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THE ROYAL SOCIETY OF CHEMISTRY Journal of the Chemical Society Faraday Transactions Scientific Editor Dr. Peter J. Sarre Department of Chemistry University of N otti ng ham University Park Nottingham NG7 2RD, UK Faraday Editorial Board Prof. M. N. R. Ashfold (Bristol) (Chairman) Dr. J. A. Beswick (Paris) Prof. A. R. Hillman (Leicester) Dr. D. C. Clary (Cambridge) Prof. J. Holzwarth (Berlin) Dr. L. R. Fisher (Bristol) Dr. D. Langevin (Paris) Dr. B. E. Hayden (Southampton) Dr. P. J. Sarre (Nottingham) Prof. J. S. Higgins (London) Dr. R. K. Thomas (Oxford) Editorial Manager and Secretary to Faraday Editorial Board Dr. Robert J. Parker The Royal Society of Chemistry Thomas Graham House Science Park Milton Road Cambridge CB4 4WF, UK Staff Editor: Dr.R. A. Whitelock Senior Assistant Editor: Mrs. S. Shah Assistant Editors: Dr. L. Milne, Mrs. C. J. Seeley Editorial Secretary: Mrs. J. E. Gibbs International Advisory Editorial Board R. S. Berry (Chicago) Y. Marcus (Jerusalem) A. M. 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ISSN:0956-5000    

DOI:10.1039/FT99490FX057

出版商:RSC    

年代:1994

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Dictionary of Substances and their Effects (DOSE) is a new, unique, user-friendly guide to 5,000 chemicals and the impact they have on life forms and the environment across the globe. Compiled with the aid of official lists from the EC, UK, USA and Canada, DOSE is being published in seven alphabetical volumes, which will be completed in 1994. Each volume contains an index of chemical names, CAS registry numbers and molecular formulae, as well as a glossary of biological organisms. A separate volume containing cumulative indices of all volumes will be published after Volume 7. 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The im ortance of coatin technology is well known yet it remains a fragmented field, where a variet of coatin methods and approaches have !,en created to so7ve operational problems.'This book acts as a platform for the exchange of iJeas and wjl encourage the search for a common, fundamental approach to tackling these problems. Special Publication No. 129 Hardcover vii + 218 pages ISBN 0 85186 695 6 1993 Price f45.00 Ref No 841 Plant Polymeric Carbohydrates Edited by F. Meuser, lnstitute of Food and Fermentation Technology, Berlin, Germany D.]. Manners, Heriot-Watt University, Edinburgh, UK W. 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The book looks at electro-optic waveguide devices based on polymers that have been demonstrated to have potentially useful properties, and considers the significant impact they could have in the medium-term.Special Publication No. 137 Hardcover xii + 362 pages ISBN 0 85186 625 5 1993 Price f59.50 To order lease contact: The RoyaPSociety of Chemistry, Turpin Distribution Services Limited, Blackhorse Road, Letchworth, Herts SG6 1HN, United Kingdom. Telephone: +44 (0)462 672555. Fax: +44 (0)462 480947. Telex: 825372. Please quote your credit card details. We can now accept AccessNisa/Mastercard/EuroCard. Turpin Distribution Services Limited is wholly owned by The Royal Society of Chemistry. For information on other books and journals lease contact: Sales and Promotion Department, The Royal gciet of Chemistry, Thomas Graham House, Science Park, Milton RoaJCambridge CB4 4WF, United Kingd Telephone: +44 (0)223 420066. Fax: +44 (0) 223 423429. E-mail: (Internet) RSCl @RSC. 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ISSN:0956-5000    

DOI:10.1039/FT99490BX059

出版商:RSC    

年代:1994

数据来源: RSC

摘要:

ISSN 0956-5000 JCFTEV(15) 2159 2302 (1994) JOURNAL OF THE CHEMICAL SOCIETY Faraday Transactions Physical Chemistry & Chemical Physics CONTENTS FARADAY RESEARCH ARTICLE 2159 Atmospheric lifetime, its application and its determination: CFC-substitutes as a case study E. R. Lovejoy A. R. Ravishankara and RESEARCH PAPERS 2171 Microwave spectrum and rotational isomerism of gaseous nitrosoethane, CH,CH,NO J. Randell, H. W. Kroto, M. Maier and D. R. Milverton A. P. Cox, J. A. Hardy, 2183 Study of the conformational equilibrium of 1-chlorobutane by free-jets and conventional microwave spectroscopy S. Melandri, P. G. Favero, the late D. Damiani, W. Caminati and L. B. Favero 2189 Dynamics calculations and isotopic effect in 0 + OH(D) -+ 0, + H(D) at low energies J.M. C. Marques, W. Wang and A. J. C. Varandas 2201 Fractal properties of homologous series of structures S. El-Basil 2211 Structure of the diamminecopper(1) ion in solution. An X-ray absorption spectroscopic study G. Lamble, A. Moen and D. G. Nicholson 2215 Crossover behaviour and critical amplitude of the viscosity of binary liquid mixtures of critical composition A. Zielesny and D. Woermann 2223 Determination of the transfer thermodynamic functions for some monovalent ions from water to N,N-dimethyl- formamide, and for some anions from water to methanol, dimethyl sulfoxide, acetonitrile and pyridine, and standard electrode potentials of some M+/M(s) couples in N,N-dimethylthioformamide H. D. Inerowicz, W. Li and I. Persson 2235 Determination of the transfer themodynamic functions for the zinc@), cadmium(@, mercury(I1) and mercury(1) ions from water to methanol, dimethyl sulfoxide, acetonitrile, pyridine and N,N-dimethylthioformamideand of standard electrode potentials of the M2'/M(s) couples in these solvents M.Chaudhry, K. C. Dash, E. Kamienska-Piotrowicz, Y. Kinjo and I. Persson 2243 Transfer thermodynamic study on the copper(I1) ion from water to methanol, acetonitrile, dimethyl sulfoxide and pyridine M. Chaudhry and I. Persson 2249 Photoelectrochemistry using quinone radical anions B. R. Eggins and P. K. J. Robertson 2257 Characterisation of iron/titanium oxide photocatalysts. Part 2.-Surface studies R. 1. Bickley, T. Gonzalez-Carreiio, A. R. Gonzalez-Eli@, G.Munuera and L. Palrnisano 2265 AlP0,-Al,O, catalysts with low alumina content. Part 1V.-Effect of fluoride ion addition on texture, surface acidity and catalytic performance in cyclohexane and cumene conversions J. M. Campelo, A. Garcia, D. Luna, J. M. Marinas, A. A. Romero, J. A. Navio and M. Macias 2277 Preparation and characterization of multiple ion-exchanged Pt/TiO, catalysts K. Hadjiivanov, J. Saint-Just, M. Che, J-M. Tatibouet, J. Larnotte and J-C. Lavalley 2283 Pd' location and absorbate interactions in PdH-SAPO-34 studied by EPR and electron spin-echo modulation spectroscopies G-H. Back, J-S. Yu, V. Kurshev and L. Kevan 2291 Synthesis of SAPO-34: High silicon incorporation in the presence of morpholine as template A. M. Prakash and S.Unnikrishnan 2297 Reactivity of zeolite hydroxy groups toward u-donor bases. H-D exchange with 3-methylpentane C.J. A. Mota, R. L. Martins, L. Nogueira and W. B. Kover Note: Where an asterisk appears against the name of one or more of the authors, it is included with the authors' approval to indicate that correspondence may be addressed to this person. COPIES OF CITED ARTICLES The Royal Society of Chemistry Library can usually supply copies of cited articles. For further details contact: The Library, Royal Society of Chemistry, Burlington House, Piccadilly, London WlV OBN, UK Tel: +44 (0)71-437 8656 Fax: +44 (0)71-287 9798 Telecom Gold 84: BUR210 Electronic Mailbox (Internet) LIBRARY@RSC.ORG. If the material is not available from the Society’s Library, the staff will be pleased to advise on its availability from other sources. Please note that copies are not available from the RSC at Thomas Graham House, Cambridge.

ISSN:0956-5000    

DOI:10.1039/FT99490FP162

出版商:RSC    

年代:1994

数据来源: RSC

摘要:

Cumulative Author Index 1994 Aas, N., 1015 Billingham, J., 1953 Cheng, C. P., 1157 Easton, C. J., 739 Hachey, M., 683Abadzhieva, N., 1987 Binet, C., 1023 Cherqaoui, D., 97, 2015 Ebitani, K., 377 Hadjiivanov, K., 2277Abbott, A. P., 1533 Black, S. N., 1003 Chesta, C. A., 69 Eggins, B. R., 2249 Haeberlein, M., 263Afanasiev, P., 193 Blackett, P. M., 845 Chevalier, S., 667,675 Egsgaard, H., 941 Hakin, A. W., 2027Agren, H., 1479 Blake, J. F., 1727 Chi, Q., 2057 El-Atawy, S., 879 Hall, C., 2095Aikawa, M., 911 Blanco, M., 2125 Child, M. S., 1739 El Baghdadi, A., 13 13 Hall, D. I., 5 17Aitken, C. G., 935 Blanco, S., 1365 Chiu, S. S-L., 1575 El-Basil, S., 2201 Hall, G., 1Akanuma, K., 1171 Blandamer, M. J., 727, 1905 Chmiel, G., 1153 Elisei, F., 279 Hallbrucker, A., 293Akolekar, D.B., 1041 Blower, C., 919,931 Cho,T., 103 Elliot, A. J., 831, 837 Halpern, A., 721Albery, W. J., 11 15 Bocherel, P., 1473 Choisnet, J., 1987 Engberts, J. B. F. N., 727, Hamnett, A., 459 Aldaz,A., 609 Boddenberg, B., 1345 Chowdhry, B. Z., 1999 1905 Hancock, G., 523, 1467 Alfimov, M. V., 109 Boas, S. A., 17 Christensen, P., 459 Enomoto, N., 1279 Handa,H., 187Al-Ghefaili, K. M., 383, Booth, C., 1961 Chek, A., 1973 Eustaquio-Rinajn, R., 113 Hann,K., 7331047 Borden, W. T., 1606,1614, Clark, T., 1669, 1678, 1783, Ewins,C., 969 Hao, L., 133, 1223,1909 Ali,V., 579,583 1616, 1671,1673,1675, 1807,1808,1809,1810 Fantola Lazzarini, A. L., Harada, S., 869 Aliev, A. E., 1323 1689,1733,1734,1735, Clegg, S. L., 1875 423 Haraoka, T., 91 1 Allegrini, P., 333 1743,1744,1802,1807 Clkment, R., 2001 Fausto, R., 689 Hardy, J.A., 2171Allen, N. S., 83 Borge, G., 1227 Climent, M. A., 609 Favaro, G., 279,333 Harland, P. W., 935 A1 Rawi, J. M. A., 845 Borisenko, V. N., 109 Coates, J. H., 739 Favero, L. B., 2183 Harper, R. J., 659 Amorim da Costa, A. M., Bottoni, A., 1617 Coitiiio, E. L., 1745 Favero, P. G., 2183 Harriman, A., 697,953689 Boutonnet-Kizling, M., Collett, J. H., 1961 Favre, E., 2001 Harris, K. D. M., 1313,Amoskov, V. M., 889 1023 Colmenares, C. A., 1285 Feliu, J. M., 609 1323Ando, M., 1011 Bowker, M., 1015 Cook, J., 1999 Fenn, C., 1507 Harrison, N. J., 55Andrks, J., 1703 Bozon-Verdure F., 653 Cooper, D. L., 1643 Fernando, K. R., 1895 Haruta, M., 101 1 Andrews, S. J., 1003 Bradley, C. D., 239 Cordischi, D., 207 Fierro, J.L. G., 2125 Hashimoto, K., 11 77 Anson, C. E., 1449 Bradshaw, A. M., 403 Corma,A., 213 Filimonov, I. N., 219,227 Hashino, T., 899Antonik, T., 1973 Braun, B. M., 849 Cornier, G., 755 Finger, G., 2141 Hasik, M., 2099 Aragno, A., 787 Breysse, M., 193 Corradini, F., 859,1089 Fleischmann, M., 1923 Hattori, H., 803 Arai, S., 1307 Briggs, B., 727, 1905 Corrales, T., 83 Flint, C. D., 1357 Hawkins, C. D., 1802 Aramaki, K., 321 Brocklehurst, B., 271, 2001 Cosa, J. J., 69 Fogden, A., 263 Hayashi, H., 2133 Aravindakumar, C. T., 597 Brogan, M.S., 1461 Costas, M., 1513 Fornks, V., 213 Haymet, A. D. J., 1245 Asai,Y., 797 Brown, N. M. D., 1357 Cottier, D., 1003 Fracheboud, J-M., 1197, Heal, M. R., 523,1467Ashfold, M.N. R., 1357 Brown, R. G., 59 Coudurier, G., 193 1205 Healy, T. W., 1251 Asmus, K-D., 139 1 Brown, S. E., 739 Courcot, D., 895 Franci, M. M., 1605, 1740, Heatley, F., 1961 Assfield, X., 1743 Bruna, P. J., 683 Coveney, P. V., 1953 1 744 Heenan, R. K., 487 Attwood, D., 1961 Brzezinski, B., 843, 1095 Cox, A. P., 2171 Franck, R., 667,675 Hefter, G., 1899 Avila, V., 69 Buckley, A. M., 1003 Cox, R. A., 1819 Freeman, N. J., 751 Helmer, M., 31,395Axford, S. D. T., 2085 Buemi, G., 1211 Cracknell, R. F., 1487 Frety, R., 773 Herein, D., 403 Baba, T., 187 Burdisso, M., 1077 Craig, S. L., 1663 Frey, J. G., 17, 817 Herod, A. A., 1357 Back, G-H., 2283 Busca, G., 1161,1293 Cramer, C. J., 1802 Frostemark, F., 559 Herrington, T. M., 2085 Badia, A., 1501 Buschmann, H-J., 1507 Crawford, M.J., 817 Fujiwara, Y., 1183 Hemnann, J-M., 1441 Badri, A., 1023 Butler, L.J., 1581, 1612, Crowther, D., 2155 Funabiki, T., 2107 HerzogB., 403 Bagatti, M., 1077 1613,1614, 1671,1677, Cruzeiro-Hansson, L., 1415 Galantini, L., 1523 Heyes, D. M., 1133,193 1 Balaji, V., 1653 1809 Cullis, P. M., 727,1905 Gandolfi, R., 1077 Higgins, S., 459 Ball, M. C., 997 Butt, M. D., 727 Curtis, J. M., 239 Gans, P., 315 Hillier, I. H., 1575 Ball, S. M., 523, 1467 Buttar, D., 1811 DAlagni, M., 1523 Gao,Y., 803 Hillman, A. R., 1533,2155Bally, T., 1615, 1674, 1733, Byatt-Smith, J. G., 493 Damiani, D., 2183 Garcia, A., 2265 Hindermann, J-P., 501 1808 Cabaleiro, M. C., 845 Dan& N-T., 875 Garcia, R., 339 Hirst, D. M., 517, 181 1 Ban, M. I., 1610 Caceres, C., 2125 Danil de Namor, A.F., 845 Garcia Fierro, J-L., 1455 Hiyane, I., 973 Baonza, V.G., 553 Caceres, M., 1217 Das,D., 1993 Garcia-Paiieda, E., 575 Hoekstra, D., 727, 1905 Baonza, V. G., 1217 Caceres Alonso, M., 553 Das,T. N., 963 Gautam, P., 697 Hoffmann, R., 1507 Barbaux, Y., 895 Cairns, J. A., 1461 Dasannacharya, B. A., 1149 Gavuzzo, E., 1523 Holmberg, B., 559 Barbero, C., 2061 Calado, J. C. G., 649 Dash, K. C., 2235 Geantet, C., 193 HokM., 849 Barker, S. A., 1689 Caldararu, H., 213 Davey, R.J., 1003 Gengembre, L., 895 Hoshino, H., 479 Barnes, J. A,, 1709 Calvente, J. J., 575 Davidson, K., 879 Gerratt, J., 1643, 1672, Hosoi, K., 349 Barthomeuf, D., 667,675 Calvo, E. J., 987 De Benedetto, G. E., 1495 1673,1801 Houk, K. N., 1599,1605.Bartlett, P.N., 2155 Camacho, J. J., 23 Defrance, A,, 1473 Getty, S. J., 1689 1614,1615,1616,1672,Basini,L., 787 Cameron, B. R., 935 Dejaegere, A., 1763 Gigbo, E., 1523 1678,1680,1810Bassat, J. M., 1987 Caminati, W., 2183 Demeter, A., 411 Gil, A. M., 1099 Hrovat, D. A., 1689 Bassoli, M., 363 Campa, M. C., 207 Dempsey, P., 1003 Gil, F. P. S. C., 689 HSU, J-P., 1435 Battaglini, F., 987 Campelo, J. M., 2265 Demri,D., 501 Gilchrist, J., 1149 Hu, W.P., 1715 Bauer, C., 517 Campos, A,, 339 Den& N-J., 1961 Gill, D. S., 579, 583 Hungerbiihler, H., 1391 Baur, W. H., 2141 Canosa-Mas, C. E., 1197, Deng, Z., 2009 Gill, J. B., 3 15 Hutchings, G. J., 203 Bell, A. J., 17,817 1205 Denkov, N. D., 2077 Goede, S. J., 327, 1363 Hutton, R. S., 345 Belton, P. S., 1099 Capobianco, J.A., 755 Derrick, P. J., 239 Gomez, C. M., 339 Igawa, K., 2119 Bender, B. R., 1449 Caragheorgheopol, A., 213 Dewing,J., 1047 GonGalves da Silva, A. M., Iizuka, Y., 1301,1307Bendig, J., 287 Carlile, C. J., 1149 Diagne,C., 501 649 Ikawa, S-i., 103 Bengtsson, L. A., 559 Carlsen, L., 941 Dickinson, E., 173 Gonzalez-Carreiio, T., 2257 Ikonnikov, 1. A., 219 Benko, J., 855 Carvill, B. T., 233 Dines, T. J., 1461 Gonzalez-Elipk, A. R., 2257 Ilczyszyn, M., 1411 Benniston, A. C., 953 Castaiio, R., 1227 Doblhofer, K., 745 Goodfellow, J. M., 1415 Imamura, H., 2119 Beno, B., 1599 Castro, S., 1217 Domen, K., 91 1 Gordillo, G. J., 1913 Indovina, V., 207 Bensalem, A., 653 Catalina, F., 83 Doney, S. C., 1865 Gouder, T. H., 1285 Inerowicz, H. D., 2223 Btirces, T., 411 Cataliotti, R.S., 1397 Dongs., 2057 Goworek, T., 1501 Inoue, Y., 797,815Bergeret, G., 773 Cavasino, F. P., 311 Dossi, C., 1335 Gray, P. G., 369 Ishiga, F., 979 Bernardi, F., 1617,1669, Ceccarani, M. L., 1397 Doughty, A., 541 Gready, J. E., 2047 Ishigure, K., 93,5911671,1672 Cense, J-M., 2015 Douglas, C. B., 471 Green, W. A., 83 Isoda,T., 869 Bertran, J., 1679, 1757, Cevc, G., 1941 Downing, J. W., 1653 Grein, F., 683 Ito, O., 571 1800,1806 Chakrabarty, D. K., 1993 Duke, M. M., 2027 Grieser, F., 125 1 Iwasaki, K., 121 Beutel, T., 1335 Chmg, T-h., 1157 Dunmur, D. A., 1357 Griffth, W. P., I105 Jacobs, W. P. J. H., 1191 Beyer, H. K., 1329 Charlesworth, D., 1999 Dunstan, D. E., 1261 Grimshaw, J., 75 Jain, S. K., 2065 Bhuiyan, L.B., 2002 Charlesworth, P., 1073 Duplltre, G., 1501 Grzybowska, B., 895 Jakobsen, H. 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E., 721 Zundel, G., 843,1095 Yu, J-S., 2283 1047 Szostak, R., 1547 1614,1670,1679,1715, Vinckier, C., 2003 Wilpert, A,, 287 ... 111 ~~ ~~ ~ FARADAY DIVISION INFORMAL AND GROUP MEETINGS ~~ ~ ~~_____ Division Autumn Meeting: Reactions and Mechanisms for Fine Chemicals To be held at the University of Glasgow on 6-9 September 1994 Further information from Dr J. F. Gibson, The Royal Society of Chemistry, Burlington House, London W1V OBN ~~ ~ ~~ Gas Kinetics Group 13th International Symposium on Gas Kinetics To be held at University College, Dublin on 11-15 September 1994 Further information from Dr H.Sidebottom, Department of Chemistry, University College, Dublin Electrochemistry Group with the SCI ELECTROCHEM 94 To be held in Edinburgh on 12-16 September 1994 Further information from Professor D: E. Williams, Department of Chemistry, University College London, 20 Gordon Street, London WClH OM Biophysical Chemistry Group with the Industrial Division Biotechnology Group Peptide + Water = Protein To be held at University College, London on 19 September 1994 Further information from Professor J. L. Finney, Department of Physics and Astronomy, University College London, Gower Street, London WClE 6BT ~~ ~ British Carbon Group Applications of Microporous Carbons To be held at the University of Leeds on 28 and 29 September 1994 Further information from Professor B.Rand, Department of Chemistry, The University, Leeds LS2 9JT Theoretical Chemistry Group with CCPl Electronic Structure: From Molecules to Enzymes To be held at University College London on 30 November 1994 Further information from Dr P. J. Knowles, School of Chemistry, University of Sussex, Falmer, Brighton BN1 9QJ Division Annual Congress: Lasers in Chemistry To be held at Heriot Watt University, Edinburgh on 1&13 April 1995 Further information from Dr J. F. Gibson, The Royal Society of Chemistry, Burlington House, London WlV OBN Division Joint Meeting with the Division de Chimie Physique de la Societe' Francaise de Chimie, Deutsche Bunsen Gesellschaft fir Physikalische Chemie and Associazione Italiana di Chimica Fisica Fast Elementary Processes in Molecular Systems To be held at the Universit6 De Lille, France on 16-30 June 1995 Further information from Dr C.Troyanowsky ,Division de Chimie Physique, Laboratoire de Chimie Physique, 11 rue Pierre et Marie Curie, 75005 Paris, France British Carbon Group Carbon '96 To be held at the University of Newcastle upon Tyne on 7-12 July 1996 Further information from Dr K. M. Thomas, Northern Carson Research Laboratories, The University, Newcastle upon Tyne NE1 7RU iv THE ROYAL SOCIETY OF CHEMISTRY, FARADAY DIVISION, GENERAL DISCUSSION 98 Polymers at Surfaces and Interfaces University of Bristol, 12-14 September 1994 Organising Committee: Professor Sir Sam Edwards (Chairman) Dr R. Buscall Professor R.H. Ottewill Dr T. Cosgrove Professor J. S. Higgins Dr R. W. Richards Dr R. A. L. Jones New experimental methods and new theoretical and computational techniques have recently led to great progress in understanding the difficult but technologically important problems associated with the conformation of polymer molecules at surfaces and interfaces. The purpose of this Discussion is to bring together experimentalists and theoreticians working towards a molecular understanding of polymers at surfaces and interactions to survey the progress in the area to date and to indicate future directions of research.The meeting will attempt to bring a unified approach to the problem, encompassing problems of the structure of surfaces and interfaces in polymer melts, the conformation of polymers at solifliquid and liquifliquid interfaces, and extensions towards more complicated biological systems. The preliminary programme may be obtained from h4rs Angela Fish, The Royal Society of Chemistry, Burlington House, Piccadillv, London W1V OBN. THE ROYAL SOCIETY OF CHEMISTRY, FARADAY DIVISION, GENERAL DISCUSSION 99 Vibrational Optical Activity: from Fundamentals to Biological Applications University of Glasgow, 19-21 December 1994 Organising Committee Professor L. D. Barron (Chairman) Dr A. F. Drake Dr D. L. Andrews Professor R. E. Hester Professor A. D.Buckingham Traditional optical activity measurements such as CD are confined to the visible and near-ultraviolet spectral regions where they provide stereochemical information on chiral molecules via polarized electronic transitions. Thanks to prompting from theory and new developments in instrumentation, optical measurements are now being made in the vibrational spectrum using both infrared and Raman methods. Studies over the past decade on a large range of chiral molecules, from small organics to biological macromolecules, have demonstrated that vibrational optical activity opens up a whole new world of fundamental studies and practical applications undreamt of in the realm of conventional electronic optical activity. The meeting seeks to bring together experimentalists and theoreticians to discuss the current and future experimental possibilities and the development of theories, including ab initio computational methods, which can relate the observations to stereochemical details.The increasing importance now being attached to molecular chirality and solution conformation in the life sciences should also encourage the partipation of biomolecular scientists. The preliminary programme may be obtained from Mrs Angela Fish, The Royal Society of Chemistry, Burlington House, London W1V OBH. V THE ROYAL SOCIETY OF CHEMISTRY, FARADAY DIVISION, GENERAL DISCUSSION 100 Atmospheric Chemistry: Measurements, Mechanisms and Models University of East Anglia, Norwich, 19-21 April 1995 Organising Committee: Professor I.W. M. Smith and Dr J. R. Sodeau (Co-chairmen) Dr R. A. Cox Dr J. C. Plane Dr J. Pyle Professor F. Taylor The priority now given by national governments to the study of atmospheric science confirms that our understanding of global climate and compositional changes depends upon measurements in both the laboratory and the field. The data obtained by the experimentalists are then applied by modellers who provide the most significant input into legislative controls on pollution matters. However there have been few opportunities for laboratory and field workers along with the modelling community to attend an "interdisciplinary" discussion in which overall progress in our understanding of specific atmospheric problems is assessed.The object of this discussion is to bring together the researchers in the diverse disciplines that make up atmospheric chemistry so that their individual results and conclusions can be communicated to each other. Some of the key issues to be discussed will include: ozone balances in the atmosphere; heterogeneous processes; the interaction of chemistry and dynamics in determining atmospheric composition and change. Particular reference will be made to the input of data to global models from the use of satellite, airborne and ground-based instrumentation. Contributions are invited for consideration by the Organising Committee covering topics within the area of chemistry, dynamics and modelling in the lower and upper atmosphere. Abstracts of about 300 words should be submitted by 31 May 1994 to: Professor I.W. M. Smith OR Dr R. J. Sodeau School of Chemistry School of Chemical Sciences University of Birmingham University of East Anglia Edgbaston, Birmingham Nonvich Bl52TT, UK NR4 7TJ, UK Full papers for publication in the Discussion volume will be required by December 1994 THE ROYAL SOCIETY OF CHEMISTRY, FARADAY DIVISION, GENERAL DISCUSSION 101 Gels Paris, France, 6-8 September 1995 Organising Committee: Dr J. W. Goodwin (Chairman) Dr R. Audebert Dr R. Buscall Professor M. Djabourov Dr A. M. Howe Professor J. Livage Professor J. Lyklema Professor S. B. Ross-Murphy During the last few years there has been an increase in both theoretical and experimental work on gels as new techniques have been applied to a wide range of gelling systems. Typical of these are gels formed from polymers by both physical and chemical interactions as well as gels formed by inorganic and surfactant systems. The meeting will deal with the structure and dynamics of gels with the latter heading covering both swelling and rheological behaviour. Mixed systems such as polymer/surfactant and polymer/particle gels will also be discussed. The Discussion will bring together experimentalists and theoreticians interested in different types of gelling systems and encourage them to interact and assess the current scene and provide a benchmark for future developments. Contributions are invited for consideration by the Organising Committee. Titles and abstracts of about 300 words should be submitted by 30 September 1994 to: Dr J. W. Goodwin, School of Chemistry, University Qf'Bristol, Cantock's Close, Bristol, BS8 lTS, UK Full papers for publication in the Faraday General Discussion 101 volume will be required by May 1995.

ISSN:0956-5000    

DOI:10.1039/FT99490BP164

出版商:RSC    

年代:1994

数据来源: RSC

摘要:

J. CHEM. SOC. FARADAY TRANS., 1994, 90(15), 2159-2169 FARADAY RESEARCH ARTICLE Atmospheric Lifetime, Its Application and Its Determination : CFC-substitutesas a Case Study A. R. Ravishankara"? and Edward R. Lovejoy Aeronomy Laboratory, National Oceanic and Atmospheric Administration, 325 Broadway, Boulder CO 80303, USA The concept of atmospheric lifetime, its application in atmospheric chemistry, and its use in defining environ- mental acceptability indices such as the ozone depletion potential and the global warming potential are described. The determination of the atmospheric lifetime from laboratory measured chemical kinetic and photo- chemical parameters is highlighted. A brief description of the laboratory methods used to determine kinetic parameters and the difficulties encountered in measuring them are given.In all these descriptions and dis- cussions, chlorofluorocarbons (CFCs) and their substitutes are used as examples. The environmental accept- ability of the currently proposed CFC substitutes, the hydrochlorofluorocarbons (HCFCs) and hydrofluorocarbons (HFCs) are discussed. Lastly, the question is raised: Should atmospheric lifetime be used as an index of accept-abiI ity ? CFCs were hailed as the most stable and non-toxic com- pounds ever produced by mankind. Thomas Midgley of General Motors Corp., the inventor of CFCs, demonstrated their non-toxicity by inhaling them at public lectures. Their thermal stability, inertness, and non-toxicity made CFCs good replacements for the corrosive and toxic NH, and SO, used previously in refrigerators.A multitude of other uses, ranging from aerosol propellants to solvents, were found for CFCs, and they became ubiquitous in western society. Now, they are considered necessities in most parts of the world. The introduction of CFCs came in an era when it was gen- erally believed that human emissions could not adversely affect the Earth's atmosphere. Even though local pollution problems such as the London fog and Los Angeles smog were known to be human induced, the global impacts of anthropogenic emissions were generally neglected. This is understandable, since even the large emissions of CFCs (e.g. cu. 4 x lo8 kg of CFCl, was released in 1990) for decades would lead to a negligible abundance in the atmosphere, at most a few parts per billion (mole fraction of lo-')! During the last two decades, many major developments have changed the perceived safety of human-produced chemicals.It is now general knowledge that CFC emissions are detri- mental to stratospheric ozone, which sustains life on Earth by filtering short wavelength radiation from the Sun. Stolarski and Cicerone' and Wofsy and McElroy2 were the first to propose that chlorine could destroy ozone catalytically in the stratosphere. Measurements by Lovelock in the 1970s3 estab-lished the ubiquity of CFCs in the atmosphere. This pioneer- ing work prompted Rowland and Molina4 to suggest that, because of their inertness, CFCs could transport chlorine to the stratosphere and promote ozone depletion.The CFCs are inert in the troposphere and are lost only by photolysis and reaction with O('D) in the stratosphere. It is the catalytic nature of ozone destruction by chlorine that causes small CFC abundances to have large effects on the ozone destruc- tion rate. t Also associated with the Department of Chemistry and Biochem- istry, University of Colorado, Boulder CO 80309. The specific reactions proposed in the early 1970s for the chlorine catalysed destruction of ozone o(3~)+ cio -+ ci + 0, (1) c1+0, -B c10 + 0, (2) net: 0 + 0, --+ 20, (3) are now known to be contributing less than cycles involving the C10 + C10 and C10 + BrO reactions to polar ozone loss5 and, possibly, to mid-latitude ozone decline.6 However, the inherent connection between CFCs and stratospheric ozone loss has withstood extensive scientific scrutiny.The discovery of the Antarctic ozone hole, though not cited in the scientific basis for the Montreal Protocol in 1985, catapulted controls on CFC emissions. The Montreal Protocol' was an international treaty signed in Montreal, Canada, under United Nations auspices which curtailed production of CFCs because of their deleterious effect on the ozone layer. Now, such controls have become international agreements with quite strident phase-out schedules and acceptability stan-dards. Amazingly, it appears that countries are coming into compliance even faster than mandated by the protocols and their amendments.In response to the phase-out of CFCs, substitutes for many applications are needed. (It appears that medical applications of CFCs may continue.) The current emphasis is to design chemicals to work in existing devices with minimal changes, mostly for economic reasons. The prime candidates for re- placing the CFCs are the HCFCs and HFCs. HCFCs and HFCs are promising replacement compounds because they are compatible with the existing technology, and are more environmentally friendly than CFCs, since they are degraded efficiently in the lower atmosphere, unlike the CFCs. The HCFCs and HFCs contain hydrogen atoms which make them vulnerable to attack by the OH radical in the lower atmosphere. The CFCs, their uses, and the potential replace- ment compounds are shown in Table 1.It is already accepted that all HCFCs are transitional rather than permanent, sub- stitutes, because they also contain chlorine and hence have finite potential to destroy stratospheric ozone. The accept- J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 1 CFC applications and potential replacement compounds ~~ CFC compound application insulation blowing agent household, commercial, and automotive refrigerant, and polystyrene extrusion agent CFC-113 (CF,ClCCl,F) solvent for cleaning and drying electronics and metal R502 commercial refrigerant [CFC-115 (CF,CF,Cl)/HCFC-22 (CHClF,) azeotrope] replacement compound HCFC-123 (CHCl2CF3) HCFC- 14 1 b (CH 3CC1,F) HCFC-22 (CHClF2) HCFC-142b (CH3CF2Cl) HFC-134a (CH,FCF,) HFC-32 (CHZF,) HFC-152a (CH,CHF,) HCFC-123 (CHCl2CF3) HCFC- 124 (CF3CHFCl) HCFC-123 (CHC1,CF-J HCFC-14lb (CH3CC12F) HCFC-225ca/cb(CF3CF,CHCl2/CHC1FCF2CClF2) HCFC-22 (CHClF2) HFC-134a (CH2FCF3) HFC-32 (CH2FJ ~ ~~~ The numbering system used to designate the chemicals containing carbon, hydrogen, fluorine, and chlorine was apparently developed by chemists at du Pont Co.as a code. This code, though decipherable, causes a lot of problems to chemists, and in that respect, the du Pont chemists succeeded! The code is as follows: The molecular formula may be obtained by adding 90 to the halocarbon number; the first digit gives the number of carbon atoms, the second digit the number of hydrogen atoms, and the last digit gives the number of fluorine atoms.The number of chlorine atoms is determined by noting that the compounds are (usually) saturated. For example, HCFC-141 gives 141 + 90 = 231 or 2 carbons, 3 hydrogens, 1 fluorine and 2 chlorines. There are many possible isomers of this molecule. The most ‘mass symmetric’ isomer is designated without a letter after the numbers (HCFC-141==CH2Cl-CHFC1).The next most mass symmetric isomers will be designated with letter a, then b, etc. (HCFC-141a=CH2F-CHCl, and HCFC-14lb=CH3-CFCl2). The alkenes are designated with a four digit code, where the first digit denotes the number of double bonds. This allows one to figure out the total of substituents on the carbon frame and hence the number of chlorine atoms.More complicated numbering systems are often used in designating alkene compounds with a large number of carbon atoms. ability of each of these HCFCs and HFCs has been the focus of recent intense research and is one of the topics of this article. The concept of atmospheric lifetime is an important parameter used in the evaluation of the environmental acceptability of releasing a chemical into the atmosphere. In this paper, we first discuss the concept of atmospheric life- times and its uses. Then, we describe how the atmospheric lifetimes of CFC substitutes are assessed and detail some of our recent efforts at evaluating this quantity. Next, the link between atmospheric lifetimes and two of the important indices for environmental acceptability, the ozone depletion potential (ODP) and the global warming potential (GWP), is made.We comment on the acceptability of some of the CFC substitutes and the future outlook for chemicals in the atmo- sphere. Lastly, the possible use of atmospheric lifetime itself as an index of acceptability is discussed. At the outset, we would like to point out the premise of this article: The readers are assumed to be physical chemists who understand kinetics and photochemistry, but are not well versed in atmospheric chemistry. We apologize to the atmospheric chemists! Also, this is a review which is not meant to break new grounds in the concept, evaluation, and uses of atmospheric lifetimes. Only the possible role of C1 in affecting lifetimes of HFCs and HCFCs and the possible use of atmospheric lifetime itself as a criterion for regulating human emission are new.The subject presented here has been developed over the past two decades by the contribu- tions of a very large number of scientists. We emphasize our work and this is not meant to belittle the contributions of other investigators. Atmospheric Lifetime The Concept The atmospheric lifetime (z, units of time) is the reciprocal of the instantaneous ‘first-order’ rate coefficient for the removal of a molecule from the atmosphere (k’, units of reciprocal time), 1 z=-k’ A few points are worth noting: (1) The lifetime is defined even when the loss process is not first order in the species being lost.This is done by computing the instantaneous first-order loss rate coefficient. (2) Lifetime can depend on the concentra- tion of the molecule itself. This is because the abundance of the species can modulate the first-order rate coefficient for its own removal by changing the concentration of the reactive species. For example, an increase in the concentration of CH, in the atmosphere will reduce the OH concentration and the CH, loss rate. The reverse, i.e. change in lifetime of CH, upon controlling its emissions, is also to be considered. (3) The atmospheric lifetime may change as a function of time owing to temporal variation of reactive species in the atmo- sphere. (4) In special cases, such as with CO,, there are mul- tiple lifetimes, i.e.the loss is not represented by a single exponential but rather by a complex loss rate which changes with time. This is mostly because of the recycling of CO, by various systems. When there are multiple simultaneous irreversible pro- cesses removing a species from the atmosphere, the atmo- spheric lifetime ztota,is given by, 1 I---C-=Cki ttotal i Ti i where the sum is over all i processes, and zi and ki are the lifetime and first-order rate coefficient, respectively, for process i. For example, methane has several significant loss processes, including chemical reactions, uptake by soil, and photolysis. The chemical reactions that remove methane include, OH + CH, +CH, + H,O (4) J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 O(’D) + CH, +products (5) Cl(’P) + CH, +HCl + CH, The major loss process for CH, in the atmosphere is the reac- tion with the hydroxyl radical [reaction (4)].Reactions (5) and (6) and soil uptake make minor, but non-negligible, con- tributions to the methane loss. The atmospheric lifetime of methane is the reciprocal of the sum of the first-order loss rate coefficients due to all these processes [eqn. (II)]. Of course, the reactions (5) and (6) are weighted suitably to take into account that they occur only in the stratosphere. There are two additional points to note: (1) The lifetime for a species may be a strong function of location in the atmo- sphere and (2) the average lifetime is weighted by the spatial variation of the species in the atmosphere.Therefore, the movement of the species between the different regions of the atmosphere can be a major factor in determining the lifetime. The transport rate is usually calculated by using numerical models which are ‘calibrated’ to fit observed tracer fields. Since mixing in the troposphere is fast (approximately a few months for complete mixing within the Northern and Southern hemispheres and a couple of years for inter-hemispheric mixing) and the majority of the atmosphere is in the troposphere, a small local removal rate in this region can be very effective in removing a species from the atmosphere. Conversely, a rapid removal mechanism in the mesosphere may represent an inefficient sink because there is very little mass in that part of the atmosphere, and transport to and from this region is slow.When removal by processes such as soil uptake or ocean dissolution are to be included, the mod- elling becomes more complex. It is important to remember that most atmospheric lifetimes are calculated and what we call ‘chemical lifetime’ can be determined by the rate of physical transport. The rate of change of concentration of a species with time in the atmosphere, dC/dt, is given by dC---=P-L dt where P and L are the production and loss rates, respectively. Generally, the production rate does not depend on the con- centration of the species in the atmosphere, while the loss rate is, usually, proportional to its concentration. (It could be pro- portional to the nth power of concentration where n # l! Here, we will not consider such cases.) Thus, dC 1 -= P -k”C] = P --[C]dt z Eqn.(IV) provides a way of obtaining lifetimes from measure- ments of atmospheric concentrations and estimates of the source strengths. Methyl chloroform (CH,CCl,, MCF) is a good example of an atmospheric species for which eqn. (IV) can be used to estimate its atmospheric lifetime. MCF is a human-made compound which has no natural sources. The rate of MCF release into the atmosphere (in reality, production) can be estimated from data supplied by the manufacturew8 Further, because of long-term field measurement programmes such as the ALE-GAGE project,’ the spatial and temporal variation of the atmospheric abun- dance of MCF is known.Thus, we know P and dC/dt. Since MCF production is recent and the production rate is chang- ing with time, dC/dt is not zero, i.e. the system has not reached steady state. The 1992 (the latest year for which data are available) input into the atmosphere was ca. 6 x lo8 kg,” i.e. ca. 25 pptvt addition for that year. The current atmo- f 1 pptv = 1 part per trillion (10-12) by volume. spheric abundance is ca. 200 pptv and it has been increasing at a rate of CQ. 5 pptv per year during the past decade. Thus, the increase per year is quite small compared to the abun- dance in the atmosphere. The atmospheric lifetime of MCF has been calculated by Prinn et al. to be 5.7 years’ based on the known input into the atmosphere and the abundances and increases measured during the ALE-GAGE project.A similar, but less accurate, lifetime can be calculated by equat- ing the production rate to the loss rate. The major atmospheric-loss process for MCF is the reaction with OH radicals, OH + CH,CCl, CH,CCl, + H20 (7) Since we know that the lifetime of MCF is 5.7 years, we can relate it to an ‘average’ atmospheric OH concentration, 1 1_----5.7 years -k’ = k,,+M,F COHI,,,z This leads to a global weighted-averaged OH concentration of ca. 9 x lo5 cm-, using our recently measured value of k, = (1.75 f0.34) x expC(1550 f60)/T] cm3 mole-cule-’ s-’.’’ This analysis is a simplification because a non- negligible fraction of MCF is removed tlia oceanic uptake.’, It is interesting to note that production of CH,CCl, is banned under the London amendment to the Montreal Pro- tocol starting in 1996. After this time, the CH,CCl, concen-tration should reach a maximum and then decay exponentially.This period will provide an opportunity to further test our understanding of the processes that control the lifetime of MCF (and, by analogy, other similar compounds). The OH concentration derived from eqn. (V) is the effective concentration that removes MCF from the atmosphere. It would not be applicable to another molecule whose rate coef- ficient for reaction with OH has a very different temperature dependence. In this case, the differences in the activation energies can be taken into account and a new ‘effective’ OH concentration ded~ced.~ For the HFCs and HCFCs, where OH abstracts an H atom from a C-H bond, the activation energies are similar to that for the OH + MCF reaction, and the OH concentration derived from eqn.(V) is appropriate for the lifetime calculations. If the activation energies are much larger than for reaction (7), the removal will take place lower in the troposphere (i.e. at warmer temperatures) and be shifted further into the tropics. In contrast, if the OH reaction has no activation energy, more of the troposphere will be available for the removal. However, reactions with small acti- vation barriers are almost always very fast. In this case the atmospheric lifetime is determined by the OH concentration in the area where the compounds are released and globally averaged removal rates based on MCF data are inapprop- riate.Uses of Atmospheric Lifetimes The atmospheric lifetime determines the abundance and rate of growth of a species in the atmosphere for a given emission. Fig. 1 shows the atmospheric abundances, as a function of time, of two species with different atmospheric lifetimes but with the same emission rates (in moles rather than by weight). The abundance of the species with a longer lifetime increases in the atmosphere faster’ and reaches a higher level for a fixed emission time. Also, it,takes longer for this species to reach steady state, as indicated by the time taken for the solid line to flatten out. If the emissions were cut off at a given time, time = 1, the atmospheric abundance of both species would decrease exponentially.The concentration of the species with I I 0 1 2 3 time (arb. units) Fig. 1 Comparison of the temporal variation of the atmospheric concentration of three species with the same emission rates but differ- ent removal rates. A compound with no loss (a) accumulates the fastest and maintains a constant concentration when emissions are stopped (time = 1). Species with significant loss processes [(b) and (c)] accumulate more slowly. The compound with the highest loss rate (c) accumulates the slowest, approaches a smaller steady-state concentration and decays faster (dotted lines) when the emissions are stopped. the longer lifetime decreases more slowly than the one with the shorter lifetime.Therefore, if the emission of a species into the atmosphere is curtailed, it will take the atmosphere longer to get back to its original state if the lifetime is longer. This is why it will take a couple of centuries for the atmo- spheric abundances of CFCs to decrease to the pre-CFC values when emissions of CFCs are stopped in or around 1995. The pre-ozone hole level of chlorine was ca. 2 ppbvt and current levels are about 3.9 ppbv. Therefore, even after the cessation of CFC emissions, the ozone hole will persist for nearly 60 years. If the currently proposed CFC substitutes had been used in place of the CFCs, we would not have accu- mulated 2 ppbv of chlorine in the atmosphere and, hence, would not have the ozone hole today! (The emission of CH,C1 from oceans is the only significant natural source of atmospheric chlorine, i.e.pre-CFC source of stratosphere chlorine, and presently, the contribution of CH,Cl to the total current chlorine budget is ca. 15%.) Two indices used commonly to express the potential for atmospheric perturbation are ODP and GWP. Both these indices depend on the lifetimes of the reference molecule and the molecule under consideration. These indices are used for societal judgement of the environmental acceptability of human-made chemicals ; therefore, a high premium is placed on the accuracy of these parameters. Definition of ODP, CLP, HGWP The ODP was originally introduced by W~ebbles'~.'~ as a way to index the ability of various CFCs to deplete strato- spheric ozone relative to CFCl, (CFC-11). The ODP is defined as AO, for emission of unit mass of X ODP(X) = (VIII)AO, for emission of unit mass of CFCl, where AO, is the amount of stratospheric 0, destroyed by emission of X or CFCl,.In the original use of Wuebbles,', ~~ ~ t 1 ppbv = 1 part per billion by volume. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 the mechanism for the destruction of all the CFCs considered was photolysis in the stratosphere. However, now the ODP concept has been extended to include molecules which have very different loss processes. For example, the HFCs and HCFCs are removed mostly in the troposphere via reaction with OH, while the reference compound, CFC1, , is destroyed in the stratosphere.In this case, the systematic errors in the calculated rates of loss processes are not cancelled by taking the ratio of the projected ozone losses, because the com-pounds have dissimilar removal pathways. However, because the ODP index is easy to use and provides a reasonable measure of the relative merits of various substitutes, the ODP is still a widely used index. In fact, the Montreal Protocol and the US Clean Air Act use ODP to judge acceptability. There are several problems with the definition of ODP. The first problem arises because the ODP is a function of time. Usually, the ODP is defined as the steady-state value which is the depletion potential when concentrations of both X and CFCl, have reached steady state.Before steady state, the ODP changes with time because species with different lifetimes accumulate at different rates. The shorter-lived sub- stitutes reach steady state faster and their short-time ODP is higher than the steady-state ODP. Therefore, the ODP must be defined for a specific time horizon. Another problem is how AO, is estimated. Model calculations underestimate the changes in 0, levels that have been measured by satellite and ground-based instruments during the past decade. Often it is assumed that ratioing the changes in 0, used in the defini- tion ODP should minimize this error. This is not always the case. Solomon et ~1.'~have defined a more realistic ODP which is based on observations of ozone losses and vertical profiles of X and/or compounds with similar loss processes.This approach, termed the semi-empirical approach, greatly offsets the errors which result from the atmospheric loss for molecule X being different from that for CFC1,. In both approaches one needs the atmospheric lifetime of molecule X and CFC1, to calculate the ODP. The semi-empirical method is more accurate because the rates of transport of molecules in the stratosphere are derived from observed verti- cal profiles, rather than by calculation. Thus, this method bypasses the calculation of transport rates, which are a major source of error. In addition to the ODP, the chlorine loading potential (CLP) is used to gauge the impact of chlorine-containing compounds on stratospheric ozone: (zxnJmolecular weight of X)CLP = (zCFCl3 ncFcl,/molecular weight of CFCl,) -(IX) where zx is the atmospheric lifetime of species X and n, is the number of c1 atoms in species x (nCFC13= 3).The CLP is a measure of the maximum amount of chlorine in a molecule that could reach the stratosphere, relative to CFC-11. There- fore, CLP is often taken to be the upper limit for ODP, i.e. ODP < CLP. The CLP does not consider where in the stratosphere chlorine is released, and the ability of a molecule to destroy ozone changes with altitude. The spatial variation of C1 release is included in the calculation of the ODP. There- fore, the ODP is still a better measure of the ozone depletion capability of a molecule while the CLP is a better measure of the chlorine introduced into the stratosphere.Note that ODP of species which do not contain chlorine can also be defined. Here, the ozone destruction efficiency of the responsible group, for example, Br atoms from brominat- ed compounds, has to be determined relative to that of chlo- rine. Another quantity that is used as an index for atmospheric perturbation is the GWP, which defines the greenhouse effi- J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 ciency of a compound relative to CO,. The halocarbon global warming potential (HGWP) expresses the greenhouse efficiency relative to CFC-11 (CFCl,) dFJmolecular weight of X)HGWP = (T~ (TCFC13 dFCFC13molecular weight of CFCl,) (X) where dF is the radiative forcing, the IR energy absorbed by unit concentration (usually 1 ppbv) of the molecule in W m-,.The GWP of CFC-11 (CFCl,) is ca. 1400 for an infinite time horizon. The time horizon issue is rather complicated and one should read the IPCC documents'6 for the dis- cussions of the time horizons and lifetime of CO,. We high- light the HGWP for two reasons: (1) In replacing a CFC with a substitute, what matters is the effectiveness of the substitute relative to the CFC. (2) The GWP is not as well defined as HGWP because the 'lifetime' of CO, is uncertain owing to various CO, recycling processes involving the atmosphere, biosphere and the oceans. Note that the above indices compare the lifetimes of species which have different pathways for their removal.The reference compound for the ODP, CFC-11, is removed via stratospheric photolysis while the reference compound for GWP, CO,, is taken up by the biosphere and oceans. The compounds whose ODP and GWP are being defined may be removed by chemical reactions, photolysis, or other physical processes in the troposphere or the stratosphere. For example, Halon 121 1 (CF,ClBr), is removed via tropospheric photolysis, HFCs uia OH reaction and COS by plant uptake. Thus, comparisons of lifetimes of species with completely dif- ferent loss mechanisms are required to estimate their effects on the atmosphere. Determination of Lifetimes In the preceding section, we noted the importance of knowing atmospheric lifetimes for evaluating the environ- mental indices, ODP, CLP, and HGWP.How can one deter- mine these atmospheric lifetimes? One method is to use atmospheric observations and estimates of source strengths, as described earlier for MCF, although this story is rather unusual. Many important atmospheric species have natural sources and their emission rates are not well understood. A current need is to estimate the lifetimes of chemicals which have not yet been introduced into the atmosphere. In this case, one must evaluate the rates for all the possible atmospheric-loss processes and calculate the lifetime with numerical models. Central to this approach is the appre- ciation that the calculated lifetimes may have systematic errors, since the calculated lifetimes are no better than the input data.However, if two molecules are removed by the same process, their relative lifetimes should be determined quite accurately by this method. This situation applies to HCFCs and HFCs, the two classes of chemicals which are forerunners as replacements for CFCs, because they, like MCF, are also removed mostly uia OH reactions. Thus, the lifetimes of HFCs and HCFCs are as good as that of MCF if the rate constants are accurate. Evaluation of the Environmental Impact of HCFs and HCFCs The criteria for the environmental acceptability of a molecule are its ODP and GWP. The Montreal Protocol restricts the production of CFCs with ODPs greater than 0.2. However, there is no international agreement on the acceptability of a greenhouse gas, although, there is a voluntary move to avoid the use of potent greenhouse gases as CFC substitutes.It is very likely that there will be future regulations on greenhouse gases using GWPs as the indices of acceptiblity. As noted above, the primary quantity required to calculate ODPs and GWPs is the atmosphere lifetime. The lifetimes of HCFCs and HFCs are determined by the rates of the important removal processes [eqn. (II)]. The common reactive species responsible for the removal of chemicals from the atmosphere are given in Table 2. In order to evaluate the atmospheric lifetime, one must know the rate coefficients for all the important loss processes. Many times, a number of gas-phase reactions can be eliminated by analogies and thermodynamic arguments.For example, in the case of HFCs and HCFCs, it is safe to assume that their reactions with ozone and NO, are not important, since the analogous reactions between these oxidants and saturated hydrocarbons are slow. It is also likely that hydroxyl radicals do react with Table 2 Oxidants in the lower atmosphere and their abundance approximate abundance molecule troposphere stratosphere origin 0.2 <1.5 ppmv 0.2 <5 ppmv biological activity 0, or NO, photolysis followed by 0 +0, reaction NO NO3c1 a few ppbv <PPbV a few pptv? a few ppbv oxidation of NO and direct emission in troposphere N,O degradation in stratosphere direct emission in troposphere. N,0 degradation in stratosphere reaction of NO, with 0, heterogeneous reactions in troposphere CFCs, CH,CI, etc.in stratosphere halogens and halogen oxides ?? <PPtV <lo7cmP3 averaged <2 ppbv (C10) <20 pptv (BrO) <PPtV <10' cm-3 averaged ?? photolysis of 0, or NO, reaction of O('D) with H,O, other small sources A > 290 nm <i03 cm-, 185 < A < 2120 nm and photolysis of 0, or 0, Sun A > 290 nm The abundances are approximate diurnal averages. HCFCs and HFCs since they react efficiently with saturated hydrocarbons. Indeed, OH reactions are expected to be the most important atmospheric-loss process for HFCs and HCFCs. In the troposphere and stratosphere, OH is pro- duced mostly via the sequence: O('D) + H,O -,20H Processes such as the photolysis of HONO, HONO &OH + NO (10) are believed to be minor contributors to the production of OH.Loss of HFCs and HCFCs by heterogeneous processes may be ruled out as a major mechanism because the halo- carbons are very weakly soluble in water. Photolysis is also negligible in the troposphere because of poor overlap between the absorption spectra of the HFC and HCFC com- pounds and the solar radiation reaching the troposphere. In the stratosphere, reactions of HFCs and HCFCs with OH are still important. The reaction with O('D), which is not important in the troposphere owing to the extremely low concentration of the electronically excited atom, is potentially important in the stratosphere. O('D) is produced mainly by ozone photolysis [reaction (8)] with minor contributions from 0, photolysis, In the stratosphere, the concentrations of O('D) are greatly enhanced because of its increased rate of production via 0,photolysis (due to the enhanced UV levels and higher 0, concentrations) and a reduced rate of quen- ching, due to the lower total pressure. Even in the strato- sphere, the O('D) concentrations are small (<lo3 molecule Reactions with the more abundant O(3P)appear to be too slow to be important; these reactions are endothermic or nearly thermoneutral.UV photolysis may be a significant sink for halocarbons containing the C1 chromophore, since radiation between 180 and 220 nm is available in the middle stratosphere. HFCs do not absorb radiation with wave-lengths longer than ca.180 nm, and photolysis of HFCs is negligible in the troposphere and the stratosphere. To evalu- ate the lifetime and fate of the CFC replacement compounds in the stratosphere, their UV absorption cross-sections, disso- ciation quantum yields, and rate coefficients for reaction with O('D) and OH are needed. Measurements of OH Rate Constants Since OH reaction is the dominant loss process for HCFCs and HFCs in both the troposphere and the stratosphere, the rate coefficents for these processes have been studied exten- sively. Many studies of CFC-substitutes have employed the discharge flow technique in which OH radicals are generated via reactions of atoms, produced in a high-energy discharge, with molecules (e.g.H + NO, -+ OH + NO or F + H,O + HF + OH). The change in the OH concentration with reac- tion time is determined by varying the contact distance between the OH and the HFC or HCFC reactant in a flow- tube reactor. The OH radical is detected at the exit of the reactor with a wide variety of methods, including laser mag- netic reasonace (LMR) spectroscopy (the NOAA group, see for example ref. 17); resonance fluorescence (RF) (Jeong and Kaufman,18 Wayne and co-worker~,'~ Clyne and Holt"); electron paramagnetic resonance (Orkin and Khama-ganor2*); and laser-induced fluorescence (LIF) (Nelson et a/.,,). The OH kinetics have also been studied with several variants of the flash photolysis technique, in which the OH radicals are generated photolytically in a short pulse of light from either a flash lamp or a laser, and the radicals are moni- J.CHEM. SOC. FARADAY TRANS., 1994, VOL 90 tored as a function of time by using fast optical techniques, including LIF (NOAA group' 7), resonance absorption (Paraskevopolous and co-worker~~~), and RF (Kurylo and co-~orkers~~and LeBras and co-workers, 5). A related tech- nique in which the OH radicals are produced by pulsed radiolysis and monitored vs. time by absorption, has also been employed in ref. 26. The OH + HFC and HCFC kinetics have also been studied by monitoring the disappearance of the HFC or HCFC species in the presence of OH, relative to the loss of another compound for which the OH rate constant is well known.This approach has two advantages: (1) The decay of the compound of interest is monitored directly, so that impu- rities in the HFC sample do not influence the measurement and (2) if measured relative to CH,CCl,, the ratio is what is needed for lifetime calculations and, hence, can be more accu- rate than individual rate constant measurements. However, care must be exercised to ensure that reactive species other than OH are not present. Several studies of the OH + HFC and HCFC kinetics have been carried out with this technique (Huder and DeM~re,~ and Sidebottom and co-workers26). The studies of DeMore and co-workers are particularly note- worthy because they systematically measured rate coefficients as functions of temperature for a large array of HFCs and HCFCs relative to different reference compounds, including MCF.We have measured OH rate constants for a wide range of proposed CFC-substitute compounds by employing the discharge-flow (DF) and pulsed-photolysis tech-nique~.'~.~*-~'In this section we describe briefly our experi- mental apparatus and methodology; the apparatus and methodology used by many other investigators are very similar. The principles of rate constant measurement with the discharge-flow technique have been described by Howard., A schematic diagram of our flow-tube apparatus is shown in Fig. 2. A laser magnetic resonance (LMR) spectrometer mon- HFC or HC reactant A Ab-, atom precursor carrier gas 1 I1 movable inlet -OH prixursor temperature regulation iacket H+N02 -OH+NO F+H20 -OH+HF 1-* pressure port L= reaction region /halocarbon wax /or Teflon ,f-OH detection -nV Pump Fig.2 Schematic diagram of the discharge flow apparatus used in the NOAA laboratory J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 itors the effluent of a Pyrex flow tube 100 cm long and with an internal diameter of 2.5 cm. OH radicals are generated in a small side-arm reactor uia the reaction of NO, with H atoms or H,O with F atoms. The atomic species are pro- duced by the dissociation of molecular hydrogen or CF, in a microwave plasma. The OH radicals enter the flow tube about 10 cm upstream from the 50 cm long reaction region. The HFC or HCFC reactant is added through a movable injector to the centre of the flow tube with a small flow of an inert carrier gas, typically He.The bulk of the flow in the reactor is the inert carrier gas, which is introduced via ports upstream from the radical source. Reaction between OH and the reactant occurs over a variable distance of about 10 to 50 cm. The total gas flow rate through the flow tube is ca. 10 STP cm3 s-(STP = 273 K and 760 Torr) at a total pressure of 1 to 2 Torr, giving linear flow velocities of 500-2000 cm s-l and reaction times ranging from 5 to 100 ms. The walls of the flow tube and injector are coated with halocarbon wax or fitted with a Teflon sleeve to reduce the loss of radicals and inhibit heterogeneous chemistry. The temperature of the reactor is controlled by flowing thermostatted fluid through a jacket surrounding the reactor.The flash photolysis-laser-induced fluorescence (FP-LIF) apparatus is illustrated in Fig. 3. OH radicals are produced in a small Pyrex reactor by the pulsed UV photolysis of various precursors. Photolysis light sources (precursor and wavelength) include Xe flash lamps (H,O between 165-190 nm, HNO,, H,O,, etc.), excimer laser (0,-H,O mixture at 248 nm; HNO, and H,O, at 248 nm; HONO at 351 nm), and harmonics of the Nd: YAG laser (0,-H,O mixture at 266 nm; HNO, and H,O, at 266 nm; HONO at 355 nm). The rapid photolytic production of OH initiates the chem- istry, and the OH concentration is monitored us. time by the laser-induced fluorescence of OH following excitation of the A ,C(v' = 1) tX 'lJ(v" = 0) transition at ca.282 nm with a pulsed laser. The laser-induced fluorescence signal provides a sensitive and rapid detection scheme for real-time monitoring of the OH concentration. The temporal profile of OH is mapped out by averaging the fluoresence signal for a range of delay times between the photolytic production of OH and its LIF interrogation. The DF--LMR and FP-LIF techniques are complemen- tary, well tested kinetic methods. The DF method offers the advantage of isolated OH source chemistry, although hetero- geneous chemistry on the walls of the reactor is a potential problem. The LMR detection offers excellent sensitivity. The FP-LIE' method is not complicated by heterogeneous pro- cesses since the radical detection volume is isolated from the ~ _____ ____ JI.-YM,,,, i--, Fig.3 Schematic diagram of the pulsed-photolysis-laser-induced fluorescence apparatus used in the NOAA laboratory 2165 walls of the reactor and diffusion times are long compared to reaction time. However, this technique requires in situ photo-lytic production of the radicals and reactions of photo- products with the OH radicals is a major concern in these systems. The use of lasers and multiple precursors has greatly enhanced the applicability of this method. In our laboratory, multiple OH source schemes have been employed to examine possible secondary chemistry associated with the OH pro- duction method. In particular, use of HONO photolysis at 351 or 355 nm avoided photodissociation of the HCFCs.In both the DF and FP techniques, the OH concentration is monitored as a direct function of time or some parameter related to time (e.g. distance in a constant velocity flow). This type of measurement may be complicated by the presence of reactive impurities in the excess reactant sample and care must be taken to ensure that the samples are not contami- nated in the system. The FP-LIF technique does offer very good sensitivity coupled with excellent time resolution. This allows one to maximize [X]/[OH],,, where X refers to the stable excess reactant, by working with small radical concen- trations and large reactant concentratiom. The large [XI facilitates the measurement of its concentration which directly influences the accuracy of the measured rate con- stant.A potential drawback to this approach is that large concentrations of pure reactant samples are required. Recir- culation of the reactants is a possible method to minimize sample use. However, production of reactive species has to be minimized and measured. Evolution of the OH + HCFC-14lb(CH3CFCI2) Rate Constant As an example of the great effort expended to characterize the reactivity of the proposed CFC replacement compounds, we describe the measurements of the OH + HCFC-141b rate constant over the past six years. The HCFC-14lb story is exemplary because of the wide range of experimental tech- niques which have been applied and the difficulties encoun- tered in the measurement of a small OH rate constant.The rate constant data for the OH + HCFC-141b reaction is summarized chronologically in Table 3, and shown in Fig. 4. The first measurements of the rate constant were reported '0-131 lo c 1VI t k1 10-15 2.0 2.5 3.0 3.5 4.0 4.5 103 KIT Fig. 4 Summary of the rate coefficients measured for the OH + HCFC-14lb reaction as a function of temperature; (0)ref. 19, ref. 29, (0)(-. -) ref. 32, (0) ref. 34, (---) ref. 27. The solid line is a fit to the data of Talukdar et dZ9and Zhang et J. CHEM. SOC. FARADAY TRANS., 1994, VOL,. 90 Table 3 Measured values of the rate coefficients for the reaction of OH with HCFC-141b k(298 K)" Ab EIR tK) T range (K) method 16.3 f5.6 5.8 1100 & 250 238-426 DF-RF 7.0 & 1.2 3.6 & 1.1 1140 f210 243-400 FP-RF 5.9 k 0.5 14.7 _+ 3.2 1640f 100 253-393 DF-LMR and FP-LIF 6.1 14.2 6.0 1623 & 293 250-400 FP-RF 5.9 14 1630 298-358 chamber All quoted errors are those from the authors.'Rate coefficients in the units of cm3 molecule-' s-', k(T)= A exp(-EIRT). ref. 19 32 29 34 27 In units of 10-l~cm3 molecule-'^^^ by Brown et ~1.'~and Liu et aL3, who employed the DF-resonance fluorescence and the FP-resonance fluorescence techniques, respectively. Liu et aL3, noted an upward curva- ture in the Arrhenius plot of the In k us. 1/T at low tem- perature and reported a room-temperature rate constant which was one half the value reported by Brown et al.Early experiments in our laboratory reported similar curvature in the Arrhenius analysis.33 This curvature has been attributed to the presence of CH,CCl, as an impurity at the lo00 ppmv level in the CH3CFCl, sample.,' The OH + CH,CCl, rate constant is large (k29, w 1 x lo-" cm3 molecule-' s-' at the pressures employed) and exhibits a slight negative tem- perature dependence. The OH + HCFC and HFC rate con- stants are generally small and the reactions have large activation energies (E/R = 1000-2000 K). Therefore, at low temperatures the relative contribution of the impurity reac- tion to OH loss increases, leading to upward curvature in the Arrhenius plot. Gas chromatographic analysis of the HCFC- 141b sample identified CH,CCl, as an impurity, which is a starting material in the synthesis of HCFC-14lb.Talukdar et ~1.~~the OH + HCFC-141b rate constant with measured highly purified HCFC-141b samples and obtained a slightly lower rate constant at room temperature and significantly reduced curvature in the Arrhenius plot. Careful studies of the dependence of the measured rate constant on the energy of the flash lamp used to photolyse H20 (H,O + hv + OH + H) demonstrated that photolysis of the reactant CH,CFCI, generated radicals which react with OH. Taluk- dar et al. avoided this complication by photolysing HONO at 355 nm to generate OH. A re-measurement of the rate constant by Zhang et aL3, (same group as Liu et a/.) in which the potential systematic problems, especially those involved with the reactions of OH with the photo-fragments of HCFC- 141 b, were carefully addressed, produced a result in very good agreement with the work of Talukdar et al.These results were confirmed by Huder and DeM~re,~ who used a relative rate technique. This is an important confirmation because the relative rate technique is not prone to inter- ferences from impurities which plagued the early OH kinetic measurements. In the relative technique, OH is generated by the continuous photolysis of ozone at 254 nm in the presence of water [0, + hv -+ O('D) + 0,; O('D) + H20+20H1, and the loss of the HCFC is monitored relative to the loss of CH, and CH,CCl, for which the OH rate constants are well established.This technique is complementary to the OH-monitoring methods because the decay of the HCFC reactant is analysed directly, and the presence of impurities should not influence the measurement. The Wayne group3' has since carefully analysed their system and deduced that the problem associated with their earlier measurements was due to hetero- geneous reactions. They confirm that the lower rate contants measured by Talukdar et al., Zhang et al., and Huder and DeMore are the more accurate values. This historical accounting shows why measurement of these rates coefficients is very time-consuming and how different systematic errors lead to erroneous results. It has probably taken more than ten person-years of effort to establish this rate coefficient! Of course, such efforts are justified because of the policy implica- tions of the results.Measurement of O('D) Rate Constants The O('D) reactions proceed by several channels. o(~D)+ R -+ o(3~)+ R (114 -+ products (lib) Channel (a) represents physical quenching of the electronic energy of the excited atom. It is assumed that the electronic energy released by the quenching process (ca. 45 kcal mol- ') does not fragment the reactant. Channel (b) represents all reactive channels where bonds are broken and/or formed. In order to evaluate the importance of the O('D) reaction in the atmospheric degradation of the replacement compounds, the rate constant for the reactive channel (b) is needed. The rate constants for the reactive channel in the O('D) reaction with the replacement compounds have been measured by several investigators using different tech-nique~.~~-~~laboratory, we have used the pulsed In our photolysis-time-resolved vacuum UV atomic resonance fluo- rescence technique.,' Electronically excited 0 atoms are pro- duced by the pulsed excimer laser photolysis of ozone at 248 and 308 nm.0, -+ O('D) + 0, (84 -+ o(3~)+ 0, The quantum yield for O('D) production is 0.9 at 248 and 0.7 and 308 nrn.,' The temporal evolution of the ground-state oxygen atom is monitored by resonance fluorescence excited by a cw atomic fluorescence lamp at CQ. 130 nm. The kinetics of reaction (1 1) are studied by monitoring the evolution of the ground-state 0 atom [O(3P)]produced in the quenching process and by the reaction of O('D) with 0, O('D) + 0,+ 20(3P)+ 0, (1 24 O('D) + 0,-+ 20, (W The rate constant of the reactive channels (llb) of the O('D) + HCFC and HFC reactions are determined by measuring the total rate constant for the loss of O('D) and the yield for the quenching step (lla).The rate constant for the total loss of the reactant is extracted from the temporal evolution of the O(3P)product. The yield for the quenching channel is determined by comparing the O(3P) resonance fluorescence signal in the presence of the reactant and in the presence of a very efficient non-reactive quencher (N,) which converts all of the O('D) to O(3P). The details of the data analysis are presented by Warren and Ra~ishankara.~, The O('D) reactions with HCFCs are fast [k,, = (0.9-2.6) x 10-'' cm3 molecule- ' s-'3 and proceeded predominantly via reaction [channel (1 lb) yield = 70-80%].42 The HFC J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 reactions are also efficient [k,, = (0.5-2.0) x lo-’’ em3 molecule-’ s-‘3 but proceed predominantly uia quenching of the O(’D) [channel (1 lb) yield < 50%].42Preliminary experi- ments in our laboratory also indicate that the yield of OH in the O(’D) + HCFC and HFC reactions is small. Therefore, formation of C10 when possible, and insertion into the C-C bond appear to be significant. Measurement of UV Absorption Cross-sections The CFC substitutes which contain only carbon, hydrogen, and fluorine (HFCs) absorb strongly only in the VUV region of the spectrum and photolysis is not an important atmo- spheric removal mechanism for these compounds.The HCFCs, which contain the chlorine chromophore, usually have significant absorption in the ultraviolet region. Com- pounds with more chlorine atoms have larger absorption cross-sections at A > 180 nm, and compounds with more C1 atoms per C atom have absorption spectra that are further red shifted. Photolysis can be an effective atmospheric loss process for an HCFC molecule if it absorbs in the wavelength region above 290 nm with cross-sections greater than ca. cm2 molecule-’. These weak absorption cross-sections, which decrease monotonically with increasing wave- length, usually decrease with decreasing temperature.Therefore, for atmospheric purposes, the temperature depen- dences of the cross-sections need to be determined accurately. Cross-section measurements have been carried out for the HCFCs and HFCs by a large number of groups. Details of the measurement methodology can be found in papers from our Molina et aZ.,4, Simon and co-w~rkers,~’ and NIST.46 In practice, there are difficulties encountered in measuring small cross-sections. Possible problems include the presence of impurities, condensation on windows, variation in the refractive index matching between the cell window and the gas and lack of precision in measuring small absorptions. Readers are referred to the articles mentioned above for further details.Other Atmospheric Reactions In addition to photolysis and the reactions with species such as OH and O(’D), several other atmospheric-loss processes, including reactions with halogen atoms, NO,, and halogen oxides, should be considered. The reactions of NO, with HCFCs and HFCs have been found to be extremely and are probably not important in either the troposphere or the stratosphere. The halogen oxides are also unlikely to be reactive with the rather strongly bound HFCs and HCFCs. Below, we discuss the possible roles of C1 atom reactions and Lyman-or photolysis. Reactions of CI Atoms Reactions with C1 atoms in the troposphere and lower strato- sphere have been largely ignored as a removal process for HFCs and HCFCs because there are no well established sources of C1 in the troposphere, unlike the case of the OH radical.However, it has been postulated that significant con- centrations of chlorine atoms may be present in the tropo- sphere due to the liberation of photo-labile NOCl from the heterogeneous reaction of N,O, with NaCl in sea salt aerosols4* and other processes.49 Some C1 atoms may also be produced by the reaction of OH with HCl in the tropo- sphere.’’~’’ In this case, if C1 atoms react rapidly with HCFCs, the lifetimes of HCFCs would be lower than the current estimates. To assess this possibility, the rate coeff- cients for the reactions of C1 atoms with HFCs and HCFCs have been mea~ured.~~*’~-~~ These studies show that the reactivity of C1 with the partially halogenated ethanes is similar to that of OH radicals.In the troposphere, where most of the HCFCs are degraded, the concentrations of C1 atoms must be at least 10 times smaller than that of the OH radical. This assertion comes from detailed analyses of the methane budget and vertical profiles of some organic com- pounds and is too complex to recount here. Therefore, the reactions of the HFCs and HCFCs with C1 cannot compete with the OH reactions in the troposphere. If C1 atom concen- trations in the marine boundary layer are comparable to OH due to high sea salt aerosol concentrations, the atmospheric lifetimes of the HFCs and HCFCs would still not be greatly affected by C1 atom reactions, because of the small volume of the marine boundary layer compared to the rest of the tropo- sphere.The concentrations of C1 atoms in the stratosphere (<lo5 cm-,) could be larger than in the troposphere. However, HCFCs with two chlorine atoms on the same carbon atom are mostly destroyed via photolysis in the stratosphere. Other HCFCs react with OH. We conclude that the reactions of HCFCs with C1 are not an important loss process for HCFCs in the atmosphere. It is possible that the C1 atom reactions contribute to the degradation of some HFCs in the stratosphere because of the slow HFC photoly- sis rates. However, it is unlikely to be more important than their reactions with OH. It is interesting to note, however, that in the future the stratosphere concentrations of CI should decrease with the elimination of CFCs.Lyman-a Photolysis The perfluorocarbons (PFCs, C,F,) are an example where none of the traditional reactions (see Table 2) are effective loss proces~es.~~*’~ The PFCs do not react with OH, their interaction with O(’D) proceeds mainly via quenching of O(’D), they do not absorb radiation below ca. 130 nm, they are water insoluble and they are most probably biologically inactive. The most likely degradation path for these mol- ecules is photolysis in the upper stratosphere and lower mesosphere by the weak Lyman-a radiation at 121.6 nm. Some of these molecules may also be lost uia reactions with ions and thermal electrons in the mesosphere. For some of the perfluorinated compounds, e.g.CF, and C2F6, even Lyman-a photolysis is not a likely degradation pathway. Destruction in combustion systems is probably the most important loss mechanism for these compounds. Lyman-a photolysis may be a significant sink for the HFC-23, CHF,, which is unreactive and has a long atmospheric lifetime of ca. 400 years (neglecting Lyman-a photolysis). If CHF, absorbs Lyman-a radiation strongly, its lifetime may be ca. 10% lower. Estimation of Atmospheric Lifetimes As mentioned at the outset, most atmospheric lifetimes are calculated by using numerical models which include atmo- spheric motions and chemistry. These calculations require accurate rate data for the major loss processes in addition to a thorough knowledge of the spatial and temporal distribu- tion of the reactive species, solar flux, etc.In general, the spatial distributions of the reactive species are only known from modelling exercises and the temporal variations are averaged for lifetime calculations. Without direct measurements of the concentrations of the reactive species which determine the lifetimes of compounds added to the atmosphere, it is difficult to assess the accuracy of the calculated lifetimes. Fortunately, the majority of the HFCs and HCFCs are removed by reactions with OH and J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 4 Approximate atmospheric lifetimes, ozone depletion potentials, and global warming potentials for currently-considered CFC- substitutes molecule CHClF, (HCFC-22) CH2F2 (HFC-32) CHF, (HFC-23) CFCl, (CFC-11) CF2C12 (CFC-12) CH,CCl, (MCF) CF,CHFCl (HCFC-124) CH,CF,Cl (HCFC-142b) CF3CHC12 (HCFC- 123) CH3CFC12 (HCFC-14lb) CF,CH,F (HFC-134a) CH,CHF, (HFC-152a) CH ,CH,F (HFC- 16 1) ___~ No.of m ? C1 atoms /g mol-I /years ODP GWP 1 86 15 0.05 510 0 52 6 0 180 0 70 ca. 400 0 8OOO 3 136 66 1 1400 2 120 104 0.9 4500 3 132 6 0.15 34 1 136 8 0.02 150 1 100 25 0.06 540 2 152 1.7 0.0 1 30 2 116 13 0.13 150 0 104 18 0 420 0 68 2 0 50 0 48 0.25 0 4 The lifetime (T), ODP, and GWP values are approximate. Whenever possible, the quoted lifetimes are those calculated in our laboratory. The GWP values were either calculated using our IR data by Dr.Ramaswamy of NOAA’s GFDL or were taken from IPCC.16 The ODP for HCFC-22 was taken from the AFEAS report.,, the OH concentration field can be reasonably well defined because of the MCF data and model calculations, as dis- cussed earlier. Note that model calculations can give good relative concentrations of OH in the atmosphere at various locations as functions of time and season. These values are placed on an absolute scale by the MCF lifetime data. In almost all lifetime calculations, the OH concentrations and their temporal and spatial variation, are calculated from measured or estimated abundances of the precursors and photon fluxes using 1-, 2-, or 3-D models. This OH field is then scaled to reproduce the lifetime of MCF (5.7 years).This method does not necessarily lead to the correct OH fields. However, as long as reaction with OH is the important loss process and the activation energies for the OH reactions with the substitute and MCF are approximately the same, the cal- culated lifetimes should be quite accurate. This is especially true for species with lifetimes longer than ca. 2 years. If the lifetime is less than 2 years, the species will not be well mixed in the troposphere. The point of injection then becomes important and one needs to know the spatial distribution of OH, and the MCF-determined OH field is not appropriate. The other factor that makes the MCF-determined OH field applicable to the HFCs and HCFCs is that the reactions of OH with these species have activation energies very similar to that with MCF.4’ This ensures that the location of maximum degradation in the troposphere are the same for both MCF and the compound of interest, i.e.the tropical upper troposphere. Readers should refer to the papers by Prather and SpivakovskyS7 and Prinn et al.’ for further details on use of MCF-standardized OH concentration fields. It is also worth noting that the impact of species with life- times much smaller than 2 years is quite small on either the stratospheric ozone or global warming issues, except in some special cases. The calculated lifetimes and ODPs of some of the CFC- substitutes are listed in Table 4. It is clear that species which have short atmospheric lifetimes also have small ODPs.A few factors such as the molecular weight and number of chlo- rine atoms in the molecules make a difference in ODP values, but order of magnitude changes in the ODP are associated mainly with variation in the atmospheric lifetimes. The majority of the HCFCs have ODPs much less than 0.2, the current acceptability threshold according to the Montreal Protocol and the US Clean Air Act. The estimated GWPs are also listed in the table. Currently, there are no acceptability standards for GWP. However, it is likely that there will be a Climate Convention, similar to the Montreal Protocol, in the future. In general, if the GWP of the substitute is not too much greater than that of CFC-11 (or the HGWP I), it will probably be deemed acceptable. Should Atmospheric Lifetime be a Measure of Acceptability? The majority of species emitted by natural processes into the atmosphere have lifetimes of less than a few years.The hydrocarbons emitted from trees, for example, live for a few hours or possibly a few days. Methane, which has significant natural sources, has an atmospheric lifetime of about 10 years. CO, and N,O are exceptionally long-lived natural emissions which have lifetimes of nearly a century. The main sink for CO, is conversion into carbonates in the oceans while N,O is removed primarily by photolysis in the strato- sphere. All the natural species are short-lived compared to some of the compounds produced by humans.The most stable gases emitted by humans appear to be the perfluoro compounds. These molecules, which are very potent green- house gases, have atmospheric lifetimes of thousands of years. As mentioned earlier, the time it takes to cleanse the atmo- sphere increases proportionately with the atmospheric life- time. Therefore, even though there may be no currently identified harm to the atmosphere due to the emissions of a very long-lived species, one cannot be certain that they are benign. When CFCs were invented and released into the atmosphere, their deleterious effects were not known. Fortu- nately, CFCs are relatively short lived, compared to PFCs, and it will take only about a century for CFCs to be removed from the atmosphere once their emissions are curtailed.The release of any very long-lived species in the atmosphere should be viewed with the greatest concern. The PFC life- times, though long on historical timescales, are short com- pared to the evolutionary timescales. Hence, life on Earth may not be able to adopt to the changes these emissions may cause. Thus, it seems prudent to ask if the long-lived mol- ecules must be considered ‘guilty’ unless proven otherwise. The benefit to humanity may have to be weighed against the unknown risks. A.R.R. dedicates this paper to Professor R. J. Hanrahan on he occasion of his 60th birthday. Much of the work described here was performed by co-workers in the Aeronomy Labor- atory. We are grateful to J. B. Burkholder, T.Gierczak, L. Goldfarb, S. A. McKeen, A. Mellouki, J. J. Orlando, A. M. Schmoltner, S. Solomon, R. K. Talukdar, G. L. Vaghjiani, R. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 2169 F. Warren and R.R. Wilson. A.R.R. thanks S. Solomon, S. A. McKeen, D. L. Albritton and C. J. Howard for many stimu- lating and useful discussions on the CFC-substitute issues. Assistance from D. Sueper during the preparation of this manuscript is greatly appreciated. We also thank Professor Ian Smith for the invitation to write this paper. 29 30 31 32 louki, L. Goldfarb, T. Gierczak, S. A. McKeen and A. R. Ravi-shankara, J. Phys. Chem., 1993, W,8976. R. Talukdar, A. Mellouki, T. Gierczak, J. B. Burkholder, S. A. McKeen and A. R. Ravishankara, J. Phys. Chem., 1991,95,5815. A.R. Ravishankara, S. Solomon, A. A. Turnipseed and R. F. 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WMO, Scientific Assessment of Stratospheric Ozone: 1991, World Meteorological Organization, WMO Global Ozone Research and Monitoring Project-Report No. 25, 1992. Montreal Protocol on Substances that Deplete the Ozone Layer, Final Act, UNEP, 1987; Revised, 1990, London Amend- ment. P. M. Midgley, Atmos. Enuiron., 1989,23, 2663. R. Prinn, D. Cunnold, P. Simmonds, F. Alyea, R. Boldi, A. Crawford, P. Fraser, D. Gutzler, D. Hartley, R. Rosen and R. Rasmussen, J. Geophys. Res., 1992,97,2445. P. M. Midgley, personal communication, 1993. R. K. Talukdar, A. Mellouki, A-M.Schmoltner, T. B. Watson, A. R. Ravishankara and S. A. Montzka, Science, 1992,257,227. 36 37 38 39 40 41 J. A. Davidson, G. E. Streit, C. M. Sadowski, C. J. Howard, D. A. Jennings, H. I. Schiff and A. L. Schmeltekopf, J. Chem. Phys., 1976,64,57. L. S. Fletcher and D. Husain, J. Phys. Chem., 1976,80, 1837. R. Atkinson, G. N. Breuer, J. N. Pitts Jr. and H. L. Sandoval, J. Geophys. Res., 1976,81, 5765. R. G. Green and R. P. 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Sidebottom, L. Nelson, J. J. Treacy and D. J. O’Farrell, Int. J. Chem. Kinet., 1989,21, 834; (b)R. K. Bera 53 54 55 56 437. E. C. Tuazon, R. Atkinson and S. B. Corchnoy, Int. J. Chem. Kinet., 1992, 24, 639. J. P. Sawerysyn, A. Talhaouli, B. Meriaux and P. Devolder, Chem. Phys. Lett., 1992,198,197. J. E. Thompson, M.S. thesis, University of Colorado, Boulder, 1993. R. J. Cicerone, Science, 1979,206, 59. and R. J. Hanrahan, Radiat. Phys. Chem., 1988,32,579. 57 M. Prather and C. M. Spivakovsky, J. Geophys. Res., 1990, 95, 27 K. Huder and W. B. DeMore, Geophys. Res. Lett., 1993, 20, 18723. 1575. 28 A. M. Schmoltner, R.K. Talukdar, R. F. Warren, A. M. Mel- Paper 3/06918D;Received 19th November, 1993

ISSN:0956-5000    

DOI:10.1039/FT9949002159

出版商:RSC    

年代:1994

数据来源: RSC

摘要:

J. CHEM. SOC. FARADAY TRANS., 1994, 90(15), 2171-2182 2171 Microwave Spectrum and Rotational Isomerism of Gaseous Nitrosoethane, CH,CH,NO A. Peter Cox,* Judith A. Hardy and Jeremy Randell School ofChemistry, University ofBristol, Cantock's Close, Bristol, UK BS8 ITS Harold W. Kroto, Michael Maier and David R. Milverton School of Molecular Sciences, University ofSussex, Falmer, Brighton, UK BN I 9QJ The microwave spectrum of gaseous nitrosoethane has been measured in the 7-40 GHz region. The monomeric vapour is shown to exist as two rotational isomers, one the cis form with a planar heavy-atom structure, the other a staggered gauche conformer. The microwave spectrum of gauche-nitrosoethane shows large centrifugal distortion shifts and additional splitting arising from tunnelling through the trans barrier.Relative intensity measurements show the cis to be more stable than the gauche form by 2.1 +_ 0.4 kJ mol-'. The dipole moments were determined through the Stark effect: pa = 2.316 (2), pb = 0.623 (4) and pf= 2.398 (2) D (1 D z3.33564 x C m) for the 15N cis, and pa = 2.288 (4), pb = 0.814 (5),pc = 0.460 (9) and pf= 2.471 (4) D for the 15N gauche form. Nitrogen-I4 quadrupole coupling constants have been determined to be zaa = -2.525 (56) and (xbb -xcc) = -7.311 (97) MHz for the cis, and (xbb -xcc) = 3.518 (40) MHz for the gauche conformer. Molecular structures have been calculated for both conformers on the basis of the oxygen-18, nitrogen-15 and main species data. The LCCN angle opens up by 8" on going from gauche- to cis-nitrosoethane.The barrier hindering internal rotation of the methyl group is the same for both conformers within experimental error, V, = 10.9 0.3 kJ mol-' for the cis form and 10.9 f 0.3 kJ mol-' for thegauche conformer. The microwave spectrum of nitrosoethane, CH,CH,NO, has Broad frequency scans were made in the range 18-40 GHz been studied by the Sussex group.'T2 Under normal condi- using backward wave oscillators, and accurate frequency tions nitrosoethane exists as a solid dimer, (CH,CH,NO), , measurements were made using klystrons with oscilloscope and a low-pressure, gas-phase technique such as microwave presentation. Radiofrequency microwave double-resonance spectroscopy is ideally suited to the study of the monomer.(RFMDR) spectra were measured by the method of The monomer spectrum was obtained by allowing the vapour Wodarczyk and Wilson.' Radiofrequencies from 10 to 470 which evolves from the solid dimer, at room temperature, to MHz were supplied by a Marconi TF801D signal generator flow directly into the spectrometer cell. Two sets of tran- and TF2 172 amplifier. The radiofrequency was square-wave sitions were identified and assigned to two rotational isomers modulated at 100 kHz via a Hewlett-Packard 1054A double of CH,CH,NO, a cis conformer and a staggered gauche con- balanced mixer. Samples at Bristol were prepared by the pho- former. The lines belonging to the conformers were found, tolysis of either n-propyl nitrite or tert-amyl nitrite in a 350 under high resolution, to show splitting which could be cm3 silica flask positioned near a Hanovia 400 W UV lamp.ascribed to several effects: (a) 14N-nuclear quadrupole coup- Repeated exposure times of about 3 min were used. The blue ling, (b) hindered rotation of the CH, group, (c) tunnelling monomer was condensed into a Pyrex glass tube after each between the equivalent gauche forms. exposure and allowed to warm to room temperature forming The Bristol group became involved with the detailed the white cis-nitrosoethane dimer.' Volatile impurities were microwave study of CH,CH,NO because of concurrent pumped off and the sample stored at liquid-nitrogen tem- of the isoelectronic molecule propanal, perature to prevent gradual isomerisation to the oxime.CH,CH,CHO, and following their earlier work on nitroso- Nitrosoethane monomer was generated by gentle warming methane, CH,N0.7.8 The work on analogous systems has under vacuum with a hot-air blower and dosed directly into helped greatly in understanding the complexity of the the waveguide cell. Most spectra were run at dry-ice tem- nitrosoethane spectrum. Molecular details derived from these perature. Under these conditions the monomer pressure joint studies are reported below. dropped fairly quickly from an initial value of 50 pm Hg (ca. 7 Pa) and a spectroscopic dose lasted about 30 min. The isotopic forms of nitrosoethane were prepared by the Experimental photolysis of the appropriately substituted n-propyl nitrite. The spectra at Sussex were recorded on a Hewlett-Packard "N-Enriched n-propyl nitrite was prepared by esterifying 8460A microwave spectrometer operating in the range 26.5-propan-1-01 (0.004 mol) with gaseous 5N203, itself prepared 40 GHz.Nitrosoethane dimer was prepared by the pyrolysis from "NO (98.5% enriched). The l80 species was prepared of tert-amyl nitriteg at 185 "C. The collected dimer was found by a similar procedure. The source of was 95% atom to have sufficient vapour pressure at room temperature to be enriched 1802 gas, which was converted to enriched N203by flowed through the waveguide cell cooled to dry-ice tem- reaction with normal NO. This led to a 20% enrichment of perature. Under these conditions a pressure of ca. 20 pmHg the nitrosoethane produced as indicated by relative intensity (ca.3 Pa) could be sustained giving rise to a strong monomer measurements of the isotopic spectra. CH,CH,NO spectrum. Originally the yield of nitrosoethane was monitored using a mass spectrometer. Microwave spectra at Bristol were studied in the range Microwave Spectrum 8-40 GHz using a conventional 100 kHz Stark modulated Two distinct sets of asymmetric rotor transitions were identi- spectrometer with a 3 m X-band stainless-steel waveguide. fied in the microwave spectrum (see Fig. 1) and the fre- 2172 J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 I 17I I I I I I I I I 1 CH31114-3 gauche I 3-2 C",O CH3 H' \H3-2 I I I ,,NI cis I 1 I 1 I I I I 1 I I I I Fig. 1 Microwave spectrum of CH,CH,NO.Two sets of spectra are identified: one for the gauche isomer and the other for the cis isomer. The lines of a Q-branch series of the gauche isomer (split by tunnelling) are identified by markers below the spectrum (see also Fig. 2 and 3). quencies fitted using least-squares analysis to give two sets of rotational constants. In order that the observed constants could be correlated with molecular structures, certain assumptions were made about the geometries of the rota- mers. The initial assumption was that the two sets of con- stants were related to each other by a simple rotation of the N=O relative to the ethyl group about the C-N bond. Additional changes of structure from one rotamer to the other were anticipated, but to a first approximation the one- degree-of-freedom model was adequate for identifying the individual conformers.Parameters taken from CH,NO and CH,CH,CN were used in the model structure.8*12 Rotational constants were computed using these parameters allowing the dihedral angle (the angle between the CC and NO bond direction) to vary from 0" and 180". The results showed that the molecule exists in a cis form, with the heavy atoms copla- nar, and a gauche form with c1 z 120". cis-CH,CH,NO The spectrum of the cis isomer is that of an almost-rigid asymmetric rotor K = -0.75. Strong a-type, R-branch lines dominate the spectrum (pa= 2.3 D) with weaker b-type, Q-and R-branch lines occurring throughout the spectrum (pb = 0.62 D). Some transitions show the effect of 14N quadrupole coupling.The satellite spectrum is very rich as one might expect for a molecule with two low-lying vibrational modes, the CH, and N=O torsions. The hypothetical centre frequencies for CH,CH,NO and its isotopic species were fitted with Watson's reduced quartic Hamiltonian in an Ir representation, Table 1. The derived constants are presented in Table 2. The observed quadrupole splittings, Avl , , were analysed using the first-order pertur- bation expression of Bragg and Golden,', which may be con- veniently rearranged as follows; where Y(Z,J, F) is Casimir's function, xgg = eQd2V/ag2,and (P:,) and (Pig) are the expectation values of the square of the components of the rotational angular momentum for levels 1 and 2. The quadrupole coupling fits are given in Table 3.Several high-J a-type, Q-branch transitions showed small A, E splittings (<1 MHz) due to the methyl group's internal rotation. Where appropriate, the hypothetical centre frequency has been calculated from the relationship vCentre= (2v, + vA)/3. The internal rotation analysis is discussed later. Spectroscopic predictions for the 15N species were based on an approximate structure generated from the normal species constants. The J = 3 + 2, a-type transitions were identified by their characteristic Stark effects and relative intensities. Using improved predictions based on these fre- quencies, the 22, t21,, transition, highly dependent on the A rotational constant was identified by RFMDR using the 2,.2,, pump transition at 152 MHz. Subsequent assign- ments were made in a stepwise fashion employing character- istic Stark effects. The microwave spectrum of CH,CH,N"O was assigned in a similar manner to that described above. The frequencies are listed in Table 1. Unfortunately, no b-type transitions could be assigned owing to the density and intensity of the normal species spectrum. However, good B and C rotational constants and a reasonable A constant were derived. gauche-CH, CH, NO The gauche conformer is a near-prolate rotor (K TC -0.98). The main features of the spectrum are a-type, R-branch bunches (paTC 2.3 D) with weaker b-type, Q-branch series (pb z0.8 D).There is also a c-component of the dipole moment, connecting levels in the symmetric (0.) and anti- symmetric (0-)torsional substates.It is expected, and found, to be comparatively small and no c-type transitions have been observed. Initial identification of the gauche spectrum was made using low-resolution scans which quickly identified the J = 3 + 2, J = 44-3 as well as the characteristic Jl,J-tJo, series. All the latter transitions for the 14N iso- topomer appear as doublets each with a complicated quartet fine structure when observed under higher resolution (see Fig. 2). Early in the investigation it was difficult to assign unequivocally this hyperfine structure. The 2 : 1 intensity ratio within the quartet patterns collapsed into 1 : 1 doublets on I5N substitution thus establishing the 14N quadrupole components within the quartet.The quadrupole coupling was treated as previously described for the cis conformer; the J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 1 Experimental" and calculatedb centre frequencies (MHz) for cis-nitrosoethane normal 15N 180 obs obs -calc obs obs -calc obs obs -calc 1 0 1 0 0 0 11 370.02 0.13 1 1 1 0 0 0 21 821.60 0.00 2 0 2 1 0 1 22 809.12 0.07 22 591.43 0.01 2201 1.84 0.03 2 1 1 1 1 0 24 459.01 -0.07 24 229.74 0.00 23 590.23 -0.03 2 1 2 I 1 1 21 457.34 0.17 21 249.69 0.02 20 712.30 0.20 2 2 0 2 1 1 31 503.14 0.04 2 2 1 2 1 2 35 824.96 -0.06 3 0 3 2 0 2 33 850.23 -0.07 33 525.81 0.03 32 677.58 -0.05 3 1 2 2 1 1 36 589.96 -0.02 36 246.36 -0.13 35 293.33 0.05 3 1 3 2 1 2 32 096.62 0.00 31 785.87 0.03 30 984.62 -0.10 3 2 1 3 1 2 30 236.98 0.02 3 2 1 2 2 0 35 023.57 -0.03 33 775.39 -0.05 3 2 1 2 2 0 34 692.79 -0.07 3 2 1 2 2 0 34 692.79 -0.07 3 2 2 2 2 1 34 437.12 0.01 34 109.60 0.1 1 33 226.72 0.01 4 0 4 3 1 3 36 706.90 0.02 4 1 3 4 0 4 20 356.26 0.03 4 1 3 3 2 2 18 914.46 0.01 4 2 2 4 1 3 28 855.63 0.02 28 581.25 0.03 5 1 4 5 0 5 26 143.44 0.04 25 935.72 0.00 5 1 4 5 1 5 22 093.26 0.00 5 1 4 4 2 3 33 373.28 0.00 5 2 3 5 1 4 28 142.16 -0.04 27 878.20 0.02 6 1 5 6 0 6 33 043.91 0.00 6 1 5 6 1 6 30 535.63 0.01 6 2 4 6 1 5 28 526.22 0.00 28 266.73 0.01 6 2 4 5 3 3 19 150.83 0.02 7 2 5 7 1 6 30 341.72 -0.01 30 078.26 -0.03 7 2 6 6 3 3 19 249.43 -0.02 8 2 6 8 1 7 33 836.02 -0.01 33 558.08 -0.01 8 2 7 7 3 4 27 068.87 -0.02 9 2 7 9 2 8 30 240.42 -0.04 9 3 8 8 3 5 33 099.13 0.02I 13 3 10 13 3 11 36 437.18 0.03 16 4 12 16 4 13 30 403.39 0.02 19 5 14 19 5 15 23 366.22 -0.02 20 5 15 20 5 16 33 054.18 0.02 23 6 17 23 6 18 24 653.59 -0.02 24 6 18 24 6 19 34 792.03 -0.02 27 7 20 27 7 21 25 321.22 0.03 28 7 21 28 7 22 35 739.37 -0.01 a k0.05 MHz.Calculated frequencies from the constants of Table 2; reduction A Ir representation used for fit, i.e. axes (x, y, z) = (b,c, a) as in J. K. G. Watson, J. Mol. Spectrosc., 1977,65, 123. A€ A€ 36 275 36 265 36 255 36 245 O+ frequency/M Hz 0-Fig. 2 16,. +-160.16 transition of gauche-CH,CH,NO demonstrating ''N-quadrupole splitting, CH, internal rotation and gauche-gauche splitting J. CHEM.SOC. FARADAY TRANS., 1994, VOL. 90 Table 2 cis-Nitrosoethane: rotational constants (MHz), distortion constants (kHz)" and 14N quadrupole coupling constants (MHz); errors are lo from the fitting procedure CH,CH,NO CH,CH2'5N0 CH,CH,N "0 17041.596(13) 6490.0701 (65) 4989.0473 (63) b b b ---1.668 (45) b--6.22749' 16881.7113 (74) 6430.0052 (29) 4939.9038 (27) 5.339 (30) -14.21 (25) 38.8 (12) 1.5665 (61) 3.82 (1 7) -6.22802 16652.2 (17) 6257.396 (22) 4818.250 (22) b b b b b ------6.22565 XCC -2.525 (56) -7.311 (97) -2.052 (23) (-7.311) Watson's A reduction Ir representation. Constrained to the values of C,H,'5N0. 'A' = Zc -Zb -I,, conversion factor B x Z = 505379 MHz u A'. results are shown in Table 4. The quadrupole splittings are found to be fitted by a single constant (xbb-xcc)= 3.518 (40) MHz.Having identified the quadrupole structure the problem was to assign the remaining splittings. The two possible sources are CH, or gauche-gauche tunnelling. According to the theory of Quade and Lin14 the O+-O-splittings of the Jl,J-tJo,J series should be proportional to J(J + 1).The larger Q-branch splittings obeyed this relationship very well, see Fig. 3. The perturbation below J = 3 suggests that there is a near degeneracy between the 0, and 0-states at either the K -= 0 or 1 levels with the closest degeneracy at J = 1. It was observed that the a-type R-branch K-, = 0 tran-sitions were unperturbed (any small splitting being accounted for by differences in B + C for the 0, and 0-substates) whereas the R-branch K-= 1 splittings were anomalously large at J = 1.Further evidence was provided by the obser- vation of anomalous Stark effects and quadrupole splittings of the 21,2t 11, and 2', +-fl,o lines. As gauche-nitrosoethane is near prolate it is expected that a-type coup- ling between 0, and 0-states will be dominant. With this model the interacting states are chiefly the (+) ll,o and (-)11, with the torsional splitting, AE* of the order (B -C),see Fig. 4.The observed transitions corrected for A, E and quadrupole splittings were fitted to a version of Pickett's coupled level Hamiltonian including all quartic cen- 'il23 0 0 0 0 0 0 0 0. 18 O 174 0 50 100 150 200 250 300 J(J + 1) Fig.3 0+4-splittings of the Ji,J-,cJ,, series of transitions of ~U~C~~-CH,CH,'~NO T2'121'-r 212 212 110 110 -. il111T-' 111 aLAE O+ 0-Fig. 4 Schematic energy level diagram for gauche-CH,CH,NO showing observed microwave transitions, (a) 18 358.6, (b) 18 692.3, (c) 18 368.0, (d) 18 701 .O MHz, with radiofrequency pump frequency p = 190 MHz, and AE, = 126 MHz trifugal distortion (qcd) terms in Watson's A-reduction,' 5,1 H+ = A+ Pi + B+ Pi + C+Pi + qcd H-= A-P: + B-Pi + C-P$ + qcd + AE * 4= GAP, p, + p,PC) A value of the coupling constant, Gc,was calculated using the Eckart axis ~ystern'~ based on the structure determined below. Table 5 gives the analysis of the observed spectrum. The spectroscopic constants resulting from the least-squares analysis are presented in Table 6.The A, E splittings due to internal rotation of the methyl group referred to earlier on the Jl,J-l-Jo,Jseries are shown in Table 4. The internal rotation analysis associated with the methyl group is now given. Methyl Barrier (cis and gauche Conformers) The barrier analysis for both conformers was made using the internal-axis method following the treatment of Woods.' The splittings and barrier calculations are presented in Table 7. There are insufficient data to determine I, and La from the internal rotation fit, and values for these parameters have been taken from the structural determination. For the gauche species the CH, splittings are adequately treated as being simply superimposed upon the & splittings arising from internal rotation about the C-NO bond.This procedure gives a satisfactory fit and probably cannot be improved J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 2175 Table 3 Observed cis 14N-quadrupole hyperfine structure (MHz) for isotopomers of cis-nitrosoethane“ normal *O J Ka KC J KO KC F“ F, obs obs -calc. obs obs -calc 2 1 2 1 1 1 2 2 2 1 1 1 1 3 2 1 1 1 1 0 1 1 2 1 3 2 2 2 1 0 3 2 0 2 4 3 3 2 3 2 1 2 4 3 3 2 2 2 1 1 2 1 4 3 3 2 2 2 2 1 3 2 4 3 2 1 1 2 2 0 4 3 3 2 2 1 4 6 1 5 6 6 7 5 7 2 5 7 1 6 7 7 8 6 8 2 6 8 1 7 8 8 9 7 a The coupling constants from the least-squares fit are given in Table 2.within the rigid toprigid frame single degree of freedom model employed. Dipole moment The CH,CH,”NO species was used for dipole moment determination in order to avoid any Stark-quadrupole inter-actions. The Stark effects of several transitions were studied using the dc bias method.” The determination of the dipole components for the cis conformer is straightforward ; the Stark components are given in Table 8. The Stark effect of several transitions of gauche-CH,CH,’5N0 has been investigated. The transitions studied 21 455.94 -0.05 21 456.77 0.07 21 459.13 -0.03 21 457.48 0.01 20 712.33 0.00 24 457.13 -0.05 24 458.46 0.09 23 589.72 0.01 24 459.08 0.00 23 590.27 -0.01 24 459.80 -0.05 24 460.88 0.01 33 850.29 -0.03 33 850.17 0.03 32 096.72 -0.02 32 096.49 0.02 36 590.23 0.01 36 589.98 -0.01 36 589.75 0.00 34 436.45 -0.04 33 226.20 -0.01 34 437.32 0.02 33 227.05 0.01 34 437.78 0.03 35 023.71 0.02 35 023.09 -0.02 35 024.09 0.00 28 526.48 -0.02 28 526.09 0.02 30 342.2 1 0.03 30 341.45 -0.03 33 836.63 -0.03 33 835.72 0.03 were chosen to avoid gauche-gauche mixing, i.e.so as not to involve near degeneracies with levels in the other torsional substate. For example, M = 0, 21, t11, is not seriously affected by the mixing of the (+)ll,o and (-)1 levels. Whereas, the M = 1 components are severely affected, as shown in the Stark plots of Fig.5. These affected plots can be interpreted in terms of the theory outlined by Hirota et al. for deuteriopropene.20 The Stark coefficients for unperturbed transitions in the gauche conformer are given in Table 8. The effective dipole moment component usually deter-mined by rotational spectroscopy is the average value of the dipole moment operator pgin the particular vibrational state. However, where close-lying torsional states are involved, as 2176 J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 4 Observed and calculated 14N-quadrupole hyperfine structure (MHz) for gauche-nitrosoethane" (+) state (-) state J Kll Kc J KO Kc F" F, obs obs -calc obs obs -calc 4 1 3 4 0 4 4 4 23 077.29 -0.04 23 053.15 0.04 5 3 23 078.04 0.04 23 053.75 -0.04 6 1 5 6 0 6 0.02 6 6 24 082.43 -0.01 24 057.92 -0.02 7 5 24 083.15 0.01 24 058.58 7 1 6 7 0 7 7 7 24 737.96 0.04 24713.21 0.07 8 6 24 738.59 -0.04 24713.78 -0.07 8 1 7 8 0 8 8 8 25 501.84 0.05 25 476.86 0.05 9 7 25 502.46 -0.05 25 477.49 -0.05 9 1 8 9 0 9 9 10 8 9 lo8 I 26 379.77 26 380.51 0.00 0.00 26 354.51 26 355.13 0.06 -0.06 10 1 9 10 0 10 10 10 27 378.10 0.04 27 352.49 0.03 11 9 27 378.78 -0.04 27 353.19 -0.03 11 1 10 11 0 11 11 12 10 11 10l2 I A 28503.31 28 504.14 -0.03 0.03 28 477.40 28 478.21 -0.02 0.02 11 12 10 10l2 I11 E 28502.99 28 503.82 -0.03 0.03 28 477.08 28 477.90 -0.02 0.02 12 1 11 12 0 12 12 13 11 11l3 I12 A 29762.31 29 763.16 -0.03 0.03 29 736.04 29 736.88 -0.02 0.02 12 12 E 29761.98 -0.02 29 735.69 -0.02 13 11 11 29 762.82 0.02 29 736.53 0.02 13 1 12 13 0 13 13 14 12 13 12l4 I A 31 162.19 31 163.04 -0.02 0.02 31 135.54 31 136.36 0.00 0.00 13 14 12 12l4 I13 E 31 161.82 31 162.67 -0.02 0.02 31 135.16 31 135.99 -0.01 0.01 14 1 13 14 0 14 14 14 A 32709.94 -0.02 32 682.86 -0.01 15 13 13 32 710.81 0.02 32 683.71 0.01 14 14 E 32709.53 -0.02 32 682.45 -0.01 15 13 13 32 710.40 0.02 32 683.30 0.0 1 15 1 14 15 0 15 15 15 A 34412.32 -0.02 34 384.78 -0.01 16 14 14 34 413.21 0.02 34 385.66 0.01 15 15 E 34411.89 -0.01 34 384.34 0.00 16 14 14 34412.77 0.01 34 385.20 0.00 J.CHEM.SOC. FARADAY TRANS., 1994, VOL. 90 Table kontinued (+) state (-) state J Ka Kc J Ka Kc Fu F, obs obs -calc obs obs -calc 16 1 15 16 0 16 16 16 A 36275.68 -0.01 36 247.64 0.01 17 36 216.57 0.01 36 248.51 -0.0115 15 16 16 E 36275.19 -0.01 36 247.13 -0.02 17 36 276.09 0.01 36 248.04 0.0215 15 17 1 16 17 0 17 17 17 A 38305.59 0.00 38 276.99 0.01 18 38 306.49 0.00 38 277.88 -0.0116 17 17 E 38305.06 -0.01 38 276.46 0.00 18 38 305.98 0.01 38 277.36 0.0016 16 5 0 5 4 1 4 5 4 24 954.81 0.10 24 978.91 0.00 4 24 955.26 -0.10 24 979.56 0.006 a The coupling constant from the analysis is given in Table 6.in gauche-nitrosoethane, a more careful consideration of the parity 0, and 0-,and the effective value of pc is given by symmetry of the dipole operators is required to describe the (0,IPcIO-). Thusdetermined dipole components. Since the a and b axes are symmetric with respect to the tunnelling motion, the effective PZff =(0,lPaIO+)=(0-IPaW-) values of pa and pb are the expectation values in the 0, and pZff =(0, Ipblo+) (O-Ipblo-)0-torsional substates. On the other hand, p, changes sign with the tunnelling and therefore connects levels of different /Cff =(0,lPcIO-) =(0-lPClO+) These approximations work well in the present instance since 30 T the ground-state torsional splitting is small (ca. 130 MHz) and the 0, and 0-are largely localised in the potential minima.In particular, (0,Ip, lo-) is expected to be close to the effective out-of-plane component of the dipole 1 / moment. Molecular Structure With the limited isotopic data available from the present 10 work it is impossible to determine all the structural param- eters of nitrosoethane. However, by using a suitable approx- imation for some bond lengths and angles reasonable structures may be calculated for both conformers. NIcis-CH,CH,NO6 There is good evidence for the planarity of the heavy-atom framework given by the quantity A = -6.227 u A' (Table 2) which agrees closely with that calculated for two pairs of -1 0 out-of-plane hydrogens using the nitrosomethane structure, -6.394 u A2, and that found experimentally for cis propa-na1,6 -6.180 u A2.Further evidence of the planarity of the structure is given by the fact that A' does not change signifi- cantly on l80or "N substitution.\0 (-) Substitution coordinates were calculated for nitrogen and oxygen from the observed moments of inertia using Kraitch- 211-(-1 110 man's equations." In order to locate the other atoms the \ following assumptions were made: all C-H bond lengths are -30 1.092 A, the methyl group has tetrahedral symmetry and the Fig. 5 Anomalous Stark effects for M = 1 components of LHCH angle of the CH, group is 105.2" (from but-l-ene22) J = 2 c1, K-= 1 transitions in ga~che-CH,CH,'~N0,showing with its bisector coincident with the LCCN bisector and the the perturbation between 1', 1,1and+) ,,(-) states C-C bond length constrained to that in propanal.' The Table 5 Experimental" and calculatedb centre frequencies (MHz) for gauche-nitrosoethane normal "N J Ka Kc J Ka Kc obs obs -calc obs obs -calc 1 0 1 0 0 0 9264.50 0.21 922 1.90 0.14 1 0 1 0 0 0 9264.50 0.05 922 1.90 0.26 1 1 0 1 0 1 2229 1.37 0.48 21956.75 -0.04 1 1 0 1 0 1 22257.65 0.17 22257.65 0.17 1 1 0 1 1 1 190.00 -1.33 1 1 0 1 1 1 190.00 -1.32 2 0 2 1 0 1 18527.49 0.2 1 18442.23 -0.05 2 0 2 1 0 1 18527.49 -0.07 18442.23 0.13 2 1 1 1 1 0 18691.75 -0.72 18601.94 0.1 1 2 1 1 1 1 0 18692.77 0.30 2 1 1 1 1 0 18700.99 -0.24 18607.06 -0.70 2 1 1 2 0 2 22456.1 1 0.03 221 16.60 0.26 2 1 1 2 0 2 2243 1.14 0.00 22097.42 0.24 2 1 2 1 1 1 18358.61 0.28 18281.70 0.7 1 2 1 2 1 1 1 18367.54 0.42 18286.98 -.0.06 2 1 2 1 1 1 18368.48 1.36 3 0 3 2 0 2 27787.92 0.26 27660.28 -0.05 3 0 3 2 0 2 27787.92 -0.09 27660.28 0.11 3 1 2 2 1 1 2805 1.94 -0.11 27910.89 -0.51 3 1 2 2 1 1 28052.72 -0.27 2791 1.42 --0.13 3 1 2 3 0 3 22720.39 -0.08 22367.42 0.02 3 1 2 3 0 3 22696.28 0.16 22348.57 0.02 3 1 3 2 1 2 27533.54 -0.03 27419.10 0.1 1 3 1 3 2 1 2 27534.61 0.05 27419.75 0.43 3 2 1 2 2 0 27802.08 -0.51 27673.64 -1.25 3 2 1 2 2 0 27802.08 -0.90 27673.64 -1.21 3 2 2 2 2 1 27802.08 1.08 27673.64 1.38 3 2 2 2 2 1 27802.08 0.62 27673.64 1.48 4 0 4 3 0 3 37043.93 -0.19 36874.51 --0.17 4 0 4 3 0 3 37044.37 -0.10 36874.51 --0.17 4 1 3 3 1 2 37401.50 -0.16 37213.1 1 --0.34 4 1 3 3 1 2 37401.94 -0.09 3721 3.11 --0.33 4 1 3 4 0 4 23077.77 -0.24 22706.11 --0.06 4 1 3 4 0 4 23053.55 -0.13 22687.23 -0.07 4 1 4 3 1 3 36707.96 -0.20 36555.74 -0.07 4 1 4 3 1 3 36708.62 -0.03 36556.17 0.16 4 2 2 3 2 1 37070.35 -0.59 36898.98 --2.19 4 2 2 3 2 1 37071.67 -0.28 36900.00 1.75 4 2 3 3 2 2 37067.33 0.33 36896.27 1.62 4 2 3 3 2 2 37068.38 0.18 36897.47 2.37 4 3 1 3 3 0 37080.77 0.2 1 36908.94 0.02 4 3 1 3 3 0 37080.77 -0.07 36908.94 -0.08 4 3 2 3 3 1 37080.77 0.22 36908.94 0.02 4 3 2 3 3 1 37080.77 -0.06 36908.94 -0.07 5 0 5 4 1 4 24955.1 3 0.33 25023.88 0.12 5 0 5 4 1 4 24979.33 0.16 25042.78 0.40 5 1 4 5 0 5 23531.10 0.09 23 134.98 0.06 5 1 4 5 0 5 23506.68 0.1 1 231 16.00 -0.08 6 0 6 5 1 5 3461 3.95 -0.08 34620.52 0.03 6 0 6 5 1 5 34639.36 --0.20 6 1 5 6 0 6 24082.90 -0.12 23657.30 --0.06 6 1 5 6 0 6 24058.36 -0.06 23638.19 -0.06 7 1 6 7 0 7 24738.39 -0.04 24277.17 0.00 7 1 6 7 0 7 247 13.6 1 -0.02 24257.9 1 0.01 8 1 7 8 0 8 25502.27 0.0 1 24999.18 0.01 8 1 7 8 0 8 25477.29 0.06 24979.69 0.00 9 1 8 9 0 9 26380.26 0.05 25828.63 0.03 9 1 8 9 0 9 26354.94 0.02 25808.97 0.08 10 1 9 10 0 10 27378.56 0.10 26771.27 0.06 10 1 9 10 0 10 27352.96 0.08 26751.31 0.07 11 1 10 11 0 11 28503.64 0.01 27833.21 0.04 11 1 10 11 0 11 28477.72 -0.01 278 12.94 0.02 12 1 11 12 0 12 29762.64 0.02 29020.99 0.03 12 1 11 12 0 12 29736.36 -0.01 29000.42 0.03 13 1 12 13 0 13 31162.50 0.00 30341.20 .-0.03 13 1 12 13 0 13 31135.83 -0.01 30320.33 0.00 14 1 13 14 0 14 327 10.24 -0.02 3 1800.64 .-0.01 14 1 13 14 0 14 32683.15 -0.01 31779.36 0.0 1 15 1 14 15 0 15 34412.62 -0.04 33405.69 .-0.04 15 1 14 15 0 15 34385.06 -0.02 33384.01 -0.04 16 1 15 16 0 16 36275.95 -0.03 35 162.59 .-0.02 16 1 15 16 0 16 36247.89 0.00 35 140.43 -0.06 17 1 16 17 0 17 38305.84 0.04 37076.96 0.03 17 1 16 17 0 17 38277.23 0.01 37054.34 0.05 f0.05 MHz.Calculated frequencies from the constants of Table 6. The centres are deduced from the ''N-quadrupole analysis (Table 4) and methyl barrier analysis (Table 8). J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 6 gauche-Nitrosoethane: rotational constants (MHz), distortion constants (kHz)," torsional parameters (MHz) and ''N-quadrupole coupling constants (MHz), errors are lo from the fitting procedure CH,CH,NO CH,CH,"NO CH,CH,N'*O 125.85 (49) 48.1 130.35 (59) 31.2 123 32.6' (+I A B C 268 12.05 (18) 4704.073 (49) 4560.268 (26) 26472.06 (1 3) 4686.696 (35) 4535.1 10 (20) 26501' 4479.59 (17) 4358.665 (69) 11.4 (14) 12.94 (82) -d -334.0 (71) 334.5 (74) 167.2 (29) -321.6 (44) 321.6 (44) 159.2 (2) -316.5 -(63) d -d 0.0' 0.0' 0.0' 26808.75 (1 8) 26462.43 (13) 26501' 4704.147 (62) 4686.602 (34) 4479.47 (1 7) 4560.349 (37) 4535.085 (20) 4358.647 (69) 13.0 (20) 10.78 (81) d- 338.0 (78) 165.6 (29) -336.7 (75) -320.6 (45) 320.6 (45) 160.5 (19) -320.6 -(62)d -d 0.0" 0.0" 0.0" 3.518 (40) 'Watson's A reduction Ir representation.'See text for details. ' zero. remaining parameters C-N, LCCN and LCNO were then calculated by least-squares fitting.The structure is given in Table 9. gauche-CH, CH, NO Again with the limited isotopic data available it is necessary to assume some of the structural parameters. It is reasonable to assume that the most important structural differences between the cis and gauche conformers (apart from the dihe- dral angle) will be the atoms in the heavy-atom framework, as for 3-fl~oropropene~~ and but-l-ene.22 Therefore, the ethyl fragment of the molecule and the C-N and N-0 bond lengths were assumed to be the same as for cis nitrosoethane and the dihedral angle (a),the LCCN and the LCNO angles were fitted to the observed isotopic shifts. The results are shown in Table 9. Discussion It is evident that microwave studies of molecular systems exhibiting rotational isomerism can provide a vast amount of structural information.The present study of nitrosoethane has yielded several interesting results. Of particular impor- tance is the conformational problem where we have clearly shown the existence of two eclipsed conformers, cis-and gauche-C2H,N0. The cis conformer was found to have a plane of symmetry and to behave as a straightforward asymmetric-top molecule. The gauche exists in two equivalent enantiomorphic forms and quantum mechanical tunnelling between the forms affects certain aspects of the gauche spec-trum. A full consideration of the excited torsional states and potential function will be given in a further paper. No inter-action effects between the cis and gauche forms have been observed in their microwave spectra, allowing the molecular properties to be reported here individually for the two con- formers isolated in their respective potential minima.The structure of cis-nitrosoethane is closely similar to that of nitrosomethane. The N=O bond lengths are the same with the central C-N bond lengthening by ca. 0.01 A in nitrosoethane. More significantly, LCCN opens up by ca. 5" from the corresponding LHCN in nitrosomethane; the effect Calculated from structure. Constrained to "N values. " 6, constrained to for LCNO is less, ca. 0.6". The opening up of the LCCN angle in the cis is shown to be all the more remarkable by being ca. 8" larger than that in the gauche conformer. The difference in angles (8 2") is clearly established, notwith- standing the number of assumptions involved in the structur- al calculation. This structural change in the cis conformer is believed not to arise from steric causes for two reasons.First, the methyl barriers for the two conformers are identical within experimental error. Steric interaction between the methyl group and cis oxygen might be expected to increase the barrier in the cis form. In contrast, V3 in isoelectronic but-l-ene is increased from 13.22 kJ mol-' in the gauche to 16.69 kJ mol-' in the cis conformer, presumably owing to steric repulsion between out-of-plane methyl hydrogen atoms and the closest vinyl hydrogen.22 Secondly, the cis conformer is more stable than the gauche conformer by 2.1 (4) kJ mol- ', which again would be inconsistent with steric hindrance.It seems more likely that the structural change in the cis is associated with the planarity of the heavy-atom framework, i.e. a conjugative mechanism allowing some delocalisation of n electrons to be maximised via the planar framework. The 8" structural relaxation occurs almost entirely at the LCCN which formally involves an sp3 carbon; the LCNO with an sp2 hybridised nitrogen atom is virtually the same in the cis and gauche forms and only 1" larger than that in nitro- somethane. Comparison with isolectronic molecules is of interest. In but-l-ene22 the CH3-CH2-CHCH (sp3) angle opens up by 2.7", while the CH,CH2-CH=CH (sp2) angle increases only 1.3" on going from the gauche to the cis form.In 3-fl~oropropene,~~ the LCCC increases by 3.0" between the gauche and cis conformations, whereas L FCC increases slightly by 0.8". In cis-propanal,6 the LCCC opens up by 2" relative to the gauche structure, in constrast to the 8" for LCCN in nitrosoethane. The dihedral angle in gauche-nitrosoethane (123.6") is probably smaller than that in gauche-propanal(128.2"). The hybridisation of the atoms forming the central axis of internal rotation is a useful predictor of which of the possible conformations will be stable. Nitrosoethane with internal rotation about an sp3-sp2 (C-N) bond results in stable cis and gauche forms as in propana16 and other cases. sp3-sp3 J. CHEM. SOC. FARADAY TRANS., 1994, VOL.90 Table 7 (a) Methyl group internal rotation splitting measurements (MHz) and (b)barrier parameters for cis-and gauche-nitrosoethane; the errors are la from the fitting procedure CH3CH,' 5N0 CH,CH,NO J K, K, J K, Kc obs obs-calc obs obs-calc cis 23 6 17 23 6 18 A 24 653.73 0.2 1 -0.04 E 24 653.52 24 6 18 24 6 19 A 34 792.26 0.34 0.02 E 34 79 1.92 27 7 20 27 7 21 A 25 32 1.43 0.3 1 0.04 E 25 321.12 28 7 21 28 7 22 A 35 739.60 0.34 -0.00 E 35 739.26 31 8 23 31 8 24 A 25 462.10 0.26 -0.02 E 25 461.84 gauche 11 1 10 11 0 11 A 27 833.38 0.25 -0.02 28 503.85 0.32 0.0 1 E 27 833.13 28 503.53 A 27 8 13.13 0.28 0.01 28 477.93 0.32 0.00 E 27 812.85 28 477.62 12 1 11 12 0 12 A 29 021.19 0.30 0.00 29 762.87 0.34 -0.01 E 29 020.89 29 762.53 A 29 000.62 0.30 0.00 29 736.59 0.35 0.01 E 29 W.32 29 736.24 13 1 12 13 0 13 A 30 341.43 0.35 0.02 31 162.75 0.37 -0.01 E 30 341.08 31 162.38 A 30 320.56 0.35 0.02 31 136.08 0.38 0.00 E 30 320.21 31 162.75 14 1 13 14 0 14 A 31 800.87 0.34 -0.02 31 135.71 0.41 0.00 E 31 800.53 32 710.51 A 31 779.57 0.32 -0.04 32 710.10 0.41 0.00 E 31 779.25 32 683.01 15 1 14 15 0 15 A 33 405.96 0.40 0.01 34 412.91 0.44 -0.01 E 33 405.56 34412.47 A 33 384.28 0.41 0.02 34 385.36 0.45 0.01 E 33 383.87 34 384.9 1 16 1 15 16 0 16 A 35 162.86 0.41 -0.02 36 276.27 0.49 0.00 E 35 162.45 36 275.79 A 35 140.70 0.40 0.03 36 248.22 0.49 0.00 E 35 140.30 36 247.72 17 1 16 17 0 17 A 37 077.27 0.47 0.00 38 306.19 0.52 -0.01 E 37 076.80 38 305.67 A 37 054.67 0.50 0.03 38 277.58 0.53 -0.01 E 37 054.17 38 277.06 - (b)Bamer parameters for nitrosoethane ~~ ~~ cis gauche 15~0 NO 15~0 ~~ F/GHz 170.44 180.57 180.29 S 71.35 (42) 66.821 (37) 67.76 (13) I/,/kJ mol-' 10.9 (3) 10.8 (3) 10.9 (3) leads to stable trans and gauche conformers, while for sp2-sp2 CH, +C bond moment contributes only ca.0.1 D to the usually only the trans is observed. Table 10 gives a number of dipole moment and that the dipole moment of nitrosoethane examples.Further discussion of the isomerism will be given is constrained close to the CNO plane. In the nitroso com- in the paper on the potential function. The charge properties pounds the dipole moment direction approximately bisects determined in the present work are of interest. Accurate the N-0, lone pair directions, whereas in the aldehydes the dipole moments have been obtained for both rotamers and dipole moment direction is close to the C=O bond direction. are given in Table 11 with some related nitroso compounds The classical lone pair direction is also an important refer- and isoelectronic aldehydes. The dipole moments tend to ence axis for the I4N quadrupole coupling constants. Con- increase with increasing methyl substitution. Ethanal is sidering cis-nitrosoethane, only 1, with its axis normal to the exceptional in this respect. Comparison of dipole orientations C,plane is a principal axis component in both the inertial with that determined in nitrosomethane7.* shows that the tensor and the quadrupole coupling tensor.Using a simple dipole moment in cis-nitrosomethane lies within 7" of the Townes-Dailey appr~ach,~' the zCcvalues of HNO, CH,NO C-N bond direction (see Fig. 6). The dipole components of and cis-C,H,NO can be used to compare the pn orbital the gauche conformer are well predicted from the cis dipole populations n, (see Table 12). There is no obvious trend in moment with this orientation; this indicates that the the effective out-of-plane p population, with substitution with J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 8 (a) Stark coefficients (MHz kV-, m2) and (6) dipole moments (D) of cis-and gauche-nitrosoethane; the errors are la from the fitting procedure J K, K, J K, K, M v Av/E obs -calc ~ ~~ cis-CH ,CH ,5N0 10100 00 64.8 (2) 0.2 31321 20 -1.232 (3) 0.001 32122 00 5.283 (9) -0.006 gauche-CH ,CH,' 5N0 2 3 0 0 2 3 1 2 0 0 l 2 o 0 + f -26.0 (1) 4.13 (2) 0.0 -0.03 2 2 1 1 1 1 1 1 1 1 1 o 1 2 0 o 0 f * -+ - 5.66 (1) 10.37 (9) 11.37 (5) 15.7 (2) 15.4 (4) -0.03 0.06 0.00 0.0 -0.03 (6) Dipole moments (D) of nitrosoethane cis gauche Pa 2.316 (2) 2.288 (4) 0.623 (4) 0.814 (5) Pb 0.460 (9)Pe PZ 2.398 (2) 2.471 (4) tan -'(p,/pb)/degrees 74.9 Table 9 Structural parameters (bond lengths in A, bond angles in degrees) of cis- and gauche-nitrosoethane; the errors are la from the fitting procedure cis gauche ref.-0N-0 1.213 (6) a-C-N 1.490 (9) LCCN 116.3 (7) 108.2( 5) LCNO 113.7 (3) 114.3 (4) a(CN0) 0.0 123.6 (9) C-CH, (1.523) (1.523) 5 C-H (1.092) (1.092) LHCH; CH, (105.2) (105.2) 22 'Constrained to the cis values. Table 10 Stable conformations' of various molecules (cis) (trans) cis gauche gauche trans azW az60° azl20" azl80" ref. sp2-sp2 CH ,=CHCF=CH , 24 CH,=CHC(CH ,)=CH, 25 CH,=CHCH=CF, 26 CH,=C(CH,)CH=CF, 27 CH,=CHCHO 28 CH,=CHCFO Jb 29 sp3-sp2 CH ,CH ,CH=CH , 22 CH ,FCH=CH , 23 CH,FCF=CH, 30 CHF,CHCH, 31 CH,CH,CHO 32 CH,CH,CFO 33 CH,CH,NO 1 sp3-sp3 CH,CH2CH,F 34 CH3CH ,CH ,C1 35 CH ,FCH F 36 CH,CH,CH,OH 37 CH,CH,ONO, 38 'Gas-phase conformers observed by microwave spectroscopy.cis conformer stabilised by an attractive H- * OFinteraction. 2181 Table 11 Comparison of dipole moments for CNO and CCHO molecules molecule PP ref. CH,NO 2.320 8 cis-CH ,CH ,NO 2.398 gauche-CH ,CH,NO 2.471 (CH,),CNO 2.57 39 HCHO 2.35 40 CH,CHO 2.75 8 cis-CH,CH,CHO 2.53 6 gauche-CH ,CH ,CHO 2.86 6 trans-(CH,),CHCHO 2.86 41 gauche-(CH,),CHCHO 2.69 41 (CH,),CCHO 2.717 42 Table 12 Quadrupole coupling constants (MHz) of some nitro- soalkanes and effective out-of-plane p-orbital populations at nitro- gen molecule XCC nc ref. HNO 5.10 0.8 1 4394 CH,NO 5.52 0.77 798 cis-CH,CH,NO 4.92 0.83 CH,NO having the smallest value.The similarity of the coupling tensors in CH,NO and cis-C,H,NO may be used to calculate an approximate principal-axis quadrupole coup- ling tensor in the two molecules. A rotation of zaaand Xbb for CH,NO into the inertial axis system of cis-C,H,NO gives xab = 3.29 MHz for cis-C,H,NO and xab = -0.45 MHz for CH,NO. The quadrupole coupling principal axis approx- imately bisects the CNO angle in both molecules (within 2"), presumably close to the lone-pair direction. The reasonable result for this calculation allows us to probe the 14N coupling information obtained for gauche-C,H,NO, particularly in view of the dipole moment comparison above, implying the similarity of the charge distribution in the CNO plane.The cis quadrupole coupling constants were rotated into the gauche inertial axis system assuming that the quadrupole coupling tensor axis system is unchanged and still in the CNO plane. This calculation leads to a value of (Xbb -x,) = 1 MHz, significantly smaller than the experimental value of 3.518 (40)MHz. The experimental value is an effective one derived from one set of transitions without taking into account effects of torsional averaging. There is ample evi- dence of unusual quadrupole splitting elsewhere in the spec- Ib Q\I W Fig. 6 cis structure (see Table 9) with dipole moment orientation (distances in A) 2182 J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 trum attributable to the strong mixing of the rotational states in the 0, and 0-torsional substates.Otherwise, the differ- ence implies a significant change in the quadrupole tensor for the two rotamers. 19 20 21 A. P. Cox, I. C. Ewart and W. M. Stigliani, J. Chem. SOC., Faraday Trans. 2, 1975,71,504. E. Hirota, T. Hirooka and Y.Morino, J. Mol. Spectrosc., 1968, 26, 351. J. Kraitchman, Am. J. Phys., 1953,21, 17. We thank SERC for research funding and research student- 22 S. Kondo, E. Hirota and Y. Morino, J. Mol. Spectrosc., 1968,28, 471. ships. We also thank Professor B. G. Gowenlock for his 23 E. Hirota, J. Chem. Phys., 1965,42,2071. interest in this work. 24 D. R. Lide Jr., J. Chem. Phys., 1962,37,2074. 25 D. R. Lide Jr. and M. Jen, J. Chem. Phys., 1964,40,252. References 26 27 R.A. Beaudet, J. Chem. Phys., 1965,42,3758. Y.S. Huang and R. A. Beaudet, J. Mol. Spectrosc., 1970,34,1. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 M. Maier, Ph.D. Thesis, University of Sussex, 1977. H. W. Kroto, Chem. SOC. Rev., 1982,11,435. J. A. Hardy, A. P. Cox and H. Dreizler, Z. Naturforsch, Teil A, 1984,37,1671. J. Randell, A. P. Cox and H. Dreizler, 2. Naturforsch, Teil A, 1987,42,957. J. Randell, A. P. Cox, K. W. Hillig, M. Imachi, M. S. LaBarge and R. L. Kuczkowski, 2. Naturforsch, Teil A, 1988,43,271. J. Randell, J. A. Hardy and A. P. Cox, J. Chem. SOC., Faraday Trans. 2, 1988,84, 1199. D. Coffey, C. 0. Britt and J. Boggs, J. Chem. Phys., 1968, 49, 591. P. H. Turner and A. P. Cox, J. Chem. SOC., Faraday Trans. 2, 1978,74, 533. B. G.Gowenlock and J. Trotman, J. Chem. SOC., 1955,4190. F. J. Wodarczyk and E. B. Wilson, J. Mol. Spectrosc., 1971, 37, 445. B. G. Gowenlock and J. Trotman, J. Chem. SOC.,1956,1670. H. M. Heise, H. Lutz and H. Dreizler, Z. Naturforsch, Teil A, 1974,29,1345. J. K. Bragg and S. Golden, Phys. Rev., 1949,75,753. C. R. Quade and C. C. Lin, J. Chem. Phys., 1963,38,540. H. M. Pickett, J. Chem. Phys., 1972,56,1715. L. Halonen and P. H. Turner, personal communication. H. M. Pickett and H. L. Strauss, J. Am. Chem. SOC., 1970, 92, 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 E. A. Cherniak and C. C. Costain, J. Chem. Phys., 1966,45, 104. J. J. Keirns and R.F. Curl Jr., J. Chem. Phys., 1968,48,3773. A. D. English, L. H. Scharpen, K. M. Ewool, H. L. Strauss and D. 0.Harris, J. Mol. Spectrosc., 1976,60,210. I. Botskor and E. Hirota, J. Mol. Spectrosc., 1976,61,79. S. S. Butcher and E. B. Wilson Jr., J. Chem. Phys., 1964, 40, 1671. 0. L. Stiefvater and E. B. Wilson Jr., J. Chem. Phys., 1969, 50, 5385. E. Hirota, J. Chem. Phys., 1962,37,283. T. N. Sarachman, J. Chem. Phys., 1963,39,469. S. S. Butcher, R. A. Cohen and T. C. Rounds, J. Chem. Phys., 1971,54,4123. A. A. Abdurakhmanov, R. A. Ragimova and L. M. Imanov, Phys. Lett. A, 1970,32, 123. D. G. Scroggin, J. M. Riveros and E. B. Wilson Jr., J. Chem. Phys., 1974,60,1376. M. J. Corkill, Ph.D. Thesis, University of Bristol, 1978. J. N. Shoolery and A. H. Sharbaugh, Phys. Rev., 1951,82,95. 0.L. Stiefvater,2.Naturforsch, Teil A, 1986,41,482. A. P. Cox, A. D. Couch, K. W. Hillig 11, M. S. LaBarge and R. L. Kuczkowski, J. Chem. SOC.,Faraday Trans., 1991,87,2689. S. Saito and K. Takagi, J. Mol. Spectrosc., 1973,47,99. F. W. Dalby, Can. J. Phys., 1958,36, 1336. C. H. Tomes and B. P. Dailey, J. Chem. Phys., 1949,17,782. 728 1. 18 R. C. Woods, J. Mol. Spectrosc., 1966,21,4. Paper 4/01444H; Receioed 11th March, 1994

ISSN:0956-5000    

DOI:10.1039/FT9949002171

出版商:RSC    

年代:1994

数据来源: RSC

ISSN:0956-5000    

DOI:10.1039/FT9949002183

出版商:RSC    

年代:1994

数据来源: RSC

摘要:

J. CHEM. SOC. FARADAY TRANS., 1994, 90(15), 2189-2200 2189 Dynamics Calculations and Isotopic Effect in 0 + OH(D) +0, + H(D) at Low Energies Jorge M. C. Marques, Wenli Wang and Antonio J. C. Varandas” Departamento de Quimica, Universidade de Coimbra , P3049 Coimbra Codex, Portugal The deuterium isotopic effect in the gas-phase reaction O(3P) + OH(211)4O2(R3C,-) + H(’S) has been studied in detail over the range of translational energies 0.125 < E,,/kcal mol-’ < 1.0, which correspond to the tem- perature range 40 < T/K < 340. State-to-state dynamics calculations covering the range of rotational quantum numbers 0 <j < 14 have been carried out using both the quasi-classical internal energy quantum mechanical threshold (QCT-IEQMT) and quasi-classical rotational and vibrational energy quantum mechanical threshold (QCT-NVEQMT) methods.The QCT-NVEQMT calculations show an inversion of population in the vibrational distributions of the product 0, molecules, with v’ = 1 being the most populated level. It is also found, by both the QCT-IEQMT and QCT-NVEQMT methods, that the initial rotational state of the reactant OH(D) molecule plays an important role in determining non-statistical recrossing. All calculations used the double many-body expansion (DMBE IV) potential-energy surface for ground-state HO,. The magnitude of the isotopic effect is shown to depend to some extent on the approach used for the dynamics calculations. The contributions of the various terms to the thermal rate coefficient are also examined.1. Introduction The gas-phase reaction O(3P)+ OH(%) -+O,(g 3Zg-)+ H(’S) plays a major role in atmospheric’*2 and extra- terrestrial chemistry,* while its reverse, H(’S)+ Oz(x3C,-) -P OH(’H) + O(3P),is the single most impor- tant reaction in the oxidation mechanisms of H, and most hydrocarbon fuels. Therefore, it is not surprising that these reactions have been the subject of many experimental3-I3 and theoretical’ 4-3 studies over a wide range of tem-peratures; the reader is referred to previous articles3 1732*35 for further references to these experimental studies and a survey of their most important conclusions. Theoretically, the 0 + OH reaction provides a prototype for atom-diatom exothermic reactions occurring over bar-rierless potential-energy surfaces with deep chemical wells for which long-range forces are known to play a major role in the dynamics of the approaching reactants.Moreover, because of a high endothermicity (AH = 16.4 kcal mol-’), the thermal rate coefficient of the H + 0, reverse reaction is usually estimated from the equilibrium constant and the corresponding rate coefficient for the title reaction. In fact, the 0 + OH reaction is more illuminating for reaction dynamics studies since it displays more clearly the dynamical aspects related to the topographical details of the potential- energy surface, especially at low energies. surface of HO,(’A”) have also been used to study the dynamics of the 0 + OH reaction,’9~22~26-28~31-33and its reverse.’5, ’7*2593 ’934*3 Of these studies, some have employed26.31-33 93 5 the reliable DMBE IV26 potential- energy surface for the ground electronic state of the hydro- peroxyl radical, obtained from the double many-body expan~ion~~-~~method (for recent developments, see ref.39-41). Conversely, rather few studies31,42-48 have been published for the deuteriated reaction analogue. Related to the present work are our own recent theoretical ~tudies~’,~~ of the dynamics and kinetics of the title deuteriated reaction over a wide range of temperatures, also employing the DMBE IVZ6 potential-energy surface. Specifically, ref. 31 provides a study of the isotopic effect on the thermal rate coefficient for both the direct and reverse title reactions using the QCT and QCT-IEQMT methods (temperature ranges are 250 < T/K < 3000 and lo00 < T/K < 3000 for the direct and reverse reactions, respectively) ; see also this reference for a study of the isotopic effect in the equilibrium constant.In addition, state-to-state QCT-IEQMT calculations of the 0 + OD reaction over the range of translational energies 0.125 < E,,/kcal mol-’ < 1.0 have been reported recently48 using the DMBE IV potential-energy surface. Quantum zero-point energy threshold effects are known to be important in assessing chemical reactivity, and cannot be adequately described by classical mechanics. Because of this, Besides various capture theories, both ~lassi~a1~~~~~*~~,~~ simple classical models have been suggested to mimic such theand quantum chemi~al,’~.~~ title reaction has been studied using quasi-classical trajectory 1*32 and variational transition-state theory.l6 Amongst the clas- sical capture theories, Davidsson and N~man~~ used the so-called extended Langevin model ;another approach suggested by one of us23,30(named CES + R, capture-energy-sudden plus recrossing) also accounted approximately for the possi- bility of trajectories recrossing back to reactants after having formed an HO; complex. In turn, Clary and Werner” reported quantum mechanical scattering calculations using an adiabatic capture infinite order sudden approximation (ACIOSA) theory, while Graff and Wagner” studied the fine structure effects and long-range forces in the 0-OH poten-tial energy surface and estimated thermal rate coefficients using the ACIOSA method.Trajectory calculations employing the full potential-energy effects. One of the first attempts to include quantum effects in classical dynamics calculations goes back to the traditional quasiclassical trajectory (QCT) where the tra- jectory is initialized with the reactant molecule in a specific quantum vibrational-rotational state. Although good results can be obtained from the QCT method for real chemical systems, it ignores any quantum threshold effects such as the vibrational zero-point energy during the collisional process. Approaches that preserve the simplicity of the QCT method but constrain ‘non-actively ’ the zero-point energy in the products have also been sugge~ted.’~*~ 1*32,35In particular, a whole hierarchy of such procedures ranging from QCT- IEQMT to QCT-NVEQMT methods has recently been tested35 on the reaction H(’S) + 0,(83Cg-)4OH(,lT)+ O(3P).Note that in QCT-NVEQMT35one also accounts approximately for the fact that a non-C diatomic molecule J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 1 Isotopic effect on capture and reactive cross-sections 0.125 0 8.0 7.75 105.49 103.47 1.02 102.94 102.52 1 .00 1 7.5 7.25 144.32 135.96 1.06 138.19 131.00 1.05 151.09 143.66 1.05 150.50 126.87 1.19 2 7.5 7.25 144.32 135.13 1.07 130.18 125.50 1.04 3 7.5 7.25 145.20 142.56 1.02 118.69 129.63 0.92 4 7.5 7.25 150.50 141.46 1.06 1 13.69 1 18.62 0.96 149.32 140.64 1.06 14.78 119.99 1.17 5 7.25 7.25 146.69 142.01 1.03 108.44 106.23 1.02 6 - 7.25 - 145.59 - - 104.03 - 10 7.5 7.25 139.49 145.3 1 0.96 89.42 83.94 1.06 144.02 141.46 1.02 121.34 99.08 1.22 14 - 7.25 - 143.66 - - 83.66 - 0.25 0 7.0 6.75 75.17 65.13 1.15 72.35 62.50 1.16 1 6.5 6.5 103.31 90.70 1.14 97.34 84.73 1.15 109.50 99.99 1.10 109.06 83.84 1.30 2 6.25 6.5 104.92 98.99 1.06 92.45 90.48 1.02 3 6.25 6.5 104.11 105.30 0.99 84.27 90.48 0.93 4 6.25 6.5 102.67 103.53 0.99 74.04 84.5 1 0.88 100.83 101.32 1 .00 95.3 1 83.18 1.14 5 6.25 6.5 100.63 101.32 0.99 70.77 72.56 0.98 6 - 6.5 - 98.22 - - 69.90 - 10 6.25 6.5 98.99 94.90 1.04 60.1 3 53.3 1 1.13 102.27 94.90 1.08 87.54 67.25 1.30 14 - 6.5 - 100.66 - - 58.18 - 0.50 1 5.25 - 66.10 - - 60.18 - - 5.5 69.13 59.87 1.15 68.12 51.16 1.33 4 5.0 - 63.62 - - 47.39 - - 5.0 59.04 61.26 0.96 54.72 49.09 1.1 1 10 5.5 - 61.61 - - 41.50 - - 5.0 62.25 58.12 1.07 53.38 39.27 1.36 1.o 0 4.25 4.5 29.70 30.64 0.97 25.44 25.23 1.01 1 4.5 4.5 42.62 39.97 1.07 37.85 34.04 1.11 44.96 34.88 1.29 42.73 28.84 1.48 2 4.5 4.75 46.86 43.24 1.08 37.32 36.27 1.03 3 4.25 4.5 45.49 43.90 1.04 33.95 34.88 0.97 4 4.25 4.5 43.69 46.97 0.93 3 1.78 35.20 0.90 42.37 44.53 0.95 37.92 34.78 1.09 5 4.25 4.5 44.45 45.59 0.97 29.79 31.60 0.93 6 - 4.5 - 44.32 - - 28.94 - 10 4.25 4.25 42.56 43.69 0.97 27.99 22.41 1.25 43.22 39.82 1.08 35.47 26.01 1.36 14 - 4.25 - 44.36 - - 24.87 - The amplitudes of the error bars are shown in Fig.12 and 14. Note that, for j = 1, 4 and 10, the second entry refers to the QCT-NVEQMT calculations; all other entries refer to the QCT-IEQMT method. always notates in accordance with Hund's rules; for the spe- 2. Computational Procedure cific case of the title reaction, OH has been assumed to be a Hund's case (b) molecule. In addition, 'active' models have 2.1 Survey of Methods been ~uggested~~-~~ to control the zero-point energy flow Since the methods used in this work have been described in amongst normal modes over the whole trajectory; in these detail el~ewhere,~~,~~ only the more relevant aspects will be methods an instantaneous external force is turned on to presented here.As for the traditional QCT appr~ach,~'-~' avoid a specific mode energy falling below the corresponding the cross-sections are obtained from zero-point energy. Preliminary calculations for the title reac- tion using one of these models have also been reported.54 The major aim of the present work is to report a detailed state-to-state dynamics study of the isotopic substitution for where x = r or c stand for reactive and capture cross-the title system, covering translational energies in the range sections, respectively, and the remaining symbols have their 0.125 < E,,/kcal rno1-l < 1.0.Besides QCT-IEQMT usual meaning (e.g. N, is the number of reactive trajectories we present novel QCT-NVEQMT calculations out of a total of N trajectories considered for the statistical res~lts,~~,~* for both the 0 + OH (u = 0, j)and 0 + OD (u = 0, j)reac-analysis). Similarly, the 68% confidence intervals are given by tions. Moreover, we examine many attributes of the title reac- tions : opacity functions, reactive cross-sections as a function of the initial translational energy and rotational quantum number of the reactant diatomic, thermal rate coefficients, with N,, ox and Ao, depending on the initial state of the recrossing factors as a function of the initial translational system.Although the total number of trajectories, N, may energy and temperature, vibrational and rotational distribu- also be chosen to depend on the same variables, this depen- tions, and angular distributions. Finally, we study the effect dence is clearly arbitrary and, hence, it is not explicitly stated of isotopic substitution using both the QCT-IEQMT and in the aforementioned formulae. QCT-NVEQMT methods. The thermal rate coefficient is obtained by averaging over J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 the appropriate distributions of the vibrational-rotational states. Thus, k(T) = QidQi: C (2+ l)exP(--uj/kWu,4T) (3) 0, j where Qviband Q,,, are the vibrational and rotational parti- tion functions of the reactant diatomics, and kUj is the specific thermal rate coefficients obtained, as usual, by where k is the Boltzmann constant and ,u the reduced mass of an atom-diatomic molecule.In turn, f(T) is the electronic degeneracy factor’ given by f (T)= 2 [5 + 3 exp( -y)+ exp( -3][2 + 2 exp( -31 (5) which accounts in the usual way for the electronic degener- acies of O(3P)+ OH(DX211). Since the traditional QCT method does not account ad- equately for zero-point energy threshold effects, we use here two variant^^,,^^ of that method which approximately mimic such quantum effects without introducing any significant complication into the usual trajectory methodology. These ‘non-active’ methods consist basically of rerunning every unphysical trajectory (i.e.any trajectory that reaches prod- ucts or reforms reactants failing to satisfy the associated quantum energy thresholds) until a physical one is obtained, keeping unaltered the initial randomly generated value of impact parameter b. In general, one warrants by this pro- cedure the correct distributions for the randomly chosen vari- ables, especially those expected to play a key role in controlling the dynamics of the chemical reaction. Therefore, in the QCT-IEQMT3, method, we compare the internal and zero-point energies of the diatomic molecule at the end of the trajectory, while in the QCT-NVEQMT35 method we con- sider the quantum thresholds for both the vibrational and rotational energies. Of course, QCT-NVEQMT is more restrictive than QCT-IEQMT, although both approaches control only the quantum energy thresholds at the end of the trajectory.2.2 Technical Specifications All technicalities referring to the QCT-IEQMT calculations are the same as in previous work,32 and hence only those rela- ting to the QCT-NVEQMT calculations need to be given here. For the latter, batches of 600 physical trajectories have been run for E,, = 0.125, 0.25, 0.50 and 1.0 kcal mol- ’,and j = 1, 4 and 10. To select the maximum value of the impact parameter for which there is reaction, b,,,, we followed the usual procedure by computing batches of 40 or 60 trajec-tories for fixed values of b. The values of b,,, so obtained are given in columns three and four of Table 1.Note that, for simplicity, identical values of b,,, have been assumed for both the QCT-IEQMT and QCT-NVEQMT calculations at a specific set of initial conditions (&, j). 3. Collisional Details The energetic features of both O(3P)+ OH(,H) -+ 0,(8’Xg-)+ H(’S) and O(3P)+ OD(,lI) +0,(83Zg-) + D(,S) reac-A B 1.2 kcal mol-’1 distance Fig. 1 Energetic features of the title system. A, Diatomic curve for OH(D): the horizontal full lines refer to OH, while the broken ones refer to OD; (a)u = 0, j = 10, (b) u = 0,j = 0. B, Diatomic curve for 0,:u’ = 0 (a), l(b), 2 (c), 3 (4, 4 (e), 5 0,6 (g), 7 (h). Although relevant to the QCT-NVEQMT method, the j = 1 and j’ = 1 levels are not shown, since they are almost coincident with those corre- sponding to the vibrational ground states.tions are presented in Fig. 1. It is seen that, for OH in the (u = 0, j = 0) initial state, the reaction exothermicity to produce H(,S) + 0,(2 3C,-) with the diatomic in the (u’ = 0, j’ = 0) state is 16.4 kcal mol-’, while for the OD reactant molecule, the corresponding value reduces to 15.0 kcal mol-’. Thus, for OH and OD at zero translational energy, if this entire amount of energy were channelled into product vibration it would be sufficient in both cases to produce 0, in the u’ = 3 state. However, if the diatomic is in the (v = 0, j = 10) state at zero translational energy, all product channels of 0, up to u’ = 5 become open in the case of OH while, for OD, the open vibrational states go only up to u’ = 4.3.1 Opacity Function The opacity functions, reaction probability P,(Et,, u = 0,j, b) us. impact parameter b, obtained using the QCT-IEQMT and QCT-NVEQMT methods are shown in Fig. 2 and 3, respec-tively. Note that to reduce the statistical fluctuations the his- togram widths were taken as proportional to bl/,. Moreover, for low impact parameters, the reaction probability has been assumed to be zero. This is simply due to the fact that there have been no trajectories generated for such a range of impact parameters, and hence it does not mean that P, is really zero. A first glance at Fig. 2 and 3 immediately shows that, for all translational energies and rotational states in the two methods we have considered, the reaction is more effective for 0 + OH than for 0 + OD.This is true for almost the whole range of impact parameters that lead to reaction (i.e. from b = 0 to b = b,,,). Two other interesting features are worth commenting on from these figures. The first concerns the shape of the j = 1 opacity function, which, for both methods at E,, = 0.125 kcal mol-’, is seen to be a flat curve with almost maximum reactivity at all values of b [Fig. 2(a) and 3(a)]. However, for the 0 + OD reaction by the QCT-NVEQMT method [Fig. 3(a)(.--a)], the probability of reac- tion reaches its maximum value for lower impact parameters and then tends to decrease slightly until becoming zero at 2192 Fig. 2 b J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 I 1 and hence to decreasing reaction probabilities, independent of the reaction being considered and method used.Equiva- lently, we may say that to produce a given value of L (and hence a given centrifugal barrier or reaction probability), low energies have to be associated with high values of the maximum impact parameter, and, conversely, high energies require low values of b,,,. Moreover, for a given Ab, the variation of the centrifugal barrier (and hence the variation of the reaction probability) increases with the initial trans- I 1 I I lational energy.48 In addition, an increase in mass by going from 0 + OH to 0 + OD at a given b and specific initial state, leads to an increase of the orbital angular momentum (i.e. an increase of the centrifugal barrier and hence a decrease in reactivity).The value of the initial rotational quantum number also affects reactivity, although through a different mechanism (for the dependence of the reaction probability on reactions with barriers, see ref. 55 and references therein). Indeed, for low values of j, the diatomic (OH or OD) can reorient to give the 0 O 4 a 0 4 a blA pacity function for the title reactions obtained by the highest chance of reaction with the approaching oxygen atom. Conversely, for j = 10 [Fig. 2(b),(6)and Fig. 3(b),(41, the approaching oxygen atom 'feels' the spherical 0-OH(D) interaction potential due to the high rotation of the diatomic CT-IEQQ = 0.125MT method. (a),(c) j = 1; (b), (d)j = 10. (a),(b) E,, molecule, and hence cannot choose its most favourable al molkc(-... .) 0 (-) 0 + OH reaction;-'; (c), (d) E,, = 1.0 kcal mol-'. + OD reaction. attacking angle. As a result, we observe a decrease in reaction probability with increasing initial value of j.48 We now examine how the opacity function varies with the = b,,,. ction.se An explanation is deferred to the end of this sub- [Fig. 2(c) and 3(c)],Instead, for E,, = 1.0 kcal mol-' method used for the statistical analysis. This is shown in Fig. 2 and 3, which show, for the 0 + OH reaction, an increase of e opacthm ity function not only shows lower reactivities, but reactivity when going from QCT-IEQMT to QCT- common anifestcreasinethodsinm to both the QCT-IEQMT and QCT-NVEQMT s also a marked tendency to decrease smoothly with g value of the impact parameter; this pattern is .These observations may be rationalized from the NVEQMT. A similar trend is not always observed for the 0 + OD reaction. In fact, a decrease in reactivity is even observed at many values of b, especially for high values of the impact parameter, as clearly seen for j = 1 at E,, = 0.125 and ct that fa the centrifugal barrier for reaction results from a 1.0 kcal mol-' [Fig. 2(a), (c) and Fig. 3(a),(c)]. This may be attributed to the slightly larger reduced mass, since the cen- cesumoment related to the orbital angular lance of the long-range interaction potential and the al energy, being btle ba trifugal barrier for large values of b (at a given translational ntrifug L = (2pE,,)'% (6) um through the expression energy) would tend to increase, providing the more restrictive QCT-NVEQMT method with a lower limit to reactivity.Conversely, for low b values, it is easy to overcome the cen- here pw is the is the atom-diatom reduced mass, and b pact parameter for the specific collision leading to reaction. trifugal barrier, and hence the QCT-NVEQMT method offers an upper limit to reactivity. Thimtra erefore, for a fixed value of b, increasing values of the onal energy lead to increasing centrifugal barriers, 3.2 Vibrational Distributions nslati In this section, we analyse the vibrational distributions of the r t product 0, molecule, pointing out the differences due to the method used, i.e. QCT-IEQMT us. QCT-NVEQMT. For comparison purposes, all distributions presented in Fig.4 and 5 have been normalized to 100. Fig. 4 shows that, for a fixed translational energy and using the QCT-IEQMT method, as j increases from 1 to 10, the distributions in u' broaden to include one extra u' state for both reactions. Nevertheless, because the OD molecule has a I lower zero-point energy than the OH molecule and a higher density of rotational states (see Fig. l), the number of popu-lated vibrational states in the products is always smaller by one or two (the latter value applies to j = 10 at 1.0 kcal mol-') for the deuteriated reaction than for the 0 + OH reaction, see Fig. 4. Also plotted for comparison in Fig. 4 are the corresponding Boltzmann curves, assuming thermal equilibration at a temperature defined by T = AE/3k; LIE is 0 Fig.3 4 a 0 4 8 b/A As in Fig. 2, but now using the QCT-NVEQMT method the reaction exothermicity, which has been calculated from the difference between the OH (OD) and 0, thermodynamic bond dissociation energies (i.e. including the corresponding zero-point energies). It is seen that, for small values of j and low translational energies, the product vibrational distribu- tions show a marked decrease with u' (this is particularly J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 I loo loo 50 k 0 100 -C > 1Q2 50 uL y. 0 100 50 0 024 602 46 V‘ Fig. 4 Vibrational product quantum-state distributions obtained by the QCT-IEQMT method, irrespective of diatomic rotational state, for the 0 + OH reaction (-) and 0 + OD reaction (---).(a)-(c) E,, = 0.125 kcal mol- ’;(d)-(f) E,, = 1.0 kcal mol-’. (a),(d)j = 1; (b), (e)j= 4;(c), cf)j = 10. Boltzmann distributions for 0 + OH (0)and 0+ OD (0). notorious for the deuteriated reaction), suggesting a nearly statistical (or indirect-type) behaviour for the involved dynamics. Although a similar decreasing dependence on u is observed for highj values, it is not unambiguous to assign a vibrational temperature in such cases. Fig. 5 shows the vibrational distributions obtained from the QCT-NVEQMT method. It is seen that the u’ = 1 state is more populated than the vibrational ground state, with this inversion of vibrational population in the products not being observed for the corresponding distributions obtained by the QCT-IEQMT method (see Fig.4). Clearly, this stems from the more restrictive requirements imposed in the QCT-NVEQMT method in assigning physical validity of the tra- jectory outcomes and may be rationalized as follows. As explained in Section 2.1, in QCT-NVEQMT a physical tra- jectory must end up with an energy E:2 2 E:2 and EYz 2 EY2,where E:2 (Ey2) is the vibrational (rotational) energy cor- responding to the ur (’j’)state of 0,. These requirements are almost always satisfied when u’ b 1, since thej = 1 rotational energy is too small to become a bottleneck in the application of this physical criterion to the product 0, molecule. However, for u’ = 0, in spite df the great exothermicity of the title reactions, it may happen that the outcome products will be formed in highly excited rotational states, and hence carry out a deficit of vibrational energy, i.e.EY < Thus, because of the high exothermicity, whenever an unphysical reactive trajectory is repeated until a physical one occurs, the tendency may be to populate the excited vibrational states of 02.Conversely, in the QCT-IEQMT approach the only restriction is that the internal energy of the products exceeds loo (c)] 2. 50 3 D L w-0 02 46 0246 V’ Fig. 5 As in Fig. 4, but for the QCT-NVEQMT method EE;. Clearly, this can be more easily achieved for any u’, since it can be done through excitation of the vibrational and/or rotational degrees of freedom.Whether the populations inversion predicted by the QCT-NVEQMT method is realis- tic cannot be verified without independent evidence from other calculations and/or experimental data. 3.3 Rotational Distributions Fig. 6 and 7 show, for the reactions 0 + OH(D) (u = 0,j = 1) +O,(u’,j’) + H(D) at E,, = 0.125 kcal mol- *,histograms of the rotational quantum number distributions in the 0, molecules for the various product vibrational states. Similar histogram representations are reported in Fig. 8 and 9 for j = 10 at the same translational energy. Fig. 6 and 8 corre-spond to the QCT-IEQMT calculations, while Fig. 7 and 9 are for QCT-NVEQMT. In all distributions the number of reactive trajectories per bin has been divided by the total number of reactive trajectories N,, and then multiplied by 100. Except for the high u’ states, for which the number of reactive trajectories is too small to be conclusive, they all show that the product rotational energy distributions resem- ble Boltzmannian distributions.For the 0 + OH reaction, using the QCT-IEQMT approach, the mean values (marked by the arrows) of the j = 1 distributions vary fromj’ x 24 for u‘ = 0 to j’ x 19 for v’ = 2, while for the 0 + OD reaction the mean values vary from j’ z26 for u’ = 0 to j’ x 17 for u’ = 2 (note that for v’ = 3 the reactivity is already too small, becoming zero for u’ = 4). In addition, for the rotational dis- tributions corresponding to j = 10, the mean value for 0 + OH ranges from j’ z 28 for u’ = 0 to j’ x 19 for u’ = 3, while for 0 + OD it ranges fromj’ sz 29 for u’ = 0 toj’ x 20 for v’ = 2 (note that for u’ = 3 and ur = 4 the reactivity is too small, being zero for u’ = 5).Thus, there is a shift of the mean J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 4 I >. C ;4 ? w-2 0 1 21 41 61 1 21 41 61i' Fig. 6 Rotational product quantum-state distributions obtained for the 0 + OH (-) and 0 + OD (a . . * -) reactions at E,, = 0.125 kcal mol-' and j = 1 (QCT-IEQMT results). uf = 0 (a),1 (b),2(c),3(4, 4 (e). Note that in all cases the jf axis is labelled from 1 to 61 with marks at intervals of 10 (only odd rotational states are allowed for 02).In this figure, and in Fig. 7-9, the solid arrows indicate the mean values of the 0 + OH distributions, while the open arrows refer to the corresponding values for 0 + OD reaction.2 0 1 21 41 61 1 21 41 i' Fig. 8 As in Fig. 6, but forj = 10,with (f)u' = 5 value associated with a given rotational distribution towards lower jf values with increasing v'. Note also that the mean value for both reactions becomes nearly the same when uf = 1,j = 1, and u' = 2,j = 10. Moreover, Fig. 6 and 8 show that, for both reactions, part of the initial rotational energy of the reactants has been converted into vibrational energy of the product 0, molecules. .. . . ......... .. hu 1: .i i .i .* :, ..! . ,.%........ ,.-. . 0 ''.'.'i ... ... . o~n,~21 41 61 1 21 41 61 1 21 41 61 1 21 41J' 1' Fig.7 As in Fig. 6, but for the QCT-NVEQMT results Fig. 9 As in Fig. 7, but forj = 10, with (f) = 5u' J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 1 xm EP .. 20 I I I II I t I -,, ......i (f) 7'--.;-1....... ..... ... ... ... ....... ......... ...... ................ i.....:Ij....... i.....; ...... ....... I0 I I -0 90 180 0 90 180 scattering angle/degrees Fig. 10 Differential cross-sections (divided by the maximum value obtained in each distribution) for the diatomic product 0, molecule (QCT-IEQMT results).(a),(c),(e)j= 1; (b),(4,cf)j = 10. (a),(b)E,, = 0.125 kcal mol-'; (c),(d)El, = 0.25 kcal mol-'; (e),cf)El, = 1.0kcal mol-'. From Fig. 6 and 7, we observe that the main differences between the distributions obtained by the QCT-IEQMT and the QCT-NVEQMT methods occur for of = 0, for which the mean values of the 0 + OH and 0 + OD reactions become lower, and closer to each other, in the QCT-NVEQMT method. This may be explained from the fact that the deple-tion occurring in the QCT-NVEQMT method for uf = 0 (see Section 3.2) affects mainly the trajectories leading to high-j' rotational states, which, having enough internal energy to be physically acceptable in the QCT-IEQMT method, fail to have a vibrational energy higher than the 0, zero-point value, and hence are discarded in the QCT-NVEQMT method.Although this may also occur for the case ofj = 10, we observe from Fig. 8 and 9 that this does not happen to a ........x m ....... .......... EU ..-?c .. .. ::::.: ........ . ,........ .i; :: ..... i... . :.j 0 90 180 significant extent. This is probably due to the initial extra rotational energy, which allows population of higher jf values, independent of the method used for the calculations. Clearly, the differences between the two methods for the high u' values cannot be assigned any special meaning, since the distributions are not Boltzmannian, mainly due to the lack of trajectories for such vibrational states. 3.4 Angular Distributions Fig. 10 and 11 show the detailed form of the calculated differ-ential cross-sections for the diatomic product 0, molecule, ud = 7tbrfiaxN,(O')/(N,sin 0'). These distributions have been normalized in each case by dividing by the maximum value ......C"" :.....I... ._........ \.....> ....... j....... -...\ ...... .,i ...... ,............. . : :: 1....,. ....,: :....i .., .. I II I 0 90 180 scattering angle/degrees Fig. 11 As in Fig. 10 but for the QCT-NVEQMT method (orx).For collisions such as the present ones, which are expected to proceed through the formation of a long-lived complex (see ref. 32 and 48), the angular distributions should be determined mainly by the disposal of angular momentum, while their anisotropy is expecteds6 to increase with increas- ing L,, the maximum orbital angular momentum with which the complex is formed. Thus, at small collision energies, when the orbital angular momentum is smaller than, or of the same order as, the rotational angular momentum, one expects the differential cross-sections to become nearly isotropic.As illus-trated in Fig. 10 for the QCT-IEQMT methad, this is prob- ably the case for the 0 + OH reaction for j = 10. Conversely, the corresponding distributions for the 0 + OD reaction (where the rotational angular momentum for j = 10 is expected to be smaller than for 0 + OH at the same value of j) show some forward-backward peaking at E,, = 0.125 kcal mol-', becoming backwards at El, = 0.25 kcal mol-' and forwards at E,, = 1.0 kcal mol-'. Instead, if the collision energy is raised, or L, becomes larger than the rotational angular momentum, then the forward-backward peaking tends to become more pronounced, thus increasing the anisotropy of the angular distributions. This is the case for the title reactions for j = 1, the forward-backward peaking being more pronounced as the translational energy increases from El, = 0.125 to 1.0 kcal mol-' [Fig.lqa), (c) and (e)]. Note also that on going from QCT-IEQMT (Fig. 10) to QCT-NVEQMT (Fig. 1 1) the forward-backward peaking becomes slightly more pronounced, especially for the 0 + OD reaction. Note, especially, the very pronounced peak for backwards scattering of the angular distribution for 0 + OD at E,, = 0.25 kcal mol-' and j = 10 [Fig. 11 (43. 4. Reactive Cross-sections For reactions occurring on potential-energy surfaces with deep chemical wells, it is usually considered that a long-lived triatomic complex is formed, which then decays to form the products. In the case of the title reactions, this suggests the two-step mechanism 0 + OH(D)= HO: (DO:) +0,+ H(D); note that the double arrow does not imply the exis- tence of an equilibrium but means only that the complex can recross back to reform the reactants.Accordingly, the title reactions proceed by (Q) formation of a triatomic HO: (DO:) complex, (b) decay to form the products or to reform the reactants. Clearly, in step (a)the major factors influencing the collisional process are the long-range attractive forces and the value of the orbital angular momentum (L),given by eqn. (6).Thus, the capture cross-section (a,) is directly related to the height of the centrifugal barrier, which is in turn related to the orbital angular momentum.Finally, step (b)involves the dynamics relating not only to the triatomic complex but also to the formation of the products or reformation of the reactants. This may be accounted for by the recrossing factor P,/P,, which is a measure of the amount of 0, products formed from the trajectories that have entered the complex region, defined2, as the region of configuration space lying at least 0.2 eV below the 0 + OH(D) dissociation limit; note that P, and P, are the reactive and capture probabilities, respectively. Thus, the reactive cross-section assumes the form pra, = a, -(7)PC with P,Pc-' < 1 by definition. The results of this two-step mechanism are illustrated in Fig. 12-14.Thus, Fig. 12 shows, for El, = 0.125, 0.25 and 1.0 kcal mol-', the capture cross- sections as a function of the initial rotational quantum number j; the corresponding conversion factors are illus- J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 85P'' I *' 1 I I I I I I I1011 I I 0 5. 10 I Fig. 12 Capture cross-sections as a function of initial diatomic rota- tional quantum number, j. A, 0 + OH; B, 0 + OD. Initial trans- lational energy: (a) 0.125, (b) 0.25, (c) 1.0 kcal mol-'. (-, A),QCT-NVEQMT calculations; (---, 0)QCT-IEQMT calculations. 100 80 ++ ..'a "+60 t t I Fig. 13 Recrossing factors as a function of initial diatomic rota- tional quantum number, j.(a)-(c)0 + OH; (4-0 0 + OD. (a),(4 E,, = 0.125 kcal mol-'; (b), (e) El, = 0.25 kcal mol-'; (c), (f)E = 1.0 kcal mol- l. Lines and symbols are as in Fig. 12. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 160 85 160 B 0 5 10 i Fig. 14 Reactive cross-sections as a function of initial diatomic rotational quantum number, j. A, 0 + OH; B, 0 + OD. Initial translational energy: (a)0.125, (b)0.25, (c) 1.0 kcal mol-'. Lines and symbols are as in Fig. 12. trated in Fig. 13. In turn, the reactive cross-sections are shown as a function ofj in Fig. 14, while Table 1 summarizes the specific numerical values of the capture and reactive cross-sections ; for completeness, the conversion factors P,/P, are given in Table 2. The variation of the capture or reactive cross-sections with isotopic substitution can be given by the ratio where, as before, x = r or c, and the superscripts H and D label the 0 + OH and 0 + OD systems, respectively.The numerical values of these ratios, for both QCT-IEQMT and QCT-NVEQMT methods, are collected in Table 1. As seen, the values of r,14and r,~? do not appear to follow any special trend, apart from being greater than one in most cases. More- over, we conclude from a comparison of Fig. 12A and B that, for most j values, especially at low initial translational ener-gies, the complex-formation step is considerably enhanced in the case of 0 + OH (see also Table 1). This discrepancy in the capture cross-sections for the title reactions is particularly significant when the QCT-NVEQMT method is applied.This isotopic effect may partly be rationalized by noting, from eqn. (6), that the orbital angular momentum increases with increasing reduced mass of the system. Thus, for the same translational energy and impact parameter, the centrifugal barrier to be overcome for capture will increase on going from O-OH to O-OD collisions (see Section 3.1). However, for large rotational quantum numbers (at any collisional energy), it is the spherically averaged component of the atom-diatom potential that controls the capture cross-section, the mass factor being of little relevance. Moreover, at even higher translational energies, for which the diatomic molecule can hardly rotate at all before collision occurs, the results for both reactions become closer to each other.Another interesting feature from Fig. 12 is the near coin-Table 2 Calculated recrossing factors for the title reactions 'E,,/kcal mol - j 102PyP; 102Pp/P: 0.125 0 97.59 f3.44 99.09 f5.22 1 95.76 f1.75 96.36 f2.72 99.61 f2.38 88.31 2.42 2 90.20 f2.81 92.87 f2.78 3 81.74 f2.80 90.93 f2.44 4 75.54 rt 2.63 83.85 f2.56 94.28 f2.55 85.32 f2.58 5 73.92 f2.43 74.81 f2.58 6 - 71.46 k2.47 10 64.10 k 1.84 57.77 f2.48 84.25 f2.84 70.04 k 2.61 14 - 58.24 f2.52 0.25 0 96.25 f5.80 95.97 f6.18 1 94.22 f3.10 93.41 f3.88 99.60 k 2.66 83.85 f3.27 2 88.11 f2.54 91.50 f3.36 3 80.94 f2.63 85.92 2.99 4 72.1 1 f2.72 81.62 f3.07 94.52 k 2.74 82.10 f3.19 5 70.33 2.80 71.62 f3.12 6 - 71.17 f3.25 10 60.74 f2.81 56.18 f3.15 85.60 f2.71 70.86 k 3.39 14 - 57.80 2.99 6.50 1 91.05 f3.22 - 98.54 f2.91 85.45 f4.19 4 74.69 f2.87 - 92.68 k 3.31 80.13 _+ 3.07 10 67.35 f3.72 - 85.75 f4.00 67.57 k3.21 1.o 0 85.67 f5.12 82.35 f5.42 1 88.81 f3.93 85.15 f4.20 95.05 k 3.69 82.67 f4.81 2 79.64 f3.35 83.88 k4.32 3 74.64 2.92 79.47 f 3.66 4 72.73 f3.09 74.94 3.29 89.51 f3.34 78.10 f3.58 5 67.02 f2.97 69.30 f3.36 6 - 65.31 f3.41 10 65.78 f3.13 51.30 2.83 82.06 f3.20 65.32 f3.38 14 - 56.08 f2.86 Note that, for j = 1, 4 and 10, the second entry refers to the QCT- NVEQMT calculations; all other entries refer to the QCT-IEQMT method.cidence of the QCT-IEQMT and QCT-NVEQMT results with increasing energy. In fact, for high translational energies and high rotational quantum numbers, the zero-point energy effects lose importance, as has been noted32 for the QCT and QCT-IEQMT methods. In Fig. 13 we present, for various values of Etr, the re-crossing factors PJP,. A first glance at this figure imme- diately shows that the two methods produce quite different results at all translational energies considered in the present work, with those obtained from the QCT-NVEQMT method for 0 + OH [Fig. 13(a)-(c)] always being larger than the cor- responding ones from the QCT-IEQMT method. This result is in good agreement with the recent findings33 of Nyman, although based on a different definition of the HOT complex (see Section 5 for further discussion); for the 0 + OD reac-tion [Fig.13(d)-Cf)] the QCT-IEQMT results intercept those from QCT-NVEQMT in the vicinity ofj = 4, the latter being larger for high values ofj (see also Table 2). These findings may be understood by noting that the energetic requirements associated with the QCT-NVEQMT approach are more restrictive than those associated with QCT-IEQMT, espe- cially for the reactant diatomic, which has the largest zero- point vibrational energy (see Fig. 1). Thus, the probability of recrossing decreases on passing from QCT-IEQMT to QCT- NVEQMT, since it is energetically more difficult to reform the reactants than to form the products. The difference between the 0 + OH and 0 + OD recrossing ratios can also be ascribed to the difference in the zero-point vibrational energies of OH and OD.Although decreasing in both methods for large j values, the QCT-NVEQMT recrossing factors show a somewhat smoother decay than the QCT- IEQMT ones. From the results of Fig. 12 and 13 one then obtains the reactive cross-sections as a function of E,, andj, as shown in Fig. 14 for both the QCT-IEQMT and QCT-NVEQMT methods. One observes that the largest reactive cross-sections refer to the 0 + OH reaction (Fig. 14A) at low j values while, for the intermediate values of j studied here, the 0 + OD reactive cross-sections (Fig. 14B) become largest; for even higher j values, the 0 + OH reactive cross-sections become larger again (see also Table 1).In fact, we have previously48 noted that in the case of OD the maximum for the reactive cross-sections at a specific initial translational energy is reached between j = 1 and 4, while for OH it is clearly reached for j = 1 or 2. This was explained on the basis that OD is heavier than OH; accordingly, OD has a density of rotational states higher than that of OH, and hence the ideal value of the rotational energy for the former arises at a higher j state. From both panels of Fig. 14 we observe that the iso- topic effect in the reactive cross-sections is clearly enhanced in the results obtained using the QCT-NVEQMT method, especially for low translational energies.Moreover, we con- clude from Table 1 that, unlike qim, the values of qp are always greater than one for the QCT-NVEQMT calculations, while oscillating around one for the QCT-IEQMT method. Another interesting feature from Fig. 14 is related to the decrease of the reactive cross-sections with increasing trans- lational energy, which is intimately associated with the behaviour encountered for the capture cross-sections. More- over, the decrease of the reactive cross-sections with increas- ing rotational energy, i.e. with increasing j, is closely related to the behaviour of the recrossing factors. (For an explana- tion of the dramatic increase of the reactive cross-section on going from j = 0 and j = 1, see ref. 32.) Note that these two factors contributing to the behaviour of the reactive cross- sections are nearly separable, since the capture cross-sections do not vary significantly with j (only for QCT-IEQMT it is found to vary from j = 0 to j = 1 or 2) and the recrossing factors are nearly constant with increasing initial trans-lational energy.5. Thermal Rate Coefficients and Recrossing Fig. 15 shows the thermal rate coefficients for the 0 + OH [Fig. 15(a)] and 0 + OD [Fig. 15(b)] reactions as a function of temperature. In both panels the QCT-IEQMT results are indicated by the broken lines, while the solid lines represent those for QCT-NVEQMT. As bef~re,~*,~~,~’ the OH mol- ecule has been assumed to belong to Hund’s case (b), and hence the rotational statej = 0 was not included.We observe from Fig. 15(a) for 0 + OH that the two curves are further apart at low temperatures, while their separation tends to decrease with increasing temperature. Note also that the QCT-NVEQMT curve provides an upper bound to the results obtained from the QCT-IEQMT method, which could be anticipated from the values obtained for the reactive cross- sections. In fact, the QCT-IEQMT curve, and the best experi- mental value^,^',^^ all lie below the QCT-NVEQMT curve (note, however, that the recent values of N~man~~ are in better agreement with the present QCT-NVEQMT results). A similar observation can be made for the 0 + OD reaction [see Fig. 15(b)], with the QCT-NVEQMT curve being above J. CHEM. SOC. FARADAY TRANS., 1994, VOL.90 12 10 8 76 -3u $4 E 72 &lOh 21 I I I I 40 100 160 220 280 340 TIK Thermal rate coefficients as a function of temDerature. (4 0%OH reaction: (-) QCT-NVEQMT method; (---) QCT: IEQMT method; (A) experimental measurements of Lewis and Watson;” (V) experimental measurements of Howard and Smith.s8 (b) 0 + OD reaction. Note that we have not considered the rota- tional statej = 0 in the evaluation of the thermal rate coefficients. the QCT-IEQMT one except for temperatures below T x50 K, where the situation appears to be reversed. However, the two curves lie close to each other over the whole range of temperatures considered in the present work. This may be explained by the fact that the zero-point vibrational energy of OD is closer to that of 0, than in the case of OH (3.8 kcal mol-’ for OD and 5.2 kcal mol-’ for OH, in comparison to 2.2 kcal mol-I of 0,);the additional restriction in the rota- tional energy of OD in QCT-NVEQMT is nearly balanced by the equivalent one in 0,.Fig. 16 shows the isotopic effect in the thermal rate coeffi- cient for both QCT-IEQMT [Fig. 16(a)] and QCT-NVEQMT [Fig. 16(b)] methods. Also shown in this figure are the ratios between some quantities that contribute directly to the isotopic effect in the thermal rate coefficient, namely those corresponding to the rotational partition func- tions (Qrot),reduced masses of the triatomic systems (p),and x.((2j + l)exp(-Evj/kT) V, J x [Etr br(u, j, Etr)exp(-Etr/kT) dEtr) (9) which accounts for the influence of the reactive cross-section.Fig. 16(a) shows that, for the QCT-IEQMT method, the isotopic effect is almost constant, and somewhat larger than unity, over the temperature range 40 < T/K < 340. Clearly, the small magnitude of the isotopic effect in the thermal rate coefficient obtained by the QCT-IEQMT method appears to be the result of a strong cancellation involving the above statistical-thermodynamics and dynamical factors. In turn, Fig. 16(b) shows the isotopic effect in the thermal rate coeffi- cient obtained using the QCT-NVEQMT method. The more pronounced isotopic effect is now essentially due to an increase of the influence of the reactive cross-section, eqn.(9), since the reduced masses and rotational partition functions are as in QCT-IEQMT. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 31 1 ........................... ...... " _ "........... ". I 1 I I ..........-,,,,,,_.,I,_, ..._._._.I._." ......__........_.. ......I 00 40 100 160 220 280 340 TIK Fig. 16 Isotopic effect in the thermal rate coefficients for the title reactions as a function of temperature (-), obtained by the QCT- IEQMT (a) and QCT-NVEQMT (b) methods. Also considered, in each case, are the effect of the rotational partition functions (--), the mass factors (---) and the factor of eqn. (9) related to the j-specific thermal rate coefficients weighted with the respective rota- tional distribution (.....). Note that we have considered, as usual, the ratio obtained by dividing the factors relative to the 0 + OH reaction by those for the 0 + OD reaction, according to eqn. (3) and (4). For further comparisons, including experimental estimates at higher temperatures, see ref. 3 1. I---.-L I 60 40 100 160 220 280 340 TIK Fig. 17 Recrossing factors as a function of temperature. (a) 0 + OH reaction, (b) 0 + OD reaction, by (-) QCT-NVEQMT and (---) QCT-IEQMT methods. Note that we have not considered the rotational statej = 0 in the evaluation of the recrossing factors. Knowledge of the magnitude of recrossing as a function of temperature is another important tool in understanding chemical reactivity for reactions proceeding in a potential- energy surface with deep chemical wells such as the title ones.Thus, we show in Fig. 17 the recrossing factors for the 0 + OH [Fig. 17(a)] and 0 + OD [Fig. 17(b)] reactions as a function of temperature, obtained by both QCT-IEQMT and QCT-NVEQMT methods. It is seen, for the 0 + OH reac- tion, that recrossing diminishes (i.e. F,,, increases) substan- tially on going from QCT-IEQMT to QCT-NVEQMT, although it is significant at the highest temperatures studied in this work. This is in good agreement with the recent trajec- tory results of N~man,~~ also obtained using the DMBE IV potential-energy surface. However, in his statistical EFFEJ simulation, this author has utilized a different definition of the HOT complex, which may probably account for some of the disparity between his results and our own using the QCT- IEQMT approach.For the 0 + OD reaction, the recrossing predicted from the QCT-NVEQMT method exceeds that cal- culated using QCT-IEQMT for temperatures below T z210 K. This is in agreement with the behaviour encountered for the factors PJP,as a function ofj, which is shown in Fig. 13. 6. Conclusions We have studied the effect of isotopic substitution in the dynamics and kinetics of the title reactions, using the QCT- IEQMT calculations we have previously reported. We have also carried out new trajectory calculations using the recently proposed QCT-NVEQMT method, in order to study the influence of imposing a more restrictive quantum limit in the analysis of the final diatomic molecule.A striking result from the QCT-NVEQMT calculations is an inversion of popu- lation observed for the vibrational distributions in the product 0, molecules; instead, the corresponding QCT- IEQMT distributions show the usual Boltzmannian stat-istical behaviour. From the trajectory calculations we have concluded that, for the 0 + OH reactive cross-sections and thermal rate coefficients, the values obtained using the QCT- NVEQMT method are systematically above those based on QCT-IEQMT; for 0 + OD, the values obtained from the QCT-NVEQMT method are nearly identical to the QCT- IEQMT ones. Thus, we have a small isotopic effect in the thermal rate coefficients obtained using the QCT-IEQMT method, while a much larger value is observed for QCT- NVEQMT.We have also found that, for the 0 + OH reac-tion, non-statistical recrossing is less important when predicted from the QCT-NVEQMT method. Indeed, for 0 + OH, most of the differences between the two methods arise essentially from the recrossing factors, which means that they can be attributed to the dynamical aspects of the colli- sion after formation of the HOZ complex. However, for the deuteriated reaction, recrossing is predicted to be significant by both QCT-IEQMT and QCT-NVEQMT methods, even at low temperatures. 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Phys., 1993,173, 159. 34 V. Klimo, M. Bittererova, S. BiscupiE and J. Urban, Chem. Phys., 1993, 173, 367. Paper 4/00456F; Received 25th January, 1994

ISSN:0956-5000    

DOI:10.1039/FT9949002189

出版商:RSC    

年代:1994

数据来源: RSC

摘要:

J. CHEM. SOC. FARADAY TRANS. 1994 90(15) 2201-2210 Fractal Properties of Homologous Series of Structures Sherif El-Basil Faculty of Pharmacy Kasr El-Aini St. Cairo Egypt 11562 The concept of lattice-graph generation considered earlier (S. El-Basil J . Chem. SOC. Faraday Trans. 1993 89 909) h a s been studied further. It is demonstrated using methods of symbolic dynamics and block-renaming that the sequence which defines these graphs is a fractal while t h e generation operation bears remarkable simi- larity to t h e various stages of the Cantor dust. Furthermore Kekule counts of several homologous series of quasicrystal-like benzenoids form mathematical structures which possess the scaling properties of fractals. Self-similarity is extended to other homologous series of graphs (which represent chemical species) and it is demonstrated in all cases that the golden mean (T = 1.618033989) is their characteristic scaling factor.Recently three papers on deterministic fractals have been p~blishedl-~ which deal with fractal benzenoids and their synthetic possibilities,' their Clar structures3 and a fractal family of recently termed c~ro[n]enes.~ In this paper an homologous series of structures (that rep- resent chemical species) which are not self-similar are shown to have very definite fractal properties. Namely the work here is not concerned with the deterministic fractals4 (such as the Cantor set the Sierpinski gasket etc. or other classes of self-similar benzenoids considered elsewhere '-') but rather about discovering the self-similarity that must be 'hidden' in homologous series of structures.It is a well known fact that the physical and chemical properties of higher members of homologous series of compounds are very similar to those of the lower members. Some examples are as follows; (1) The natural logarithms of the number of Kekule struc- tures the total number of self-avoiding paths and the total number of conjugated circuits of homologous series of benze- noid hydrocarbons were found to give exact linear relations when plotted against the connectivity indices of certain caterpillar trees.'T6 (2) The electronic absorption spectra and heats of atom- ization were also found to behave similarly.6-8 (3) In their work on the fractal nature of alkanes Rouvray and Pandey' related physical properties of the normal alkanes with Wiener indices of members of this homologous series.(4) In his work on the problem of graph recognition Randik" demonstrated that the characteristic polynomial of a homologous series of arbitrary graphs has a general mathe- matical form which is characteristic of the given series. (5) The concept of Fibonacci graphs' which generate recursive relations which are self-similar among themselves and similar to those of the paths and cycles poses the follow- ing question Fibonacci graphs (which are homologous series of specially designed graphs) are not self-similar but they do lead to fractal (self-similar) properties; where are the self- similarities hidden in all the above and other such cases? It must be recalled at this point that Fibonacci graphs have strong potential in computational chemistry and mathe- matics which already has been demonstrated.l6 The aim of the present work is to attempt to disclose some of the self-similarities that must be hidden in the structure of a homologous series of molecular graphs which may rep- resent real chemical compounds. The approach will be that of modelling by two groups of structures uiz. quasicrystalline-like benzenoid hydro- c a r b o n ~ ' ~ - ' ~ and Fibonacci graphs."-' Quasicrystal-type benzenoids have several peculiar properties which make them more interesting than other classes of benzenoids. Of the isomeric catacondensed benzenoid systems the quasi- crystalline ones have (a) The shortest wavelength (/? and p bands) of their UV spectra." ( b ) The highest resonance energy.21 (c) The highest Kekule count.22 (d) The largest sum of non-adjacent numbers 3.As to our second model the Fibonacci graphs,"-'6 the topic is worth re-examinination due to their structural and c o r n p u t a t i ~ n a l ' ~ ~ ' ~ ~ ' potential. 2201 ' v 5 (1) where K[B(L)] is the number of Kekule structures of the ben- zenoid system and L is the number of rings in its longest chain. Throughout this paper the rings are hexagons and B(L) B(L + l) B(L + 2) are members of a given homologous series of hydrocarbons. Fig. 1 shows three homologous series of quasicrystalline systems and four types of Fibonacci graphs.(2) The second property of quasicrystalline benzenoid hydrocarbons is related to their Kekule spaces" x(B). In general the latter is given by eqn. (2) uiz. (2) Quasicrystalline Benzenoid Systems This class of benzenoids has been introduced previously.' 7-1 These peculiar systems are catacondensed benzenoids in which all rings but the terminal? ones have angularz4 annel- lation modes. In addition to this very particular connectivity the following two properties are characteristic of a quasicrystal-like benzenoid system uiz. (1) Their Kekule counts recur in a Fibonac~i-like'~ rela- tion i.e. K[B(L + 2)] = K[B(L + l)] + K[B(L)] x(B) = ( k l 7 kz * * * 7 k K @ J where ki is an ith Kekule structure EB. In ref. 17 and 18 an equivalence relation I is defined on x(B) which partitions it into equivalence classes of Kekule structures; the cardinality of any such classes can only be an integral power of two.This fundamental property is general to any catacondensed system if each equivalence class con- tains only those Kekule structures which possess identical counts of terminal conjugated circuits (a terminal conjugated circuit is to be one which is entirely located in a terminal ring and since in this work all rings are hexagons a terminal circuit will always contain 67r electrons as three con- t. A terminal ring is one which has only one edge in common with the adjacent ring. See ref. 17 for definitions. 2202 c 0' P~O-O-O:? 0 D o/o,o'o,o - o/o\o/o,o/o - ~ ; o - o - o < ~ - ~;o-o-o~o-~ - 0 0 I 0 0 I 0 I where in general 2' represents an equivalence class which contains 2' Kekule structures and l j is the multiplicity of this equivalence class.Finally t is the maximum possible number of terminal conjugated circuits (which has six n electrons) in B. Eqn. (3) is general for all catacondensed benzenoids. In the case of quasicrystalline benzenoids however the I j s are F = 1 F = 1 F = F + F,). This is proven in Fibonacci numbers26 (Fibonacci numbers are defined by (3) The Kekule space of a catacondensed benzenoid hydro- carbon can be made to generate a set of n-cubes or hyper- cubes (which incidentally are often convenient models for describing parallel computers)26 by the following steps (a) Apply 1 to the given x(B).(b) In each equivalence class which contains 2' Kekule structures define any two to be adjacent if the orientations of their terminal circuits? is identical except one pair in which one circuit is the mirror-image of the other. (c) Transform the individual Kekulk structures into vertices then connect pairs of vertices which correspond to pairs of adjacent Kekule structures. In this way the Kekule space is said to cluster into a sequence of hypercubes ( n - c u b e ~ ) ~ ~ ~ ~ 2' + G (0-cube = point); 2 + G (2-cube = line segment); 22 + G (2-cube = square); 23 + G (3-cube = cube); t A terminal conjugated circuit is one which is entirely located in a terminal ring. See ref. 15 for definitions. (3) - Fig. 1 Three homologous series of quasicrystalline benzenoid hydrocarbons and four series of Fibonacci graphs.The last one rep- resents external homologation the others internal homologation. Numbers in parentheses are K values. jugated double bonds). In ref. 17 this assertion is proven. Eqn. (3) describes this particular equivalence relation lx(B) = {1020UIl 2'U12 22U. - *Ul,2'} Theorem 1 of ref. 17. 24 4 (316 (4-cube = tesseract) . . . The above steps are illustrated in detail in ref. 18 - o/o\o/o,o'o,o 'o.O J. CHEM. SOC. FARADAY TRANS. 1994 VOL. 90 Fig. 2 Generation of the cube using an equivalence class of a B,(L) type c$ Fig. 1. Fig. 2 is isomorphic to Fig. 5 of ref. 17 but here we use Kekule structures rather than their factor graphs. These n-cubes have importance in recent computer designs26 and also as models for certain stereochemical transformations28 while others represent three-connected transition-metal c1uste1-s.~~ The generation of these hyper- cubes has been dealt with in an earlier publication.17 In this work the generation process itself is shown to have self- similar properties characteristic of the well known determin- istic fractals although the cubes themselves are not of course fractals.Fig. 2 shows the generation of the traditional 3-cube from an equivalence class which belongs to the homologous series B,(L) of Fig. 1. Note that Fig. 2 of this paper is isomorphic to Fig. 5 of ref. 17. Fractal Properties associated with Quasicrystalline Benzenoid Hydrocarbons It must be made clear at the outset that not all self-similar structures are fractal^.^' For example a line segment a square or a cube can each be divided into smaller copies which are obtained by a similarity transformation.These structures however are not fractals because the scaling factor in such objects is arbitrary. On the other hand the typical deterministic fractals4 (such as the Cantor set the Sierpinski gasket the Koch curve etc.) have scaling factors which are indeed characteristic of each object. Analogously the fractal benzenoids of Klein et uI.'-~ have in fact a characteristic scaling factor. That is why these latter cases are not just self- similar systems but are also fractals. However the word fractal may also be associated with a sequence of numbers such as the sequence of Fibonacci numbers 1 1,2 3 5 8 13 .the scaling factor of which is the well known golden mean,31 z = 1.618033989 which is not an arbitrary scaling factor. We shall see here that z persistently scales almost all the homologous series considered in this work. Now we consider the fractal properties of the graph gener- ation process associated with quasicrystalline benzenoid hydrocarbons. J. CHEM. SOC. FARADAY TRANS. 1994 VOL. 90 (3) Self-similarity of the Graph Sequence We start with the main recursive relation characteristic of quasicrystalline benzenoids namely eqn. (1) which together with eqn. (2) leads to XCBW + 2)1 = XCBW + 1)1 u XCB(L)l Now we apply the equivalence relation 1 to both sides of eqn.(3) to give A[B(L + 2)] = A[B(L + l)] u A[B(L)] lB1(3) (Gl 7 G8) W 4 ) - (G2 G4 GJ Y G 3 G4 7 G8 3 G8) lBl@) + 1B1(6) (4) where in general A[B(L)] = 1x[B(L)] is the sequence of lattice graphs generated when x[B(L)] is exposed to 1. One observes that eqn. (1) and (4) are similar. Indeed this simi- larity leads to self-similarity of the graph-generation process as will be demonstrated. Eqn. (4) is Theorem 3 of ref. 17. One can explicitly write the graph sequences resulting from 1 oper- ation on the first few members of the Bl(L) homologous series shown in Fig. 1 (6) (GI G2 7 G G4 G4 G8 G8 G8) etc. The above type of expansion is considered in ref. 17 and 18. The above sequences clearly demonstrate eqn. (4). Denot- ing 1B1(3) by S lB,(4) by T then lB,(5) can be written as TS while 1B,(6) as TST and so on.Repetitive application of the 1 operation yields a sequence which is reminiscent of a qua~icrystal.~~? Thirteen 1 applications on the members of B,(L) series (or in fact any homologous series of quasi- crystalline benzenoid hydrocarbons) generate the following graph sequence T S T T S T S T T S T T S (5) Strict self-similarity of sequence (5) can be demonstrated in many ways (a) Underline all the TS pairs and read them as Ts and read the non-underlined Ts as Ss and the sequence repro- duces itself - TS T = - * * - + TS T . * . + T S - + T - + S Each sequence might be envisaged as a the length of which is the number of symbols in it. Interestingly the above ‘block-renaming’ process (Le.the map TS -+ T; T -+ S) reduces the length of a given sequence by a Fibonacci number. The lengths in eqn. (6) decrease as follows -+ 13 -+ 8 - 5 - 3 - 2 -* 1 - 1. Indeed starting with a word the length of which is F generates a word with length F,- i.e. its length is decreased by F - 2 . Naturally the reverse process (i.e. the build-up of the sequence) requires the map T + TS; S -+ T. If one calls the reduction operation deflation (as it is called in renormalization theories in physics) then the build-up process might be called inflation.35 The scaling factor for the latter process will be limn+00 FJF,,- = 1.618033989 = z which is the golden mean. For the inverse (deflation) operation the scaling factor is the reciprocal of t The first quasicrystal was the alloy AI,,Mn, which showed sham suots the arrangement of which is consistent with the for- bidden five-fold symmetry.See ref. 33. 2203 z = 7-l = 0.618033989. These scaling factors are not arbi- trary. This behaviour is quite similar to that of deterministic fractals. Consider the Koch curve as an example,36 the con- struction of which proceeds in stages. In each stage the number of line segments increases by a factor of four such that each part of the four parts in the kth step is a scaled down version by a factor of three of the entire curve in (k - 1)st step. Fig. 3 illustrates the fractal character of the earlier stages of the Koch curve and of the graph sequence considered here.There is a remarkable correspondence between self- similarity of the Koch curve and the sizes of the generated lattice graphs which form the coeficient of a geometric series. One may express such a series as 00 (7) C rk = 1 + r + r 2 + r3 + - . . k = O Eqn. (7) may be scaled by a factor of r to yield m cc k = O k = O Thence as in the case of the Koch curve and the TS sequence [eqn. (5)] self-similarity holds for the limits rather than for the finite stage. It is instructive here to observe that the golden mean [the scaling factor of sequence (5)] is attain- able in the limit as the 1 operation is applied ad infiniturn (F,/F1 = 1; F1/F2 = 0.500; F2/F3 = 0.667; F3/F4 = 0.600; F,/F5 = 0.625; .; F 2 / F 2 = 0.61803399; . ; limn-,m F,/F,+ = z - ’).The block-renaming process adopted here to show the self- similarity and fractal character of the TS sequence is an iter- ation process which involves repeated application of some ‘self-same’ operation (in this case the deflation-inflation lx= iXT I x 3 IX 3 1 x 3 lXT Fig. 3 Self-similarity of the Koch curve compared with those of our TS sequence [eqn. ( 5 ) ] . The scaling factor in the latter is a factor of 7 the golden mean. 0 0 e12 T S + S TST+T; J. CHEM. SOC. FARADAY TRANS. 1994 VOL. 90 -- 0 9 I I I A 6 I I I I el 1 e22 e14 (9) sum of two successive Fibonacci numbers i.e. F + F,- . With this map the length of each sequence decreases by the Thence the scaling factor here would be in the limit of an infinite number of applications of I z2.(c) A third way to envisage self-similarity of the TS sequence is to count the number of symbols in the respective blocks TST and TS which leads to the sequence 3 2 3 3 2 ,. 2204 maps defined above). This type of operation is always a rich source of self-similarity. (b) Another block-renaming process which also demon- strates self-similarity of the TS sequence requires the map We illustrate self-similarity using eqn. (9) as follows Now define the map 2 4 s 3 - T ; (10) and one obtains a scaled down version (by a factor of 2,) of the original sequence uiz. TSTTS . . . el 8 e80 Numerical Self-similarity of Quasicrystal-like Benzenoid Systems The three homologous series of quasicrystalline benzenoids shown in Fig.1 will be taken as models their Kekule and Clar counts4' will be investigated for scaling (self-similar) properties. Fig. 4 Correspondence between the build-up of G, lattices from G ones (respectively from top to bottom n = 1 +line segment n = 2 + square n = 3 - cube and n = 4 -* tesseract). The set of labelled (solid) edges are in one-to-one correspondence with a third stage Cantor dust (boldly outlined edges). cf bijection eqn. ( 1 1). itself is a self-similar operation which gives rise to the well known fractal the Cantor dust. (cf. Fig. 4). (12) (13) Kekulb Counts The following eqns. can be derived for the respective K values in terms of Fibonacci numbers KCBO(L)I = FL+' KIBl(L)] = 4F,- + FL-2 K[B,(L)] = l6F,- + 8FL- + F L - 5 The limits of the above counts as L - co lead to lim KIBo(L)] z F L+ rn Self-similarity of Graph Generation The operation of graph-generation itself is indeed self-similar and bears strong resemblance to various stages of one of the most popular of the deterministic (old) fractals the Cantor dust (or the Cantor middle-thirds set).37 First one observes that graph sizes show a very clear period-doubling phenome- non.Period-doubling of attractor cycles has been observed with the logistic equation in ref. 38. Namely the number of vertices in the respective lattice graphs increases in the fol- lowing way 1 + 2 -+ 4 -+ 8 + 16 + . . - . Each lattice graph can be constructed from two units of its immediate precursor.For example G (the line segment) might be thought of as two units of G,s linked by one edge a G (the square) as two units of G,s linked through their vertices by two edges a G8 (the 3-cube) requires two G4 units and four edges and so on. There is a (one-to-one onto) function between the set of edges required to connect two G units (to generate G,,) and the (n - 1) stage of the Cantor dust. In order to write such a function we must label the set of edges required to connect two G units to form G, lattice and also label the intervals of the various stages of the Cantor set. The latter is adopted.,' as follows The initiator (i.e. the interval [0 13) is given the symbol C . Then the first stage will have two inter- vals [0 1/31 and [2/3 13 which are labelled respectively as L and R (L = left R = right).The second stage includes the four intervals [0 1/91 = LL; [2/9 1/31 = LR; [6/9 7/91 = RL; [8/9 13 = RR and so on. Now the set of lines (edges) required to link two G units forming a G, will be labelled thus el, e,, . . . en, . Fig. 4 illustrates these concepts. Thence we can correspond the sets of edges which link two units of G,s G2s G,s G8s etc. with the intervals of a Cantor dust by the following bijection.39 {(ell? cO); L) (e22 R); (el49 LL) L+ a2 (e24 9 LR) (e34 7 RL) (e44 RR); (el8 LLL) lim K[B,(L)] z 5FL lim K[B,(L)] z 25FL L+ 03 (14) (17) assuming that when L -+ co L + j z L j being an integer. Eqn. (15)-(17) show that the sequence of K values obtainable (e28 LLR) .-.(e88 RRR); -,} (11) where parentheses between two semicolons correspond to the generation of a lattice graph. Indeed the graph generation J. CHEM. SOC. FARADAY TRANS. 1994 VOL. 90 where B is a quasicrystalline benzenoid hydrocarbon. i.e. any such sequence has a characteristic scaling factor of z. (The golden mean = 1.618033989.) In Table 1 self-similarity is tested for the K values of the B,(L) branched quasicrystalline hydrocarbons. The limit of z appears to be reached at L = 25. Scaling with z yields almost exact values from L = 23. The last column demonstrates the fractal character of the sequence of K(L) values (a) being self-similar and (b) having a characteristic (not arbitrary) scaling factor (z-’ or z). It is considered whether the Bl(L) homologous series (Fig.1) shows a similar scaling behaviour. Note that the members of the B,(L) series possess two branched centres while those of the B,(L) series possess only one branched centre. Table 2 presents the relevant data. The scaling behaviour is for the B,(L) series similar to that of the B,(L) series. Again scaling yields almost exact values starting at L = 23. In fact at L = 23-25 the products zK(L) are exact figures; namely 8179 z = 132339 etc. To find K(L = 26) we find 346468 7 = 560597.0001. In Table 3 we investigate scaling behaviour of the Kekule counts of the prototype of quasicrystalline benzenoids the unbranched B,(L) series. This is equivalent to studying the fractal properties of the sequence of the Fibonacci numbers [eqn.(12)]. A very similar behaviour is observed z seems to be reached at L = 23; the last few numbers are scaled out exactly. From Tables 1-3 one concludes that the three series of quasicrystalline hydrocarbons are self-similar among themselves and that the sequences of their Kekuli structures have fractal properties with just one characteristic scaling factor z the golden mean. Table 1 Scaling (self-similar) properties of Kekule counts K(L)s of B,(L) homologous series (cf Fig. 1) 4 5 6 7 8 9 24 41 65 106 171 277 10 1 1 12 13 14 448 725 1173 1898 307 1 4969 8040 13009 2 1049 34058 55107 89165 144272 233437 377709 61 1146 988855 16oooO1 2588856 4188857 39 66 105 1.708 333 333 1.585 365 854 1.630 769 23 1 1.613 207 547 1.619 883 041 1.617 328 52 171 277 448 725 1173 1898 1.618 303 571 1.617931 034 1.618073316 1.618018967 1.618039 726 1.618031 797 307 1 4969 8040 13009 2 1049 34058 1.618034826 1.618033669 1.618034 111 1.618033 942 1.618034007 1.618033 982 55107 89165 144272 233437 377709 61 1 146’ 988855 160001b 2588856 1.618033991 1.618033 988 1.6 18 033 989 1.618033989 1.618033989 1.618033989 4188871 1.618033989 The value of T appears to be reached at L = 25.a Rounded numbers 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 T = 1.618033989.’ Exact values. L 9 14 23 37 4 3 6 5 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 The value of 7 appears to be reached at L = 25- Rounded figures 60 97 157 254 41 1 665 1076 1741 2817 4558 7375 11933 19308 31241 50549 8 1790 132339 214129 346468 560597 = 1.618033989- ’ Exact Clar Counts A ‘lar structure is defined here as stated by Herndon and Hosoya41 to be a hexagons* This definition has been independent Set42 Of the Present author and others,43 although it differs slightly from the orig- inal definition of Clar.44 The number of Clar structures [(B)s of a homologous series of quasicrystalline benzenoids recur in Table 3 Self-similarity of Kekule counts of the B,(L) series (Fig.1) 2 1 4 3 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 1771 1 28657 46368 75025 121393 196418 1.500000000 1.666 666 667 1.600000000 1.625000000 1.615384615 1.619047 619 1.61 7 647 059 1.618 181 818 1.617977 528 1.618055 556 1.618025 751 1.618037 135 1.618 032 787 1.61 8 034 448 1.618033 813 1.61 8 034 056 1.618 033 963 1.618033 999 1.618 033 985 1.618 033 990 1.618 033 988 1.618 033 989 1.618 033 989 1.618033 989 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368 75025‘ 121 393’ 196418 317811’ 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 The ratio K(L + l)/K(L) appears to reach r at FZ4 i e .L = 23. Rounded figures 7 = 1.618033989. ’ Exact figures. 1.555 555 556 1.642 857 143 1.608 695 652 1.621 621 622 1.616666667 1.618 556 701 1.617 834 395 1.618 110236 1.618 004 866 1.618045 113 1.618 029 74 1.618035 612 1.618 033 369 1.618 034 226 1.618 033 898 1.618034023 1.618 033 976 1.618 033 994 1.618 933 987 1.618 033 989 1.618 033 988 1.618033 989 1.618033 989 2205 15 23 37 60 97 157 254 41 1 665 1076 1741 2817 4558 7375 11933 19308 31241 50549 8 1790 132339’ 214129’ 346468’ 560597 2206 (2 (0 il 2 4 3 2 1 3 series B,(L = n + 1) B,(L = n + 3) B,(L = n + 4) the following way where Table 4 Clar counts ins of homologous series of quasicrystalline benzenoids shown in Fig.1 4 2 5 (19) (23) (24) (25) i" LIB L + 3) = 5(B L + 1) + i(B L) The solution of eqn. (19) depends on the initial conditions which are outlined below in Table 4. Traditional algebraic methods4' lead to the following solu- tions for the three series of benzenoid hydrocarbons shown in Fig. 1. [,[B,(L = n + l)] = 1.2669~ - 0.26696 + 0.25764 (20) [ [ B l ( L = n + 3)] = 2.2233~ - 0.22336 - 0.16684 (21) [,[B2(L = n + 4)] = 2.9450~ - 0.05506 + 0.24004 (22) c = 1.324717957" = V" 6 = 0.868" cos 139.67n 4 = 0.868" sin 139.67n As n - cc the Clar counts become increasingly dependent on the first term only.Indeed in Table 5 it is demonstrated that the sequence of Clar counts is the same for the three homologous series and is self-similar with a scaling factor = v = 1.324717957 which might be called Clar's mean (cf. the golden mean). v is defined as the following limit Cf eqn. (20) and (22). Eqn. (37) (later) is a general form of recursive relation for which v is a scaling factor. Table 5 Scaling properties of the sequence of Clar counts i s for the homologous series of benzenoids shown in Fig. 1 (in + l/iJ 1.500000000 1.333 333 333 2 4 3 1.250 000 OOO 1.400000000 1.285 714 286 1.333 333 333 1.324 528 302 1.324 786 325 1.324731 183 1.324 716 553 1.324717 562 1.324718956 (vi,)b 4 3 7 5 9 12 351 465 616 5842 7739 10252 7 5 9 12 265 35 1 465 616 4410 5842 7739 10252 1.324 717 957 1.324 717 957 1.324717 957 2143648 2839729 376 1840 4983377 2839729 3761840 (exact) 4983377 (exact) The scaling factor is v = 1.324717957.It is slowly reached at L = 52 (cf Tables 1-3 for Ks). For B and B L starts at 3 while for B the initial L value is 4. Rounded figures. larly J. CHEM. SOC. FARADAY TRANS. 1994 VOL. 90 From Table 5 one sees that Clar counts form a fractal which is scaled by v.At L b 20 the scaled out values are almost exact. The last two figures are in fact exact. However the limit is reached more slowly than in the case of Kekule counts. (27) (31) (32) (33) Fractal Properties of Fibonacci Graphs In Fig. 1 four series of Fibonacci graphs are shown. In homologous series A-C the members are internally homolo- gated while in the last series members are designed by exter- nal homologation. These terms and others are defined in a review paper.I3 These graphs represent generalizations of paths and cycles i.e. the theory behind their construction leads to modulation of the characteristic polynomial of a graph with that of a path. H o ~ o y a ~ ~ defined the quantity pk(G) the number of selections of k edges in G so that no two are incident upon each other.These (non-adjacent) numbers are identical to the absolute magnitudes of the coefficients of the characteristic polynomial of acyclic graphs. The members of a homologous series of graphs obey the following Fibonacci-like recursion (whence the name Fibonacci graphs) m where rn is maximal value of k with po(G) = 1. Now we demonstrate that for a set of Fibonacci graphs the following scaling factor exists p k ( G n ) + P k + l(Gn+ 1) = P k + 1(Gn+2) Cf. eqn. (1); n being number of vertices in G. The sum of p k values of G will be called o(G) Consequently P k Of paths lim a(G + l)/o(Gn) = t "-+ a3 For the paths eqn. (29) is trivial because o(L,) = F where L is a path on n vertices.The cycles Cns (which are the graphical representation of Lucas sequence47) behave simi- and whence as n - 00 we have a(C,) x 2a(Ln) x 2F lim o(C + Jo(C,,) = t n+ a All other types of graphs can in principle be regressed in the form of paths using the relation46 p k ( G ) = Pk(G - + P k - + P k - l ( L j + 1) -/- P k - - 2 ( L j + 1) @ (Terms have their conventional meanings)46 E.g. for the series A of Fibonacci graphs P k can be expressed using eqn. (33) as P k = P k ( L j + 3 ) + P k - 1(Lj+3) + 2 P k - l ( L j + Z ) (34) At j - co eqn. (34) takes the following approximate form 6 P k ( L j ) P k (35) From eqn. (28) and the fact that o(Lj) = F j eqn. (29) results. This behaviour which is illustrated in Tables 6-9 is a J.CHEM. SOC. FARADAY TRANS. 1994 VOL. 90 Table 6 Self-similarity of o(G,) eqn. (28) of Fibonacci graphs of type A Fig. 1 10 16 26 42 68 16 17 18 19 20 21 21892 35422 573 14 92736 150050 242786 392836 22 26 27 28 2692538 4356618 7049 156 The limit of T appears to be reached at j = 19 where j + 5 = n the number of vertices in G . direct result -of the fractal property of the sequence of the respective sums of nonadjacent numbers of the corresponding homologous series of graphs. The same 'fractal effect' is observed in the case of Kekule counts (Tables 1-3) and Clar counts (Table 5) of the homologous series of benzenoid hydrocarbons shown in Fig.1. The scaling factor depends on Table 7 Fractal properties of a(G,) eqn. (28) of Fibonacci graphs of type B Fig. I 20 36 56 2 1 4 3 92 10 11 1644 2660 21 22 23 24 25 26 27 28 327 160 529336 856516 1385872 2242388 3628260 5870648 9498908 2 3 1 32 54 86 140 226 4 5 22 23 24 25 807564 1306666 41 14230 3420896 The limit of 7 appears to be reached at j = 24 where j + 5 = n the number of vertices in G,. Table 8 Scaling behaviour of a(G,) eqn. (28) of Fibonacci graphs of type C Fig. 1 The limit of 7 which appears to be reached at j = 23 wherej + 6 = n the number of vertices in G . - 1.687 500 OOO 1.592 592 593 1.627 906 077 1.614 285 714 1.618033989 1.618033989 1.618 033 989 - 1.800000000 1.555 555 556 1.642 857 143 - 1.618004866 1.618033989 1.618033989 1.618033989 1.61 8 033 989 1.618033 989 1.618033989 1.618033989 1.600 000 000 1.625 OOO 000 1.615 384 61 5 1.619 047 619 1.618033985 1.618 033 988 1.618033 989 1.618033989 1.6 18 033 989 1.618033 989 1.61 8 033 989 1.618033989 1.618 033 989 2207 Table 9 Self-similar scaling behaviour of o(G,) values eqn.(28) of Fibonacci graphs of type D Fig. 1 17 27 44 2 1 4 3 1.588 235 294 1.629 629 630 1.613 636 364 5 1.619 718 310 71 115 59898 969 17 156815 253732 410547 664279 18 19 20 21 22 23 1074826 1.618 033 99 1 1.618 033 989 1.618 033 989 1.618033989 1.618 033 989 1.618 033 989 24 The scaling factor seems to be reached at j = 21 j + 6 = n the number of vertices in G .the type of recursive relation obeyed. In this paper two cases are investigated uiz. for which the characteristic value is the golden mean t = 1.618033989 where o(G,) is a graph theoretical param- eter of graph G which is located in the nth position in the respective homologous series. The second type of recursion is the following (37) for which the characteristic scaling factor is the Clar mean v = 1.324717957. These scaling factors are understood to be limits of o(G,+ ,)/u(G,,) as n -P co for which case only the term which corresponds to the largest zero in the relevant auxilliary equation (r2 - r - 1 = 0 and r3 - r - 1 = 0 respectively) determines the value of the limit. In the case of eqn. (36) the two zeros are (1 + 4 5 ) / 2 and (1 - J5)/2 and the general solution takes the general form C,(*y + C 2 i T ) 1 - J 5 ' where C and C are constants which depend on the initial conditions. At very large values of n the term containing the second zero becomes negligible and the required limit is whence z is the characteristic scaling factor regardless of the initial conditions. The same sort of arithmetic holds in the case of eqn. (37). This loss of dependence on initial conditions is the reason for the observed self-similarity of graph proper- ties shown in the Tables. Although this result is 'almost trivial' its mention seems without precedence. One is tempted to conclude that the fractal characters associated with homologous series of arbitrary structures may allow almost exact solutions of recursive relations at the higher positions of the series. 1 1 Self-similarity of Kekule and Clar Counts Kekule Counts the Golden mean The expressions [a, u 2 .I and [a,; a a 2 .I are short- hand notations respectively for the continued fractions :48 and (38) 1 1 a + a +- a +- a + . u2 + .

ISSN:0956-5000    

DOI:10.1039/FT9949002201

出版商:RSC    

年代:1994

数据来源: RSC

摘要:

J. CHEM. SOC. FARADAY TRANS. 1994 90(15) 2211-2213 Structure of the Diamminecopper(1) Ion in Solution An X-Ray Absorption Spectroscopic Study Geraldine Lamble National Synchrotron Light Source Brookha ven Laboratory Upton NY USA Arild Moen* and David G. Nicholson Department of Chemistry(A VH) University of Trondheim N-7055 Trondheim Norway X-Ray absorption spectroscopy (XAS) using synchrotron radiation has been used to probe the structure of copper(i) species in an aqueous ammonia solution that contains hydrazine to prevent any oxidation to copper(ii) species. Combining a characteristic copper(1) pre-edge feature with the extended X-ray absorption fine structure (EXAFS) of the XAS enabled t h e stereochemistry and bond distances to be extracted for the predominant species which is shown to be t h e diamminecopper(1) ion.The structure is linear with CU-N bond lengths of 1.88 0.02 A. Although to a large extent studies on the chemistry of copper have centred around the copper(I1) valence state there is an increased awareness that the copper(1) state also has important roles to play. Certainly it has been known for processes as exemplified in a number of metalloproteins. '-' some time that copper(1) has important functions in some life In this context studies on the inorganic chemistry of copper(1) are particularly relevant even for simple complexed species. Investigations on the XAS of copper(1) sites in simple species are especially useful because an understanding of the different spectral processes can with advantage be trans- ferred to more complex systems.Copper(1) forms neutral anionic and cationic complexes. The strength of the copper(1)-ligand bonds increases in the order Cu-0 Cu-S CU-N and whilst the highest coordi- nation number attained is four intermediate values of two and three are also In the older literature,6 two- coordination is attributed to complexes with ligands with oxygen-donor atoms and also for the acetonitrile (CH,CN) complex. However we note that Persson et aL7 report that the acetonitrile dimethyl sulfoxide aqua- and pyridine com- plexes are four-coordinate most probably tetrahedral. Unlike the case of the analogous silver(1) complexes there is rela- tively little in the literature about the formation and equi- libria of copper(1)-ammonia complexes.With ammonia under the appropriate conditions copper(1) forms the mono- ammine the diammine and the trisammine complex ion. The fact that they are so readily oxidised by air to the intense violet-blue and very stable tetraamminecopper(I1) cation has probably precluded their detailed study. Nevertheless there has been sporadic activity in copper(1) chemistry over the past century one of the first results being a study on ammonia complexes reported over 90 years ago by Bodlander' who established that the primary copper(1) species in aqueous media is [Cu(NH,),] +. Subsequent elec- trochemical and polarographic studies'.' indicate the pres- ence of [Cu(NH,)J+ at low ammonia concentrations with a stability constant of 0.86 x lo5 at 2 mol dm- strength for the reaction [Cu(NH,)]+ + NH,=[Cu(NH,),]+ [Cu(NH,),]+ + NH,e[Cu(NH,),]+ (1) More recently Braish et al." observed that the molar absorption coefficient at all wavelengths in the 210-330 nm region increases as the concentration of ammonia increases indicating that there may also be a trisammine species formed at higher ligand concentrations as follows (2) The equilibrium constant for reaction (2) is less than 2 x 10-3.Braish et al. concluded that solutions with ammonia con- centrations between 0.4 and 14.2 mol dm- consist largely of [Cu(NH,),]+ with only very small amounts of [Cu(NH,),]+. Reaction (2) is therefore the only important one at these ligand concentrations since the equilibrium constant for reac- tion (1) essentially rules out the existence of [Cu(NH,)]+ in any significant amount.In contrast with the more stable diamminecopper(1) cation aqua-complexed copper(1) species are very unstable in solu- tion. This is reflected by the magnitude of the dispro- portionation constant (5.4 x 10' mol-')'2 for the reaction 2Cu'=Cu" + cuo Experimental Preparation An aqueous solution containing the copper(1) diammine complex cation [Cu(NH,),] + (0.14 mol drn-,) was prepared as follows Cu(NO,) . 3H20 (0.6 g) (Merck) was dissolved in water (5 ml) and 0.880 NH (3 ml) added to give the deep violet-blue tetramminecopper(I1) complex { [Cu(NH,),]' + >. [The initial precipitate of Cu(OH) redissolved when all of the ammonia solution had been added].The pH of the solu- tion was now adjusted (pH 9) by adding HNO (5 mol dm-3; 221 1 (3) This explains the very low concentration of copper(1) in aqueous solution and the fact that typically an aqua- complexed copper(1) ion exists in solution for less than a second.13 Whether or not the coordination number is two or higher the aquacopper(1) ion exists only in low concentra- tions in the presence of a large excess of copper(I1). This insta- bility in aqueous media and increased stability in other complexing solvents has been rationalised in terms of the high heat of hydration of copper(^^).^ Although impossible to determine directly because of the low concentration Persson et al.' propose that the tetraaquacopper(1) ion consists of four water molecules tetrahedrally coordinated to copper with Cu-0 distances of ca. 2.13 A. Here we describe a method for preparing an aqueous solu- tion in which total reduction of copper(r1) is ensured and in which copper(1) is complexed as the diammine ion. The system is designed to be fairly robust to oxidation within a time interval that permits study by XAS and other physical methods. We report the results of a synchrotron XAS investi- gation on a solution containing the two-coordinate diamminecopper(1) complex ion.

ISSN:0956-5000    

DOI:10.1039/FT9949002211

出版商:RSC    

年代:1994

数据来源: RSC