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Journal of the Chemical Society, Faraday Transactions,
Volume 90,
Issue 19,
1994,
Page 073-074
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THE ROYAL SOCIETY OF CHEMISTRY Journal of the Chemical Society Faraday Transactions Scientific Editor Prof. Peter J. Sarre Department of Chemistry University of Nottingham 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) Prof. 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) R. A. Marcus (Pasadena) A. M. Bradshaw (Berlin) Y. Marcus (Jerusalem) A. Carrington (Southampton) B. J. Orr (North Ryde) G. Cevc (Munich) R. H. Ottewill (Bristol) M. Che (Paris) R. Parsons (Southampton) M. S. Child (Oxford) S. L. Price (London) B. E. Conway (Ottawa) F. Rondelez (Paris) G. R. Fleming (Chicago) D. K. Russell (Auckland) R. Freeman (Cambridge) J. P. Simons (Oxford) H. L. Friedman (Stony Brook) S. Stoke (Amsterdam) H. H. J. Girault (Lausanne) J. Troe (Gottingen) H. lnokuchi (Okazaki) J. Wolfe (Kensington, NSW) J.N. lsraelachvili (Santa Barbara) C. Zannoni (Bologna) M. L. Klein (Philadelphia) R. N. Zare (Stanford) A. C. Legon (Exeter) A. Zecchina (Turin) C. Zhang (Dalian) Journal of the Chemical Society, Faraday Transactions (ISSN 0956-5000) is published twice monthly by The Royal Society of Chemistry, Thomas Graham House, Science Park, Milton Road, Cambridge CB4 4WF. UK. All orders accompanied with payment should be sent directly to The Royal Society of Chemistry, Turpin Distribution Services Ltd., Black- horse Road, Letchworth, Herts. SG6 1 HN, UK. NB Turpin Distribution Services Ltd., dis- tributors, is wholly owned by the Royal Society of Chemistry. 1994 Annual subscription rate EC f744.00, Rest of World f800.00, USA $1400.00.Canada f840 (excl. GST). Customers should make payments by cheque in sterling payable on a UK clearing bank or in US dollars payable on a US clearing bank. Second class postage is paid at Rahway, NJ. Airfreight and mailing in the USA by Mercury Airfreight International Ltd. Inc., 2323 Randolph Avenue, Avenel, NJ 07001, USA and at additional mailing offices. USA Postmaster: send address changes to Journal of the Chemical Society, Faraday Trans- actions, c/o Mercury Airfreight International Ltd. Inc., 2323 Randolph Avenue, Avenel, NJ 07001. All despatches outside the UK by consolidated Airfreight. PRINTED IN THE UK. @ The Royal Society of Chemistry, 1994. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form, or by any means, electronic, mechanical, photographic, recording, or otherwise, without the prior permission of the publishers.Advertisement sales: tel. +44(0)71-287-3091 ; fax. +44(0)71-494-1134, INFORMATION FOR AUTHORS The Royal Society of Chemistry welcomes submission of manuscripts intended for pub- lication in two forms, Research papers and Faraday Communications. These should describe original work of high quality in the sciences lying between chemistry, physics and biology, and particularly in the areas of physical chemistry. biophysical chemistry and chemical physics. Research Papers Full papers contain original scientific work which has not been published previously. However, work which has appeared in print in a short form such as a Faraday Communi- cation is normally acceptable. 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In the latter case, the top copy of the manuscript including any figures etc., together with the name of the person through whom the Com- munication is being submitted, should be sent simultaneously to the Editor at the Cambridge address. Proofs of Communications are not normally sent to authors unless this is specifically requested. Faraday Research Articles Faraday Research Articles are occasional invited articles which are published follow- ing review. They are designed to be topical articles of interest to a wide range of research scientists in the areas of Physical Chemistry, Biophysical Chemistry and Chemical Physics. Full details of the form of manuscripts for Articles and Faraday Communications, con- ditions for acceptance etc. are given in issue number one of Faraday Transactions, published in January of each year, or rnay be obtained from the Editorial Manager. There is no page charge for papers published in Faraday Transactions. Fifty reprints are supplied free of charge. Prof. P. J. Sarre, Scientific Editor. Tel.: Nottingham (0602) 513465 (24 hours) E-Mail (JANET): PCZPSF@UK.AC.NOTTVAX Fax: (0602) 51 3466 Telex: 37346 UNINOT G Dr. R. J. Parker, Editorial Manager. Tel.: Cambridge (0223) 420066 E-MaiI (INTERNET) : RSCI @RSC.ORG (For access from JANET use RSCI o/a RSC.0 RG @UK.AC. NSF NET- RELAY) Fax: (0223) 423623 or 420247 Telex: 81 8293 ROYAL G
ISSN:0956-5000
DOI:10.1039/FT99490FX073
出版商:RSC
年代:1994
数据来源: RSC
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Back cover |
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Journal of the Chemical Society, Faraday Transactions,
Volume 90,
Issue 19,
1994,
Page 075-076
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ISSN:0956-5000
DOI:10.1039/FT99490BX075
出版商:RSC
年代:1994
数据来源: RSC
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Contents pages |
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Journal of the Chemical Society, Faraday Transactions,
Volume 90,
Issue 19,
1994,
Page 200-201
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ISSN 0956-5000 JCFTEV(19) 2849-3022 (1994) JOURNAL OF THE CHEMICAL SOCIETY Faraday Transactions Physical Chemistry & Chemical Physics CONTENTS 2849 Microwave spectrum and conformation of 5,6-dihydro-2H-thiopyran L. A. Leal, D. G. Lister, J. L. Alonso, M. M. J. Tecklenburg, J. R. Villarreal and J. Laane 2857 A multiple hard-ellipsoid model for rotationally inelastic collisions A. J. Marks 2865 Leapfrog transformations and polyhedra of Clar type P. Fowler and T.Pisanski 2873 Ab initio study of the molecular structure, polarizability and first hyperpolarizability of 6-hydroxy- 1- formylfulvene S. Millefiori and A. Alparone 288 1 Delft molecular mechanics : A new approach to hydrocarbon force fields. Inclusion of a geometry-dependent charge calculation A.C.T. van Duin, J. M. A. Baas and B. van de Graaf 2897 Luminescence from irradiated butadiene solutions : Fluorescence of ally1 radicals? B. Brocklehurst and D. N.Tawn 2901 EPR studies of the formation of alkene cations due to ion-molecule reactions in the 77 K radiolysis of pentane and hexane containing additives T. Ichikawa, N.Ohta and M. Shiotani 2905 Ligand-controlled oxidation state ambivalence in copper-quinone complexes. Replacement of N-donor by S-donor ligands favours the copper(1bsemiquinone over the copper(II)-catecholate form J. Rall and W. Kaim 2909 Oxotungsten(v) and (VI) complexes of 1,3-dimethyllumazine as models for the tungstopterin cofactor F. M. Hornung and W. Kaim 2913 Thermodynamics of liquid binary (alkanenitrile-alkane) mixtures.Part 2.-Experimental excess molar heat capacity at 298.15 K and structure in solution R. Eustaquio-Rincon, B. E. Garcia and A. Trejo 2921 Studies of light-induced nickel EPR signals in desulfovibrio gigas hydrogenase M. Medina, R.Williams, R.Cammack and E. C.Hatchikian 2925 Entropy change in the two-dimensional phase transition of adenine adsorbed at the Hg electrode/aqueous solution interface C.Fontanesi 2931 Electrochemical studies of the conformational and sodium cation complexation properties of calixC4larene-diquinones Z. Chen, P. A. Gale, J. A. Heath and P.D. Beer 2939 Kinetics of reductive dissolution of sodium bismuthate by Ce"' and Mn" ions A. Mills and X.Li 2945 Non-isothermal crystallization from liquid solutions: Effect of heat of crystallization on growth rate J-P.Hsu and B-T. Liu 2953 Investigation of the structure of the columnar liquid-crystalline phase of copper(I1) carboxylates. An FTIR spectro- scopic study M. F. Ramos Moita, M. L. T. S. Duarte and R. Fausto 2961 29Si Solid-state NMR study of the surface structure of Aerosil silica V. V. Brei 2965 Physisorption of argon, nitrogen and oxygen by MCM-41, a model mesoporous adsorbent P. J. Branton, P. G. Hall, K. S. W. Sing, H. Reichert, F. Schiith and K. K. Unger 2969 Chemisorption of H, and H,-0, on polymorphic zirconia K-H. Jacob, E. Knozinger and S. Benfer 2977 Hydrogenation of carbon monoxide and ethene over Ni-doped supported Pt catalysts F. Eder and J. A. Lercher 2981 Nature of vanadium species on Sn0,-V,O,-based catalysts. Chemistry of preparation, characterization, thermal sta- bility and reactivity in ethane oxidative dehydrogenation over V-Sn mixed oxides S.Bordoni, F. Castellani, F. Cavani, F. Triiiro and M. Gazzano 3001 Reaction mechanism of methane oxidation to synthesis gas over an activated PdY zeolite H. Matsumoto and S. Tanabe 3007 Evaluation of concentration-dependent diffusivity with uptake curve L. Zhongmin, Z. Lubin, C. Guoquan, C. Guangyu and W. Qingxia 3011 Study of fast diffusion in zeolites using a higher harmonic frequency response method D. Shen and L. V. C. Rees 3017 Frequency response study of single-file diffusion in theta-1 D. Shen and L. V. C. Rees 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/FT99490FP200
出版商:RSC
年代:1994
数据来源: RSC
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Back matter |
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Journal of the Chemical Society, Faraday Transactions,
Volume 90,
Issue 19,
1994,
Page 202-209
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Cumulative Author Index 1994 Aas,N., 1015 Benko, J., 855 Butt, M. D., 727 Corma,A., 213 Engberts, J. B. F. N., 727, Abadzhieva, N., 1987 Benniston, A. C., 953,2627 Buttar, D., 1811 Cormier, G., 755 1905,2703,2709 Abbott, A. P., 1533 Beno, B., 1599 Byatt-Smith, J. G., 493 Corradini, F., 859, 1089 Enomoto, N., 1279 Abraham, R. J., 2775 Bensalem, A., 653 Cabaleiro, M. C., 845 Corrales, T., 83 Eustaquio-Rincon, R., 11 3, Abramowicz, T., 2417 Bensch, W., 2791 Caceres, C., 2125 Cosa, J. J., 69 2913 Afanasiev, P., 193 Berbaran-Santos, M. N., Caceres, M., 1217 Costas, M., 1513 Ewins, C., 969 Agren, H., 1479 2623 Caceres Alonso, M., 553 Cottier, D., 1003 Fantola Lauarini, A. L., Aikawa, M., 911 Berces, T., 41 1,2635 Cairns, J. A., 1461 Coudurier, G., 193 423 Aitken, C.G., 935 Bergeret, G., 773 Calado, J. C. G., 649 Courcot, D., 895 Farhoud, M., 2455 Akanuma, K., 1171 Bernardi, F., 1617, 1669, Caldararu, H., 213,2643 Coveney, P. V., 1953 Fausto, R., 689,2953 Akolekar, D. B., 1041 1671, 1672 Callens, F. J., 2541, 2653 Cox, A. P., 2171 Favaro, G., 279,333 Alava, I., 2443 Berndt, H., 2837 Calvaruso, G., 2505 Cox, R. A., 1819 Favero, L. B., 2183 Albert, I. D. L., 2617 Bertran, J., 1679, 1757, Calvente, J. J., 575 Cracknell, R. F., 1487 Favero, P. G., 2183 Albery, W. J., 1115 1800, 1806 Calvo, E., 2395 Craig, S. L., 1663 Favre, E., 2001 Alcober, C., 2395 Beutel, T., 1335 Calvo, E. J., 987 Cramer, C. J., 1802 Fawcett, W. R., 2697 Aldaz,A., 609 Beyer, H. K., 1329 Camacho, J. J., 23 Crawford, M. J., 817 Feliu, J.M., 609 Alfimov, M. V., 109 Bhuiyan, L. B., 2002 Cameron, B. R., 935 Crisafulli, C., 2809 Fenn, C., 1507 AI-Ghefaili, K. M., 383, Bickelhaupt, F., 327, 1363 Caminad, W., 2183 Crowther, D., 2155 Fernando, K. R., 1895 1047 Bickley, R. I., 2257 Cammack, R., 2921 Cruzeiro-Hansson, L., 1415 Fierro, J. L. G., 2125 Ali, V., 579, 583 Biczok, L., 41 1,2635 Campa, M. C., 207 Cullis, P. M., 727, 1905, Filimonov, I. N., 219, 227 Aliev, A. E., 1323 Bielanski, A., 2099 Campelo, J. M., 2265 2703,2709 Finger, G., 2141 Allegrini, P., 333 Biggs, P., 1197, 1205 Campos, A., 339 Curtis, J. M., 239 Fisher, I., 2425 Allen, N. S., 83 Billingham, J., 1953 Canosa-Mas, C. E., 1197, DAlagni, M., 1523 Flamigni, L., 2331 Alonso, J. L., 2849 Bilmes, S. A., 2395 1205 Damiani, D., 2183 Fleischmann, M., 1923 Alparone, A., 2873 Binet, C., 1023 Capitan, M.J., 2783 Dang, N-T., 875 Fletcher, P. D. I., 2743 A1 Rawi, J. M. A., 845 Binks, B. P., 2743 Capobianco, J. A., 755 Danil de Namor, A. F., 845 Flint, C. D., 1357 Amorim da Costa, A. M., Black, S. N., 1003 Caragheorgheopol,A., 2 13 Das, D., 1993 Fogden, A., 263 689 Blackett, P. M., 845 Carlile, C. J., 1149 Das, T. N., 963 Fontanesi, C., 2925 Amoskov, V. M., 889 Blake, J. F., 1727 Carlsen, L., 941 Dasannacharya, B. A., 1149 FornCs, V., 213 Ando, M., 1011 Blanco, M., 2125 Carrizosa, I., 2783 Dash, K. C., 2235 Fowler, P., 2865 Andre, J-M., 2319 Blanco, S., 1365 Carvill, B. T., 233 Datka, J., 2417 Fracheboud, J-M., 1197, Andres, J., 1703,2365 Blandamer, M. J., 727, Castaiio, F., 2443 Davey, R.J., 1003 1205 Andrews, S. I., 1003 1905,2703,2709 Castaiio, R., 1227 David, G., 261 1 Franci, M. M., 1605, 1740, Anson, C. E., 1449 Blaszczak, Z., 2455 Castellani, F., 2981 Davidson, K., 879 1744 AntoniC, T., 1973 Blower, C., 9 19,93 1 Castells, R. C., 2677 Davies, M. J., 2643 Franck, R., 667,675 Aragno, A., 787 Bocherel, P., 1473 Castro, S., 1217 De Benedetto, G. E., 1495 Franke, O., 2821 Arai, S., 1307 Boddenberg, B., 1345 Catalina, F., 83 de Boer, E., 2663 Freeman, N. J., 751 Aramaki, K., 321 Boesman, E., 2541 Cataliotti, R. S., 1397 Defrance, A., 1473 Frety, R., 773 Aravindakumar, C. T., 597 Boggis, S. A., 17 Cavani, F., 2981 Dejaegere, A., 1763 Frey, J. G., 17, 817 Asai, Y., 797 Bohm, F., 2453 Cavasino, F. P., 31 1,2505 de Leng, H.C., 2459 Frostemark, F., 559,2401, Ashfold, M. N. R., 1357 Booth, C., 1961 Ceccarani, M. L., 1397 Delhalle, J., 2319 2531 Asmus, K-D., 1391 Borden, W. T., 1606, 1614, Cense, J-M., 2015 Demeter, A., 41 1, 2635 Fujiwara, Y., 1183 Assfield, X., 1743 1616,1671, 1673,1675, Centeno, M. A,, 2783 Dempsey, P., 1003 Funabiki, T., 2107 Attwood, D., 1961 1689,1733,1734, 1735, Cevc, G., 1941 Demri, D., 501 Galantini, L., 1523 Aveyard, R., 2743 1743,1744,1802,1807 Chakrabarty, D. K., 1993 Deng, N-J., 1961 Gale, P. A., 2931 Avila, V., 69 Bordiga, S., 2827 Chang, T-h., 1157 Deng,Z., 2009 Galvagno, S., 2803, 2809 Axford, S. D. T., 2085 Bordoni, S., 2981 Charlesworth, D., 1999 Denkov, N. D., 2077 Gandolfi, R., 1077 Baas, J. M. A., 2881 Borello, E., 2827 Charlesworth, P., 1073 Derrick, P.J., 239 Gans, P., 315,2351 Baba,T., 187 Borge, G., 1227 Chaudhry, M., 2235,2243, Dewing, J., 1047 Gao,Y., 803 Baba, Y., 2423 Borisenko, V. N., 109 2683 Diagne, C., 501 Garcia, A., 2265 Back, G-H., 2283 Bottoni, A., 1617 Che, M., 2277 Dickinson, E., 173, Garcia, B. E., 2913 Badia, A., 1501 Boutonnet-Kizling, M., Chen, J-S., 429,717 2737 Garcia, R., 339 Badri, A., 1023 1023 Chen, J. S., 2765 Diebler, H., 2359 Garcia Fierro, J-L., 1455 Bagdtti, M., 1077 Bowker, M., 1015 Chen, L., 2467 Dines, T. J., 1461 Garcia-Pafieda, E., 575 Balaji, V., 1653 Bowmaker, G. A., 2579 Chen, Y-H., 617 Doblhofer, K., 745 Gautam, P., 697 Ball, M. C., 997 Bozon-Verduraz, F., 653 Chen, Z., 2931 Domen, K., 911 Gavuuo, E., 1523 Ball, S. M., 523, 1467 Bradley, C.D., 239 Cheng, A., 253 Doney, S. C., 1865 Gazzano, M., 2981 Bally, T., 1615, 1674, 1733, Bradshaw, A. M., 403 Cheng, C. P., 1157 Dong, S., 2057 Geantet, C., 193 1808 Branton, P. J., 2965 Cheng, Y., 2517 Donnamaria, M. C., 2731 Gengembre, L., 895 Ban, M. I., 1610 Bratu, I., 2325 Cherqaoui, D., 97,2015 Dore, J. C., 2497 Gerratt, J., 1643, 1672, Baonza, V. G., 553 Braun, B. M., 849 Chesta, C. A., 69 Dory, M., 2319 1673, 1801 Baonza, V. G., 1217 Brei, V. V., 2961 Chevalier, S., 667,675 Dossi, C., 1335 Gerry, M. C. L., 2601 Barbaux, Y., 895 Breysse, M., 193 Chi, Q., 2057 Doughty, A., 541 Getty, S.J., 1689 Barbero, C., 2061 Briggs, B., 727, 1905, 2703, Child, M. S., 1739 Douglas, C. B., 471 Ghiggino, K. P., 2845 Barczynski, P., 2489 2709 Chiu, S.S-L., 1575 Downing, J. W., 1653 Giglio, E., 1523 Barker, S. A., 1689 Brocklehurst, B., 271,2001, Chmiel, G., 1153 Duarte, M. L. T. S., 2953 Gil, A. M., 1099 Barnes, J. A., 1709 2897 Cho,T., 103 Duke, M. M., 2027 Gil, F. P. S. C., 689 Barthel, J., 2475 Brogan, M. S., 1461 Choisnet, J., 1987 Dunmur, D. A., 1357 Gilbert, B. C., 2643 Barthomeuf, D., 667,675 Brown, N. M. D., 1357 Chowdhry, B. Z., 1999 Dunstan, D. E., 1261 Gilchrist, J., 1149 Bartl, H., 2791 Brown, R. G., 59 Christensen, P., 459 Duplltre, G., 1501 Gill, D. S., 579, 583 Bartlett, P. N., 2155 Brown, S. E., 739 Chung, Y-L., 2547 Duxbury, G., 1357 Gill, J. B., 315,2351 Basini, L., 787 Bruna, P. J., 683 Cihnek, A., 1973 Dwyer, J., 383, 1047 Gillies, D. G., 2345, 2547, Bassat, J.M., 1987 Brzezinski, B., 843, 1095 Claridge, J. B., 2799 Dyke, J. M., 17 2671 Bassoli, M., 363 Buchner, R., 2475 Clark, T., 1669, 1678, 1783, Dziembaj, R., 2099 Goede, S.J., 327, 1363 Battaglini, F., 987 Buckley, A. M., 1003 1807, 1808, 1809, 1810 Eastoe, J., 487, 2497 Gomez, C. M., 339 Bauer, C., 517 Buemi, G., 121 1 Clegg, S.L., 1875 Easton, C. J., 739 Goncalves da Silva, A. M., Baur, W. H., 2141 Bujan-Nuiiez, M. C., 2737 Clement, R., 2001 Ebitani, K., 377 649 Beagley, B., 2775 Biilow, M., 2585 Climent, M. A., 609 Eder, F., 2977 Gonzalez-Carreiio, T., 2257 Beer, P. D., 2931 Burdisso, M., 1077 Coates, J. H., 739 Eggins, B. R., 2249 Gonzalez-Eli@, A. R., 2257 Bell, A. J., 17,817 Burget, D., 2481 Coitiiio, E. L., 1745 Egsgaard, H., 941 Goodfellow, J.M., 1415 Belton, P.S., 1099 Busca, G., 1161,1293 Collett, J. H., 1961 El-Atawy, S., 879 Gordillo, G. J., 1913 Bender, B. R., 1449 Busch, T., 2611 Colmenares, C. A., 1285 El Baghdad;, A., 1313 Gouder, T. H., 1285 Bendig, J., 287 Buschmann, H-J., 1507 Cook, J., 1999 El-Basil, S., 2201 Goworek, T., 1501 Benfer, S., 2969 Butler, L. J., 1581, 1612, Cooney, R. P., 2579 Elisei, F., 279 Gray, P. G., 369 Bengtsson, L. A,, 559,2401, 1613, 1614, 1671, 1677, Cooper, D. L., 1643 Elliot, A. J., 831, 837 Gready, J. E., 2047 253 1 1809 Cordischi, D., 207 Endregard, M., 2775 Green, M. L. H., 2799 i Green, W. A., 83 Grein, F., 683 Grieser, F., 1251 Grifith, W. P., 1105 Grigera, J. R., 2731 Grimshaw, J., 75 Grzybowska, B., 895 Guangyu, C., 3007 Guelton, M., 895 Howard, E.I., 2731 Hrovat, D. A., 1689 Hu, W. P., 1715 Hubberstey, P., 2753 Hummel, A., 2459 Hungerbuhler, H., 1391 Hutchings, G. J., 203 Hutton, R. S., 345 HSU, J-P., 1435,2945 Kida, I., 103 Kiennemann, A., 501 Kim, J-H., 377 Kimura, M., 1355,2423 King, F., 203 Kingston, P. A., 2743 Kinjo, Y., 2235,2683 Kirby, A. R., 2551 Kirchner, S., 1941 Loginov, A. Yu., 219,227 Lohse, U., 1033 Long, A., 1547 Longdon, P. J., 315 Lopez Agudo, A., 2125 Lorenzelli, V., 1293 Loveday, D. C., 1533 Lovejoy, E. R., 2159 Lu, J-X., 39 Medina, F., 1455 Medina, M., 2921 Melandri, S., 2183 Melrose, J. R., 1133 Menduiiia, C., 2677 Meng, Z., 2591 Merga, G., 597 Mesbah, A., 2015 Meunier, F., 369 Guilhaume, N., 1541 Guillaume, F., 1313 Guldi, D. M., 1391 Ichikawa, T., 2901 Igawa, K., 2119 Iizuka, Y., 1301, 1307 Kirschner, J., 403 Kita, H., 803 Kitchen, D.C., 1581 Lubin, Z., 3007 Ludemann, H-D., Lui, Y-P., 1735 2071 Mezyk, S. P., 831 Michi, J., 1606, 1675, 1677, 1678,1680,1733,1809 Gulliya, K. S., 953 Gunning, A. P., 2551 Guoquan, C., 3007 Hachey, M., 683 Hadjiivanov, K., 2277 Haeberlein, M., 263 Ikawa, S-i., 103 Ikonnikov, I. A., 219 Ilczyszyn, M., 141 1 Il'ichev, Y. V., 2717 Ilyas, M., 2413 Imamura, H., 21 19 Klein, M. L., 253,2009 Kleshchevnikova, V. N., Klissurski, D., 1987 Kloss, A. A., 2697 Knoche, W., 1507 629 Luna, D., 2265 Lunelli, B., 137 Luthjens, H., 2459 Ma, J., 1351 Mabuchi, M., 899,1979 MacFarlane, A. J. B., 251 1 Michl, J., 1653 Micke, A., 2585 Miessner, H., 2837 Millar, G. J., 2579 Millefiori, S., 2873 Mills, A., 1429, 2939 Hakin, A.W., 2027 Hall, C., 2095 Hall, D. I., 517 Hall, G., 1 Hall, P. G., 2965 Hallbrucker, A., 293 Halpern, A., 721 Hamnett, A., 459 Hancock, G., 523,1467 Indovina, V., 207 Inerowicz, H. D., 2223 Inoue, Y., 797,815 Ishiga, F., 979 Ishigure, K., 93, 591 Ishikawa, T., 2567 Isoda, T., 869 Ito, O., 571 Iwasaki, K., 121 Knozinger, E., 2969 Knozinger, H., 1335 Kobayashi, A., 763 Kobayashi, H., 763 Kobayashi, T., 101 1 Koga, N., 1789 Kondo, Y., 121 Kong, Y. C., 2375 Kontturi, A-K., 2037 Machado, V. G., 865 Macias, M., 2265 Mackenzie, K., 1810 Mackie, J. C., 541 Mackintosh, J. G., 1121 Macpherson, A. N., 1065 Madariaga, J. M., 1227 Maeda, T., 899, 1979 Maerker, C., 1799 Milone, C., 2803 Milton, D. M. P., 1373 Milverton, D. R., 2171 Min, E-z., 1351 Minaev, B.F., 1479 Minchev, L., 1987 Minyaev, R. M., 1831, 1839 Misono, M., 1183 Mitchell, P. C. H., 1606, Handa, H., 187 Jacob, K-H., 2969 Kontturi, K., 2037 Maes, F., 2541 1802 Hann, K., 733 Jacobs, W. P. J. H., 1191 Kornatowski, J., 2141 Maestre, A., 575 Mitchell, P. J., 1133, 1931 Hao, L., 133, 1223, 1909 Harada, S., 869 Haraoka, T., 91 1 Hardy, J. A., 2171 Harland, P. W., 935 Harper, R. J., 659 Harriman, A., 697,953, Harris, K. D. M., 1313, Harris, P. J. F., 2799 Harrison, N. J., 55 Haruta, M., 1011 Haselbach, E., 2481 Hashimoto, K., 1177 Hashino, T., 899 Hashitomi, O., 2423 Hasik, M., 2099 Hatchikian, E. C., 2921 Hattori, H., 803 Hawkins, G. D., 1802 Hayashi, H., 2133 Haymet, A. D. J., 1245 Heal, M. R., 523,1467 Healy, T. W., 1251 Heath, J.A., 2931 Heatley, F., 1961 Heenan, R. K., 487,2497 Hefter, G. T., 1899,2475 Heinzle, M. G., 2337 Helmer, M., 31, 395 Hemptenmacher, P., 2753 Herein, D., 403 Hernanz, A., 2325 Herod, A. A., 1357 Herrero, C. P., 2597 Herrington, T. M., 2085 Herrmann, J-M., 1441 Herzog, B., 403 Heyes, D. M., 1133, 1931 Higgins, S., 459 Hillier, I. H., 1575 Hillman, A. R., 1533,2155 Hindermann, J-P., 501 Hirst, D. M., 517, 1811 Hiyane, I., 973 Hobbis, C. M., 2579 Hoekstra, D., 727, 1905, Hoffmann, R., 1507 Hogan, P., 2691 Holden, K. M. L., 2351 Holmberg, B., 559,2401, Holz, M., 849 Horio, M., 2573 Horiuchi, T., 2573 Hornung, F. M., 2909 Hoshino, H., 479 Hosoi, K., 349 Houk, K. N., f 599,1605, 1614, 1615,1616, 1672, 1678, 1680, 1810 2627 1323 2703,2709 2531 Jacques, P., 2481 Jain, S.K., 2065 Jakobsen, H. J., 2095 Jakubov, T., 783 Jameel, A. T., 625 Janchen, J., 1033,2837 Jancke, K., 2141 Jayakumar, R., 161,2725 Jayasooriya, U. A., 1265 Jeevan, R. G., 2725 Jenneskens, L. W., 327, Jennings, B. J., 55 Jiang, D-z., 1351 Jiang, P-Y., 591 Jiang, P. Y., 93 Jiao, H., 1559 Jobic, H., 1191 Johansson, L. B.-A., 305 Johari, G. P., 883, 1143, John, S. A., 1241 Jones, M. N., 2511 Jones, R. L., 1819 Jones, V. W., 2061 Jorgensen, W. L., 1727 Jorgenson, W. L., 1735, Joseph, E. M., 387 Joshi, P. N., 387 Joswig, W., 2141 Jurs, P. 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A., 383, Maksymiuk, K., 745 Malatesta, V., 333 Malcolm, B. R., 493 Malet, P., 2783 Malitesta, C., 1495 Mallard, X., 255 1 Mallon, D., 83 Malmgren-Hansen, B., Mandal, A. B., 161,2725 Manoharan, P. T., 2725 Marcheselli, L., 859 Marchetti, A., 859, 1089 Marcus, Y., 1899 Mariani, M., 423 Marinas, J. M., 2265 Marks, A. J., 2857 Marques, J. M. C., 2189 Marsden, I., 2775 Marston, G., 2453 Martin, A., 2837 Martin, G., 2155 Martinez, L., 2043 Martinez, M. T., 2443 Martini, L., 1961 Martins, A., 143 Martins, R. L., 2297 Marty, J. L., 2027 Martyna, G. J., 2009 Maruya, K-i., 91 1 Masatoki, S., 2769 Masetti, F., 333 Mason, R. S., 1373 Massucci, M., 445 Masuda, H., 2573 MatijeviC, E., 167 Matsuda, J., 321 Matsumoto, H., 3001 Matsumura, Y., 1177,2133 Matsuura, H., 2769 Matthys, P.F., 2653 May, I. P., 751 Mazzucato, U., 333 McCann, G. F., 2579 McDouall, J. J. W., 1575, McGilvery, D., 1055 Mchedlov-Petrossyan, N. O., McKay, H. A. 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F., 1381 Navaratnam, S., 83,2467 Navarro, R., 2325 Navio, J. A., 2265 Neel, J., 2001 Neoh, K. G., 355 Neri, G., 2803 Nerukh, D. A., 297 Nguyen, M. T., 1610,1616, 1669,1733,1734,1739, 1771,1807 597, 703, 711, 825 1737, 1738 2319,2617 2423 Nguyen, Q. T., 2001 Nicholas, C. V., 1961 Nicholson, D., 181, 1487, Nicholson, D.G., 2211, 2775 2375 ii Nickel, U., 617 Niecke, E., 2611 Nigar, R., 2413 Ninomiya, J., 103 Nishihara, H., 321 Posadas, D., 2395 Potter, C. A. S., 59 Powell, D. B., 1449 Poyato, J. M. L., 23 Poiniczek, J., 2099 Sanada, M., 1307 Sano, T., 869 Sapre, A. V., 825 Sarmiento, F., 251 1 Sarre, P. J., 517 Stanley, D. R., 1003 Stefanov, P., 1987 Stewart, B., 969 Steytler, D. C., 2497 Stoeckli, F., 783 Tsuchiyama, T., 1355 Tsuji, H., 803 Tsuji, M., 1171 Tsunashima, S., 549 Tsunetoshi, J., 1307 Nishimura, N., 2021 Nogami, T., 763 Nogueira, L., 2297 Nonaka, O., 121 Prakash, A. M., 2291 Prenosil, J. E., 587 Preuss, K. E., 2027 Previtali, C. 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P., 865 Zundel, G., 843,1095 1733,1810 Xiao, Shaorong, 1983 Yanes, C., 575 Zecchina, A., 2827 iv FARADAY DIVISION INFORMAL AND GROUP MEETINGS Surjace Reactivity and Catalysis Group with the Royal Microscopical Society Microscopy and Catalysis To be held at The Royal Institution, London on 27 October 1994 Further information from: The Administrator, The Royal Microscopical Society, 37/38 St. Clements, Oxford OX4 1AJ ~ ~~ Division Endowed Lecture Symposium: Simulation of Condensed Matter from First Principles To be held at Cambridge University on 23 November 1994 Further information from Mrs.Y.A. Fish, The Royal Society of Chemistry, Burlington House, London WlV OBN 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 Colloid and Interjace Science Group Surface Forces and Probe Microscopy To be held at Imperial College, London on 19 December 1994 Further information from Dr. D. Clark, Institute of Food Research, Norwich Laboratory, Nonvich Research Park, Colney, Norwich NR4 7UA ~~ ~~ ~ ~ ~ ~ ~ ~~ ~~ ~~ Division Endowed Lecture Symposium: Recent Advances in the Study and Preparation of Novel Surfaces To be held at The Royal Institution on 26 January 1995 Further information from Mrs.Y.A. Fish, The Royal Society of Chemistry, Burlington House, London WlV OBN Division Endowed Lecture Symposium: Spectroscopy and Dynamics of Electronically Excited States To be held at University of Manchester on 29 March 1995 Further information from Mrs. Y.A. Fish, The Royal Society of Chemistry, Burlington House, London W1V OBN Colloid and Interjace Science Group Concentrated Dispersions To be held at the University of Bristol on 29-31 March 1995 Further information from Dr. A. Lips, Unilever Research, Colworth Laboratory, Colworth House, Sharnbrook, Bedford MK44 ILQ Statistical Mechanics and Thermodynamics Group with the Experimental Thermodynamics Society Experimental Thermodynamics Conference To be held at the University of Reading on 5-7 April 1995 Further information from Dr.J. Henderson, School of Chemistry, University of Leeds, Leeds LS2 9JT Division Annual Congress: Lasers in Chemistry To be held at Heriot Watt University, Edinburgh on 10-13 April 1995 Further information from Dr. J. F. Gibson, The Royal Society of Chemistry, Burlington House, London W1V OBN Division Endowed Lecture Symposium: Molecular Complexes and Interactions To be held at the University of Bristol on 4 May 1995 Further information from Mrs. Y. A. Fish, The Royal Society of Chemistry, Burlington House, London W1V OBN V Division Joint Meeting with the Division de Chimie Physique de la Societe' Francaise de Chimie, Deutsche Bunsen Gesellschaj? fir Physikalische Chemie and Associazione Italiana di Chimica Fisica Fast Elementary Processes in Molecular Systems To be held at the Universitk 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 Biophysical Chemistry Group Dynamic Processes in Biophysics To be held at the University of East Anglia on 6-8 September 1995 Further information from Dr. D. C. Clark, Institute of Food Research, Norwich Laboratory, Norwich Research Park, Colney, Norwich NR4 7UA Polymer Physics Group Biennial Meeting To be held at the University of Leeds on 6-8 September 1995 Further information from Professor G.R. Davies, Department of Physics, University of Leeds, Leeds LS2 9JT 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 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. vi 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 qf Chemical Sciences University oj Birmingham University of East Anglia Edgbaston, Birmingham Norwich Bl52lT 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 of Bristol, Cantock's Close, Bristol, BS8 1TS, UK Full papers for publication in the Faraday General Discussion 101 volume will be required by May 1995. vii THE ROYAL SOCIETY OF CHEMISTRY, FARADAY DIVISION, GENERAL DISCUSSION 102 Unimolecular Reaction Dynamics Exeter College, Oxford, 19-21 December 1995 Organising Committee: Professor M. J. Pilling (Chairman) Professor J. P. Simons Professor M. S. Child Professor I. W. M. Smith Dr D. C. Clary Professor J. Troe Professor R. Walsh Unimolecular reactions, defined as processes occurring in the ground electronic state, depend on the interplay between microcanonical dissociation or isomerisation and energy transfer. Recent years have seen developments in both experimental and theoretical techniques for probing aspects of such reactions. The Discussion will highlight these latest developments and promote interaction between a potentially wide range of fields. Topics of inclusion are: Theories of microcanonical reactions: quantum dynamics calculations, quantum resonances, developments beyond RRKM -Experimental studies including dissociation of ions,clusters and Van der Waals molecules; real time and frequency domain studies; IVR; multi-channel reactions -Relaxation and supercollisions -Unimolecular dynamics in condensed phases Contributions are invited for consideration by the Organising Committee. Titles and abstracts of about 300 words should be submitted by 15 January 1995 to: Professor M. J. Pilling, School of Chemistry, University of Leeds, Leeds LS2 9JT. Full papers for publication in the Faraday General Discussion 102 volume will be required by 31 August 1995. ... Vlll
ISSN:0956-5000
DOI:10.1039/FT99490BP202
出版商:RSC
年代:1994
数据来源: RSC
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Microwave spectrum and conformation of 5,6-dihydro-2H-thiopyran |
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Journal of the Chemical Society, Faraday Transactions,
Volume 90,
Issue 19,
1994,
Page 2849-2855
Luis A. Leal,
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PDF (794KB)
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摘要:
J. CHEM. SOC. FARADAY TRANS., 1994, 90(19), 2849-2856 Microwave Spectrum and Conformation of 5,6=Dihydro=2H=thiopyran Luis A. Leal, David G. Lister and Jose L. Alonso* Departmento de Quimica-Fisica, Facultad de Ciencias, Universidad de Valladolid, E-47005 Valladolid, Spain Mary M. J. Tecklenburg, John R. Villarreal and Jaan Laane Department of Chemistry, Texas A& M University, College Station, TX 77848, USA The microwave spectrum of 5,6-dihydro-W-thiopyran has been observed between 12.4 and 40 GHz. Rotational and quartic centrifugal distortion constants have been obtained for the ground and seven excited vibrational states. The fundamental wavenumbers of the two lowest vibrations have been obtained from relative intensity measurements as v36 = 134 (12) cm-' and v35 = 219 (18)cm-'.The electric dipole moment of the ground vibra- tional state has been determined from Stark effect measurements as [in D, 1 D (Debye) z3.33564 x C m], pa = 1.35 (l), pb < 0.1, pc = 0.74 (2), with a total dipole moment of p = 1.54 (2). The rotational constants and relatively large pc component of the electric dipole moment are consistent with 5,6-dihydro-W-thiopyran having a twisted or half-chair conformation. A molecular structure has been derived from the ground vibrational state rotational constants and planar moments of inertia using the method of predicate observations. The equilibrium twist angle of the ring is determined as z = 32.5 (1.5)'. Introduction Cyclohexene and a number of six-membered ring molecules related to it by the replacement of methylene groups by oxygen atoms have a twisted or half-chair (I) rather than a bent (11) or planar ring equilibrium conformation.' 11 111 Recently, the conformation of a sulfur-substituted analogue of cyclohexene, 5,6-dihydro-2H-thiopyran (111), has been determined from its vibrational spectrum and molecular mechanics computations;2 it has also been found to have a twisted equilibrium conformation.In this paper we present a study of the microwave spectrum of 5,6-dihydro-2H-thiopy- ran with the aim of making another determination of its molecular conformation. Such a study would be expected to give further information on the lowest-wavenumber vibra- tions of the molecule. Experimental The sample of 5,6-dihydro-2H-thiopyranwas that used in the study of its vibrational spectrum.2 Microwave spectra were observed using a computer-controlled 33 kHz Stark modula- tion ~pectrometer.~ The microwave absorption cell was main- tained at a temperature of 250 K, with sample pressures of 15-25 mTorr.Frequency measurements are estimated to be accurate to 0.05 MHz. Radiofrequency-microwave double re~onance~.~was used in the initial assignment of the spec- trum. The wavenumbers of the excited vibrational states were obtained from relative intensity measurements made using the method of Esbitt and Wilson.6 The electric dipole moment of the ground vibrational state was obtained from Stark effect measurements on the nine components of three J = 3 +-2 transitions which occur in the frequency range 12.4-18GHz.The square-wave Stark modulation was super- imposed on the dc voltage from a Fluke 415 high-voltage power supply. The J = 1 +0 transition of carbonyl sulfide with an electric dipole moment7 of 0.71521 D was used for calibration purposes. Analysis of the Spectrum A molecular model of 5,6-dihydro-2H-thiopyran (see below) showed that both bent and twisted conformers of the mol- ecule were expected to be very asymmetric oblate rotors with Ray's asymmetry parameter K 0.1. Bond dipole calcu-lations in which only the C-S bonds, with a bond dipole moment of 1.0 D, were assumed to be polar indicated that the main electric dipole component would lie along the a inertial axis for both types of conformer. The initial assign- ment of the pa Q-branch series of lines was made using radiofrequency-microwave double resonance.After this, some weaker pa and p, R-branch lines were assigned. Measure- ments were made up to J = 18 in order to be able to deter- mine the quartic centrifugal distortion constants. The line frequencies were fitted using Watson's A reduced semirigid rotor Hamiltonian* and 111' axis representation. The spectra of seven of the most intense excited vibrational states were also assigned. Measurements were also made up to J = 18 and the line frequencies were fitted in the same way as for the ground vibrational state. The measured line fre- quencies are given in Table 1 and the derived rotational and quartic centrifugal constants, details of the least-squares fits and the vibrational wavenumbers of some of the vibrational states are given in Table 2.Entries for the centrifugal distor- tion constants, S, and S,, without standard errors in Table 1 mean that these have been constrained to the values of the ground vibrational state constants in the least-squares fits. The assignment of the excited vibrational states given in Table 2 is discussed in detail below. Electric Dipole Moment The frequency displacements of the observed Stark com-ponents were found to be proportional to the square of the electric field and therefore second-order perturbation theoryg was used to derive the principal inertial axis components of the electric dipole moment.The pc component was treated in the same way as pa and pb. This will be justified in the Dis- cussion (below). Several fits were made to the observed Stark coefficients and from these it became apparent that pb was small and not particularly well determined. The small value of & is consistent with our inability to observe transitions due to this electric dipole component even though these were 2850 J. CHEM. SOC. FARADAY TRANS., 1994,VOL. 90 Table 1 Measured line frequencies and differences between the observed and calculated line frequencies (in MHz)for the ground and excited vibrational states of 5,6-dihydro-2H-thiopyran 0 36, 36, 363 transition obs obs -calc obs obs -calc obs obs -calc obs obs -calcJ; ,'K+,' 'Jk-~"K+I" 0.02 28 645.98 -0.014 1.3' 3 0.3 28 665.86 -0.02 27 780.43 0.014 2,Z' 3 1.2 27 799.99 0.00 29 223.12 -0.004 2.3' 3 1.3 29 239.36 4 3.14-3 2,l 28 984.88 0.04 4 3.2' 3 2,2 30121.66 0.00 0.04 36 182.82 -0.045 1.4' 4 0.4 36 205.96 -0.01 35115.56 0.045 2.3' 4 1.3 35142.30 0.02 28 756.30 0.04 28 735.41 0.01 28 714.29 0.055 2.34-4 2.2 28 776.87 5 2.4' 4 1.4 36 389.36 0.01 -0.01 34 895.59 0.00 34 874.06 -0.035 3.24-4 2.2 34 917.02 -0.02 29 485.60 -0.02 29457.12 -0.01 29 428.9 1 -0.0 15 3.2' 4 3.1 295 14.49 0.02 36 633.62 0.025 3,3' 4 2,3 36 652.79 26 928.85 0.01 26 906.44 0.005 3,3' 4 3,2 26 972.98 -0.04 26951.00 -0.0 1 0.02 37 310.86 -0.0 1 37 298.09 -0.015 4.14-4 3.1 37 322.90 28 156.65 -0.02 28 127.79 -0.0 1 28 099.32 -0.035 4.1 '4 4.0 38 102.44 -0.015 4.2' 4 3, 2 38 116.33 -0.00 5 4.24-4 4,l 27 624.43 -0.03 27 599.09 0.0 1 27 573.87 0.04 -0.01 29 126.70 -0.00 29 107.42 0.02 29 087.30 0.076 1.5' 5 1.4 29 145.14 0.02 33013.62 0.02 32 993.55 0.026 2.4' 5 2-3 33032.93 0.0 1 28 970.20 -0.01 28 949.72 0.0 16 2.54-5 2.4 28 989.94 0.04 35482.23 0.03 35452.34 0.00 35422.50 0.036 3.3 '5 3.2 35512.21 0.03 31716.34 -0.02 31692.17 0.01 31667.48 0.006 3.4' 5 3.3 31740.18 -0.02 34 772.75 -0.0 1 34736.20 -0.01 34700.13 -0.016 4.2' 5 4.1 34 810.00 7 0-7' 0, 6 29 762.74 0.05 29 741.99 0.06 33091.86 -0.02 33070.13 0.04 33047.32 0.00l.6+ 1.5 29 761.84 -0.05 29 741.08 -0.031.7 ' 1.6 0.01 36 745.69 0.02 36 723.77 0.037 2.54-6 2.4 36 766.62 33050.89 0.03 33028.53 -0.09 33005.41 -0.022.6' 2.5 0.02 36 129.78 0.00 36 103.90 0.01 36077.18 -0.077 3.5' 6 3.4 36 154.99 7 4.44-6 4.3 38 326.79 -0.02 38 295.73 -0.01 38 264.48 -0.00 38 232.89 -0.01 8 0.84-7 0.7 33778.25 -0.07 33754.63 -0.05 33729.68 -0.08 33703.40 -0.07 37 086.09 0.03 37061.22 0.01 37 035.24 0.02 37 007.99 -0.021.7' 1.6 33778.25 0.08 33703.40 0.09l,8' 1.7 37 076.44 -0.03 37 025.38 0.01 36 998.05 0.012.7' 2.6 6.2' 7 5, 2 59 62 1.59 -0.04 60 272.09 -0.036.3' 5.3 62 968.24 -0.02 62 952.14 -0.027.1' 6.1 8 7.2' 6, 2 63018.18 -0.02 9 0,9' 8 0, 8 37 794.32 -0.00 37 767.82 0.01 37 739.85 -0.01 37 710.33 -0.0 1 37 794.32 0.02 37 767.82 0.04 37 739.85 0.02 37 710.33 0.21.9' 1.8 10 0.10 10 2, 9 31096.59 0.06+ +10 1.10 10 1.9 31096.59 -0.04 11 0.11 4-11 2.10 34 393.03 0.01 34 378.21 -0.01 11 1.11 '11 1,lO 34 393.03 -0.01 34 378.21 -0.03 30167.33 -0.08l3 3.10 'l3 5, 9 14 3,ll '14 5.10 33521.81 -0.01 33502.65 0.01 33485.50 0.01 33470.38 -0.04 l4 4.10 l4 6, 9 29 687.33 -0.03 14 4.11 14 4.10 33513.26 0.03 33493.93 0.02 33476.61 -0.01 33461.28 -0.03 + 14 5.10 14 5, 9 29 546.56 -0.00 + l5 0.15 'l4 0.14 61 890.57 0.00 61 846.86 0.00 l5 1.15 'l4 1.14 61 890.57 0.00 61 846.86 0.00 l5 3.12 'l5 5.11 36 867.57 -0.03 36 847.30 0.0 1 36 829.21 -0.00 36 813.16 0.05 l5 4.11 'l5 6.10 33067.57 -0.04 l5 4.12 l5 4.11 36 865.48 0.03 36 845.19 0.03 36 827.03 0.03 36 8 10.98 0.04 l5 12, 3 4-l5 13. 3 35578.89 -0.01 35630.20 -0.01 35678.18 -0.6 35723.46 0.0 1 l5 12, 4 'l5 13.2 35581.60 -0.02 35632.83 -0.02 35680.64 0.06 35725.99 0.00 l6 4.12 'l6 6.11 36 447.67 0.00 36 425.3 1 0.01 36 405.24 0.01 36 387.42 0.01 l6 5.11 4-l6 7.10 32 522.64 0.00 32499.16 -0.01 32 477.98 0.00 32 459.1 1 -0.04 l6 5,12 'l6 5.11 36 437.41 0.05 36414.84 -0.00 36 394.51 0.0 1 36 376.54 -0.09 l6 6.11 'l6 6.10 32 370.32 0.02 32 343.38 0.01 32 319.04 -0.10 32 296.87 0.05 l7 5.12 'l7 7.11 35934.73 -0.01 35909.92 -0.05 35887.53 -0.04 35867.46 0.05 l7 6.12 'l7 6.11 35891.24 0.01 17 7.11 17 7.10 31412.44 0.01 31376.75 0.02 31344.12 0.03 31314.41 0.00+ l7 13, 4 'l7 38 007.84 0.01 38 064.82 0.0014. 4 l7 13, 5 l7 14, 3 38013.05 0.02 38 069.89 0.0 1 + l8 5.13 'l8 7.12 39 341.99 -0.06 l8 6.12 'l8 8.11 35328.44 0.01 35301.13 -0.03 35276.38 0.04 35254.31 -0.00 l8 7.12 l8 7.11 35168.03 0.03 35136.72 0.0 1 35108.27 0.00 35082.56 -0.00 18 13, 5 4-l8 14, 5 37 326.05 0.02 +l8 13.6 l8 14, 4 37 354.56 -0.04 J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 2851 Table 1 Continued 351 35, A B 4 l,3' 3 0.3 28 643.58 -0.02 4 2.2' 3 1, 2 27 778.65 0.01 4 2.3' 3 1.3 29 213.40 -0.02 5 1.4' 4 0. 4 36 176.28 0.07 5 2.3' 4 1. 3 35 116.98 -0.02 5 2.3' 4 2. 2 28 754.48 0.06 28 731.44 0.03 28 774.41 0.06 5 3.2' 4 2.2 34 887.58 -0.03 5 3.2' 4 3. 1 29 498.00 -0.01 29 512.16 -0.01 29 51 1.76 0.05 5 3.3' 4 3.2 26 954.01 -0.03 26 969.92 -0.01 26 975.50 0.03 5 4.1' 4 3.1 37 282.66 -0.01 5 4.1 '4 4. 0 28 141.88 0.01 28 153.9 1 0.02 5 4.24-4 4,l 27 607.43 0.01 27 589.42 0.06 27 62 1.56 0.02 61,5+-5 1.4 29 119.83 -0.02 29 093.87 -0.01 29 140.44 -0.05 29 154.15 -0.03 6 2.4' 5 2.3 33 003.41 -0.02 32 973.51 -0.04 33 029.51 0.02 33041.16 0.03 6 2.5' 5 2. 4 28 965.87 -0.02 28941.10 0.05 28985.17 -0.04 28 997.97 -0.04 6 3.3' 5 3.2 35 488.40 0.04 35 463.57 0.04 6 3.4' 5 3.3 31 716.00 0.01 31 690.95 -0.02 31 736.25 -0.02 31 745.05 -0.03 6 4.2' 5 4, 1 34 793.13 -0.00 34 774.59 -0.02 34 806.98 -0.01 34 804.72 -0.02 0.7' 0.6 29 737.97 0.08 1.6' 1.5 33 063.68 -0.05 33 034.70 0.02 33 086.22 0.7 33 102.32 0.07 7 1.7' 1. 6 29 737.04 -0.06 7 2.5' 6 2.4 36 733.09 -0.05 36 699.17 -0.02 36 762.06 -0.0 1 36 777.47 0.00 2.6' 2.5 33 023.17 0.03 32 994.43 -0.04 33 045.06 -0.06 33 060.85 -0.05 7 3.5+ 6 3.4 36 125.78 0.00 36 095.60 -0.09 36 150.20 0.01 36 162.68 0.01 7 4.4' 6 4.3 38 299.71 -0.02 38271.40 -0.08 38 322.67 0.00 38 329.95 -0.08 0.8' 0.7 33 750.15 -0.06 33 770.42 -0.08 33 791.22 -0.07 1.7' 1.6 37 054.74 -0.05 37 022.43 0.04 37 079.33 0.04 37 097.97 -0.01 1.6' 1.7 33 750.15 0.09 33 720.68 0.06 33 770.42 0.7 33 791.22 0.08 2.7' 2.6 37 045.35 0.04 37 013.04 0.02 37 069.68 -0.01 37 088.28 -0.0 1 0.9' 0.8 37 762.89 0.00 37 729.92 -0.01 37 785.54 -0.02 37 808.98 -0.00 1.9' 1.8 37 762.89 0.03 37 729.92 0.01 37 785.45 0.01 37 808.98 0.02 l4 3.11 'l4 5.10 33 495.42 -0.04 33 470.57 0.01 33 532.36 -0.02 33 506.12 -0.02 l4 4.11 'l4 4.10 33 487.02 0.03 33 462.40 0.0 1 33 523.81 0.02 33 497.41 0.03 l5 0.15 l4 0.14 61 839.20 -0.00 l5 1.15 'l4 1.14 61 839.20 -0.00 l5 3.12 'l5 5.11 36 837.83 -0.02 36 809.93 -0.01 36 879.15 -0.01 36 850.9 1 -0.03 l5 4.12 'l5 4.11 36 835.81 0.01 36 808.00 -0.03 36 877.07 0.03 36 848.8 1 -0.01 l5 12, 3 'l5 13, 3 35491.80 0.01 35 412.19 -0.04 35 590.83 -0.08 35 61 5.85 0.00 l5 12.4 'l5 13. 2 35 494.59 -0.03 35 414.90 0.04 35 593.37 0.08 l6 4.12 'l6 6.11 36 420.24 -0.04 36 459.1 1 -0.00 36 429.42 0.02 l6 5.11 'l6 7.10 32 501.07 -0.0 1 32 480.72 -0.01 32 532.79 0.03 32 503.67 0.06 l6 5.12 'l6 5.11 36 410.19 0.03 36 384.59 0.02 36 448.89 -0.00 36419.00 0.03 l6 6.11 'l6 6. 10 32 35 1.79 -0.00 32 334.10 0.00 32 380.42 0.03 32 348.86 -0.02 0.02 35 886.64 -0.03 35 945.99 -0.02 35 914.68 -0.04l7 5.12 l7 7.11 35 909.93 l7 7.11 l7 7.10 3 1 402.23 0.04 31 422.19 -0.01 31 384.47 -0.02 + l7 13.4 l7 14, 4 37912.91 0.01 l7 13, 5 'l7 14. 3 37 918.23 0.01 l8 6.12 'l8 8.11 35 306.53 -0.03 35 285.82 -0.05 35 339.48 -0.00 l8 7.12 'l8 7,11 35 149.56 0.01 35 131.81 0.07 35 179.01 0.00 35 143.16 0.00 Table 2 Rotational constants (in MHz), quartic centrifugal distortion constants (in kHz), vibrational wavenumbers and planar moments of inertia, P, ,for the ground and excited vibrational states of 5,6-dihydro-2H-thiopyran 4213.808 (2)" 4213.136 (2) 4212.352 (4) 421 1.432 (3) 4208.745 (5) 4203.862 (3) 4214.00 (1) 4215.135 (3) 3236.812 (1) 3233.956 (1) 3231.776 (1) 3228.364 (3) 3234.776 (1) 3232.656 (3) 3236.670 (3) 3236.546 (3) 2008.2265 (7) 2006.7896 (7) 2005.266 (3) 2003.653 (4) 2006.564 (1) 2004.817 (3) 2007.703 (3) 2009.071 (3) 0.831 (6) 0.833 (6) 0.82 (2) 0.83 (2) 0.83 (1) 0.85 (2) 0.83 (3) 0.83 (2) -1.59 (1) -1.57 (2) -1.57 (4) -1.59 (1) -1.55 (3) -1.56 (1) -1.58 (6) -1.59 (1) 0.95 (1) 0.92 (2) 0.91 (3) 0.92 (2) 0.90 (2) 0.91 (1) 0.92 (4) 0.93 (2) 0.066 (2) 0.070 (2) 0.068 (5) 0.066 0.069 (3) 0.066 0.070 (9) 0.066 -0.69 (2) -0.65 (3) -0.65 (6) -0.69 -0.63 (4) -0.69 -0.67 (8) -0.69 70 52 37 30 49 31 35 31 0.03 0.03 0.03 0.05 0.04 0.04 0.04 0.04 -134 (12) --219 (18) -339 (24) 412 (18) 12.207 12.196 12.180 12.158 12.225 12.236 12.175 12.248 a Standard error in units of the least significant digit.Number of transitions in fit. Standard deviation of fit. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 3 Zero-field line frequencies for the transitions used in the electric dipole moment determination, and the electric dipole moment components and total electric dipole moment for $6-dihydro-2H-thiopyran transition v,/MHz 16990.29 15735.07 17631.10 electric dipole moments" 1.35 (1)Pa pb <0.1 Pc 0.74 (2) Pr 1.54 (2) " In D.accurately predicted. The transitions used in the electric dipole moment determination are listed in Table 3 together with the derived electric dipole moment components and the total dipole moment. The total electric dipole moment of 1.54 (2) D may be compared with that of 1.50 (1) D in dimethyl sulfide" and that of 1.78 (1)D in thiane." Molecular Conformation and Discussion If 5,6-dihydro-2H-thiopyran has a planar heavy-atom equi- librium conformation the ground vibrational planar moment of inertia,' h apart from a small vibrational contribution, would be due to the out-of-plane methylene hydrogen atoms and would have a value of 4.9 x lo4 u pm2.t The observed value of 12.2 x lo4 u pm2 is considerably larger and leaves little doubt that 5,6-dihydro-2H-thiopyran has a non-planar heavy-atom skeleton.A model structure based on that of cy~lohexene'~~'~(with the C-S bond lengths and <CSC angle taken from saturated six-membered ring molecules con- taining a sulfur atom"*'5) was used as a starting point for the determination of the molecular conformation. Starting from the planar ring conformation, the model structure was distorted first along the twisting and then along the bending coordinate.These calculations indicated that only a twisted conformation was likely to be able to reproduce the observed rotational constants. In order to have more quantitative information about the molecular structure, least-squares fitting to the ground vibrational state rotational constants and planar moments of inertia using the method of predicate Observations' was adopted. In this method, estimates of some or all of the parameters to be determined, the predicate observations, are added to the experimental data. This ensures that, when the number of parameters to be deter- mined is larger than the number of experimental data, the problem of the singularity of the least-squares normal equa- tion matrix is removed. The definitions of the twisting (z) and bending (p) coordi-nates given by Wells and Malloy17 have been used.The num- bering of the ring atoms is shown in Fig. l(a). A Cartesian coordinate system is chosen with the origin at the mid-point of the C(2)-C(5) diagonal and with the x axis along this diagonal. The y axis is chosen to lie in the plane of the C(2)C(3)C(4)C(5)atoms. Because of the lack of symmetry of the non-planar ring conformers, it is helpful to visualize these using the projections of the S-C(6) bond in the xz and yz t 1 u z 1.66054 x kg. 2 5 I=Is I= ,.0 ;:!GS , 0 /0' -3 Y tZ s + Z P Y (e1 Fig. 1 (a)Numbering of the ring atoms in 5,6-dihydro-2H-thiopy- ran. Projection of the S-C(6) bond in (b)the xz plane for a pure twist conformation, (c) the yz plane for a pure bent conformation and (d),(e)the xz and yz planes for a mixed conformation.J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 planes and the coordinates of the point (0')of intersection of this bond with the yz plane. In a pure twisted conformation [Fig. l(b)] the projection of the S-C(6) bond passes through the origin and the coordinates of a point on the bond are related by x tan(z) -z = 0 (2) In a pure bent conformation [Fig. l(c)] the coordinates of a point on the S-C(6) bond are related by y tan(p) -z = 0 (3) A mixed conformation may be achieved, starting from the planar ring, first by twisting the S-C(6) bond by t about the y axis and then rotating 0-0' by p about the x axis. For this type of conformation, the coordinates of a point on the S-C(6) bond are related by x tan(t) + y sin(p) -z cos(p) = 0 (4) A series of preliminary computations using the experimental data and structure of cy~lohexene'~ was made in order to choose the weights to be given to the rotational constant and planar moments of inertia.Satisfactory results were obtained with a weight of 0.1 for the rotational constants and 1.0 for the planar moments of inertia. Each predicate observation was given a weight equal to the reciprocal of its estimated uncertainty. For 5,6-dihydro-2H-thiopyran the predicate observations and their uncertainties were obtained from a survey of the structures of cyclohexene and related molecules and from the structures of ring molecules containing sulfur atoms.Table 4 gives the results of fits for 5,6-dihydro-2H-thiopy- ran, In all of these fits the following restrictions were placed on the molecular structure: (i) equality of the C(2)-C(3) and C(4)-C(5) bond lengths; (ii) equality of the two H-C(sp2) bond lengths; (iii) equality of all the H-C(sp3) bond lengths; (iv) local C,, symmetry at all C atoms; (v) equality of all <HCH angles. In fit (a) the further restriction of a pure twisted conformation was also imposed. In fits (b)and (c) this restriction was removed. In fit (b),the dihedral angles of the C(2)-S (&) and the C(5)-C(6) (&(6J bonds with respect to the plane of the C(2)C(3)C(4)C(5) atoms were fitted rather than determining j3 and z directly. In fit (c), z and j3 were determined directly.The calculations give very similar values of z,and this appears to be the best determined feature of the structure. The experimental data do not depend significantly on p. This is shown by fits of type (c) where the partial derivatives of the experimental data with respect to j3 are small and the final value of p is close to its predicate value even for appreciable values of /3. The estimated uncertainty in t (three standard errors) is ca. 1.5". The reasonableness of the structure may be judged by examining the ring parameters that were not fitted but may be calculated from the fitted parameters. These are also given in Table 4 together with their errors, estimated from the least-squares variance-covariance matrix.The S-C(6) bond length is equal within its calculated error to that of the S-C(2) bond. These bond lengths are expected to be very similar because they are both of the type S-CH,. The <C,SC, angle is similar to that in thiane" and other four-, and five- and six-membered ring molecules containing a sulfur atom. The <SC(6)C(5) angle is close to the tetrahedral angle for an sp3 carbon. The requirement of near equality of the two S-C bond lengths makes it unlikely that the absol- ute value of j3 is greater than 10". For negative predicate values of 8, the S-C(6)- becomes longer than S-C(2), while for positive values it becomes shorter. Also, for appre- ciable predicate values of /3 the ethenic ring angles become quite different, as do the ring angles at C(2) and C(5).Table 5 gives a comparison of the twist angles in 5,6- dihydro-2H-thiopyran and its oxygen analogue (which is called 3,6-dihydro-2H-thiopyranin ref. 17 and 19), as deter- mined from microwave spectroscopy,' 'molecular mechanics c~mputations'~~'~and the minima of the IR two-dimensional (2D) vibrational potential-energy The trend of the results is the same for both molecules with the microwave and molecular mechanics values of z being very similar and somewhat smaller than the IR value. In spite of the large differences between C-0 and C-S bond lengths and <COC and <CSC bond angles, the equilibrium twist angles of the two molecules are not very different.The preference for the twisted conformation in cyclohexene and similar mol- ecules can be attributed to the need to accommodate the C-C bond, and the much longer single bond across the ring from it, without increasing the ring-angle strain energy unnecessarily. This can be achieved more efficiently in the twisted conformation than in a bent one. Fig. 2 gives stick diagrams showing the vibrational depen- Table 4 Predicate observations and final molecular structures for 5,6-dihydro-2H-thiopyran (bond lengths in pm and angles in degrees) (4 (4 (4 predicate final predicate final predicate final 181.5 (2.0)" 181.5 (1.5)b 181.9 (1.4) 181.5 (1.5) 150.5 (1.0) 150.5 (1.1) 151.0 (1.0) 150.8 (1.1) 133.5 (1.0) 133.7 (1.1) 133.8 (1.0) 133.7 (1.1) 152.5 (1.0) 152.5 (1.1) 152.6 (1 .O) 152.5 (1.1) 108.5 (1.0) 108.5 (1.1) 108.5 (1.0) 108.5 (1.1) 109.5 (1.0) 109.6 (1.1) 109.6 (1.0) 109.6 (1.1) 113.0 (5.0) 114.8 (1.1) 114.5 (1.0) 114.8 (1.1) 123.0 (5.0) 125.5 (1.4) 125.4 (1.3) 125.5 (1.4) 123.0 (5.0) 124.8 (1.2) 125.0 (1.0) 124.9 (1.2) 113.0 (5.0) 11 3.9 (1.6) 113.8 (1.4) 113.9 (1.6) 109.5 (4.0) 109.5 (2.2) 109.3 (2.1) 109.5 (2.3) 30.0 (5.0) 32.5 (0.4) 36.4' 32.6 (0.4)' 30.0 (5.0) 32.5 (0.4) 0" 0' 1.9' 1.2 (1.2)' 0.0 (5.0) 0.2 (1.8) 9.8' 15.3 (0.5)' 15.0 (5.0) 16.1 (1.3) 9.8' 15.5 (1.8)' 16.3' 22.5 20.0 (5.0) 21.1 (1.3) 16.3' 22.2 (2.2)d 138.0' 182.1 (2.6)' 154.9' 180.9 (2.3)' 138.V 182.0 (2.6)' 103.6' 97.4 (0.6)' 98.5' 97.3 (0.6)' 103.6' 97.4 (0.7)' 118.3' 109.2 (1.2)d 1 10.6' 109.9 (1.1)' 1 18.3' 109.3 (1.4)d ~~ ~~~ Unless indicated otherwise the predicate observations for fits (b) and (c) are the same as for fit (a).a Estimated uncertainty.'Standard error. 'Parameter calculated from fitted parameters. Estimated uncertainty calculated from the variance-covariance matrix. " Constrained value. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 5 Comparison of the twist angle, z, as determined by microwave spectroscopy, molecular mechanics calculations and from the minima of the IR potential-energy surfaces for 5,6-dihydro-2H-thiopyran and its oxygen analogue, 3,6-dihydro-2H-pyran microwave spectroscopy 5,6-dihydro-2H-thiopyran 32.5 (1.5)11 3,6-dih ydro-2H-pyran 31.5 (3.0)E This work. Ref. 2. Ref. 17. 'Ref. 19. dence of the rotational constants.From these diagrams, on the basis of both the regular changes in the rotational con- stants and the relative intensities of the vibrational states (the relative heights of the sticks), it is possible to assign the pro- gressions 36,, 362, 36, and %,,35, in the two lowest-wavenumber vibrations. The fundamental wavenumbers of v36 and v35given in Table 2 are in very good agreement with the values of 139.0 and 235.6 cm-', respectively, from the IR spectrum. 0.8 1 B 3225 3230 3235 3240 BIMHz I 0I (c' B 1 0 C/M Ht Fig. 2 Stick diagrams showing the variation of the rotational con- stants with vibrational state: (a)A, (b)B, (c) C. The stick heights are equal to the relative intensities of the vibrational states.molecular mechanics IR spectroscopy 30Sb 37.tIb 33.6' 38.2d The assignment of the two highest-wavenumber states labelled A and B in Table 2 is not so obvious. The wavenum- ber of state A is consistent with it belonging to either the first excited state of the third lowest vibration, v34,or to the com- bination state, 35,36,. The fundamental of v34 has been observed at ca. 360 cm-' in the Raman spectrum of liquid 5,6-dihydro-2H-thiopyran2' while the combination state 35'36, should have a wavenumber of ca. 353 cm-'. The rota- tional constants of A are somewhat different from those expected for 35,36, on the basis of the additivity of the differ- ences in the rotational constants of 35, and 36, and those of the ground vibrational state.For this reason state A may be tentatively assigned to 34,. The wavenumber of state B is in reasonable agreement with bands at ca. 383 and ca. 453 cm-' in the liquid-phase Raman spectrum." It is somewhat lower than the ca. 500 cm-' expected for the combination states 34,36, or 35,36,. It therefore appears that B may be the first excited state of the fourth or fifth lowest vibration (v33 or v32)*The assignment of the ring-bending and ring-twisting vibrations for 5,6-dihydr0-2H-thiopyran'~~' was made on the basis that v36 and v35 occur ca. 40 cm-' below the ring- bending and -twisting vibrations of cyclohexene. An attempt to confirm the assignment of these vibrations, via an exami- nation of the changes in the rotational constants and planar moments of inertia upon excitation of v36 and v,~was largely inconclusive.The simple models for the twisting and bending of the ring, with the planar ring as a reference conformation, predict that the three rotational constants should decrease and the planar moments of inertia increase as the ring is dis- torted along either z or p. If the equilibrium conformation is taken as a reference, the rotational constants are still expected to decrease and the planar moments of inertia increase as z is increased. As p is changed about this refer- ence, A and Pb are expected to behave differently from the other two rotational constants and planar moments of inertia. Experimental excitation of v35 leads to a decrease in the three rotational constants and an increase in the three planar moments of inertia.This is the behaviour expected for twisting the ring about either reference. Excitation of v36 leads to a decrease in the three rotational constants, although the change in A is smaller than those in B and C.The change in P, is negative while those in Pa and P, are positive. This is not the behaviour expected for bending the ring about either of the reference conformations. In four- and five-membered ring molecules the planar moment of inertia, P, , usually increases upon excitation of the ring-puckering vibrations because the vibrationally averaged non-planarity of the ring increases. A similar decrease in P, has been found upon exci- tation of the lowest-wavenumber vibration in 4-methylenecyclohexene.2 When, as in the present case, the barrier separating the equivalent equilibrium conformers is very high, the lowest vibrational states consist of almost degenerate pairs of vibra-tional levels.This is often referred to as inversion doubling. The difference in energy between the members of a pair of nearly degenerate level depends on the potential-energy surface, the reduced mass for motion on this surface and the vibrational wavefunctions. The pa and pb components of the J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 electric dipole moment are symmetric while the pc com-ponent is antisymmetric with respect to inversion of the ring (z, B + -7, -p). The pa and & components of the electric dipole moment give rise to pure rotational semirigid rotor transitions, but the ,uc component gives transitions between the rotational levels of the two nearly degenerate vibrational levels.The pc transitions occur in pairs at frequencies of v,,, fvinv, where v,,, is the semirigid rotor frequency of the pure rotational pc transition and vinv is the frequency correspond- ing to the energy difference between the almost degenerate vibrational levels. In the present work, some pc transitions have been observed for the ground and all of the excited vibrational states and none of the observed transitions showed any splitting. The inversion splitting in the states 36, and 35, must be smaller than CQ. 0.1 MHz. This implies a very high barrier to ring inversion, in agreement with the conclusion from the IR spectrum.2 Since the pc electric dipole moment connects different inversion states, the quantity listed as pc in Table 3 is really the transition moment (O+I pc lo-)z (0-I pc 10').The small value of Ainv jus-tifies its neglect in the calculation of the perturbation sums involving pc in the determination of the Stark coefficients. In conclusion, it can be stated that the microwave spec- trum of 5,6-dihydro-2H-thiopyran confirms the twisted or half-chair equilibrium conformation of the molecule deduced from its vibrational spectrum and molecular mechanics com- putations.2 The microwave spectra of the excited vibrational states also confirm the fundamental wavenumbers of the two lowest vibrations. As found previously2' the changes in the rotational constants and planar moments of inertia upon excitation of the ring-puckering vibrations in some six-membered ring molecules appear to be smaller and more dif- ficult to interpret than those for five-membered ring molecules.We thank the following for financial support: The comision Asesora de Investigacion Cientifica y Tecnica (CAICYT, grant PB90-345) (L.A.L. and J. L. A.). The University of Val- ladolid, the MURST 60% funds and the CNR (D.G.L.). The European Union 'Human Capital and Mobility' Program (Contract CHRX CT 93-0157) (L.A.L, J.L.A. and D.G.L.). The National Science Foundation and the Robert A. Welch Foundation (M.M.J.T., J.R.V. and J.L.).References 1 J. Laane, in Structures and Conformations of Non-Rigid Mol-ecules, ed. J. Laane, M. Dakkuri, B. van der Veken and H. Obberhammer, Kluwer, Dordecht, 1993, pp. 45-64. 2 M. M. J. Tecklenburg, J. R. Villarreal and J. Laane, J. Chem. Phys., 1989,91, 2771. 3 A. G. Lesarri, M. E. Charro, R. H. Villamanan, D. G. Lister, J. C. Lopez and J. L. Alonso, J. Mol. Spectrosc., 1991, 149, 317. 4 F. J. Wodarczyk and E. B. Wilson, J. Mol. Spectrosc, 1975, 37, 445. 5 F. J. Pelaez, J. L. Alonso and J. M. Muiioz, Opt. Pura Apl., 1983, 16, 83. 6 A. S. Esbitt and E. B. Wilson, Rev. Sci. Instrum., 1963,34, 901. 7 J. S. Muenter, J. Chem. Phys., 1968,48,4544. 8 J. K. G. Watson, in Vibrational Spectra and Structure, ed. J. R. Durig, Elsevier, Amsterdam, 1977, vol. 6, ch. 1. 9 S. Golden and E. B. Wilson Jr., J. Chem. Phys., 1948,16, 669. 10 L. Pierce and M. Hayashi, J. Chem. Phys., 1961,35,479. 11 R. W. Kitchen, T. B. Malloy and R. L. Cook, J. Mol. Spectrosc., 1975, 57, 179. 12 W. Gordy and R. L. Cook, Microwaoe Molecular Spectra, Wiley, New York, 3rd edn., 1984, ch. 12. 13 L. H. Scharpen, J. E. Wollrab and D. P. Ames, J. Chem. Phys., 1968,49,2368. 14 T. Ogata and K. Kozima. Bull. Chem. SOC.Jpn., 1969,42, 1263. 15 R. W. Kitchin, T. K. Avirah, T. B. Malloy and R. L. Cook, J. Mol. Struct., 1975, 24, 337. 16 L. S. Bartell, D. J. Romenesko and T. C. Wong, in Molecular Structure by Diffraction Methods, ed. G. A. Sim and L.E. Sutton, Specialist Periodical Reports, The Chemical Society, London, 1975, vol. 3, ch. 4. 17 J. A. Wells and T. B. Malloy, J. Chem. Phys., 1974,60, 3987. 18 U. Burkert and N. L. Allinger, Molecular Mechanics, ACS Monographs Series 177, American Chemical Society, Washing- ton DC, 1982. 19 M. M. J. Tecklenburg and J. Laane, J. Am. Chem. SOC., 1989, 111,6920. 20 M. M. J. Tecklenburg, Ph. D. Dissertation, Texas A&M Uni- versity, 1989. 21 R. Cervellati, D. Damiani, L. Dore and D. G. Lister, J. Mol. Spectrosc., 1990, 139, 328. Paper 4/02 163K ;Received 12th April, 1994
ISSN:0956-5000
DOI:10.1039/FT9949002849
出版商:RSC
年代:1994
数据来源: RSC
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A multiple hard-ellipsoid model for rotationally inelastic collisions |
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Journal of the Chemical Society, Faraday Transactions,
Volume 90,
Issue 19,
1994,
Page 2857-2863
Alison J. Marks,
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PDF (882KB)
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摘要:
J. CHEM. SOC. FARADAY TRANS., 1994, 90(19), 2857-2863 A Multiple Hard-ellipsoid Model for Rotationally Inelastic Collisions Alison J. Marks School of Chemistry and Molecular Sciences, University of Sussex, Brighton, UK BN I 9QJ A multiple hard-ellipsoid model is developed to describe atom-diatom rotationally inelastic collisions. The model is designed to be used for ‘soft’ and anisotropic repulsive intermolecular potentials for which single hard-shape models fail to reproduce the integral cross-sections. It is shown for the Na,-He system that a small number of ellipsoids representing different regions of the repulsive intermolecular potential can be used within a classically impulsive approximation to reproduce the integral J = 0 +J’ cross-sections. The model facilitates investigation of how different regions of the intermolecular potential contribute to rotationally inelastic scattering processes.The use of simple hard-shell models to describe rotationally inelastic collisions of atoms with diatomic molecules has been extensively investigated. ‘-14 Such models provide insight into the mechanism of rotational excitation and in certain cases can usefully describe inelastic cross-sections’ and rota- tional rainbow structure^.^*^.^^'^ However, hard ellipsoid models have been shown to be of limited when the intermolecular potential has ‘soft’, long-range repulsive behaviour, as, for example in alkali-metal dimer-rare gas systems7 The advantage of hard-shell models lies in their simplicity and the ease with which quantities of interest can be calcu- lated.With this in mind we have extended the single hard- shell idea to a ‘multiple hard-ellipsoid model’ in which we use a small number of nested hard ellipsoids to represent the repulsive region of an intermolecular potential. Thus, outer and inner ellipsoids correspond to equipotential surfaces of low and high energy, respectively. The question that we ask is: when the single hard-shape model fails, will a classical model involving a small number of nested hard ellipsoids suffice? The model is not intended to supersede or replace existing classical or quantum-mechanical methods utilising analytical potential surfaces, but is offered as a simple conceptual approach examining the breakdown of single hard-ellipsoid models, and illustrating how, for example, two hard ellipsoids representing the ‘inner’ and ‘outer’ regions of the repulsive potential can be used to improve significantly integral inelastic cross-sections. This simplistic approach allows us to explore the contributions made to rotationally inelastic cross-sections by different regions of the repulsive part of the intermolecular potential.In addition (but not investigated here), it should be possible to use the model as an inversion procedure14-18 to obtain a crude representation of an unknown intermolecular potential directly from experimental cross-sections. As an illustration of the multiple hard-ellipsoid model, we have calculated integral cross-sections for the Na,-He system for which 10s calculations and potential surfaces are avail- Model and Method Modelling the Intermolecular Potential The interaction between an atom and a diatomic molecule is approximated by a series of K hard ellipsoids, with each shell representing a region or surface of equipotential. The centre of each ellipsoid corresponds to the centre-of-mass of the diatomic molecule, which is assumed to be a rigid rotor having bond length, re.The ith ellopsoid surface can be written as: x2 Y2 2,-+-+-=IA? B? Bf (1) in the molecule-fixed (X,Y, 2)coordinate system, where Ai and Biare the semi-major and semi-minor axes of the ith ellipsoid, respectively. In our application of the model to the Na,-He system, values for A, and Bi were chosen to match contours of the potential-energy surface, using an analytical function derived by Schinke et a!.: V(R,y) = a, exp(-a,R,) + a, exp(-a, R2) + b, exp(-b,~ + b,R2) + c1 exp(-c, R + c3R2)P,(cos y) + d, exp(-d, R)P,(cos y) + RP6[e, + e, P2(c0s y)]G2(e3 R) where R is the distance between He and the Na, centre-of- mass and y is the orientation angle between R and the inter- nuclear axis of Na,; R,, R, are the distances between the He atom and each of the Na atoms, P,(cos y) are Legendre poly- nomials and G(x) = 1 -(1 + x + x2/2)exp(-x) is a cut-off function.The coefficients ai, bi,..., e, are as given in ref. 19. The Na-Na bond length is fixed at 3.1 A. Ellipsoid parameters A, B for a specified contour energy were extracted from this potential-energy function by finding the value of R at that energy for y = 0 and y = 42 rad, respectively.The potential-energy function [eqn. (2)] was obtained by fitting to ab initio data and was shown to repro- duce these data to a satisfactory acc~racy.’~ The 10s calcu-lations with which we compare our results were performed using a more sophisticated analytical potential, obtained using the same ab initio data.” However, in view of the sim- plicity of the multiple ellipsoid model, extraction of the ellip- soid parameters from eqn. (2) was considered to be adequate. Having selected a set of ellipsoids to represent the intermo- lecular potential we next need to consider the atom-diatomic molecule inelastic scattering process.The model is based on the assumption that an atom undergoes an impulsive colli- sion with one of a series of hard ellipsoids. Thus the problem reduces to one of selecting the single hard ellipsoid from which a given incoming atom is scattered. We therefore describe first the methods used to compute inelastic cross- sections for scattering from a single hard ellipsoid, and then describe the extension to multiple ellipsoids. Inelastic Scattering from a Single Hard Ellipsoid In this section, we describe the standard classical, impulsive model for rotational energy transfer in atom-diatom systems.‘-5*9 The relative translational energy (collision energy) of an atom and a diatomic molecule is given by E, = 1/2puf (3) where u, is the relative speed of the colliding pair and p is the reduced mass of the system. Since the collisions are assumed to be impulsive, only the component of u, normal to the ellip- soid surface will change during the energy-transfer process.The orbital angular momentum available for transfer into molecular rotation at the point of impact is 1 = punb, (4) where u, is the normal component of relative velocity and b, is the effective impact parameter (‘torque arm’) given by the distance from the centre of the ellipsoid to the surface normal at the point of impact (see Fig. 1): (A2-B2)sin y cos y (5)b, = [(A2-B2)sin2y + B2]’/’ The maximum possible torque arm is b, = A -B, the anisotropy of the ellipsoid.It arises at an angle of The angle y is therefore dependent on the size and anisotropy of the ellipsoid, taking a maximum value of y = n/4 rad in the isotropic (spherical) limit where A = B. For the Na,-He ellip- soids considered here, 2n/9 < y/rad < 44. In all our calculations we assume that the diatomic mol- ecule is initially non-rotating. Conservation of angular momentum then requires that l=j’+I’ (7) where j’ and 1‘ are the final values of the rotational and orbital angular momenta, respectively. Conservation of Y X Fig. 1 Two-dimensional representation of the single hard-ellipsoid model showing a cut through the xy plane. The incoming point par- ticle (atom) approaches the ellipsoid in the xy plane, with relative speed ur and impact parameter b.b, is the effective impact parameter (torque arm) at the point of impact, and is used in defining the orbital angular momentum 1 = punb, where u, = u,. n^ is the com- ponent of relative velocity normal to the ellipsoid at the point of impact. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 energy (and up, the parallel component of relative velocity) requires that : -1 pu; = -j1 puk2 +j’-2 21 or (9) where I is the moment of inertia of the diatomic molecule. From these considerations of energy and angular momen- tum conservation, the final rotational angular momentum of the diatomic molecule is given classically by : The classical values j’ are ‘quantised’ using a standard binning procedure.’ ’*” For Na, the rotational angular momentum quantum number takes even values only (J’ = 0, 2,4, .. .) and we assume that if (J’ -1)h <j’ < (J’ + 1)h (11) thenj’ = J’h. To compute integral cross-sections for the process J = 0 -+ J’ we need to find the transferred rotational angular momentum for a large number of atom-diatom trajectories. We have used a Monte Carlo approach similar to that used by Kreutz and Flynn” in which the diatomic molecule, rep- resented by a hard ellipsoid, is assumed to be fixed in some random orientation whilst an atom is aimed at it with an impact parameter b and relative velocity u, along the space- fixed x-axis (see Fig. 1). Each Monte Carlo ‘trajectory’ at a specified collision energy requires selection of an impact parameter, b, and two angles 8, 4 desribing the orientation of the diatomic molecule in the space-fixed frame.Only two angles are needed to specify the ellipsoid orientation, because of its rotational sym- metry. The initial conditions are selected using a standard procedure :” b = Aq;I2 (12) where q1 E [0, 11 is a random number and A is the maximum impact parameter for collisions. e = COS-~(~-2q2); 4 = 2nq3 (13) where q,, q3 E: [0, 13. 8 E [0, n] describes the angle between the semi-major axis of the ellipsoid and the space-fixed y-axis, and 4 E [0,2n]is the azimuthal angle. Once the impact parameter, b, and ellipsoid orientation have been specified, we find the point of impact (if any) as follows:” The atom approaches the ellipsoid in the xy plane, along the line y = b, and hits the ellipsoid at the point (x*, b, 0) in the space-fixed frame.To find x*, we rewrite the equa- tion of the ellipsoid [eqn. (l)]in terms of space-fixed coordi- nates, using the transformation equations : X = x sin 8 cos 4 + y cos 8 -z sin 8 sin 4 Y = -x cos 8 cos 4 +y sin 8+zcos 8sin 4 2 = x sin 4 + z cos 4 (14) and, substituting y = b, z = 0, solve the resulting quadratic equation for x*. If x* is imaginary, then the atom has missed the ellipsoid. Otherwise, we take the smallest real root as the x-coordinate of the point of impact. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Once the point of impact is known, we can then calculate the orbital angular momentum from eqn.(4). This requires a knowledge of the torque arm b,, and the component of rela- tive velocity normal to the ellipsoid surface, 0,. A unit vector normal to the surface can be written as: in the space-fixed coordinate system, where @(x, y, z) is the equation of the ellipsoid surface [eqn. (l)]written in terms of the space-fixed coordinates. The relative velocity vector is directed along the x-axis so the required normal velocity component is : The torque arm b, is given by: b, = R sin x (17) where (see Fig. 1) R2 = X2 + Y2+ Z2 x= cos-l(--) R4 and 19 is a unit vector normal to the surface defined in the molecule-fixed (X,Y, 2) coordinate system. The transferred angular momentum is then calculated from eqn. (lo), and quantised according to the criterion given in eqn.(1 1). This procedure is performed for a large number, N (typically 20 000-50 OOO), of Monte Carlo trajectories and the integral cross-sections are given by: (19) where n(J’) is the number of Monte Carlo trajectories resulting in a final rotational quantum number J’, and b,,, = A is the maximum impact parameter. The total collision cross-section is given by the sum of these state-to state cross-sections: nhits 2 dtot= 1 a(J = 0 -h J’) = -N nb,,, (20) J’=O, 2, 4... where nhits is the total number of trajectories in which the atom hits the ellipsoid. Multiple Hard-ellipsoid Model The K hard ellipsoids [with parameters Ai,Bi, (i = 1, 2, . . . , K)] used in this model are extracted from the analytical potential given in eqn.(2), and together form an approx-imation to the repulsive part of the intermolecular potential. The basic procedure that we use to compute cross-sections using nested ellipsoids is very similar to that described for a single hard ellipsoid. We imagine the incoming atom as before, moving along the positive x direction with impact parameter b towards a randomly oriented set of ellipsoids. The maximum allowed value of b is A,, the semi-major axis of the largest (lowest energy) ellipsoid. We solve the equation of intersection of the atom trajectory with the outermost ellipsoid to find the point of contact (if any), as described above. If there is a hit, we compare the ‘normal component’ of kinetic energy En = 1/2,uv,2 with the energy assigned to that ellipsoid surface.If 1/2p0,2 < V, then we assume that the atom is scattered impulsively by this ellipsoid and compute the transferred angular momentum as described earlier. If 1/2& > 6 then we assume that the atom does not ‘feel’ this equipotential surface and continues unperturbed along a straight-line path until it encounters the next ellipsoid surface q+l or misses the molecule altogether. The process is repeated inwards until the atom is either scattered by one of the ellipsoids or flies past the molecule. Thus, each incoming atom is scattered impulsively from a single ellipsoid and its trajectory is unaltered by the outer surfaces of lower energy through which it initially passes.The physical outcome of the kinetic energy criterion used in this model is that an atom which approaches the ellipsoid surface at a glancing angle (small component of velocity v,,) is more likely to be scattered from a low-energy, outer contour of the intermolecular potential than from the core of the potential. Conversely, an atom which approaches normal to the surface will penetrate further and scatter from an inner ellipsoid of higher energy. This should be contrasted with the well known single hard-ellipsoid model, in which all trajec- tories are scattered from the same equipotential surface. Application to Na,-He Collisions As an illustration of the multiple-ellipsoid model, we have applied it to Na,-He inelastic collisions. This provides a typical example of an alkali-metal dimer-rare gas system having a soft, anisotropic intermolecular potential with a negligible (maximum 1meV) attractive intera~tion.~.~.’~ We have calculated integral inelastic cross-sections as described in the previous sections, using first a single hard ellipsoid, and then multiple hard ellipsoids to represent the intermolecular potential.The results are compared with the quanta1 infinite-order sudden approximation (10s) cross-sections of Schinke et ~1.’~at collision energies of 0.05, 0.1 and 0.2 eV. We note that Korsch and Schinke have discussed briefly the failure of the single-ellipsoid model for calculating integral state-to-state cross-sections in the Na2-He ~ystem.~ The calculations described below were performed on an IBM RS/6000 workstation.The CPU time required was minimal, ranging from 1.5 s for a single-ellipsoid calculation, to 9.5 s for the largest calculation (50000trajectories and 16 ellipsoids). Single-ellipsoid Cross-sections for Na,-He Before discussing the results of using multiple hard ellipsoids, we first illustrate the limitations of the single hard-ellipsoid model for calculating integral state-to-state cross-sections in the Na2-He system. We have calculated cross-section a(J = 0 -+J’) at collision energies E, of 0.05,O.l and 0.2 eV, in each case using a single ellipsoid surface corresponding to potential energy V, extracted from the Na,-He intermolecular potential [eqn. (2)]. We found no single ellipsoid that reproduces the behav- iour of the 10s cross-sections, in particular for low values of J’ the hard-ellipsoid cross-sections vary slowly as a function of J‘, whereas the 10s results show a sharp decrease in mag- nitude.An example is given in Fig. 2, for E, = 0.05 eV. Three dif- ferent ellipsoids were used to represent the atomdiatom interaction, one in which the ellipsoid parameters A, B were taken from the intermolecular potential V at I/ = E,, one in which I/ = E,/2 and a third with I/ = 0.002 eV. The best cor- respondence with 10s cross-sections was found for the V = E,/2 ellipsoid. However, as can be seen from the figure, the J’ = 2, 4 cross-sections are much too small, and the varia- tions in cross-section as a function of J’ are poorly repro- duced.J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 the model by increasing the number of hard-shape ellipsoids 30 Iused to represent the intermolecular potential. The basic question that we ask is: how few ellipsoids are necessary to obtain a reasonable representation of the inte- gral cross-sections? Our approach is to select representative hard ellipsoids for both the low-energy and high-energy regions of the repulsive potential. Incoming atoms with ‘normal’ kinetic energies En= 1/2pv,2 in the range q-l < En < & (i = 2, 3, ..., K)are then scattered from the ith ellip- soid, which has an assigned potential energy 5. For these representative surfaces, the assigned potential energy of the ith ellipsoid does not correspond exactly to the intermolecu- lar potential contour V from which the ellipsoid parameters Ai,Biwere extracted.However, the assigned energies always satisfy the condition: q-l < v< and thus correspond to a crude representation of the true intermolecular potential. At a collision energy of 0.05 eV a double hard-ellipsoid model was found to improve greatly the inelastic cross-sections. This is illustrated in Fig. qa),where a comparison is made between the single hard-ellipsoid results, the 10s cross-sections and cross-sections obtained using a double-ellipsoid model. Only the J’ = 2 cross-section is poorly estimated. The ellipsoid parameters, corresponding intermolecular potential energies V and assigned potential energies q are J’ Fig.2 Na,-He integral cross-sections for rotational transitions J = 0 +J’ at a collision energy of 0.05 eV. 10s cross-sections (0);’’ hard ellipsoid taken from the potential surface at V = 0.05 eV (+); at V = 0.025 eV (D);at V = 0.002 eV ( x). At collision energies of 0.1 and 0.2 eV the ‘best’ single hard-ellipsoid cross-sections (at V = E,/2) were significantly poorer than those obtained at 0.05 eV [see Fig. 5(a) and 6(a) later]. The range of accessible final rotational states, J’, at a given collision energy provides a measure of the anisotropy given in Table 1. Essentially, in the double-ellipsoid model (maximum torque arm b,) of the hard shape or p~tential,~.~ glancing collisions are scattered from a representative low- A -B.The magnitude of the cross-sections increases with the dimensions of the ellipsoid, since a larger shape presents a greater ‘target area’ for collisions. However, the relative varia- tion in cross-sections as a function of J’ depends primarily on the anisotropy A -B rather than on the size of the hard shape. This is illustrated in Fig. 3, where we show normalised cross-sections at E, = 0.05 eV for ellipsoids of varying dimen- sions (and ratio A/@, but having the same anisotropy (A -B = 0.7 A). From the above results, it is clear that the required sharp decrease in cross-section as a function of J’ cannot be modelled in the Na,-He system with a single hard ellipsoid. Multiple Hard-ellipsoid Cross-sections for Na,-He Because no single hard ellipsoid could be found to reproduce the IS0 integral cross-sections, the next step was to build on 5..0.16-oa 0.14-7 T 0.12-0 ”3 0.10-0.08-0.06-0.04 /2 4 6 8 10 IC J‘ Fig. 3 Normalised integral cross-sections for rotational transitions J = 0 --+ J‘ obtained from single ellipsoids of different sizes, with anisotropy A -B = 0.7 A, at a collision energy of 0.05 eV. (+) A = 4.0 A, B = 3.3 A; (0) A = 20.0 A, B = 19.3 %i and (0)4 = 1ooO.O A, B = 999.3 A. (b 25 -2 4 6 8 10 12 14 16 J’ Fig. 4 (a) Na,-He integral cross-sections for rotational transitions J = 0 -+ J’ at a collision energy of 0.05 eV. (0)10s cross-sections;” (+) single hard ellipsoid taken from the potential surface at V = 0.025 eV; (0)double-ellipsoid model (parameters in Table 1).(b) Na,-He integral cross-sections for rotational transitions J = 0 +J’ at a collision energy of 0.05 eV. (0‘)10s cross-sections;” (+) four-ellipsoid model (parameters in Table 1). J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 1 Parameters used in the multiple ellipsoid model at a colli- sion energy, E, = 0.05 eV; the table shows the parameters Ai, Bi, (i = 1, 2, ...,K) of K representative ellipsoid surfaces extracted from the intermolecular potential at energy V and with assigned potential energies V;. AJA BJA V/eV VJeV I two-ellipsoid model 6.11 5.33 0.002 0.01 1 4.93 4.23 0.02 0.05 2 four-ellipsoid model 6.11 5.33 0.002 0.005 1 5.51 4.76 0.007 0.01 2 4.93 4.23 0.02 0.03 3 4.52 3.85 0.04 0.05 4 energy ellipsoid surface, and the remaining trajectories from an 'inner ellipsoid' of higher energy.With four ellipsoids, a very good representation of the 10s cross-sections was obtained [see Fig. 4(b)].The ellipsoid parameters used are given in Table 1. At a collision energy of 0.1 eV the double-ellipsoid model again provides a large improvement to the cross-sections, [see Fig. 5(a)].However, the low AJ cross-sections are greatly underestimated. Extension to five ellipsoids resulted in a very good representation of all except the AJ = 2 cross-section [see Fig. 5(b)].The ellipsoid parameters are given in Table 2, illustrating the importance of the 0-0.01 eV region of the intermolecular potential in the scattering process.At a collision energy of 0.2 eV the double hard-ellipsoid model provides some improvement to the single-ellipsoid 25 7 I 20 h 04 J' 2h I(b) i 0 11 10-2 5-0i 4 6 8 10 12 14 16 18 20 J' Fig. 5 (a) As Fig. 4(a) but at a collision energy of 0.1 eV. (0)10s cross-sections;'g (+) single hard ellipsoid taken from the potential surface at V = 0.05 eV; (0)double-ellipsoid model (parameters in Table 2). (b) As (a) but for a five-ellipsoid model. (0)10s cross-section^;'^ (0)five-ellipsoid model (parameters in Table 2). 2861 Table 2 As Table 1, but for a collision energy of 0.1 eV AJA BJA V/eV VJeV I two-ellipsoid model 6.41 5.60 0.001 0.02 1 4.38 3.72 0.05 0.1 2 five-ellipsoid model 6.41 5.60 0.001 0.005 1 5.59 4.84 0.006 0.008 2 5.32 4.59 0.0 1 0.02 3 4.52 3.85 0.04 0.06 4 4.10 3.44 0.08 0.1 5 cross-sections [see Fig.qa)], but is not sufficient to describe the AJ = 2, 4 cross-sections. In fact, as illustrated in Fig. qb), use of five or eight ellipsoids was not suficient to reproduce the J' = 2 10s cross-sections, although the eight-ellipsoid model gave very good results for the remaining cross-sections. As can be seen from Table 3, it was again necessary to select ellipsoids from the outer, low-energy region of the intermolecular potential in order to reproduce the 10scross-sections. In addition to using small numbers of representative ellip- soids, we also performed calculations using ellipsoid surfaces with assigned energies corresponding exactly to the appro- priate intermolecular potential energy (4= V).For example, we used 11, 14 and 16 ellipsoids to reproduce the E, = 0.05, 0.1 and 0.2 eV cross-sections, respectively. Once again, we found that it was important to select ellipsoids from the low- J' 22 I2oi18 N h 14'"1 \5 t 0 I1 2 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 J' Fig. 6 (a) As Fig. 4(a) but at a collision energy of 0.2 eV. (0)10s cross- section^;'^ (0)single hard ellipsoid taken from the potential surface at V = 0.1 eV; (0)double-ellipsoid model (parameters in Table 3). (b) As (a) but for five- and eight-ellipsoid models. (0)10s cross-sections;lg ( +) five-ellipsoid model (parameters in Table 3); (0)eight-ellipsoid model (parameters in Table 3).Table 3 As Table 1, but for a collision energy of 0.2 eV ~~ ~ AJA BiIA VleV VJeV 1 ~~~ ~ two-ellipsoid model 6.41 5.60 0.00 1 0.04 1 3.97 3.30 0.1 0.2 2 five-ellipsoid model 6.4 1 5.60 0.001 0.005 1 5.59 4.84 0.006 0.008 2 5.32 4.59 0.01 0.02 3 4.52 3.85 0.04 0.06 4 3.97 3.30 0.1 0.2 5 eight-ellipsoid model 6.41 5.60 0.00 1 0.002 1 5.93 5.15 0.003 0.004 2 5.68 4.92 0.005 0.006 3 5.51 4.76 0.007 0.008 4 5.38 4.64 0.009 0.01 5 5.10 4.38 0.015 0.02 6 4.52 3.85 0.04 0.06 7 3.97 3.30 0.1 0.2 8 energy (0-0.01 eV) region of the intermolecular potential (see Table 4)in order to reproduce the AJ = 2 cross-sections. The cross-sections at all three energies are given in Fig.7(a),for comparison with the 10s cross-sections shown in Fig. 7(b). The similarities in the cross-section behaviour as a function of both J' and collision energy are clearly illustrated. In summary, to reproduce the cross-sections it is necessary at all collision energies to use contours taken from the outer regions of the intermolecular potential (see Tables 1-4). Fewer ellipsoids are needed to represent the 'core' of the potential. That is, for a soft potential the best strategy appears to be a selection of ellipsoids approximately equidis- tant in R (measured by A or B) rather than equally spaced in energy. The major contribution of outer ellipsoids is to the low-AJ cross-sections, since glancing collisions with small u, (and hence relatively small orbital angular momentum) are subject to the influence of the long-range repulsive region of the potential.Because these outer ellipsoids present a large target area for collisions, their contribution to low-AJ cross- sections is relatively large. The importance of the long-range region of the potential to low-AJ cross-sections is illustrated in Fig. 8, at a collision energy of 0.05 eV. The surfaces used are those given in Table Table 4 Parameters used in the multiple ellipsoid model at collision energies of 0.05,O.l and 0.2 eV, using 11, 14 and 16 ellipsoids, respec- tively, and assigned energies = V taken directly from the intermo- lecular potential V AJA BJA A -B/A VleV 1 6.41 5.60 0.81 0.001 6.1 1 5.33 0.78 0.002 5.93 5.15 0.78 0.003 5.79 5.03 0.76 0.004 5.59 4.84 0.75 0.006 5.44 4.70 0.74 0.008 5.38 4.64 0.74 0.009 4.93 4.23 0.70 0.02 4.69 4.0 1 0.68 0.03 4.52 3.85 0.67 0.04 4.38 3.72 0.66 0.05 4.27 3.61 0.66 0.06 4.10 3.44 0.66 0.08 3.97 3.30 0.67 0.1 3.78 3.08 0.70 0.14 3.61 2.84 0.77 0.2 J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 30 25 (y9. 20 h5 t 15 0 II I, 10 v b 5 0 J' 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 J' Fig. 7 (a) Na,-He integral cross-sections for rotational transitions J = 0 +J' at collision energies, E, ,of 0.05, 0.1 and 0.2 eV. The ellip- soid parameters are given in Table 4.(0)11 ellipsoids,E, = 0.05 eV; (+) 14 ellipsoids, E, = 0.1 eV; (0)16 ellipsoids, E, = 0.2 eV. (b) Na,-He 10s integral cross-se~tions'~ for rotational transitions J = 0 +J' at collision energies of 0.05, 0.1 and 0.2 eV, showing similar trends to the multiple ellipsoid results of (a). (0)E, = 0.05 eV; (+) E, = 0.1 eV and (0)= 0.2 eV.E, 4, taken directly from the intermolecular potential. The potential is built up by working inwards from the low-energy region and including additional ellipsoids until finally the whole range 0-0.05 eV (11 ellipsoids) is included. The cross- section curves in the figure are obtained from the 0-0.004 eV, 30 14 J' Fig. 8 Contributions made by different regions of the intermolecu- lar potential V to Na,-He integral cross-sections at E, = 0.05 eV.The potential is built up using the ellipsoid surfaces given in Table 4. (+) Four ellipsoids, V = 0.0-0.004eV; (0)seven ellipsoids, V = 0.0-0.009 eV; ( x) eight ellipsoids, V = 0.0-0.002 eV; (A) nine ellipsoids, V = 0.0-0.003 eV; (*) ten ellipsoids, V = 0.0-0.004eV; (0)eleven ellipsoids, V = 0.0-0.005 eV. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 0-0.009 eV, 0-0.02 eV, 0-0.03 eV, 0-0.04 eV and 0-0.05 eV regions of the potential. Scattering from the 0-0.01 eV region contributes more than 50% to the total AJ = 2 cross-section. The figure also illustrates how the multiple ellipsoid model can be used to investigate the contribution of different regions of the potential to inelastic cross-sections. The main conclusion from our results is that with the exception of the AJ = 2 transition at ‘high’ collision energies, we can reproduce the inelastic cross-sections with a model involving a small number of representative ellipsoids.The higher the collision energy, the greater the number of ellip- soids required and the poorer the J‘ = 2 cross-section. This is, at first sight, unexpected because we might imagine that at higher energies the incoming atom is less influenced by the low-energy (repulsive or attractive) part of the intermolecular potential and should therefore be easier to model with a small number of ellipsoids. However, it is important to note that contributions to the AJ = 2 cross-section arise from scattering by a large range of the intermolecular potential (both high-energy and low-energy regions) whereas high AJ transitions arise only from the inner, high-energy (V = E,) region of the potential which is penetrated by ‘normal’ coll- sions having a large relative velocity component u,.In terms of our model, this means that every ellipsoid contributes to the AJ = 2 cross-section but only the innermost ellipsoids contribute to high AJ cross-sections. The range of the intermolecular potential which contrib- utes to the AJ = 2 cross-section is significantly larger for high collision energies than for lower collision energies. In the case of Na,-He, at E, = 0.05 eV, AJ = 2 transitions arise from scattering by the 0.001-0.05 eV region of the potential, corre- sponding to a range of approximately 2.0 A.At E, = 0.2 eV, this transition arises from scattering by the 0.001-0.2 eV region of the intermolecular potential, a range of ca. 2.8 A. From this analysis, we expect that a larger number of ellip- soids is required to model the cross-sections as the collision energy is increased. In addition, it is possible that quantum diffraction scattering7 contributes to the 10s cross-sections for J‘ = 2. This quantum effect arises for forward and small-angle scat- tering. In an anisotropic system such as Na,-He, we can imagine that inelastic processes arise at very small centre-of- mass scattering angles (glancing collisions) if the normal com- ponent of velocity, u,, is large enough.This can be seen from eqn. (4) and (10). Thus, the higher the collision energy the more likely it is that glancing-angle collisions will result in a J = 0 + 2 transition and that quantum diffraction effects will increase the quantum cross-section accordingly. These effects cannot be reproduced within a classical model and to investi- gate more fully the importance of quantum effects the 10s calculations must be compared with classical trajectory calcu- lations performed using the same analytical potential surface. Finally, we note that in the Na,-He system there is not much variation in the anisotropy of the potential in the V = 0.001-0.2 eV region (see Table 4). Thus, the main reason for requiring a multiple ellipsoid approach in this application is to provide a measure of the softness of the intermolecular potential, rather than to model large variations in anisotropy.Clearly, in other systems both factors may be important. Conclusions We have presented a classical multiple hard-ellipsoid model for calculating rotationally inelastic cross-sections in atom- diatom collisions. The model allows a simple picture to be built up of the way in which different parts of the potential contribute to the rotationally inelastic scattering process. By adding or subtracting ellipsoids, we can make simple deduc- tions regarding contributions to the cross-sections. We argue that, although a single hard-ellipsoid model can be used to describe certain systems’ 2-14 (‘hard’ repulsive potentials, and almost isotropic potentials), in those that have a large aniso- tropy and a long-range soft repulsive potential, it is not pos-sible to find a single ellipsoid that adequately reproduces the low-AJ integral cross-sections.We have applied the model to Na,-He collisions to illustrate this point. An important message from our results is that even when the single hard-ellipsoid model fails to reproduce integral inelastic cross-sections, a small number of nested hard ellip- soids defining a crude repesentation of the repulsive potential can give very good results. For example, at a collision energy of 0.05 eV, a double-ellipsoid model representing the inner and outer regions of the repulsive Na,-He potential gave an excellent representation of the integral inelastic cross-sections. At higher collision energies, four or more ellipsoids were required.In all cases, inclusion of ‘outer’ ellipsoids rep- resenting the low-energy region of the intermolecular poten- tial was necessary for reproduction of the low-AJ cross-sections. Finally, the simplicity of the multiple ellipsoid model allows insight to be gained into the way in which inelastic cross-sections vary as a function of the softness and aniso- tropy of the intermolecular potential. Thus, the model may have potential as a simple inversion procedure giving a crude representation of an intermolecular potential directly from experimental cross-sections. This is currently being investi- gated for other alkali-metal-rare gas systems.The author wishes to thank Jadson Belchior, John Murrell, Mark Osborne and Tony McCaffery for useful discussions, and the SERC for the award of an Advanced Fellowship. References 1 R. A. La Budde and R. B. Bernstein, J. Chem. Phys., 1971, 55, 5499. 2 D. Beck, U. Ross and W. Schepper, 2.Phys. A., 1979,293, 107. 3 W. Schepper, U. Ross and D. Beck, Z. Phys. A, 1979,290, 131. 4 D. Beck, U. Ross and W. Schepper, Phys. Reu. A, 1979,19,2173. 5 S. Bosanac, Phys. Reu. A, 1980,22,2617. 6 R. Schinke, J. Chem. Phys., 1980,73,6117. 7 H. J. Korsch and R. Schinke, J. Chem. Phys., 1981,75,3850. 8 M. H. Alexander and P. J. Dagdigian, J. Chem. Phys., 1980, 73, 1233. 9 J. A. Serri, R. M. Bilotta and D. E. Pritchard, J. Chem. Phys., 1982,77,2940. 10 M. A. Hoffbauer, S. Burdenski, C. F. Giese and W. R. Gentry, J. Chem. Phys., 1983,78, 3832. 11 T. G. Kreutz and G. W. Flynn, J. Chem. Phys., 1991,93,452. 12 S. D. Bosanac and J. N. Murrell, J. Chem. Phys., 1991,94, 1167. 13 J. C. Belchior, J. N. Murrell, and S. D. Bosanac, Mol. Phys., 1992,77, 727. 14 J. C. Belchior and J. N. Murrell, J. Chem. Phys., 1994,101,2016. 15 P. L. Jones, U. Hefter, A. Mattheus, J. Witt, K. Bergmann, W. Miller, W. Meyer and R. Schinke, Phys. Rev. A, 1982,26, 1283. 16 A. J. McCaffery and 2. T. Alwahabi, Phys. Rev. A, 1991,43,611. 17 A. J. McCaffery, Z. T. Alwahabi, M. A. Osborne and C. J. Wil- liams, J. Chem. Phys., 1993, 98,4586. 18 P. M. Agrawal, V. Garg and K. R. Patidar, Chem. Phys. Lett., 1993,208,204. 19 R. Schinke, W. Muller, W. Meyer and P. McGuire, J. Chem. Phys., 1981, 74, 3916. 20 R. A. La Budde and R. B. Bernstein, J. Chem. Phys., 1973, 59, 3687. 21 L. M. Raff and D. L. Thompson, in Theory of Chemical Reaction Dynamics, ed. by M. Baer, Chemical Rubber Co., Boca Raton, FL. 1985. Paper 4/03342F; Received 6th June, 1994
ISSN:0956-5000
DOI:10.1039/FT9949002857
出版商:RSC
年代:1994
数据来源: RSC
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Leapfrog transformations and polyhedra of Clar type |
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Journal of the Chemical Society, Faraday Transactions,
Volume 90,
Issue 19,
1994,
Page 2865-2871
Patrick Fowler,
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摘要:
J. CHEM. SOC. FARADAY TRANS., 1994, 90(19), 2865-2871 Leapfrog Transformations and Polyhedra of Clar Type Patrick Fowler Department of Chemistry, University of Exeter, Stocker Road, Exeter, UK EX4 400 Toma2 Pisanski IMFM University of Ljubljana, Department of Theoretical Computer Science, Jadranska c. 19, Ljubljana, Slovenia The so-called leapfrog transformation that was first introduced for fullerenes (trivalent polyhedra with 12 pentag-onal faces and all other faces hexagonal) is generalised to general polyhedra and maps on surfaces. All spher-ical polyhedra can be classified according to their leapfrog order. A polyhedron is said to be of Clar type if there exists a set of faces that cover each vertex exactly once. It is shown that a fullerene is of Clar type if and only if it is a leapfrog transform of another fullerene. Several basic transformations on maps are defined by means of which the leapfrog and other transformations can be accomplished.1. Introduction The leapfrog transformation, first invented in the context of qualitative electronic structure theory of carbon cages, can be generalised to arbitrary maps.?' For our purpose it turns out to be useful to look at the leapfrog transformation as a trun- cation of the dual map,' rather than the dual of an omni- capping$ (the dual of a two-dimensional subdivision) as it is usually defined. In addition, some other important transform- ations of maps are treated in the present paper. They are composed of four basic transformations : subdivision, the dual and medial transformations and simplification.A map, M = G 4 S, can be described by a connected graph, G, in which each edge, e, is replaced by a pair inverse arcs, e+ and e-, with each arc, a, determining a unique vertex, u = i(a), that is its origin. Furthermore, in order to specify the map, M, completely, the set of angles composed of pairs of arcs (a, b) with common origin, i(a)= i(b),and rep- resenting adjacent arcs in the rotation about each vertex on the surface, S, is given. Although we are primarily interested in the sphere, the surface, S, that figures in the definition of a map can be an arbitrary closed surface. It is well known that closed surfaces can be classified into two infinite series. The orientable surfaces are So, S,, S2, ..., the sphere, torus, double torus, triple torus, .. .The non-orientable surfaces are N,, N,, N, , . . .,the projective plane, double projective plane or Klein bottle, triple projective plane, ... A map on an orientable surface is called orientable, otherwise it is non- orientable. A map is orientable if and only if its faces can be consistently oriented. For details, see, for instance, ref. 1. Before dealing with the mathematics, it may be useful to give a summary of the chemical background. Several members of the new class of all-carbon molecules, the ful- lerenes, have been characterised since the first preparation of macroscopic amounts of C,, in 1990.3-7 The accepted pattern of their chemistry is that they behave as conjugated x-systems.A fullerene molecule C, consists of n atoms arranged as a polyhedral cage with 12 pentagonal faces and all other faces hexagonal. Each atom is bonded to its three nearest neighbours by bonds spanning the edges of the CJ t A map is a graph embedded cellularly in some surface. An embedding of a graph is called cellular or two-cell, if each face is topologically equivalent to an open disk. For a precise definition and examples, see for instance ref. 1. 1Omnicapping is known as two-dimensional subdivision in topol- ogy. polyhedron§ and in addition contributes one electron and one radial atomic orbital to a surface x system.' In the simplest model, Huckel theory, the molecular-orbital energies are determined by diagonalising the vertex adjacency matrix of the graph of the carbon cage.(Two vertices are adjacent when they share an edge.) Positive eigenvalues cor- respond to bonding and negative to antibonding orbitals. Let the eigenvalues be sorted as follows: A, 2 A2 3 .. . 2 A, . If the eigenvalues A,,, and An/,+ ,are equal, then the configu- ration is open-shell. If, conversely, A,,, > AnI2+ ,,then three possibilities arise. If the n x n matrix has exactly n/2 positive eigenvalues, A,,, > 0, A,,, + < 0, then the neutral carbon cage has a properly closed-shell configuration in which all n/2 bonding orbitals are doubly occupied. If A,,, > A,,, + ,> 0, then the neutral carbon cage has a pseudo-closed shellg in which all electrons are in doubly occupied orbitals but some bonding orbitals are left empty.The third possibility, 0 2 A,,, > in which all electrons are also in doubly occupied orbitals but some are forced to be in non-bonding or antibonding orbitals, has not yet been encountered for neutral fullerenes and could be called meta-closed. A properly closed shell is no guarantee of maximal overall stability, as steric and electronic requirements generally pull in opposite directions," but there is considerable chemical interest in identifying the conditions under which closed shells occur. In passing, we note that Huckel theory is essentially a graph-theoretical model of some basic chemical concepts. We can therefore envisage transfer of this chemical terminology to arbitrary graphs.Given a graph G on n vertices and an arbitrary integer k, 0 < k d 2n (which plays the role of the electron count), we can define a shell type S(G, k) by suppos- ing that k particles 'fill' the n sorted eigenvalues of G accord-ing to the rules used for electrons (i.e.double occupancy, the Aufbau principle and the rule of maximum multiplicity).' The five disjoint cases are S(G, k) = 1 (open, k odd), S(G, k) = 2 (open, Ak/2 = ,), S(G, k) = 3 (properly closed, Ak/2 > 0 2 &/I + I), S(G, k) = 4 (pseudo-closed, Ak/2 > Ak/2 + 1 > o),S(G, k) = 5 (meta-closed, 0 3 Ak,, > + '). Note that k must be an even number in the cases S(G, k) = 2, 3, 4, 5. The natural choice for k is k = n, the number of vertices of G, and we can define a graph shell type S(G) = S(G, n).This choice is appropriate in a chemical context for e.g. trivalent graphs 4 In our terminology a polyhedron is a simple map with some additional information. For each vertex the coordinates in some 3D space are known. The edges can then be visualised as line segments and faces as (in general non-planar, self-intersecting) polygons. modelling neutral carbon cages. As an example of the use of the shell type, consider the cubic graph G = Q3 which has spectrum (3, 1, 1, 1, -1, -1, -1, -3). Different electron counts, k, give shell types as follows: S(Q3,1) = 1 (open), S(Q3,4) = 2 (open), S(Q3,8) = 3 (properly closed), S(Q3, 2) = 4 (pseudo-closed),S(Q3, 14) = 5 (meta-closed).Most fullerenes have open- or pseudo-closed-shell elec- tronic configurations, but two constructions are known that always generate isomers with properly closed shells. One is the cylinder construction' which gives rise to single, closed- shell isomers C, for n = 70, 100, . .. 70 + 30m and 84, 120, ... 84 + 36m. The isomers in these series can be described by the ring spirals of Manolopoulos et ~1.'~In a concise and trans- parent notation? the spirals for the first series are and for the second series More important as a route to closed shells is the leapfrog constr~ction~.'~which gives rise to well defined closed-shell isomers at n = 60 + 6k (k # 1) by a process of omnicapping the smaller cage of 20 + 2k (k # 1) atoms and taking the dual of the resulting deltahedron.(A deltahedron is a polyhedron made up exclusively of triangular faces.) The symmetry properties of the leapfrog operation have been discussed:9,' it preserves molecular symmetry and the reducible represen- tation of the point group spanned by the bonding orbitals of the leapfrog is that spanned by the edges of the smaller cage. A graph-theoretical proof' shows that leapfrogging any tri- valent polyhedron, not all of whose faces have multiples of three edges, will lead to an adjacency matrix with exactly 42 positive eigenvalues. Leapfrog fullerenes have also been shown to have at least one Kekule structure containing the maximum number (43)of benzenoid hexagons and thus to be maximally stable in a localised valence bond picture.17 In a chemical context such a structure is often called the Fries structure after the organic chemist who proposed in the early decades of this century that stability of a hydrocarbon corre- lated with the number of benzenoid rings in its molecular formula. The chemical concept of a Fries structure is well defined only by planar benzenoid or for fullerene graphs.A fullerene has a Fries Kekule structure when a Kekule can be drawn that has the maximum possible number (43) of benzenoid (alternating single-double) hexagonal faces. This structure has a property that every double-bond edge of the Kekulk structure is simultaneously present in two benzenoid hexa- gons. One possible generalisation of this concept is as follows.Define an alternating face as follows: if we have a graph embedded in some surface and we select a l-factor,$ then a face whose edges alternate on and off the l-factor is called a single-double or an alternating face. A l-factor is then a Fries structure if and only if for every edge, e, that belongs to the l-factor the two adjacent faces are single-double faces. In a t Many trivalent polyhedra can be described by the ring spiral code which is a sequence of face sizes that will reconstruct the poly- hedron when tightly wound. For instance, the trigonal prism can be represented by the codes 34443 or 43434 and the dodecahedron by 555555555555. These codes can be abbreviated using repetition counts as (3)(4)J3), (43),(4) and (5),2,respectively.$ Recall that a k-factor in a graph is a regular k-valent spanning subgraph. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 planar benzenoid we are given an additional item of informa- tion in that the infinite face is distinguished. We may regard it as a graph embedded in the disk, i.e. a surface with a boundary. In such a case we will make an additional require- ment, namely, that the infinite face be alternating and in general, that each boundary cycle be alternating. We remark that (i) all alternating faces are of course even. This implies that all odd faces of a map with a Fries structure are com- posed entirely of single bonds and (ii) though this definition is applicable to non-trivalent polyhedra, in chemical terms only those maps where every vertex has a valency of 2 or 3 are suitable for frameworks of carbon n-systems.The present paper uses the theory of polyhedral graphs both to unify concepts from qualitative chemical theories of benzenoids and fullerenes, and to extend them to a wider range of polyhedral systems on various surfaces. A second concept from the chemical theory of the stability of benze- noids can be given a mathematical form that allows extension to general polyhedral systems. This is the Clar structure. A ifbenzenoid has a perfect Clar ~tructure'~.'~its carbon atoms are spanned by a disjoint set of Clar sextets; the gener- alisation for a polyhedral graph, G, is that a perfect Clar structure is a vertex-disjoint collection of faces that include each vertex of G once and only once.The following result then connects Fries and perfect Clar structures. Theorem 1 A trivalent polyhedral graph has a perfect Clar structure if and only if it has a Fries structure. Proof The edges that do not belong to a perfect Clar structure form a l-factor that is a Fries structure. On the other hand if there is a Fries structure then each vertex belongs to two alternat- ing faces and a non-alternating face. Obviously, the non-alternating face can have no edges from the l-factor. All non-alternating faces form a perfect Clar structure. The connection between leapfrogs and the Clar theory of aromatic ~extetsl~,'~ will be explored in the present paper. The main chemical conclusion of this work can be antici- pated as follows.Leapfrog fullerenes are all Clar polyhedra and any fullerene that is a Clar polyhedron is a leapfrog. Additional results are proved for more general trivalent poly- hedra showing that all leapfrogs of trivalent polyhedra are of Clar type. Although originally defined as an operation on polyhedral fullerenes, the leapfrog transformation can also be applied to planar benzenoids if the parent graph is first capped on inter- nal faces only and then the inner dual rather than the dual is taken. Leapfrogging one planar benzenoid in this manner always generates another that has a properly closed-shell n-system. The leapfrog benzenoid is a total resonant sextet molecule, i.e. it is composed entirely of Clar sextets.20 Not every Clar-sextet benzenoid is a leapfrog, in contrast to the case of the fullerenes where all Clar fullerenes are leapfrogs, as we show here.The plan of the paper is as follows. In Section 2 the basic transformations on maps are defined. In Section 3 these are used to build up the leapfrog transformation. Section 4 pre- sents the notion of a Clar polyhedron and lists a number of its properties, including the connections between leapfrogs and Clar polyhedra. The chemically important fullerene poly- hedra are discussed in Section 5 where it is shown that leap- frog fullerenes coincide with Clar fullerenes, with implications for the electronic structures of these molecules and their anions. Section 6 gives a brief description of a generalisation of Clar structure, and Section 7 concludes the paper.J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 2. Basic Transformations Before we give a precise definition of the leapfrog transform- ation we will define four simple and well known transform- ations on maps. One-dimensional Subdivision The one-dimensional subdivision map, S,(M) is obtained from M by dividing each edge of G(M)into two. Hence S,(M) has u + e vertices, 2e edges and f faces. Clearly a one-dimensional subdivision of a polyhedron is not a ‘proper’ polyhedron? as it has vertices of valency 2. Proposition 1 If a map M has e edges, f faces of size r,, r,, . . .,rf and u vertices of valency d,, d, , .. . ,d, then the one-dimensional subdivision map S,M has e new vertices of valency 2 and f faces of size 2r,, 2r,, ...,2r,.Proof Follows directly from the definition of S. Dual Transformation Let M be a map. Then we shall denote by 9(M) the (Poincare) dual map of M. In the dual map the role of vertices and faces are interchanged. The dual map has f vertices, e edges and u faces. The dual of a cube is an octahedron and uice versa. Similarly the dual of a dodecahedron is an icosa- hedron and uice uersa. The tetrahedron is self-dual. Proposition 2 If a map M has e edges, f faces of size rl, r2, . . ., rf and u vertices of valency dl, d, ,...,d, then the dual map 9M has e edges andf vertices of size rl, r, ,...,rf and u faces of size d,, d,, ..., d,. Proof Follows from the definition.Medial Transformation By &(M) we denote the Medial map.$ The medial map is obtained from M as follows. The vertices of A(M) are given by the edges of M. Each adjacency of A(M)corresponds to a pair of edges that share a common angle in M. For instance, the medial map of the cube is the cuboctahedron which is also the medial map of the octahedron. The medial map of the tetrahedron is the octahedron and the medial map of the cuboctahedron is the small rhombicuboctahedron.21 Proposition 3 If a map M has e edges,ffaces of size rl, r2,rf and u vertices of valency dl, d,, ..., d, then the medial map .k(M) has e vertices, the graph is regular, 4-valent, so it has 2e edges and v +f faces. Let us colour the f faces blue and the u faces green.The blue faces correspond in a one-to-one way to thef original faces and are of size rl, r2, ..., rf. In a similar way there is a one-to-one correspondence between the u medial faces and the u original vertices. The sizes of medial, green, faces match the valencies of the original vertices and are of t From now on, we use the term proper polyhedron to denote a map of which all vertices are of valency at least 3. $ The medial map is called the edge figure by Johnston; see ref. 2. size d,, d,, ..., d,. The map 9A is bipartite and has quadri- lateral faces. Proof Follows directly from the definition. Here are two facts about dual and medial maps: 99 = id. Taking the dual twice gives rise to the original map.This is not true if we make a simplification of the graph after each step (i.e.9,%lo# id). A9 = A.A map M and its dual 9(M) have the same medial map. Simplification If G is the general graph then we shall denote by Go its sim- plicial skeleton. This is obtained from G by deleting all loops and replacing sets of parallel (i.e. coterminous) edges by single edges. In a similar way we denote by doa map that is obtained from a general map M by deleting loops and paral- lel edges. In general, M can give rise to non-isomorphic maps M, and so the operation 0 that maps M into M, is not well defined in general. However, when all parallel edges bound digom,§ the operation is well defined and that is the only case in which it will be used here.The operation 0 will be called simplification. For each transformation 9 we will use a shorthand 9, for the composition 09. We say that a map, M, is simple if all faces of M are bounded by simple cycles of length >2 (i.e. no digons all0 wed). Since we will be working with composition of operations it may happen that an operation produces some digons. Let 9 be such a transformation and let M be a map. Then 9M is a map that can have some digons that arise as a result of 9 and not as a structure of M. In such a case we will assume that 09 removes only the above-mentioned parallel edges. With this assumption the results that follow may be viewed in a much more general context because we do not have to restrict our attention to simplicial maps that have simplicia1 duals.3. Leapfrog and Truncation Transformations The chemical importance of the leapfrog transformation has been mentioned in the introduction to the present paper, and is discussed at length el~ewhere.~~’~~~’ ’Here we introduce a definition of this transformation that applies to a general polyhedral, not necessarily trivalent, graph and relates it to an operation well known from solid geometry, the operation of truncation. Both can be defined in terms of the basic trans- formations of maps defined in the previous section. Let I? = .KOS,. Then G represents truncation. If a map is viewed as a polyhedron, then the truncated map corresponds to a truncated polyhedron, that is to a polyhedron obtained from the original by cutting away each vertex with a plane passing through the polyhedron ‘close’ to the vertex.Note that AS, is almost the same as ‘G except that in MS, the original edges are transformed into parallel edges forming digons. This argument shows that the truncated map is tri- valent (regular of degree 3, sometimes called ‘cubic’) and that the original edges are transformed first to digons and subse- quently into a 1-factor. In chemistry such I-factors are called Kekule structures, and the digons correspond to double bonds. 9 A digon is a disk bounded by a pair of parallel edges. Therefore digons can exist only in non-simplificial maps. Let C = T7.D = A,S,9. This is the leapfrog transformation. It is simply the truncation of the dual.For an arbitrary map M = G 4 S with u vertices, e edges and f faces the leapfrog transformation C(M)= C(G) 4 S pro-duces a 2-cell embedding of a trivalent graph C(G) with 2e vertices, 3e edges and v +f faces into the same surface S. It is possible to colour the edges in the following way: e edges are coloured red and 2e edges are coloured blue in such a way that the red edges form a perfect matching (1-factor) and the blue edges form a 2-factor composed of f vertex-disjoint cycles. Furthermore, the blue edges bound precisely f faces. The remaining u faces are bounded by edges that are alternat- ing blue-red-blue ... and are thus of even size. These faces will be referred to as the green faces. The chemical significance of this colouring operation is that when the map is a fullerene the red edges correspond to double bonds and the blue to single bonds in the Fries Kekule structure of the leapfrog. The green faces are then benzenoid hexagons in this structure.4. Polyhedra of Clar Type We say that a polyhedron (simple map) M is of Clar type if it has a collection of faces whose boundaries form a 2-factor in G(M).Each face of size k in such a collection is then called a Clar k-tet, and the whole collection is called a perfect Clar structure.? Thus the Clar faces are disjoint and taken together they exhaust the vertices of the map. The reader is referred for terminology to recent work2, by Kirby, in which toroidal benzenoids are studied. Proposition 4 If a map M has f faces of size rl, r2, .. ., rJ and u vertices of valency d,, d,, ..., d, then the truncation map EM is tri- valent and the blue faces are of size d,, d,, ..., d, and the green faces are of size 2r1, 2r2, 2r,. Furthermore, the blue faces form a perfect Clar structure. Proof Using the geometric interpretation of truncation it follows that the map is trivalent. By the same argument the blue faces, i.e. the faces that were obtained as a result of trunca- tion, form a perfect Clar structure. The face sizes can be cal- culated directly from the definition of E. Proposition 5 If a map M has e edges, f faces of size r,, r, ,rf and u vertices of valency d,, d, ,. . . ,d, then the leapfrog map CA is trivalent and the blue faces are of size rl, r2,.. .,rJ and the green faces are of size 2d,, 2d2, ...,2d,. Furthermore, the blue faces form a perfect Clar structure. The number of vertices of CM is equal to 2e. Proof Since the leapfrog is a truncation it is obviously trivalent. By the same argument the blue faces, i.e. the faces that were obtained as a result of truncation form a perfect Clar struc- ture. The face sizes can be calculated directly from the defini- tion of C. Since the blue faces form a 2-factor, the number of vertices of CA is equal to r, + r2 + * + rf = 2e. Proposition 6 If L is a trivalent map that is of Clar type then there exists another map M on the same surface, such that L = C(M). t In the book by Gross and Tucker' such a collection is called a patchwork.SysIoz3calls it a VIFC (vertex-independent face cover). J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Proof Let L be a trivalent map of Clar type. Let us select a perfect Clar structure in it. Furthermore, let us colour the edges of the selected Clar structure blue and other edges red. Clearly, the blue edges form a 2-factor and the red edges form a 1-factor. Consider the faces of L. The faces belonging to the selected Clar structure are bounded by blue edges, so let us colour them blue and all other faces green. Now, select an arbitrary green face. Obviously it contains at least one red edge on the boundary. Since the red edges form a 1-factor it cannot contain two consecutive red edges. Neither can it contain two consecutive blue edges.Hence, it contains alter- nating blue-red edges. So each green face is of even size. Now define the following map. Take the dual of L, and colour the edges of 9Lblue and red corresponding to the colours of the edges of L. Now, delete the blue edges and obtain the map M. It is not difficult to see that CM = L. The following proposition is implicit in the work of Sys10~~ who prefers to work with deltahedra which are in effect duals of our trivalent maps. Proposition 7 If a trivalent map has a perfect Clar structure, then all odd faces belong to it. Proof From the proof of Proposition 6 it follows that the faces that do not belong to the perfect Clar structure are green and have even size. Therefore all odd faces must belong to the perfect Clar structure.Proposition 8 Each trivalent map with odd faces has at most one perfect Clar structure. Proof It is not difficult to see that for a trivalent map and a selected face there is at most one way to adjoin new faces in order to build a perfect Clar structure. Since all odd faces must belong to a perfect Clar structure, we can start building all perfect Clar structures with the same odd face. Hence there is no more than one perfect Clar structure available. The proof of Proposition 8 contains an interesting argu- ment, namely that each face of a trivalent map belongs to at most one perfect Clar structure. This fact can be rewritten in the following way. Proposition 9 For a trivalent map any two perfect Clar structures either completely coincide or have no face in common.This idea can be pursued a little further. Here it is pre- sented as a Proposition whose proof can be omitted. In the planar case it is equivalent (in its dual form) to Corollary 5 of ref. 23. Proposition 10 For a trivalent map M exactly one of the following state- ments is true: (0) M has no perfect Clar structure. (1) M has exactly one perfect Clar structure. (3) M has exactly three face-disjoint perfect Clar structures that cover each face of M exactly once. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 This proposition determines a classification of trivalent maps. Each trivalent map is then of Clar class 0, 1, or 3 according to the statement in Proposition 10 that holds for it.Hence a polyhedron (map) of Clar type is either of Clar class 1 or Clar class 3, whereas a polyhedron that is not of Clar type is of Clar class 0. It is clear that trivalent maps having two adjacent odd faces are of Clar class 0 and the trivalent maps of Clar class 3 have only even faces. However, a complete characterisation of Clar classes is not known to the authors. The planar (spherical) case has been studied in the past from various viewpoints. Here we reproduce Theorem 2-5 from Saaty and Kainen’s where a proof by induction is given. Theorem 2 A cubic mapt is three-colourablel if and only if each region5 is bounded by an even number of sides. Using Theorem 2 we can now prove the following conse- quence; see also Theorem 1 of ref.23. Proposition 11 A trivalent planar map is of Clar class 3 if and only if each face is bounded by an even number of sides. Proof Given a planar map of Clar class 3, a partitioning of its faces into perfect Clar structures is equivalent to face-colouring with three colours. By Theorem 2 the conclusion follows. Unfortunately, the Proposition 11 does not generalize readily to maps on surfaces different from that of the sphere. For example, the complete graph K, embeds into the torus with two faces (one 4-gon and one 8-gon). It also embeds into the projective plane with three faces (all 4-gons). Both maps have only even faces but the first is of Clar class 1 and the second of Clar class 3. The complete bipartite graph K3,3 embeds in the projective plane with four faces (one 6-gon and three 4-gons) to produce a map of Clar class 1.Fig. 1 shows a trivalent six-vertex map with three faces (one 8-gon and two 4-gons) embedded in a torus and a Klein bottle. The 8-gon is not a simple face; it hits some vertices more than once. The map is therefore of Clar class 0. It is an open question whether there exists a Clar class 0 trivalent map with only even, simple faces (on a surface other than the sphere). Another consequence of the definition of Clar class is Proposition 12. Proposition 12 A trivalent map of Clar class n (n = 0, 1, 3) has exactly n inverse leapfrog transforms. A simple example of a trivalent polyhedron that is simultaneously a leapfrog of three other maps is the cube.The cube is a leapfrog of three isomorphic squares each cor- responding to a plane that bisects four faces of the cube. Fig. 2 gives another example of a trivalent polyhedron that is a leapfrog of three different maps. Note that since we are dealing with maps on the sphere, at most one inverse leapfrog transform is a proper polyhedron. Any others must contain at least one divalent vertex. This follows from the fact24 that t Cubic map = trivalent planar map. 1This refers to colouring faces of the map, or, equivalently, the vertices of the dual triangulation. $ Region = face in our terminology. I I \ I d a Fig. 1 The faces and Clar classification of a map can depend upon the surface chosen for its embedding.The trivalent graph K3,3has six vertices and three even faces when embedded in (upper) a torus or (lower) a Klein bottle. The torus is formed by identifying opposite edges a and b of the dotted rectangle without twisting, the projective plane by making the same identification but with a twist on edge b. In each case the map is of Clar class 0. each planar trivalent map contains at least one face of size less than six. The fact that a polyhedron has at most one proper poly- hedral inverse leapfrog transform can be used as the basis of a classification of all polyhedra. Given an arbitrary poly- hedron P, then either P is a basic polyhedron i.e. one that has no proper polyhedral inverse leapfrog transform, or P can be traced back by inverse leapfrog transformations to a unique basic polyhedron.The number of steps required to reach a P A B C Fig. 2 A given leapfrog polyhedron can sometimes be obtained by transformation of different original maps. The trivalent polyhedron, P, represented here as a Schlegel diagram, can be considered as the leapfrog of any of the maps A, B, C, i.e. P = C(A)= C(B)= C(C). basic polyhedron starting from P is the leapfrog order of P; basic polyhedra are of leapfrog order 0. Note that the cube is of leapfrog order 0 even though it is the leapfrog of a square, whereas the truncated octahedron is of leapfrog order 1 as it is the leapfrog of the cube. Trivially, all non-trivalent poly- hedra are of leapfrog order 0.The fullerenes form a closed subclass of polyhedra under the leapfrog transformation in the following sense: a leapfrog of a fullerene is itself a ful- lerene and the inverse leapfrog transforms of all fullerenes are themselves fullerenes. Proposition 13 If a trivalent map has two odd faces sharing an edge then such a map does not have a perfect Clar structure. Proof By Proposition 7 all odd faces must belong to a perfect Clar structure, hence all odd faces must be pairwise edge-disjoint. Note that the fact that a map is a leapfrog transform of some map is equivalent to the fact that the map is a trunca- tion of another, not necessarily trivalent map. Only trivalent maps can be leapfrogs (or equivalently truncations). Hence leapfrogs are precisely the trivalent maps of Clar class 1 or 3.Another characterisation of trivalent polyhedra of Clar type was obtained by Syslo and is here recast in our termin- ology; see ref. 23, Corollary 6. Proposition 14 A trivalent planar map has a perfect Clar structure if and only if no two odd-length faces are connected by an even sequence of faces. 5. Fullerenes A fullerene is a polyhedron (spherical or planar) whose faces are only pentagons and hexagons. Proposition 15 A fullerene has exactly 12 pentagons. Proof This fact is a part of mathematical folklore. Here is one proof. For a fullerene with p pentagonal and h hexagonal faces f= p + h and 2e = 5p + 6h. By the Euler formula for the sphere u +f = e + 2, and for a trivalent polyhedron ZI = 2e/3.Hence, p = 12 and h is undetermined. Proposition 16 A fullerene has at most one perfect Clar structure. Proof Follows from Propositions 15 and 8. Proposition 17 If a fullerene F has a perfect Clar structure, it has isolated pentagons, all pentagons belong to such a structure, the number of vertices of F is divisible by 6, say, n = 6no and there exists another fullerene E on 2n, vertices such that F = C(E). Proof The fact that it has isolated pentagons on the Clar structure follows from Propositions 15 and 7. By Proposition 6 it is a J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 leapfrog transform of some map which has to be a fullerene. The latter fact and the numerical conditions of the proposi- tion are the consequence of Proposition 5.We remark that the number of vertices of a leapfrog ful- lerene is n = 60 + 6k (k # l)’ of which 60 belong to penta- gons. The link between the perfect Clar structure and the valence-bond picture of Clar sextets is made el~ewhere.~’ If we notionally add an electron to each pentagonal ring, the localised picture of the electronic structure of the fulleride anion CL2- has the k + 12 ‘aromatic’ rings (12 pentagons and k hexagons), each bearing a Clar sextet. In contrast, the Fries Kekule structure gives a localised picture of the bonding in a neutral leapfrog fullerene C, in terms of n/2 double bonds along edges of hexagonal rings. The conse- quences for the chemistry of fullerenes are discussed in ref.25. Proposition 18 Fullerenes are either of Clar class 0 or of Clar class 1. Ful-lerenes of Clar class l are exactly the ones that are leapfrog transforms (of some other fullerene). Proof This is just a restatement of Propositions 16 and 17. Proposition 19 The number of fullerenes on n vertices is the same as the number of fullerenes of Clar type on 3n vertices. Proof By Propositions 5 and 6 the leapfrog transformation is a one-to-one map between the set of all fullerenes on n vertices and the fullerenes of Clar type on 3n vertices. This means that we obtain for each fullerene on n vertices exactly one ful- lerene of Clar type on 3n vertices and vice versa: each ful- lerene of Clar type on n,-vertices determines exactly one fullerene on n,/3 vertices.Let us restate the connection between fullerenes of Clar type and leapfrog transforms. Clearly the leapfrog transform of a fullerene is a fullerene. If a fullerene is a leapfrog trans- form of another map then this map too has to be a fullerene. Finally, a fullerene is of Clar type (and hence of Clar class 1) if and only if it is a leapfrog transform and therefore of leap- frog order greater than 0. This relationship generalises to leapfrog transforms of any trivalent map. The faces of the leapfrog transform CM of a trivalent map M can be coloured black and white. The black faces are the old faces of map M that compose a perfect Clar structure in CM. The white faces are all new hexagons. This can be seen nicely for instance in the soccer ball c6, which is the leapfrog transform of the dodecahedron C,,, and in the C,,, leapfrog of c60 (see Fig.3). Fig. 3 An illustration of the result that the leapfrog fullerenes are Clar polyhedra and can therefore be coloured like footballs, with the black faces disjoint but including all vertices. Note that the penta- gons are always black in a leapfrog fullerene. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 6. Sachs Structures The notation of a perfect Clar structure can be generalised in at least two ways. One is a (general) Clar structure, which is simply a collection of vertex disjoint faces of a map, not nec- essarily containing all vertices of the map. This would be a two-dimensional analogue of a matching.On the other hand we should like to have a generalisation that would cover both l-factors and 2-factors in connection with the structure of the map. One such is the Sachs struc- ture. A Sachs structure, s, of a polyhedron, M, is a vertex disjoint collection of (bounding cycles of) faces and indepen- dent edges such that each vertex of the polyhedron is hit by exactly one element of the collection. Let sf denote the number of faces and s, the number of independent edges of s. Let s,-(M) denote the maximum number of faces of any Sachs structure of M and let se(M)denote the minimum number of edges of any Sachs structure of M. A Sachs structure can be viewed as a generalisation of a perfect Clar structure: a Sachs structure that is composed of faces only is a perfect Clar structure.Furthermore, the poly- hedron M is of Clar type if and only if s,(M) = 0. A consequence of the four-colour theorem is, that each planar trivalent polyhedron has a proper three-edge-colour- ing; see for instance ref. 24, Theorem 4-3. This implies that each fullerene has a Sachs structure. It would be an inter- esting problem to find, for a given n, a fullerene C, with the maximal (minimal) number s,(C,). For vertex numbers n = 60 + 6k (k # 1) the limit s,(C,) = 0 is realised by the leapfrog fullerenes. A chemical example of a Sachs structure is the ground- state electronic structure of C70, which can be described as a belt of five benzenoid hexagons separating two staggered ‘halves’ of the c60 Fries structure26 i.e.as a Sachs structure with sf = 5 and s, = 20, whereas the anion C$i- would be represented by a belt of five double bonds separating two staggered halves of the c60 Clar structure, i.e. with sf = 12 and s, = 5. 7. Conclusions Although the leapfrog transformation was first defined in a chemical context, as a way of expanding fullerene frameworks to yield cages with specific electronic structures, it can be applied to maps of a much more general kind. Conversely, the study of map transformations can suggest chemical appli- cations. Study of the notion of Clar polyhedra shows, in a way that is made precise in Section 5, that the terms ‘carbon football’ and ‘leapfrog fullerene’ are synonyms, suggesting a localised model of electronic structure for fulleride anions.Combinations of the basic transformations can be used to define other operations on maps and, for example, to gener- ate all Platonic and Archimedean solids from the tetra-hedron. These combinations will be described in detail elsewhere. In future work the generalisation of Clar to Sachs structures, and extensions of the list of basic map transform- ations can be expected also to bear fruit in chemistry. This work was supported by the MZT contract No. T1-0010-0101-94. References 1 J. Gross and T. W. Tucker, Topological Graph Theory, Wiley-Interscience, New York, 1987. 2 R. L. Johnston, J. Chem. SOC.,Faraday Trans., 1991,87, 3353. 3 W. Kratschmer, L. D. Lamb, K. Fostiropoulos and D.R. Huffman, Nature (London), 1990,347,354. 4 F. Diederich, R. L. Whetten, C. Thilgen, R. Ettl, I. Chao and M. M. Alvarez, Science, 1991,254, 1768. 5 R. Ettl, I. Chao, F. Diederich and R. L. Whetten, Nature (London),1992,343, 149. 6 K. Kikuchi, T. Wakebayashi, N. Nakahara, S. Suzuki, H. Shiro- maru, Y. Miyake, K. Saito, I. Ikemoto, M. Kaishono and Y. Achiba, Nature (London), 1992,357, 142. 7 R. Taylor, G. J. Langley, A. G. Avent, T. J. S. Dennis, H. W. Kroto and D. R. M. Walton, J. Chem. SOC., Perkin Trans. 2,, 1993, 1029. 8 P. W. Fowler and J. M. Woolrich, Chem. Phys. Lett., 1986, 127, 78. 9 P. W. Fowler, J. E. Cremona and J. I. Steer, Theor. Chim. Acta, 1988, 73, 1. 10 P. W. Fowler, S. J. Austin and D. E. Manolopoulos, in Chem-istry and Physics of the Fullerenes, Proceedings of the NATO ARW,Crete,ed. K. Prassides, Dordrecht, Amsterdam, 1993. 11 C. A. Coulson, Valence, Oxford University Press, Oxford, 1963. 12 P. W. Fowler, J. Chem. SOC.,Faraday Trans., 1990,86,2073. 13 D. E. Manolopoulos, J. C. May and S. E. Down, Chem. Phys. Lett., 1991, 181, 105. 14 P. W. Fowler, Chem. Phys. Lett., 1986, 131,444. 15 P. W. Fowler and D. B. Redmond, Theor. Chim. Acta, 1992, 83, 367. 16 D. E. Manolopoulos, D. R. Woodall and P. W. Fowler, J. Chem. SOC., Faraday Trans., 1992,88,2427. 17 P. W. Fowler, J. Chem. SOC., Perkin Trans. 2, 1992, 145. 18 E. Clar, Polycyclic Hydrocarbons, Academic Press, London, 1964. 19 E. Clar, The Aromatic Sextet, Wiley, New York, 1972. 20 J. R. Dias, Chem. Phys. Lett., 1993,204,486. 21 H. M. Cundy and A. R. Rollett, Mathematical Models, Tarquin Publications, Diss, Norfolk, 3rd edn., 1981. 22 E. C. Kirby, Croat. Chem. Acta, 1993,66, 13. 23 M. Syslo, in Combinatorics and Graph Theory, Banach Centre Publications, PWN-Polish Scientific Publishers, Warsaw, 1989, vol. 25. 24 T. Saaty and P. Kainen, The Four Color Problem; Assaults and Conquest, McGraw-Hill, New York, 1977. 25 P. W. Fowler and A. Ceulemans, to be published. 26 J. Baker, P. W. Fowler, P. Lazzeretti, M. Malagoli and R. Zanasi, Chem. Phys. Lett., 1991, 184, 182. Paper 4/02630F; Received 4th May, 1994
ISSN:0956-5000
DOI:10.1039/FT9949002865
出版商:RSC
年代:1994
数据来源: RSC
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Ab initiostudy of the molecular structure, polarizability and first hyperpolarizability of 6-hydroxy-1-formylfulvene |
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Journal of the Chemical Society, Faraday Transactions,
Volume 90,
Issue 19,
1994,
Page 2873-2879
Salvatore Millefiori,
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摘要:
J. CHEM. SOC. FARADAY TRANS., 1994, 90(19), 2873-2879 Ab initio Study of the Molecular Structure, Polarizability and First Hype rpola riza biIity of 6-H ydroxy-1 -form yIfu lvenet Salvatore Millefiori* and Andrea Alparone Department of Chemistry, University of Catania, Viale A. Doria 8,95125-CataniaI Italy Ab initio calculations have been carried out on 6-hydroxy-1-formylfulvene (HFF) to study (a) the ground-state molecular structure and relative stability of conformers, (b)the strength and main features of the intramolecular hydrogen bond, including harmonic vibrational frequencies and proton tunnelling, (c) hydrogen-bond effects on linear and quadratic polarizabilities, (d) the role of electron correlation (at the MP2 level) on the computed quantities. The results show that the intramolecularly hydrogen-bonded C, structure is the most stable form of HFF, the barrier height for hydrogen transfer and the hydrogen-bond energy being 16.8 (MP3/6-31G**//MP2/6- 31G**) and 66-78 kJ mol-', respectively.The electron correlation and H bonding greatly affect the vibrational frequencies and intensities,vOH being lowered by 932 and 1074 cm-', respectively, while on H-bond formation, a,, and yOH are raised by 267 and 665 cm-' respectively. A one-dimensional (1D) model for H-transfer tunnel-ling leads to a tunnelling splitting of 142 cm-', and a proton tunnelling time of 0.12 x s, in good agreement with the experimental microwave data. The overall magnitude of the calculated hyperpolarizability, It, of HFF is comparable to that of nitrobenzene.It is strongly dependent on electron correlation, increasing by a factor of even more than three with respect to the SCF results. The intramolecular H bond favours an optical response within the chelate structure, but its effect is overwhelmed by enhancement of the mono-dimensionality of the system, following OH group rotation. CI-singles calculations show that in the lowest five excited states, dipole moments are essentially in the same direction as in the ground state. HFF (Fig. 1) is characterized by a seven-membered ring with a strong intramolecular H bond, which is further strength- ened by z-electron conjugation with the cyclopentadiene ring. This could result in a single minimum proton potential surface with the proton atom symmetrically shared between the two oxygen atoms.Indeed the microwave spectrum' of HFF is consistent with either a Czvor a C,form with 0-0 distance near to 2.5 A, indicative of a strong H bond.2 The CZv molecular symmetry is supported by NMR data,3 while IR data1v3 suggest the presence of rapidly interconverting C, forms. Solid-state X-ray and neutron-diffraction data4 indi- cate a slightly asymmetric H bond with 0-H distances at 1.214 and 1.343 8, and an 0-0 separation of 2.550 A. Gas-phase X-ray photoelectron (XP)spectra5 show two dominant ionizations arising from a C, structure. Strong H bonds may be efficiently used to control molecular arrangement; they also produce significant perturbations in the electronic struc- ture, so they can be directed towards the synthesis of mol- ecules with specific electronic properties.There is, in particular, much interest in developments of organic materials with large (hyper)polarizabilities for non-linear optical applications.6 Molecules with strong electron donors and acceptors and exhibiting intramolecular charge-transfer interactions within an extended conjugated framework are promising candidates. Besides classical groups such as NOz and NH, groups, non-benzenoid aromatics have also been considered as suitable interacting fragments7-' Cyclo-pentadiene derivatives, for example, produce fl hyperpolar-izabilities comparable to those of nitro- and cyano-benzene compounds.' The effect of H bonds on (hyper)polarizabilities have been little investigated, specifically intramolecular H bonds, although they have been demonstrated to be effective as organizing forces in materials for optoelectronics.' O Pre-vious papers ' deal essentially with intermolecular H-bond effects on linear polarizability, a, and cubic hyperpo- larizability, y.They gave valuable information on environ- mental interaction effects showing the non-additive nature of t Part of the 'Tesi di Laurea' of A.A. the H bond and its substantial contributions to a and y. The first hyperpolarizability, j?, should also be sensitive to environmental effects, although, being a vector quantity, it is expected to be markedly dependent on variations in molecu- lar geometry. H-Bond effects on fi have been investigated in the p-nitroaniline dimer by means of the semiempirical AM 1 method16 and in urea clusters by means of ab initi~'~,'~and semiempirical PPP''*'' methods. In the first case the extra- ordinary increase of j? obtained in linear p-nitroaniline dimers was argued to be essentially due to intermolecular donor- acceptor interactions; in the urea clusters, while the mean values of o! and y are little affected by H bonds, #Icomponents deviate significantly from linearity,' 'and in specific configu- rations of the H-bonded linear chain the intramolecular non- linear processes are enhanced by cooperative H bond and charge-transfer effects.' ' Computational Met hods All computations were performed by running the GAUSS-IAN 92 program" on an IBM RISC 6000/550 computer.Molecular geometries were fully optimized at the restricted Hartree-Fock (HF) 6-31G and 6-31G** level and at the cor- related Moller-Plesset second-order perturbation theory (MP2) level using the 6-31G** basis, with the reasonable restriction of a planar molecular arrangement. Optimal struc- tures are essential for obtaining reliable (hyper)polarizability values and H-bond energetics. The static (hyper)polarizability Fig. 1 6-Hydroxy-1-formylfulvene(HFF) J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 tensor components were computed analytically via electric-diffuse d and p functions on heavy atoms and an s function field derivatives of the total energy, following a coupled per- on hydrogen atoms was investigated.We found it most con- turbed HF approach.21 venient from a numerical and computational point of view to use a 6-31G(+p + s) basis with cp and c, exponents of 0.075 and 0.04, respectively. p values were properly scaled to the Bloemberg model22 by dividing the calculated figures by a factor of two. where p is the dipole moment. The average polarizability LY is expressed as Results and Discussion <a> = &XX + ayy + azz) Geometries and Energies and /3 hyperpolarizability vectors are expressed in terms of The equilibrium geometries of the A, B and C forms of HFF obtained at SCF and MP2 levels are collected in Table 1 andxi PiBi , i=x,y,z compared with the available experimental structures. Com- &=-a parison between calculated and experimental data reveals IPl that the structural parameters are better represented when electron correlation is taken into account.This is expected from the work of Frisch eta!. on the representative intramol- as well as ecularly H-bonded compound mal~naldehyde.~~ Specifically the O---H---0angle is correctly predicted to be almost linear B, = (a: + B: + B31'2 only at the correlated level, the calculated figure (170.3") being in excellent agreement with neutron-diffraction data where p, is the projection of the vector part of the first hyper- (171.8°).4Similarly, the 0-0 distances in the H-bonded C, polarizability on the dipole axis. and C,, forms (2.556 and 2.403 A,respectively) are much MP2 linear and quadratic polarizabilities were obtained by closer to the experimental value (ca.2.5 A) than those double numerical differentiation of energies and dipole obtained at the SCF level, which are too long and too short, moments, respectively. The standard 6-31G basis set was respectively. The 0-0 distance in the A form is slightly used as a starting basis. The effect of adding various sets of shorter than that in malonaldehyde (2.592 and longer Table 1 Calculated and experimental geometries of HFF; basis set, H = HF/6-3lG**, M = MP2/6-31G** HFF(0H cis), C, HFF(0H trans), C, - HFF, c,, H M exp." expb exp.' H M H M exp." 1.464 1.454 1.476 1.447 1.462 1.471 1.460 1.452 1.451 1.476 1.361 1.395 1.340 1.398 1.41 1 1.352 1.382 1.398 1.414 1.408 1.445 1.435 1.476 1.408 1.408 1.461 1.454 1.398 1.414 1.408 1.438 1.422 1.462 1.385 1.408 1.450 1.439 1.393 1.402 1.401 1.353 1.383 1.340 1.389 1.403 1.342 1.370 1.393 1.402 1.401 1.351 1.377 1.347 1.392 1.386 1.337 1.361 1.396 1.401 1.412 1.445 1.429 1.476 1.397 1.391 1.466 1.458 1.396 1.401 1.412 1.301 1.310 1.312 1.274 1.274 1.321 1.340 1.248 1.278 1.278 1.207 1.252 1.244 1.271 1.253 1.191 1.229 1.248 1.278 1.278 1.072 1.079 1.100 1.03 1.03 1 1.072 1.080 1.072 1.080 1.100 1.074 1.08 1 1.100 1.10 1.087 1.074 1.08 1 1.074 1.08 1 1.100 1.075 1.082 1.100 1.01 1.064 1.075 1.082 1.074 1.08 1 1.100 1.076 1.086 1.100 0.96 1.081 1.078 1.087 1.083 1.092 1.100 1.092 1.099 1.100 0.99 1.084 1 .O98 1.108 1.083 1.092 1.100 2.682 2.556 2.440 2.5 13 2.550 2.894 2.808 2.368 2.403 2.440 0.964 1.019 0.950 1.01 1.214 0.942 0.966 1.187 1.203 1.220 1.746 1.546 1.490 1.03 1.343 105.6 106.9 105.6 107.1 106.6 105.6 106.9 106.8 107.0 106.7 107.3 106.9 107.9 106.2 106.1 107.0 106.5 106.8 107.0 106.7 109.7 109.2 109.3 109.7 110.3 110.3 110.0 109.1 108.6 108.6 108.2 108.6 109.3 106.4 106.7 108.0 108.3 108.3 108.8 109.3 123.3 123.9 127.2 124.6 125.4 120.8 120.3 126.3 125.7 125.3 124.1 124.8 123.3 125.0 124.6 121.5 122.2 126.3 125.7 125.3 128.3 127.2 124.3 125.2 125.4 125.8 124.8 125.2 125.7 124.3 125.6 125.7 124.3 126.0 126.5 127.4 127.0 125.2 125.7 124.3 11 1.6 109.1 109.0 112.0 108.7 111.7 109.1 112.0 109.8 107.7 162.8 170.3 180.0 163.0 171.8 171.7 173.4 180.0 119.3 119.6 118.0 119.7 118.2 118.6 118.3 118.4 115.3 116.1 117.0 117.5 112.5 112.7 118.3 118.4 125.0 125.8 129.0 126.6 124.7 125.4 125.7 126.3 125.2 125.4 129.0 126.9 125.2 125.5 125.8 125.8 126.3 126.7 126.0 126.1 126.6 127.1 125.7 126.3 103.5 102.3 ~~ ~ ~~ Bond lengths in A, bond angles in degrees." Microwave spectrum.' X-Ray diffra~tion.~ 'Neutron diffra~tion.~ J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 than that in hydrogen maleate (2.406 computed at the same level of theory, suggesting that the H bond in HFF is stronger than that in malonaldehyde and weaker than that in hydrogen maleate.Bond angles are adequately reproduced at all the levels of calculation. Overall, the MP2/6-31G** results are in excellent agreement with neutron-diffraction data,4 except for the 0-H and 0---H distances which in the experiment are almost symmetric (Table 1). In this case, however, solid-state effects are likely to distort the H equi- librium position. The H bond has a strong effect on the molecular structure. Specifically the 0---0distance in the C form increases by 0.252 and 0.405 A with respect to the A and B forms, respectively, while the C=C and C=O double bonds are lengthened and single bonds are shortened.The overall effect is a great electron delocalization in the H- bonded structures that was also encountered in other conju- gated intramolecularly H-bonded corn pound^.^^,^^ Electron correlation greatly favours this process, moving the HFF structure towards the C,, form. Total and relative energies together with dipole moment values are reported in Table 2. From the reported figures one can easily establish the most stable configuration, the H-bond energy, the barrier height for hydrogen transfer, the effect of the basis set and electron correlation. At all the levels of calculation the H-bonded A form is the ground state of HFF. Vibrational analysis shows that A and C structures are true minima in the potential- energy surface, while the B form has an imaginary vOHO at 1082i cm-' (Table 3) and is a transition state in the proto- merization process.The barrier height is 31 kJ mol-' at the HF/6-31G level and is slightly affected by polarization func- tions. The electron correlation correction is very important, Ebarrierbeing reduced to 7.5 kJ mol-' (MP2/6-31G**). An hIP3 calculation at the MP2/6-31G** geometry mitigates the MP2 tendency to favour conjugate structures by raising the barrier to 16.8 kJ mol-'. Semiempirical estimates are much higher: 74, 111 and 65 kJ mol-' following MIND0/3, MNDO and AM1 results, re~pectively.'~ Note that at the same level of theory the malonaldehyde molecule shows a higher barrier C43.1 (HF/6-31G**), 15.0 (MP2/6-31G**// MP2/6-31G**) and 25.5 kJ mol-' (MP3/6-31G**//MP2/6-31G**)],24 while in hydrogen maleate the C, and C,, H-bonded forms are practically i~oenergetic.'~ The inclusion of the zero-point vibrational energy changes Ebarriersignifi-cantly, so that at the MP2/6-31G** level the A and B forms are almost isoenergetic, with the latter slightly favoured by 2.2 kJ mol-' (Table 2).In agreement with the trend in the H-bond energy (vide infra), the higher the H-bond energy the lower is the barrier. EHB can be evaluated by comparing the total energies of the A and C forms according to the two-step process,' 2875 C(equi1ibrium geometry) -+ C(distorted geometry); AEdisr (1) C(distorted geometry) --+ A(equi1ibrium geometry); AEFnd (2) C(equi1ibrium geometry) -+ A(equi1ibrium geometry); AE-, (3) where C(distorted geometry) is obtained by a rigid 180" rota-tion of the OH group from A(equi1ibrium geometry).In the literature, EHB has been evaluated from both eqn. (2) and (3).29 In HFF the remarkable influence of H-bond energy on charge redistribution and molecular structure generates size- able AEdistvalues causing AET and AEpndto differ appre- ciably, up to 20 kJ mol-' at the MP2/6-31G** level. This figure may be compared with the corresponding values of 12.8 kJ mol-' for malonaldehyde and 90 kJ mol-' for hydrogen maleate.24 Accordingly, HFF shows an EHB value C78.7 kJ mol-' (MP2/6-31G**), eqn. (3)] higher than that in malonaldehyde (58.4 kJ mol- ') and lower than that in hydro- gen maleate (100 kJ mol-'),24 at the same level of theory. The change with the level of theory is characterized by bal- ancing effects of the correlation energy (MP2) and diffusion functions, although it is interesting to note that the MP3/6- 31G**//MP2/6-31G** value is practically equal to that for HF/6-3 lG**//HF/6-3 1G** when the equilibrium geometry C is taken as a reference level, and to that for HF/6-31G**// HF/6-31G** if the distorted C structure is considered, indi- cating a considerable dependence of the electron correlation on geometry changes.AM1 gives an E, -E, difference of 42 kJ mol-'. Notoriously, however, semiempirical methods overestimate 0--0separation. Vibrational Frequencies and Proton Tunnelling The experimental IR spectrum of HFF is characterized by an intense carbonyl absorption at 1631 cm-' and by a broad absorption extending over the range 2900-2500 cm- ',with a peak at 2853 cm-', attributed to the vOHO ~tretching.~This assignment has been criticized on the basis of a V~~-R,...~ Table 2 Total (ET/E,") and relative (ER/kJ mol-') energies, and dipole moments @IDb)of HFF; values in parentheses include zero-point vibrational energy HFF(0H trans), C, HFF(0H trans), C, HFF(0H cis), C, equilibrium geometry distorted geometry HFF, C,, basis set ET ER ET E, P ET ER cc ET ER cc HF/6-31G// -418.080 14 0 3.76 -418.05008 78.9 4.73 -418.04409 94.3 4.35 -418.06854 30.5 3.68 HF/6-3 lG HF/6-31G**// -418.26946 0 2.84 -418.244 19 66.3 4.11 -418.23994 77.5 3.93 -418.25720 32.2 2.48 HF/6-31G** (-418.146 16) (0) (-418.12229) (62.4) (-418.13890) (19.0) MP2/6-31G**// -419.54492 0 3.20 -419.51493 78.7 4.42 -419.50727 98.8 4.32 -419.54206 7.5 3.03 MP2/6-31G** (-419.43002) (2.2) (-419.401 13) (77.8) ( -419.430 86) (0) MP3/6-31G**// -419.562 83 0 -419.53755 66.4 4.42 -419.52671 94.8 -419.55645 16.8 MP2/6-31G** 1 E, (hartree)= 4.35975 x J.1 D (Debye) z 3.33564 x C m. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 3 Calculated harmonic vibrational frequencies (v/cm-’) and IR intensities (Z/km mol-’)of HFF; symmetry notations and intensities are referred to MP2 results HFF(0H cis), C, HFF(0H trans), C, HFF, c2, MP2/6-3 lG** HF/6-31G** MP2/6-31G** HF/6-3 1G** MP2/6-31G** HF/6-31G** sym.V 1 V sym. V 1 V sym. V 1 V a‘ a‘ 3316 3290 7 4 3732 (VOH)3410 a‘ a’ 3874 (VOH)33 14 184 10 4205 (‘OH)3407 3316 3289 7 6 3409 3381 a‘ 3282 3 3382 a’ 3287 5 3379 3283 0 3375 a‘ 3243 6 3375 a’ 3279 4 3373 3176 1 3289 a‘ 3092 57 3364 a‘ 3215 13 3327 3175 66 3288 a‘ a‘ a’ a’ 2800 (VOH) 1752 (vc=o) 1678 1591 460 679 60 21 3184 1809 1750 1911 (vC=o) a’ a’ a’ a’ 2972 1752 1607 1768 (vC=o) 146 368 86 5 3 109 1877 1773 1996 (vc=o) 1780 (60HO) 1770 (‘OHO) l7 (80HO)1584 66 1 587 149 22 I9O4 (60HO) 1815 (VOHO) 1782 (do€Io)1700 a’ a’ a‘ 1577 (60H) 1525 (60H)1493 4 94 31 (dOH) 1609 (60H)1566 a’ a’ a‘ 1539 1501 1445 85 15 5 1653 1595 1551 1532 1497 1494 112 71 26 1620 1576 1539 a’ 1446 66 1528 a‘ 1434 10 1520 1423 102 1524 a’ a’ a‘ 1424 1357 1327 36 105 36 1505 1435 1389 a’ a‘ a‘ 1367 1286 l3l0(‘OH) 55 274 44 1458 1350 1396 (60H) 1386 1330 1384 (YOHO) 70 109 6 1424 1409 1483(YOHO) a‘ 1289 98 1338 a‘ 1242 99 1311 1328 9 1402 a’ 1233 6 1278 a’ 1187 1 1239 1243 0 1325 a” a’ 1120 146 (YOHI 114 6 1196 1145 a’ a‘ 1123 1067 7 15 1196 1137 1113 1105 20 38 1168 1145 a’ 1080 28 1123 a“ 1001 0 1097 992 0 1142 a’’ 1001 2 1110 a’’ 905 2 1068 986 1 1141 a” 94 1 8 1058 a” 848 1 1052 862 0 105 1 a’ 856 2 997 a’ 847 4 994 852 0 986 a” a” 853 804 0 7 909 938 (YOHI a” a’ 816 764 16 54 899 852 829 789 126 0 925 871 a’ 782 79 857 a’ 727 28 815 785 4 861 a’ 757 9 826 a” 7 14 37 756 742 56 834 a’‘ 733 46 778 a” 568 4 715 640 3 710 a” 562 1 706 a‘ 553 11 629 560 0 687 a” 556 0 636 a’’ 549 4 589 548 0 648 a” a’ a“ 548 456 378 0 1 0 594 482 403 a‘‘ a’ a” 440 306 481 (YOH) 86 1 21 472 330 440 (YOHI 519 467 396 0 1 0 544 499 429 a’ 29 1 10 3 19 a” 250 45 288 309 14 358 a‘ 284 7 288 a‘ 22 1 3 248 29 1 2 317 a‘ 276 2 265 a’ 188 8 189 176 0 198 a“ 176 0 197 a’’ 166 0 187 138 0 167 a” 127 0 137 a’’ 43 3 58 1082i (vOHO) 160 1637i (vOHO) Correlation.’ The computed vibrational frequencies of HFF rnaleate3’ and substituted pentane-2,4-dione~.~~ Note that in are reported in Table 3.A detailed assignment of the spec- support of the accuracy of the MP2/6-31G** results, the cor- trum is not within the scope of the present work; we restrict responding value in malonaldehyde is 517 cm-‘,24 in fair our attention to the most important vibrations related to the agreement with an estimated value of 500-800 cm-’ from the H-bond bridge: the 6-fi-6 stretching v,, the 9-h-Q experimental results,34 vOHO = 2800-3100 cm-’ and the in-plane bending 6, the O-H-0 out-of-plane bending y, free3’ vOH value of 3600 cm-’. and the carbonyl stretching vc=o. The comparison between The in-plane do, and out-of-plane yo, deformation modes SCF and MP2 results reveals the enormous effect of electron are recognizable in the calculated spectrum of HFF.Both correlation on vibrational modes involved in the H bond. these frequencies increase significantly upon H-bond forma- Specifically, in the C, structure A, vOHO and vc=o are lowered tion (yOH is more than doubled). In the C,, structure two by 932 and 159 cm-’, respectively, while yOH is raised by 208 extremely intense do,, vibrations are computed in the cm-’. The effect is less important in the C,, form. MP2/6- highest-energy region, one of which is at a higher wavenum- 31G** calculations put vOHO of the chelate C, form at 2800 ber than vOHO, as was also found in acid salts of carboxylic cm-’. In contrast, the C,, form does not show any absorp- acids with strong H bond^.^',^^ tion in the 3100-1800 cm-’ range.This result is in agreement Surprisingly, the carbonyl stretching frequency (7% higher with the experimental assignment3 of voHo and strongly sug- than in the experiment) is only slightly decreased (16 cm-’) gests a C, ground-state structure in HFF. Thus MP2/6- upon H-bond formation, whilst its intensity is greatly 31 G**//6-3 1G** calculations appear to overestimate the enhanced. relative stability of the C,, form. Both the wavenumber shift, The above results indicate that HFF has a strong intra- Av~==vOH -vOHO, and intensity magnification are character- molecular H bond with a proton motion coupled into a istic of the H b0nd.j’ Ava has been related to the H-bond C,-C,, arrangement. We then studied the proton transfer en erg^.^'^^ The calculated MP2/6-31G** value in HFF is between the two oxygen atoms by the procedure recently relevant (1074 cm-’), in agreement with the high E,, value.employed by Bicerano, Schaefer and Miller (BSM)37 and by AY, shifts of as much as 2000 cm-’ are reported for particu- Rios and Rodriguez38 in malonaldehyde and tropolone, lar intramoIecularly H-bonded compounds such as hydrogen respectively. This procedure gives a one-dimensional (1D) J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 description of the process and allows calculation of the split- ting due to proton transfer in a symmetric double-well poten- tial as:3g hAE = -wF exp(-0)71 where wF is the classical vibrational frequency in one of the wells and 8 is given by where E" = *ha,,wi is the imaginary frequency at the top of the barrier and v,ff= V, + F-c1 +(ho,f -ha,) k= 1 where uk and cvkf are the reactant (C,) and transition-state (C2J frequencies (Table 3), while V, is the classical barrier height of Table 2.Within the 1D approximation the 0-H stretch of the C, form is chosen as the reaction coordinate, the other F1 vibrational modes behaving adiabatically. The results are summarized in Table 4. The calculated splitting is extremely dependent on the barrier height and on the computation level of the vibrational frequencies. There- fore, these results must be considered with caution. In the absence of experimental data, a comparison with the corre- sponding figures obtained in the malonaldehyde may be useful where the experimental splitting (ca.21 cm-') is known.40 For this molecule we calculated a AE of 6 cm- ' at the 6-31G** level and a value of 32 cm-' if V, and hw are obtained at the MP3 and MP2 levels, respectively. A splitting Table 4 Calculated splitting, AE, for proton tunnelling in HFF; o, vibrational frequency; V, ,barrier height calculation level 0 vo AEJm-' HF/6-3 1 G** MP2/6-31G** MP2/6-3 1 G* * H F/6-3 1 G* * MP2/6-31G** MP3/6-31G** 35 1521 142 greater in HFF than in malonaldehyde is expected from the smaller V, values in the former. Therefore, we may argue that in HFF, 6-31G** calculations underestimate AE, while MP2 calculations greatly overestimate AE, owing to a too small V, value. The best estimate of AE at present is 142 cm-', which compares very well with the microwave intensity data, which suggest' 150 cm-' as a lowest limit.This represents, via the equation t = (h/2AE),4' a proton tunnelling time of 0.12 x s, quite close to the value of 0.13 x s obtained in 9-hydro~yfenalenone,~~ a strong intramolecularly H-bonded compound with an 0-0 distance (2.486 A)com-parable to that of HFF. (Hyper)polariza bilities The calculated dipole moments, linear and quadratic polari- zabilities are given in Table 5. In the chelate structures the dipole moment direction lies practically along the major axis of the molecule. The addition of polarization p and s func-tions to the 6-31G basis does not change p appreciably although it does affect the electron correlation.The use of the MP2/6-31G** geometry through the calculations using dif- ferent basis sets gives p values close to those reported in Table 2. The results in Table 5 clearly show the effect of the basis set, electron correlation and H bond on a and p. The mean a value increases when polarization functions and correlation are included in the calculations, the first effect (ca.+ 15%) being more important than the second one (ca. +7%). Note that electron correlation is more important in the chelate structures; (a} [MP2/6-31G( +p + s)] increases in the H-bonded structures by ca. 7%, this increase being due essentially to azz. By applying eqn. (1)-(3) to (a) it can be seen that about one third of this value is due to geometry distortion as a consequence of H-bond formation. Polarization functions and electron correlation both cause an increase in the p, vector, while p, displays the opposite behaviour by decreasing, and even changing sign in the open structures.The electron correlation effect is noteworthy, as p, increases by even more than a factor of three in the open configurations. This is a decisive factor in determining the relative p, values : only when electron correlation is taken into account is the fi, of the non-H-bonded structure higher than that of the H-bonded ones. Important correlation effects Table 5 Calculated dipole moments (p/D), linear (a/A3) and quadratic (/3/10-37 esu) polarizabilities of HFF; basis set, A = HF/6-31G, B = HF/6-31G + p(0.075) + s(O.O4), C = MP2/6-31G + p(0.075) + ~(0.04);calculations are performed on MP2/6-31G** geometries; the mol- ecule is in the xz plane, with the z axis along the major (C,) molecular axis HFF(0H trans), C, HFF(0H trans), C, HFF(0H cis), C, equilibrium geometry distorted geometry HFF, c,, basis set A B C A B C A B C A B C ~~ ~~ ~~ ~~~~~ ~~ ~ PX 0.28 0.30 0.16 4.23 4.17 3.98 4.24 4.28 4.01 0 0 0 ClL 3.95 4.02 2.96 2.47 2.59 1.62 1.99 2.09 1.17 3.88 3.93 2.83 Clr 3.96 4.03 2.96 4.9 1 4.9 1 4.30 4.69 4.76 4.18 3.88 3.93 2.83 Qxx 13.7 14.6 15.6 13.8 14.7 15.0 13.9 14.8 15.3 13.9 14.9 16.1 QYY 3.7 6.4 6.7 3.6 6.4 6.7 3.6 6.5 6.7 3.6 6.4 6.8 Qzz 17.5 19.0 20.0 17.4 18.8 18.6 18.1 19.6 19.4 17.8 19.4 21.0 <a> 11.6 13.3 14.1 11.6 13.3 13.4 11.9 13.6 13.8 11.8 13.6 14.6 Bxxx 58 64 182 60 71 200 48 59 200 0 0 0 BXYY -1 0 2 -3 -2 -1 -2 0 0 0 0 0 BXZZ 27 36 138 13 32 155 -1 19 153 0 0 0 Bx 84 100 322 70 101 354 45 78 353 0 0 0 BZZZ 9 15 26 -33 -43 -73 2 -3 -46 40 49 78 Bxxz 153 166 113 96 103 32 120 128 44 184 198 159 PYYZ -4 -29 -36 -3 -31 -36 3 -33 -39 -4 -30 -39 B: 158 152 103 60 29 -77 125 92 -41 220 217 198 B,' 179 164 182 159 338 120 92 90 105 102 362 298 133 94 120 110 355 328 220 220 217 217 198 198 J.CHEM. SOC. FARADAY TRANS., 1994, VOL.90 were previously noted in other conjugated systems such as p-nitr~aniline,~~.~~aminonitropolyenes and carboxylate anions.43 The H bond essentially influences b,, which '4increases as a consequence of an enhanced electron delocal- ization, thus reaching its maximum value in the Czvstructure. \ The latter, however, shows, at the MP2/6-31G**( + p + s) level, a total fi, value much less than that of the H-bonded C, form, owing to the lack of the p, contribution. Moreover, b, of the non-H-bonded structure is somewhat higher than the H-bonded ones. If the /I,quantity is considered, the H-bond effects are more dramatic, and are essentially related to the components of the dipole moment. The very small (or vanishing) px value in the chelate C,(or CZv)forms, drasti- cally reduces (or nullifies) the p, component, making the b, value of the open structure much higher than that of the H- bonded one.The relative orientations of the p and fi, vectors are shown in Fig. 2. As a result, the intramolecular H bond favours an optical response of the system within the chelate structures, but its effect is completely overwhelmed by rela- tive group orientations following OH rotation, which enhance the monodimensionality of the system. The effects of structural distortion on H-bond formation are within lo%, with b, and /3, varying in opposing manners. According to the two-level model4' the mean /3 value depends on the optical properties associated with the elec- tronic transition: fbe-g where is the dipole moment difference between excited and ground state, while f and E are the oscillator strength and transition energy, respectively. The optical properties of the lowest-energy transition of the A, B and C forms of HFF, obtained using CI singles theory,46 are reported in Table 6.H. 00 Fig. 2 MP2/6-31G(+p + s)//MP2/6-31G** relative orientations of the dipole moments, p, and second-order polarizability, b,, of HFF; relative intensities are arbitrary The lowest-energy allowed transition is invariably of HOMO-LUMO character, representing a charge shift from the five-membered ring towards the chelate six-membered ring. The dipole-moment components in all the excited states are in the same direction as in the ground states, although some of them show a decreased value (Table 6, Fig.3). This is, however, insufficient to change the positive fl, value. The overall magnitude of the calculated hyperpolarizability of HFF is comparable to that of nitrobenzene at the same level Table 6 6-31G CI singles optical properties of HFF ~~~~ ~ state transition energy/eV composition oscillator strength PeP APe+gP HFF(0H cis) 4.68 5.1 1 5.48 7.18 7.88 -0.68 (32-33) -0.13 (31-33) 0.51 (30-33) -0.44 (30-34) -0.65 (31-33) -0.16 (32-34) -0.53 (32-34) 0.40 (31-34) 0.54 (31-34) 0.40 (32-34) 0.217 O.OO0 0.507 0.238 0.7 18 5.63 1.40 3.80 6.82 6.04 1.87 -2.36 -0.04 3.06 2.28 HFF(0H trans) 4.48 4.71 5.83 7.68 0.50 (30-34) 0.44 (30-33) -0.69 (32-33) 0.67 (31-33) -0.13 (32-34) 0.62 (32-34) -0.22 (31-34) O.OO0 0.164 0.663 0.498 2.73 5.29 5.32 8.07 -1.00 0.56 0.59 3.34 H WC 2,) 4.46 5.15 5.96 6.68 7.37 0.67 (32-33) 0.13 (31-34) 0.68 (31-33) -0.14 (32-34) -0.64 (30-33) 0.17 (28-34) 0.68 (31-34) 0.67 (32-34) 0.12 (31-34) 0.252 0.445 0.002 0.003 0.993 5.14 4.74 0.33 6.20 5.09 1.46 1.06 -3.35 2.52 1.41 J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 2879 5O1" 2" 3" 4" 16 P. J. Jasien and G. Fitzgerald, J. Chem. Phys., 1990, 93, 2554. 17 J. Perez and M. Dupuis, J. Phys. Chem., 1991,95,6525. 18 J. Zyss and S. Berthier, J. Chem. Phys., 1982,77, 3635. 19 C. W. Dirk, R. J. Twieg and G. Wagniere, J. Am. Chem. SOC., 1986,108,5387. 20 M. J. Frisch, G. W. Trucks, M. Head-Gordon, P.M. W. Gill, M. W. Wong, J. B. Foresman, B. G. Johnson, H. B. Schlegel, M. Robb, E. S. Repogle, R. Gomperts, J. L. Andres, K. Raghava-chari, J. S. Binkley, C. Gonzales, R. L. Martin, D. J. Fox, D. J. Defrees, J. Baker, J. J. P. Stewart and J. A. Pople, GAUSSIAN 92, Gaussian Inc, Pittsburg, 1992. 21 C. E. Dykstra and P. G. Jasien, Chem. Phys. Lett., 1984, 109, 388; S. P. Karna and M. Dupuis, J. Comput. Chem., 1991, 12, 487.1" 3"2O 4O U 22 N. Bloemberg, Nonlinear Optics, Benjamin, New York, 1965. 23 J. Frisch, A. C. Scheiner, H. F. Schaefer III and J. S. Binkley, J. Chem. Phys., 1985,82,4194. 24 S. Millefiori, work in progresss. 25 G. Gilli, F. Bellucci, V. Ferretti and V. Bertolasi, J. Am. Chem. SOC.,1989, 111, 1023. 26 J. S. Craw and G.B. Bacskay, J. Chem. SOC., Faraday Trans., 1992,88,2315. 27 M. Eckert-Maksic, Z. B. Maksic and D. Margetic, Croat. Chem. Fig. 3 6-31G relative orientations of the ground-state, pLg,and Acta, 1989,62, 645. excited-state dipole moment, pLe,in the lowest excited states of 28 P. George, C. W. Bock and M. Trachtman, J. Comput. Chem., HWCJ 1980, 1, 373. 29 P. Schuster, in The Hydrogen Bond, ed. P. Schuster, G. Zundel and C. Sandorfy, North-Holland, New York, 1976, vol. 1, p. 123. 30 D. Hadzi and S. Bratos, in ref. 29, vol. 11, p. 565.of theory (142 x esu at the 6-31G level), which displays 31 R. M. Badger and S. H. Bauer, J. Chem. Phys., 1937,5,839.much higher in the lowest allowed excited ~tate.~' 32 F. Avbelj, M. Hodoscek and D. Hadzi, Spectrochim.Acta, Part Clearly f and the relative orientations of fie and fig favour A, 1985,41,89. large hyperpolarizability in HFF. 33 (a)J. Emsley, L. Y. Y. Ma, P. A. Bates and M. B. Hursthouse, J. Mol. Struct., 1988, 178, 1988; (b) J. Emsley, L. Y. Y. Ma, P. A. This work was partially supported by CNR and MPI, Roma. Bates, M. Motevalli and M. B. Hursthouse, J. Chem. SOC.,Perkin Trans. 2, 1989, 527; (c) J. Emsley, L. Y.Y. Ma, S. A. Karaulov, M. Motevalli and M. B. Hursthouse, J. Mol. Struct., 1990, 216, 143; (6)J. Emsley, N. J. Freeman, P. A. Bates and M. B. Hurs- References thouse, J. Chem. SOC.,Perkin Trans. I, 1988,297. 1 H. M. Pickett, J. Am. Chem. SOC.,1973,95, 1770. 34 C. J. Seliskar and R. E. Hoffmann, J. Mol. Struct., 1982, %, 146; 2 J.Emsley, Chem. SOC.Rev., 1980,9,91. Z. Smith, E. B. Wilson and R. W. Duerst, Spectrochim. Acta, 3 K. Hafner, H. E. Kramer, H. Musso, G. Ploss and G. Schultz, Part A, 1983,39,117. Chem. Ber., 1964,97,2066. 35 S. Bratos, D. Hadzi and G. Rossmy, Trans. Faraday SOC.,1956,4 H. Fuess and M. J. Lindner, Chem. Ber., 1975,108, 3096. 52, 464. 5 R. S. Brown, A. Tse, T. Nakashima and R. C. Haddon, J. Am. 36 D. Hadzi and B. Orel, J. Mol. Struct., 1973, 18,227. Chem. SOC., 1979,101,3157. 37 J. Bicerano, H. F. Schaefer and W. H. Miller, J. Am. Chem. SOC.,6 Nonlinear Optical Properties of Organic Molecules and Crystals, 1983,105,2550.ed. D. S. Chemla and J. Zyss, Academic Press, New York, 1987; 38 M. A. Rios and J, Rodriguez, Can. J. Chem., 1991,69,201.P. N.Prasad and D. J. Williams, Introduction to Nonlinear 39 W. H. Miller, J. Phys. Chem., 1979, 83, 960, and references Optical Eflects in Molecules and Polymers, Wiley, New York, therein.1991. 40 (a)W. F. Rowe Jr., R. W. Duerst and E. B. Wilson, J. Am. Chem. 7 G. F. Williams, J. Mol. Struct. (Theochem),1987, 151,215. SOC., 1976, 98, 4021; (b) S. L. Baughcum, R. W. Duerst, W. F.8 (a) J. 0. Morley, J. Am. Chem. SOC., 1988, 110, 7660; (b) Rowe, Z. Smith and E. B. Wilson, J. Am. Chem. SOC., 1981, 103, J. Pranata and C. J. Murray, J. Phys. Org. Chem., 1993,6, 531 ;(c) 6296; 1984,106,2260; 2265. D. Q. Li, T. J. Marks and M. A. Ratner, J. Phys. Chem., 1992, 41 K. M. Khristoffel and J. M. Bowman, J. Chem. Phys., 1981, 74, 96,4325. 5057.9 H. Ikeda, Y. Kaware, T. Sakai and K. Kawasaki, Chem. Phys. 42 R. Rossetti, R. C. Haddon and L. E. Brus, J. Am. Chem. SOC.,Lett., 1989, 157, 576. 1980,102,6913.10 J. M. Andre and J. Delhalle, Chem. Rev., 1991,91, 843, and refer- 43 S. Millefiori, work in progress. ences therein. 44 F. Sim, S. Chin, M. Dupuis and J. E. Rice, J. Phys. Chem., 1993,11 M. G. Papadopulos and J. Waite, J. Chem. SOC.,Faraday Trans., 97, 1158. 1989,85, 1885. 45 (a)J. L. Oudar and D. S. Chemla, J. Chem. Phys., 1977,66, 2664; 12 J. Waite and M. G. Papadopulos, J. Chem. Phys., 1988,66, 1440. (b) L. Oudar, J. Chem. Phys., 1977, 67, 446; (c) J. Zyss, J. Chem.13 J. Waite and M. G. Papadopulos, Chem. Phys. Lett., 1985, 114, Phys., 1979, 71,909. 539. 46 J. B. Foresman, M. Head-Gordon, J. A. Pople and M. J. Frich, 14 Z. Kecki, J. Sadley and A. J. Sadley, J. Mol. Struct. (Theochem), J. Phys. Chem., 1992, %, 135.1982, 5, 71. 15 T. Yasukawa, T. Kimura and M. Uda, Chem. Phys. Lett., 1990, 169, 259. Paper 4/02884H ; Received 16th May, 1994
ISSN:0956-5000
DOI:10.1039/FT9949002873
出版商:RSC
年代:1994
数据来源: RSC
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Delft molecular mechanics: a new approach to hydrocarbon force fields. Inclusion of a geometry-dependent charge calculation |
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Journal of the Chemical Society, Faraday Transactions,
Volume 90,
Issue 19,
1994,
Page 2881-2895
Adri C. T. van Duin,
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摘要:
J. CHEM. SOC. FARADAY TRANS., 1994, 90(19), 2881-2895 288 1 Delft Molecular Mechanics: A New Approach to Hydrocarbon Force Fields Inclusion of a Geometry-dependent Charge Calculation Adri C. T. van Duin, Jan M. A. Baas and Bastiaan van de Graaf Delft University of Technology, Laboratory of Organic Chemistry and Catalysis, Julianalaan 136,2628 BL Delft, The Netherlands A new hydrocarbon force field for saturated and non-conjugated unsaturated hydrocarbons has been developed. The most important difference between this force field and existing ones is its ability to produce a realistic, geometry-dependent charge distribution, the charges being calculated by the geometry-dependent method of Mortier (W. J. Mortier, S. K. Ghosh and S. Shankar, J.Am. Chem. SOC.,1986, 108, 4315).The use of this charge calculation means that polarization effects can be reproduced. Charge charge interactions are used between all the atoms in the molecules. Results show that by using this method a good hydrocarbon force field can be constructed. Heats of formation for a hundred compounds are calculated with an average absolute difference from experimental values of 1.02 kJ mol-’ . Geometries, IR frequencies and conformational energies are also well reproduced. Partial charges on atoms are a useful model for depicting the charge distribution in molecules and are used widely to understand and predict their physical and chemical proper- ties. These partial charges can be obtained from quantum chemical calculations by a variety of schemes.Of these schemes, the Mulliken population analysis is used most fre- quen t 1y. All of these schemes yield charges which are structure and geometry dependent and include the effect of polarization when intermolecular interactions are present. Obviously, it would be an advantage if empirical force fields were able to produce these geometry and external potential-dependent partial charges. The concept of introducing charges in empirical force fields is not new. Fixed charges allocated to the various atom types and fixed or structure-dependent point dipoles allocated to the various bonds have been applied to empirical force fields with some, or sometimes even considerable, success. These methods, however, do not produce a charge distribution dependent on geometry and are not able to deal with an external potential.A first attempt to include the geometry dependence of charges in molecular mechanics was made by Dosen et al. by modifying the Del Re method2 to include polarization. This method, however, has never been worked out in a general scheme for energy minimization. Moreover, a drawback of this method is the large number of parameters that are required because the Del Re scheme depends on bond properties. Recently, Mortier et aL3 developed, on the basis of density functional theory, a new method to calculate realistic geometry-dependent charges of atoms in molecules with only electronegativity and hardness for each atom type as para- meters.The Mortier method automatically includes polariza- tion and can easily be combined with an external potential. This method was successfully applied in empirical force fields for zeolites4 and aluminium phosphate^.^ The success of these applications prompted us to develop a new force field for organic molecules and ions in which this charge calculation method is included. In creating a force field for organic molecules, some of the additional advantages of calculating realistic charge distribu- tions become clear. Whilst for saturated hydrocarbons, owing to the small size of the charges in these types of compound, good empirical force fields have been created without the inclusion of electrostatic interactions, when a force field is extended to unsaturated or charged hydrocarbons or is to include electronegative atom types like oxygen, good descrip- tions of these interactions are of importance.Furthermore, the ability to deal with an external potential makes the force field well suited to reproduce the effect a catalyst has on the charge distribution of a molecule. These additional advan- tages contribute greatly to the usability and versatility of the force field. In this paper the basis of the organic force field, a force field for alkanes and non-conjugated alkenes, is presented. Parameters for tertiary carbocations and conjugated systems are to be added soon. We shall refer to this force field as the Delft Molecular Mechanics (DMM) force field. Force Field In the Mortier method, two parameters are assigned to each atom type, an electronegativity (x*) and a hardness (q*). Using these and the distances between the charged atoms in the molecule, the charges on each of these atoms can be cal- culated using the following equation : where 2 is the electronegativity of the molecule.For each atom in the molecule an equation like this can be set up. This set of equations can be solved using the total charge of the molecule as a constraint. This method obviously produces geometry-dependent charges and can easily deal with an external potential. In this force field, charge-charge interactions are calculated between all the atoms in the molecule, not excluding atoms on the same bond, valency angle or torsion angle.The interactions included in the force field are given in Table 1, with the exception of the Coulomb interaction resulting from the calculated charges. These potential func- tions aim to produce a reliable hydrocarbon force field without an excessive number of parameters. The inclusion of more parameters, for example by adding a cubic term in the valency-angle function, is not believed to contribute signifi- cantly to the quality of the force field. Adding more para- meters means having to optimize more parameters; this J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 1 Potential functions in the force field charge calculation bond energy valency-angle energy torsion-angle energy out-of-plane angle energy energy of non-bonding interaction energy of stretch-bend interaction energy of torsion-stretch interaction might not be a problem for the hydrocarbon force field because of the abundance of experimental data for these com- pounds, but it will become a problem when the carbocation parameters, and at a later stage those for hetero atoms, are added. The scarce reliable experimental data for carbocations will not be suflicient to optimize a large number of param- eters.In addition to this, the reason for the inclusion of cubic and higher terms in potential functions has the aim of repro-ducing the anharmonicity of, for example, valency-angle opening and closing. In this force field this anharmonicity is introduced by means of the charge-charge interaction, so there is less need for cubic and higher terms in the potential functions.To reproduce geometries of highly strained molecules, two cross interactions, torsion-stretch and stretch-bend, were included. Adding more cross interactions might improve the calculation of IR frequencies, but this was not done since the results in the reproduction of these IR frequencies did not directly call for such improvement. The parameters present in the potential functions were optimized, resulting in the values given in Tables 2-9. The sum of the values of the equilibrium valency angles around an sp3 centre were constrained to 656.82”, and those around an sp2 centre to 360”.The reason for this is to avoid artificial strain in non-strained compounds.This constraint also reduces the number of independent parameters in the force field. Allinger-type out-of-plane angles were used.6 However, in the calculation of E, and E,, the real angles around the sp2 centre were used, not the so-called in-plane angles. Table 2 Charge-charge interaction parameters ~ ~ ~ ~~ ~-~~~~ type of atom x*/eV A-’ ?lev C 8.5812 13.7696 H 5.9627 15.6261 C= 8.2401 12.4759 C=,sp2-hybridized carbon atom. Table 3 Bond parameters type of bond RolA a/A-1 DJkJ mol-’ 1.52221 1.98123 355.3936 C-H 1.11538 1.80474 433.8934 c-c-1.49546 1.87156 389.4321 H-C-1.10186 1.84698 444.2529 -c==c-1.33562 2.202 19 55 1.73 15 Table 4 Valency angle parameters type of valency atoms on angle central C 6,Idegrees k, c-c-c 109.47 408.4 109.07 334.3 109.64 334.3 C-C-H 109.87 396.8 109.97 396.8 110.52 396.8 H-C-H 107.30 334.8 108.42 334.8 -c-c-c 109.47 207.1 110.37 207.1 110.34 207.1 42-C-H 107.27 430.4 109.62 430.4 110.52 430.4 c-c=-c 115.62 505.2 C-C=-H 117.12 278.4 H-C’-H 116.96 225.4 c-c-c 122.19 283.5 123.15 283.5 H-C-C 119.73 372.7 121.52 372.7 Force constants, k,, in kJ mol-’ rad-’, angles are converted to radians in the calculation.Table 5 Torsion angle parameters type of torsion angle Vl v2 v3 c-c-c-c -0.828 1.568 1.416 C-C-C-H 1.154 H-C-C-H 1.074 c-c-c-c== -2.877 2.017 0.425 H-C-C-C= 1.995 c-c-c-c -0.857 37.402 C-C-C-H 36.978 H-C-C-H 38.920 c-c-c-c -5.566 -2.541 -1.356 H-C-C-C -0.728 H-C-C’-H 1.754 H-C-C’-C 1.794 C-C-C’-H 0.969 c-c-c=-c -4.426 5.335 3.538 Torsional barriers are given in kJ mol-’.For torsion angles contain- ing hydrogen atoms V, and V, were omitted, C=. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 6 Out-of-plane angle parameters C=.Iprefers to the in-plane projection of the central sp2 carbon. Force constants are given in kJ mol-' rad-'. Table 7 van der Waals parameters atom type &/kJ mol-' RVdWIA b ~~~~ ~ ~ ~ C 0.20560 1.9206 12.709 H 0.09710 1.5581 12.121 C= 0.21983 1.9501 1 1.943 Table 8 Stretch-bend parameters bond in valency angle ksb c-c 155.23 C-H 243.09 C-C-(H-C-C-, C-C-C-) 230.54 c-c-(C-c-C) 122.97 H-C-61.92 c-c 130.54 ~~ ~ Force constants are given in kJ mol-' A-' rad-'.For valency angles containing two hydrogens no stretch-bend interaction was taken into account. Table 9 Torsion-stretch parameters central bond in central bond in torsion angle kL9 torsion angle 4s c-c-c-c -2.021 H-C-C-H C-C-C-H -2.021 c-c-c-c -4.230 H-C-C-H -2.021 H-C-C-C -1.125 c-c-c-c== -2.021 H-C-C'-H -3.180 H-C-C-C= -2.021 H-C-C'-C -3.180 c-c-c-c C-C-C'-H -3.180 C-C-C-H c-c-c=-c -3.180 No torsion-stretch interaction was used when the central bond was C-C. Force constants are given in kJ mol-' A-'. For the non-bonded interactions, a modified Buckingham (6-exp) potential' was used.For each atom type, in principle five non-bonded parameters can be optimized (E, RvdW, a, b and c). E and rv in the non-bonded potential function (Table 1)are calculated by the following formulae : .. =R i + K~w,v(rj) vd~, j &.. = [&..&..]1/2Y 11 JJ However, if E and rv are to represent the depth of the poten- tial well and the minimum-energy distance, only one more important parameter remains: the steepness of the potential. This leads to the following relationships between a, b and c:~ a = 6 exp(b)/(b -6) c = b/(b-6) So, for each atom type, only three parameters can be opti- mized freely (E, RvdWand b). For the interaction between two atom types, b is calculated using bij= [biibjj]1'2.Table 7 shows the optimized values for these parameters.The foreshortening applied to the positions of the hydro- gen atoms in the C-H bond was optimized to a value of 9.19%. This arises from the observation that the electron cloud around hydrogen is translated somewhat along the C-H bond towards the carbon. Since the van der Waals interaction finds its origin in the interactions of these electron clouds, a correction to the positions of the hydrogens is required. Training Set and Parameter Optimization To optimize the parameters of a force field, a set of experi- mental and/or theoretical data, the training set, is required. This training set must contain the kind of data the force field must be able to produce. Since one of the reasons for developing this force field is its use as a basis for a force field capable of predicting enthalpies and entropies for carbo- cations, the reproduction of these kinds of experimental data for hydrocarbons is of prime concern.This means that a large number of reliable experimentally determined heats of forma- tion and IR frequencies must be present in the training set. An accurate calculation of enthalpy and entropy, however, cannot be expected without a reasonable reproduction of the geometry. Therefore, the experimentally observed values of a number of valency angles and bond lengths were included in the training set. These geometry data were taken from both small, relatively strainless molecules, whose geometries any force field must be able to deal with, as well as from some more strained compounds.The quality of reproduction of the experimentally observed geometries of these strained com- pounds indicates the versatility of the force field, a versatility that is required for reliable predictions of thermodynamic data of new compounds. To optimize the non-bonded para- meters specifically, X-ray data of crystalline organic com- pounds were added to the training set. In total, the training set consisted of 839 experimental observations, which were derived from measurements on 156 molecules. Table 10 shows the composition of the training set. These 839 experimental observations were used to opti- mize a total of 96 independent parameters. Using these experimental observations, the parameters of the force field were optimized successively to minimize the following sum of squares : n sum of squares = C [(xi,exp -xi,calc)/o]2 (2) i= 1 which is the definition of error. Here xexpis the experimental value and xCalcthe calculated value.The acceptance criterion (a)mentioned in this equation was used as a tool to impose our demands on the force field, since, owing to the definition of the error, a deviation between the calculated and the Table 10 Composition of the training set number of experiments in type of experiment training set bond 59 valency angle 102 torsion angle 15 heat of formation 100 IR frequency 484 dipole moment 10 crystal data 44 conformational energy 25 total 839 2884 J. CHEM. SOC.FARADAY TRANS., 1994, VOL. 90 Table 11 Acceptance criteria Table 13 Ab initio valency angles for propane and isobutane ctypes of data acceptance criterion valency angle 1.0" bond length 0.005 A torsion angle 2.0" heat of formation 2.09 kJ mol-' " valency angle/degrees valency angle/degrees a 0.5 kcal mol-'. angle ab initio exp." angle ab initio exp.b ~~ experimental data of more than this acceptance criterion has 1-2-3 112.76 112.40 3--1-2 111.04 111.2 a relatively large influence upon the total sum of squares. 2-1-4 111.36 -5--1-2 107.90 -1-2-7 109.41 -1--2-6 110.87 -Table 11 shows the 0 values for the different types of data. When the experimental error was large the acceptance cri- 2-1-5 111.09 -1-2-7 111.29 -terion was increased.On the other hand, when an experimen- 7-2-8 106.26 106.10 6--2-7 107.72 107.9 4-1-5 107.76 107.00 7--2-8 107.78 108.5tal observation was of particular importance for the final 5-1-6 107.60 107.00 shape of the force field, its acceptance criterion was reduced. To obtain a force field able to meet our demands, reliable " Structure derived from electron diffraction." Assumptions: Methyl experimental data are of major importance. Great care was groups have C,, symmetry, H-C-H angle on secondary carbon is taken in selecting data vital for the final shape of the force 106.1". Structure derived from microwave spectroscopy." Assump- field. Among these vital data are the geometries of small mol- tion: The three atoms of a CH, group form an equilateral angle.ecules. Examination of studies on structures of these small molecules shows that on a number of occasions structural constraints were imposed. Often a certain degree of symmetry is assumed or a fixed value is given to structural features to Table 14 Ab initio valency angles for propene and isobutene reduce the number of parameters to be refined. Of course, this affects the conclusions reached. Sometimes conclusions on the geometry in different studies contradict each other. For this reason we decided to use ab initio calculations with the basis 6-31G* to produce reliable 'experimental' data on Uvalency angles in small hydrocarbons. As a bonus, the ab initio calculation produces information about the entire valency angle/degrees valency angleldegrees structure.Experimental observations sometimes concentrate on the values for just one or two valency angles or bond angle ab initio exp." angle ab initio exp.'*' lengths; information about the rest of the geometry is not 1-2-3 125.24 124.30 1-2-3 122.26 122.2'given. Specifically, the experimental data on valency angles 2-3-7 11 1.39 -2-3-7 11 1.76 111.5' containing hydrogen atoms are usually absent or are subject 2-1-5 121.87 -2-1-6 121.80 121.3' to large experimental errors. 2-1-4 121.65 -2-3-8 110.78 110.7' Ab initio calculations were performed on ethane, propane, 1-2- 6 118.90 --5-1-6 1 16.40 1 1 7.4' 3-2-4 115.48 1 15.6'isobutane, ethene, propene, isobutene, but- l-ene (gauche and 2-3-8 110.90 syn), (2)-and (E)-but-2-ene and butane (anti and gauche).3-2-6 115.86 -7-3-9 108.22 108.2b 7-3-8 108.22 -8-3-9 106.88 105.8'In Tables 12-16 the results from these calculations are 4-1-5 1 16.48 compared with experimental values. 8-3-9 107.04 a Structure derived from electron diffraction.I2 Assumption : All C-C-H and C-C-H angles are 110.7" and 121.3", respectively.Methods 'Structure derived from microwave spectroscopy.' Structure Calculations were performed on a DEC5000-200 workstation derived from electron diffra~ti0n.l~ with the DELPHI molecular mechanics program." A suc-cessive one-parameter search was used to optimize the force field. By assuming a parabolic relation between the total error and the value of a single parameter (an assumption Table 15 Ab initio valency angles for syn and gauche but-l-ene which is usually correct in small intervals, owing to the defi- 5nition of the total error of the force field) the optimal value 5 11 gauche-but-l-ene 6hsyn-but-l-ene 69---12 Table 12 Ab initio valency angles for ethene and ethane 709 10 11 valency angle/degrees valency angle/degrees angle ab initio exp." angle ab initio exp." valency angle/degrees valency angle/degrees 1-2-3 127.19 126.7 1-2-3 125.37 125.4 2-3-4 115.87 114.8 2-3-4 112.49 112.1 angle ab initio exp." angle ab initio exp.* 2-1-5 122.76 -2-1-5 121.79 -2-1-6 121.04 -2-1-6 121.76 -2-1-3 121.82 121.4 2-1-3 111.21 111.5 1-2-7 118.24 -1-2-7 118.92 -3-1-4 116.36 117.20 3-1-4 107.67 107.9 " Structure derived from molecular orbital constrained electron dif- Structure derived from electron diffraction.* 'Structure derived fra~tion.'~ Assumption: C( 1)=C(2)-H(7) = 119.1' (gauche).from electron diffraction and ~pectroscopy.~ C( 1)=C(2)-H(7) = 118.4' (syn).J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 16 Ab initio valency angles for (E)-and (Z)-but-2-ene valency angle/degrees valency angle/degrees angle ab initio exp." angle ab initio exp." 1-2-3 128.35 125.4 1-2-3 125.20 123.8 3-2-8 117.16 114.5 3-2-8 118.92 121.5 2-1-5 113.03 -2-1-5 111.48 -2-1-6 110.48 -2-1-6 111.03 -1-2-8 114.49 -1-2-8 115.88 -5-1-6 107.86 -5-1-6 108.07 -6-1-7 106.89 -6-1-7 106.98 -" Structure derived from electron diffraction.'6 Assumption : Methyl groups have C,,symmetry. for a parameter in the force field can be found by calculating the total error at three different parameter values.These three points define the parabola from which the optimal value for the parameter can be found. Since most parameters in the force field are in some way related, the optimal value of each parameter shifts whenever another parameter is changed. This means that the opti- mization process must be repeated until the total error no longer decreases. This simple optimization scheme has pro- vided us with an easy to follow optimization process, which could be interrupted whenever a parameter seemed to reach an unrealistic value. More elaborate multi-parameter opti- mization schemes might seem faster but, owing to the mathe- matical complexity of the problem, have proved to be quite difficult to control in this case.Geometries were optimized using full-matrix Newton-Raphson or SHANNO conjugate gradient' * minimization techniques. The influence of geometry upon the charge distribution is assumed to be a second-order effect. Therefore, charges were calculated only at the beginning of the optimization, once in every six iterations and at the end. No derivatives of charges with respect to geometry were calculated, since this would extend computer time dramatically. Results from the charge calculations justify this approach; the same types of carbon atoms (primary, secondary etc.) are calculated to have similar charges in molecules possessing entirely different geometries.The geometries of the small molecules were obtained via ab initio calculations, using the 6-31G* basis set, performed on the Convex computer of the CAOS/CAMM in Nijmegen using the GAUSSIAN 8619 program. Results Valency Angles Fig. 1-3 show the results for the different types of valency angles in the force field. The valency-angle data were obtained from our ab initio calculations and from experimen- tal observations on (E)-~ent-2-ene,~' cyclohexene,2 cyclo-pente11e,~~2,3-dimethylbut-2-ene,~~ neopen tane,' cy~lohexane,~'exo,exo-tetracyclododecane,26 cis-cisoid-cis-perhydr~anthracene,~~cyclopentane (envelope and half-chair conformations),22 norbornene,'' trans-cycl~octene,~~ bicycl0[2.2.2]octene,~~ n~rbornane,~1,16-dimethyldodeca-hedrane3 and tetr ai~opropylethene.~ The results in Fig.1-3 show that the average errors for the C-C-H, -C-C-H and H-C-H valency angles (Fig. 2) are higher than those for the other types of angles. At least part of this is probably due to the relatively high experimen- 2885 120 , I 90 100 110 120 experimental angle/degrees Fig. 1 Reproduction of C-C-C and C-C-C= valency angles: (0)C-C-C; (A) C-C-C= 105 110 115 experimental angle/degrees Fie. 2 Reproduction of C-C-H, -C-C-H and H-C-H C-C-H; (A) =C-C-H; (0)vaiency angles: (0) H-C-H 130 /'Iv)f 125. 8 Tt-120-a m ,.s' /' 105 I/'''105 110 115 120 125 130 experimental angle/degrees Fig. 3 Reproduction of valency angles with a central sp' carbon: (0)C-C=-C; (A) C-C'-H; (0)H-C'-H; (0)C-C-C; (V) H-C-C tal error in the experimental observations of these types of angles.The most strongly deviating point in Fig. 3 is derived from an experimental observation on a trans-cyclooctene derivative. The fact that the observations were made on the derivative and not on trans-cyclooctene itself probably means that this observation is less well suited for use in the opti- mization of this force field. In Table 17 the reproduction using this force field of the valency angles of exo,exo-tetracyclododecane, a highly strained compound, are given. The overall results of the valency-angle calculations are given in Table 18. The mean deviation is derived from the absolute differences between the calculated and the observed valency angles. The results show Table 17 Reproduction of some valency angles in exo,exo-tetra- cyclododecane" && QiO1 3 valency angle/degrees angle obs.calc. 1-2-3 106.10 106.71 3-2-12 99.70 99.10 1-2-12 105.00 106.32 2- 1 2-5 94.60 93.43 2-1-10 119.80 119.01 2-1 2-H 115.50 114.85 H-12-H' 107.60 107.80 Ref. 26. Table 18 Summary of the results of the force field in the repro- duction of the valency-angle data source of data number of angles A/degrees ab initio structure 49 0.380 other 53 0.560 total 102 0.474 1-A is defined as : A = -I Oi, ca,c. -Oi, obs. I. "cxp. i= I that the force field is capable of reproducing valency angles well within the acceptance criterion.Torsion Angles Table 19 shows the results of the force field for the torsion angles present in the training set. The torsion-angle para- meters have a major influence on the conformational ener- gies, heats of formation and some IR frequencies, so these parameters are primarily optimized by these types of experi- mental observations. Bonds Fig. 4-6 show the results of the force field for the different types of bonds. The bond data were derived from experimen- Table 19 Results for torsion angles ~~ torsion angIe/degrees molecule angle exp. calc. ~~ ~ ~ cyclopentene" c-c-c-c-21 20.04 cyclopentaneb (envelope) C- C- C-C 24.20 23.90 c-c-c-c 39.40 38.73 c-c-c-c 0.00 0.00 trans-c yclooctenec c-c-c-c 138.10 138.30 norbornaned c-c-c-c 0.00 0.00 c-c-c-c 71.40 71.36 c-c-c-c 35.45 35.79 c-c-c-c 55.90 56.19 cyclopentaneb (half-chair) C-C-C-C --41.10 -40.78 c-c-c-c 12.60 12.57 c-c-c-c 33.10 32.95 " Ref.21, 33, 34, 35. Ref. 22. Ref. 29. Ref. 31. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 tal observations on ethene,8 propene," i~obutene,'~cyclo-hexane,2' ~yclopentene,~~ ethane,g propane," i~obutane,~~ ne~pentane,~~ exo,exo-tetracyclododecane,26cy~lohexane,~~ cis-cisoid-cis-perhydr~anthracene,~~cyclopentane (half-chair and envelope),22 eclipsed propene and i~obutene,~~nor-bornene,28 tr~ns-cyclooctene,~~ bicycl0[2.2.2]octene,~~ nor- b~rnane,~ 1,16-dimethyld~decahedrane~' and tetraoiso-propylethene. A total of 59 bond lengths were present in the training set.The force field was optimized to produce r,-type bond lengths, which refer to the thermal average distances. X-Ray measurements usually produce r,-type bond lengths which are slightly shorter than rg values. For this reason a small correction (0.003 A) was made to X-ray bond lengths before 158 .J 0 154 156 experimental bond length/A Fig. 4 Reproduction of C-C and C-C-bonds: (0)C-C; (A) 1.360 1.354 1.348 1.330 1.342 1.354 experimental bond length/A Fig. 5 Reproduction of C-C bonds 1.13 1.12 1.11 1.10 1.09 1.08 1.08 1.09 1.10 1.11 1.12 1.13 experimental bond length/A Fig. 6 Reproduction of C-H and -C-H bonds: (0)C-H; (A)-C-H J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 2887 Table 20 crystal a b ethane' pentaneb 4.23 (4.27) 4.10 (4.11) 5.62 (5.51) 9.07 (8.72) octanec cyclo hexaned ethenee 4.22 (4.13) 11.2 (11.3) 4.63 (4.51) 4.79 (4.47) 6.44 (6.31) 6.62 (6.45) tetraisopropylethene/ 6.42 (6.16) 7.59 (7.47) Results of crystal calculation C a 5.85 (5.49) 90 (90) 14.9 (14.8) 90 (90) 11.0(11.0) 94.7 (94.7) 8.20 (8.15) 90 (90) 4.07 (4.01) 90 (90) 7.85 (7.74) 80.4 (80.2) B Y 'sub 90.4 (90.5) 90 (90) 20.5 (23.3) 90 (90) 90 (90) 41.8 (47.7) 84.3 (84.6) 105.8 (103.3) 68.1 (64.2) 108.9 (108.4) 90 (90) 46.4 (47.1) 94.4 (96.5) 90 (90) 18.9 (19.7) 70.1 (72.5) 70.6 (70.51 -Experimental results are given first, with calculated values in parentheses.a, b and c are given in A,angles in degrees, AsubH in kJ mol-'.Heats of sublimation were taken from Kitaig~rodsky.~~ 'Z = 2, T = 90 K.41 2 = 4, T = 143 K.42 2 = 1, T = 216 K.42 2 = 4, T = 186 K.43 2 = 2, T = 85 K.44 '2 = 1, T = 170 K.32 including them in the training set.The magnitude of this cor- rection is derived from Allinger et uI.,~' although we applied a slightly larger correction. The average absolute difference between the calculated and experimentally observed bond lengths for the 59 experiments is 0.0032 A. The =C-C single bond in trans-cyclooctene is not taken into account in calculating this average since its experimental observation was performed on a derivative of trans-cyclooctene rather than on trans-cyclooctene itself. The acceptance criterion for the bond lengths was set to 0.005 A.The average error lies well within this criterion. Non-bonded Interactions To optimize the van der Waals parameters explicitly, calcu- lations on six crystalline organic compounds were performed. The crystal was represented by a central unit cell, surrounded on each side by an equal number of identical cells. The carte- sian coordinates of the molecule and all six lattice dimensions were optimized simultaneously in the energy minimization, following the method described by Van de Graaf et The van der Waals parameters were optimized to reproduce the cell parameters and the sublimation enthalpy of the crystals; the latter was calculated using the following equation :39 (3) where Z is the number of molecules in the unit cell, and Ecryst and Egasare the calculated steric energies of a molecule in the crystal and the gas phase.To correct for the difference in translational and rotational degrees of freedom in the crystal and in the gas phase 2RT is added. Epopis a correction for the population of higher-energy conformations in the gas phase (to be applied for pentane and octane). A more elabo- rate description of E,, is given in the section on heats of formation. The calculations were performed on crystals of size 7 x 7 x 7 unit cells. The optimization of the force field was started using the parameter values recommended by Ponder4' for the non-bonded interactions. These values were left unchanged during the first stages of optimization, until the force field reproduced reasonable heats of formation.Then the experimentally observed crystal data were added to the training set. Only minor changes to the non-bonded parameters were required to produce the results shown in Table 20. After reaching these results the crystals were removed from the training set (to reduce computer time). From this point no further optimization was performed upon these parameters. Fig. 7 shows the different types of H.0.H van der Waals interactions present in several force fields. To check our non- bonded parameter optimization we also looked at the repro- duction of the geometries of molecules containing very short H-..H distances. The experimentally observed26 short H--.H distance in exo-exo-tetracyclododecane,1.75 A, was suc-cessfully reproduced by calculation.Cis-cisoid-cis-Perhy-droanthracene contains two hydrogens at a distance of 1.92 A,27 for which DMM gives a value of 1.86 A. IR Frequencies IR frequencies play an important role in optimizing this force field. Table 10 shows that almost half of all experimental observations in the training set are IR frequencies. These 429 IR data are derived from the assigned spectra of ethane,47 propane:7 isob~tane,~' cy~lohexane,~~ne~pentane,~~ 2,2,3-trimethylbutane,48 trans-de~alin,~~ iso-ethene,49 pr~pene,~~ butane:' (E)-and (Z)-b~t-2-ene,~~ 3-methylbut-b~t-l-ene,~~ l-ene5't and 2-methylb~t-l-ene.~'. The IR data were ordered according to their symmetry assignments.Fig. 8 shows the distribution of these data in the training set over the interval 0-3200 cm-'; each bar sum-marizes an interval of 200 cm-'. For each interval the average error is given. Table 21 shows the calculated and experimentally observed IR frequencies for ethene, ethane, isobutane, (Z)-but-2-ene and cyclohexane. Conformations and Rotational Barriers A number of experimentally observed rotational barriers, transition-state energies and energy differences between con- formations are included in the training set. These data are essential for optimization of the torsion parameters. Table 22 shows the results of the force field for these experiments. For 1-0.402.50 2.90 3.30 3.70 4.10 4.50 RIA Fig. 7 Comparison of H..,Hvan der Waals interaction^:^^,^^ (-) MM3; (---) DMM;(.-..-)Ponder t After comparison with the spectra of 2-rnethylb~t-l-ene,~' the assignments were changed somewhat before using them in the opti- mization. J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 21 IR data results for selected molecules assignment v,,,,/cm-Acalc,"/cm-assignment v,,,,./cm-l AcalC./Cm-assignment veXp,/cm-Acalc,/cm--~ ethaneb Alu 279 -10 826 -153 2930 -54 EU 822 -89 943 -46 2948 -4 995 -20 949 +93 2988 +35 1190 + 110 1023 +32 2992 + 15 1370 -42 1222 + 12 3035 + 12 1388 +8 All 1342 + 18 3052 +41 1460 +5 B3u 1444 -9 1469 +25 1623 +22 cyclohexaneb 2915 +5 2989 +1 EU 232 + 13 Alll 2915 +5 3026 +7 383 +30 2950 + 11 3 103 +20 425 +32Ell EU 2974 +1 3106 + 19 524 -1 785 +10 isobutaneb 802 +9 A2 210 -3 1 02 +2 862 +23 E 240 0 133 0 862 -17 E 367 0 258 -38 905 +1 A1 433 + 12 396 -21 1029 -74 A1 797 -5 566 +21 1046 -93 E 918 -19 685 -5 1157 + 131 A2 965 -14 864 +28 1192 -15 E 966 -16 950 -12 1201 -37 E 1166 + 19 97 1 -10 1259 +5 A1 1177 +73 1010 -60 1267 +36 E 1333 +20 1037 +3 1340 -30 E 1371 -36 1050 -20 1348 +3 1394 -16 1134 +57 1350 -20A1 A2 1450 +2 1268 -2 1451 + 16 E 1475 +23 1384 -24 1444 +6 E 1477 +20 1408 +32 1451 + 17 A1 1488 +26 1422 -6 1454 + 19 A1 2880 +42 1444 -30 1461 + 18 E 2894 -10 1454 +3 2853 -36 A, 2904 -1 1458 +5 2855 -35 A2 2958 +4 1464 + 17 2863 -27 E 2962 +5 1668 -14 Ell 2885 -15 E 2962 +5 2894 -11 Ell 2932 +7 A1 2962 -2 2902 -4 EU 2932 +7 2934 -4 2938 -2 " Acnlc.= veXp.-vCalc..Ref. 47. Ref. 49. cyclohexane, OSRT is added to the calculated barrier because lower than the experimentally observed values. This is of the presence of a free pseudo-rotation in the transition because these experimental values are necessarily based on states. In most cases good agreement between calculated and measurements of mixtures of conformations, whilst the calcu- experimentally observed conformational energy differences lated values are derived from calculations on the most stable was found. conformation only. To reproduce the experimentallyobserved results the enthalpies and entropies of the various conformations present in the experimental mixture must be calculated. Using these enthalpies and entropies one canHeats of Formation The heat of formation is calculated using the following equa- =number oftion.experiments "8 H, = Ester+ C 1, + 4RT + EPOP-tETORS (4) 100 100 n= 1 v) 80 80 c, In this formula, Esteris the calculated steric energy. For all rI molecules, both rigid and non-rigid, a 4RT term (to account 60 E$ 6o 8for translation, rotation and pV work) and the group increments are added. The increments for the various groups 40 40 $' defined in the force field are shown in Table 23. for calculation of the heats of formation of the rigid mol- bons, however, conformations with a higher energy are present. This means that the calculated heats of formation, The addition of 4RT and the group increments is sufficient ecules.For non-rigid molecules, such as long-chain hydrocar- 20 0 200 600 1000 1400 1800 2200 2600 3000 wavenumber/cm-' 20 0 using group increments based on rigid molecules, will be Fig. 8 Results for IR frequency calculation J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 22 Results for conformational energy calculation; the barriers are AAH unless noted otherwise conformational energy/kJ mol conformation 1 conformation 2 exp. calc. anti-butane" c-c-c-c 60" 3.14 3.74 c-c-c-120" 14.35 13.58 c-c-c-c 0" 19.08 19.47 gauche-but-1-eneb syn-but- 1-ene 2.22 2.75 anti-but-1-ene 7.24 10.84 cyclohexene' cyclohexene (boat) 22.18 25.15 isobutene;d o~~-~~ = 0" OH<< =c = 180" 6.28 7.07 (E)-but-2-ene;' o~= 0" ~ ~ =o~ ~= 180"~~= 6.40 6.61~ cyclopentenef cyclopentene (flat) 2.51 1.22 cyclohexane (chair) cyclohexane (twist)# 23.01 23.01 cyclohexane (chair-twist)h 45.19-5 1.04 44.00 ethane' ethane (eclipsed) 12.05 10.86 2,2,3,3-tetramethylbutane' eclipsed (AAG) 42.68 42.06 propanek eclipsed 13.81 11.38 propene;' o~=~-~-~ = 0" aC=c-c-H = 180" 8.33 6.7 1 eq-meth ylcyclohexane' ax-meth ylcyclohexane 7.53 7.65 cy clodecanem TBC 4.23 2.65 TBCC 6.69 5.8 1 BCC 13.93 8.20 3-methyl-but-1-ene" (C-C-C-HO") C-C-C-H 60" 10.46 10.17 C-C-C-H 120" 1.76 2.30 C=C-C-H 180" 4.14 3.76 JRef.52-54. * Ref. 15. 'Ref. 55. Ref. 14. 'Ref. 56. Ref. 35. Ref. 57. Ref. 58. Ref. 59. Ref. 60. Ir Ref. 61. Ref. 62. Ref. 63. " Ref. 50. establish the contribution of each conformation in the Following this procedure about 1300 different conformers of mixture.From these contributions, a heat of formation com- decane were found, from which E,,ddecane) could be calcu- parable to the experimental result can be calculated. This dif- lated. This was done for all of the longer acyclic compounds ference between the calculated heat of formation of the most in the training set. (E,,, values for the different compounds stable conformer and that of the total mixture is expressed in are given in Table 25, later.) the term Ern,. For the cyclic alkanes, the different conformations cannot The various conformations of the open-chain hydrocar- be found by stepping the torsion angles. For these com-bons were found by stepping all their C-C-C-C torsion pounds, we tried to find E,, by reproducing their stable con- angles along starting values of 60°, 180" or 300" (for formations known from the literature.Table 24 shows the C-C-C-C, angles of 0", 60", 120", 180" 240" and 300" conformations found for the different cycloalkanes. were used as starting points), after which normal energy mini- Flexible molecules like acyclic hydrocarbons often show mization was performed. This procedure produced for a mol- low rotational barriers, indicating the presence of low rota- ecule like decane 2187 starting geometries. tional energy levels. Since the group increments are based on It was not always possible to optimize these starting rigid molecules, the population of these rotational energy geometries to energy minima and sometimes different starting levels is not accounted for.Only the C-CH, group points led to the same final geometry. If the latter happened, increment possibly contains a correction for the low barriers, a check was made to see whether these geometries, with since methyl groups attached to rigid molecules show com- exactly the same enthalpy and entropy, could be enantiomers. parable rotational barriers to methyl groups attached to If this was not the case, the duplicate results were removed. more flexible compounds. This means that calculated heats of formation of flexible hydrocarbons are, even after EPOPcor-rection, still lower than the experimental results. The flex- Table 23 Group increments in the force field ibility in a molecule is increased by the presence of -CH,-CH, groups because of their low rotational barrier.central atom group increment Quarternary and tertiary carbons usually lower the flexibility. in group atoms attached /kJ mol-' C -7.741 Table 24 Conformations for cycloalkanes C -10.216 C -17.949 cycloalkane conformations found C -30.195 C 10.216 cycloheptane" TC, TB C 0.545 cyclooctanea BC, TCC, TBC, TB C -10.963 cyclononane" TBC, TCC, TBC C -30.195 cyclodecane"*b BCB, TBCC, TBC, BCC, TCCC C= 48.212 C= 41.286 " Ref. 56, this reference also defines the conformation notation. Ref. C= 31.743 63. 2890 J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 It was therefore decided to optimize nine bond increments, E,,), 31 compounds with an average error of 0.855 kJ one bond increment for each type of C-C bond present in mol-', a total average error of 1.02 kJ mol-' is obtained for the molecule.the 100 compounds in the training set. Since the presence of high-energy conformations and that of low rotational barriers are closely related, we also tried to optimize these increments without adding EmP to the calcu- Charge Calculations lated heats of formation. Optimization resulted in relatively small bond increments for the three types of CH3-C bond. The starting parameters for the charge calculation were These results, combined with the assumption that the derived by Mortier et aL3 from Mulliken populations C-CH, group increment already deals with the contribution obtained using STO-3G calculations.Comparison with of low methyl rotors, led us to remove these three bond experimentally measured dipole moments showed that the increments. Mortier parameters produced dipole moments that were too Table 25 shows the results of the optimization of the bond low. Since the STO-3G calculations also produced low dipole increments with and without Emp. It can be seen that almost moments, we decided that the ab initio charges needed adjust- comparable results are obtained in each case which seems to ment. To optimize the parameters some dipole moment data support our belief that the time-consuming calculation of were added to the training set. Fig. 9 compares our calculated Em, can be avoided using this method. charges for propane, propene, isobutane and isobutene with Table 26 shows the heat of formation results for small or Mulliken charges, obtained using a 6-31G** basis set and the rigid molecules.The average error for the 69 compounds in GAUSSIAN 9267 program. Table 27 shows the results of the this table is 1.10 kJ mol-'. Adding the results for the longer, dipole-moment calculation. Charges were calculated using a correction without relative permittivity of 1.flexible alkanes (results from the ETORS Table 25 Bond increments and results of heat of formation calculations (a) Bond increments bond increment with E,,/kJ mol-' increment without E,,/kJ mol-' 2.354 3.25 1 0.349 0.537 -0.332 -0.072 -2.072 -1.564 Ctcrt-'quart -1.910 -1.780 Cquart-'quart -1.130 -1.260 (b) Heat of formation molecule 4H, 2,3-dimethylpentane 0.33 -1.73 -1.03 -195.2 -194.8 -198.9 3.7 4.1 2,3-dimethylhexane 1.OO 0.63 2.23 -216.2 -215.6 -213.8 -2.4 -1.8 3,3-dimethylpentane 0.84 -0.66 -0.14 -200.2 -200.6 -201.2 1.o 0.7 2,2-dimethylhexane 1.21 4.38 6.43 -226.0 -225.2 -224.6 -1.4 -0.6 3-ethyl-2-methylpentane 1.63 -1.38 -0.49 -211.2 -212.0 -211.0 -0.2 -1.0 3,3-dimethylhexane 1.oo 1.69 3.11 -222.0 -221.6 -220.0 -2.0 -1.6 3-ethylhexane 1.21 3.40 4.86 -210.4 -210.1 -210.7 0.3 0.6 2,2-dimethylpentane 0.46 2.02 3.18 -205.1 -204.4 -205.9 0.8 1.5 3-ethylpentane 0.84 1.05 1.61 -189.2 -189.5 -189.6 0.4 0.1 2,rldimethylhexane 0.7 1 1.04 1.61 -220.1 -220.3 -219.2 -0.9 -1.1 3-methylheptane 2.18 5.40 7.58 -213.1 -213.1 -212.5 -0.6 -0.6 2,5dimethylhexane 1.13 3.05 4.32 -221.7 -221.6 -222.5 0.8 0.9 3,rldimethylhexane 1.09 -1.38 -0.49 -213.9 -214.1 -212.8 -1.1 -1.3 pentane 2.47 4.71 6.50 -145.9 -146.6 -146.9 1.o 0.4 2,rldimethylpentane 0.00 0.69 1.07 -201.4 -201.0 -201.7 0.4 0.7 nonane 5.65 14.12 19.50 -228.6 -228.9 -228.2 -0.4 -0.7 octane 4.77 11.77 16.25 -208.0 -208.3 -208.6 0.7 0.4 2-methylhexane 1.80 5.05 7.04 -194.4 -194.2 -194.6 0.2 0.4 2-methylpentane 0.92 2.70 3.79 -173.7 -173.5 -174.8 1.2 1.3 hexane 3.01 7.06 9.75 -166.8 -167.1 -167.1 0.3 0.0 decane 6.07 16.48 22.75 -249.7 -249.5 -249.5 -0.2 0.0 2-methylheptane 2.68 7.41 10.29 -215.0 -214.8 -215.4 0.4 0.6 2,2,3- trimethypen tane 0.46 -1.56 -1.24 -221.0 -221.1 -220.0 -1.0 -1.1 heptane 3.85 9.41 13.00 -187.4 -187.7 -187.7 0.3 0.0 2,2,3,3-tert-methylbutane 0.00 -1.13 -1.26 -224.7 -224.8 -225.6 0.9 0.8 2,2,3,3-tert-methylpentane 0.00 -1.46 -1.33 -238.0 -237.9 -237.1 -0.9 -0.8 2,2,3-trimethylbutane 0.00 -1.91 -1.78 -203.5 -203.4 -204.5 1.o 1.1 3,3-diethylpentane 1.51 -1.33 -0.29 -231.4 -231.9 -232.3 0.9 0.4 butane 1.46 2.35 3.25 -125.5 -126.0 -125.6 0.1 -0.4 2,3-dimethylbutane 0.20 -2.07 -1.56 -177.4 -177.1 -178.3 0.9 -1.2 di-tert-but ylmethane 0.00 -0.66 -0.14 -242.0 -241.2 -241.6 -0.4 0.4 .~~Experimental heats of formation are derived from Pedley et ~ 1 ArHexp.: Experimental heat of formation (kJ mol-').EToRs,: Sum of bond increments using Em, terms. ETORs2: Sum of bond increments not using Em, terms. A, H,: Calculated heat of formation using Em, and Ej,sl terms. Af H, : Calculated heat of formation using Ejons, term.error(Af H,):Af Hex,,,-Af HI. error(AfH,):Af Hex, -Af H,. Average for error(AfHl) (31 compounds): 0.862 kJ mol-'. Average for error(A,H,): 0.855 kJ mol-'. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 289 1 Table 26 Heat of formation calculations compound exp. calc. Em, ETORS diff.“ small non-cyclic alkanesb ethane -83.8 -82.4 1.4 propane isobutane -104.7 -134.2 -105.5 -133.3 0.9 -0.8 neopen tane -168.1 -167.4 0.7 non-cyclic alkenesc ethene 52.5 51.4 -1.1 propene isobutene 20.0 -16.9 19.9 -17.0 -0.1 -0.1 3,3-dimethyl but- 1 -ene 3-methylbut-1 -ene (E)-but-Zene (2)-bu t-2-ene 2-methylbut-2-ene 2-methylbut-1 -ene 2,3-dimethylbut-2-ene -60.3 -27.6 -7.1 -11.4 -41.8 -35.3 -68.2 -58.5 -30.8 -6.9 -11.2 -42.0 -35.1 -66.8 2.8 -2.9 0.2 -0.2 -0.2 0.5 1.4 2,3-dimethylbut- 1-ene but- 1 -ene -62.6 0.1 -61.5 -1.6 1.4 -1.9 (E)-pent-2-ene 2,3,3-trimethylbut-l-ene2-ethyl-3-methylbut- 1 -ene -31.9 -85.5 -79.5 -32.7 -85.5 -78.3 -1.5 1.o 0.3 (2)-pen t-2-ene 2-methylpen t-2-ene (Z)-di-tert-but ylethene (E)-di-tert-butylethene -27.6 -66.9 -126.7 -165.5 -29.1 -64.6 -128.0 -168.5 -1.7 2.1 -0.3 -1.0 (Z)-4,4-dimethylpen t-2-ene (E)-4,4-dimethylpent-2-ene -72.6 -88.8 -75.7 -89.7 -1.2 0.1 polycyclic alkanes” trans-decalin -182.1 -182.8 -0.7 cisdecalin -169.2 -171.4 -2.2 trans- h ydrindane cis-h ydrindane norbornane -131.5 -127.1 -52.0 -132.8 -128.2 -51.7 -1.3 -1.1 0.3 1,4-dimethylnorbornane bicyclo[ 2.2.2loctane trans-bicyclo[3.3.0] octane cis-bicyclo[3.3.0]octane bicyclo[3.3.l]nonane adamantanee -128.1 -99.0 -66.6 -92.9 -127.5 -132.9 -126.6 -97.2 -64.6 -91.6 -127.2 -131.9 1.5 1.8 2.0 1.3 0.3 1.o diamantanee -145.9 -148.1 -2.2 tetramethyladamantane protoadamantanee perh ydroquinacene trans-syn-trans-perhydroanthracene -283.4 -85.9 -92.1 -243.2 -283.8 -82.6 -87.7 -241.1 -0.4 3.3 4.3 2.1 polycyclic alkenesf norbornene 90.0 88.9 -1.1 bicyclo[2.2.2]octene 7-methylenebicycloC2.2.llheptane 2-methylenebicyclo[2.2.2]octane 24.9 60.2 -9.2 26.0 47.5 -11.8 1.1 -12.7 -2.6 monocyclic alkanesB cyclopentane (env.)e cyclohexane cycloheptane cyclooctane cyclononane cyclodecane eq-meth ylcyclohexane 1,l-dimethylcyclohexanelax,2eqdimethylcyclohexane leq,2eq-dimethylcyclohexane 1,l -dimethylcyclopen tane et hy lcyclopen tane methylcyclopentane -78.4 -123.4 -118.1 -124.4 -132.8 -154.3 -154.7 -180.9 -172.1 -179.9 -138.2 -126.9 -106.2 -78.8 -124.6 -116.1 -120.9 -134.1 -157.5 -154.4 -181.5 -172.2 -179.6 -139.0 -131.9 -109.6 0.8 -1.2 2.9 5.0 0.9 0.3 -0.6 -0.1 0.3 0.4 -0.3 2.2 -0.4 monocyclic alkenes” cyclopentene’ cyclohexene cycloheptene 35.8 -5.0 -9.2 38.2 -6.1 -8.7 2.4 -1.1 0.5 2892 ~~ J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 compound Table 26 Continued exp. calc. ETORS diff." trans-cyclooctene 19.6 17.9 ---1.7 --3.1cis-cyclooctene -25.9 -22.8 3-meth ylcyclopentene 7.4 8.5 --1.1 --1-methylcyclopentene -3.8 -3.1 --0.7 l-ethylcyclohexene -63.4 -62.9 --0.5 1-methylcyclohexene -43.3 -43.7 -0.4 methylenecyclohexane' -34.4 -34.6 ---0.2 methylenecyclopentane' 11.6 10.5 -1.24 0.1 ethylidenecyclopentane -18.1 -19.2 -1.54 0.4 1-ethylcyclopentene -19.7 -23.1 0.84 1.79 -0.7 .~~ 'Average error (fourExperimental heats of formation are derived from Pedley et ~1 unless noted otherwise. "diff.= AfHex,,.-At HCPIC.. compounds) = 0.95 kJ mol-'. Average error (21 compounds): 1.05 kJ mol-'. For the non-cyclic alkenes, three bond increments are used to calculate their E,,,, terms. These bond increments have values of 1.00, -1.00 and -1.00 kJ mol-'for, respectively, bonds between quaternary, tertiary and secondary carbons and an sp2 carbon atom. Average error (excluding perhydroquinacene and trans-syn-trans-perhydroanthracene because of their large experimental errors): 1.39 kJ mol-(14 compounds).'Ref. 65. Average error (excluding 7-methylenebicyclo[2.2.1]-heptane and 2-methylenebicyclo[2.2.2]octane because of their large experimental errors): 1.10 kJ mol-(two compounds). Average error (15 compounds): 1.03 kJ mol-'. Average error (13 compounds): 0.99 kJ mol-'. Ref. 66. 4s11 -methylcyclohexene uu 'U methvlenecvclohexane 3-methylcyclohexene 4-methylcyclohexene (equatorial/axial) (equatorial/axial) Scheme 1 Composition of the mixture of methylcyclohexenes71 The calculated dipole moment for isobutane using a calculated the enthalpies and entropies of the different con-6-31G* basis set, the GAUSSIAN 8619 program and Mulli-formers in this mixture. Entropies were calculated using the ken populations was 0.0986 D.? statistical mechanical approach and the harmonic approx-imation. Using these enthalpies and entropies we were able to Calculations on Mixtures calculate the contributions of the conformers to the equi-librium mixture, which could be compared with the experi-Scheme 1 shows the conformers present in a mixture of mental observations.The composition of this mixture was methylcyclohexenes and methylenecyclohexane. To test the not present in the training set, making this a test for the reli-enthalpy and entropy calculations of the final force field we ability of the optimization procedure. The results of the enth-alpy and entropy calculations and the calculated composition at 473 K are given in Table 28.Table 29 compares our results 0.1 50 +& with those of other force fields in the reproduction of the 0.040 -A composition of the experimental mixt~re.~Similar calcu-lations have been performed to reproduce the contributionsfA 0, of the different conformers in a mixture of perhydroantha---0.070 r0 D A.? -Table 27 Experimental and calculated dipole moments.t= -0.180.s A 2 molecule Pap.P Pca1c.P -0.290 -D propane" 0.084 0.05 -0.400 tA isobutane* 0.13 0.07 I 1 I isopentane" 0.12 0.07 norbomane' 0.09 0.05 propene" 0.366 0.20 isobutene" 0.500 0.23 cyclohexene" 0.33 0.30 cyclopentene" 0.22 0.28 cis-cyclooctened 0.43 0.37 trans-cyclooctened 0.82 0.48 ~~~~~~~~ ~~ t 1 D (Debye) x 1.60218 x lo-'' C m." Ref. 68. 'Ref. 13. Ref. 69. Ref. 70. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 28 Results for the methylcyclohexene mixture calculation isomer AfH,,,/kJ mol-' S,,,/J mol-' K-' chiral mixture composition (Yo) 1-MCH -15.02 419.36 75.4 eq-3MCH -6.49 418.11 12.6 UX-~MCH -5.56 417.06 eq4MCH -7.57 417.27 10.6 ax4MCH -2.22 415.14 MECH -6.36 410.74 1.5 Table 29 Comparison between different force fields DMM Bovill" Allingerb MM3' expd ~ ~ ~ ~ ~ ~ _ _ _ _ 75.4 76.7 76.4 86.7 71.2 12.6 12.0 7.9 5.3 11.4 10.6 10.8 11.8 6.8 15.9 1.5 0.5 3.9 1.2 1.6 0.9968 0.9964 0.9958 0.9853 - cenes. Scheme 2 and Table 30 show the conformers present in the mixture and their experimentally observed contributions to the equilibrium composition at 471.5 K.74The calculated energies and entropies of the conformers in the mixture at 473 K, as well as the calculated and experimental mixture composition, are given in Table 30.Results for Some Elongated C-C Bonds Table 31 shows the results of this force field in reproducing experimental data on some extremely elongated C-C bonds. These data were not present in the training set. For compari- son, the results of the MM3 force field46 are also given. These results show that it is difficult to reproduce the experimen- tally observed geometry78 of isododecahedrane with this force field. The DMM force field does not seem to be applic- able for this quite extreme compound. Comparison of Our Results with Those of MM3 To check whether our approach using the chargesharge interactions could lead to an acceptable hydrocarbon force field we compared our results with those of the widely accepted force field MM3.46 The results of this comparison are shown in Table 32. One should, of course, mention that the DMM force field is specifically optimized on this training set, giving it an advantage in reproducing these experimental observations.Discussion The aim of this work was to produce a force field using charge-charge interactions, calculated from geometry-dependent charges. The calculation of these charges had to yield a realistic charge distibution. The force field should also be able to produce thermodynamic data and acceptable geometries reliably.With the implementation of these charges in the force field an additional problem to conventional force-field opti- mization is introduced. For valency angles, bond lengths, heats of formation etc., reasonably reliable experimentally observed values are obtainable for optimization of the force field, but information on charges on atoms in a molecule is more difficult to obtain. The relative electronegativity of an atom in a molecule with respect to its surrounding atoms isomer 1-MCH 3MCH 4MCH MECH cos cos y is the cosine of the simularity angle, which is defined as: cos y = [a2 + b2 -c2]/2ab. a, b are the experimental and calculated mixture composition vectors, respectively, and c is the difference between these two vectors.a Ref. 72. Ref. 73. 'Ref. 46. Ref. 71. ---d tst Ct cac in tat csc (chair/boat) Scheme 2 Composition of the perhydroanthracene mixture7' Table 30 Results for the perhydroanthracene mixture calculation mixture composition (YO) isomer AfH,,,/kJ mol-' S,,,/J mol-' K-' chiral calc. exp.' tst -185.98 590.99' no 86.7 85.7 ct -175.02 592.45 Yes 12.7 13.4 tat -159.66 595.59 Yes 0.4 0.5 cac -163.18 588.27 no 0.2 0.3 csc chair -153.09 590.45 no 0.02' 0.1' csc boat -142.09 593.75 Yes cos y = 0.99996. " Values of CT are given in parentheses. Ref. 74. 'Chair and boat configurations. Table 31 Results for some elongated C-C bonds for the DMM and MM3 force fields bond length f A compound bond exp.DMM MM3" tri-tert-butylmethaneb 2,2,3,3-tetramethy1-butanec 1,2-diadamantyl-l,2-di-tert 1-2 2-3 1-2 1.611 1.580 1.640 1.6010 1.5658 1.6244 1.6229 1.5770 1.6454 butylethanedisododecahedrane' 1-2 1.691 1.5898 1.6200 ~~ ~ " Ref. 46. Ref. 75. Ref. 76. Ref. 77. 'Ref. 78. Table 32 Comparison of the results of DMM with the results of MM3. The average absolute difference between the experimental and calculated data is given ~~ ~ type of experiment error MM3" error DMM ~~~ ~ valency angle 0.5360" 0.4740" bond length 0.0042 A 0.0032 8, IR frequency 26.5 cm-' 20.3 cm-' heat of formation 1.553 kJ mol-' 1.02 kJ mol -' 'Ref. 46. dictates whether its charge should be negative or positive, but gives only an indication of the magnitude.Information about the entire molecule can be obtained using observed dipole moments, but this also does not produce exact information about the charge on each atom. Ab initio calculations can provide this information, but the charges produced by the various techniques are often quite different. As the results in Fig. 9 show, the force-field charges are systematically lower than ab initio charges, calculated using a 6-31G** basis set and Mulliken population analysis. However, there is clearly a good relationship between the DMM results and the ab initio derived charges. The geometry dependence of the charges is clear. The dipole moment results also indicate that the DMM charges are rather low.Most calculated dipole moments are slightly lower than experimentally observed ones. This might partly be due to our use of a relative permittivity of unity. Increasing the relative permittivity would allow us to use higher charges, leading to higher dipole moments. However, it is not clear what value to use for the relative permittivity, and so the value of unity was retained, and the discrepancy between the experimental and calculated dipole moments accepted. Introducing larger charges in the force field also led to difficulties in the reproduction of the heats of formation. A comparison between the ab initio calculated valency angles and the experimental observed data (Tables 12-16) shows that the results of our calculations are roughtly equal to the more reliable experimental observations, indicating that they are a reliable basis for the optimization of the hydrocarbon force field.The final equilibrium angle para- meters in Table 4 therefore look reasonable, and the valency angle constraint has proved to be quite usable. The discrep- ancies between the calculated bond lengths, valency angles and torsion angles and the experimental observations on these bonds and angles lie well within our acceptance criteria. The force field seems to be able to reproduce the experimen- tally observed geometries accurately. The largest deviation between calculated and experimental wavenumbers in the IR results (Fig. 8, Table 21) occurs in the interval 1OOO-1400 cm- '.As already mentioned, these results might be improved by adding extra cross-interactions. Since, however, the low-wavenumber experiments (with large influ- ence upon entropy) are reproduced acceptably and the error J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 in the 1000-1400 cm- ' interval does not seem to be extraor- dinarily large, we decided not to add additional cross-interactions. This force field seems to reproduce the experimental rota- tional barriers and conformational energies reasonably well (Table 22). The calculated barriers between the different con- formations of cyclohexane are slightly lower than the experi- mentally observed ones. Attempts to improve the fit by giving the barriers extra weight in the optimization adversely affected the calculated heats of formation, especially those of the five-membered rings.The final results are, therefore, a compromise between good reproduction of these barriers and of the heats of formation. The relatively low calculated barriers for the cyclohexane conformations do not seem to affect the perhydroanthracene mixture calculation seriously, as shown in Scheme 2 and Table 30. The almost equally good results obtained for the longer acyclic alkanes for both bond increment schemes (Table 25) support the hypothesis that the presence of higher-energy conformations is usually related to low rotational barriers. Hence, both phenomena may be described by a single term. Application of the bond increment scheme not using E,,, terms might save considerable amounts of time in calcu- lations of high-energy conformations of longer acyclic hydro- carbons.The bond scheme method is easily expandable to other groups of compounds, the only major drawback being the somewhat large numbers of parameters that need to be optimized for the proper use of this method. The final value for the most significant bond increments (the Csec-Csecincrement), is 2.354 kJ mol-' for the scheme using E,,, terms and 3.251 kJ mol-' for the scheme without EPOPterms, a difference which follows directly from the removal of the Em, terms. Both increments are larger than the bond increment obtained from MM328 (1.76 kJ mol-'). This is probably due to the absence of negative bond increments in MM3 for the bonds between tertiary and quat- ernary carbons.If we constrain these bond increments to a value of zero, the Csec-Csec bond increment using E,, terms approaches the MM3 value. Since the IR results show this force field to be able to reproduce the experimentally obtained spectra accurately, good entropy calculations can be expected. This is confirmed by the results from the mixture calculations. Conclusions The results show that this force field meets our demands; geometries are reproduced well (average error in 59 bond lengths, 0.0032 A; average error in 11 1 valency angles, 0.474") and, more importantly, satisfactory results are obtained in the calculation of IR frequencies (average error for 429 IR experiments of ca.20 cm-') and heats of formation (average error for 100 compounds of 1.02 kJ mol-'). This seems to compare favourably with the results of widely accepted hydrocarbon force fields like MM3,46 proving our geometry- dependent charge calculation using the Mortier method3 to be applicable in molecular mechanics. A force field able to deal with and to produce realistic geometry-dependent charges yields a more reliable description of molecules. This indicates its potential as a starting point for the creation of the carbocation force field. 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Squillacote, R. S. Sheridan, 0. L. Chapman and F. A. L. Anet, J. Am. Chem. SOC.,1975,97,3244. B. D. Ross and N. S. True, J. Am. Chem. SOC.,1983,105,4871. E. Hirota, Y. Endo, S. Saito and J. L. Duncan, J. Mol. Spec-trosc., 1981,89,285. J. E. Anderson and H. Pearson, J. Am. Chem. SOC.,1975,97,764. E. Hirota, C. Matsumura and Y. Morino, Bull. Chem. SOC.Jpn., 1967,40,1124. H. Booth and J. R. Everett, J. Chem. SOC.Perkin Trans. 2, 1980, 255. R. L. Hilderbrandt, J. D. Wieser and L. K. Montgomery, J. Am. Chem. SOC., 1973,95,8598. J. B. Pedley, R. D. Naylor and S. P. Kirby, Thermochemical Data of Organic Compounds, Chapman and Hall, London, 1986. J. D. Cox and G. Pilcher, Thermochemistry of Organic and Organometallic Compounds, Academic Press, London, 1970. S. W. Benson, F. R. Cruickshank, D. M. Golden, G. R. Haugen, H. E. O’Neal, A. S. Rodgers, R. Shaw and R. Walsh, Chem. Reu., 1969,69,279. M. J. Frisch, G. W. Trucks, M. Head-Gordon, P. M. W. Gill, M. W. Wong, J. 8. Foresman, B. G. Johnson, H. B. Schlegel, M. A. Robb, E. S. Replogle, R. Gomperts, J. L. Andres, K. Raghava-chari, J. S. Binkley, C. Gonzalez, R. L. Martin, D. J. Fox, D. J. Defrees, J. Baker, J. J. P. Stewart and J. A. Pople, GAUSSIAN 92, Revision A, Gaussian Inc., Pittsburgh, PA, 1992. Handbook of Chemistry and Physics, CRC Press, West Palm Beach, 58th edn., 1977, pp. E63-65. A. Choplin, Chem. Phys. Lett., 1980,71, 503. N. L. Allinger, J. Am. Chem. SOC.,1958, SO, 1953. M. Peereboom, B. van der Graaf and J. M. A. Baas, Recl. Trau. Chim. Pays-Bas, 1982,101,336. D. N. J. White and M. J. Bovill, J. Chem. SOC.,Perkin Trans. 2, 1977,1610. N. L. Allinger, J. A. Hirsch, M. A. Miller, I. J. Tyminski and F. A. van Catledge, J. Am. Chem. SOC.,1968,90, 1199. N. L. Allinger and M. T. Wuesthoff, J. Org. Chem., 1971, 36, 205 1. H. B. Burg and L. S. Bartell, J. Am. Chem. SOC.,1972,94 5236. L. S. Bartell and T. L. Boates, J. Mol. Struct., 1976, 32, 379. M. A. Flamm-Ter Meer, H. D. Beckhaus, K. Peters, H. G. von Schnering, H. Fritz and C. Rueckhardt, Chem. Ber., 1986, 119, 1492. H. Imgartinger, U. Reifenstahl, H. Prinzbach, R. Pinkos and K. Weber, Tetrahedron Lett., 1990,31, 5459. 5319. 40 41 J. Ponder, personal communication. G. J. H.van Nes and A. Vos, Acta Crystallogr., Sect. B, 1978,34, 1947. Paper 4/01722F; Received 22nd March, 1994
ISSN:0956-5000
DOI:10.1039/FT9949002881
出版商:RSC
年代:1994
数据来源: RSC
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Luminescence from irradiated butadiene solutions: fluorescence of allyl radicals? |
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Journal of the Chemical Society, Faraday Transactions,
Volume 90,
Issue 19,
1994,
Page 2897-2900
Brian Brocklehurst,
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摘要:
J. CHEM. SOC. FARADAY TRANS., 1994, 90(19), 2897-2900 Luminescence from Irradiated Butadiene Solutions :Fluorescence of Ally1 Radicals? Brian Brocklehurst* and D. Nicholas Tawn Chemistry Department, University of Sheffield, Sheffield, UK S3 7HF Solutions of butadiene and its derivatives show strong luminescence near 500 nm on warming after y-irradiation at 77 K. Possible sources of the emission are radiative charge-transfer processes in the ion pairs, the excited dienes themselves and the radicals formed from them by addition of a hydrogen atom, although these species are not known to luminesce. The last assignment appears most probable, i.e. excitation following neutralisation of the corresponding carbanion. The mechanism of formation of these anions is not known: it is teniatively suggested that spur processes are involved. Some years ago, a systematic study was made of the thermo- luminescence, TL, of solutions in alkane glasses’ following y-radiolysis at 77 K.It was shown that trapped radical ions were released on warming; emissions from aromatic solutes could be easily identified by comparison with photoexcita- tion. Visible emissions from solutions of butadiene derivatives were observed’ which were tentatively ascribed to twisted excited states. Alternative emitters are free radicals : phenyl-alkanes and phenylalkenes in similar experiments give rise to fluorescence of radicals formed by loss or gain of a hydrogen at~m.~-~In this paper, results obtained with a number of butadiene derivatives are described in detail and the assign- ment discussed in the light of recent work.Experimental Methylcyclohexane (Hopkin and Williams) and isopentane (J. Preston Ltd.) were passed down activated silica gel columns to remove unsaturated compounds; this was repeated until there was no further change in the UV absorption around 200 nm. Most of the work was carried out using solutions in ‘MP’ a 2 : 1 mixture of these alkanes. This forms a glass at 77 K which is hard enough to trap ions and electrons for many hours, but which does not shatter. Most of the solutes studied are listed in Table 1 and will be referred to by the numbers given there. Except in the case of butadiene (Instrument grade, Matheson Co. Inc.) which was handled on the vaccum line, samples were made up in air, transferred to the sample cells and then deaerated by a number of freeze- pumpthaw cycles.The methylbutadienes (Fluka Ltd., purum or puriss grade, ~99% purity) were supplied in ampoules, containing some 0.1% of inhibitor to prevent poly- merisation; to remove this, samples were degassed and dis- tilled on the vaccum line and used as quickly as possible. Hepta-1,3,5-triene (K and K Laboratories) was purified by gas chromatography which removed some 10% of a more volatile impurity. Because of the high volatility of some of the solutes, samples were made up with a precooled syringe, which may have introduced small amounts of water. The sample cells were made of 16 mm id ‘Spectrosil’ tubing.They were irradiated with a 6oCo y-ray source; the dose rate, measured by Fricke dosimetry, was 7.5 krad min -’. Doses were kept low to obviate second-order effects. For the data in Table 1, samples of each diene, 2 and 10 mmol dm-3, were used and irradiated for 10 and 5 min, respectively, giving a dose of 750 or 375 Gy (4.6 or 2.3 x 1021 eV kg-I). The smaller dose gave adequate intensities at 10 mmol dm-3 but not at 2 mmol dm-3 (I,,, and 1360 values in Table 1 have been divided by two to correct for the difference in dose.) As described previ~usly~,~.~ TL spectra were scanned while allowing the sample to warm up in a pre-cooled empty Dewar vessel in the sample compartment of a calibrated Aminco-Bowman spectrofluorimeter. Of necessity, the inten- sity changes with time; the spectra shown were recorded close to the maximum of the glow-curve.The following pro- cedure was adopted to obtain relative intensities: glow-curves were recorded in a separate run using a fixed wavelength, maximum intensities are listed in Table 1; the integrated curve was multiplied by the area under the corrected spec- trum. Absolute G values were obtained by comparison with the luminescence of naphthalene, studied its phos- phorescence lies in the same region. The uncertainties in the absolute values are considerable, the relative values should be more accurate. Table 1 Peak wavelengths, maximum intensities and G values for the diene emissions, for solutions of concentrations 2 and 10 mmol dm-3 solute none 1 2 3 4 5 6 7 8 9 10 11 buta-1,3-diene 2-methylbutadiene (E)-penta-1,3-diene (Z)-penta-1,3-diene Cmethylpenta- 1,3-diene (E,E)-hexa-2,4-diene (Z,E)-hexa-2,4-diene 2,3-dimethylhexa-1,3-diene2,4-dimethylpenta-l,3-diene 2,5-dimethylhexa-2,4-diene hepta-1,3,5-triene ~~ ~~~~ 450 0.15 ~ 0.0028 480 0.045 0.040 0.35 0.87 0.0027 0.0063 505 0.035 0.036 0.57 1.44 0.0072 0.016 510 0.032 0.022 0.70 1.50 0.0087 0.018 497 0.022 0.020 0.52 0.96 0.0054 0.0099 510 0.034 0.042 1.70 3.60 0.01 3 0.031 480 0.032 0.024 1.21 2.49 0.011 0.024 500 0.026 0.026 1.90 3.80 0.0 15 0.032 510 0.040 0.050 0.22 0.83 0.0028 0.01 1 520 0.036 0.046 1.03 4.20 0.0089 0.032 495 0.015 0.030 0.055 0.075 <0.0008 <0.0013 550 0.19 0.37 0.0027 0.0047 Results Spectra obtained from the solvent and some solutions are shown in Fig.1; the main emission maxima and the yields are listed in Table 1. The solvent itself gives an emission band in TL at 450 nm at low doses. The maximum intensity is about ten times weaker than that of the dienes; however, the band is much broader and the emission both starts earlier and dies out later than those of the dienes so that the inte- grated intensity is not much less. In addition, a band at 235 nm is observed; it appears weaker, but, given the low effi- ciency of the grating in this region (where we have been unable to calibrate it), the emission is probably considerably stronger than the visible band.At higher doses, new bands appear, notably at longer wavelengths, 510 nm,2 and the luminescence behaviour becomes very complicated. Sawai' has made a detailed study of the dose dependence of the emissions from 3-methylpentane. Our results for MP closely resemble his. Irradiated solutions of dienes luminesced strongly on warming, the intensity rising fairly slowly to a maximum around 85-90 K and then falling rapidly. The solvent emis- sion was observed first, its intensity decreasing with solute concentration; it was replaced by a much stronger emission in the region 480-520 nm. Both the widths of the spectra (FWHM ca. 85 nm) and of the glow peaks were narrower than those of the solvent.New weak bands were also seen at 360-365 and ca. 420 nm; the latter was hard to study because of overlap of the main band. Maximum intensities were reached in the order: 420, 360, 500; the early decay of the 420 nm emission left the other two bands more clearly resolved at longer times. Maximum intensities (Z360) of the other band are shown in Table 1. A few experiments were carried out with diene 9 at concentrations of 5 and 100 mmol dmF3; they confirmed the differences in the concentration dependence of the 500 and 360 nm bands, the former giving comparable intensities, the latter showing a reduction by a factor of five between 2 and 100 mmol dmP3. The 500 nm band could not be detected in the isothermal luminescence (ITL) at 77 K; there only the solvent band was seen though it could have masked the diene bands to some extent.Fig 1 shows some corrected spectra; most of the dienes give a single peak in the green, the wavelengths varying slightly. 3 (see Table 1) shows weak shoulders at 450 and 525 nm, while 8 differs in several respects: the glow lasts longer and the spectrum has a shoulder at 530 nm; like 9, it also shows a steeper concentration dependence (Table 1). Only in the case of hepta-1,3,5-triene is a well defined structure t* I I I J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 visible. The luminescence of 2,4-dimethylhexadiene, 10, was much weaker than that of the other dienes; it could not be easily separated from that of the solvent and only upper limits could be put on its intensity.No emission could be detected when the solutions were excited by UV light, either before or after irradiation, even when large doses were used. Since radical ion recombination produces triplets directly,' we attempted to sensitize triplet emission by energy transfer from benzophenone. Millimolar solutions in MP at 77 K excited in the range 250-350 nm gave strong benzophenone phosphorescence. Addition of penta-1,3-diene or 2-methylbuta-1-3-diene quenched the emission but no new bands were detected; this suggests that energy transfer does take place but that the resulting diene triplets do not emit. Addition of sulfur hexafluoride to naph- thalene solutions quenches the fluorescence in TL but not the phosphorescence.' It was found to quench the emission of the dienes.A number of experiments were made with related com-pounds : these included cyclohexene, cyclohexa-1,3- and 1,4- diene, hex- 1-yne, and the allene derivative, 2,4-dimethylpenta- 2,3-diene. These had the effect of modifying the solvent lumi- nescence, in some cases producing new bands. None of these solutions gave strong emissions at low doses. The allene showed emission mainly at 450 nm, like the pure solvent, with a shift to 480 nm and appearance of a shoulder at 365 nm late in the glow-curve. With a larger dose, 4500 Gy, peaks emerged more clearly at 365 and 490 nm with a shoulder at 540 nm. Hex-1-yne behaved similarly. Discussion Dienes: The 500 nm Emission A range of dienes was studied in the hope of obtaining clues to the nature of the emitters.In fact, the effect of substitution on the spectra is very small. Since the spectra themselves give little information, one has to argue by analogy with the parallel work on aromatic solutes;'-4 excited states of the parent compounds and radicals derived from them by loss or gain of a hydrogen atom must be considered. To our knowledge, there are no reports of triplet-singlet emission from the alkenes and our experiments with benzo- phenone and sulfur hexafluoride appear to rule them out. It is now well established"*" that the first excited singlet states of the higher polyalkenes are 2 'A, states derived largely from a doubly excited configuration. Transitions from the ground, 1 'A,, state are very weak; strong absorption is observed to the 1 'B, lying a little higher in energy.In the case of butadiene, the 1 'B, state is at 46 260 cm- above the ground state, the 2 'A, at 45 0o0 cm-in the gas phase. Fluorescence yields of mono-alkenes are very small (< this would be undetectable in our experiments. Molecules with long conjugated chains (more than four double bonds) fluoresce quite strongly. Fluorescence of tetra- enes has been detected both in the crystalline stateI3 and the vapour. Recently the excited singlet states of deca-2,4,6,8- tetraene have been studied in detail at low temperatures in supersonic jets ;I4 weak fluorescence has been detected from hexatriene in the same way" but no wavelengths are report- ed.Butadiene is said not to luminesce'0*" when excited in the UV, but a recent resonance-Raman study16 led to a value of ca. 6 x loP6for the fluorescence yield from the 1 'B, state of isoprene, 2, in Table 1. In the tetraene~,'~ short-lived fluo- rescence from the 1 'B, state is observed; the lifetime of the lower, 1 'A, state falls slowly as the exciting wavelength is lowered from the 0-0 band at 347.6 nm, but in the excitation spectrum of hexatriene' a non-radiative deactivation J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 process, very probably involving intramolecular twisting, is observed with a sharp onset 220 cm-' above the origin. These results suggest that butadiene behaves similarly but with no barrier to deactivation.This is supported by the cal- culations of Olivucci et who have found that S, and So are connected by a funnel. The huge Stokes shift (ca. 25000 cm-') between absorp- tion and emission led us to propose that the emitters are twisted excited singlet^,^ more readily observable in our experiments because of the low temperatures and the high viscosity which might stabilise shallow minima on the potential-energy surface. Formation of a distorted molecule by ion recombination, e.g. reaction (1) A+ + A-+A* +A (1) (where A represents the diene) would be favoured if the radical cation had a different structure than the parent mol- ecule. The ethene cation is twisted through some 22";18 however, in glassy solids, the absorption spectrum of buta- diene cation^'^ agrees with that expected from photoelectron spectroscopy and a planar symmetrical structure for the cation is consistent with its EPR2' and IR spectra and with theoretical calculations.2' Theoretical calculations22 support the idea, long used by experimentalist^,^^ of a distortion of the 1 'B, state to give a highly polar allyl-methylene species, C,H,+-CH, -, the methylene group being non-planar, but this local minimum still lies above the 2 'A, state: internal conversion and deactivation would be expected to be very rapid.Another major contribution to the thermoluminescence of aromatics comes from excimer emission following neutral- isation of dimeric cations; these species have been identified in irradiated solutions of some dienes' 9724 but comparison of the concentration dependence of the glow-curves with that for naphthalene7*25 rules out this process. It is noteworthy that the two dienes, 8 and 9 (Table l),show a steeper concen- tration dependence; central methyl substitution may prevent the formation of dimers which otherwise lead to quenching.It, therefore, seems likely that excited dienes deactivate far too rapidly to give significant yields of luminescence. The assignment also fails to explain why the luminescence is not seen in ITL (electron tunnelling or early in the glow-curves, electrons become mobile before anions '). This requirement is met by reaction (2): A+ + AH--+A + AH'* (2) the electron affinity of the radical is high so that the electron tunnelling to the cation26 will be negligible in the solid (see further, below).Aromatic radicals are observed in emi~sion:~-~ they may be derived from the parent molecule by loss or gain of a hydrogen atom; e.g. ethylbenzene and styrene give the same luminescence spectrum around 450 nm,, so too do indane and indene.6 The excitation mechanisms remain ~ncertain.~ There is no evidence for the presence of the corresponding positive ion at 77 K: radical emission does not appear when electrons are liberated by IR stimulation at 77 K2' or in ITL or very early in the glow-curves except at high doses;3 reac- tion (2) is therefore a possibility but formation of AH- has yet to be confirmed.The behaviour of the diene 500 nm emis- sion closely parallels that of the aromatic radicals ;butadienes and pentadienes give nearly identical spectra, so H addition to give allyl radicals is more probable than H loss. Addition of an alkyl radical rather than an H atom cannot be excluded. The first two excited configurations of excited alternant radicals are degenerate : configuration interaction leads to a strong absorption at short wavelengths and a weak one at 2899 long wavelengths, to which fluorescence should correspond. The low-energy transition of allyl has been detected in the gas phase at 409 nm using flash photolysis;26 the bands were broad, suggesting pre-dissociation, probably of the central hydrogen atom. Fluorescence has not been reported, but possibly substitution and the presence of the solvent reduce the rate of dissociation.No clear trends emerge from the data in Table 1. The Stokes shift is large but not unreasonable. The similarities in the behaviour of the dienes and hep- tatriene suggest that the latter produces excited pentadienyl radicals though the red shift is small. Neither the emission nor the long-wavelength absorption spectra of such radicals appear to have been reported. Other Emissions:Pure Alkanes Assignment of the other bands associated with the dienes is even more difficult: that at 420 nm belongs to the early part of the glow-curve suggesting reaction of a cation with an elec- tron trapped in the solvent. The band at 360-365 nm differs from that at 500 nm in its dependence on time in the glow- curve and on molecular structure and concentration [which suggests that it results from reactions such as reaction (3) but it is not possible to assign the emitter].SH,' + A-+SH, + A*? (3) The 235 nm emission band of the pure solvent is readily identified as alkane fluorescence, probably from methylcyclo- he~ane,~and resulting from reaction (4). SH,+ + e--+SH; (4) The 450 nm emission has been the subject of a number of st~dies.~,~'-~~The same spectrum is observed at 77 K (ITL) and over the whole temperature range, unlike the dienes, which suggests that the emitter corresponds to the cation in this case. It has been variously identified as a triplet alkane or an excited alkyl radical but none of these assignments has been substantiated. One possibility is that no molecular excited state is involved but the process is one of radiative recombination of an ion pair.30,32,33 Re cent theoretical and experimental work on radiative electron tran~fer~~'~' sup-ports the earlier argument,, that the radiative process is competitive if radiationless processes have very small Franck-Condon factors.Also, Trifunac and co-~orkers~~ have found evidence that proton transfer is a major process in the radiolysis of alkanes. Reaction (5) would release a maximum of some 4 eV; SH, probably has no low-lying excited states so the assignment appears reasonable. SH3+ + e--,SH, + H + hv (5) Sawai' made a detailed study of the radioluminescence of 3-methylpentane.He found two emissions, I, at ca. 425 nm, and 11, at 530 nm. I1 predominated at high doses because its yield was linear with dose while I reached a saturation level. I could be converted into I1 by exposure to IR light, I1 into I with UV. These and other results suggest strongly that I involves trapped electrons, I1 molecular anions. The behav- iour of TI closely resembles that of the 500 nm emission reported here for the dienes. With pure MP we find a similar emission at 510 nm at high doses. It is difficult to see how allyl anions could be formed in this system except, perhaps, in a spur consisting of two or more primary ionisations etc. Cer-tainly alkenes appear to be involved: Sawai reported that the addition of 2-methyl- 1-pentene enhances the emission of I1 ; our results, for MP solutions of propene at high con-centrations' and of hex-1-yne and the allene derivative 2900 suggest that the 365 and 500 nm emissions can be produced after extensive reactions of the ions.Sawai’s results do not rule out reaction (6); butadiene anion might have been detected by its absorption at 590 nm;37 however, this is a weak band. Possibly a different anion, such as SH-is involved. SH,+ + A-+SH, + H+ A + hv (6) Concluding Remarks The G values for luminescence, which give a lower bound for the formation of the emitters, show that the process must be a major one. Emission from impurities can be ruled out since random diffusion is negligible in these highly viscous liquids.Excited ally1 radicals appear to be the most probable source of the 500 nm emission. If so, the excitation mechanism remains unclear. It would be of great interest if a spur process were confirmed. Experimental work at lower energies would throw light on the problem, expecially if an excitation spec- trum of the emission could be measured. Multiphoton ionis- ation with a laser is one possibility, provided that wavelengths could be chosen to ionise the solvent rather than the solute. The authors thank the SERC for a research grant to one of them (D.N.T.),Mr. J. S. Robinson who carried out prelimi- nary studies and Prof. M. A. Robb for a helpful discussion about diene excited states. References 1 B.Brocklehurst, Znt. J. Radiat. Phys. Chem., 1974,6,483. 2 B. Brocklehurst and J. S. Robinson, Chem. Phys. Lett., 1971, 10, 277. 3 C. Deniau, A. Deroulede, F. Kieffer and J. Rigaut, J. 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Jonah, Radiat. Phys. Chem., 1989, 33, 505; M. C. Sauer Jr., D. W. Werst, C. D. Jonah and A. D. Trifunac, Radiat. Phys. Chem., 1991,37,461. 37 T. Shida, Electronic Absorption Spectra of Radical Zons, Elsevier, Amsterdam, 1988. Paper 4/00779D;Received 8th February, 1994
ISSN:0956-5000
DOI:10.1039/FT9949002897
出版商:RSC
年代:1994
数据来源: RSC
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