change the system in any essential manner. Thus the hamiltonian can be made diagonal in the (I, + S,)representation and analyti- cal expressions derived for the line frequencies and intensities.' It is well-known that completedecouplingcan beaffected for such a system when ysBz % 2n(JAx+ 20Ax) &-(XI SYSTEM WITH BOTH NUCLEAR SPINS 3 In these systems, the transformed hamiltonian contains 2;; this extra inter- action makes the anisotropic system differ in behaviour from the isotropic one.The time independent part of the transformed hamiltonian is, rn J. W.EMSLEY, J. C. LINDON AND J. M. TABONY A unitary transformation by the operator R = exp [ie(t&tA)sy] has the effect of bringing (2) into a form involving only the z component of the angular momentum operator for the X nuclei, thus HTR = RHTR-' (3) = [ -(coA %)Iz -Zw 2DAA(I~dzq .-tr+ pl -q --+ q) f a(mA)sz] (4>P<Q where e(mA)and A@,) are given by A(mA) = [{ax-w2-2n(JAX + 2DAX)mA)2 +(YXg2)']'* (6) A comparison of (5) and (6) with those for an isotropic A,X system shows that the only change is the inclusion of DAX, and this does not affect the kind of double resonance behaviour observed. Thus complete decoupling is not possible when n > 1 and the spectrum shows residual splittings whose magnitude at high values of yxB, is given by, WJAx + ~DAx)'(~A-3>'hx&-This behaviour is illustrated in fig.1 where we show some computed spectra for an A3X system in which DAA = 500 Hz and (JAx+2DAx)= 650. It is noted that the outer pair of lines move towards one another, whilst the centre pair are replaced by a single intense line at the centre and two weak lines which move out and decrease in I E2=2000 c -1500 0 1500 frequency/Hz FIG.I.-Computed double resonance spectra for a system A3-{X) with IAand Ix both 4.The value of DAAis 500 HzandJ'+ 2DAX = 650 Hz. intensity on increasing B2. At high irradiating power, the spectrum tends towards a triplet of separation ~DAA,but with residual splittings in the outer components. More complex systems of the type A,B,C,. . . X where irradiation is at X, will show similar behaviour, such that virtual decoupling can be achieved, but some residual splittings will remain depending inversely on the strength of Bz. A-(X,) WITH ALL SPINS 4 The hamiltonian for this system includes a term 2';.The time-independent part of the transformed hamiltonian is r n n DOUBLE RESONANCE SPECTRA The presence in (7) of the term 2;means that it is not possible to transform the hamiltonian to a factorisable form using a simple unitary operator as before.It is not possible, therefore, to write out expressions for the double resonance energy levels and residual splittings. In this sense, the system is more analogous to a AX(Y) isotropic system than to A(X,). The behaviour of such systems at different values of B2 can, however, be computed numerically, and in fig. 2 we show spectra for the A-[X2} with In=b2 Ix = 82'0 I 1 Jxx=600Hz -I000 0 I000 frequency/Hz FIG.2.-Coniputed double resonance spectra for a system A-{X2) with IA and Zx both 8. The value of Juf2D.4~= lo00 Hz. Spectra are shown for both DXX = 600and &X = 1200 Hz. system A-(X,) irradiated at w2 = cox. In the example, D,, = 600 or 1200 Hz, JAx+ 2DAx = 1OOO Hz. The effect of irradiating strongly is that the outer compon- ents of the triplet move outwards and decrease in intensity, whilst the centre line remains and increases in intensity.Thus virtually complete decoupling is easily achieved in this system. The spectra also illustrate that the double resonance A spectrum depends on the magnitude of (JAx+2DAx). A3-{X2) SYSTEM WITH ALL SPINS 4 In this case, thc hamiltonian contains 2;and %; ; computed spectra are shown in fig. 3 for a system with DAA = 500 Hz, D,, = 150 or 300 Hz, and (JAX+2DAX) = 82=2000 Dx)(=150 II I up2000 nxx=300 It I I I1 J. W. EMSLEY, J. C. LINDON AND J. M. TABONY 310 Hz. The computed spectra show that virtual decoupling can be achieved, but that residual splittings remain in the outer components of the triplet.The magnitude of the residual splittings depend upon Dxx as well as (JAx+~DAX).Note also that the outer components are not symmetrical, hence measuring DAA from the decoupled spectrum will involve an error which depends on how large B2 is. SYSTEMS IN WHICH THE x NUCLEI HAVE s= i Anisotropic systems X, where the spin of X is greater than + pose new problems in double resonance because of the presence of the term 2; in the hamiltonian. There is a further complication in that no true magnetic equivalence exists, that is both 8‘;and i%?y should be included in the hamiltonian for all pairs of X * In the systems of most interest, those with X as deuterium, the magnitude of J2t1-2tI is usually negligibly small, and we have not examined the consequences of large Jij values for these systems.A-{X) WITH I = 4,s = 1 In this, the simplest of these spin systems, the presence of 2”; in the hamiltonian makes it impossible to write down analytical expressions for the double resonance energy levels and intensities. We therefore rely on computed spectra to illustrate the properties of this system for irradiation at w2 = wx, and which has (2DAX +JAx)= 285 Hz, and qD = 6666 or 13 332 Hz. On increasing B2 it is seen that the outer A-{X} with Z,.,=k2 2,=1 82=OIll a= 6666 HZ 82=2000 o = 6666 82=3000I 4=6666 82 =3OOO 4= 13332 1 I 1 -500 0 500 FIG.4.-Computed double resonance spectra for a system A-{X} with rA = 8, JX = 1.The values of J=+2Dm = 285 Hz. Spectra are shown for qx = 6666 Hz and 13 332 Hz. components of the single resonance triplet spectrum move outwards and decrease in intensity, giving virtually complete decoupling. It is also seen from fig. 4 that the value of qD affects the extent of decoupling, and for large B2the separationof the centre and outer lines is approximately linearly dependent on 4D. At very high irradiating powers, in this case 6000 Hz low intensity lines begin to reappear in the spectrum. A3-(X) WITH Z = *, S = I Computer spectra for this system are shown in fig. 5. lrradiation is at o2= ox =and JAX+2DAX 110 Hz, DAA= 600 Hz and qD = 6666 or 13 332 Hz. On in-creasing B2 the lines 2,5 and 8 stay at the same position. Lines 1 and 3 move towards 4=0 9=6666Hz 82=3000 I I 9=6666 A,-(X] WITH Z=&, S= I Fig.6 shows some computed spectra for this system, again for irradiation at co2 = wx, and with Dxx = DAA = 600, JAX+2DAX = 110 Hz, qD = 6666 or 13 332 Hz. For large B,, virtual decoupling does occur but there are residual split- tings in both halves of the A doublet whose magnitude depends on DAx,qD, B2and Az-{xz) withI',,=1f2 Ix"I 82~0 4=6666Hz 12345 678910 82=1000 6=6666 I. I. 82=2000 4=13332 -900 900 FIG.6.-Computed double resonance spectra for a system A2-{X2)with IA = 4, IX = 1. The value of DAA = 600 Hz and Ja+2Dm = 110 Hz, Dxx = 12 Hz. Spectra are shown for qx = 6666 Hz and 13 332 Hz. Dxx. The behaviour of individual lines in this system is as follows.On increasing B2 the centre lines in each half of the spectrum, lines 3 and 8, remain unchanged. Lines 2 and 4 split, one component moving outwards and decreasing in intensity, the other maintaining intensity and moving towards 3. Similar behaviour is shown by lines 1 and 5, and by the corresponding lines in the other half of the spectrum. J. W. EMSLEY, J. C. LINDON AND J. M. TABONY The computation of double resonance spectra requires a larger computer store than is the case for the single resonance spectrum. This arises because the hamil- tonian matrix cannot be factorised according to the values of S, and, for systems where X has S = 1, this has limited us to the relatively simple systems discussed above. However, it is apparent that for anisotropic systems double irradiation can provide a means of simplifying spectra, provided large B2 values can be generated at the sample.EXAMPLES OF DECOUPLING OF ANISOTROPIC SYSTEMS BY DOUBLE IRRADIATION 9F-{'H).-The systems with all spins + are the easiest to decouple, except that in practice the dipolar couplings DAX tend to be large. Homonuclear decoupling for protons is rarely possible as the spins are almost invariably very strongly coupled. For fluorine some examples of homonuclear decoupling may be possible, but again most systems do not have coI and ws sufficiently far apart. The systems most amen- able to decoupling experiments are where the A nuclei are protons and X fluorine, or vice-versa. We have attempted one such experiment, the results of which are shown in fig.7. The system is the molecule CF3CH20Hdissolved in the nematic phase of N-(p-eth0xybenzylidene)-p-n-butylaniline(EBBA), which is an A3X2Y spin system. Fig. 7 shows the single resonance I9F spectrum, first after leaving to equilibrate in the magnetic field for many hours, and which shows considerable fine structure. We also show the single resonance spectrum under the same conditions for recording the FIG.7.-Single and double 19F spectra of CF3CHz0Hdissolved in N-(p-ethoxybenzy1idene)-p-n-butyladine, The top spectrum was recorded after equilibrating in the magnet of a HA 100 spectro-meter for several hours. The middle spectrum was recorded shortly after placing into a magnet and with the proton irradiation on but far from resonance. The bottom spectrum was recorded under the same conditions but with wz in the centre of the proton resonances.The ''F-{'H}double resonance spectra were recorded on an XL 100-15 spectrometer by Dr. D. Shaw of Varian Associates Ltd., England. (a) 19Fspectra; (b) "F-{ 'H} spectrum. DOUBLE RESONANCE SPECTRA double resonance spectrum, that is with the decoupling field applied, but far from the proton resonances. In this case, temperature inhomogeneities give a poorly resolved spectrum. The bottom spectrum in fig. 7 is recorded under the same con- ditions as the one above, except that w2 is applied near the centre of resonances of the two protons. In this case, the spectrum shows a definite 1 :2 : 1 triplet corres- ponding to DFF= 100 Hz, which is the value found from an approximate analysis of the proton and fluorine single resonance spectra.The other couplings in this molecule are DCHz = 500 Hz and DCFSPH2 = 50 Hz. H -i2H).-The most generally applicable technique for simplifying the proton spectra of partially oriented molecules is to replace some hydrogens by deuterium, followed by decoupling of the 'H -2H interactions. We present here some results showing that this is a practicable technique for real spin systems using currently available spectrometers. The ease of decoupling clearly depends upon the magnitudes of qDy DIIDand ODD. The value of DDDis DHI1x (0.153 51)2, and is therefore usually not important in determining the strength of I'D& needed for effective decoupling.The magnitude of DHD is usually no more than a few hundred hertz, and is comparable for example to 'J13ca, an interaction routinely decoupled in 3C spectroscopy. However, qD varies widely and in our experience ranges from 500 to 30000Hz! I FIG.8.-Single and double resonance spectra of CHD,OH dissolved in N-(p-ethoxybenzy1idene)-p-n-butylaniline. The coupling constants are DcmZ= +25 Hz, DOH-" = -30 Hz, DCD~= +3 Hz, DCH+-JH = -195 Hz, and qD = 820 Hz. Both spectra were recorded on an HA 100 modified to accept two r.f. fields. (a) 'H spectrum ; (6) 'H-{2H} spectrum. Thus the success of the decoupling experiment is largely determined by qD. In fig. 8 we show the 'H and 'H -i2H) spectrum of CHD20H dissolved in EBBA.In this case, qD is 820 Hz and decoupling is easily achieved by strong irradiation at o2= wD, giving an AB spectrum. The values of the coupling constants in this system are DCH-D = t-25 Hz, Do1r-D = -30 Hz, DCH-oH = -195 Hz. J. W. EMSLEY, J. C. LINDON AND J. M. TABONY Fig. 9 shows the proton spectrum of CH3CD20Hdissolved in EBBA, and which has DCH3= 292 Hz, DCH3-cD2= -18 Hz and qD = 2175 Hz. There are poorly resolved couplings DCH3--OH= -19 Hz and DCDzaH= -25 Hz. Strong irradiation removes the H-D interactions, as shown in fig. 9, leaving unresolved couplings to the OH protons and between CH, and OH. Fig. 10 shows a more extreme example of decoupling. The molecule is C6D5COCH3, d,-acetophenone, dissolved in the nematic phase IV produced by 876 HZ -FIG.9.-Single and double resonance spectra of CH3CD20Hdissolved in N-(p-ethoxybenzy1idene)-p-n-butyaniline. The coupling constants are DCH~= 292 Hz, DCH~-CD~= -18 Hz,DCH~-OH= -19 Hz, qD = 2175 Hz.The spectra were recorded in the FT mode on a Bruker Physik HFX 90 by Dr. R. Price and Mr. T. Keller of Bruker-Physik, Karlsruhe. The peak labelled A is from the residual protons in the C6D6used as lock signal. (a)'H spectrum; (b) 1H-(2H> spectrum. FIG. 10.--'H-i2H) double resonance spectrum of C6D5COCH3,&-acetophenone, dissolved in nematic phase IV of E. Merck. The spectrum was recorded in the FT mode on a Bruker HFX 90 by Dr. R. Price and Mr. T. Keller of Bruker-Physik, Karlsruhe. DOUBLE RESONANCE SPECTRA E.Merck ; the single resonance spectrum cannot be observed owing to the large number of transitions. Strong irradiation at the deuterium frequency gave the spectrum in fig. 10. It is interesting to note that the centre line is very sharp compared to the outer lines of the triplet. This broadening is presumably caused by many small unresolved lines, similar to the A3-(X) case discussed earlier. However, some of the broadening may also arise from temperature inhomogeneities caused by the heating effect of the large B, field. MODULATED DOUBLE RESONANCE It is well-known that niodulating the field B, can in some cases lead to more effi- cient spin-dec~upling.~-l~Noise modulation, frequency, amplitude and phase modulation are all possible ways of improving the decoupling experiment.For situations where there are large couplings, but small chemical shifts, the most efficient method of decoupling should be frequency modulation of 0,(or the equivalent amplitude modulation). In all the experiments described so far, the addition of noise modulation made no improvement on the decoupling achieved by coherent irradiation alone. We have not yet achieved a stable system for frequency modula- tion of co,, but the similar phase modulation experiment has proved simple experi- mentally, and does give an improvement for some types of system. Since the theory of this experiment has not been given previously we will present the details for iso-tropic systems, the extension to anisotropic systems then being easily seen.PHASE MODULATED DOUBLE RESONANCE FOR THE ISOTROPIC SYSTEM AKX We consider the system AKX in which all spins have spin 4,and in which A refers to observed and X to irradiated spins. We use the symbols and 1, for the spin operators for nuclei A and K, but for the irradiated spins X we use S. The phase modulated B, field is produced by square wave modulation of the phase, that is by diode switching from 0" to 180" in a similar way to that commonly used to produce pseudo random noise modu1ation.l The B2 field is therefore modulated according to the expression,12 *pBz cos (co, + W,)t -3pB2 cos (a2-am)f provided that the modulation index p is less than about 0.5. This is equivalent to carrier suppressed frequency or amplitude modulation. Expanding the cosine terms gives the following expression for Yf,(t).Z2(t)= -/3yxB2 sin co,t(S, sin cu,t+Sy cos w2t) which may be written as Z2(t)= -pyxB, sin mmt exp (iw2tSz)Sy exp ( -iu2tSZ). Thus the full hamiltonian for the AKX system is f~KI~K -~~~JAK~~AI~K&? = -[C~)AI~A + OxS, -~~JAxI,AS, -2d,xIz~Sz-yxB2Psin wmtexp (io,tS,)S, exp (-~~~~SZ)+YAB~(IA~ sin u2t)].cos Transforming to a frame rotating about the x-axis with angular frequency 0.1, gives a transformed hamiltonian, Z'l-= -[(WA -m2)I2.4+ (WK -w2)Iz~ -+ ((Bx-c02)sz-~~JAXIZ,SZ-2d&Iz~Iz~ k&x&&-yXP& sin wmtSy+yAB,(IxA cos (ml-cu2)t-I,,*sin (w,-02)t]. The term PyxB, sin wmtSyrepresents in the rotating frame a magnetic field J.W. EMSLEY, J. C. LINDON AND J. M. TABONY applied along the y-axis and oscillating with frequency am.This may be expressed as the sum of two counter-rotating fields, thus sin omtSy= 4byxB2(Sy sin wmt + S, cos omt + S,, sin omt- S, cos mmt). If corn and JKxare large compared with pyxB,, then only one component appreciably perturbs the ~ystem,~ and we can write '%2T(t) as %2T(r) = $PyxB2(Sx COS W,t-sySin u)mt). (9) The action of the operator exp [-immtSz] removes the time-dependence from all terms except XI(I), when the time-independent transformed hamiltonian has the form, xTT = -[(UA -m2)zzA + (WK -m2)zzK + (ox -a2 -mm)sz -2n JAXz~AS~-271.JAKZz AZzK -~~JKxLJZ ~Sxl-(10)+ ~PY The haniiltonian (10) can be brought into a form diagonal in the product spin re- presentation by the transformation exp [ie(mA, mK)Sy], where giving STTT = -[(wA-w~)~zA+(oK-co2)~zK-2nJAK~zA~zK+A(mA,mK)Sz] (11) where A(mA,m,) = [(WX-02 -mm-2nJ~xm~ + &Q2B$]'.-~~JKX~K)~ (12) From the hamiltonian of eqn (11) it can be shown that, in the laboratory frame, A transitions will occur at frequencies u)(mA,mx; mA-1, mi) = ~A+~~JAK~K$-A(~A,~,)~x-A(~A-~,mK)mi.For low values of B2 it was shown by Anderson and Freeman that mx and mi may each take all the (2S+ 1) allowed values of mx. For high irradiating fields, i.e., when p')JxB29 2(Wx -u)2 -W, -2nJ~xm~-2nJ~xm~) then the only transitions with appreciable intensities have mx = nzk. When PyxB2becomes much larger than the other term in A(mA, mK) then A(mA, InK) ,!% A(mA-1, mK), (13) giving a decoupled spectrum.When u), = 0 the spectrum will always contain some residual splitting given by (2nJAXJKXmX)2 / yXB2 however, examination of eqn (12) shows that when cox = cu2 and omis set equal to dKX, then the condition (13) can be exactly satisfied when P2yj@i is much larger than 2nJAx. Thus the efficiency of decoupling is increased. This can be visualised as equivalent to irradiating with two B2 fields, each of strength 3PyxB2,and centred at c~x+nJKxrespectively. It should be noted that phase modulation does not give an increase in efficiency of decoupling as great as that produced by frequency modulation.g*lo For anisotropic systems, the same theory applies with the replacement of Jij+ 20,, for Ji,when only spin 3 nuclei are involved. For systems in which S = 1, i.e., 'H-(2H) experiments the theory cannot be given in such a simple form, but the DOUBLE RESONANCE SPECTRA method does lead to improved clecoupling in some cases.This is particularly true for systems with a large value of qD, and is illustrated by the spectrum in fig. 11. The molecule is CH30Ddissolved in EBBA. The deuterium spectrum was recorded by the INDOR technique and consists of a broad doublet of separation 24 100 Hz. FIG.11.-(a) 'H single and (b) 'H-{ 2H} double resonance spectra of CH30D dissolved in N-(p-ethoxybenzy1idene)-p-n-butylaniline. Coupling constants are DCH~= 21 5 Hz, DCH~-D= 35 Hz, qD = 24 100Hz. The double resonance spectrum has w2 at the centre of the deuterium spectrum and phase modulated with a frequency of 12 050 Hz and a modulation index of approximately 0.5.The other couplings are DH~= 215, DH,,= 35 Hz. Irradiating strongly at co2 = ox did not succeed in appreciably perturbing the spectrum, but when phase modulated at 12 050 Hz the spectrum shown in fig. 11 was obtained. Complete decoupling has not been achieved but the improvement over coherent irradiation is considerable. We thank Dr. R. Price and Mr. T. Keller for recording the spectra shown in fig. 9 and 10 and Dr. D. Shaw for the spectra shown in fig. 7. W. A. Anderson and R. Freeman, J. Chem. Phys., 1962,37,85. R. A. Hoffman and S. Forsen, Prog. Nucl. Mag. Res. Spectr., 1965, 1, 15. J. W. Emsley, J.C. Lindon, J. M. Tabony and T. H. Wilmshurst, Chem. Comm.,1971, 1277. S. Meiboom, paper presented at the 4th International Symposium on Magnetic Resonance, Jerusalem, 1971. P. Diehl and C. L. Khetrapal, N.rn.r. Basic Princbles and Progress, ed. P. Diehl, E. Fluck and R. Kosfeld (Springer Verlag, Berlin, 1969). G. Govil and D. H. Whiffen, Mol. Phys., 1967, 12,449. 'J. I. Musher, J. Chem. Phys., 1967, 46, 1537. A. Saupe and J. Nehring, J. Chem. Plzys., 1967, 47, 5459. W. A. Anderson and F. A. Nelson, J. Chem. Phys., 1963, 39, 183. lo R. Freeman and W. A. Anderson, J. Chem. Phys., 1965,42,1199. R. R. Ernst, J. Chem. Phys., 1966,45,3845. l2 J. A. Betts, SignaZProcessing, Modulation and Noise (EnglishUniversities Press, London, 1970).

ISSN:0300-9238    

DOI:10.1039/F29736900010

出版商:RSC    

年代:1973

数据来源: RSC

摘要:

"+"A Transition of the Hexa-amminechromium(II1) Ion in Non-cubic Environments BY C. D. FLINT,*P. GREENOUGHAND A. P. MATTHEWS Department of Chemistry, Birkbeck College (University of London),Malet Street, London WClE 7HX Received 10th August, 1972 The 2E+4Azg transition of a series of carefully purified salts containing the Cr(NH&' ion has been measured in emission and absorption at 80 and 5 K. The vibronic spectra show splittings which are interpreted in terms of the symmetry of the lattice site occupied by the ion. These splittings confirm the assignments given previously for the Cr(NH&' ion in cubic environments and remove some of the ambiguities. They also provide some structural information. We have previously reported the vibronic structure of the 2Eg-+4A2,phosphor-escence spectrum of the Cr(NH,):+ ion in lattice sites of Ohsymmetry (neglecting the hydrogen atoms).The transition is magnetic dipole allowed and electric dipole forbidden but vibrations of symmetry T~~ and zZUact as electric dipole vibronic origins.2 The introduction of a component of lower than cubic symmetry into the crystal field will split the initial and terminal electronic states into two Kramers doublets but the separations are small since both states are derived from the (t2g) strong field configuration. When the six ligands are chemically identical the splitting of the 2Estate is typically less than 30 cm-I but that of the 4A is only ca. 1 cm-1 since this state is separated by over 20 000cm-l from states derived from other strong field configurations.This ground state splitting is not resolved in our spectra. Thus the 80 and 5 K absorption spectra will be similar except for the better resolution of the spectra at the lower temperature. In the emission spectrum rapid radiationless relaxation between the split components of the 2Estate ensures that they are in thermal equilibrium. The relative intensities of the two 0'4 lines and their vibra- tional structure will be given by exp( -AE/kT)where AE is the separation between the lines. If the low symmetry field is of odd parity, the pure electronic transitions become electric dipole allowed. The relative intensity of the electronic origins and the vibronic bands in the absorption or emission spectra can then indicate the presence or absence of inversion symmetry at the Cr3+ ion.The low symmetry will also remove the threefold degeneracy of the vibronic origins so that each vibrational line in the electronic absorption or emission spectrum of CT(NH~)~(CIO~)~ may split into four or six components. In this work we have studied the influence of small external low symmetry fields on the vibronic structure of the 2E+4A2transition. When the crystal structure of the compounds is known, comparison of the observed and predicted splittings of the electronic origin and the vibronic bands helps to suggest or confirm spectral assign- ments for the hexa-amminechromium(II1) ion. In other cases the splittings of the vibronic and electronic origins and the intensity of the 0-0' line(s) may indicate the site symmetry of the Cr3+ ion.23 TRANSITION OF HEXA-AMMINECHROMIUM(III) ION EXPERIMENTAL MATERIALS All preparations were carried out at room temperature or below in subdued light to reduce photodecomposition or aquation. In spite of these precautions, it was not possible to eliminate traces of penta-animine impurities. Several samples of each compound were prepared and any weak bands whose intensity varied from sample to sample or which had a different temperature dependence from the rest of the spectrum were attributed to impurity emissions. [Cr(NH,),][Co(CN),] and CI-(NH~)~(N& were prepared metathetically from carefully purified Cr(NH,) &I3 and [Cr(NH,) &(S04)3,5H20respectively.INSTRUMENTATION Luminescence spectra were measured using the apparatus previously described. Elec-tronic absorption spectra were measured on samples mulled in Voltalef 3soil using an Oxford Instruments continuous flow cryostat, the 600 mm monochromator and a tungsten source. Spectral slit widths were typically 3 cm-l for both emission and absorption measurements and did not limit the resolution achieved. Infrared spectra were measured on a Perkin-Elmer 457 spectrometer. RESULTS Single crystal X-ray studies of [Cr(NH,),][cuCI,] and [Co(NH,),][CdCI,] have shown that the Cr (Co) ions occupy sites of S6symmetry. The co-ordination geo- metry of the chromium ion is very nearly octahedral, the N-Cr-N angle being just significantly different from 90" at 89.45". The X-ray powder photograph of [Cr(NH,) 6][CdC15] is substantially identical to those of [Cr(NH,),][CuCl,] and [Co(NH,) 6][CdC15] and these three compounds are probably isostructural.In s6symmetry it would be expected that the 2Eg(oh) state would split into two components and that each of the triply degenerate vibronic origins observed for the 2E,+4kf2,transition in compounds where the Cr3+ ions occupy sites of Oh symmetry would split into two components. However, no splittings of the electronic origin or of the vibronic origins were detected in the 80K absorption and 80 and 5 K luminescence spectra of [Cr(NH,),][CdCI,] or [Cr(ND,),][CdCl,) (table 1) and the appearance of these spectra are generally rather similar to those of the corresponding perchlorate salts.Presumably, the deviation from cubic symmetry is insufficient to cause splittings greater than the half-width of the lines (5-10 cm-l). The first members of progressions in the v2(cg) modes (notation as ref. (1)) on the vibronic origins are again observed in the luminescence spectra and are rather stronger than in cubic hexa-amminechromium(II1) salts, the derived frequencies of this vibra- tion being [Cr(NH,),][(CdCI5)], 406 cm-l ; [Cr(ND,),][CdCI,] 376 cm-l. No pro- gressions involving v1(alg)were detected. Some bands were located in the regions expected for combinations involving 8,(eg) but emission from traces of impurities which we could not remove prevented any definite assignments. Our work with the cubic hexa-amminechromium(II1) salts failed to locate the das(~2u)vibrational mode ; the only strong band in the asymmetric N-H bend region being 8as(~lu).For this compound we find two strong bands in that region.The similar intensity of these bands and the failure to resolve any splitting of v7 and v8 indicates that these are not the split components of das(~lu)and it is probable that the second band is &,(T~~),although the possibility of a Fermi resonance cannot be ruled out. The deuterated compound shows only a single band in the D-N-D asym- C. D. FLINT, P. GREENOUGH AND A. P. MATTHEWS metric bending region. Three bands are observed in the N-H and N-D stretching regions but since each band is also observed in the infrared spectra the middle one is probably a Fermi resonance (table 1).TABLE INTERVALS (cm-l) FROM THE ZERO PHONON LINE a AT 80 K1 .-VIBRATIONAL emission -776* 788 v$(au) -541 -430 -733* -451* -771* -702* -460* 711 701 467 775 v&,)vg(a,)vl, V$(&u) -379 -239 -194 -269 -224 - -271 -228 281 269 228 vi(au)v;(&J Vl,(&,) -149 -150 -209 209 v;(au) -111 -117 -85 -87 147 -74 -75 119 lattice' -57 -66 79 75 -40 -40 0 0 0 0 0'4 45 63 77 89 46 62 82 89 --- 115 144 } lattice 118 119 - 128 155 153 173 I 210 202 230 233 245 272 27 1 282 378 - 431 468 466 v3 638 678 695 546 724 712 617 785 775 804 872 789 926 1134 1114 993 1190 1183 1016 1391 1360 1042 1450 1431 1499 1477 1557 1533 1171 1611 1613 1630 1658 2296 3142 3124 2403 3231 3283 2453 3286 3325 *Measured at room temperature.-fThe expected lattice vibration is obscured by an impurity emission. a Positions of the zero phonon line at 80 K :[Cr(ND3)6J[COC15]15 224 cm-' ;[Cr(NH3)6][CdC15] 15 211 cm-' ;[Cr(NH3)6][CO(CN)6] 15 230 Cm-'. TRANSITION OF HEX A -A MM I N EcHRO M I UM (I I I) I oN The 5 K luminescence spectra show at least eight bands between the 0’4 line and 0’ -+O+Y,. These bands do not shift significantly on deuteration and are therefore probably due to lattice vibrations. There are eight formula units in the primitive unit cell and a large number of vibronically active lattice vibrations are expected.As the temperature is raised the antistokes lattice vibrations appear together with broad bands on either side of the 0’4 line. The appearance of the spectra are rather similar to those of CT(NH~)~(C~O~)~except that the broad band is relatively weaker in the CdC15 salt. In the analogous cobalt(II1) compound the NH3 groups are not freely rotating even at room temperature and it is unlikely, therefore, that the broad bands in these compounds are due to restricted rotation of ammine groups but their origin remains obscure. I I n c.* c 2gi J sl I 21 ...1$1 3 Two strong vibronic lines are observed in the region of a,, (table 1). Following the reasoning used for [Cr(NH,),][CdCl,] these are assigned to the expected zlu and 22uvibrations. The smaller vibrational interval is coincident with a strong band in the infrared spectrum, whereas there is no infrared band corresponding to the larger interval.Since the small trigonal field would not be expected to give appreciable intensity to the z2u vibration (which is inactive in Ohsymmetry) the 1651 cm-I vibra- tional mode is assigned as this mode. In both the luminescence and infrared spectra the N-H stretching regions closely resemble those of the pentachlorocadmate salt and are similarly assigned. The 4A 29480 K absorption spectrum (table 1) closely mirrors the luminescence 2Eq spectra. C. D. FLINT, P. GREENOUGH AND A. P. MATTHEWS The isostructural [Cr(NH,) 6][Fe(GN)6]does not luminesce presuniabiy because the hexacyanoferrate(II1) ion causes the Crrrr ion to relax, radiationlessly, either directly or via excitation transfer to the Ferrrspecies.The differentiation of these processes is difficult since no luminescence from the Fe"' ion could be detected. However [Cr(NH,),](MnO,),, which is isostructural with [Cr(NH,),](CIO,),, does not luminesce and it is unlikely that the diamagnetic permanganate ion could enhance radiationless relaxation in the Cr3+ ion without involvement of its excited states. The lowest excited state of the MnO; ion is of similar energy to the 2Eostate of Cr(NH&* and energy transfer is therefore favourable. There is no crystallographic information available on this compound. The 80 K luminescence spectrum (fig.2(a)) has two strong 0'4 lines separated by 27 cm-' and a complex vibronic pattern to low energy. On cooling to 5 K the 0'-0 line at highest energy disappears, together with its vibronic bands (fig. 2(b)). The vibronic structure may then readily be analysed (table 2). Every band and inflexion in the 80 K spectrum can be accounted for using these vibrational intervals.' The splitting of the vibronic origins into doubly degenerate and singly degenerate components indicates that the hexa-amminechromium(II1)ion retains (or nearly retains) either a threefold axis or a fourfold axis but the intensity of the 0'4lines show that the ion is not centrosyrnmetric. The H-N-H bending and N-H stretching regions are poorly resolved and of little I I I I I I 1 650 670 690 wavelength/nm FIG.2.-Luminescence spectrum of Cr(NH3)6(N3)3at (a)80 and (b)5 K.TRANSITION OF HEXA-AMMINECHROMIUM(III) ION interest. The splittings of v6 and v7 in this compound and the hexacyanocobaltate(II1) provide further evidence for the correctness of our assignments in the cubic hexa- amminechromium(II1) salts. TABLE2.-vIBRATIONAL INTERVALS FROM THE ZERO PHONON LINE FROM THE 5 K EMISSION SPECTRUM 0 0'4 94 128 I lattice 150 202 229 260 290 418 468 479 704 720 762 789 Position of zero phonon line at 5 K, 15 163 cm-' ; position of zero phonon lines at 80 K, 15 161 and 15 188 ern-'. We thank the S.R.C., London University Central Research Fund and I.C.I. Ltd. for grants for the construction of the apparatus used in this work and the S.R.C. for research studentships (to P.G. and A.P.M.). 'C. D. Flint and P. Greenough, J.C.S. Furaday 11, 1972, 68, 897. C. D. Flint, J. Mol. Spectr., 1971, 37,414. W. E. Estes, D. Y.Jeter, J. C. Hempel and W. E. Hatfield, Inorg. Chem., 1971, 10,2074. K. N. Raymond, D. W. Meek and J. A. Ibers, Inorg. Chem., 1968,7, 1111. T. V. Long, A. W. Herlinger, E. F. Epstein and I. Bernal, Inorg. Chem., 1970, 9, 459. H. Steinmetz, 2.Kryst., 1922, 57, 233. 'P. Day, L. Oleari and L. DiSipio, Chem. Phys. Letters, 1970, 5, 533. P. Greenough, Thesis (University of London, 1972).

ISSN:0300-9238    

DOI:10.1039/F29736900023

出版商:RSC    

年代:1973

数据来源: RSC

摘要:

Microwave Spectrum of Tellurium Pentafluoride Chloride BY A. C. LEGON Christopher lngofd Laboratories, University College London, 20 Gordon Street, London WC1 Received 17th August, 1972 'The microwave spectra of twelve isotopic species of tellurium pentafluoride chloride are reported. Each spectrum shows rigid symmetric top behaviour with nuclear quadrupole coupling effects due to the 35Cl and 37Cl nuclei unresolved. The rotational constants, Bo, for the ground vibrational state of the various isotopic species of C1TeF5 are as follows. I 22Te 124Te lzsTe 126Te 12sTe 13 OTe 35CI 1396.335 1396.150 1396.058 . 1395.964 1395.776 1395.595 MHz 37Cl 1363.637 1363.418 1363.314 1363.205 1362.987 1362.772MHz The r, distance for the Te-Cl bond is directly determined from the rotational constants as 2.250_+0.002A. Although a unique determination of the remaining three structural parameters is not possible, a graph is presented which shows the variation ofr(Te-F)axial and r(Te-F)equatorial as a function of the angle (F-Te-Faxial) assuming a structure of symmetry.Thus, if one of the three unknown parameters can be determined by another method, the remaining two can be obtained uniquely from the graph. If equality of the axial and equatorial Te-F distances is assumed the resulting structure is : V(T-F) = 1.8305 f0.0012 A, angle (F-Te-F)axial = 88'15' If:7'. An excited vibrational state, probably the Te--CI wagging vibration, vll, has been assigned and the values all = 0.775 and 0.718 MHz for the 35Cl and 37CIspecies respectively are reported.Structures of CISFS and CIWFS derived from their microwave spectra have previously been reported. Unfortunately, in both cases a complete structure is unavailable from the spectroscopic measurements. However, the reasonable assumption of C4"symmetry and the useful assumption of equal axial and equatorial M-F distances lead to a distorted octahedral structure in which the central atom M is raised above the plane of the four equatorial fluorine atoms (as shown for M = Te in fig. 1) for both CISFS and ClWF5. Indeed, the angle (F-M-Faxial) is strikingly similar, 88'22' and 88'41' for the sulphur and tungsten compounds respectively. Now that the corresponding tellurium compound, ClTeF5, has been prepared by Peacock and co-worke~s,~ it is of interest to investigate whether this structural similarity extends also to such compounds involving other Group VI elements.EXPERIMENTAL The sample of tellurium pentafluoride chloride was kindly provided by Professor R. D. Peacock and Dr. G. W.Fraser of the University of Leicester. No polar impurities of sufficient abundance to give microwave spectrawere detected and the other likely irnp~rities,~ C1, and TeF6, being non polar, do not present serious experimental difficulties. The microwave spectrum of ClTeF5 was studied using a conventional 100 kHz Stark modulated spectrometer operating in the frequency range 27 to 40GHz. Samples were 29 MICROWAVE SPECTRUM OF TELLURIUM PENTAFLUORIDE CHLORIDE stable for long periods in the copper wave-guide absorption cell when cooled to dry-ice temperature.Kel-F vacuum grease was used for lubrication of taps and joints in the gas-handling system. z !i c1 f FIG.1.-Inertial axis system and structure of tellurium pentafluoride chloride (assuming equal .axial and equatorial Te-F bond lengths). RESULTS SPECTRUM The microwave spectrum exhibited by tellurium pentafluoride chloride is character- istic of a symmetric top molecule in which the 35Cl and 37Cl isotopes lie on the top axis. Thus, there are two sets of equally spaced transitions, one set about three times stronger than the other. Closer investigation of the transitions of both sets reveals for each transition a fine structure which can be assigned, in the manner discussed below, as arising from a given rotational transition in the ground and vibrationally excited states of molecules containing the various isotopes of tellurium.TELLURIUM ISOTOPE EFFECTS The fine structure of each transition of the 35ClTeF5 and 37C1TeF5 species is similar and characteristic. In both cases the most prominent feature consists of three equally spaced strong lines accompanied immediately on the high frequency side by three weaker lines so as to form a distinct group of six transitions. The remaining fine structure of each transition falls to low frequency of this group of six. The spacings between adjacent transitions within the group of six are very nearly in the ratio 2 : 1 : 1 : 2 :2, from high to low frequency, as required if adjacent lines belong to the same rotational transition in molecules containing the tellurium isotopes 122Te,lZ4Te, Iz5Te, 126Te, 128Te, and I3OTe respectively near to the mass centre.Each component of the group was therefore assigned to the corresponding tellurium isotopic species. Such behaviour is illustrated by the measured frequencies for the six lines of the J = 12 t 11 transition of the 35C1TeF5 species displayed in table 1. The relative intensities of the six transitions were consistent with the natural abundance of the tellurium isotopes which is,4 in the order written above, 2.46, 4.61, 6.99, 18.71 A. C. LEGON 31.79, and 34.48 % respectively. The low abundance isotope 123Te(0.87 %) was not observed.Since the components assigned to 126Te, 128Te,and l3'Te in the group were the strongest transitions in the compleie set of fine structure, it was clear that the group of six lines due to the six tellurium isotopes belonged to molecules in the vibrational ground state. Several weaker triplets, presumably due to vibrationally excited molecules containing 126Te,128Teand I3OTe isotopes, were observed to low frequency of the ground state group. A selection of measured transition frequencies for ground state rotational transi-tions of each of the six tellurium isotopic species for both 35ClTeF5and 37ClTeF5 are recorded in table 2. Precision of measurement is estimated to be kO.1 MHz or TABLE1.-TELLURIUM ISOTOPE EFFECT IN THE J = 12 t11 TRANSITION OF 35CITeF5 isotopic species frequency/MHz differences 35C122TeF5 33 512.04 C1 24TeF5 33 507.67! 4.37 9 q-iL.LLCll5TeF 33 505.45' 2.355C1126TeF5 33 503.10; 4.505C1128TeF5 498.60 C1 OTeF5 33 494.10) 4.50 TABLE2.-oBSERVEI) TRANSITION FREQUENCIES, OBSERVED AND CALCULATED ROTATIONAL CONSTANTS FOR TELLURIUM PENTAFLUORIDE CHLORIDE observedisotopic species J+l+-J frequency/MHz Bo(0bs.)IMHk Bo(calc.)*/MHz Cll2TeF5 12 +- 11 33 512.04 1396.335 1396.343 Cll24TeFs 12 +-11 33 507.67 1396.150 1396.1 53 11 t-10 30 715.25 C1' 5TeF5 12 4- 11 33 505.45 1396.055 1396.059 11 +- 10 30 713.24 C1 6TeF5 12 4- 11 33 503.10 1s +- 10 30 711.18 1395.964 1395.966 10 + 9 27 919.32 12 +-11 33 498.60 11 +lo 30 707.13 1395.776 1395.782 10 69 27 915.49 CllOTeE;, 12 f-11 33 494.10 11 + 10 30 703.26 1395.595 1395.601 10 +9 27 911.88 C1' 2TeF5 13 +- 12 35 454.57 1363.637 1363.644 Cl 4TeF5 13 t12 35 448.82 1363.418 1363.423 11 +- 10 29 995.25 7C1 'TeF5 13 t12 35 446.09 1363.314 1363.314 11 +- 10 29 992.95 7C116TeF5 13 +- 12 35 443.27 12 +-11 32 716.83 1363.205 1363.206 11 +- 10 29 990.54 7C1 8TeF5 13 t12 35 437.68 12 +- 11 32 711.60 1362.987 1362.992 11 +-lo 29 985.75 7C11 OTeF5 13 i-12 35 432.10 12 +-- 11 32 706.46 1362.772 1362.781 11 +- 10 29 982.05 * calculatcd rotational constants are those derivcd from thc structure shown in fig.1.MICROWAVE SPECTRUM OF TELLURIUM PENTAFLUORIDE CHLORIDE better. Also included is the rotational constant for each isotopic species, the value quoted representing the mean derived from all measured transitions in each case. The range of individual values about the mean is generally less than +0.005 MHz, which indicates that each molecular species behaves as a rigid rotor within the limit of error in the frequency measurements. Rigid rotor behaviour is further indicated by the absence of detectable K-splitting effects due to centrifugal distortion. Also, no structure in transitions attributable to quadrupole coupling of the chlorine nuclear spins with the molecular rotation was apparent. It was argued in ref. (2) that failure to resolve chlorine nuclear quadrupole hyperfine structure in transitions with a similar J-value range for ClWF5 is not unexpected if the chlorine coupling constant observed in CISFS could be transferred to CIWFS.Similar arguments apply in the case of CITeF5. Little progress was possible in the analysis of vibrational satellite transitions because of overlapping problems. However, the three tellurium isotope species 126Te, lz8Te and 130Te in the strongest satellite adjacent to the ground state could be discerned even though the weaker species, lz2Te, lZ4Te and 125Te, were obscured. By analogy with ClSF5 and CIWFS,z this satellite can be assigned tentatively to the u = 1 state of the Te-C1 wagging vibration, v11. The rotational constants (averaged from several transitions) and a,, values for this doubly degenerate vibration are shown in table 3.The differences in rotational constants between the lZsTe and 130Te species for 3sClTeF5 and for 37C1TeF5 are similar to those observed in the corres- ponding ground state rotational constants. Values for Cll 26TeF5 species have been omitted from table 3 since it was noted that in the u = 1 state of the vll vibration transitions due to this species were consistently broad and difficult to measure accurately. This difficulty was evident from the differences in B1between the 126Te and lz8Te species, for these did not agree with the corresponding Bo differences. The source of the difficulty is probably interference from vibrational satellites associ- ated with other vibrations.TABLE3.-ROTATIONAL CONSTANTS AND VIBRATION-ROTATION CONSTANTS FOR THE U = 1 STATE OF THE V11 VIBRATION OF TELLURIUM PENTAFLUORJDE CHLORIDE isotopic species 35C1126TeFs Bi/M%* a11lMHz* 3sC1128TeF5 1395.006 0.770 3sC1130TeF5 37C1126TeFS 1394.816 * 0.779 * 37C1128TeFs 1362.261 0.726 37C1130TeF5 1362.062 0.710 * see text for discussion. MOLECULAR STRUCTURE The symmetric top nature of the rotational spectrum together with the chemical evidence point to a structure for ClTeF, with C,, symmetry of the general form shown in fig. 1. Thus, if the molecular structure of ClTeF5 is to be derived completely from the observed rotational constants the four independent structural parameters r(Te-F)axial, r(Te-F)equatorial, r(Te-Cl), and 8 = angle (F-Te-FaXial) must be determined.Unfortunately only r(Te-C1) can be obtained uniquely from the observables herein reported, for the remaining parameters cannot be determined independently. Nevertheless, a graphical expression of the relationship between the r(Te-F) and 9 is possible so that all three are fixed if one can be determined by another method. A. C. LEGON With the choice of a particular isotopic species as the parent molecule, the changes in rotational constant on isotopic substitution at the tellurium and chlorine atoms can be used in Kraitchman’s equation to give the z-coordinates, z,, and zcl, of those atoms in the principal axis system of the parent molecule. Kraitchman’s equation is 505376 AB 22 = -~ p BB‘ where AB is the difference in the rotational constants, B and B’, of the parent and isotopically substituted molecules and p = MAmI(M+ Am), in which Am is the mass change on isotopic substitution and M is the mass of the parent molecule.The factor 505 376 ensures that z is expressed in A if B is in MHz and p in atomic mass units on the I2C scale. The six isotopes of tellurium available allow five values of z,, referred to the principal axis system of a given parent molecule to be determined from Kraitchman’s equation. Similarly, the two chlorine isotopes give a single value of zcI. Thus, five values of r(Te-Cl) are possible for the given parent molecule. However, any one of twelve isotopic species can be selected as the parent so that sixty values of r(Te-CI) can be obtained from different combinations of the observed rotational constants.The range of these values will give an indication of the seriousness of experimental errors and zero point vibrational effects. Table 4 shows an example of the zcl, z,, and r(Te-C1) resulting when 35C1126TeF5 is taken as the parent molecule. The internal consistency of the over-determined ZTe is typical of similar sets obtained when different parent molecules are used. It is well-known that r,-coordinates as small as the z,, in table 4 are underestimated when effective ground state rotational constants are used in Kraitchman’s equation. The reason is that isotopic substitution modifies the zero point vibrational motion over which the observed rotational constants are averaged.When the coordinate to be determined by substitution is small, the change in rotational constant is small also but the contribution from the changed zero point motion to the observed change of rotational constant can be large. Clearly, the effect is the more serious the lighter is the substituted atom. On the other hand, changes in zero point motion tend to be small for isotopic substitutions at heavy atoms. Consequently, small rs-coordinates from substitution at heavy atoms are likely to be more reliable than those of similar magnitude obtained through light atom substitution. The consistency of the zTein table 4 obtained when various Te isotopes are substituted indicates that here the effects of changes in zero point motion are small and that the z,, are reliable.4.f‘MRDINATES AND r(T-Cl) REFERRED TO 35C1126TeF5TABLE (A) isotopesubstituted zc 1 ZT9 r(TH1) 37c1 -2.0953 --”Te -0.1539 2.2492 24Te -0.1547 2.2500 lZsTe -0.1559 2.2512 12*Te -0.1567 2.2520 130Te -0.1558 2.2511 The mean of the thirty values of v(Te-Cl) which result from using each of the six 35C1TeF5 species as the parent molecule is r(Te-Cl) = 2.250& 0.002 A. 11-2 MICROWAVE SPECTRUM OF TELLURIUM PENTAFLUORIDE CHLORIDE The indicated error is just the range about the mean. When the six 37C1TeF5 species are so used the result is r(Te-C1) = 2.250_+ 0.003A. The internal consistency of the results is better in the former case. As already discussed, the remaining structural parameters cannot be determined uniquely from the observed rotational constants. However, if 0, say, is assumed, the coordinates zTeand zcl can be used with the first and second moment conditions, xmizi = 0 and zrni(z;+y') = I, i 1 to give the other two parameters r(Te-F)axial and r(Te-F)esuatorial.The variation of the two bond lengths as a function of 8 can then be displayed graphically, as in fig. 2. For each value of 0 in fig. 2 the bond lengths are the average of the thirty resulting when the six 35C1TeF5 species are chosen as parent molecules. The corres- ponding graphs constructed using the 37C1TeF5 species would be indistinguishable from those of fig. 2. It should be noted that the Te-F distances are quite sensitive to small errors in the rotational constants.Thus, the range of axial distances about the mean value for a given 8 indicate that the precision to be associated with it is about kO.01 A. For the equatorial distances limits of kO.005A should be used. weg FIG. 2.-r(Te-F) axial (A) and equatorial (E) values as a function of 8. An interesting conclusion follows from fig. 2. If, as seems reasonable, the axial and equatorial Te-F distances differ by no more than a few hundredths of an ang- strom, then the angle 8 is constrained to lie within the range 88'6' to 88'22'. For the purpose of comparison of the C1TeF5 structure with those of other mole- culessimilarly determined it is convenient to choose one particular set of 8, r(Te-F),,ial and r(Te-F)esuatorial.An obvious choice is that in which the equatorial and axial A. C. LEGON Te-F distances are equal. When this constraint is placed upon the use of z,, and zclin the first and second moment equations, the resulting structure is r(Te-F)axial = r(Te-F),,,a,,,i,, = 1.8305 0.0012 A, 6 = 88"15'+7', u(Te-Cl) = 2.250+0.003A. The errors represent the range of the sixty possible structures based on the twelve 35C1TeF5 and 37ClTeF5 parent isotopic species about the mean. Table 2 includes ground state rotational constants calculated from this structure. The agreement between observed and calculated values is close. DISCUSSION The Te-Cl distance of 2.250+0.003 A determined for CfTeFS appears to be the first for such a bond in a TeV1 compound.The only other Te-C1 bond distances measured in the gas phase which are available for comparison are 2.36k0.03 A in TeClz 'and 2.33k0.02 A for TeC14,8 both from electron diffraction studies. The figures suggest that the Te-Cl bond shortens as the tellurium atom changes from Te", through TetV to Tev'. Some discussion of the remainder of the ClTeF5 structure is possible. It has already been pointed out that the angle 6 is constrained to lie in the range 88'6' to 88'22' if the axial and equatorial Te-F bond distances differ by less than 0.03A. A similar calculation indicates that the corresponding ranges for C1SF5 and CIWFS are 88'12' to 88'33' and 88'31' to 88'52' respectively. Thus, it is probable that in all of these molecules the central atom lies above the plane of the equatorial fluorine atoms to a similar extent (see fig.1) and that the effect of the chlorine atom when replacing fluorine in MF6 is to move the equatorial atoms away from it. When for the purpose of comparison, equality of the axial and equatorial M-F distances is assumed, a family relationship is clearly seen among the angles 8 for these molecules, as shown in table 5. The close similarity of the M-F distances with those of the corresponding MF compounds derived from electron diffraction, which are included in table 5, is also of interest. TABLE5.-cOMPARISON OF ClMFs AND MF6 STRUCTURES central atom M r(M--F)lA angle 6 S{t?S 1.576&0.01 88'22'1: 10' ref. (1) 1.564+ 0.010 90'00' (4ClTeF5 1.830+0.O01 88'15'+7' (b) Te(TeF, 1.824&0-004 90"00' (d W{YY5 1.836+ 0.001 88'41'+ 10' ref.(2) 1.833+ 0.008 90'00' (4 (a) V. C. Ewing and L. E. Sutton, Trans. Faruday Suc., 1963,59,1241; (b) this work ; (c) H. M. Seip and R. Stralevik, Acta Chem. Scand., 1966,20, 1535 ; (d) M. Kimura, V. Schomaker, W. Smith and B. Weinstock, J. Clzern.Phys., 1968, 48, 4001. I thank Professor R. D. Peacock and Dr. G. W. Fraser for the gift of the sample. R. Kewley, K. S. R. Murty and T. M. Sugden, Trans. Faraduy SOC.,1960, 56, 1732. A. C. Legon, Trans. Faraday SOC., 1969, 65,2595. G. W. Fraser, R. D. Peacock and P. M. Watkins, Chem. Comm., 1968, 1257. Microwave Molecular Spectra, W. Gordy and R. L. Cook, Technique of Organic Chemistry Series, ed. A. Weissberger, Vol. 9 (Wiley-Interscience, New York, 1970).J. Kraitchman, Amer. J. Phys., 1953, 21, 17. V. W. Laurie and D. R. Herschbach, J. Chem. Phys., 1962, 37, 1687.'W. Grether, Ann. Phys., 1936, 26, 1. D. P. Stevenson and V. Schomaker, J. Anter. Chem. Soc., 1940, 62, 1267.

ISSN:0300-9238    

DOI:10.1039/F29736900029

出版商:RSC    

年代:1973

数据来源: RSC

摘要:

Effects of Induction and Resonance in the Calculation of Ionization Potentials of Substituted Benzenes by Perturbation Molecular Orbital Theory BY R.A. W. JOHNSTONEAND F. A. MELLON The Robert Robinson Laboratories, The University, Liverpool L69 3BX Received 24th April, 1972 Using perturbation theory, an equation has now been derived relating the ionization potentials of disubstituted benzenes to those of monosubstituted benzenes. The theoretical equation is closely related to the empirical one and the calculated ionization potentials for a series of benzenoid com- pounds compare well with measured values obtained by electron-impact and photoelectron methods. In a few cases with substituents which interact strongly with the benzene ring, the poor agreement between calculated and observed ionization potentials led to a closer examination of the measured effects.The molecular orbital method used here applies strictly to the resonance effects of substitu-ents, whereas the parameters initially used in the equations are resonance plus induction effects combined, as obtained from photoelectron spectroscopy measurements. The photoelectron spectra of the benzenes appear to allow a separation of the resonance and induction effects and, when this is done, the calculated and observed ionization potentials agree in all cases. Interest in the ionization potentials of substituted benzenes has been stimulated by the observation of Hammett-type correlations in mass spectrometry and by investigations using photoelectron spectroscopy.2* Recent work resulted in an empirical equation for calculating the ionization potentials of disubstituted benzenes. The importance of ionization potentials as a measure of some of the properties of molecular systems has long been recognised. Mulliken’s “ magic formula ” related bond strengths to atomic valence state ionization potentials and Walsh has related ionization potentials to bond orders and electronegativities.’ Ionization potentials are also of considerable value in testing molecular orbital methods and in solution chemistry where one-electron transfers are important.8 Molecular orbital calculations yield orbital energies, and, assuming Koopmans’ theorem is reasonably correct, ionization potentials can be equated with these orbital energies.The calculation of ionization potentials of a variety of compounds by empirical 49 lo and semi-empirical molecular orbital methods 11* l2 suggests a useful approach to the calculation of ionization potentials of benzenoid compounds. In the present work, substituents in a benzene ring are regarded as perturbations to the n-orbitals rather than being an inseparable part of the benzenoid system. Such an approach was used by Matsen l3 to estimate the effects of single substituents on the electronic spectrum of benzene, and Godfrey l4 has applied a combination of charge-transfer and per- turbation theory to, inter alia, the photo-electron spectra of monosubstituted ben- zenes. The derivation by perturbation molecular orbital methods of all the equations used in the following discussion is given in the appendix. EXPERIMENTAL Electron-impact ionization potentials were measured on an A.E.I.MS902/FerrantiArgus 500 mass spectrometer/computer system using the IE/EDD technique.15 Samples 36 R. A. W. JOHNSTONE AND F. A. MELLON were obtained commercially and used without further purification. A Perkin-Elmer PS16 photoelectron spectrometer was used to measure the remainder of the ionization potentials reported here. Samples used in this apparatus were first purified by vacuum distillation through a Vigreux column. RESULTS AND DISCUSSION To a first-order approximation, the ionization potential I for any substituted benzene is given by eqn (l), r = IO+CAI-, (1) where AZx is the difference between the ionization potential I" of benzene itself' and that of the corresponding monosubstituted benzene C6H5X.Various AIx values are listed in table 1.Ionization potentials for para-disubstituted benzenes calculated by this first-order treatment (PMO I) are compared with experimental values in tables 2, 3. The ionization potentials in table 2 are those of compounds with substituents which interact strongly with the benzene ring and were measured by us using an electron-impact method l6 ; the values listed in table 3 were taken as best values from the 1iterature.l' The PMO I method affords a good calculation of the ionization potentials of most of the 23 compounds in the tables (r.m.s. = kO.37eV).Good results are obtained for substituents which individually exert only small effects, e.g., the calculated and experimental ionization potentials of p-xylene (ACH3 = -0.44 eV) are close (table 3). However, for substituents which individually exert large effects, the discrepancy between calculated and experimental ionization potentials can become large as, e.g., with the worst case in the tables of p-phenylenediamine (AINH2= -1.44 TABLEVALUES OF AI; AND k, USED FOR THE CALCULATION OF IONIZATION POTENTIALS WITH EQN (3) substituent (X) AIind. a A?, b A?: C kx H 0.00 0.00 0.00 -F +0.48 -0.05 -0.53 0.7 c1 +0.38 -0.18 -0.56 0.4 Br +0.36 -0.19 -0.55 0.3 CF3 +0.46 +0.46 0.00 1 .o CHO +0.45 +0.38 -0.07 1.o C02CH3 +0.38 +0.11 -0.27 1.o CH3 -0.15 -0.44 -0.29 0.7 NO2 +0.73 +0.68 -0.05 1.o OH +0.11 -0.70 -0.81 0.8 OCH3 -0.061 -0.96 -0.90 0.8 NH2 -0.163 -1.44 -1.28 0.8 N(CH3)2 -0.34 -1.74 -1.40 0.8 SH +0.14 -0.86 -1.00 1.o SCHj -0.04 -1.20 -1.16 1.o CN +0.55 +0.44 -0.11 1.o UAIind.= adiabatic I.P. (732 in C6H5X)-9.24 eV; bar, = adiabatic I.P, (723 in C6H5X)- 9.24eV ; CAZ; = AIx-AIind. ; d the separation of 7r3, r2levels is too close to resolve with certainty e and the mean values reported here were obtained as follows. From table 4, for a para-disubstituted benzene CsHsXY, AIind.(XY) =AIind.(X) +.Alind.(Y). Therefore, knowing &d.WY) and AIind.(Y),a value for &,d.(X) can be obtained ; this procedure was adopted for several A1ind.m to give each estimated AZind.(X) ; e all the values reported here were measured by us using benzene as an internal standard because previous results were either obtained on a low resolution instrument or the adiabatic m2 levels are not reported.2* We are indebted to Mrs.S. A. Cowling for many of these measurements. EFFECTS OF INDUCTION AND RESONANCE eV). Contrariwise, the calculated and experimental values for p-nitroaniline, also having strongly interacting substituents, are close (table 2). These effects of sub-stituents which interact strongly with the benzene ring are probably to be expected in this first-order treatment in which second order effects are ignored. It has been noted previously that introduction of substituents into the para positions of benzenes leads to a separation of the 7r3 and n2 orbitals in such a way that the splitting (n3-n,) is almost equal to the sum of the splittings in the monosubstituted benzenes, except for some compounds where one of the substituents causes large perturbations (OCH3, NH2, etc.), and appears to prevent the other substituent from exerting as large an effect as expected.Thus, the PMO I method is probably adequate for weakly interacting substituents but it also has another drawback in its failure to predict differences, sometimes large, between the ionization potentials of ortho, meta, and para isomers (table 3). TABLE2.-cALCULATED AND OBSERVED * IONIZATION POTENTIALS OF SOME Para-DISUBSTITUTED BENZENES observed ionization calculated ionization compound potent ial/eV potential/eV -I______ PMOI PMOIL PMOII' p-cresol p-ni tro toluene p-nitrophenol p-tolunitrile p-anisidine p-phenylenediamine p-nitroaniline 8.34 9.56 7.38 9.31 9.39 7.16 8.43 8.10 9.48 9.22 9.24 6.74 6.36 8.48 8.19 9.43 9.17 9.24 7.1 5 7.1 1 7.91 8.16 9.48 9.23 9.24 7.25 6.95 8.50 * These values were obtained by us with the electron impact method described in ref.(20). TABLECA CALCULATED AND OBSERVED * IONIZATION POTENTIALS OF SOME meta-AND para-DISUBSTITUTED BENZENES obs. I.P./eV calc. I.P./eV compound PMOI PMOII PMOII' m-xylene 8.56 5.36 8.47 8.40 p-xylene 8.45 8.36 8.42 8.38 m-bromotoluene 8.77 * 8.61 8.67 8.78 p- bromo toluene 8.67 * 8.61 8.64 8.72 m-chlorotoluene 8.83 8.62 8.66 8.74 p-chlorot oluene 8.69 8.62 8.64 8.70 m-dichl or0 benzene 9.12 8.88 8.91 9.14 p-dichlorobenzene 8.94 8.88 8.90 9.09 NN-dimet hyl-m- toluidine 7.35 6.82 7.21 7.06 NN-dimet hyl-p-t olui dine 7.33 6.82 7.16 7.02 p-bromophenol 8.69 8.35 8.42 8.56 p-chlorophenol 8.52 8.36 8.41 8.58 p-chlor0benzladehy dde 9.33 9.36 9.43 9.46 p-hydroxybenzaldehyde 9.32 8.79 8.89 8.93 p-methoxybenzaldehyde 8.60 8.51 8.56 8.67 NNN'N' -tetramet hyl- 5.28 6.60 6.24z::5}p-phenylenediamine * All values are taken from ref, (16) unless stated otherwise.Values obtained by Mrs. S. A. Cowling are marked (*), R. A. W. JOHNSTONE AND F. A. MELLON Corrections to the first-order effects of substituents can be obtained using eqn (2), AIx,y= +AIx{l +1/(1+ AIx -AIy/c:k:/3g)} ++AIy{ 1+1/(1+ AIx * My/c:k;/%)) (2) which is based on a second-order treatment (PMO 11, appendix).In this equation, AZ, and AIy are as before and A&,,, is the difference between the ionization potentials of benzene and a disubstituted benzene C6H4XY. The parameters kx,kyadjust the standard C-C resonance integral Po for C-X, C-Y bonds and are the best values recommended by Streitwieser l8;substituents such as NO2, CHO, CN were treated as “ pseudoheteroatoms ” l8 with kx = 1.0. The coefficients c, are the n3 orbital coefficients for positions 1-6 of the benzene ring, i.e., c1 = c4 = 21 J12 and c2 = c3 = c5 = c6 = 1/ J12. Eqn (2) can be approximated to the empirical equation derived earlier which gave a good account of the ionization potentials of disubstituted benzenes.Using eqn (2)with Po equal to 3.0 eV,13 AZx,y for the 23 compounds of tables 2, 3 were calculated (PMO 11) and compared with the experimental values and the results of PMO I calculations. The calculated values are in good agreement (r.m.s. = +O. 19 eV) with experimental ionization potentials and differences are predicted between the ionization potentials of meta and para isomers. For strongly interacting substituents, as e.g., p-phenylenediamine, the agreement between calculated and experimental values is much improved over the PMO I treatment. Despite this good agreement, one case in particular, p-nitroaniline, suggests that eqn (2) is inadequate. PMO I calculations predict the correct ionization potential for p-nitroaniline but not for other compounds with strongly interacting substituents, whereas PMO II acts in the opposite way.Both PMO I and I1 are adequate for weakly interacting substit- uents. Rather than attempt to adjust parameters in eqn (2) as is frequently done to improve the correspondence between theoretical and experimental estimates of physi- cal quantities, we have considered whether the AIx parameters used in PMO I1 do reflect true resonance effects. The results of these considerations set out below lead to calculated values (PMO 11’) for the ionization potentials of disubstituted benzenes which are close (r.m.s. = k0.16 ev) to the experimental ones in all cases including p-nitroaniline. The range of ionization potentials covered by PMO I1 and PMO 11‘ calculations is large and encompasses all available literature values of compounds with strongly interacting substituents which might be used to distinguish the two methods.Thus, although PMO 11’ is marginally better than PMO I1 in its predicted values (r.m.s. = k0.16,O. 19 eV respectively) and deals effectively with p-nitroaniline, a thorough evaluation of the relative merits of the two methods must await many more experimental results. Nevertheless, the arguments leading to the PMO 11’ method could possibly be evaluated in other ways and are therefore detailed below. Examination of the list of ionization potentials of the n3 and n2 orbitals of monosubstituted benzenes reveals that although the n, orbital is theoretically predicted to be unaffected by conjugation with a substituent (node at the substituent position), and the n3 orbital to be strongly interacting, sometimes the n3 orbital is apparently littlelaffected but the n2orbital is affected strongly.As examples, the shifts of the n3and n2orbitals in the halogenobenzenes and toluene from the levels in benzene at 9.24 eV may be compared (AZind. and AI, values in table 1). These figures suggest that photoelectron spectroscopy can distinguish the inductive or field effect in n, from the resonance or mesomeric effect in n3. Two deductions may be made. First, the shift in the n2 orbital of a disubstituted benzene should be the simple sum of the shifts in the x2 orbitals of the corresponding monosubstituted benzenes. Secondly, it may be supposed that the inductive or field effect found in the n2 orbital can be applied to the x3 orbital which is shifted by both resonance and inductive effects.This latter EFFECTS OF INDUCTION AND RESONANCE suggestion is only a different, but now quantitative, presentation of electronic theory in aromatic chemistry where, e.g., the halogenobenzenes have required a balance of strong resonance and inductive effects to explain their chemical reacti~ities.'~ The first deduction was tested by calculating the shifts expected in the 7r2 orbitals of a number of para-distributed benzenes and comparing them with the observed shifts (table 4). TABLE4.-cALCULATED * AND OBSERVED SHIFT IN THE 7t2 ORBITAL OF SOMEPARA-DISUBSTITUTED BENZENES substituents obs.shiftlev2 calc. shiftlev F, C1 +0.77 +0.86 C1, CH, +0.04 +0.23 C1, NO2 + 1.17 + 1.01 C1, OH +0.36 +0.49 C1, NH2 +0.02 +0.22 Br, CF3 +0.88 +0.69 Br, CN + 1.00 +0.91 CH3, NH2 -0.56 -0.31 OCHS, OCH3 -0.06 -0.12 * calculated from AIjnd. (table 1) for the two substituents. A good correspondence is found between the calculated and observed shifts and suggests the first deduction is reasonably accurate. The second deduction was tested as follows. " True " shifts in the n3 orbital caused only by resonance effects which are the AI' values required for eqn (2) are not simply the observed shifts in n3 because these observed shifts are sums of inductive and "true " resonance effects. For example, in bromobenzene the shift in the 7c2 orbital from that in benzene is -0.19 eV and, assuming the inductive shift Arind of a substituent is the same in both the 7r3 and n2 orbitals, the " true " resonance shift AZx in 7r3 is the actual shift in 7r3 less the actual shift in n2,i.e., A&, = -0.19 -0.36 = -0.55 eV.Values for AZ; and Alind for other substituents are given in table 1. To illustrate the use of eqn (2) with inductive (or field) effects included, the ionization potential for p-nitroaniline is calculated in the appendix. CONCLUSION Equations derived by perturbation molecular orbital theory for predicting the ionization potentials of substituted benzenes provide a theoretical basis for empirical equations deduced earlier. The theoretical equations based on second-order per- turbation methods (PMO I1 and 11') give good predictions for the the ionization potentials of a variety of meta- and para-disubstituted benzenes.It is suggested that photoelectron spectroscopy allows a quantitative distinction to be made between inductive (or field) and resonance effects in substituted benzenes. When this distinc- tion is made, the PMO 11' calculations predict the ionization potentials of 23 benzene compounds marginally better than PMO I1with no serious errors and, unlike PMO 11, does not fail for p-nitroaniline. No other cases of ionization potentials which could be used for distinguishing between the relative merits of PMO I1 and PMO 11' were found in the literature. The overall correlations between calculated and observed ionization potentials for PMO I1 and PMO 11' methods are significantly better than for PMO I.APPENDIX First-order perturbation theory 2o corrects the energy of a slightly perturbed system bysumming the zeroth-order energy and the perturbation. For a perturbed system, the energy E. is equal to E,"+E,' where E'; is the energy of the unperturbed system and Ej is the change R. A. W. JOHNSTONE AND F. A. MELLON in energy due to the perturbation. If Koopmans' theorem holds then the ionization poten- tial (I= -El)of a multisubstituted benzene is the ionization potential of benzene (Io= -EY) plus the sum of the perturbations, i.e., the sum of the differences (AI, = -Ei) between the ionization potentials of benzene and the corresponding monosubstituted benzenes C6H5X (esn (1)).I = Io+ZAIx. (1) First-order perturbation theory is satisfactory for small perturbations and a more accurate estimation of ionization potentials can be expected through the use of second-order perturba- tion theory. Following Matsen,l who implicitly puts the first-order perturbation coefficient equal to zero, the energy Eiof an orbital by second-order perturbation theory 2o is given by the following expression, where Hii,Huhave the usual significance and refer to the un- perturbed system and the perturbing substituent : Ei = Hii +H$/(Ep-E,"). Thus, for a monosubstituted benzene, C6H5X (1 ; Y = H), the energy E3 of the n3orbital is given by eqn (3). As above, Ez = -Io and E3 = Ez +Hi,/(Eg -E707).(3) E3-Eg = AI, so that eqn (3) yields (4) : therefore Consider now a para-disubstituted benzene (I). If the monosubstituted benzene 32 56 C&X is perturbed by insertion of a substituent Y then eqn (3) leads to (5) in which E3(x,y) is the energy of the 7t3 orbital of the disubstituted benzene, and an expression corresponding to 175 (4)has been inserted for Ess : E3(x,y) = E3(x)+H$8/(E3(x)-E88), therefore -E3(x,y)= 1"+AIx+Hg8/(H$8/AIy+AIJ. (5) Similarly, putting a substituent X into the monosubstituted benzene C6H5Yyields eqn (6). Since -E3(x,y) = -E3(y,x) = 10+AIx,y -E3(y,x) = I"+AI,+ H~7/(H$,/AIx+AI,,); (6) and adding eqn (5) and (6),we obtain (7) : AIx,y= +(AI, +My)+H$7/(H$7/AIx+AIy)+H$8/(HZ8/AIy+AIx). (7) The quantities H3,, HS8are the resonance integrals of Hiickel theory and HS7= crkxPO, H38 = crkypo,where Pois the " standard " C-C resonance integral, k,, ky are parameters for X-C, Y-C bonds, and c, is the coefficient of the n3 orbital in benzene at the position of substitution.Thus, for any disubstituted benzene, eqn (7) may be transformed to eqn (2) and, for a para-disubstituted benzene, cf = c;4 = 4 so that, with Po= 3 eV, eqn (2) yields eqn (81, AIX,,,= +AlX(l+1/(1 +AI, .AIy/3k5))++Iy(l +1/(1 +AIx .AIY/3k;)) (8) which was used to calculate (PMO 11) the ionization potentials listed in tables 2, 3 CAI, values taken from table 1). EFFECTS OF INDUCTION AND RESONANCE For PMO 11' calculatioiis, AZ: rather than AI-rvalues were used. For example, for p- nitroaniline, AZLo2 = -0.05eV, A&!, = -1.28 eV and therefore, from eqn (S), A&O~,NH~= -1.31 eV.To take account of the inductive effects, since AIjnd.(NO2)+ AIind.(NH2) = +0.57 eV, the measured shift, AINo*,NH~= -1.32+0.57 = -0.74 eV, and the ionization potential, IN02,NHz = 9.24- 0.74 = 8.50 eV. For meta-substituted benzenes, the coefficients, c,, are not equal and to apply eqn (7) we have assumed that the substituent with the largest AI; value reacts most strongly with the n,-orbital at the position with the largest coefficient. Thus, for AZ; > AI;, eqn (7) reduces to (9) for meta-disubstituted benzenes : AIX,, = +AI,(l + 1/(1 +AIx .AIy/3k:)]+%AI,(l+ 1/(1+4AI, .AIy/3k;)]. (9) For more highly substituted benzenes, e.g., 1-X,3-Y,4-Z-C6H3, the ionization potential may be obtained by first calculating A& and then using this value in eqn (2) again to calculate Al,,,,,.Eqn (2) can be approximated to the empirical equation derived ea~lier.~ If AIx. AIJ c,2k.$p$ < 1, as when AIx, AIy = 1-1.2 (approx.), then binomial expansion of (2) gives eqn (10) : 2AIx,y = AI,(l+ 1-(AIx .Aly/C~k~fl~)]+AIy{l + 1 -(AIx .Al,,/c~k~fl$)), therefore AIx,y = AIx+AI, -AIx . AI,((AI,/c~k~)+(Al,/~~k~)]/2/?~. (10) The latter equation is identical with the empirical equation except for the last term inside the square brackets. The empirical equation worked because interactions between strongly perturbing substituents and the benzene ring were reduced by the term incorporating AIx .AI,,; the theoretical equation has a similar property.For a review of early work, see M. M. Bursey, Org. Mass Spectr., 1968,1,31 ; for more recent work, see F. W. McLafferty, T. Wachs, C.Lifschitz, G.Innorta and P.Mine, J. Amer. Chem. SOC.,1970, 92, 6867 and I. Howe and D. H. Williams, J. Amer. Chem. SOC., 1969,91, 7137. A. D. Baker, D. P.May and D. W.Turner, J. Chem. SOC. B, 1968,22.'D. W. Turner, C. Baker, A. D. Baker and C. R. Brundle, Molecular Photoelectron Spectroscopy (Wiley-Interscience, London and New York, 1970), pp. 279-289. T. W. Bentley and R. A. W. Johnstone, J. Chem. SOC. B, 1971,263. R. S. Mulliken, J. Phys. Chem., 1952,56, 295. A. D. Walsh, Trans. Faraa'ay Soc., 1946,52,779.'A. D. Walsh, Proc. Roy. SOC.A, 1951,207,13,22. see, for example, R.Foster, Organic Charge-Transfer Complexes (Academic Press, London and New York, 1969) for many leading references. T. Koopmans, Physica, 1933,1, 104. loJ. J. Kaufmann and W. S. Kosiki, J. Amer. Chem. SOC., 82,3262; J. Phys. Chem., 1962, 66, 2269. l1 J. L. Franklin, J. Chem. Phys., 1954,22,1304. l2 B. Cantone, F. Grasso, A. Foffani and S.Pignataro, 2.phys. Chem. (Frankfurt), 1964,42, 237. l3 F. A. Matsen, J. Amer. Chem. SOC.,1950,72, 5243. 14M. Godffey, J. Chem. Soc. B, 1971, 1534, 1537, 1540,1545. l5 R.A. W.Johnston, F. A. Mellon and S. D. Ward, Adv. Mass Spectr., 1971,5,334 ; Int. J. Mass Spectr. Ion Phys., 1970, 5, 241. l6 R. A. W. Johnstone and F. A. Mellon, J. C. S. Faraday II, 1972,68, 1209. l7 J. K. Franklin, J. G. Diilard, H. M. Rosenstock, J. T. Herron, K. Draxl and F. H. Field, Ionization Potentials, Appearance Potentials, and Heats of Formation of Gaseous Positive Ions (Nat. Bur.Stand., Washington, 1969). A. Streitwieser, Molecular Orbital Theory for Organic Chemists (Wiley, New York, 1961), p. 135. l9 Many text-books and papers deal with this point but see, e.g., J. Hine, Physical Organic Chemistry (McGraw-Hill Kogakusha, New York and Tokyo, 1962), p. 92. 2oL. Pauling and A. Wilson, Introduction to Quantum Mechanics (McGraw-Hill, New York, N.Y., 1935), p. 191 ; M. J. S. Dewar, The Molecular Orbital Theory of Organic Chemistry (McGraw-Hill, New York,1969), p. 50.

ISSN:0300-9238    

DOI:10.1039/F29736900036

出版商:RSC    

年代:1973

数据来源: RSC

摘要:

Unstable Intermediates Part 122.1-Electron Spin Resonance Studies of Radicals from Irradiated Trimethylphosphine Oxide : the Me,PO Radical BY A. BEGUMAND M. C. R. SYMONS' Dept. of Chemistry, The University, Leicester LEI 7RH Received 10th May, 1972 Exposure of trimethylphosphine oxide to 'y-rays at 77 K gave, after slight annealing, e.s.r. spectra with separate features assigned to Me3@O- (or Me3POR), Me2M and H2CPO(Me)2 radicals. At ca. 140 K the spectrum assigned to Me3J!O-radicals was lost irreversibly, whilst that assigned to MezPO radicals changed reversibly to reveal well resolved proton hyperfine structure, with a(H) = 5.6 G. This temperature effect is explained in terms of extensive librations of the radicals, coupled with concerted restricted rotation of the methyl groups.In alcohol media, only Me390 or Me$OH radicals were detected, whilst in sulphuric acid the main phosphorus radicals were Me3P+ and H2&-P(OH)Met. Continuing our studies of various phosphorus centred we have turned our attention to mixed alkyl-oxy radicals. The radical PO:-is well estab- lished magnetically,* and various alkyl-phosphine cations, R3P+-, have recently been studied in the solid-state. Although several tetra-coordinated alkyl-alkoxy derivatives, R,P(OR)+, are now known in the liquid stateYg* lothe only ter-coordin- ated species detected in fluid solution, to our knopledge, are the dialkoxy-radicals OP(OR),.'l These are simply alkyl derivatives of PO:-, and the results l1 show that alkylation has only a minor effect on the magnetic properties, having the same form as environmental effects.EXPERIMENTAL Purified trimethylphosphine oxide was kindly supplied by Dr. D. J. H. Smith. Methanol, ethanol and sulphuric acid were reagent grades. Small spherical beads were prepared byrapidly freezing the oxide in liquid nitrogen, prior to exposure to 6oCoy-rays at 77 K in a Vickrad cell for up to 2 h at a nominal dose rate of 4 Mrad h-l. E.s.r. spectra were obtained using a Varian E3 spectrometer, either at 77 K using a quartz dewar insert, or between ca. 85 K and the softening point of the solid using a Varian variable temperature accessory. Q-band spectra were run on a superheterodyne spectrometer con- structed in these laboratories. RESULTS AND DISCUSSION Typical e.s.r.spectra obtained from y-irradiated trimethyl-phosphine oxide are illustrated in the figures. The central features at 77 K were characteristic of radicals of type HzcPR3,2 (fig. l(a))and the derived parameters (table 1) are in accord with expectation.2* l3 On annealing to ca. 140 K, better resolution was achieved (fig. l(b)), but extra lines appeared in the wings which were barely discernible at 77 K. These were selectively broadened again on cooling; we can offer no clear identification of the species responsible for these extra features. 43 UNSTABLE INTERMEDIATES The features assigned to Me,PO radicals varied markedly with temperature, as exemplified in fig. 2(a) and 2(b). These changes, which were completely reversible, involve the apparent 'H hyperfine coupling as well as the 31Pand g-tensors (table 1).These radicals, which were very much more stable than those associated with the -1 3270G FIG.1.-First derivative e.s.r. speqtrum of trimethylphosphine oxide after exposure to y-rays at 77 K, showing features assigned to H2CP(0)Me2 radicals; A, at 77 K; 13, at cu. 140 K showing extra lines (a). TABLE1.-E.s.R. DATA FOR RADICALS IN IRRADIATED TRIMETHYLPHOSPHINE OXIDE radicals proton coupling/G 31Pmpling/G AX A, AZ g-values g,, 91 H2cP(0) Me2 H&P(OH)Mef Me2P0 (77 K) (140 K)Me3PO-or ca. 21 20 5.6 20( 11) 174I) not resolved ca. 38 40 3 10 295 375 295 433 535 ca. 2.003 2.003 1.997 2.009 Me3POH not resolved 738 548 548b 1.997 2.015 (inEtOH) Me,P+ not resolved 600 290 290 2.002 2.01 (in H2S04)Po;- 706.5 540.2 540.2 1.992 2.007 (in Na2HP03) * apparent coupling only (see text) ; b error cu.k 10 G because of broad lines, ; C ref. (12). A. BEGUM AND M. C. R. SYMONS outermost features, were only lost when the glasses became soft. Their identification as Me,PO follows from the folfowing observations : (i) they contain only one strongly coupled phosphorus nucleus; (ii) they contain at least two equally coupled methyl groups ; (iii) the isotropic hyperfine coupltng to 31P(375 G)is far too small for the only other reasonable species, namely Me,PO-or Me3POR. (iv) the derived orbital populations (table 2) show a clear gradation in the values for Me,P+*, Me,PO and PO$-, both with respect to the fall in total spin-density on phosphorus with increase in the number of oxygen ligands, and the fall in pls ratio, and hence increase in pyramidal character, as methyl ligands are replaced by oxygen ligands.FIG.2.-First derivative e.s.r. spectrum of trimethylphosphine oxide after exposure to y-rays at 77 K and annealing to remove features assigned to Me3PO-and related species. a,At 77 K ; 6, at ca. 140 K. TABLE2.-DERIVED ORBITAL POPULATIONS 03 .%) a,(%) af+aB(%) P/S Me,P+ 10.8 100 110.8 9.3 Me2P0Poi- 10.3 16.4 78 53.8 88.3 71.2 7.6 3.3 Me PO-( H+) 17 61.5 78.5 3.6 The changes in the proton features on cooling to 77 K almost certainly reflect some form of restricted rotation of the methyl groups.We suggest that this takes the form of slow, coupled rotations such that the sum of the coupling constants for all six protons remains ~0nstant.I~ This would leave the MI = _+ 3 lines independent of time, whilst the remainder would change continuously with time, except for one componea of the MI= 0 line. If, at 77 K, this motion is at such a frequency as to result in a major broadening of the +2 and 1 lines, then only the k3 and 0 lines would be detected, and the intensity of the Mr = 0 line would tend to equal those of the MI= +3 lines. UNSTABLE INTERMEDIATES It is interesting that for the radicals Me2cOH or Me2cO-, the methyl groups are rotating rapidly on an e.s.r. time-scale at 77 K.lS*l6 This suggests that the two methyl groups are forced together by the tendency for Me2P0 radicals to have a locally pyramidal structure at the phosphorus atom.NOproton hyperfine coupling was detected for Me,P+- and related ions,3*l7 but the lines were broad, possibly reflecting the absence of free rotation. However, for the isoelectronic R3Si* radicals, IH hyperfine coupling constants of ca. 6.3 G were observed,l* which is very close to the value now assigned to Me2P0 radicals. Since the magnitude of the coupling to fl protons clearly falls as the deviation from planarity increases, we would argue that Me2P0 radicals have about the same pyra- midal character as R,Si. radicals. Since we have previously concluded that R3P+* radicals are more nearly planar than R,Si.radicals, this means that replacing an alkyl ligand by 0-has slightly increased the degree of bending at the phosphorus atom. That this is indeed the case can be judged more conclusively from the changes in the 31Ptensor components on going from R3P+- to Me2P0 and then to -PO:-radicals (table 1). (There is only slight delocalisation onto oxygen in Me,PO radicals, and the consequent reduction in coupling to the methyl protons is small. When allowance is made for this, the coupling (6.3 G) remains close to that for Me3% radicals (6.3 G).) The temperature dependence of the 31P hyperfine components is best understood in terms of librations about the x and y axes, as arbitrarily defined in the insert. We suggest that libration about one axis (say x) is greater than that about the other (y).Thus a partial averaging of 80G by libration about x gives A; = 375 G and = 455 G which, taken together with a smaller partial averaging of ca. 17 G about y, gives A, = 312 G, A; = 375 G and A: = 438 G, the new experimental values being 310, 375 and 433 G respectively. ldentification of the species responsible for the outermost features is less com- pelling, since only the 31Pcoupling was detected. However, the fact that a very similar species was formed in alcohol glasses containing the phosphine oxide, whilst the concurrent formation of e,_centres in the alcohol was suppressed, leads us to suggest the radical anion Me3PO- or its conjugate acid, Me3pOH, as the most probable species. The calculated isotropic coupling to phosphorus of ca.610 G is very close to those observed by others 9* lo for R3POR radicals (cu. 618 G), thus strongly supporting our identification. (The significance of these results will be discussed more fully in conjunction with our solid-state results for other radicals of A. BEGUM AND M. C. R. SYMONS this class.) The species formed in the pure material could also be Me,POMe, if reaction (4) given below is correct, since methyl radicals were not detected. Curiously, sulphuric acid solutions, which probably contain mainly Me3POH+ ions, had e.s.r. spectra, after exposure to 6oCoy-rays at 77 K, quite different from those discussed above. The major phosphorus centred radical (fig. 3) had parameters closely similar to those for R3P+.radicals and we therefore assign these features to Me3P+* radicals. The central portion of the spectrum was very similar to that in fig. 1 and we therefore identify the species responsible as H,cP(OH)Mei. Broad features with a marked g-value variation (confirmed by Q-band studies) may well be due to Me3PO+ radicals, but further studies are needed to check this suggestion. I 32206 n IOOG, I' FIG.3.-First derivative e.s.r. spectrum of trimethylphosphine oxide in sulphuric acid after exposure to y-rays at 77 K, showing features assigned to Me,P+ radicals. POSSIBLE MECHANISMS In accord with our previous analyse~,~" we suggest an initial ionization and electron trapping for the pure material : 2Me3Pd -+ Me3PO++ Me3PO-(1) followed by Me3Pd+-+ H,@(O)Me,( + H+) (2) Me3PO++ Me,PO--+ 2Me3PO* (3) Me3PO* -+ Me+Me2P0 (4) Me,PO+Me -+Me,POMe.(5) In alcoholic solutions, we may also have Me3PO-+ ROH -+ Me,POH + RO-(6) and in sulphuric acid 48 UNSTABLE INTERMEDIATES Me,POH++e 3 Me3POH (7) Me3POH+2H2S0, + Me3P+-+H30++2HSOi. (8) We do not usually find it necessary to postulate homolytic fission, as in (4), but the formation of Me2P0 radicals in good yield is difficult to explain in terms of ionic processes. We thank the S.R.C. for a grant to A. B. and Mr. J. A. Brivati for experimental assistance. 'Part 121. K. V. S. Rao and M. C. R. Symons, J.C.S. Faraday 11, 1972, 68, 2081. A. Begum, A. R. Lyons and M. C. R. Symons, J. Chem.SOC. A, 1971,2388. A. Begum, A. R. Lyons and M. C. R. Symons, J. Chem. SOC. A, 1971,2290. M. C. R. Symons, J. Chem. Phys., 1970,52, 857. S. Subramanian, M. C. R. Symons and H. W. Wardale, J. Chem. SOC. A, 1970, 1239. A. Begum, S. Subramanian and M. C. R. Symons, J. Chem. SOC. A, 1970, 1334. A. Begum, S. Subramanian and M. C. R. Symons, J. Chem. SOC.A, 1971,700. P. W. Atkins and M. C. R. Symons, The Structure of Inorganic Radicals (Elsevier, Amsterdam, 1967). A. G. Davies, D. Griller and B. P. Roberts, Angew. Chem. Int. Edn., 1971, 10, 738. loJ. K. Kochi and P. J. Krusic, Chem. SOC. Spec. Publ., 1970,24, 147. ''A. G. Davies, D. Griller and B. P. Roberts, J. Amer. Chem. SOC.,1972, 94, 1782. l2 M. C. R. Symons, J. Chem. SOC. A, 1970, 1998. l3 A. R. Lyons, G. W. Neilson and M. C. R. Symons, J.C.S. Faraday ZI, 1972, 68, 807. l4 P. B. Ayscough, Electron Spin Resonance in Chemistry (Methuen, London, 1967). l5 J. F. Gibson, M. C. R. Symons and M. G. Townsend, J. Chem. SOC., 1959,269. l6 J. E. Bennett, B. Mile and A. Thomas, J. Chem. SOC.A, 1968, 298. l7 A. R. Lyons and M. C. R. Symons, unpublished results. l8 S. W. Bennett, C. Eaborn, A. Hudson, R. A. Jackson and K. D. J. Root, J. Chem. SOC.A, 1970,348.

ISSN:0300-9238    

DOI:10.1039/F29736900043

出版商:RSC    

年代:1973

数据来源: RSC

摘要:

Nitrogen Quadrupole Hyperfine Splitting in the Microwave Spectrum of Dinitrogen Trioxide BY A. PETER COX” AND DAVIDJ. FINNlGANt Department of Physical Chemistry, The University, Bristol BS8 ITS Received 19th June, 1972 Nitrogen quadrupole splittings in the microwave spectra of NzO3, Ol5NNO2 and ON”NO2 have been examined. Analysis of splittings due to single and double nitrogen coupling has yielded coupling constants at both nuclei ; accurate values have been obtained for xm(NO2)= -2.0 & 0.I and xaa(NO)= -1.9kO.1 MHz respectively. The coupling constants have been interpreted, using a Townes-Dailey approach, in terms of the coupling found in nitric oxide and nitrogen dioxide perturbed by the weak N-N bond. This description, while predicting a moderately large value for Xab at the nitrosyl nitrogen, satisfactorily accounts for the unusual structure and the value of the dipole moment in NzO3.The detailed structure of N203(see fig. 1) has recently been determined from its microwave spectrum,l* and several aspects of the structure point to an unusual form of chemical bonding. The N-N bond is 0.4A longer than a normal single bond being 0.1 A longer than that in N204,yet the structure of N203is planar. In addition 6 / FIG.1.-Structure of N203. the NO and NOz groups have been found to be tilted towards each other. The purpose of the present paper is to report quadrupole coupling constants at each of the nitrogen nuclei as derived from microwave spectra of the normal species and the isotopic species O1W”N2and ON15N02.The coupling constants should provide further information about the unusual electronic structure of N203. p present address: Department of Chemistry, Harvard University, Cambridge 02138, Massa- chusetts, U.S.A. 49 NITROGEN QUADRUPOLE HYPERFINE SPLITTING EXPERIMENTAL The study of quadrupole hyperfine structure in the microwave spectrum of dinitrogen trioxide required careful choice of the experimental conditions. The spectra were observed using a Stark spectrometer operating with a modulation frequency of 100 kHz. A second spectrometer operating at 15 kHz, although offering advantages in resolution, was not sufficiently sensitive for the present studies. Spectra were studied at dry-ice temperatures with total sample pressures of approximately 10 N m-2, dosed from a bulb containing equal pressures of NO and N02+N204.Under these conditions N203 constitutes approxi-mately 0.5 %of the total pressure. The study of the single substituted lSN-species had to be carried out on -0.1 %of the gas because of isotopic exchange between the two nitrogen positions. The largest quadrupole splittings found in N203 were N 0.8 MHz, comparable with the line-widths for optimum intensity conditions. Reducing the pressure improved resolution but also increased the dissociation of N203 leading to poorer signal-to-noise ratios. Further lowering of the temperature to just above the freezing point of NzO3 (--102°C) should have definite advantages for the study of dinitrogen trioxide, but cannot conveniently be achieved in the present system.Instead we have resorted to slow electronic sweeping of the klystron source, with and without source-stabilisation (Micro-Now 101/201 system), plus large time constants in the detector system with recorder display. RESULTS MICROWAVE SPECTRA AND QUADRUPOLE HYPERFINE STRUCTURE Most transitions previously assigned for N,03 and its isotopic species were pa,9 R-branch lines with J values between 1 and 5. One pb transition, 313+-202,was measured but in general ,ub transitions are much weaker and therefore more difficult to assign, because of the smaller b-component of the dipole moment; the ratio of pi/pz is -14 (ref. (2)). The weakness of the pb spectrum plus the broad nature of the lines provided the main difficulties in determining the coupling constants for dinitrogen trioxide.The 6,,+6,, transition of N,03, shown in fig. 2, belongs to one of the .... f38 087.00 38086.00 38085.00 frequency/MHz FIG.2.-Experimental and synthesised line-shapes of 625t616 transition of Nz03. The experi-mental trace has been obtained with a sweep rate of 0.01 MHz/s and a time constant of 3 s. A. P. COX AND D. J. FINNIGAN strongest pb-series assigned. It is the only pb-series for which we have been able to establish measurable quadrupole splitting. The normal species of dinitrogen trioxide contains two nonequivalent quadrupolar nuclei (l 4N) and the hyperfine structure is complicated. The two single-substituted 5Nspecies contain only one quadrupolar nucleus and the hyperfine structure may be simply analysed using the first-order theory of Bragg and G01den.~ The perturbation energy, EQ,is conveniently expressed in terms of the coupling constants xUa and &,-&) and Casimir's function Y(I,J, F) as follows : In this expression xaU(= eQqau),Xbb and xccare the diagonal elements of the quadrupole coupling tensor in the principal inertial axis system of the molecule.The (P:), etc. are the expectation values of the square of the components of the rotational angular momentum ; quantum numbers I, J and F have their accepted meanings. The quadrupole splittings previously reported for ON15N02have been confirmed in the present study. In addition the data has been reanalysed* to give more accurate constants (see table 1).A least squares treatment based on eqn (1) has been used ; the standard deviations on the constants indicate that xUuis well determined whereas the asymmetry in the coupling (zbb-xcc)is poorly determined. TABLE STRUCTURE OF Oi4N1w02 AND QUADRUPOLE COUPLING CONSTANTS 1.-HYPERFINE OF THE NITROSYL NITROGEN ATOM OF N203(MHz) transition hypotheticalJ'tJ observed frequency Av a centre frequency { f F' +-Fi} 22 458.55 0.0132,i C 22,o 22 458.28 3t2 22 457.75 -0.02 { i} 22 075.43 -0.02 +-22,1 22 075.20 32,~ 3i-2 22 074.74 0.02 30 283.91 -0.01 30 283.81 42,2 +-32,1 30 283.59 0.01 29 357.87 0.02 29 357.76 c4t-3 29 357.55 -0.02 xaa, -1.9&0.1 ';Xbb, 1.6k0.6; xcc, 0.3k0.6; Xhb-Xcc, 1.3+1.2.(1Av = (obs.-calc.) shift from the hypothetical centre frequency ; quadrupole shifts were calcu- lated from experimental coupling constants given above ; b quoted errors are standard deviations of least squares fit ; rotation of the inertial axes with ISNsubstitution (-0.1') has negligible effect on the x values. The search for quadrupole structure, due to the nitrogen atom in the NO, group, was based initially on constants predicted from SCF calculations made in this depart- ment using the structure given in fig. 1. These calculations had given good agree-inent for the dipole moment of N203but only moderate agreement for the quad- rupole coupling constants at the nitrosyl nitrogen. The microwave spectrum of the normal species was first examined (rather than that of OI5NNO2)to take advantage * An error was made in the coefficients of the x values used for the analysis of this data inref.(2). NITROGEN QUADRUPOLE: HYPERFINE SPLITTING of the larger intensities avai!able. Particular attention was paid to those lines for which quadrupole splitting was predicted to be small for the nitrosyl nitrogen but measurably large for the Nitro nitrogen. Quadrupole structure attributable to the nitro nitrogen was eventually observed in N2O3for the 625+616,pb transition. This line was observed as a pai*tially resolved doublet (intensity ratio 1 :2) see fig. 2. The splitting was measured as 0.51 MHz and was found to be reproducible to better than 0.1 MHz in a series of measurements.Other members in this series which also exhibited hyperfine structure were the 524+-5,5 and 4236-414transitions. The latter appears as a triplet which may be interpreted as a quadrupole doublet plus an intruder line to lower frequency. Calculations of quadrupole patterns due to coupling at both nuclei, over a reasonable range of coupling constants for the two nitrogen nuclei, failed to reproduce the triplet structure. The calculations do however predict a doublet split by 0.63 MHz, using the coupling constants derived for both nuclei. The two upper members are identified as the quadrupole doublet on the basis of centrifugal distortion shifts ;* the observed splitting of 0.89 MHz, while undoubtedly perturbed by the other transition, is in satisfactory agreement with calculations and the other members of the series.The double coupling calculations for N203have been made TABLE2.-HYPERFINE STRUCTURE OF 015N14N02AND 014N14N02AND QUADRUPOLE COUPLING CONSTANTS OF THE NITRO NITROGEN ATOM OF N203(MHz) 015N14N02 transition F'c I; observed frequency Ava hypotheticalcentre frequency 21 920.19 -0.01 21 919.99 t2 21 919.50 0.01 29 407.04 0.02432 + 331 29 406.80 4t3 29 406.33 -0.03 014N14N02 transition relative hypotheticalJ'cJ observed frequency intensity b Av centre frequency 31 822.28 1 0.13 42,s +-41,4 31 821.39 2 -0.13 31 821.73 -(31 820.97) 2 34 662.72 1 -0.02 34 662.26 2 0.02 34 662.41 38 086.32 1 0.0362,5 c-61,6 38 085.81 38 086.012 -0.04 XQ~,-2.03-0.1 e; Xbb, 0.15k0.4; xcc,1.85k0.4; Xbb-Xcc, -1.7k0.8. Av = (obs.-calc.) shift, quadrupole shifts were calculated from experimental coupling constants given above ; b approximate intensity relative to the other observed components of the same rota- tional transition ; C Av = (obs.-calc.) shift, quadrupole shifts were calculated from the theory of Bardeen and Townes (see text) using the experimental coupling constants given in table 2 and in table 1 ; dadditional feature not assigned to 42,3.<-41,4 transition (see text) ; e rotation of the inertial axes with '5N-substitution (-0.7") has negligible effect on the jy values. * The rigid rotor frequencies for the 423c414,524 t515 and the 625 t616 transitions of Nz03 were calculated from the rotational constants of ref.(2) as 31 822.09, 34 662.46 and 38 086.22 MHz respectively. The displacement of the quadrupole components from the rigid rotor frequencies in this series has allowed the 423c414 doublet to be identified. A. P. COX AND D. J. FINNIGAN using a computer programme based on the theory of Bardeen and Townes.' Spectra synthesised using a Lorentzian line-shape with an assumed line-width were compared with the observed peaks (see fig. 2). Further information on coupling at the nitro nitrogen resulted from studies of O15NN02. Splittings of the pa transitions, 322+221 and 432+331,yielded xaa = -2.OkO.l MHz. The 202~ loltransition also showed splitting due to Xaa but signal intensities did not allow accurate measurement. xbb and xCcfor the nitro nitrogen have been derived from the splitting of the 625~616 transition in the normal species assuming negligible coupling at the nitrosyl nitrogen and the xaa value obtained for O15NN02.The expression for the splitting of the 625-616 transition by one nucleus is given by : AV= -0.080 31xaa-0.204 17kbb-& (2) where Av is the splitting between F = 6-+F= 6 and a combination of I: = 5-+5 and 7+7. The contribution of the nitrosyl coupling to the splitting is expected to be small, -0.1 MHz. Moreover, the doublet splittings of the 625+6,, and 524+515 transitions have been accurately reproduced by a Bardeen-Townes calculation using the coupling constants of tables 1 and 2 for both nuclei. The doublet splittings for this series are essentially invariant to values of (Xbb-xcc) for the nitrosy1 nitrogen within the range 0-2.5 MHz.The quadrupole coupling constants for the nitro nitrogen are given in table 2 together with a summary of relevant quadrupole structure in the spectra of N203and O15NN02. DISCUSSION The central N-N bond in N203 is extremely weak (enthalpy of dissociation * AH = 39.7 kJ mol-l) even weaker than that in N204(AH = 57.3 kJ mol-').' Also structural parameters of N203are only slightly modified from those of NO (N=O = 1.151A) l9 and NO, (N-0 = 1.193& LONO = 134.1°).20 It might be expected therefore that the coupling constants in N203would be similar to those of NO (Xaa = -1.8, Xbb = xcc = 0.9 MHz) lo and NO,[~(bisecting LONO = -1.71, x(paralle1 to 0...0)= 0.45 and xcc = 1.26MHz].ll The values are in fact very similar although a direct comparison is not valid (particularly for the nitrosyl group) since the axis systems do not correspond. In N203, apart from the xcc values, the coupling constants are almost certainly not the principal axis components of the quadrupole coupling tensor for each nitrogen, in contrast to those given for NO and NO2. Good agreement is obtained for the nitro coupling constants by transforming the NO, constants into the principal inertial axis of Nz03,after including -20 % of the nitrite ion contributor [x(bisecting LONO = -5.792, X(paralle1 to 0 . . . 0)= 1.723 and xCc = 4.068 MHz] l2expressed by the resonance forms : About 15 % of this contributor would account for the experimental value of the dipole moment,2 p = 2.12 D.Such a contribution is further suggested by the shortening of the nitrosyl bond length relative to NO and the movement of the struc- NITROGEN QUADRUPOLE HYPERFINE SPLITTING ture of the NO2 group towards that of NOY(LON0 = 114.9", N-0 = 1.24OA).I8 It would also provide a rationalisation of the tilted NO2 group towards the NO group, but this suggestion is not supported by the result that the cis N-0 bond is probably shorter than the trans distance. The interpretation of the coupling constants at the nitrosyl end is less straight- forward. First the experimental x values are very different from other molecules containing the uitrosyl group, see ref.(13). For example NOF, with inertial axes corresponding closely to those in N2O3, has the values l4 ;Caa = 1.7, xbb = -5.0 and xcc = 3.3 MHz. The contrast with NOF is made more striking by certain similarities in their structures ;2* l5 both have nitrosyl bond lengths shorter than NO and both have very long N-X bonds. However, the valency angle of the nitrosyl group in N203(105.1") is much smaller than other nitrosyl molecules including NOF which has an angle of 110.1". Secondly it becomes clear in the interpretation that neither the N=O bond direction nor the a- and b-inertial axes can be principal axes of the coupling tensor. A comparison of observed and calculated x values cannot simply be achieved by performing Townes-Dailey calculations l6 in the x, y, z axis system of the nitrosyl group (z along the N-0 bond, x perpendicular to the N=O bond and y perpendicular to the N203 plane).These values must be transformed into the prin- cipal inertial axis system of N203 and this involves a large rotation (N 51") between the 2-and a-axes. This transformation has the effect of producing values of xaa which are too small or positive, from contributors chosen to give a small xcc value required by experiment. The most reasonable model has the unpaired electron of nitric oxide localised in a pn* orbital in the plane of N203. Magnetic hyperfine measure- ments l7 on nitric oxide show that the unpaired electron is associated with the nitrogen atom for 65 % of the time; this would lead to x values, for the localised model, of xz = -1.75, xx = 3.5 and x,, = -1.75 MHz.Sixty percent of this form would give the experimental bond order for the N-N bond (0.22), and following the resonance description of the nitro end we take 20 % of NO itself with 20 % NO+. Fitting this model to the experimental xaa necessitates an off-diagonal element xxz = 2.7 MHz or in the inertial axis system a value of xab = -3.1 MHz. These are not unreasonable since clearly neither the N=O bond system nor the inertial axis system are the principal axis system of the coupling tensor. It should be noted that although in principle xab, for the nitrosyl nitrogen, could be determined by isotopic substitution (with oxygen-18) the sensitivity and accuracy required is not attainable in the isotopic spectra of N203.Further interest in the quadrupole coupling of N203 would lie in a comparison of the constants reported here with values for the solid-state should they become available. The authors thank Dr. A. H. Brittain and Professor R. L. Kuczkowski for their earlier contribution to this work. We also thank the S.R.C. for their financial support. l R. L. Kuczkowski,J. Amer. Chem. SOC.,1965,87, 5259. A. H. Brittain, A. P. Cox and R. L. Kuczkowski, Trans. Faraday SOC.,1969,65, 1963. I. R. Beattie and S. W. Bell, J. Chem. SOC.,1957, 1681 ; W. F. Giauque and J. D. Kemp, J. Chem. Phys., 1938, 6,40. J. K. Bragg and S. Golden, Phys. Rev., 1949, 75, 735. J. R. Yandle, I. S. Woolsey and N. S.Hush, personal communication.D. J. Finnigan, B.Sc. Thesis (University of Bristol, 1968).'J. Bardeen and C. H. Townes, Phys. Rev., 1948,73,97.* I R. Beattie and S. W. Bell, J. Chem. Suc., 1957, 319. W. F. Giauque and J. D. Kemp, ref. (3). lo J. J. Gallagher and C. M. Johnson, Phys. Rev., 1956, 103, 1727. A. P. COX AND D. J. FINNIGAN 'I R. M. Lees, R. F. Curl, Jr. and J. G. Baker, J. Chem. Phys., 1966,45,2037. l2 T. Oja, R. A. Marino and P. J. Bray, Phys. Letters, 1967, %A, 11. l3A. P.Cox,A. H. Brittain and D. J. Finnigan, Truns.Furuday SOC.,1971,67,2179. l4 A. Guarnieri, G. Zuliani and P. G. Favero, Nuovo Cimento, 1966,45, 84. l5 K. S. Buckton, A. C. Legon and D. J. Millen, Truns. Furduy SOC.,1969,65, 1975. C. H. Tomes and B. P. Dailey, J. Chem.Phys., 1949, 17,782. l7 G. C. Dousmanis, Phys. Rev., 1955,97,967. l8 M. I. Kay and B. C. Frazer, Acfu Crysf.,1961,14,56. l9 C. A. Burrus and W. Gordy, Phys. Rev., 1953,92, 1437. 2o G. R. Bird, J. C. Baird, A. W.Jache, J. A. Hodgeson, R. F. Curl, Jr., A. C. Kunkle, J. W. Bransford, J. Rastrup-Anderson and J. Rosenthal, J. Chem.Phys., 1964, 40, 3378.

ISSN:0300-9238    

DOI:10.1039/F29736900049

出版商:RSC    

年代:1973

数据来源: RSC

摘要:

Optical Properties of Sub-monolayer Molecular Films BY M. J. DIGNAM*AND M. MOSKOVITS Department of Chemistry, University of Toronto, Toronto 181, Ontario, Canada Received 26th June, 1972 Equations for the change in both the specular reflectance and the ellipsometric parameters for a flat surface following formation of a sub-monolayer molecular film are derived by taking explicit account of the particulate nature of the adsorbed film, while treating the substrate as a continuum. A dielectric constant tensor, E, can be defined for the adsorbed film which, upon choosing an effective film thickness, de, so that E is isotropic whenever the mean molecular polarizability of the adsorbed species is isotropic, takes a form essentially identical to that obtained using the Lorentz-Lorenz equation.In general, both E and de vary with coverage in the range zero to one monolayer. For films consisting of island patches, however, E is constant and de is proportional to coverage ; while for films consisting of more or less randomly distributed molecules, d, is approximately equal to the molecular diameter at all coverages up to one monolayer and e varies with coverage. 1. INTRODUCTION The application of specular reflectance and ellipsometric spectroscopy to the study of adsorbed films has been increasing steadily in recent year~.l-~ Equations which relate the changes in specular reflectance and in the ellipsometric parameters for a flat surface, following formation of a thin isotropic film, to the macroscopic properties of the film and substrate (complex dielectric constant and thickness) have long been a~ailable.~More recently, equations which apply to the formation of a uniaxial film have been deri~ed.~ The question as to how to relate the “ macroscopic ” complex dielectric constant tensor for a monomolecular layer, or sub-monomolecular layer, to the complex polarizability tensor for the adsorbed species is, however, still unsettled, even for the case of an isotropic and has not been attempted for a uniaxial film.In this paper, the problem of an oriented sub-monomolecular layer is treated, with that for an “ isotropic film ” arising as a special case. Since equations have already been derived which relate the observables to the ‘‘macroscopic parameters ” for the the most economical method for achieving the above goal is to relate these “ macroscopic parameters ” to the microscopic ones.For monomolecular and sub-monomolecular layers, the molecules are bound to be at least partially oriented relative to the normal to the substrate surface. It is apparent, therefore, that in general the adsorbed layer will be optically anisotropic. If it is assumed that the molecules are randomly oriented with respect to rotation about a normal to the surface, and furthermore that their distribution in the surface plane is isotropic, then the molecular layer will display the same symmetry properties as a uniaxial film with its optic axis oriented normal to the surface. In such a case, a macroscopic complex dielectric constant tensor for the molecular layer can perhaps be defined and be represented by its two principal components, E, and E,, corresponding to the electric field vector oriented normal to and tangent to the surface respectively (i.e., parallel to and transverse to the optic axis).The problem then reduces to relating E, and E, to the complex polarizability tensor for the adsorbed molecules, a,and their 56 M. J. DIGNAM AND M. MOSKOVITS spatial distribution. In the following section, the approximation of assigning a macroscopic dielectric constant tensor to a two dimensional array of molecules is examined and the components of this tensor quantity are related to the polarizability tensor for the adsorbed species. Expressions relevant to specular reflection spectro- scopy are then derived in Section 3.2. DIELECTRIC CONSTANT TENSOR FOR PLANAR MOLECULAR ARRAY Since absorption by a single molecule via electric dipole transitions is propor- tional to the scalar product of the induced dipole moment and the electric field vector, the optical properties of a planar array of molecules will be in part determined by these scalar products. If the array takes the form of a two dimensional regular lattice, then the local electric field vectors generating the induced dipole moments will be of equal amplitude and direction. In such a case, the molecular array can be treated as optically homogeneous, the optical properties of the array being determined by the complex molecular polarizability tensor, a,and the relation- ship between the local and external field strengths.If, however, the molecules are randomly oriented and/or randomly distributed in the plane, the local electric vector will vary in amplitude and direction from molecule to molecule in the array. To treat such an array as optically homogeneous is equivalent to replacing the products of the local electric field amplitude and polarizabilities by an area averaged value. In this section, this approximation is employed for an adsorbed layer displaying uniaxial symmetry. In addition, it is assumed that the spacing between the molecules is small compared with the wavelength of light in vacuo, &, so that the phase difference between the field acting on neighbouring molecules may be neglected. Since the contributions to the local field for a particular molecule arising from the induced dipole moments of the other molecules falls off very rapidly with their separation (i.e., cc1/(~eparation)~),this latter approximation should be a good one even for low surface coverages.DefiningE$)as that contribution to the local field at thejth molecule due to the u-component of the dipole moment of the kth molecule, where u = x,y or z, the dipole moment of the jth molecule, pj, is given by : where El is the external electric field vector associated with the electromagnetic field (i.e., the field that would obtain in the absence of the adsorbed species). Averaging over j, (2.1) can be written : (2.2) where the subscript u’ denotes the u‘-component of the vector, u’ = x,y or z.Takingthe plane of the molecules as the x-y plane, it follows from the symmetry assumed that : (2.3) where &,up is the Kroneker delta and the scalars, aju,are defined by : a, 5ar,6.6, u = x, y or z, (2.4) where Q is the unit vector in the u direction. The field components EjE? are re- lated to dipole moment components through the equation : OPTICAL PROPERTIES OF MOLECULAR FILMS with the functions F$) being given by : and Xjk (Yjk) is the xb) coordinate of the kth particle less that of the jth particle. Substituting (2.3) and (2.5)into (2.2) now gives : so that we have : (2.lo) where y, is 471 times the u-component of the polarization per unit area divided by the u-component of the external field strength, N is the mean number of molecules per unit area, a, = (aj,), and (2.11) If all of the molecules are the same, then aj, and E$i will be uncorrelated to a very good approximation, in which case (2.11) reduces to : (2.12) The final expression in (2.12) is obtained on interchanging the order of summation and noting that F$) = F$).If, in addition, the molecules form a regular two-dimensional array, then &fjF;!i) will be independent of j so that for this case 8, = 1. If the molecules form a dilute, two-dimensional, gas, then pju and xjfkFj(E)become un- correlated so that once again 8, = 1. In general, however, 8, will not be precisely unity, although it will be close to unity whenever the contribution to the local field strength due to induced dipole moments is not too large compared with the external field strength. Since the molecular distribution is assumed to be isotropic in the x-y plane, it follows that : (2.13) Substituting for Fx) and F$) from (2.6) and (2.7) then gives : (2.14) where t = x or y and n = z.M. J. DIGNAM AND M. MOSKOVITS Defining a according to (2.15) where rjkis the distance between thejth and kth molecules, (2.14) becomes : < mi9 = (443)(N/a) (2.16) k#j ( Fg)) = -(8n/3)(N/a). (2.17) k#j An alternative expression for a can be written as follows : a, 03 a = (8/3)nN// 2nrNg(r)dr/r3 = 413 [g(r)/r2]dr = 8/91 [f (r)/r2]dr (2.18)s: 0 where g(r) is the pair probability density function (i.e., g(r)dr is the probability of finding a molecule displaced between r and r+dr from any molecule, divided by the corresponding probability for a random distribution of points on a plane) andf(r) is the pair distribution function (i.e., the expectation value of the number of molecules within distance r of any given molecule divided by the corresponding number for a random distribution of points on a plane.) If the adsorbed molecules behave as hard discs, then as N+O, a becomes (413) times the diameter of the molecules.If, on the other hand, the film takes the form of patches of molecules in a two dimensional crystalline pattern of nearest neighbour distance d', a can be evaluated from (2.15). Thus for a square planar array, a = (8/3)ndI3N/C(j2+k2)-%= 0.935d'3N (2.19) j,k where the sum is over all integer values of j and k,excluding the case j = 0 = k.Thusfor monolayer coverage and a square planar array (N = d'-2),a = 0.9358. For a hexagonal array, a is about 20 % smaller. Substituting for &+&;I from (2.16) and (2.17), eqn (2.10)becomes : (2.20) (2.21) where the subscript t designates the tangential component (x-or y-component) and n the normal component (2-component). Note that to calculate a, and anfrom a,the orientational distribution function for the array must be known. The difference in sign of the terms appearing in the denominators of the expres- sions for yt and yn arises from the fact that for a tangentially oriented external field, the field due to the induced dipole moments augments the external field, while for a normally oriented external field, the opposite is the case.The dielectric constant tensor for any phase is defined by EE = E+4nP where P is the polarization per unit volume and Eis the Maxwell field within the phase, not the external field, El. For a tangentially oriented field, Et = El,(tangential component of electric field continuous across a boundary) so that : E, = 1 +y# (2.22) which, on substituting according to (2.20), gives : (2.23) OPTICAL PROPERTIES OF MOLECULAR FILMS where d is the assumed film thickness. In Section 3 it is shown that It may be given any value consistent with the condition d4&. For a normally oriented field on the other hand, E~E, (normal component of electric displacement continuous = E~E~, across a boundary) so that on setting E~ = 1, En = 1 + (Ynld)En (2.24) which, on solving for c, and substituting according to (2.21), becomes (2.25) or En= 47wid)anl+ 1 -(4n/3)(3a/d-28,)( N/a)a, (2.26) Note that for a, = a,, E, and E, will only be the same provided that d is chosen accord- ing to d = d, = 3a f(29, + 6,) IZ: a.(2.27) Choosing this value for d, (2.23) and (2.26) become : (2.28) where 0 = 38,/(26,+8,). It can be shown (see Appendix) that 9, = O,, and hence 0 = 1, if the polarizability ellipsoid for all the molecules takes the form of an ellipsoid of revolution oriented with its axis normal to the surface, the ellipticity being the same for all the molecules.Thus in particular, 8 = 1 for films consisting of molecules all of which have isotropic polarizabilities, and also for films consisting of identical and normally oriented long chain polymers. On setting 8 2: 1 and interpreting (N/de) as a volume concentration, (2.28) becomes the Lorentz-Lorenz expression for the dielectric constant of a macroscopic phase. One prescription for calculating E, and et for a planar array of molecules is therefore to use the Lorentz-Lorenz expression, with the effective film thickness defined by (2.27). For a monolayer film, (2.27) will reduce very nearly to d, Ed’, which coincides with one’s intuitive choice. This is fortunate as it suggests that for films greater than one monolayer in thickness, the use of the Lorentz-Lorenz equation will not lead to very serious errors.For the problem at hand, the quantities required for calculating the optical changes accompanying adsorption are not E, and E, themselves, but rather 7, and yt, quantities which are independent of d. Explicit expressions for 7n.t in terms of cn,tare obtained from (2.22) and (2.24)’ viz : (2.29) (2.30) 3. OPTICAL EQUATIONS The required equations are taken from ref. (5). Thus for thin films (dgA,) the equation for the complex optical density function for v-polarized light, = s,p,becomes (on setting, T20<1 in eqn (3.20) ref. (3)) : M. J. DlGNAM AND M. MOSKOVITS where Dzf' = loge[R,/R,J, and R, is the complex reflection coefficient for the film- substrate system and u-polarized light, and R, the corresponding quantity for the bare substrate ; 41is the angle of incidence ; and E~ are the complex dielectric constants of the ambient and substrate phases respectively; and i = ,/T.The observable quantities are related to D';f),which is not itself an observable, by the equations : &) = 2Re(D3 (3.2) @ = DJ;f'-DjS' (3.3) where Re denotes, " the real part of ". The reflectance absorbance for u-polarized light, ALf) = 10ge[IKv1~/[R,[~]is, for d</Zo,equal to the relative decrease in intensity of the reflected light following adsorption ; while the relative complex optical density function, W')= Din -Dif),is related to the conventional ellipsometric parameters, A and $, through the equation : D(f)= log,[tan $/tan $1 +i(A -A) (3.4) 21 [tan $ +cot $I($ -@) +i(A -A) where the bar designates the bare substrate condition as before, and the second expression is a thin film approximation.It is clear from (3.2) and (3.3) that any imaginary quantity which is independent of the polarization state of the light (i.e., does not contain may be added to DV) without changing the observables Azf) and D(f). Thus an equivalent optical density function may be defined through the equation : if)' = D$f)-i(4nd/A0) cos 41et (3.5) provided that g1 is real valued. Substituting for Dtf) from (3.1) and rearranging then gives : which on setting cl = 1 and substituting far 6, and E, from (2.29) and (2.30) becomes : Thus it can be seen that the observables are independent of d for d<lo, confirming the statement to this effect in Section 2.Extension of these equations to the case of adsorption of polarizable species which are immersed in a dielectric continuum of dielectric constant is straight forward and leads to the results : Yt = (&tlEl-1)4 ~n = (1-&I/En)d (3.8) which with (3.6) gives : The equations relating yn,t to a,,, remain unchanged; however an,tmust be inter- preted not as the vacuum polarizability but rather as the polarizability defined in relation to the Maxwell field strength within the ambient medium. OPTICAL PROPERTIES OF MOLECULAR FILMS Finally, a rather useful property of yt and yn can be deduced by noting that D:f)' is a linear function of yt and yn with an absolute term of zero.Accordingly, (3.10) where Ayn,t = yn,t-y,",t. Thus if reflectance changes or ellipsometric changes are measured for a thin film system characterized initially by (y,", y;) and finally by (yn, yt), these changes will be given simply by the usual equations, (i.e., eqn (3.2) and (3.4) to (3.9)) with Yn and yt replaced by Ay, and Ay, respectively. This follows from (3.10) and the definition of Dif). 4. SUMMARY AND DISCUSSION Bootsma and Meyer have shown that for physical adsorption on silicon, ellipso- metric data are well represented by the standard thin film ellipsometric equations (i.e., (3.1), (3.3) and (3.4) with E, = E, = EJ with the film dielectric constant related to the molecular polarizability through the Lorentz-Lorenz equation.That this should be the case for films which behave as a two dimensional gas is apparent from the results of Sections 2 and 3. Thus, if the physically adsorbed molecules have isotropic polarizabilities, or are randomly oriented on the surface, a, = a,= a, where a is the gas phase (or liquid phase) molecular polarizability. The dielectric constant, e2, for this "isotropic film " is then given by (2.28), which for 8 N 1 is of the form of the Lorentz-Lorenz equation : where the " effective film thickness ", d,, is related to the pair distribution function, f(r), and for 8, f: 1 f: 8, is given by : d, 2i 8/9[ 0m[f(r)/r2]dr (4.2) obtained from (2.18) and (2.27). As noted earlier, for low coverages, d, !z (4/3)d', where d' is the molecular dia- meter, while for monolayer coverage and a square planar array, d, 21 0.9358.From low to monolayer coverages, therefore, d, varies from somewhat greater than d' to a value close to d'. Setting d, = d' will therefore lead to only a small error at all coverages, since for low coverages where the approximation appears to be the poorest, (4n/3)(Nlde)a will be < 1, and hence for these conditions the choice of d, will have a negligible effect on the observables. Note that in using (4.1)in conjunction with the conventional optical equations, J must be chosen to give the correct local field effect, that is in accordance with (4.2). It is not in any sense the '' actual thickness " of the molecular layer. The fact that for two dimensional gaseous films, d, can to a good approximation be set equal to the molecular diameter, is coincidental.This will not be the case for island type films, where d must be chosen proportional to surface coverage (i.e., d, = 0.935d' 3N for a square planar molecular array within the islands). It is easily shown from (2.20), (2.21) and the definition of a, that for island type films in general, E, and E, are given by : E, -1 = (N/N,)(&',") -1) (4.3) 1 -1/gn = (N/Nm)(i-l/ii$"')) (4.4) M. J. DIGNAM AND M. MOSKOVITS where N, is the concentration corresponding to monolayer coverage, and is assumed to be the same as that within any given island ; while &tm) and &Lm) are the values for E, and E, corresponding to monolayer coverage.Once again, choosing d, SO that En = E, when a, = a,, we may write in place of (4.3) and (4.4) E t - ,(m) , 8, = &(,“I,, d, = (N/N,)a, (4.5) where a, is the value of a corresponding to monolayer coverage. Substituting (4.5) into (3.6)and setting = 1, gives the same equation as is obtained on substituting (4.3) and (4.4) into (3.6). The question as to whether the dielectricconstant or the “ film thickness ” remains constant in the range zero to one monolayer is therefore answered. In general, neither remain constant. If, however, the molecules are more or less randomly distributed on the surface, then to a good approximation the effective film thickness may be taken as constant, whereas for an island type film, the dielectric constant may be taken as constant.It is interesting to note that a thin isotropic film requires three parameters to characterize its optical behaviour (the real and imaginary parts of 8, = E,, and the effective film thickness d,) while a uniaxial film requires only one additional parameter (i.e., 4 in all-the real and imaginary parts of yn and y,). To extend the treatment presented in this paper to take account properly of the finite thickness of the molecular layer would be a formidable task, and the result of doubtful value. Such a treatment would not only require taking account of the phase differences between the various components making up the local electric field vector, but also of the contributions of the induced quadrupole (and higher) moments to the local field vector and its gradients.Finally, it should be pointed out that the optical equations ((3.7) with (3.2) to (3.4)) are valid only for adsorption onto a flat surface. The influence of roughness on a scale small compared with Lo is treated in the following paper.8 APPENDIX CONDITIONS FOR 8, AND Ot TO BE EQUAL Only the case of an adsorbed film displaying uniaxial symmetry is considered. In addition, we assume initially that the conditions leading to (2.12) are satisfied, in particular that ccj, and Ef;b are uncorrelated. Eqn (2.12) to (2.14) then give for OJO, = OJO, the following expression : From (2.6)to (2.8), it can be showii that where the final result follows from symmetry. Substituting (A2) into (Al) gives OPTICAL PROPERTIES OF MOLECULAR FILMS Thus On/& will be unity for all molecular distributions, i.e., for all (Fj’;)],if and only if pjz/(j+z> = pjX/(pjx)for allj.This in turn requires that pjXand pjz be proportionally related, i.e., 8, = 8, if pjx = (const.) pjz. Condition (A4) will be satisfied for all external field directions and for a film displaying uniaxial symmetry if and only if the polarizability ellipsoid for all molecules takes the form of an ellipsoid of revolution oriented with its axis normal to the surface, the ellipticity being the same for all the molecules. Assuming these conditions at the outset, and beginning with (2.11) rather than (2.12) (i.e., beginning without making the assumption that ajuand EfE?are uncorrelated) again gives 8, = Ot. N. J. Harrick, Internal Refection Spectroscopy (Wiley, New York, 1967). Symp. Faraday SOC.,1970,4. M. J. Dignam, B. Rao, M. Moskovits and R. W. Stobie, Canad. J. Chem., 1971, 49, 115. P. Drude, Lehrbuch der Optik (Leipzig, 3rd edn 1912). M. J. Dignam, M. Moskovits and R. W. Stobie, Trans. Faraday SOC.,1971, 67, 3306. G. A. Bootsma and F. Meyer, Surface Sci., 1969, 14, 52.’H. C. Van De Hulst, L&ht Scattering by Small Particles (Wiley, London, 2nd edn, 1962), Chapter 2.* M. J. Dignam and M. Moskovits, J.C.S. Faraday ZZ, 1973, 69, 65.

ISSN:0300-9238    

DOI:10.1039/F29736900056

出版商:RSC    

年代:1973

数据来源: RSC

摘要:

Influence of Surface Roughness on the Transmission and Reflectance Spectra of Adsorbed Species BY M. J. DIGNAM*AND M. MOSKOVITS Department of Chemistry, University of Toronto, Toronto 181, Ontario Received 26th June, 1972 A model is developed for the changes in the transmission and reflection properties of an interface accompanying adsorption which takes into account explicitly the microscopic roughness character- istics of the interface. Approximate equations are derived from this model and applied successfully to data obtained for the adsorption of various gases onto vacuum deposited silver films. It is concluded that spectral information calculated from the optical changes accompanying adsorption, on the assumption that the surface is smooth, will in general be misleading, particularly so in the case of metal substrates in the visible-u.-v.spectral region. Methods for approaching this complica- tion are discussed briefly. The possibility of characterizing the micro-roughness structure of a metal surface from measurements of reflectance changes accompanying physical adsorption is also noted. Many investigations of the changes in the specular reflectance and ellipsometric parameters of a metal surface accompanying adsorption from the gas or solution phase have been reported in recent years. The results have been interpreted with few exceptions in terms of a Drude model in which the adsorbate-adsorbent system is assumed to consist of a homogeneous film of uniform thickness on a mathematically flat metal surface.This model cannot, of course, be strictly correct even in the case of a single crystal surface, since at temperatures above absolute zero, surface defects will exist, some of which will take the form of metal atoms displaced from the surface into the region where one expects only adsorbate to reside. Polycrystalline surfaces prepared by vapour deposition or by polishing will show even more extreme irregu- larities. These facts have not escaped the notice of several investigators. Archer,l for example, explained the variation in ellipsometric data obtained from two appar- ently identical samples of silicon by postulating that they differed in the degree of surface roughness. He proposed a model in which the surface was covered with cubical irregularities and proceeded to calculate the change in the ellipsometric parameters, assuming the refractive index of the rough region to be the volume average of the refractive indices of the adsorbate and substrate phases. Models which take explicitly into account the presence of a roughness region have not been actively pursued.This is due in part to the fact that most ellipsometric studies have been carried out at a single wavelength. In these cases there are in general more system unknowns than there are data points, hence the deficiencies in the Drude model have been difiicult to spot. Those optical studies which have been carried out as a function of wavelength have, for the most part, been i.-r. transmission and reflection measurements made for the purpose of observing the vibrational spectrum of the ad~orbate.~-~ Little of this work has been analyzed quantitatively.A number of studies have recently been reported 59 relating to the change in the specular reflectance of electrodes in electrochemical cells on changing the electrode potential. Several of these have been carried out as a function of wavelength. In II-3 65 SPECTRA OF ADSORBED SPECIES one such study reflectance changes were measured using both p-polarized (electric vector parallel to plane of incidence) and s-polarized (electric vector normal to plane of incidence) light. The spectrum of these reflectance changes show considerable structure. It is the object of this paper to develop an optical model for a metal surface- adsorbate system which includes roughness effects, and to test the predictions of the model against both published and new data.Data have been obtained for this purpose from studies of adsorption of various gases onto evaporated silver films formed under ultra-high vacuum conditions. OPTICAL MODEL In developing the model, the roughness layer, along with any adsorbed niolecules present, will be treated as an optically homogeneous film on a flat surface. This approach should lead to a good approximation provided that both the sizes of the bumps in the roughness layer and their nearest neighbour separation are small compared with the wavelength of the light employed for the e~periment.~ It will also be assumed that the roughness layer possesses the symmetry of a uniaxial film with its optic axis normal to the surface.The optical properties of the transition layer will therefore be characterized by yy, u = n or t which is 47r times the u-component of the polarization per unit area in the transition layer divided by the u-component of the field in the incident medium, the subscripts n and t designating the components normal to and tangent to the mean geometrical surface of the metal substrate respec- tively. Given these quantities and the complex dielectric constants of the bulk metal substrate, c3, and the incident medium, gl,the optical properties of the system can be calculated directly using the equations derived by Dignain et aL8* The problem therefore reduces to one of obtaining expressions for y,, and yt which relate them to the surface geometry, the surface coverage, and the complex polariza- bility of the adsorbed species. For a planar array of species of mean polarizability au,u = n or t, yn and yt are given to a good approximation by the following equations, taken from ref.(8) : Yn 2: 4nNan/11+ (8~13)(N/a)anI (1) Yt fr: 4nmm -(4743)w/a)4 (2) where N is the mean surface concentration of the species and a is related to the pair distribution function for the species, f(r),through the following equation : a = 8\91 [f(r)/r2]dr. (3) 0 If the molecular distribution is that for randomly distributed hard discs of diameter d’, it was shown that a 2: (413) d’ at low coverage, decreasing to about 0.9 d’ at full coverage. Interpreting a,,, as the mean polarizability of the metal bumps on the surface, then a will be of the order of the mean diameter of the bumps, a result which we shall use later.Dividing up the surface species into Nobumps per unit area of mean polariz- abilities a, and a,, and n adsorbed species per unit area of mean polarizability a,, we may write : 3avnU+4nnaa Yn 21 1-+2v,U +(8~/3)(na,/a) (4) 3av,U -I-4nna,Yt N -___1-v,U -(4n/3)(naa/a) M. J. DIGNAM AND M. MOSKOVITS 67 where v,U = (4n/3)(Noa,/a), u = n, t. (4) Representing the initial value of the parameters by a superscript zero, and treating a as essentially constant, the changes in yn and yt giving rise to the optical changes may be written : 3aA(v,U)+ 4nA(na,). ..AYn = 8n na, (7) 3a 1 3aA(u,U)+-4nA(na,) 4n na, 3a 3a 1 where A(u,U) = vuU-u~Uo,and arises from a possible change in a,,, due to chemi- sorption of the adsorbed species, or in the case of reflection studies from electrodes, as a result of field effects. Where more than one adsorbed species is involved, na, must be replaced by a sum over the species present, i.e., by CjZjaaj, and A(naa) by jC(A~,)%,*j In the previous paper it was shown that the changes in the reflection properties of a flat surface upon replacing a thin film characterized by (yz, 7:) by one character- ized by (?,, y,) can be calculated from the complex optical density function, Dy)’,on replacing (y,, yt) by (A?,, A?,).If changes in measured optical quantities following adsorption are interpreted on the basis of the “ Drude model ”, without regard to roughness effects, the effective dielectric constant components for the adsorbed film so calculated are given below in terms of Ayn and A?, (cf. eqn (3.8) in ref. (8)) ~enf~= E1/(l-Ayn/d)-’ E:‘~ = ~~(1+Ay,/d) where d is the arbitrarily assigned film thickness. Substituting for AYn,t from (7) and (8), it can be seen that even for u, U = q,U, the “adsorbed film ’’ will appear to behave as if it were anisotropic (i.e., &teff # &Eff). Such behaviour is apparent rather than real, however, and arises from interpreting the optical changes on the incorrect assumption that the surface is initially film free, whereas in fact there is initially present on the surface a roughness film, according to the model chosen.The “ true ” expressions for E, and Et must be defined in terms of yn and y,, rather than Ayn and Ayt. If this is done, on proper choice of the effective film thickness (i.e., setting d = a) E, = Et for a, = at.8 It is evident that &iffand &teff will display some of the properties of e3, since v,,,U depends on a:,t which in turn will be some function of g3, since the bumps are com- posed of the substrate material. Hence, even a non-absorbing adsorbate will appear to be absorbing, and even strongly absorbing in some wavelength regions, if the optical data is interpreted on the basis of a smooth surface model. In order to proceed further, we require expressions for u,U and utU relating them to E~ and the properties of the roughness region.To do this in a manner leading to equations which may be tested against experimental data, fairly drastic approximations must be made. In this paper, we test the results obtained on using the simplest possible approximation for u,,,U, namely that obtained on assigning the bumps polarizabilities which take the same form as those for spherical particles. SPECTRA OF ADSORBED SPECIES SPHERICAL PARTICLE APPROXIMATION The effective complex polarizability of a homogeneous sphere of material im- mersed in a continuum of dielectric constant E~,and having a complex dielectric constant E* and a radius Y small compared with the wavelength of light, is given by : a, = r3(E*-&1)/(E4:+2E1). (11) We now approximate the polarizability of thejth bump, ajt,for the electric vector parallel to the surface by an expression of the form of (1 l), viz : where c3j is the complex dielectric constant of the metal forming the jth bump, corrected for the additional electron scattering processes introduced by the boundaries of the bump and for the change in conduction electron concentration brought about by chemisorption.The effective radius of the bump when subjected to a tangentially oriented field vector, rjtis defined through eqn (12) in the sense that it is to be regarded as chosen to minimize the difference between the left and right hand sides of (12) over the wavelength range of interest.It is difficult to assess just how good an approximation (12) will be. It seems unlikely, however, that it will be seriously in error.* In any event, we proceed on the basis of this approximation. For the electric vector normal to the surface, eqn (12) with t replaced by n will be used. Combining (12) and (6) leads to the result Thus if (4n/3)rju is proportional to the volume of thejth bump, then on interpreting U as the volume average of (E?~~--c~)/(E;~+2g1), L’, is given by : As noted earlier, a will be of the order of the mean diameter of the bumps, i.e., of the order of the thickness of the roughness layer. If the thickness of the roughness layer is taken to be a,and the volume of the bumps to be (4n/3)rj3,, then u, becomes the fraction of the roughness layer occupied by metal.Thus v, and u, can be regarded as effective volume fractions, and are accordingly expected to be of the order of 3. The complex dielectric constant of a simple metal can be expressed in the form lo c3 = E~ -o,2/(w2-io/z) (15) where i,/electrons to c3, all other contributions being contained in the term E = -1. The term on the extreme right is the contribution of the conduction .~~The relax- ation time for electronic conduction, z, is defined as one half the mean time between scattering collisions; while w is the angular frequency of the radiation and w, the so called plasma frequency, given by : wp” = 4nN:e21mX (16) where e is the charge on the proton, and NZ and rn‘$ the effective concentration and mass respectively of the conduction electrons.* Note that for any realistic assumption concerning the actual shape of a bump, a; for a bump will be a tensor quantity, in that a tangentially oriented electric field vector will give rise to a normally as well as tangentailly oriented induced dipole moment. From symmetry, however, the mean normal component of the dipole nioment induced by a tangential field, averaged over a number of bumps, will be zero. M. J. DIGNAM AND M. MOSKOVITS The correction to the dielectric constant of a bump arising from the scattering processes at its boundary is calculated as follows. Using Mathiessen's rule lo (the total resistivity of a metal is the sum of the resistivities due to each contributing effect) and the fact that each contribution to the resistivity is inversely proportional to the relaxation time for the scattering process giving rise to it, we obtain : l/z? = 1/T+2VF/lj (17) where 77 is the mean relaxation time for the conduction electrons within thejth bump, uF the Ferrni velocity, and Zj the mean distance travelled by a conduction electron within the bump between scattering collisions with the surface of the bump.The term Zj/2uF is simply the mean relaxation time corresponding to the scattering pro- cesses at the surface of the bump, being one half the mean time between scattering collisions with the surface. Substituting z* for zin (1 5) we obtain E:~= E~ -w,"/(co2-ico/zg) (1 8) or, since U is the volume average of (E:~-E~)/(E:~+~E~),we have, correct to first order terms in the fractional displacement of Ij from its volume average value, the following relations : u = (E3-El)/(&; +24 (19) 8; N E~ +co,2/(02 -ico/z*) (20) l/z* = 112 +2v,/l (21) where I is the volume average value of Zj.Assuming the electrons to be scattered at every encounter with the surface of a sphere, it can be shown that Ij = 1.5rj so that 2 is expected to be of the order of 1.5 times the volume average of the "radii " of the bumps, and hence of the order of ($)a. An expression for A(vuU) = v,AU can be obtained from (19), (20) and (16) for the particular case of ionic chemisorption where electron transfer is the only effect contributing to AU. Assuming further that the sole effect of electron transfer is to alter the value of N: in the metal bumps, we have : where An* = auPAN:.Substituting this result into (7) and (8) and retaining only first order terms in A(naa) and An*, the resulting equations may be written : where Nt is the conduction electron concentration in the bulk metal and &go, E; and U"are given by (15), (20) and (19). Note that if u, is regarded as the true volume fraction of the metal in a roughness region of thickness a, An* becomes the increase in the conduction electron concentration per unit projected area of the metal substrate SPECTRA OF ADSORBED SPECJES accompanying the adsorption process, i.e., the change in surface charge in units of electron charge.Alternatively, under certain conditions chernisorption can perhaps be considered as altering v, U simply by causing a decrease in the effective volume fractions, zit and u,, and a corresponding change in /, as a result of decreasing the volume of the bumps through product formation. In that case, on setting Avt/r;p = AvJvZ and neglecting the accompanying small change in I, (24) and (25) are modified only in that u*An* is given by Since the wavelength dependence of a*Arz* given by (27) is not the same as that given by (23) and (26), these two treatments of chemisorption do not lead to equivalent optical effects. Furthermore, it is apparent that other models for chemisorption may be used to evaluate A(vuU), which will lead to contributions to Ayn and Ay, which differ from the above two.Thus, no general treatment of the effect of chemisorption for ellipsometric and reflectance measurements is possible. It is therefore best to test the present optical model against data for physical adsorption of species from the gas phase, since for such cases, A(u,U) should be zero to a very good approximation. The expressions derived for Ay, and Ayt can now be used with eqn (3.9) of ref. (8) to calculate DLf)',v = s, t, and hence the change in reflectance and in the ellipsometric parameters accompanying adsorption onto a rough surface. The resulting equations are reproduced below for convenience, along with that for the change in normal incidence transmittance, which can be calculated directly from the Fresnel coefficients in a straight forward manner.where 6v,pis the Kronecker delta (= I for v = p and = 0 for u = s), R and Tare the reflectance and transmittance respectively, t,b and A the usual ellipsometric parameters with $ being the value of $ for the initial " bare substrate "measurement, and Re and Im denote the " real part of " and " imaginary part of " respectively. Given Z, values for U" can be calculated from data for e3 as follows. Noting that c3 is essentially real valued and wavelength independent in the near infra-red spectral region, analysis of data for c3 in this region gives cog and z (cf. eqn (15)). Taking these to be independent of wavelength in the wavelength region of interest, cgo can be calculated as a function of wavelength using (15).Similarly, using (20), c: can be calculated, given z* or Z, and hence U (or any other functions of E; and cJo) deter-mined as a function of wavelength.Thus provided cl and g3 are known as functions of wavelength, the only unknown parameters required to calculate Ayn and Ay,, and hence the changes in reflection properties, for the case of physical adsorption onto a reasonably clean surface (nou,N 0) are vn, ut, Z, A(naa) and a. The number of disposible parameters can be M. J. DIGNAM AND M. MOSKOVITS reduced by two by making the further approximations a 2i 4113 and v, 2: u, = v. Since a does not appear in the first order expansions of Ay, and Ay, (see (24) and (25)), this first approximation will not introduce a significant error.The validity of the second approximation is less certain. In any event, we shall make these approxima- tions in the subsequent analyses, and shall furthermore restrict considerations to cases in which a,is taken to be real valued and independent of wavelength in the spectral region of interest. This leaves a total of 3 wavelength independent disposible para- meters, increasing to 4 in the case of chemisorption. The nature of the approxima- tions made to reach this point, however, are such that we cannot expect better than fair agreement with data. To gain some insight into the optical behaviour predicted by (7) and (8) in con-junction with (19) to (21), it is instructive to consider the nature of some of the processes which will give rise to apparent absorption properties for the adsorbed species.We restrict our attention to the tangential components of the optical con- stants, as the behaviour of the normal components is identical. Thus setting c1 = 1, the dielectric constant of the roughness region may be defined as * E, = I +yJa (33) which, on substituting for yt from (5) and for U from (19), becomes for the case of a bare surface in vacuo &,o = 1-3vt(&; -1) V,(E$ -1)-(ES + 2) ' (34) As the absorption properties of the roughness film are determined largely by Im( -E:), we evaluate this quantity. It is easily shown that Im{ -E;) = 9Vt&f"/( 1-v,)2 [E:' -k (2 + Ut)/( 1--k [E;"] (35) where E:' and -8;'' are the real and imaginary parts of E: respectively. By virtue of the term E;" in the numerator of (39, E: will display the absorption properties of cf (i.e., essentially that of the substrate) and in addition will show an absorption maxi- mum at a wavelength for which E:/ = -(2 + u,)/(l -u,).Since 6;'' is a function of z* (cf. eqn (20)), the width of this additional absorption peak will depend on z* or Z, while the precise position of the absorption maximum will depend on v,. Thus from (20), E;' = E; -Oi/(W2-k l/Z*2) (37) which on substituting into (36), gives the following expression for the resonance frequency, co; : For an isolated sphere (i.e., for u,+O), (38) becomes This in turn reduces to wi = a,/J3 for &i0 = 1 and l/z*40,, which is the plasma resonance frequency for an isolated metal sphere as given by Ritchie.ll Thus the " extra " absorption process associated with E: is due to plasma resonance in the bumps.Plasma oscillations cannot be excited in a smooth surface by s-polarized radiation (i.e., in the t-direction), but can be in a rough surface region. Repeating the analysis for the case of a non-absorbing, adsorbed layer leads to the results SPECTRA OF ADSORBED SPECIES Im(--Et) =-9Vt&y/( 1-u,-x)2 1w; = 4 --&k0+(2 +21, -2x)/(1-21, -x) T*2 where x = (4n/3)(n/a)cca. (41)Note that in the limit as ut=0, the presence of the adsorbed species has no effect on CO~. For any other value of ut, however, the presence of the adsorbed species leads to a decrease in the resonance frequency, CO~.Since the reflection changes depend on Ayt = aAE, (e.g.(AR/R)s= (8n/ho)cos 41aIm{ -AEt/(E3 -l)}) then the observed reflectance spectra will contain features characteristic of a derivative spectrum, the derivative being with respect to frequency. In addition to the surface plasma resonance phenomenon, it is apparent that A&, will show pronounced features wherever c3 undergoes a rapid change with frequency. Thus interband transitions should be apparent in general in ctff and E:~~. EXPERIMENTAL In order to test the equations of the previous section, measurements of the changes in the normal incidence transmittance and reflectance of thin silver films were made following adsorption of various gases. The all metal, bakable, vacuum system used for this purpose I FIG.1.-Schematic diagram of the apparatus (A, main vacuum chamber ; B, accessories nipple ; C, Vacion pump ; D, Vacsorb pump ; E, elbow ; F, bakeable valve ; G, gas bottle ; H, valve ; I, leak valve ; J, auxiliary pumping line ; L, Pirani gauge head ; M, ionization gauge head ; N, lock-in amplifier ; P, chart recorder ; Q, light source ; R, monochromator and detector ; EE, refrigerant inlet ; GG, gas inlet).M. J. DIGNAM AND M. MOSKOVITS is shown schematically in fig. 1.12 It consists of an inner, thermostatted, copper cell sur-rounded by an outer, stainless steel, v~cuum vessel which is connected to an ion pump. The system can be maintained at about Torr during evaporation of the silver film (<loF1* Torr otherwise).The films were formed by vapour deposition from a tantalum filament positioned outside the inner cell, onto a Vycor slide and piezoelectric balance within the inner cell. The aperture through which the silver film was deposited was closed, following deposition, using a bellows-sealed linear motion device. The gas to be studied was then introduced directly into the inner cell, while maintaining the vacuum in the outer vessel, and hence the thermal isolation of the inner cell. The optical measurements were made using the double-beam spectrophotometer shown schematically in fig. 2. The heart of the instrument is a rotating glass wheel made up of sectors which are alternately reflecting and transmitting. This divides the incident light beam into signal and reference components which differ in phase by n, Ultimately, the two beams are again combined, using the rotating wheel, passed through a monochromator and detected S4: ilRF M 12 FIG.2.-Schematic diagram of the optical system (L, lenses; M, front surface mirrors; CW, rotating beam splitter ; MC,D, monochromator and detector ; S, light source ; PH and A, apertures ; RF, reference film ; SF, sample film ; BS, stationary beam splitter used in reflectance studies ; VP and PCS, glass plates used as optical attenuators). wavelength/nm FIG.3.-(AT/n0 at normal incidence (41 = 0) versus wavelength for diethyl ether, 0.6 Torr, adsorbed onto an evaporated silver film. 74 SPECTRA OF ADSORBED SPECIES by a photomultiplier.The difference between the signals generated by the two beams is measured using a phase sensitive detector (lock-in amplifier) while the reference beam signal is obtained by blocking the other bearn.I2 All of the experiments reported herein were carried out at room temperature for silver films of approximately 470 8, in thickness. The observed transmittance or reflectance changes are shown in fig. 3 to 6 as a function of wavelength for the adsorption of respectively diethyl ether, methanol, carbon dioxide and oxygen onto freshly deposited silver films. Transmittance changes following exposure to room air of a silver film which was previously contaminated with adsorbate are also shown in fig. 6. 0:015 1 I 1 1 wavelength/nm FIG. 4.-(AT/T)o versus wavelength for ethanol, 25 Torr, adsorbed onto an evaporated silver film.0.03 I I 1 II 1 0 --0 Ol 400 I 500 1 600 I,o'oll0 I I 400 500 600 wavelength/nm FIG.5.--(AT/T), as a function of wavelength obtained for carbon dioxide adsorbed onto an evapor-ated silver film for pressures of: 0,8 x Torr ; 0,2.4 x Torr; 0,0.7 Torr ; (3, 12 Torr. M. J. DIGNAM AND M. MOSKOVITS waveIength/nm FIG.6.-Wavelength dependence of (AT/n0(lower curve) and (AR/R)o(upper curve) for, respectively air (760Torr) and oxygen (8 Torr) adsorbed onto evaporated silver films. DATA ANALYSIS The results presented in fig. 3 to 5 were fitted to the approximate equations devel- oped for the roughness model, setting = 1, AU = 0 and adjusting u, I and na, to minimize the variance in the transmittance. The data of Irani et al.' and Schultz ' were used for E~ (and hence to calculate cJo and z).The generated curves are shown as solid lines in fig. 3-5. For the data in fig. 6, the electron transfer model of chemi- sorption was employed, giving in total four disposible parameters, u, Z, nu, and An". The values for the parameters which generate the solid curves are given in table 1. TABLE1 adsorbate V 1iA &&)/A An+lA-2 ether on Ag ethanol on Ag COz on Ag : 0.008 Torr 0.024 Torr 12 Torr 0.25 0.1 0.25 30 13 30 0.40 1.3 0.40 0.55 0.73 ---- O2 on Agair on Ag 0.56 0.55 18 16 2.1 0.35 -0.27 -0.165 The following values were used in the calculations. wp = 1.38x 1OI6 s-' and 7 = 1.35x s (determined from the optical constants) VF = 1.38 x lo8cm/s and ZV; = 5.76x loz2 ~m-~ (from ref.(15)). Although no independent estimates have been found for u, the effective fraction of metal in the roughness region, the range of 0.1 to 0.5 seems reasonable. Inde-pendent measurements of the surface roughness expressed as r.m.s. departures from the mean surface plane have, on the other hand, been reported. From electron microscopy measurements, Bennett et al.' report 7 A, while from electron scattering measurements Raether reports 15%i r.m.s. roughness for SPECTRA OF ADSORBED SPECIES deposited silver films of approximately the same thickness as those used here. As noted earlier, the spherical particle model gives 1 = 1.5@.For purposes of estimating the r.1n.s. roughness from I, we take the mean surface plane to be completely covered with hemispherical caps and cavities of varying radii. This gives r.m.s. roughness N vs;"/J2, or since vp>@,we have r.m.s. roughness<1/2.1. (42) Taking the equality sign in (42), the values for 1 in table 1 give estimates of the r.m.s. roughness value ranging from 7.6 to 14.3 A,in good agreement with the above values. Estimates of the surface coverage in the case of physically adsorbed species may be obtained by setting a, equal to the polarizability appropriate for the gas or liquid phase. Thus setting a,= 8.8 A3for diethyl ether, one obtains n = 4.5 x 1014 crn-,, which for a roughness factor -2 corresponds to about one monolayer.In an inde- pendent experiment, a value of na, of 0.29 A was obtained corresponding to a pressure of diethyl ether of 0.058 Torr, which on setting a, = 8.8 A3gives n = 3.2x loi4 em-,. The weight uptake for this run, as measured by the piezoelectric balance gave n = 2.7 x 1014 cnr2 in satisfactory agreement with the above. As the performance of the balance was generally erratic, however, not much credence can be given to those few runs done at low pressures in which the balance appeared to function properly. Nevertheless, for the four cases in which apparently meaningful balance readings were obtained, satisfactory agreement between the two estimates of n was obtained. For the ethanol data, setting a, = 5.2 w3gives n = 2.5 x 1015cm-2, which for a roughness factor of 2 corresponds to about 2 monolayers, a not unreasonable value for a relative pressure of 0.6.Again, for the CO, data (12 Torr), setting a, = 2.7 l(L3 gives n = 2.7 x 1015 cm-2 which, for a roughness factor of 2 corresponds to about 2.5 monolayers, a somewhat higher value than one would expect. This could be due either to molecular orienta- tion leading to an effective polarizability substantially larger than the mean gas phase value, or to deficiencies in the equations resulting from the many approximations made. For molecules which ionize on the surface to give negative ions, one expects a large value for the polarizability. This expectation is reflected in the large value for na, for O2adsorbed on Ag.Note that An* is negative in the case of this run (as well as the one with air, where 0, is probably the major adsorbate) as expected, since oxygen chemisorption onto silver will be anionic. Assuming monolayer coverage and a roughness factor of 2 (i.e. n-8 x 1014cm-2) the electron charge per O2 molecule, An*/n, can be calculated, giving about three to four electrons per molecule, a result consistent with oxygen chemisorption as 02-,while a, N 30 A3. Not much reliance can be placed in these particular values, however, since the values calculated for A(naa)and An* were found to be very sensitive to the value chosen for a. (In these calculations the relation a = 41/3 has been used). This was not the case for physical adsorption (AU = 0) however, the parameters in that case being almost independent of the value chosen for a.It is in addition worth noting that satisfactory agreement with the data of fig. 6 was also achieved using the model in which u and I are assumed to decrease due to formation of a non absorbing film. None of the data obtained can be fitted even approximately using the standard equations for a non absorbing film on a flat surface, despite the fact that three of the adsorbates studied are physically adsorbed and do not absorb in the wavelength region studied. It is, of course, entirely possible to account for the data on the assumption that the adsorbed species are absorbing. In this case, however, one requires a large number of parameters to fit the data. Furthermore, one must conclude that the M.J. DIGNAM AND M. MOSKOVITS 77 adsorbed species are strongly absorbing over the entire wavelength range examined. It is evident that optical data for adsorption onto metal surfaces which are rough on a scale small compared with the wavelength of light, if analysed assuming the surface to be flat, can lead to seriously inaccurate conclusions. To illustrate this point further, we examine the reflectance data of McIntyre and Kolb obtained for an evaporated gold electrode immersed in an 0.1 M HC104 electrolyte (Ar-saturated). They obtained values for (AR/R)sand (ARIR), accom-panying the electrodeposition of an oxygen layer onto a gold electrode, their results being reproduced in fig. 7. The solid line is calculated using the roughness model and setting E~ = 1.33 (i.e.that for water at optical frequencies), AU = 0, u = 0.62, I = 8.5& and A(naa) J0.5A. The optical constants for gold, as reported by Irani et all2and Schultz et were used for these calculations. Bearing in mind the nature of the approximations made in developing equations for the roughness model, and the fact that only three disposible constants have been used to fit both (AA/R)sand (AR/l?)pover the full wavelength region investigated, the fit to the data is quite good, and suggests that most of the experimental features, if not all of them, arise as a direct consequence of the presence of roughness. In particular, the feature near 2.5 eV photon energy is due to the plasma resonance effect discussed earlier.I I1 I II I I 1 0.4.., -8:O k0 2.0 3:O 4.0 5.0 photon energy/eV FIG.7.-Wavelength dependence of (ARIR), and (LIR/R)~ = 45") as measured by McIntyre and Kolb for the electrodeposition of oxygen onto a gold electrode (dashed curve). The solid curves are calculated on the basis of the approximate equations for the roughness model. CONCLUSIONS In the case of strongly absorbing substrates, changes in the reflection properties of the surface accompanying adsorption (or field effect modulation) will be very largely determined by the microscopic roughness characteristics of the surface. Thus it would appear that measurements of reflectance changes from, say, electrode surfaces can be much more readily analysed to give information about the roughness character- istics of the electrode than they can to give information on the adsorbate or the change in double-layer structure, etc.The prospects for completely eliminating this difficulty by producing " smooth " surfaces do not appear promising. One might be able to characterize the roughness properties of a surface by measuring reflectance changes accompanying inert gas adsorbtion from the gas phase, then using this information SPECTRA OF ADSORBED SPECIES to interpret reflectance data obtained for the same surface when used as an electrode in an electrochemical cell, say. One should be able to study with some precision double-layer effects in this way. It is doubtful, however, that this procedure would prove successful for studying either chemisorption or product film formation.Roughness effects do not invalidate the use of reflectance changes at a fixed wave- length to follow electrochemical adsorption and desorption processes, since the reflectance changes are approximately proportional to the coverage parameter, nu,, for both smooth and rough surfaces. Furthermore, for reflectance measurements on a non-absorbing substrate (Ureal valued) or a very good reflecting surface (1~~1b 1 and hence U N 1) Ay,, and Ayt differ very little from those for adsorption onto a flat surface (cf. (24) and (25)), certainly not enough to effect the qualitative features of an absorption spectrum calculated from data for such a surface assuming the surface to be flat.It is evident that much experimental and theoretical work needs to be done before one can interpret reliably and quantitatively reflectance changes accompanying adsorption onto, or field modulation of, metal electrodes. The authors wish to thank Dr. J. D. E. McIntyre for providing them with reflect- ance data in tabular form (fig. 7), the National Research Council of Canada for supporting the research and for a Scholarship (M. M.), the Province of Ontario for a Fellowship (M. M.) and the Defense Research Board of Canada for supporting the research. R. J. Archer, U.S.Dept. of Commerce N.B.S., Misc. Publ. 256, p. 255. A. M. Bradshaw and J. Pritchard, Surface Sci., 1969, 17,372. F. S. Baker, A. M. Bradshaw, J. Pritchard and K.W. Sykes, Surface Sci., 1968, 12,426. J. Pritchard and M. L. Sims, Trans. Faraday SOC., 1970, 66,427. B. D. Cahan, J. Horkans and E. Yeager, Symp. Faraday Suc., 1970,4, 36.'J. D. E. McIntyre and D. M. Kolb, Symp. Faraday SOC., 1970,4,99. H. C. Van de Hulst, Light Scattering by Small Particles (Wiley, London, 2nd Edn., 1962). Chap. 2. a M. J. Dignam and M. Moskovits, J.C.S. Faraday ZI, 1973, 69, 56. M. J. Dignam, M. Moskovits and R. W. Stobie, Trans. Farahy SOC.,1971, 67, 3306. lo M. F. Mott and H. Jones, The Theory of the Properties of Metals and Alloys (Oxford University Press, London, 1936). R. H. Ritchie, Phys. Rev., 1957,106,874 quoting H. Jensen, Z. Phys., 1937,106,620. l2 M. Moskovits,Ph.D. Thesis (University microfilms, Ann Arbor, Michigan.) l3 G. B. Irani, T. Huen and F. Wooten, J. Opt. Soc. Amer., 1971, 61, 128. l4 L. G. Schultz, J. Opt. SOC. Amer., 1954, 44, 357; also L. G. Schultz and F. R. Tangherlini, J. Opt. Sci. Amer., 1954, 44, 362. l5 C. Kittel, Introduction to Solid State Physics (John Wiley, N.Y., 3rd Edn., 1966), p. 208. l6 H. E. Bennett, R. L. Peck,D. K. Burge and J. M. Bennett, J. Appl. Phys., 1969,40, 3351. H. Raether in The Structure arid Chemistry of Solid Surfaces ed. Gabor A. Somorjai, (John Wiley and Sons Inc. 1969), p. 10-11.

ISSN:0300-9238    

DOI:10.1039/F29736900065

出版商:RSC    

年代:1973

数据来源: RSC

摘要:

Surface Relaxation Effects in the Adsorption of Neon on Xenon Crystals t BY ROBERTO CESARE PISANI AND FRANCODOVESI, RICCA" Istituto di Chimica Teorica, UniversitA di Torino, 10125 Torino, Via Pietro Giuria, 5, Italy Received 26th July, 1972 Surface relaxation has been considered for the (fOO), (110) and (111) faces and for the cube edges of a Xe crystal. The effects of relaxation on the potential energy of adsorption of Ne and on the probability distribution and total energy of the adsorbed atoms have been studied. It is shown that changes in the adsorption energies are within a few percent of the values obtained with unrelaxed models. Relaxation effects are quite different on various adsorption sites, and opposite effects may be found on different crystal faces.The quantum states of rare gas atoms adsorbed on rare gas crystals have been theoretically st~died.l-~ Heterogeneities corresponding to different adsorptionsites at different crystal faces of the adsorbing solid were discussed hrst. More recentlys attention has been given to heterogeneities occurring at the edges and vertices of the crystal. In the first approach to both these problems ideal discontinuities in perfect crystals were considered, without taking into account any crystal relaxation. The general features of the results obtained in this way must now be tested against a more realistic model for the adsorbent, chosen to enable us to evaluate the effect that changes in the lattice structure occurring at the surface of the crystal may exert on the adsorption process.The Xef Ne system has been considered for the following reasons : (1) the Xe atoms have a mass large enough to be treated as fixed at their equilibrium position in the crystal; (2) the Ne atom has a mass large enough to justify a strictly local approximation, except for the (111) face ; (3) the Ne-Xe interaction is low enough, compared to the Xe-Xe interaction, to produce negligible local relaxation of the crystal on adsorption. The (loo), (110), (111) infinitely extended faces, and the edge of an infinite cube have been examined in studying surface relaxation, where no other defects have been considered in the crystal besides those macroscopic discontinuities that just define surfaces and edges.The extent of surface relaxation, the changes produced in the adsorption potential, and the effect upon the states of the adsorbed atom are discussed in the following sections. RELAXATION EFFECTS IN Xe CRYSTALS The equilibrium structure of the relaxed crystal has been determined by minimizing the potential lattice energy, without taking into account any contribution due to residual vibrations. The potential energy for the Xe crystal has been evaluated in the t This work was partially supported by the Italian Council of Research (C.N.R.). 79 SURFACE RELAXATION EFFECTS additive pairwise approximation, using the Lennard-Jones potential law E(Y) = -2(r"/~)~]~'[(rO/r)l~ where E' = 31 1.0x erg has been used, as suggested by Hollis-Hallett,6 while r' = 4.54A has been adopted (different from the Hollis- Hallett value ro = 4.574 in order to obtain the experimental equilibrium value of the lattice parameter a.= 6.24A in the infinite perfect crystal. Relaxation at the infinite surface faces has been considered as a vertical displace- ment of each plane parallel to the surface taken as a whole, without any lateral rearrangements leading to surface superstructures. Such a model is quite reasonable for dense planes as here considered. With the above assumptions, the difference introduced in the lattice energy per unit surface area by changing interlayer spacings may then be expressed in the form : la where ~i",,j, is the single pair interaction between the i-th atom in the m-th layer and the j-th atom in the n-th layer for the perfect infinite crystal, while E;~,,~,is the modified value of this interaction due to spacing variations.A is the area of the surface unit cell, containing aatoms, and the sum Cjmextends just to these a atoms, while the sum Cjnextends in principle to all the atoms in the n-th layer. Both Emand Enextend in principle to all the planes in the semi-infinite crystal, subject to the indicated condition n> m (layers are numbered from the surface downwards). In practice the first sum can be truncated after a few terms, since relaxation is rapidly quenching, so that the difference E'-Pvanishes with increasing m. The two sums En and Cj, can be evaluated with the usual approximation, by performing the sums over those atoms which are contained within a hemisphere of given radius R, centred at the i,-th atom, and then by adding the contribution of outer atoms as calculated through integration over a continuous solid of the same density.R = 40A and m<9 have been assumed in our calculations. The value of AE will then depend on the interlayer spacings hi(i = 1,2, ...9) between the i-th and the (i+ 1)-th layer, and minimization can be effected with respect to these nine independent parameters. A minimization programme of the same type as proposed by Bard '* was used and the results are given in table 1. TABLE1.-SURFACERELAXATION EFFECTS IN SEMI-INFINITE Xe CRYSTALS crystal Surf? interlayer spacings face density hi h2 h3 h4 hco (111) 5.93 -0.210 3.65 3.61 3.60 3.60 3.60 (100) 5.14 -0.531 3.20 3.14 3.13 3.12 3.12 (110) 3.63 -0.449 2.29 2.22 2.22 2.21 2.21 Surface densities are in units of 1014atom cm-2 ; energies in erg cm-2 ; interlayerspacings in A.(AE),indicates the relaxation energy at the equilibrium ; h, is the uniform interlayer spacing in the infinite perfect crystal. It can be seen from this table that, for all the examined faces, relaxation does not involve planes beyond the fourth one, and that only the first spacing undergoes a significant change. Also it is seen that relaxation effects increase with decreasing density of the exposed face, i .e. with decreasing interlayer spacing. Edge relaxation was studied by considering the infinite cube's edge formed by two semi-infinite faces of the (100) form. The model we assumed is as follows : (1) no new structures appear due to the presence of the edge; (2) the interlayer spacing for R.DOVESI, C. PISANI AND F. RICCA both the converging faces is as previously established for the relaxed infinite (100) face at sufficient distance from the edge; (3) atom displacements may occur only in planes perpendicular to the edge and must be symmetrical with respect to the bisector plane. The displacements were expressed in a functional form sufficiently rich in para- meters so as to assure quenching of the edge perturbation at a sufficient distance from the edge. By minimizing the difference in the lattice energy per unit length with respect to these parameters, it was found that only the atoms in the edge row undergo a slight displacement (-0.01 A) towards the interior of the crystal. It may then be concluded that in fact the faces intersecting at the cube's edge do relax independently of each other.ADSORPTION POTENTIAL ON THE RELAXED CRYSTAL The interaction of a Ne atom with the Xe crystal has been evaluated in the additive pairwise approximation using a Lennard-Jones potential law with 8" = 123.7 x 10-l6 erg and YO = 3.82 A. These parameters have been derived from ref. (6) through the usual combination rules and are the same as used in previous papers. For any point P = (x,y) of the surface a potential energy of adsorption Uo(x,y) may be defined, corresponding to the minimum of the potential energy of interaction U(x,y, z) with respect to the distance z of the adsorbed atom from the surface.Table 2 gives the values of U, for a Ne atom adsorbed on various faces of a semi- TABLE2.-MINIMUM POTENTIAL ENERGIES uo AND EQUILIBRIUM DISTANCES 20 FROM THE SURFACEPLANE FOR A Ne ATOM ADSORBED AT DIFFERENT POINTS OF THE SURFACE CELL crystalface adsorption site uo zo saddle point UO 20 surface atom uo 20 relaxed -521.86 2.788 -455.90 3.008 -294.82 3.706 ('11) unrelaxed -523.16 2.788 -457.01 3.008 -295.53 3.703 relaxed -637.27 2.118 -402.84 3.032 -268.37 3.713 ('O0) unrelaxed -642.81 2.106 -405.42 3.032 -269.95 3.715 (1 10) relaxed unrelaxed -704.10 -695.72 1.363 1.436 -500.94 -512.71 {-354.52 {-358.09 1.899 1.887 3.057) 3,057} -232.66 -234.85 3.739 3.739 Energies are in units of 10-l6 erg; distances in A.The couples of saddle point values given for the (110) face, refer to saddle points 1 and 2 of fig.4, respectively. infinite crystal in relaxed and unrelaxed form at three points of particular interest. These points correspond to the minimum of Uo(adsorption site), to the maximum of Uoand to the minimum height of the potential energy barrier from site to site (saddle point). In all cases the maxima of Uocorrespond to the surface atoms of the adsorbing crystal ; the adsorption sites occur at the centre of four (faces (100) and (1 10)) or of three (face (1 11)) surface atoms ; the saddle points lie midway between adjacent adsorption sites.Table 2 shows that the influence of relaxation on the adsorption potential is markedly different from face to face. For the high density (111) face, a slight shallow- ing in the potential hole is produced by relaxation, due to a decrease in the attractive contribution from inner layers. Similar effects are observed for the (100) face. In SURFACE RELAXATION EFFECTS this case, however, the greater importance of the attractive contribution from under- lying layers results in a more significant change on relaxation. A more complex situation is shown by the (110) face. Due to the greater distance existing between the surface atoms, the extent by which the adsorbed atom penetrates the surface array is mainly limited in this case by the repulsive interaction with the Xe atom located in the second layer, just below the adsorption site.Relaxation then reduces such repulsive interaction and allows the equilibrium distance zo to decrease, so that the attractive interaction with the surface atoms increases, as is shown in fig. 1. This -550-~-650 I8 I I 1. 1.5 2. ZlA FIG.1.-Interaction potential Uof a Ne atom with the Xe crystaI, at the adsorption site on the (110) face, as a function of distance zfrom the surface plane : -, relaxed crystal ; ---,unrelaxed crystal. does not apply to different positions in the surface cell. Both on atoms and saddle points, where the equilibrium distance of the adsorbed atom is mainly determined by the interaction with the atoms of the surface layer, relaxation acts in the usual way by decreasing the attractive contribution from the inner crystal.Table 3 gives the potential energy U, for a Ne atom adsorbed at the edge of a cubic TABLE3.--MINIMUM POTENTIAL ENERGIES Uo AND EQUILIBRIUM COORDINATES FOR A Ne ATOM ADSORBED AT THE CUBE EDGE OF A Xe CRYSTAL adsorption site saddle point (a) saddIe point (6) surface atom crystal model UO XO 20 UO xo=zo uo 20 uo 20 relaxed -463.61 -0.046 2.110 -395.82 1.370 -361.46 3.049 -251.13 3.743 unrelaxed -467.72 0.031 2.094 -405.83 1.360 -363.47 3.057 -2254.82 3.727 Energies are in units of 10-l6 erg; coordinates in A. The saddle points (a)and (b)are across the edge and towards the face, respectively. The surface atom is the first behind the site.Xe crystal in relaxed and unrelaxed form. In both cases the origin of the coordinates was placed on an edge atom, with the y axis along the edge and the x and z axes parallel to the converging faces and pointing outwards. It may be observed that the sign of the coordinate xo of the adsorption site changes with relaxation ; the point of minimum potential energy is slightly displaced towards the outside of the crystal in the ideal case and drawn back in the case of the relaxed crystal, partly counterbalancing the displacement of the (100) face. R. DOVESI, C. PISANI AND F. RICCA Fig. 2 shows the minimum potential energy of the adsorbed atom as a function of the distance from the edge (over the converging faces), and as a function of the angle 8 (around the edge).It appears that relaxation substantially effects the height of the saddle point across the edge, so reducing the probability for the adsorbed atom to jump from one face to the other. The shape of the potential hole at the cube’s edge is better characterized in fig. 3, where sections of the isopotential surfaces are -450 -400 UO/1O-l6erg FIG.2.-Profile of the minimum potential energy Uofor a Ne atom adsorbed at an edge of a cubic Xe crystal : -, relaxed crystal ; ---,unrelaxed crystal. XIA FIG.3.-Region of classical accessibility for a Ne atom adsorbed at an edge of a cubic Xe crystal. shown perpendicular to the edge and defining the region of classical accessibility for the ground state of the adsorbed Ne.The region of classical accessibility is here defined as the region where the potential energy is lower than the total energy of the adsorbed atom. Here too it is clearly seen that relaxed crystal exhibits a higher localization of the atom adsorbed at the edge of the cube. SURFACE RELAXATION EFFECTS QUANTUM STATES OF THE ADSORBED Ne As was said in the introduction, the motion of the adsorbed atom has been studied in the local approximation, by considering a single adsorption site and neglecting interactions with adjacent sites. This was proved feasible for the Ne-Xe system, with the possible exception of the (1 11) face. No calculations, however, have been per- formed here for the (1 11) face, since it was seen in the previous section that relaxation has negligible effects on the features of the potential field in this case, so that the pre- vious result may be corrected simply by subtracting a potential term from the calculated energies.As in previous papers, the solution of the wave equation has been found through a variational procedure, by using an approximate wave function of the form : Y'(P, 4 = 1arnnpy!in(P ,+>'Y,'(z) m,w where 'Yj,(p, 4) are the eigenfunctions of an isotropic two-dimensional harmonic oscillator parallel to the adsorbing surface and Y,'(z) the eigenfunctions of a linear harmonic oscillator normal to it. Besides the variational coefficients amnp,the coordinates of the centre and the force constants of the oscillator have also been determined variationally. This was done initially by minimizing the expectation energy for the fundamental term in the variational sum, which is correct when the major interest is in the fundamental state of the adsorbed atom.The truncation of the sums in the variational function has been effected in such a way as to comprise the first four states of the linear oscillator and a different set of radial states owing to the symmetry of the adsorption site. Those radial states which are bases for the totally symmetrical representation of the point group corresponding to the site have been considered. As far as the (100) face is concerned, the first 9 radial states belonging to the Al representation of the point group C,, have been used, giving by combination with the above 4 normal states a total basis set of 36 functions.The total energy of the Ne atom adsorbed in its fundamental state on the relaxed crystal was found to be -553.5 x 10-l6 erg, which can be compared to the value of -558.5 x 10-l6erg that is found when a perfect unrelaxed crystal is considered. The difference between these two energies is almost the same as was previously found for the potential energy of adsorp- tion. This means that also in this case relaxation does not appreciably alter the motion of the adsorbed atom, as is further confirmed by considering that the average value Z of the distance from the surface changes only from 2.242 to 2.246 A on relaxation. A different picture is shown by the (1 10) face, where the first 9 radial states belong- ing to the A, representation of the point group Czohave been considered.Here the difference between the total energies (-639.3 x erg for the relaxed, and -633.3 x 10-l6 erg for the unrelaxed crystal) means an appreciable difference between the residual energies (64.8 and 62.4 x erg, respectively). It then appears that different probability distributions characterize the adsorbed atom in the two cases. This is seen in fig. 4, where the vertical sections through the site and the lower saddle point are given of the isodensity surfaces including 95 % of the total probability. When relaxation is duly taken into account it appears that the deeper penetration of the adsorbed atom (Z = 1.43 t$ against Z = 1SOA for the perfect crystal) reduces the amplitude of its lateral motion.For the edge adsorption site, initially treated as a site located on a single face of the cube, a basis set of 48 functions was used, obtained by combining the usual 4 normal states with the first 12 radial states belonging to the A representation of the R. DOVESI, C. PISANI AND F. RICCA point group Clh(a higher number of functions is needed for balancing the poorer symmetry of the site). The total energies obtained in this way for the ground states of the adsorbed atom (-394.4 and -398.3 x lo-' erg for the relaxed and unrelaxed crystal, respectively) were used for tracing the isopotential curves in fig. 3. These curves clearly show that, from a classical point of view, the adsorbed atom should oscillate across the edge, from one site to the other.This suggests that its quantum states have to be described in terms of a dual site extending on both sides of the edge. An approximate solution of such a problem has been tried with a variational approach, by linearly combining single site solutions. No appreciable combination occurs and no lowering in energy as a consequence of such a treatment. The prob-ability distribution localizes the adsorbed atom at a single site of the couple, as shown ,-5 ,-. -0.5 0. 0.5 XlA FIG.4.-Probability distribution for a Ne atom adsorbed on the (110) face of a Xe crystal : -, relaxed crystal ; ---,unrelaxed crystal. The curves are traces of the isodensity surfaces including 95 % of the total probability on the vertical plane whose trace is indicated at the right of the figure.The origin is placed at the centre of the surface cell. FIG.5.-Probability distribution for a Ne atom adsorbed at the cube edge of a relaxed Xe crystal. Curves are traces of isodensity surfaces on the vertical plane passing through the adsorption sites. The percentages indicated in the figure give the included total probability. SURFACE RELAXATION EFFECTS in fig. 5 for the relaxed case. This result applies also, at least partially, to the unrelaxed crystal. In that case, however, residual energy exceeds the potential energy barrier by 7.6 x 10-l6erg and localization is less strict than for the relaxed crystal, where such a difference reduces to 1.4 x erg.CONCLUSION The relaxation of the adsorbing crystal near the surface changes the shape of the potential hole that defines the adsorption site, and then the probability distribution and the total energy of the adsorbed atom. However, the total energy variations are maintained within a few percent, so that crystal relaxation does not significantly alter the general picture of physisorption previously reached with simpler unrelaxed models. The changes introduced by crystal relaxation are quite different for different exposed faces : opposite effects have been found on the (100) and the (110) crystal face. A particularly interesting effect of relaxation at crystal edges is to raise the poten- tial energy barrier to surface migration of the adsorbed atom from one face to the other. F. Ricca, C. Pisani and E. Garrone, J. Chem. Phys., 1969,51,4079 ; F. Ricca and E. Garrone, Trans. Faraday Soc., 1970, 66, 959. A. D. Novaco and F. J. Milford, J. Low Temp. Phys., 1970,3,307. F. J. Milford and A. D. Novaco, Phys. Rev., 1971, A4, 1136. F. Ricca, C. Pisani and E. Garrone, in F. Ricca, Adsorption-Desovption Phenomena (Academic Press, London, 1972), p. 111. C. Pisani and F. Ricca, J. Vacuum Sci. Techn., 1972,9,926. A. C. Hollis-Hallett, in G. A. Cook,Argon, Heliunz and the Rare Gases (Interscience, New York, 1961), Vol. 1, p. 313. Y.Bard, Nonlinear Parameter Estimation and Programming, Program 360 D 13.6.003 (I.B.M., Hawtorne, New York). a Y. Bard, 1.B.M. New York Scientific Center Report 320-3902 (1967).

ISSN:0300-9238    

DOI:10.1039/F29736900079

出版商:RSC    

年代:1973

数据来源: RSC