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Fullerene graphs with more negative than positiveeigenvalues: The exceptions that prove the rule of electrondeficiency? |
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Journal of the Chemical Society, Faraday Transactions,
Volume 93,
Issue 1,
1997,
Page 1-3
P. W. Fowler,
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摘要:
pound and d the thickness of the in situ cell]. If an organic solvent of low absorption is used (such as acetone, ethanol or diethyl ether), the necessary concentration increases with increasing X-ray photon energy because the cross-section for X-rays decreases for heavier atoms. XAFS yields quantitative information on short-range order. This requires that the part of the molecule that undergoes a transformation must contain the absorbing element. To facilitate the XAFS analysis, it is advantageous if the monitored element is present only in a few di†erent local environments in the course of the reaction.The fact that the sample is continuously irradiated with X-rays during the experiment does not seem to have a strong inÑuence on the kinetics of the Finkelstein reaction. Were such an e†ect present, one would expect a much faster reaction due to an easier breaking of the BrwC bond. Being aware of these limitations, we believe that in situ XAFS on liquid-state reactions is a valuable tool to obtain structural as well as kinetic information for selected parts of a molecule.Examples could be the study of, e.g., coordination compounds or metalloproteins. Experimental Equal volumes of 1.333 M solutions of 2-bromopropane and NaI in acetone were mixed at room temperature. A tightly closed DSC aluminium crucible was completely �lled with the reaction mixture (ca. 30 ll). The crucible was placed into a Mettler FP 80/84 DSC heat-Ñux calorimeter that was mounted vertically in the synchrotron X-ray beam and heated to 55.0(5) ¡C within 30 s.The experiment was carried out at the Hamburger Synchrotronstrahlungslabor HASYLAB at Deutsches Elektronen-Synchrotron DESY, Germany, at beamline X1 (ROEMO II). This beamline is equipped with a Si(311) double crystal monochromator, yielding approximately 108 photons s~1 mm~2 at the sample. The energy resolution is approximately 2 eV at the bromine K-edge. The DORIS III storage ring was run with positrons of 4.5 GeV at 80È120 mA.Every 8 min 12 s an X-ray absorption spectrum was taken in transmission at the Br K-edge (photon energy ca. 13 475 eV). Reference spectra of crystalline NaBr were simultaneously measured (at room temperature) by use of a third ionization chamber. The sample Br absorption edge jump was limited by the solubility of NaI and the *kd\(It/I0)\0.38, �xed pathlength in the calorimeter. The measured spectra were evaluated with the programs AUTOBK, FEFF and FEFFIT of the University of Washington package.27h29 Multi-electron phenomena lead to a peak at low R in the Br XAFS spectra.30h34 This was corrected by a simpli�ed approach as described in ref. 35. BrieÑy, this peak was isolated in R-space from a NaBr spectrum and back-transformed into k-space. It was then subtracted from all spectra in k-space before evaluation. When quantitatively analysing XAFS spectra of reacting systems, it is important to keep the number of �t-parameters as small as possible to minimize correlation e†ects.13,35,36 By evaluating spectra of pure 2-bromopropane and NaBr at 55 ¡C we determined the following parameters that were kept constant in subsequent �ts of the reaction mixture: p2(BrwCa)\0.0011 ”2, p2(BrwCb)\0.0137 ”2, p2(BrwNa)\0.02593 ”2, R(BrwCb)\2.858 ”, S02(BrwCa)\S02(BrwCb)\1.082, S02(BrwNa)\1.10, eV, E0(BrwCa)\E0(BrwCb)\[0.89 E0(BrwNa)\[1.65 eV.These values are in good agreement with data for similar compounds.13,33,35 was set to Conse- N(BrwCb) 2N(BrwCa).quently, the only �t variables were the mean coordination numbers and N(BrwNa), and the mean distances N(BrwCa) R(BrwNa) and The evaluated XAFS data range R(BrwCa). was k\2.0È7.1 and R\0.8È3.1 throughout all experi- ”~1 ” ments. 2-Bromopropane (99]%), acetone (99.9%; HPLC grade) and NaI (p.a.) were purchased from Aldrich. Hydrate water of NaI was removed before experiments by heating in vacuum. are grateful to HASYLAB for beamtime.We thank A. We Reller and M. Martin for generous support. Financial support was granted by the Deutsche Forschungsgemeinschaft and by the Fonds der Chemischen Industrie. References 1 X-Ray absorption. Principles, applications, techniques of EXAFS, SEXAFS and XANES, ed. D. C. Koningsberger and R. Prins, Wiley, New York, 1988. 2 D. Bazin, H. Dexpert, N. S. Guyot-Sionnest, J. P. Bournonville and J. Lynch, J. Chim. Phys. Phys. Chim. Biol., 1989, 86, 1707. 3 B. S. Clausen, L. G. Ste†ensen, P. L. Hansen and H. Gra- b~k, Catal. L ett., 1993, 20, 23. Tops‘e, 4 G. Sankar, P. A. Wright, S. Natarajan, J. M. Thomas, G. N. Greaves, A. J. Dent, B. R. Dobson, C. A. Ramsdale and R. H. Jones, J. Phys. Chem., 1993, 97, 9550. 5 H. Bertagnolli and T. S. Ertel, Angew. Chem., 1994, 106, 15. 6 T. Maschmeyer, F. Rey, G. Sankar and J. M. Thomas, Nature (L ondon), 1995, 378, 159. 7 A. Hoser, N. Hilbrandt, M. Martin and M. Denecke, Physica B, 1995, 208/209, 321. 8 P. Andrews, J. M. Corker, J. Evans and M. Webster, J. Chem. Soc., Dalton T rans., 1994, 1337. 9 M. Tabata and K. Ozutsumi, Bull. Chem. Soc. Jpn., 1994, 67, 1608. 10 T. S. Ertel, W. Ho. rner, S. Hu. ckmann, U. Kolb, I. Abraham and H. Bertagnolli, Physica B, 1995, 208/209, 641. 11 N. Yoshida and T. Nagamura, Rev. Sci. Instrum., 1995, 66, 52. 12 A. J. Dent, L. J. Farrugia, A. G. Orpen and S. E. Stratford, J. Chem. Soc., Chem. Commun., 1992, 1456. 13 M. Epple, U. Sazama, A. Reller, N.Hilbrandt, M. Martin and L. Tro. ger, Chem. Commun., 1996, 1755. 14 L. Tro. ger, N. Hilbrandt and M. Epple, J. Phys. Coll., 1997, in press. 15 H. Finkelstein, Chem. Ber., 1910, 43, 1528. 16 S. D. Hamann, Aust. J. Chem., 1975, 28, 693. 17 C. D. Chalk, J. McKenna and I. H. Williams, J. Am. Chem. Soc., 1981, 103, 272. 18 L. Eberston, Acta Chem. Scand., Sect. B, 1982, B36, 533. 19 P. B. D. de la Mare, J. Chem. Soc., 1955, 3169. 20 E. D. Hughes, C. K. Ingold and J. D. H. Mackie, J.Chem. Soc., 1955, 3173. 21 E. D. Hughes, C. K. Ingold and J. D. H. Mackie, J. Chem. Soc., 1955, 3177. 22 P. B. D. de la Mare, J. Chem. Soc., 1955, 3180. 23 L. Fowden, E. D. Hughes and C. K. Ingold, J. Chem. Soc., 1955, 3187. 24 L. Fowden, E. D. Hughes and C. K. Ingold, J. Chem. Soc., 1955, 3193. 25 P. B. D. de la Mare, J. Chem. Soc., 1955, 3196. 26 P. B. D. de la Mare, L. Fowden, E. D. Hughes, C. K. Ingold and J. D. H. Mackie, J. Chem. Soc., 1955, 3200. 27 J. J. Rehr, R.C. Albers and S. I. Zabinsky, Phys. Rev. L ett., 1992, 69, 3397. 28 L. Tro. ger, T. Yokoyama, D. Arvanitis, T. Lederer, M. Tischer and K. Baberschke, Phys. Rev. B, 1994, 49, 888. 29 E. A. Stern, M. Newville, B. Ravel, Y. Yacoby and D. Haskel, Physica B, 1995, 208/209, 117. 30 E. A. Stern, S. M. Heald and B. Bunker, Phys. Rev. L ett., 1979, 42, 1372. 31 G. Li, F. Bridges and G. S. Brown, Phys. Rev. L ett., 1992, 68, 1609. 32 P. DÏAngelo, A. Di Cicco, A. Filipponi and N. V.Pavel, Phys. Rev. A, 1993, 47, 2055. 33 E. Burattini, P. DÏAngelo, A. Di Cicco, A. Filipponi and N. V. Pavel, J. Phys. Chem., 1993, 97, 5486. 34 J. J. Rehr, C. H. Booth, F. Bridges and S. I. Zabinsky, Phys. Rev. B, 1994, 49, 12347. 35 M. Epple, H. Kirschnick, G. N. Greaves, G. Sankar and J. M. Thomas, J. Chem. Soc., Faraday T rans., 1996, 5035. 36 M. Epple and L. Tro. ger, J. Chem. Soc., Dalton T rans., 1996, 11. Paper 7/01433C; Received 28th February, 1997 J. Chem. Soc., Faraday T rans., 1997, V ol. 93 3037pound and d the thickness of the in situ cell]. If an organic solvent of low absorption is used (such as acetone, ethanol or diethyl ether), the necessary concentration increases with increasing X-ray photon energy because the cross-section for X-rays decreases for heavier atoms. XAFS yields quantitative information on short-range order. This requires that the part of the molecule that undergoes a transformation must contain the absorbing element. To facilitate the XAFS analysis, it is advantageous if the monitored element is present only in a few di†erent local environments in the course of the reaction.The fact that the sample is continuously irradiated with X-rays during the experiment does not seemtrong inÑuence on the kinetics of the Finkelstein reaction. Were such an e†ect present, one would expect a much faster reaction due to an easier breaking of the BrwC bond. Being aware of these limitations, we believe that in situ XAFS on liquid-state reactions is a valuable tool to obtain structural as well as kinetic information for selected parts of a molecule.Examples could be the study of, e.g., coordination compounds or metalloproteins. Experimental Equal volumes of 1.333 M solutions of 2-bromopropane and NaI in acetone were mixed at room temperature. A tightly closed DSC aluminium crucible was completely �lled with the reaction mixture (ca. 30 ll). The crucible was placed into a Mettler FP 80/84 DSC heat-Ñux calorimeter that was mounted vertically in the synchrotron X-ray beam and heated to 55.0(5) ¡C within 30 s.The experiment was carried out at the Hamburger Synchrotronstrahlungslabor HASYLAB at Deutsches Elektronen-Synchrotron DESY, Germany, at beamline X1 (ROEMO II). This beamline is equipped with a Si(311) double crystal monochromator, yielding approximately 108 photons s~1 mm~2 at the sample. The energy resolution is approximately 2 eV at the bromine K-edge.The DORIS III storage ring was run with positrons of 4.5 GeV at 80È120 mA. Every 8 min 12 s an X-ray absorption spectrum was taken in transmission at the Br K-edge (photon energy ca. 13 475 eV). Reference spectra of crystalline NaBr were simultaneously measured (at room temperature) by use of a third ionization chamber. The sample Br absorption edge jump was limited by the solubility of NaI and the *kd\(It/I0)\0.38, �xed pathlength in the calorimeter. The measured spectra were evaluated with the programs AUTOBK, FEFF and FEFFIT of the University of Washington package.27h29 Multi-electron phenomena lead to a peak at low R in the Br XAFS spectra.30h34 This was corrected by a simpli�ed approach as described in ref. 35. BrieÑy, this peak was isolated in R-space from a NaBr spectrum and back-transformed into k-space. It was then subtracted from all spectra in k-space before evaluation. When quantitatively analysing XAFS spectra of reacting systems, it is important to keep the number of �t-parameters as small as possible to minimize correlation e†ects.13,35,36 By evaluating spectra of pure 2-bromopropane and NaBr at 55 ¡C we determined the following parameters that were kept constant in subsequent �ts of the reaction mixture: p2(BrwCa)\0.0011 ”2, p2(BrwCb)\0.0137 ”2, p2(BrwNa)\0.02593 ”2, R(BrwCb)\2.858 ”, S02(BrwCa)\S02(BrwCb)\1.082, S02(BrwNa)\1.10, eV, E0(BrwCa)\E0(BrwCb)\[0.89 E0(BrwNa)\[1.65 eV. These values are in good agreement with data for similar compounds.13,33,35 was set to Conse- N(BrwCb) 2N(BrwCa).quently, the only �t variables were the mean coordination numbers and N(BrwNa), and the mean distances N(BrwCa) R(BrwNa) and The evaluated XAFS data range R(BrwCa). was k\2.0È7.1 and R\0.8È3.1 throughout all experi- ”~1 ” ments. 2-Bromopropane (99]%), acetone (99.9%; HPLC grade) and NaI (p.a.) were purchased from Aldrich. Hydrate water of NaI was removed before experiments by heating in vacuum.are grateful to HASYLAB for beamtime. We thank A. We Reller and M. Martin for generous support. Financial support was granted by the Deutsche Forschungsgemeinschaft and by the Fonds der Chemischen Industrie. References 1 X-Ray absorption. Principles, applications, techniques of EXAFS, SEXAFS and XANES, ed. D. C. Koningsberger and R. Prins, Wiley, New York, 1988. 2 D. Bazin, H. Dexpert, N. S. Guyot-Sionnest, J. P. Bournonville and J. Lynch, J. Chim. Phys.Phys. Chim. Biol., 1989, 86, 1707. 3 B. S. Clausen, L. G. Ste†ensen, P. L. Hansen and H. Gra- b~k, Catal. L ett., 1993, 20, 23. Tops‘e, 4 G. Sankar, P. A. Wright, S. Natarajan, J. M. Thomas, G. N. Greaves, A. J. Dent, B. R. Dobson, C. A. Ramsdale and R. H. Jones, J. Phys. Chem., 1993, 97, 9550. 5 H. Bertagnolli and T. S. Ertel, Angew. Chem., 1994, 106, 15. 6 T. Maschmeyer, F. Rey, G. Sankar and J. M. Thomas, Nature (L ondon), 1995, 378, 159. 7 A. Hoser, N. Hilbrandt, M. Martin and M.Denecke, Physica B, 1995, 208/209, 321. 8 P. Andrews, J. M. Corker, J. Evans and M. Webster, J. Chem. Soc., Dalton T rans., 1994, 1337. 9 M. Tabata and K. Ozutsumi, Bull. Chem. Soc. Jpn., 1994, 67, 1608. 10 T. S. Ertel, W. Ho. rner, S. Hu. ckmann, U. Kolb, I. Abraham and H. Bertagnolli, Physica B, 1995, 208/209, 641. 11 N. Yoshida and T. Nagamura, Rev. Sci. Instrum., 1995, 66, 52. 12 A. J. Dent, L. J. Farrugia, A. G. Orpen and S. E. Stratford, J. Chem. Soc., Chem. Commun., 1992, 1456. 13 M.Epple, U. Sazama, A. Reller, N. Hilbrandt, M. Martin and L. Tro. ger, Chem. Commun., 1996, 1755. 14 L. Tro. ger, N. Hilbrandt and M. Epple, J. Phys. Coll., 1997, in press. 15 H. Finkelstein, Chem. Ber., 1910, 43, 1528. 16 S. D. Hamann, Aust. J. Chem., 1975, 28, 693. 17 C. D. Chalk, J. McKenna and I. H. Williams, J. Am. Chem. Soc., 1981, 103, 272. 18 L. Eberston, Acta Chem. Scand., Sect. B, 1982, B36, 533. 19 P. B. D. de la Mare, J. Chem. Soc., 1955, 3169. 20 E. D. Hughes, C. K. Ingold and J. D. H. Mackie, J. Chem. Soc., 1955, 3173. 21 E. D. Hughes, C. K. Ingold and J. D. H. Mackie, J. Chem. Soc., 1955, 3177. 22 P. B. D. de la Mare, J. Chem. Soc., 1955, 3180. 23 L. Fowden, E. D. Hughes and C. K. Ingold, J. Chem. Soc., 1955, 3187. 24 L. Fowden, E. D. Hughes and C. K. Ingold, J. Chem. Soc., 1955, 3193. 25 P. B. D. de la Mare, J. Chem. Soc., 1955, 3196. 26 P. B. D. de la Mare, L. Fowden, E. D. Hughes, C. K. Ingold and J. D. H. Mackie, J.Chem. Soc., 1955, 3200. 27 J. J. Rehr, R. C. Albers and S. I. Zabinsky, Phys. Rev. L ett., 1992, 69, 3397. 28 L. Tro. ger, T. Yokoyama, D. Arvanitis, T. Lederer, M. Tischer and K. Baberschke, Phys. Rev. B, 1994, 49, 888. 29 E. A. Stern, M. Newville, B. Ravel, Y. Yacoby and D. Haskel, Physica B, 1995, 208/209, 117. 30 E. A. Stern, S. M. Heald and B. Bunker, Phys. Rev. L ett., 1979, 42, 1372. 31 G. Li, F. Bridges and G. S. Brown, Phys. Rev. L ett., 1992, 68, 1609. 32 P. DÏAngelo, A.Di Cicco, A. Filipponi and N. V. Pavel, Phys. Rev. A, 1993, 47, 2055. 33 E. Burattini, P. DÏAngelo, A. Di Cicco, A. Filipponi and N. V. Pavel, J. Phys. Chem., 1993, 97, 5486. 34 J. J. Rehr, C. H. Booth, F. Bridges and S. I. Zabinsky, Phys. Rev. B, 1994, 49, 12347. 35 M. Epple, H. Kirschnick, G. N. Greaves, G. Sankar and J. M. Thomas, J. Chem. Soc., Faraday T rans., 1996, 5035. 36 M. Epple and L. Tro. ger, J. Chem. Soc., Dalton T rans., 1996, 11. Paper 7/01433C; Received 28th February, 1997 J.Chem. Soc., Faraday T rans., 1997, V ol. 93 3037pound and d the thickness of the in situ cell]. If an organic solvent of low absorption is used (such as acetone, ethanol or diethyl ether), the necessary concentration increases with increasing X-ray photon energy because the cross-section for X-rays decreases for heavier atoms. XAFS yields quantitative information on short-range order. This requires that the part of the molecule that undergoes a transformation must contain the absorbing element.To facilitate the XAFS analysis, it is advantageous if the monitored element is present only in a few di†erent local environments in the course of the reaction. The fact that the sample is continuously irradiated with X-rays during the experiment does not seem to have a strong inÑuence on the kinetics of the Finkelstein reaction. Were such an e†ect present, one would expect a much faster reaction due to an easier breaking of the BrwC bond. Being aware of these limitations, we believe that in situ XAFS on liquid-state reactions is a valuable tool to obtain structural as well as kinetic information for selected parts of a molecule.Examples could be the study of, e.g., coordination compounds or metalloproteins. Experimental Equal volumes of 1.333 M solutions of 2-bromopropane and NaI in acetone were mixed at room temperature. A tightly closed DSC aluminium crucible was completely �lled with the reaction mixture (ca. 30 ll). The crucible was placed into a Mettler Fat-Ñux calorimeter that was mounted vertically in the synchrotron X-ray beam and heated to 55.0(5) ¡C within 30 s. The experiment was carried out at the Hamburger Synchrotronstrahlungslabor HASYLAB at Deutsches Elektronen-Synchrotron DESY, Germany, at beamline X1 (ROEMO II). This beamline is equipped with a Si(311) double crystal monochromator, yielding approximately 108 photons s~1 mm~2 at the sample.The energy resolution is approximately 2 eV at the bromine K-edge. The DORIS III storage ring was run with positrons of 4.5 GeV at 80È120 mA. Every 8 min 12 s an X-ray absorption spectrum was taken in transmission at the Br K-edge (photon energy ca. 13 475 eV). Reference spectra of crystalline NaBr were simultaneously measured (at room temperature) by use of a third ionization chamber. The sample Br absorption edge jump was limited by the solubility of NaI and the *kd\(It/I0)\0.38, �xed pathlength in the calorimeter.The measured spectra were evaluated with the programs AUTOBK, FEFF and FEFFIT of the University of Washington package.27h29 Multi-electron phenomena lead to a peak at low R in the Br XAFS spectra.30h34 This was corrected by a simpli�ed approach as described in ref. 35. BrieÑy, this peak was isolated in R-space from a NaBr spectrum and back-transformed into k-space. It was then subtracted from all spectra in k-space before evaluation.When quantitatively analysing XAFS spectra of reacting systems, it is important to keep the number of �t-parameters as small as possible to minimize correlation e†ects.13,35,36 By evaluating spectra of pure 2-bromopropane and NaBr at 55 ¡C we determined the following parameters that were kept constant in subsequent �ts of the reaction mixture: p2(BrwCa)\0.0011 ”2, p2(BrwCb)\0.0137 ”2, p2(BrwNa)\0.02593 ”2, R(BrwCb)\2.858 ”, S02(BrwCa)\S02(BrwCb)\1.082, S02(BrwNa)\1.10, eV, E0(BrwCa)\E0(BrwCb)\[0.89 E0(BrwNa)\[1.65 eV.These values are in good agreement with data for similar compounds.13,33,35 was set to Conse- N(BrwCb) 2N(BrwCa). quently, the only �t variables were the mean coordination numbers and N(BrwNa), and the mean distances N(BrwCa) R(BrwNa) and The evaluated XAFS data range R(BrwCa). was k\2.0È7.1 and R\0.8È3.1 throughout all experi- ”~1 ” ments. 2-Bromopropane (99]%), acetone (99.9%; HPLC grade) and NaI (p.a.) were purchased from Aldrich.Hydrate water of NaI was removed before experiments by heating in vacuum. are grateful to HASYLAB for beamtime. We thank A. We Reller and M. Martin for generous support. Financial support was granted by the Deutsche Forschungsgemeinschaft and by the Fonds der Chemischen Industrie. References 1 X-Ray absorption. Principles, applications, techniques of EXAFS, SEXAFS and XANES, ed. D. C. Koningsberger and R. Prins, Wiley, New York, 1988. 2 D. Bazin, H. Dexpert, N. S. Guyot-Sionnest, J.P. Bournonville and J. Lynch, J. Chim. Phys. Phys. Chim. Biol., 1989, 86, 1707. 3 B. S. Clausen, L. G. Ste†ensen, P. L. Hansen and H. Gra- b~k, Catal. L ett., 1993, 20, 23. Tops‘e, 4 G. Sankar, P. A. Wright, S. Natarajan, J. M. Thomas, G. N. Greaves, A. J. Dent, B. R. Dobson, C. A. Ramsdale and R. H. Jones, J. Phys. Chem., 1993, 97, 9550. 5 H. Bertagnolli and T. S. Ertel, Angew. Chem., 1994, 106, 15. 6 T. Maschmeyer, F. Rey, G. Sankar and J. M. Thomas, Nature (L ondon), 1995, 378, 159. 7 A. Hoser, N. Hilbrandt, M. Martin and M. Denecke, Physica B, 1995, 208/209, 321. 8 P. Andrews, J. M. Corker, J. Evans and M. Webster, J. Chem. Soc., Dalton T rans., 1994, 1337. 9 M. Tabata and K. Ozutsumi, Bull. Chem. Soc. Jpn., 1994, 67, 1608. 10 T. S. Ertel, W. Ho. rner, S. Hu. ckmann, U. Kolb, I. Abraham and H. Bertagnolli, Physica B, 1995, 208/209, 641. 11 N. Yoshida and T. Nagamura, Rev. Sci. Instrum., 1995, 66, 52. 12 A. J. Dent, L. J. Farrugia, A. G. Orpen and S.E. Stratford, J. Chem. Soc., Chem. Commun., 1992, 1456. 13 M. Epple, U. Sazama, A. Reller, N. Hilbrandt, M. Martin and L. Tro. ger, Chem. Commun., 1996, 1755. 14 L. Tro. ger, N. Hilbrandt and M. Epple, J. Phys. Coll., 1997, in press. 15 H. Finkelstein, Chem. Ber., 1910, 43, 1528. 16 S. D. Hamann, Aust. J. Chem., 1975, 28, 693. 17 C. D. Chalk, J. McKenna and I. H. Williams, J. Am. Chem. Soc., 1981, 103, 272. 18 L. Eberston, Acta Chem. Scand., Sect. B, 1982, B36, 533. 19 P.B. D. de la Mare, J. Chem. Soc., 1955, 3169. 20 E. D. Hughes, C. K. Ingold and J. D. H. Mackie, J. Chem. Soc., 1955, 3173. 21 E. D. Hughes, C. K. Ingold and J. D. H. Mackie, J. Chem. Soc., 1955, 3177. 22 P. B. D. de la Mare, J. Chem. Soc., 1955, 3180. 23 L. Fowden, E. D. Hughes and C. K. Ingold, J. Chem. Soc., 1955, 3187. 24 L. Fowden, E. D. Hughes and C. K. Ingold, J. Chem. Soc., 1955, 3193. 25 P. B. D. de la Mare, J. Chem. Soc., 1955, 3196. 26 P. B. D. de la Mare, L. Fowden, E. D. Hughes, C. K. Ingold and J. D. H. Mackie, J. Chem. Soc., 1955, 3200. 27 J. J. Rehr, R. C. Albers and S. I. Zabinsky, Phys. Rev. L ett., 1992, 69, 3397. 28 L. Tro. ger, T. Yokoyama, D. Arvanitis, T. Lederer, M. Tischer and K. Baberschke, Phys. Rev. B, 1994, 49, 888. 29 E. A. Stern, M. Newville, B. Ravel, Y. Yacoby and D. Haskel, Physica B, 1995, 208/209, 117. 30 E. A. Stern, S. M. Heald and B. Bunker, Phys. Rev. L ett., 1979, 42, 1372. 31 G. Li, F. Bridges and G. S. Brown, Phys. Rev. L ett., 1992, 68, 1609. 32 P. DÏAngelo, A. Di Cicco, A. Filipponi and N. V. Pavel, Phys. Rev. A, 1993, 47, 2055. 33 E. Burattini, P. DÏAngelo, A. Di Cicco, A. Filipponi and N. V. Pavel, J. Phys. Chem., 1993, 97, 5486. 34 J. J. Rehr, C. H. Booth, F. Bridges and S. I. Zabinsky, Phys. Rev. B, 1994, 49, 12347. 35 M. Epple, H. Kirschnick, G. N. Greaves, G. Sankar and J. M. Thomas, J. Chem. Soc., Faraday T rans., 1996, 5035. 36 M. Epple and L. Tro. ger, J. Chem. Soc., Dalton T rans., 1996, 11. Paper 7/01433C; Received 28th February, 1997 J. Chem. Soc., Faraday T rans., 1997, V o
ISSN:0956-5000
DOI:10.1039/a605413g
出版商:RSC
年代:1997
数据来源: RSC
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Hidden symmetry in molecular graphs |
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Journal of the Chemical Society, Faraday Transactions,
Volume 93,
Issue 1,
1997,
Page 5-9
Jun Liu,
Preview
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摘要:
Hidden symmetry in molecular graphs Jun Liu Department of Chemistry, Nanjing University, Nanjing, 210093, P.R. China The concept of the Hamiltonian group of a graph is introduced to specify the full symmetry properties of the adjacency matrix (Hamiltonian operator). Three group theoretical rules and a new method are presented which allow the hidden symmetry of a graph to be systematically and rigorously investigated. Based on one subgroup of the Hamiltonian group, the hidden symmetry problem in an alternant molecular graph sharing doubly degenerate eigenvalues x\0 is solved in general. 1. Introduction A molecular graph G is said to have hidden symmetry if the d-fold degeneracy of the spectrum of graph G cannot be explained by the symmetry of the point group of the mol- Hp ecule. The hidden symmetry problem has puzzled chemists for a long time. Using the automorphism group (the graph Ha group), the group of all permutations of the vertex set which leave the graph invariant, Wild et al.1 detected the hidden symmetry of a diphenyl molecule and explained successfully the double degeneracy of eigenvalues x\^1 in the spectrum.Although the symmetry of automorphism groups has been studied by some authors2h7 in considerable depth, these groups were not always rich enough to give an insight into the hidden symmetry in molecular graphs.8 For example, the graphs 1È5 given in Fig. 1 share doubly degenerate eigenvalues x\0. Since the point groups and the automorphism groups of graphs 1È5 have only one-dimensional irreducible representations, these groups fail to explain the degeneracies of the graph spectra.Based on rule 1 (proof to be published elsewhere), if the degeneracy of a graph does not result from the symmetry of the point group or the automorphism group, then it must arise from the symmetry hidden in a group possessing higher symmetry. The Hamiltonian group of a graph suffices for describing the symmetry of its adjacency matrix, so therefore should be able to explain the degeneracy of a graph spectrum. Rule 1: In general the degeneracy of the spectrum of a graph can be interpreted in terms of the symmetry of the adjacency matrix of the graph.Fig. 1 Some molecular graphs having doubly degenerate eigenvalues x\0. The numbering of the vertices of graph 1 is given. The de�nition, introduced in the next section, of the Hamiltoniam group is the usual one. Because the elements of the Hamiltonian group may take complicated forms, few publications discussing the behaviour of this group are found.Nevertheless, we want to understand the degeneracy of the graph spectrum from some particular subgroup. In the present work, using two rules given in Sections 3 and 4, we discuss the hidden symmetry in graph 1 in detail. We conclude that, for all alternant graphs with doubly degenerate eigenvalues x\0, the Hamiltonian groups possess a common subgroup, which is isomorphic to the point group The two eigenvectors, C3v .associated with eigenvalues x\0, of each graph span a twodimensional irreducible representation of the Hamiltoniam group of the graph. 2. Hamiltonian group of an adjacency matrix The adjacency matrix (Hamiltonian operator) A of a graph G with n vertices is the square n]n symmetric-matrix which contains information about the internal connectivity of vertices in the graph.9 It is de�ned as Aij\1; if the vertices i and j are connected by an edge, Aij\0; otherwise (1) From the de�nition of an abstract group, one can see readily the fact that all unitary matrices commuting with the adjacency matrix A of a molecular graph, form a group H(T1, T2 , .. . ,Ti , . . .). T i~1ATi\A (2) where the group H is called the Hamiltonian group of a graph; the element in H is de�ned as a generalized symmetry operator. In a real vector (basis vector and eigenvector) space, these matrices are orthogonal matrices. It is well known that the symmetry operators in the point group of a molecule always commute with its Hamiltonian operator10 so H of the molecular graph must contain the point group of the graph.Hp A permutation of the vertices of a graph can be described by a permutation matrix P de�ned as Pij\1; if the vertices i is permuted to j by the permutation Pij\0; otherwise (3) A given permutation is in if the permutation matrix P Ha satis�es P~1AP\A (4) Comparing eqn. (4) with eqn.(2), the automorphism groupHa of a molecule is also a subgroup of its Hamiltoniam groupH. Since there is no routine method to construct the Hamiltonian group H of a graph, when degeneracy of the graph cannot J. Chem. Soc., Faraday T rans., 1997, 93(1), 5È9 51 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 a0 0 0 1 0 0b 0 0 0 0 1 0 0 0 0 0 0 1 T1 2 5 0 3])15 10 3[)15 10 0 [ 3 5 0 1 0 0 0 0 3[)15 10 0 1 10 6])15 10 0 3[)15 10 3])15 10 0 6[)15 10 1 10 0 3])15 10 0 0 0 0 1 0 [ 3 5 0 3])15 10 3[)15 10 0 2 5 q n t t t t t t t t t t t t t t t t t t t t s p T2 2 5 0 3[)15 10 3])15 10 0 [ 3 5 0 1 0 0 0 0 3])15 10 0 1 10 6[)15 10 0 3])15 10 3[)15 10 0 6])15 10 1 10 0 3[)15 10 0 0 0 0 1 0 [ 3 5 0 3[)15 10 3])15 10 0 2 5 q n t t t t t t t t t t t t t t t t t t s p T3 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 a0 0 1 0 0 0b 0 0 0 0 1 0 0 0 0 0 0 1 T4 2 5 0 3[)15 10 3])15 10 0 [ 3 5 0 1 0 0 0 0 3[)15 10 0 6])15 10 1 10 0 3[)15 10 3])15 10 0 1 10 6[)15 10 0 3])15 10 0 0 0 0 1 0 [ 3 5 0 3[)15 10 3])15 10 0 2 5 q n t t t t t t t t t t t t t t t t t t s p T5 2 5 0 3])15 10 3[)15 10 0 [ 3 5 0 1 0 0 0 0 3])15 10 0 6[)15 10 1 10 0 3])15 10 3[)15 10 0 1 10 6])15 10 0 3[)15 10 0 0 0 0 1 0 [ 3 5 0 3])15 10 3[)15 10 0 2 5 q n t t t t t t t t t t t t t t t t t t s p T6 Scheme 1 be explained by a point group or an automorphism group (two subgroups of H), we will hope to obtain a new subgroup (denoted by H*) from which the hidden symmetry can be understood. We note that if d-fold degenerate eigenvectors span a d-dimensional irreducible representation for H*, then they constitute automatically a d-dimensional irreducible representation for H.For graph 1, H* can consist of six elements, as shown in Scheme 1. T1ÈT6 , It is readily con�rmed that each symmetry operator in H* can commute with the adjacency matrix A of graph 1. 0 1 0 0 0 0 1 0 1 1 0 0 0 1 0 1 0 0 A\a0 1 0 1 0 0b 0 0 1 1 0 1 0 0 0 0 1 0 Before introducing the method for constructing the group H*, we begin the discussion of symmetry properties of isospectral graphs. 3. Hamiltonian group of isospectral graphs Non-isomorphic graphs with identical spectra are called isospectral graphs.9,11 Rule 2 relates the symmetry of a graph to that of its isospectral graph in terms of the Hamiltonian group. Rule 2: Isospectral graphs share the same Hamiltonian group. The proof of rule 2 is given in the following. Graphs G and G@ are isospectral graphs. The graph G and the adjacency matrix A of a conjugated hydrocarbon are established on a set of basis vectors consisting of of n carbon M/iN 2pz-orbitals atoms.The vectors in are orthonormal, that is, M/iN \/i o/j[ \dij ; i, j\1, 2, . . . , n (5) The eigenvectors of G can be written in matrix form W\CU (6) where W\1t1 t2 < tn 2; U\1/1 /2 < /n 2 and C is the coefficient matrix. Another possible system of basis vectors is determined by eqn. (7). M/i@N U@\SU (7) where S is an n-dimensional orthogonal matrix, which ensures that the basis vectors in are also orthonormal.Under M/i@N basis vectors the matrix component of the Hamilto- M/i@N, Aij { nian operator A@ is given by a graph, which \/i@ oHo/j@[ ; is denoted by G@, associated with A@ has a di†erent form from graph G. The eigenvectors of G@ can be written as W\C@U@ (8) From eqn. (6), (7) and (8), we obtain S\C@TC (9) where C@T is the transpose of the matrix C@. The above discussion shows that starting from graph G, its arbitrary isospectral graph G@ can be achieved by a transformation of basis vectors.This group representation theory12 emphasizes that no set of basis vectors is speci�ed in the de�nition of symmetry operators, so the symmetry operators have an intrinsic signi�cance. For example, suppose that in G de�ned by M/ operator T , which commutes with A; then in G@ de�ned by there will be a symmetry operator T @, M/i@N T @\S~1T S (10) 6 J. Chem. Soc., Faraday T rans., 1997, V ol. 93T @ should commute with A@. In fact, if . . . are a T1, T2 , T3 , representation of group H, . . . constitute also the T 1 @ , T 2 @ , T 3 @ , same representation, that is, two representations, T and T @, are equivalent. In di†erent bases the matrix representations of a symmetry operator inHare called equivalent matrices. 4. Symmetry of a subspectral graph A molecular graph G may have many isospectral graphs. Some isospectral graphs consist of several fragments g1, g2 .Because the spectrum of each fragment is always contained by that of G, we say that fragment is a subspectral graph13 of gi graph G. For simplifying the characteristic polynomial of the secular determinant of graph G, McClelland14 developed a factorization scheme. His procedure can break down a molecule with a symmetry plane into simpler fragments. For example as shown in Fig. 2, graph 6, which has two components 6(a) and 6(b), obtained by fragmenting the composite graph 1.In Fig. 2, symbol “4Ï signi�es that graphs 1 and 6 are isospectral. Rule 2 indicates that graphs 1 and 6 have the same Hamiltonian group H. Suppose that one of the fragments, say 6(a), belongs to the Hamiltonian group H. Then a symmetry operator T @ in group H corresponds always to a symmetry operator T in H. T acts only on this fragment and other fragment(s) remain unchanged. In other words, rule 3 applies. Rule 3: If a graph G consists of several fragments, the Hamiltonian group of each fragment is a subgroup of the Hamiltonian groupHof G.In some special cases, the hidden symmetry of a graph can be recognized directly from the point group Hp (Hp\H\H) of its subspectral graph obtained from McClellandÏs procedure. For example, graph 7 belongs to the point group D2h which contains only one-dimensional representation. However, it shares a pair of eigenvalues x\^1. On McClellandÏs procedure, we obtain its isospectral graph 8 constituted by 8(a) and 8(b) (see Fig. 3). The fragment 8(a) possesses doubly degenerate eigenvalues x\^1. Apparently the corresponding eigenvectors span a two-dimensional irreducible representation of the point group of the fragment 8(a). D6h Simultaneously, they also span the two-dimensional irreducible representations of the Hamiltonian group H of the fragment 8(a) and furthermore, the Hamiltonian group H of graphs 7 and 8, respectively. In this example, can be D6h chosen as H*.However, even if some graphs (say graph 1) can be divided into several fragments by McClelland:s procedure, it is difficult to �nd the Hamiltonian group symmetries of the fragments. Moreover, except for the molecular planes, Fig. 2 Graph 6 obtained from the reduction of graph 1 Fig. 3 Graph 8 obtained from the reduction of graph 7 some graphs (say graphs 2È5) do not have any geometrical symmetry; so McClellandÏs procedure is insufficient for understanding the hidden symmetries of a graph in the general case.Thus, we need to develop a new method of yielding proper subspectral graphs in order to explore the hidden symmetry of G from the point group or the automorphism group of Hp Ha this subspectral graph. 5. Construction of subgroupH* Using rules 2 and 3 we obtain a simple way to study the degeneracy problem of graph G. If there exists a hidden symmetry in graph G, we can always construct and explore its isospectral graph G@. Let graph G@ consist of two of more fragments.Some fragment, denoted by should satisfy two con- ga , ditions : (i) shares the d-fold degeneracy in eigenvalues ga x\ (ii) has a high symmetry structure in order to use its x0 ; ga point group or automorphism group to explain the Hp Ha d-fold degeneracy. To exemplify this way, now we discuss the case of graph 1 in detail. Graph 1 has six eigenvalues (0, 0, ^1, ^J5), the associated eigenvectors can be written as t1(x\)5) t2(x\1) t3(x\0) at4(x\0) b t5(x\[1) t6(x\[)5) 1 2)5 1 2 1 )5 1 )5 1 2 1 2)5 1 2 1 2 0 0 [ 1 2 [ 1 2 0 0 1 )2 [ 1 )2 0 0 2 )10 0 [ 1 )10 [ 1 )10 0 2 )10 1 2 [ 1 2 0 0 1 2 [ 1 2 1 2)5 [ 1 2 1 )5 1 J5 [ 1 2 1 2)5 q n t t t t t t t t t t \t t t t t t t t t t t t s p /1 /2 /3] (6a) a/4b/5 /6 Fig. 4 The isospectral graph 9 constructed in terms of the spectrum of graph 1. The edge weights and numbering are given. J. Chem. Soc., Faraday T rans., 1997, V ol. 93 7The isospectral graph 9, whose fragment 9(a) ful�lls the two conditions of graph 1, is constructed by trial and error (see Fig. 4). Graph 9 contains two fragments, 9(a) is made from some eigenvalues (0, 0, ^)5) of graph 1, 9(b) is obtained from eigenvalues (^1). Their eigenvectors are expressed as : t1(x\)5) t2(x\1) t3(x\0) at4(x\0) b t5(x\[1) t6(x\[)5) 1 )6 1 )2 1 )6 1 )6 0 0 0 0 0 0 1 )2 1 )2 0 0 1 )2 [ 1 )2 0 0 )23 0 [ 1 )6 [ 1 J6 0 0 0 0 0 0 1 )2 [ 1 )2 1 )6 [ 1 )2 1 J6 1 )6 0 0 q n t t t t t t t t t t \t t t t t t t t t t t t s p /1@ /2@ /3@ ] (8a) a/4 @ b/5 @ /6 @ Graph 9 has the adjacency matrix A@: 0 )53 0 0 0 0 )53 0 )53 )53 0 0 0 )53 0 0 0 0 A@\ .(11) a0 )53 0 0 0 0b 0 0 0 0 0 1 0 0 0 0 1 0 The transformation matrix S of basic vectors is Graph 9(a) belongs to the point group For clarity, the D3h . group can be de�ned as H*. Under basis C3v (C3v\D3h) vector the six elements inH* are M/i@N, 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 a0 0 0 1 0 0ba1 0 0 0 0 0b 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 T@(E) T@(C3) 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 a ba b 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 T@(C3 2) T@(p1) 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 a ba b 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 T@(p2) T@(p3) From eqn.(10), they can be transformed into T1, T2 , T3 , T4 , respectively. That is, representation matrices, T and T5 , T6 , T@, are equivalent matrices.The subgroup H* has three clases : (1) (2) (3) Its character table (see T1 ; T2 , T3; T4 , T5 , T6 . Table 1) is well known. It can be shown by applying the six group operations to one of the MOs that each t1, t2 , t5 , t6 of these MOs forms a basis for the representation. A1 Ti tj\tj ; i\1È6, j\1, 2, 5, 6 (12) However, if we carry out an operation of H* on one of MOs it will either go into ^1] itself, or into a linear com- t3 , t4 , Table 1 Character table ofH* H* T1 (T2 , T3) (T4,T5,T6) A1 1 1 1 t1,t2,t5,t6 A2 1 1 [1 E 2 [1 0 (t3,t4) 2)2[1 )15 0 2[)2 )30 0 1 )2 0 1[)2 )30 0 2)2])15]1 )60 1[)2 )30 0 2)2[)15]1 )60 0 1 )2 0 1 )2 0 0 qtttttS\C@TC\tttttts 2[)2 )30 0 2)2]1 )30 0 1 )2 0 2)2[)15]1 )60 0 1[)2 )30 2)2])15]1 )60 0 1[J2 )30 0 [ 1 )2 0 0 0 [ 1 )2 nttttt (9a) ttttttp 8 J.Chem. Soc., Faraday T rans., 1997, V ol. 93Table 2 Transformation matrices of MOs t3 , t4 T1 T2 T3 A1 0 0 1B 1[ 1 2 )3 2 [ )3 2 [ 1 22 1[ 1 2 [ )3 2 )3 2 [ 1 22 T4 T5 T6 A[1 0 0 1B 11 2 )3 2 )3 2 [ 1 22 11 2 [ )3 2 [ )3 2 [ 1 22 MOs bination of itself and its partner.Table 2 shows how the are transformed by each of the six symmetry operators t3 , t4 in H*. Thus together form a basis for the E represen- t3 , t4 tation, as expected. In general, for an arbitrary alternate molecular graph, graph 10, with n vertices (n is an even number, n[3), if it shares the two-fold degenerate eigenvalues x\0, then its spectrum is (0, 0, .. . , The graph 10 can ^x1, ^x2 , ^xn@2~1). always be reduced into a set of fragments, 11(a), 11(b), 11(c), . . . , 11(f) (see Fig. 5). In Fig. 5 when fragment u\o x1 o/)3, 11(a) shares the eigenvalues (0, 0, The Hamiltonian ^x1). group H of this fragment has the subgroup which can be C3v , de�ned as H*. The two eigenvectors corresponding to eigenvalue x\0 are the bases vectors of the two-fold irreducible representation of H*. With the same method introduced Fig. 5 Reduction of an arbitrary alternative graph 10 above, we �nd that Hamiltonian group H of an arbitrary alternate graph, sharing trate eigenvalues x\0, always contains the common subgroup H*, which is isomorphic with the point group and the associated C3v , eigenvectors span a two-dimensional representation of H* andH. The author thanks Prof. Yuansheng Jiang for a number of helpful discussions. References 1 U. Wild, J. Keller and Hs. H.Gu. nthard, T heor. Chim. Acta (Berlin), 1969, 14, 383. 2 (a) M. Randic� , Chem. Phys. L ett., 1976, 42, 283; (b) J. Chem. Phys., 1974, 60, 3920; (c) M. Randic� and M. I. Davis, Int. J. Quantum Chem., 1984, 26, 69. 3 (a) K. Balasubramanian, Int. J. Quantum Chem., 1982, 21, 411; (b) Chem. Rev., 1985, 85, 599; (c) J. Chem. Inf. Comput. Sci., 1994, 34, 621; (d) Chem. Phys. L ett., 1995, 232, 415. 4 (a) C. A. Shelly and M. E. Munk, J. Chem. Inf. Comput. Sci., 1977, 17, 110; (b) 1979, 19, 247. 5 A. T. Balaban, O. Mekenyan and D. Bonchev, J. Comput. Chem., 1985, 6, 538; (b) A. T. Balaban, Chemical Applications of Graph T heory, Academic Press, London, 1976. 6 S. Bohance and M. Perdih, J. Chem. Inf. Comput. Sci., 1993, 33, 719. 7 M. Razinger, K. Balasubramanian and M. E. Munk, J. Chem. Inf. Comput Sci., 1993, 33, 197. 8 P. C. Ojha, Int. J. Quantum Chem., 1989, 35, 687. 9 N. Trinajstic� , Chemical Graph T heory, CRC Press, Boca Raton, FL, 1983, vol. 1, p. 31. 10 F. A. Cotton, Chemical Applications of Group T heory, Wiley, New York, 1990. 11 I. Gutman and N. Trinajstic� , T op. Curr. Chem., 1973, 42, 49. 12 M. Hammermesh, Group T heory and its Applications to Physical Problems, Addison-Wesley, Reading, MA, 1962. 13 T. N. Trinajstic� and M. Randic� , Croat. Chem. Acta, Z� ivkovic� , 1977, 49, 89. 14 B. J. McClelland, J. Chem. Soc., Faraday T rans. 2, 1974, 70, 1453. Paper 6/02071B; Received 25th March, 1996 J. Chem. Soc., Faraday T rans.,
ISSN:0956-5000
DOI:10.1039/a602071b
出版商:RSC
年代:1997
数据来源: RSC
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Calculation of the Rydberg-state energies ofHCl |
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Journal of the Chemical Society, Faraday Transactions,
Volume 93,
Issue 1,
1997,
Page 21-23
Laurence Singleton,
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摘要:
pound and d the thickness of the in situ cell]. If an organic solvent of low absorption is used (such as acetone, ethanol or diethyl ether), the necessary concentration increases with increasing X-ray photon energy because the cross-section for X-rays decreases for heavier atoms. XAFS yields quantitative information on short-range order. This requires that the part of the molecule that undergoes a transformation must contain the absorbing element. To facilitate the XAFS analysis, it is advantageous if the monitored element is present only in a few di†erent local environments in the course of the reaction.The fact that the sample is continuously irradiated with X-rays during the experiment does not seem to have a strong inÑuence on the kinetics of the Finkelstein reaction. Were such an e†ect present, one would expect a much faster reaction due to an easier breaking of the BrwC bond. Being aware of these limitations, we believe that in situ XAFS on liquid-state reactions is a valuable tool to obtain structural as well as kinetic information for selected parts of a molecule.Examples could be the study of, e.g., coordination compounds or metalloproteins. Experimental Equal volumes of 1.333 M solutions of 2-bromopropane and NaI in acetone were mixed at room temperature. A tightly closed DSC aluminium crucible was completely �lled with the reaction mixture (ca. 30 ll). The crucible was placed into a Mettler FP 80/84 DSC heat-Ñux calorimeter that was mounted vertically in the synchrotron X-ray beam and heated to 55.0(5) ¡C within 30 s.The experiment was carried out at the Hamburger Synchrotronstrahlungslabor HASYLAB at Deutsches Elektronen-Synchrotron DESY, Germany, at beamline X1 (ROEMO II). This beamline is equipped with a Si(311) double crystal monochromator, yielding approximately 108 photons s~1 mm~2 at the sample. The energy resolution is approximately 2 eV at the bromine K-edge. The DORIS III storage ring was run with positrons of 4.5 GeV at 80È120 mA.Every 8 min 12 s an X-ray absorption spectrum was taken in transmission at the Br K-edge (photon energy ca. 13 475 eV). Reference spectra of crystalline NaBr were simultaneously measured (at room temperature) by use of a third ionization chamber. The sample Br absorption edge jump was limited by the solubility of NaI and the *kd\(It/I0)\0.38, �xed pathlength in the calorimeter. The measured spectra were evaluated with the programs AUTOBK, FEFF and FEFFIT of the University of Washington package.27h29 Multi-electron phenomena lead to a peak at low R in the Br XAFS spectra.30h34 This was corrected by a simpli�ed approach as described in ref. 35. BrieÑy, this peak was isolated in R-space from a NaBr spectrum and back-transformed into k-space. It was then subtracted from all spectra in k-space before evaluation. When quantitatively analysing XAFS spectra of reacting systems, it is important to keep the number of �t-parameters as small as possible to minimize correlation e†ects.13,35,36 By evaluating spectra of pure 2-bromopropane and NaBr at 55 ¡C we determined the following parameters that were kept constant in subsequent �ts of the reaction mixture: p2(BrwCa)\0.0011 ”2, p2(BrwCb)\0.0137 ”2, p2(BrwNa)\0.02593 ”2, R(BrwCb)\2.858 ”, S02(BrwCa)\S02(BrwCb)\1.082, S02(BrwNa)\1.10, eV, E0(BrwCa)\E0(BrwCb)\[0.89 E0(BrwNa)\[1.65 eV.These values are in good agreement with data for similar compounds.13,33,35 was set to Conse- N(BrwCb) 2N(BrwCa).quently, the only �t variables were the mean coordination numbers and N(BrwNa), and the mean distances N(BrwCa) R(BrwNa) and The evaluated XAFS data range R(BrwCa). was k\2.0È7.1 and R\0.8È3.1 throughout all experi- ”~1 ” ments. 2-Bromopropane (99]%), acetone (99.9%; HPLC grade) and NaI (p.a.) were purchased from Aldrich. Hydrate water of NaI was removed before experiments by heating in vacuum. are grateful to HASYLAB for beamtime.We thank A. We Reller and M. Martin for generous support. Financial support was granted by the Deutsche Forschungsgemeinschaft and by the Fonds der Chemischen Industrie. References 1 X-Ray absorption. Principles, applications, techniques of EXAFS, SEXAFS and XANES, ed. D. C. Koningsberger and R. Prins, Wiley, New York, 1988. 2 D. Bazin, H. Dexpert, N. S. Guyot-Sionnest, J. P. Bournonville and J. Lynch, J. Chim. Phys. Phys. Chim. Biol., 1989, 86, 1707. 3 B. S. Clausen, L. G. Ste†ensen, P. L. Hansen and H. Gra- b~k, Catal. L ett., 1993, 20, 23. Tops‘e, 4 G. Sankar, P. A. Wright, S. Natarajan, J. M. Thomas, G. N. Greaves, A. J. Dent, B. R. Dobson, C. A. Ramsdale and R. H. Jones, J. Phys. Chem., 1993, 97, 9550. 5 H. Bertagnolli and T. S. Ertel, Angew. Chem., 1994, 106, 15. 6 T. Maschmeyer, F. Rey, G. Sankar and J. M. Thomas, Nature (L ondon), 1995, 378, 159. 7 A. Hoser, N. Hilbrandt, M. Martin and M. Denecke, Physica B, 1995, 208/209, 321. 8 P. Andrews, J. M. Corker, J. Evans and M. Webster, J. Chem. Soc., Dalton T rans., 1994, 1337. 9 M. Tabata and K. Ozutsumi, Bull. Chem. Soc. Jpn., 1994, 67, 1608. 10 T. S. Ertel, W. Ho. rner, S. Hu. ckmann, U. Kolb, I. Abraham and H. Bertagnolli, Physica B, 1995, 208/209, 641. 11 N. Yoshida and T. Nagamura, Rev. Sci. Instrum., 1995, 66, 52. 12 A. J. Dent, L. J. Farrugia, A. G. Orpen and S. E. Stratford, J. Chem. Soc., Chem. Commun., 1992, 1456. 13 M. Epple, U. Sazama, A. Reller, N.Hilbrandt, M. Martin and L. Tro. ger, Chem. Commun., 1996, 1755. 14 L. Tro. ger, N. Hilbrandt and M. Epple, J. Phys. Coll., 1997, in press. 15 H. Finkelstein, Chem. Ber., 1910, 43, 1528. 16 S. D. Hamann, Aust. J. Chem., 1975, 28, 693. 17 C. D. Chalk, J. McKenna and I. H. Williams, J. Am. Chem. Soc., 1981, 103, 272. 18 L. Eberston, Acta Chem. Scand., Sect. B, 1982, B36, 533. 19 P. B. D. de la Mare, J. Chem. Soc., 1955, 3169. 20 E. D. Hughes, C. K. Ingold and J. D. H. Mackie, J.Chem. Soc., 1955, 3173. 21 E. D. Hughes, C. K. Ingold and J. D. H. Mackie, J. Chem. Soc., 1955, 3177. 22 P. B. D. de la Mare, J. Chem. Soc., 1955, 3180. 23 L. Fowden, E. D. Hughes and C. K. Ingold, J. Chem. Soc., 1955, 3187. 24 L. Fowden, E. D. Hughes and C. K. Ingold, J. Chem. Soc., 1955, 3193. 25 P. B. D. de la Mare, J. Chem. Soc., 1955, 3196. 26 P. B. D. de la Mare, L. Fowden, E. D. Hughes, C. K. Ingold and J. D. H. Mackie, J. Chem. Soc., 1955, 3200. 27 J. J. Rehr, R.C. Albers and S. I. Zabinsky, Phys. Rev. L ett., 1992, 69, 3397. 28 L. Tro. ger, T. Yokoyama, D. Arvanitis, T. Lederer, M. Tischer and K. Baberschke, Phys. Rev. B, 1994, 49, 888. 29 E. A. Stern, M. Newville, B. Ravel, Y. Yacoby and D. Haskel, Physica B, 1995, 208/209, 117. 30 E. A. Stern, S. M. Heald and B. Bunker, Phys. Rev. L ett., 1979, 42, 1372. 31 G. Li, F. Bridges and G. S. Brown, Phys. Rev. L ett., 1992, 68, 1609. 32 P. DÏAngelo, A. Di Cicco, A. Filipponi and N. V.Pavel, Phys. Rev. A, 1993, 47, 2055. 33 E. Burattini, P. DÏAngelo, A. Di Cicco, A. Filipponi and N. V. Pavel, J. Phys. Chem., 1993, 97, 5486. 34 J. J. Rehr, C. H. Booth, F. Bridges and S. I. Zabinsky, Phys. Rev. B, 1994, 49, 12347. 35 M. Epple, H. Kirschnick, G. N. Greaves, G. Sankar and J. M. Thomas, J. Chem. Soc., Faraday T rans., 1996, 5035. 36 M. Epple and L. Tro. ger, J. Chem. Soc., Dalton T rans., 1996, 11. Paper 7/01433C; Received 28th February, 1997 J. Chem. Soc., Faraday T rans., 1997, V ol. 93 3037pound and d the thickness of the in situ cell]. If an organic solvent of low absorption is used (such as acetone, ethanol or diethyl ether), the necessary concentration increases with increasing X-ray photon energy because the cross-section for X-rays decreases for heavier atoms. XAFS yields quantitative information on short-range order. This requires that the part of the molecule that undergoes a transformation must contain the absorbing element. To facilitate the XAFS analysis, it is advantageous if the monitored element is present only in a few di†erent local environments in the course of the reaction.The fact that the sample is continuously irradiated with X-rays during the experiment does not seemtrong inÑuence on the kinetics of the Finkelstein reaction. Were such an e†ect present, one would expect a much faster reaction due to an easier breaking of the BrwC bond. Being aware of these limitations, we believe that in situ XAFS on liquid-state reactions is a valuable tool to obtain structural as well as kinetic information for selected parts of a molecule.Examples could be the study of, e.g., coordination compounds or metalloproteins. Experimental Equal volumes of 1.333 M solutions of 2-bromopropane and NaI in acetone were mixed at room temperature. A tightly closed DSC aluminium crucible was completely �lled with the reaction mixture (ca. 30 ll). The crucible was placed into a Mettler FP 80/84 DSC heat-Ñux calorimeter that was mounted vertically in the synchrotron X-ray beam and heated to 55.0(5) ¡C within 30 s.The experiment was carried out at the Hamburger Synchrotronstrahlungslabor HASYLAB at Deutsches Elektronen-Synchrotron DESY, Germany, at beamline X1 (ROEMO II). This beamline is equipped with a Si(311) double crystal monochromator, yielding approximately 108 photons s~1 mm~2 at the sample. The energy resolution is approximately 2 eV at the bromine K-edge.The DORIS III storage ring was run with positrons of 4.5 GeV at 80È120 mA. Every 8 min 12 s an X-ray absorption spectrum was taken in transmission at the Br K-edge (photon energy ca. 13 475 eV). Reference spectra of crystalline NaBr were simultaneously measured (at room temperature) by use of a third ionization chamber. The sample Br absorption edge jump was limited by the solubility of NaI and the *kd\(It/I0)\0.38, �xed pathlength in the calorimeter. The measured spectra were evaluated with the programs AUTOBK, FEFF and FEFFIT of the University of Washington package.27h29 Multi-electron phenomena lead to a peak at low R in the Br XAFS spectra.30h34 This was corrected by a simpli�ed approach as described in ref. 35. BrieÑy, this peak was isolated in R-space from a NaBr spectrum and back-transformed into k-space. It was then subtracted from all spectra in k-space before evaluation. When quantitatively analysing XAFS spectra of reacting systems, it is important to keep the number of �t-parameters as small as possible to minimize correlation e†ects.13,35,36 By evaluating spectra of pure 2-bromopropane and NaBr at 55 ¡C we determined the following parameters that were kept constant in subsequent �ts of the reaction mixture: p2(BrwCa)\0.0011 ”2, p2(BrwCb)\0.0137 ”2, p2(BrwNa)\0.02593 ”2, R(BrwCb)\2.858 ”, S02(BrwCa)\S02(BrwCb)\1.082, S02(BrwNa)\1.10, eV, E0(BrwCa)\E0(BrwCb)\[0.89 E0(BrwNa)\[1.65 eV. These values are in good agreement with data for similar compounds.13,33,35 was set to Conse- N(BrwCb) 2N(BrwCa).quently, the only �t variables were the mean coordination numbers and N(BrwNa), and the mean distances N(BrwCa) R(BrwNa) and The evaluated XAFS data range R(BrwCa). was k\2.0È7.1 and R\0.8È3.1 throughout all experi- ”~1 ” ments. 2-Bromopropane (99]%), acetone (99.9%; HPLC grade) and NaI (p.a.) were purchased from Aldrich. Hydrate water of NaI was removed before experiments by heating in vacuum.are grateful to HASYLAB for beamtime. We thank A. We Reller and M. Martin for generous support. Financial support was granted by the Deutsche Forschungsgemeinschaft and by the Fonds der Chemischen Industrie. References 1 X-Ray absorption. Principles, applications, techniques of EXAFS, SEXAFS and XANES, ed. D. C. Koningsberger and R. Prins, Wiley, New York, 1988. 2 D. Bazin, H. Dexpert, N. S. Guyot-Sionnest, J. P. Bournonville and J. Lynch, J. Chim. Phys.Phys. Chim. Biol., 1989, 86, 1707. 3 B. S. Clausen, L. G. Ste†ensen, P. L. Hansen and H. Gra- b~k, Catal. L ett., 1993, 20, 23. Tops‘e, 4 G. Sankar, P. A. Wright, S. Natarajan, J. M. Thomas, G. N. Greaves, A. J. Dent, B. R. Dobson, C. A. Ramsdale and R. H. Jones, J. Phys. Chem., 1993, 97, 9550. 5 H. Bertagnolli and T. S. Ertel, Angew. Chem., 1994, 106, 15. 6 T. Maschmeyer, F. Rey, G. Sankar and J. M. Thomas, Nature (L ondon), 1995, 378, 159. 7 A. Hoser, N. Hilbrandt, M. Martin and M.Denecke, Physica B, 1995, 208/209, 321. 8 P. Andrews, J. M. Corker, J. Evans and M. Webster, J. Chem. Soc., Dalton T rans., 1994, 1337. 9 M. Tabata and K. Ozutsumi, Bull. Chem. Soc. Jpn., 1994, 67, 1608. 10 T. S. Ertel, W. Ho. rner, S. Hu. ckmann, U. Kolb, I. Abraham and H. Bertagnolli, Physica B, 1995, 208/209, 641. 11 N. Yoshida and T. Nagamura, Rev. Sci. Instrum., 1995, 66, 52. 12 A. J. Dent, L. J. Farrugia, A. G. Orpen and S. E. Stratford, J. Chem. Soc., Chem. Commun., 1992, 1456. 13 M.Epple, U. Sazama, A. Reller, N. Hilbrandt, M. Martin and L. Tro. ger, Chem. Commun., 1996, 1755. 14 L. Tro. ger, N. Hilbrandt and M. Epple, J. Phys. Coll., 1997, in press. 15 H. Finkelstein, Chem. Ber., 1910, 43, 1528. 16 S. D. Hamann, Aust. J. Chem., 1975, 28, 693. 17 C. D. Chalk, J. McKenna and I. H. Williams, J. Am. Chem. Soc., 1981, 103, 272. 18 L. Eberston, Acta Chem. Scand., Sect. B, 1982, B36, 533. 19 P. B. D. de la Mare, J. Chem. Soc., 1955, 3169. 20 E. D. Hughes, C. K. Ingold and J. D. H. Mackie, J. Chem. Soc., 1955, 3173. 21 E. D. Hughes, C. K. Ingold and J. D. H. Mackie, J. Chem. Soc., 1955, 3177. 22 P. B. D. de la Mare, J. Chem. Soc., 1955, 3180. 23 L. Fowden, E. D. Hughes and C. K. Ingold, J. Chem. Soc., 1955, 3187. 24 L. Fowden, E. D. Hughes and C. K. Ingold, J. Chem. Soc., 1955, 3193. 25 P. B. D. de la Mare, J. Chem. Soc., 1955, 3196. 26 P. B. D. de la Mare, L. Fowden, E. D. Hughes, C. K. Ingold and J. D. H. Mackie, J.Chem. Soc., 1955, 3200. 27 J. J. Rehr, R. C. Albers and S. I. Zabinsky, Phys. Rev. L ett., 1992, 69, 3397. 28 L. Tro. ger, T. Yokoyama, D. Arvanitis, T. Lederer, M. Tischer and K. Baberschke, Phys. Rev. B, 1994, 49, 888. 29 E. A. Stern, M. Newville, B. Ravel, Y. Yacoby and D. Haskel, Physica B, 1995, 208/209, 117. 30 E. A. Stern, S. M. Heald and B. Bunker, Phys. Rev. L ett., 1979, 42, 1372. 31 G. Li, F. Bridges and G. S. Brown, Phys. Rev. L ett., 1992, 68, 1609. 32 P. DÏAngelo, A.Di Cicco, A. Filipponi and N. V. Pavel, Phys. Rev. A, 1993, 47, 2055. 33 E. Burattini, P. DÏAngelo, A. Di Cicco, A. Filipponi and N. V. Pavel, J. Phys. Chem., 1993, 97, 5486. 34 J. J. Rehr, C. H. Booth, F. Bridges and S. I. Zabinsky, Phys. Rev. B, 1994, 49, 12347. 35 M. Epple, H. Kirschnick, G. N. Greaves, G. Sankar and J. M. Thomas, J. Chem. Soc., Faraday T rans., 1996, 5035. 36 M. Epple and L. Tro. ger, J. Chem. Soc., Dalton T rans., 1996, 11. Paper 7/01433C; Received 28th February, 1997 J.Chem. Soc., Faraday T rans., 1997, V ol. 93 3037pound and d the thickness of the in situ cell]. If an organic solvent of low absorption is used (such as acetone, ethanol or diethyl ether), the necessary concentration increases with increasing X-ray photon energy because the cross-section for X-rays decreases for heavier atoms. XAFS yields quantitative information on short-range order. This requires that the part of the molecule that undergoes a transformation must contain the absorbing element.To facilitate the XAFS analysis, it is advantageous if the monitored element is present only in a few di†erent local environments in the course of the reaction. The fact that the sample is continuously irradiated with X-rays during the experiment does not seem to have a strong inÑuence on the kinetics of the Finkelstein reaction. Were such an e†ect present, one would expect a much faster reaction due to an easier breaking of the BrwC bond. Being aware of these limitations, we believe that in situ XAFS on liquid-state reactions is a valuable tool to obtain structural as well as kinetic information for selected parts of a molecule.Examples could be the study of, e.g., coordination compounds or metalloproteins. Experimental Equal volumes of 1.333 M solutions of 2-bromopropane and NaI in acetone were mixed at room temperature. A tightly closed DSC aluminium crucible was completely �lled with the reaction mixture (ca. 30 ll). The crucible was placed into a Mettler Fat-Ñux calorimeter that was mounted vertically in the synchrotron X-ray beam and heated to 55.0(5) ¡C within 30 s. The experiment was carried out at the Hamburger Synchrotronstrahlungslabor HASYLAB at Deutsches Elektronen-Synchrotron DESY, Germany, at beamline X1 (ROEMO II). This beamline is equipped with a Si(311) double crystal monochromator, yielding approximately 108 photons s~1 mm~2 at the sample.The energy resolution is approximately 2 eV at the bromine K-edge. The DORIS III storage ring was run with positrons of 4.5 GeV at 80È120 mA. Every 8 min 12 s an X-ray absorption spectrum was taken in transmission at the Br K-edge (photon energy ca. 13 475 eV). Reference spectra of crystalline NaBr were simultaneously measured (at room temperature) by use of a third ionization chamber. The sample Br absorption edge jump was limited by the solubility of NaI and the *kd\(It/I0)\0.38, �xed pathlength in the calorimeter.The measured spectra were evaluated with the programs AUTOBK, FEFF and FEFFIT of the University of Washington package.27h29 Multi-electron phenomena lead to a peak at low R in the Br XAFS spectra.30h34 This was corrected by a simpli�ed approach as described in ref. 35. BrieÑy, this peak was isolated in R-space from a NaBr spectrum and back-transformed into k-space. It was then subtracted from all spectra in k-space before evaluation.When quantitatively analysing XAFS spectra of reacting systems, it is important to keep the number of �t-parameters as small as possible to minimize correlation e†ects.13,35,36 By evaluating spectra of pure 2-bromopropane and NaBr at 55 ¡C we determined the following parameters that were kept constant in subsequent �ts of the reaction mixture: p2(BrwCa)\0.0011 ”2, p2(BrwCb)\0.0137 ”2, p2(BrwNa)\0.02593 ”2, R(BrwCb)\2.858 ”, S02(BrwCa)\S02(BrwCb)\1.082, S02(BrwNa)\1.10, eV, E0(BrwCa)\E0(BrwCb)\[0.89 E0(BrwNa)\[1.65 eV.These values are in good agreement with data for similar compounds.13,33,35 was set to Conse- N(BrwCb) 2N(BrwCa). quently, the only �t variables were the mean coordination numbers and N(BrwNa), and the mean distances N(BrwCa) R(BrwNa) and The evaluated XAFS data range R(BrwCa). was k\2.0È7.1 and R\0.8È3.1 throughout all experi- ”~1 ” ments. 2-Bromopropane (99]%), acetone (99.9%; HPLC grade) and NaI (p.a.) were purchased from Aldrich.Hydrate water of NaI was removed before experiments by heating in vacuum. are grateful to HASYLAB for beamtime. We thank A. We Reller and M. Martin for generous support. Financial support was granted by the Deutsche Forschungsgemeinschaft and by the Fonds der Chemischen Industrie. References 1 X-Ray absorption. Principles, applications, techniques of EXAFS, SEXAFS and XANES, ed. D. C. Koningsberger and R. Prins, Wiley, New York, 1988. 2 D. Bazin, H. Dexpert, N. S. Guyot-Sionnest, J.P. Bournonville and J. Lynch, J. Chim. Phys. Phys. Chim. Biol., 1989, 86, 1707. 3 B. S. Clausen, L. G. Ste†ensen, P. L. Hansen and H. Gra- b~k, Catal. L ett., 1993, 20, 23. Tops‘e, 4 G. Sankar, P. A. Wright, S. Natarajan, J. M. Thomas, G. N. Greaves, A. J. Dent, B. R. Dobson, C. A. Ramsdale and R. H. Jones, J. Phys. Chem., 1993, 97, 9550. 5 H. Bertagnolli and T. S. Ertel, Angew. Chem., 1994, 106, 15. 6 T. Maschmeyer, F. Rey, G. Sankar and J. M. Thomas, Nature (L ondon), 1995, 378, 159. 7 A. Hoser, N. Hilbrandt, M. Martin and M. Denecke, Physica B, 1995, 208/209, 321. 8 P. Andrews, J. M. Corker, J. Evans and M. Webster, J. Chem. Soc., Dalton T rans., 1994, 1337. 9 M. Tabata and K. Ozutsumi, Bull. Chem. Soc. Jpn., 1994, 67, 1608. 10 T. S. Ertel, W. Ho. rner, S. Hu. ckmann, U. Kolb, I. Abraham and H. Bertagnolli, Physica B, 1995, 208/209, 641. 11 N. Yoshida and T. Nagamura, Rev. Sci. Instrum., 1995, 66, 52. 12 A. J. Dent, L. J. Farrugia, A. G. Orpen and S.E. Stratford, J. Chem. Soc., Chem. Commun., 1992, 1456. 13 M. Epple, U. Sazama, A. Reller, N. Hilbrandt, M. Martin and L. Tro. ger, Chem. Commun., 1996, 1755. 14 L. Tro. ger, N. Hilbrandt and M. Epple, J. Phys. Coll., 1997, in press. 15 H. Finkelstein, Chem. Ber., 1910, 43, 1528. 16 S. D. Hamann, Aust. J. Chem., 1975, 28, 693. 17 C. D. Chalk, J. McKenna and I. H. Williams, J. Am. Chem. Soc., 1981, 103, 272. 18 L. Eberston, Acta Chem. Scand., Sect. B, 1982, B36, 533. 19 P.B. D. de la Mare, J. Chem. Soc., 1955, 3169. 20 E. D. Hughes, C. K. Ingold and J. D. H. Mackie, J. Chem. Soc., 1955, 3173. 21 E. D. Hughes, C. K. Ingold and J. D. H. Mackie, J. Chem. Soc., 1955, 3177. 22 P. B. D. de la Mare, J. Chem. Soc., 1955, 3180. 23 L. Fowden, E. D. Hughes and C. K. Ingold, J. Chem. Soc., 1955, 3187. 24 L. Fowden, E. D. Hughes and C. K. Ingold, J. Chem. Soc., 1955, 3193. 25 P. B. D. de la Mare, J. Chem. Soc., 1955, 3196. 26 P. B. D. de la Mare, L. Fowden, E. D. Hughes, C. K. Ingold and J. D. H. Mackie, J. Chem. Soc., 1955, 3200. 27 J. J. Rehr, R. C. Albers and S. I. Zabinsky, Phys. Rev. L ett., 1992, 69, 3397. 28 L. Tro. ger, T. Yokoyama, D. Arvanitis, T. Lederer, M. Tischer and K. Baberschke, Phys. Rev. B, 1994, 49, 888. 29 E. A. Stern, M. Newville, B. Ravel, Y. Yacoby and D. Haskel, Physica B, 1995, 208/209, 117. 30 E. A. Stern, S. M. Heald and B. Bunker, Phys. Rev. L ett., 1979, 42, 1372. 31 G. Li, F. Bridges and G. S. Brown, Phys. Rev. L ett., 1992, 68, 1609. 32 P. DÏAngelo, A. Di Cicco, A. Filipponi and N. V. Pavel, Phys. Rev. A, 1993, 47, 2055. 33 E. Burattini, P. DÏAngelo, A. Di Cicco, A. Filipponi and N. V. Pavel, J. Phys. Chem., 1993, 97, 5486. 34 J. J. Rehr, C. H. Booth, F. Bridges and S. I. Zabinsky, Phys. Rev. B, 1994, 49, 12347. 35 M. Epple, H. Kirschnick, G. N. Greaves, G. Sankar and J. M. Thomas, J. Chem. Soc., Faraday T rans., 1996, 5035. 36 M. Epple and L. Tro. ger, J. Chem. Soc., Dalton T rans., 1996, 11. Paper 7/01433C; Received 28th February, 1997 J. Chem. Soc., Faraday T rans., 1997, V o
ISSN:0956-5000
DOI:10.1039/a606111g
出版商:RSC
年代:1997
数据来源: RSC
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Potential-energy surface ofH·SO2 |
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Journal of the Chemical Society, Faraday Transactions,
Volume 93,
Issue 1,
1997,
Page 25-28
Jian-Xin Qi,
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摘要:
Potential-energy surface of HÆSO2 Jian-Xin Qi, Wei-Qiao Deng, Ke-Li Han* and Guo-Zhong He State Key L aboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian, China The potential-energy surface for has been computed at the HF/6-311G** and MP2/6-311G** levels. The calculated HÉSO2 results con�rm that trans-planar HOSO is a transition state but not a stable structure. The decomposition channel for the HOSO adduct has been studied by analysing the transition states and stationary points. The kinetic stimulus for the rearrangement and dissociation of the radical HOSO was calculated by means of RRKM theory.The adduct is an important intermediate in the atmo- HÉSO2 spheric chemistry of sulfur1 and in combustion chemistry.2 Moreover, the complexes also play a key role in the HÉSO2 reaction dynamics between H and To understand the SO2 .3,4 chemistry of this adduct, many ab initio calculations5h8 have been performed.Boyd et al.5 �rst calculated the structures of at the UHF/STO-3G* level. Later Hinchli†e6 report- HÉSO2 ed UHF results with a slightly larger basis set. Recently Binns and Marshall7 and Morris and Jackson8 calculated the potential surface at the MP2 level using 3-21G* and DZP basis sets, respectively. These studies found that the H can be connected either to S, denoted as or to O, denoted as HSO2 , HOSO. However, there are apparent di†erences in the HOSO structures from di†erent calculations. Boyd et al.5 and Hinchli†e6 reported a non-planar cis structure, Binns and Marshall,7 however, obtained a planar cis structure, and Morris and Jackson8 found that the trans-planar structure is also stable which was identi�ed as a transition state by Binns and Marshall besides the planar cis structure.Recently Laakso et al.9 reported their calculated results for HOSO at the MP2\FULL/6-31G* level. They found that the HF minimum-energy conformation of HOSO is staggered but when electron correlation is considered the minimum-energy MP2 conformation of HOSO is predicted to be cis, with a trans transition state for internal rotation.This also contradicts the results of Morris and Jackson. All previous calculations used rather crude basis sets. In our work, we use a larger basis set of the type 6-311G** for calculations at the MP2 level. We hope to shed some light on the problem and to give more accurate barriers of isomerization or dissociation as well as on the vibration frequencies at the stationary points. Calculation The geometries of the various isomers of and the tran- HÉSO2 sition states of some isomeric structures are calculated at the MP2/6-311G** level.The computations were performed as follows : �rst, the geometries are obtained by HF calculations, then further optimizations are performed at the MP2 level. For some saddle points, IRC calculations are performed in order to establish which two stable points are connected.The vibrational frequencies at all stationary points are also calculated at the MP2/6-311G** level. The frequencies and zero-point energies are scaled by 0.95 for anharmonicity correction. Some of the isomerization and dissociation barriers are calculated with zero-point energy correction. Since for close to the ideal value of 0.75, SS2T\0.75È0.78 HÉSO2 , spin contamination is negligible. All the calculations are performed using the GAUSSIAN 92 program.Results and Discussion It is very important to estimate the likely accuracy of these calculations, which we do by comparison with data for experimentally and previously theoretically known species. The SwO bond length of 1.465 for at the MP2/6-311G** ” SO2 level is closer to the experimental value of 1.43 than that of ” other levels.11 The MP2/DZP and MP2/3-21G* as well as MP2/6-31G* calculations all overestimate it by about 0.05 ”. Similarly, the (unscaled) calculated vibrational frequencies of 496, 1087 and 1309 cm~1 at the MP2/6-311G** level are relatively close to the experimental values of 518, 1151 and 1362 cm~1.11 The MP2/6-311G** results underestimate the (unscaled) frequencies by 4%, while the MP2/DZP8 and MP2/ 3-21G*7 estimates are approximately 7% too low and the MP2/6-31G* estimates are 6% too low. The MP2/6-311G** bond length for OH is 0.967 with a ” predicted frequency of 3851 cm~1.Comparison with the experimental values11 of and cm~1 re\0.971 ” l0\3569 shows that the calculations underestimate by 0.004 and re ” overestimate by 6%.However, the MP2/DZP results over- l0 estimate by 0.01 and overestimate by 5% whereas the re ” l0 MP2/3-21G* results overestimate by 0.04 and underesti- re ” mate by 5%. For SO, the MP2/6-311G** geometry and l0 frequencies of 1.513 and 1098 cm~1 are within 3% of the ” experimental values, 1.481 and 1136 cm~1.11 The MP2/6- ” 31G* and MP2/DZP bond lengths for SO are 1.528 and 1.531 respectively, with frequencies of 1091 and 1093 cm~1 ”, whereas the MP2/3-21G* calculations7 do not describe SO satisfactorily.Based on these comparisons, we conclude that the more extensive basis set probably leads to more accurate geometries and frequencies. In agreement with results from previous ab initio calculations3h6 concerning the present calculation HÉSO2 , con�rms the existence of two stable structures for HÉSO2 . One such is the structure and the other is HOSO; the HSO2 results are shown in Table 1 and Fig. 1. Table 2 lists the calculated geometries of the transition states. The corresponding energies for stationary points are shown in Table 3. Vibrational frequencies are given in Table 4. In all tables refers O1 Fig. 1 Sketch of molecular structures for (A) and (B) HOSO. HSO2 The dihedral angle is q. HO1SO2 J. Chem. Soc., Faraday T rans., 1997, 93(1), 25È28 25Table 1 Geometries (bond bond angles/degrees) of the stable conformationsa lengths/”, HÉSO2 HF/6-311G** MP2/6-311G** HF/6-31G* MP2/6-31G* HF/3-21G* MP2/3-21G* UHF/DZP MP2/DZP HSO2 rSH 1.353 1.377 1.340 È 1.340 1.379 1.349 1.384 rSO 1.432 1.466 1.439 È 1.447 1.480 1.447 1.488 hOSO 123.3 125.3 123.6 È 122.5 125.1 È È hHSO 126.8 105.6 106.6 È 106.8 106.4 106.6 106.0 cis-HOSO rHO1 0.946 0.969 0.953 0.983 0.970 1.001 0.952 0.985 rSO1 1.616 1.655 1.623 1.661 1.624 1.662 1.624 1.670 rSO2 1.463 1.472 1.468 1.482 1.510 1.480 1.467 1.489 hO1SO2 108.2 106.7 108.2 109.8 107.5 111.4 107.1 109.6 hHO1S 112.4 109.7 111.5 106.9 115.2 111.0 111.5 109.7 qHO1SO2 61.1 0.0 59.5 0.0 74.7 0.0 a Results of HF/3-21G*, HF/6-31G* and MP2/3-21G* are from ref. 7; those of UHF/DZP and MP2/DZP are from ref. 8; those of MP2/6-31G* are from ref. 9. to the atom connected to H. In order to compare with the previously calculated results, we present those of Binns and Marshall,7 Morris and Jackson8 and Laasko et al.9 in the tables. However, the values for some transition states calculated by Morris and Jackson and Laakso et al.9 are not available.The structure has symmetry with the H atom out HSO2 Cs of plane with respects to the OSO geometry. The structures obtained from HF calculations with di†erent basis sets are nearly identical. The same is true for the MP2 level calculations. The di†erence between the structure geometries obtained by MP2 and HF with the same basis set is obvious. The calculations of the transition state near show the HSO2 same tendency.This suggests that for stationary structures of the electron correlation is more important than the HSO2 , basis set in determining the geometries. cis-HOSO has a planar symmetry. As shown in Table 1, Cs the UHF/6-311G** gives a symmetry, but further opti- C1 mization using MP2 leads to a structure with symmetry. Cs The same observation was made by Binns and Marshall7 and Morris and Jackson8 in their calculations. This suggests that the electron correlation plays an important role in the determination of the geometry and explains why Boyd et al.5 and Hinchli†e6 did not obtain the correct planar structure at the UHF level.We examined the geometries ary points and found that the HOSO structure is more sensitive to changes in the basis set than is The central SwO HSO2 . separation of 1.655 at the MP2/6-311G** level for HOSO, ” for example, is smaller than the distance of 1.661 at the ” MP2/FULL/6-31G* level9 and the other SwO distance of 1.472 is closer to the experimental value of 1.43 for ” ” than the results calculated by Laakso et al.9 (Table 1).SO2 10 Table 2 Geometries (bond angles/degrees) of the transition states in the potential surfacea lengths/”, HÉSO2 HF/6-311G** MP2/6-311G** HF/6-31G* HF/3-21G* MP2/3-21G* HSO2%cis-HOSO(C1) TS rO1H 1.343 1.426 1.351 1.367 1.392 rSO1 1.589 1.571 1.598 1.624 1.629 rSO2 1.430 1.458 1.438 1.448 1.481 hO1SO2 113.6 117.1 114.0 113.8 118.1 hHO1S 60.3 57.9 60.6 60.7 57.4 q 104.8 107.5 104.9 105.3 106.6 H-atom rotating about the SO1 bond rHO1 0.945 0.965 0.952 0.970 0.996 rSO1 1.626 1.663 1.632 1.637 1.667 rSO2 1.450 1.458 1.456 1.486 1.469 hO1SO2 105.3 107.2 105.3 104.3 108.6 hHO1S 110.5 107.8 110.1 114.0 110.7 H-atom transfer from O1 to O2 (C2v) rHO 1.263 1.288 rSO 1.528 1.567 hOSO 89.8 91.0 hHOS 76.2 74.2 HSO2%H]SO2 TS rHS 1.938 1.839 rSO 1.455 1.469 hOSO 120.1 121.2 hHSO 103.4 105.1 HOSO%H]SO2 TS rO1H 1.492 1.550 rSO1 1.444 1.467 rSO2 1.429 1.441 hO1SO 120.2 120.5 hHO1S 127.8 124.9 q 77.7 81.8 a Results of HF/3-21G*, HF/6-31G* and MP2/3-21G* are from ref. 7. 26 J. Chem. Soc., Faraday T rans., 1997, V ol. 93Table 3 Ab initio energies (kJ mol~1) for stationary points of HÉSO2 HF/6-311G** MP2/6-311G* HF/3-21G*a MP2/3-21G*a HSO2 Eb [547.7546 [548.2933 [545.0213 [545.4125 E0 c 43.3 cis-HOSO Eb [547.8133 [548.3392 [545.0903 [545.4553 E0 c 42.9 HSO2%cis-HOSO TS Eb [547.7100 [548.2409 [544.9725 [545.3579 E0 c 31.5 H atom rotating about the SO1 bond Eb [547.8106 [548.3321 [545.0785 [545.4444 E0 c 42.7 H atom transfer from O1 to O2 (C2v group) Eb [547.7400 [548.2911 E0 c 33.3 HSO2%H]SO2 TS Eb [548.2685 [545.3939 E0 c 75.6 HOSO%H]SO2 TS [548.2440 [545.3616 24.9 a Results of HF/3-21G* and MP2/3-21G* are from ref. 7.b Spinprojected HF energies, in atomic units. c Zero-point energies. This may be the reason why Morris and Jackson8 identify the trans-HOSO as a stable point. The trans-HOSO with symmetry is a transition state Cs because it is a stationary point and has one imaginary vibration frequency.This is in accordance with the results of Binns and Marshall and Laakso et al.9 but in contradiction to those of Morris and Jackson, although the di†erence for all theoretical bond lengths for cis-HOSO is \0.06 In order to ”.7h9 identify the transition state which connects to two stable points, we performed IRC calculations around this point.The IRC ends at the points corresponding to a rotation of the H atom around the OS bond by ca. ^33¡. Further optimization identi�ed this point as a true minimum. The optimization leads to a smooth rotation of the H atom into the cis-HOSO structure. Hence the trans-HOSO is the transition state for H atom rotation. The inner rotation barrier is 18.4 kJ mol~1 but Laakso et al.9 gave the calculated value of 7.9 kJ mol~1. This small rotation barrier means that in the H atom HÉSO2 , rotates nearly freely around the OS bond.The transition state corresponding to H atom transfer from one O to the other is associated with the planar structure C2v Table 4 Scaled vibration frequencies (cm~1) calculated at the MP2/ 6-311G** level (i\imaginary) HSO2 l\429.5, 811.9, 1053.6, 1135.8, 1543.3, 2261.3 cis-HOSO l\146.4, 347.8, 738.7, 1008.0, 1323.3, 3602.4 HSO2%cis-HOSO TS l\1499.7i, 410.2, 649.8, 845.8, 1223.8, 2144.0 H atom rotating about the SO1 bond l\68.8i, 375.7, 720.3, 978.7, 1411.1, 3653 H atom transfer from O1 to O2 (C2v group) l\1873.1i, 632.0, 964.6, 991.3, 1002.4, 1971.7 HSO2%H]SO2 TS l\1207.1i, 326.6, 485.6, 876.9, 1124.8, 9821.0 HOSO%H]SO2 TS l\2763.4i, 288.5, 509.7, 596.4, 1249.4, 1512.6 in which the H atom is positioned between the two O atoms.The IRC calculation shows that the isomerization takes place in the OSO plane. The energy barrier is 100 kJ mol~1. In the previous calculations, nobody gave this transition state although it is very important in HSO2 .The transition state for isomerization between and HSO2 HOSO can be reached by bending the H atom in HSO2 towards the O atom. The IRC shows that this saddle point connects and HOSO, but it results in a structure of HSO2 C1 symmetry on the HOSO side. Further optimization leads to the correct planar structure. The barrier is 246.7 kJ mol~1 from HOSO to and 125.8 kJ mol~1 from to HSO2 HSO2 HOSO. The transition state for dissociating to has HSO2 H]SO2 symmetry. The related zero-point energy cannot be used to Cs determine the barrier for the dissociation of to H HSO2 since the frequency has an unreasonable value in ]SO2 l6 the calculations of Binns and Marshall.7 They attributed the unreasonable value of the frequency to the discontinuity of the potential energy near the saddle point because of the energy surface crossing.7 This problem may be solved by considering a more extensive electron correlation and basis set. The energy di†erence between the transition state and is HSO2 calculated as 65.1 kJ mol~1 which is 16 kJ mol~1 larger than the value estimated by Binns and Marshall.7 The height of the barrier for dissociation of HOSO to is 284.5 kJ H]SO2 mol~1.Results from this calculation con�rm that primitive ab initio calculations of the energies along the pathway of recombination of the HOSO structure lead to an adequate result. Therefore, it is necessary to calculate the rate constants of the system using the RiceÈRamspergerÈKasselÈMarcus HÉSO2 (RRKM) theory.Similar to the calculation of Binns and Marshall, we follow the procedures described by Gilbert et al.12,13 First, the adduct HOSO decomposes into three channels in an Ar bath gas: HOSO]Ar]H]SO2 (A) HOSO]Ar]HSO2 (B) HOSO]Ar]HO]SO (C) Here we only calculate channels A and B. The LennardÈ Jones collision rate between HOSO and the bath gas was estimated by means of the LennardÈJones parameters for Ar and to give and K.14 A weak- SO2 , p1j\3.845 ” e1j\177 collision “exponential downÏ model for energy transfer between excited HOSO and Ar was assumed.The lowest vibrational frequency mode of cis-HOSO, which corresponds to the motion of the H atom away from the plane, is so SO2 low that it is regarded as an internal rotation. The pressure of the bath gas was assumed to be 133 mbar. We used the UNIMOL program to calculate the low-pressure rate constant of the two channels as a function of temperature.13 Fig. 2 shows the temperature dependence of the low-pressure limiting rate constants for HOSO]Ar. Clearly, the reaction rate constant is too small to be measured at room temperature. In the range 700È2000 K, the variation of rate for channel A kA and rate for channel B can be represented as kB kA\4.79 exp([29 845 K/T) s~1 and ]109 kB\2.02]109 exp([25 639 K/T ) s~1, respectively. We found in cal- kB[kA culations at any temperature. In other words, HOSO is the preferred arrangement for dissociation.However, the results of Binns and Marshall7 show, in contrast to ours, that the rate constant of channel B is smaller than that of channel A. Most likely, the di†erence is related to the di†erent basis sets used in the calculations. It is surprising that this leads to signi�cantly J. Chem. Soc., Faraday T rans., 1997, V ol. 93 27Fig. 2 Arrhenius plot of low-pressure limiting rate constants for HOSO]Ar reacting to give (solid line) and (dashed H]SO2 HSO2 line) di†erent values of rate constants.Moreover, neglect of tunnelling in our calculations may also contribute to this di†erence. Conclusion The stable structure and transition states for are cal- HÉSO2 culated at the MP2/6-311G** level. The calculated results show that has a symmetry, and HOSO has a planar HSO2 Cs cis structure while the H atom can rotate almost freely around the OS bond. Variation of the basis set has only minor consequences for tucture, but a†ects the HOSO struc- HSO2 ture signi�cantly.Inclusion of electron correlation is crucial for the determination of the correct geometries of HÉSO2 . The rate constants for rearrangement and dissociation of the HOSO adduct were also calculated with kA\4.79]109 exp([29 845 K/T ) s~1 for dissociation and kB\2.02]109 exp([25 639 K/T ) s~1 for isomerization. We are grateful for support from the Chinese Foundation of Sciences (Grant No. 29573132). We also thank Professor R.G. Gilbert for providing the UNIMOL programs. References 1 E. R. Lovejoy, N. S. Wang and C. J. Howard, J. Phys. Chem., 1987, 91, 5749. 2 V. A. Arutyunov, V. I. Vedeneev, V. A. Ushakov and V. V. Shumova, Kinet. Katal., 1990, 31, 6. 3 V. R. Morris, K-L. Han and W. M. Jackson, J. Phys. Chem., 1995, 99, 10086. 4 K-L. Han, R-C. Lu, Sci. China, in the press. 5 R. J. Boyd, A. Gupta, R. F. Langler, S. P. Lownie and J. A. Pincock, Can. J. Chem., 1980, 58, 331. 6 A. Hinchli†e, J. Mol. Struct., 1981, 71, 349. 7 D. Binns and P. Marshall, J. Chem. Phys., 1995, 95, 4940. 8 V. R. Morris and W. M. Jackson, Chem. Phys. L ett., 1994, 223, 445. 9 D. Laakso, C. E. Smith, A. Goumri, J-D. R. Rocha and P. Marshall, Chem. Phys. L ett., 1994, 227, 377. 10 CRC Handbook of Chemistry and Physics, ed. D. R. Lide, 71st edn., CRC, Boca Raton, FL, 1990. 11 M. W. Chase Jr., C. A. Davies, J. R. Downey Jr., D. J. Frurip, R. A. McDonald and A. N. Syverud, JANAF T hermochemical T ables, 3rd edn. (J. Phys. Chem. Ref. Data 14, Suppl. No. 1, 1985). 12 R. G. Gilbert and S. C. Smith, T heory of Unimolecular and Recombination Reactions, Blackwell, Oxford, 1990. 13 R. G. Gilbert, M. J. T. Jordan and S. C. Smith, UNIMOL programs, 1993. 14 R. C. Reid and T. K. Sherwood, T he Properties of Gases and L iquids, McGraw-Hill, New York, 1958. Paper 6/03116A; Received 3rd May, 1996 28 J. Chem. Soc., Faraday T rans., 1997, V ol.
ISSN:0956-5000
DOI:10.1039/a603116a
出版商:RSC
年代:1997
数据来源: RSC
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Abinitioconfiguration interactioncalculations of ground state and lower excited states ofZn2using optimized Slater-typewavefunctions |
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Journal of the Chemical Society, Faraday Transactions,
Volume 93,
Issue 1,
1997,
Page 29-32
Alfredo Aguado,
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摘要:
pound and d the thickness of the in situ cell]. If an organic solvent of low absorption is used (such as acetone, ethanol or diethyl ether), the necessary concentration increases with increasing X-ray photon energy because the cross-section for X-rays decreases for heavier atoms. XAFS yields quantitative information on short-range order. This requires that the part of the molecule that undergoes a transformation must contain the absorbing element. To facilitate the XAFS analysis, it is advantageous if the monitored element is present only in a few di†erent local environments in the course of the reaction.The fact that the sample is continuously irradiated with X-rays during the experiment does not seem to have a strong inÑuence on the kinetics of the Finkelstein reaction. Were such an e†ect present, one would expect a much faster reaction due to an easier breaking of the BrwC bond. Being aware of these limitations, we believe that in situ XAFS on liquid-state reactions is a valuable tool to obtain structural as well as kinetic information for selected parts of a molecule.Examples could be the study of, e.g., coordination compounds or metalloproteins. Experimental Equal volumes of 1.333 M solutions of 2-bromopropane and NaI in acetone were mixed at room temperature. A tightly closed DSC aluminium crucible was completely �lled with the reaction mixture (ca. 30 ll). The crucible was placed into a Mettler FP 80/84 DSC heat-Ñux calorimeter that was mounted vertically in the synchrotron X-ray beam and heated to 55.0(5) ¡C within 30 s.The experiment was carried out at the Hamburger Synchrotronstrahlungslabor HASYLAB at Deutsches Elektronen-Synchrotron DESY, Germany, at beamline X1 (ROEMO II). This beamline is equipped with a Si(311) double crystal monochromator, yielding approximately 108 photons s~1 mm~2 at the sample. The energy resolution is approximately 2 eV at the bromine K-edge. The DORIS III storage ring was run with positrons of 4.5 GeV at 80È120 mA.Every 8 min 12 s an X-ray absorption spectrum was taken in transmission at the Br K-edge (photon energy ca. 13 475 eV). Reference spectra of crystalline NaBr were simultaneously measured (at room temperature) by use of a third ionization chamber. The sample Br absorption edge jump was limited by the solubility of NaI and the *kd\(It/I0)\0.38, �xed pathlength in the calorimeter. The measured spectra were evaluated with the programs AUTOBK, FEFF and FEFFIT of the University of Washington package.27h29 Multi-electron phenomena lead to a peak at low R in the Br XAFS spectra.30h34 This was corrected by a simpli�ed approach as described in ref. 35. BrieÑy, this peak was isolated in R-space from a NaBr spectrum and back-transformed into k-space. It was then subtracted from all spectra in k-space before evaluation. When quantitatively analysing XAFS spectra of reacting systems, it is important to keep the number of �t-parameters as small as possible to minimize correlation e†ects.13,35,36 By evaluating spectra of pure 2-bromopropane and NaBr at 55 ¡C we determined the following parameters that were kept constant in subsequent �ts of the reaction mixture: p2(BrwCa)\0.0011 ”2, p2(BrwCb)\0.0137 ”2, p2(BrwNa)\0.02593 ”2, R(BrwCb)\2.858 ”, S02(BrwCa)\S02(BrwCb)\1.082, S02(BrwNa)\1.10, eV, E0(BrwCa)\E0(BrwCb)\[0.89 E0(BrwNa)\[1.65 eV.These values are in good agreement with data for similar compounds.13,33,35 was set to Conse- N(BrwCb) 2N(BrwCa).quently, the only �t variables were the mean coordination numbers and N(BrwNa), and the mean distances N(BrwCa) R(BrwNa) and The evaluated XAFS data range R(BrwCa). was k\2.0È7.1 and R\0.8È3.1 throughout all experi- ”~1 ” ments. 2-Bromopropane (99]%), acetone (99.9%; HPLC grade) and NaI (p.a.) were purchased from Aldrich. Hydrate water of NaI was removed before experiments by heating in vacuum. are grateful to HASYLAB for beamtime.We thank A. We Reller and M. Martin for generous support. Financial support was granted by the Deutsche Forschungsgemeinschaft and by the Fonds der Chemischen Industrie. References 1 X-Ray absorption. Principles, applications, techniques of EXAFS, SEXAFS and XANES, ed. D. C. Koningsberger and R. Prins, Wiley, New York, 1988. 2 D. Bazin, H. Dexpert, N. S. Guyot-Sionnest, J. P. Bournonville and J. Lynch, J. Chim. Phys. Phys. Chim. Biol., 1989, 86, 1707. 3 B. S. Clausen, L. G. Ste†ensen, P. L. Hansen and H. Gra- b~k, Catal. L ett., 1993, 20, 23. Tops‘e, 4 G. Sankar, P. A. Wright, S. Natarajan, J. M. Thomas, G. N. Greaves, A. J. Dent, B. R. Dobson, C. A. Ramsdale and R. H. Jones, J. Phys. Chem., 1993, 97, 9550. 5 H. Bertagnolli and T. S. Ertel, Angew. Chem., 1994, 106, 15. 6 T. Maschmeyer, F. Rey, G. Sankar and J. M. Thomas, Nature (L ondon), 1995, 378, 159. 7 A. Hoser, N. Hilbrandt, M. Martin and M. Denecke, Physica B, 1995, 208/209, 321. 8 P. Andrews, J. M. Corker, J. Evans and M. Webster, J. Chem. Soc., Dalton T rans., 1994, 1337. 9 M. Tabata and K. Ozutsumi, Bull. Chem. Soc. Jpn., 1994, 67, 1608. 10 T. S. Ertel, W. Ho. rner, S. Hu. ckmann, U. Kolb, I. Abraham and H. Bertagnolli, Physica B, 1995, 208/209, 641. 11 N. Yoshida and T. Nagamura, Rev. Sci. Instrum., 1995, 66, 52. 12 A. J. Dent, L. J. Farrugia, A. G. Orpen and S. E. Stratford, J. Chem. Soc., Chem. Commun., 1992, 1456. 13 M. Epple, U. Sazama, A. Reller, N.Hilbrandt, M. Martin and L. Tro. ger, Chem. Commun., 1996, 1755. 14 L. Tro. ger, N. Hilbrandt and M. Epple, J. Phys. Coll., 1997, in press. 15 H. Finkelstein, Chem. Ber., 1910, 43, 1528. 16 S. D. Hamann, Aust. J. Chem., 1975, 28, 693. 17 C. D. Chalk, J. McKenna and I. H. Williams, J. Am. Chem. Soc., 1981, 103, 272. 18 L. Eberston, Acta Chem. Scand., Sect. B, 1982, B36, 533. 19 P. B. D. de la Mare, J. Chem. Soc., 1955, 3169. 20 E. D. Hughes, C. K. Ingold and J. D. H. Mackie, J.Chem. Soc., 1955, 3173. 21 E. D. Hughes, C. K. Ingold and J. D. H. Mackie, J. Chem. Soc., 1955, 3177. 22 P. B. D. de la Mare, J. Chem. Soc., 1955, 3180. 23 L. Fowden, E. D. Hughes and C. K. Ingold, J. Chem. Soc., 1955, 3187. 24 L. Fowden, E. D. Hughes and C. K. Ingold, J. Chem. Soc., 1955, 3193. 25 P. B. D. de la Mare, J. Chem. Soc., 1955, 3196. 26 P. B. D. de la Mare, L. Fowden, E. D. Hughes, C. K. Ingold and J. D. H. Mackie, J. Chem. Soc., 1955, 3200. 27 J. J. Rehr, R.C. Albers and S. I. Zabinsky, Phys. Rev. L ett., 1992, 69, 3397. 28 L. Tro. ger, T. Yokoyama, D. Arvanitis, T. Lederer, M. Tischer and K. Baberschke, Phys. Rev. B, 1994, 49, 888. 29 E. A. Stern, M. Newville, B. Ravel, Y. Yacoby and D. Haskel, Physica B, 1995, 208/209, 117. 30 E. A. Stern, S. M. Heald and B. Bunker, Phys. Rev. L ett., 1979, 42, 1372. 31 G. Li, F. Bridges and G. S. Brown, Phys. Rev. L ett., 1992, 68, 1609. 32 P. DÏAngelo, A. Di Cicco, A. Filipponi and N. V.Pavel, Phys. Rev. A, 1993, 47, 2055. 33 E. Burattini, P. DÏAngelo, A. Di Cicco, A. Filipponi and N. V. Pavel, J. Phys. Chem., 1993, 97, 5486. 34 J. J. Rehr, C. H. Booth, F. Bridges and S. I. Zabinsky, Phys. Rev. B, 1994, 49, 12347. 35 M. Epple, H. Kirschnick, G. N. Greaves, G. Sankar and J. M. Thomas, J. Chem. Soc., Faraday T rans., 1996, 5035. 36 M. Epple and L. Tro. ger, J. Chem. Soc., Dalton T rans., 1996, 11. Paper 7/01433C; Received 28th February, 1997 J. Chem. Soc., Faraday T rans., 1997, V ol. 93 3037pound and d the thickness of the in situ cell]. If an organic solvent of low absorption is used (such as acetone, ethanol or diethyl ether), the necessary concentration increases with increasing X-ray photon energy because the cross-section for X-rays decreases for heavier atoms. XAFS yields quantitative information on short-range order. This requires that the part of the molecule that undergoes a transformation must contain the absorbing element. To facilitate the XAFS analysis, it is advantageous if the monitored element is present only in a few di†erent local environments in the course of the reaction.The fact that the sample is continuously irradiated with X-rays during the experiment does not seemtrong inÑuence on the kinetics of the Finkelstein reaction. Were such an e†ect present, one would expect a much faster reaction due to an easier breaking of the BrwC bond. Being aware of these limitations, we believe that in situ XAFS on liquid-state reactions is a valuable tool to obtain structural as well as kinetic information for selected parts of a molecule.Examples could be the study of, e.g., coordination compounds or metalloproteins. Experimental Equal volumes of 1.333 M solutions of 2-bromopropane and NaI in acetone were mixed at room temperature. A tightly closed DSC aluminium crucible was completely �lled with the reaction mixture (ca. 30 ll). The crucible was placed into a Mettler FP 80/84 DSC heat-Ñux calorimeter that was mounted vertically in the synchrotron X-ray beam and heated to 55.0(5) ¡C within 30 s.The experiment was carried out at the Hamburger Synchrotronstrahlungslabor HASYLAB at Deutsches Elektronen-Synchrotron DESY, Germany, at beamline X1 (ROEMO II). This beamline is equipped with a Si(311) double crystal monochromator, yielding approximately 108 photons s~1 mm~2 at the sample. The energy resolution is approximately 2 eV at the bromine K-edge.The DORIS III storage ring was run with positrons of 4.5 GeV at 80È120 mA. Every 8 min 12 s an X-ray absorption spectrum was taken in transmission at the Br K-edge (photon energy ca. 13 475 eV). Reference spectra of crystalline NaBr were simultaneously measured (at room temperature) by use of a third ionization chamber. The sample Br absorption edge jump was limited by the solubility of NaI and the *kd\(It/I0)\0.38, �xed pathlength in the calorimeter. The measured spectra were evaluated with the programs AUTOBK, FEFF and FEFFIT of the University of Washington package.27h29 Multi-electron phenomena lead to a peak at low R in the Br XAFS spectra.30h34 This was corrected by a simpli�ed approach as described in ref. 35. BrieÑy, this peak was isolated in R-space from a NaBr spectrum and back-transformed into k-space. It was then subtracted from all spectra in k-space before evaluation. When quantitatively analysing XAFS spectra of reacting systems, it is important to keep the number of �t-parameters as small as possible to minimize correlation e†ects.13,35,36 By evaluating spectra of pure 2-bromopropane and NaBr at 55 ¡C we determined the following parameters that were kept constant in subsequent �ts of the reaction mixture: p2(BrwCa)\0.0011 ”2, p2(BrwCb)\0.0137 ”2, p2(BrwNa)\0.02593 ”2, R(BrwCb)\2.858 ”, S02(BrwCa)\S02(BrwCb)\1.082, S02(BrwNa)\1.10, eV, E0(BrwCa)\E0(BrwCb)\[0.89 E0(BrwNa)\[1.65 eV. These values are in good agreement with data for similar compounds.13,33,35 was set to Conse- N(BrwCb) 2N(BrwCa).quently, the only �t variables were the mean coordination numbers and N(BrwNa), and the mean distances N(BrwCa) R(BrwNa) and The evaluated XAFS data range R(BrwCa). was k\2.0È7.1 and R\0.8È3.1 throughout all experi- ”~1 ” ments. 2-Bromopropane (99]%), acetone (99.9%; HPLC grade) and NaI (p.a.) were purchased from Aldrich. Hydrate water of NaI was removed before experiments by heating in vacuum.are grateful to HASYLAB for beamtime. We thank A. We Reller and M. Martin for generous support. Financial support was granted by the Deutsche Forschungsgemeinschaft and by the Fonds der Chemischen Industrie. References 1 X-Ray absorption. Principles, applications, techniques of EXAFS, SEXAFS and XANES, ed. D. C. Koningsberger and R. Prins, Wiley, New York, 1988. 2 D. Bazin, H. Dexpert, N. S. Guyot-Sionnest, J. P. Bournonville and J. Lynch, J. Chim. Phys.Phys. Chim. Biol., 1989, 86, 1707. 3 B. S. Clausen, L. G. Ste†ensen, P. L. Hansen and H. Gra- b~k, Catal. L ett., 1993, 20, 23. Tops‘e, 4 G. Sankar, P. A. Wright, S. Natarajan, J. M. Thomas, G. N. Greaves, A. J. Dent, B. R. Dobson, C. A. Ramsdale and R. H. Jones, J. Phys. Chem., 1993, 97, 9550. 5 H. Bertagnolli and T. S. Ertel, Angew. Chem., 1994, 106, 15. 6 T. Maschmeyer, F. Rey, G. Sankar and J. M. Thomas, Nature (L ondon), 1995, 378, 159. 7 A. Hoser, N. Hilbrandt, M. Martin and M.Denecke, Physica B, 1995, 208/209, 321. 8 P. Andrews, J. M. Corker, J. Evans and M. Webster, J. Chem. Soc., Dalton T rans., 1994, 1337. 9 M. Tabata and K. Ozutsumi, Bull. Chem. Soc. Jpn., 1994, 67, 1608. 10 T. S. Ertel, W. Ho. rner, S. Hu. ckmann, U. Kolb, I. Abraham and H. Bertagnolli, Physica B, 1995, 208/209, 641. 11 N. Yoshida and T. Nagamura, Rev. Sci. Instrum., 1995, 66, 52. 12 A. J. Dent, L. J. Farrugia, A. G. Orpen and S. E. Stratford, J. Chem. Soc., Chem. Commun., 1992, 1456. 13 M.Epple, U. Sazama, A. Reller, N. Hilbrandt, M. Martin and L. Tro. ger, Chem. Commun., 1996, 1755. 14 L. Tro. ger, N. Hilbrandt and M. Epple, J. Phys. Coll., 1997, in press. 15 H. Finkelstein, Chem. Ber., 1910, 43, 1528. 16 S. D. Hamann, Aust. J. Chem., 1975, 28, 693. 17 C. D. Chalk, J. McKenna and I. H. Williams, J. Am. Chem. Soc., 1981, 103, 272. 18 L. Eberston, Acta Chem. Scand., Sect. B, 1982, B36, 533. 19 P. B. D. de la Mare, J. Chem. Soc., 1955, 3169. 20 E. D. Hughes, C. K. Ingold and J. D. H. Mackie, J. Chem. Soc., 1955, 3173. 21 E. D. Hughes, C. K. Ingold and J. D. H. Mackie, J. Chem. Soc., 1955, 3177. 22 P. B. D. de la Mare, J. Chem. Soc., 1955, 3180. 23 L. Fowden, E. D. Hughes and C. K. Ingold, J. Chem. Soc., 1955, 3187. 24 L. Fowden, E. D. Hughes and C. K. Ingold, J. Chem. Soc., 1955, 3193. 25 P. B. D. de la Mare, J. Chem. Soc., 1955, 3196. 26 P. B. D. de la Mare, L. Fowden, E. D. Hughes, C. K. Ingold and J. D. H. Mackie, J.Chem. Soc., 1955, 3200. 27 J. J. Rehr, R. C. Albers and S. I. Zabinsky, Phys. Rev. L ett., 1992, 69, 3397. 28 L. Tro. ger, T. Yokoyama, D. Arvanitis, T. Lederer, M. Tischer and K. Baberschke, Phys. Rev. B, 1994, 49, 888. 29 E. A. Stern, M. Newville, B. Ravel, Y. Yacoby and D. Haskel, Physica B, 1995, 208/209, 117. 30 E. A. Stern, S. M. Heald and B. Bunker, Phys. Rev. L ett., 1979, 42, 1372. 31 G. Li, F. Bridges and G. S. Brown, Phys. Rev. L ett., 1992, 68, 1609. 32 P. DÏAngelo, A.Di Cicco, A. Filipponi and N. V. Pavel, Phys. Rev. A, 1993, 47, 2055. 33 E. Burattini, P. DÏAngelo, A. Di Cicco, A. Filipponi and N. V. Pavel, J. Phys. Chem., 1993, 97, 5486. 34 J. J. Rehr, C. H. Booth, F. Bridges and S. I. Zabinsky, Phys. Rev. B, 1994, 49, 12347. 35 M. Epple, H. Kirschnick, G. N. Greaves, G. Sankar and J. M. Thomas, J. Chem. Soc., Faraday T rans., 1996, 5035. 36 M. Epple and L. Tro. ger, J. Chem. Soc., Dalton T rans., 1996, 11. Paper 7/01433C; Received 28th February, 1997 J.Chem. Soc., Faraday T rans., 1997, V ol. 93 3037pound and d the thickness of the in situ cell]. If an organic solvent of low absorption is used (such as acetone, ethanol or diethyl ether), the necessary concentration increases with increasing X-ray photon energy because the cross-section for X-rays decreases for heavier atoms. XAFS yields quantitative information on short-range order. This requires that the part of the molecule that undergoes a transformation must contain the absorbing element.To facilitate the XAFS analysis, it is advantageous if the monitored element is present only in a few di†erent local environments in the course of the reaction. The fact that the sample is continuously irradiated with X-rays during the experiment does not seem to have a strong inÑuence on the kinetics of the Finkelstein reaction. Were such an e†ect present, one would expect a much faster reaction due to an easier breaking of the BrwC bond. Being aware of these limitations, we believe that in situ XAFS on liquid-state reactions is a valuable tool to obtain structural as well as kinetic information for selected parts of a molecule.Examples could be the study of, e.g., coordination compounds or metalloproteins. Experimental Equal volumes of 1.333 M solutions of 2-bromopropane and NaI in acetone were mixed at room temperature. A tightly closed DSC aluminium crucible was completely �lled with the reaction mixture (ca. 30 ll). The crucible was placed into a Mettler Fat-Ñux calorimeter that was mounted vertically in the synchrotron X-ray beam and heated to 55.0(5) ¡C within 30 s. The experiment was carried out at the Hamburger Synchrotronstrahlungslabor HASYLAB at Deutsches Elektronen-Synchrotron DESY, Germany, at beamline X1 (ROEMO II). This beamline is equipped with a Si(311) double crystal monochromator, yielding approximately 108 photons s~1 mm~2 at the sample.The energy resolution is approximately 2 eV at the bromine K-edge. The DORIS III storage ring was run with positrons of 4.5 GeV at 80È120 mA. Every 8 min 12 s an X-ray absorption spectrum was taken in transmission at the Br K-edge (photon energy ca. 13 475 eV). Reference spectra of crystalline NaBr were simultaneously measured (at room temperature) by use of a third ionization chamber. The sample Br absorption edge jump was limited by the solubility of NaI and the *kd\(It/I0)\0.38, �xed pathlength in the calorimeter.The measured spectra were evaluated with the programs AUTOBK, FEFF and FEFFIT of the University of Washington package.27h29 Multi-electron phenomena lead to a peak at low R in the Br XAFS spectra.30h34 This was corrected by a simpli�ed approach as described in ref. 35. BrieÑy, this peak was isolated in R-space from a NaBr spectrum and back-transformed into k-space. It was then subtracted from all spectra in k-space before evaluation.When quantitatively analysing XAFS spectra of reacting systems, it is important to keep the number of �t-parameters as small as possible to minimize correlation e†ects.13,35,36 By evaluating spectra of pure 2-bromopropane and NaBr at 55 ¡C we determined the following parameters that were kept constant in subsequent �ts of the reaction mixture: p2(BrwCa)\0.0011 ”2, p2(BrwCb)\0.0137 ”2, p2(BrwNa)\0.02593 ”2, R(BrwCb)\2.858 ”, S02(BrwCa)\S02(BrwCb)\1.082, S02(BrwNa)\1.10, eV, E0(BrwCa)\E0(BrwCb)\[0.89 E0(BrwNa)\[1.65 eV.These values are in good agreement with data for similar compounds.13,33,35 was set to Conse- N(BrwCb) 2N(BrwCa). quently, the only �t variables were the mean coordination numbers and N(BrwNa), and the mean distances N(BrwCa) R(BrwNa) and The evaluated XAFS data range R(BrwCa). was k\2.0È7.1 and R\0.8È3.1 throughout all experi- ”~1 ” ments. 2-Bromopropane (99]%), acetone (99.9%; HPLC grade) and NaI (p.a.) were purchased from Aldrich.Hydrate water of NaI was removed before experiments by heating in vacuum. are grateful to HASYLAB for beamtime. We thank A. We Reller and M. Martin for generous support. Financial support was granted by the Deutsche Forschungsgemeinschaft and by the Fonds der Chemischen Industrie. References 1 X-Ray absorption. Principles, applications, techniques of EXAFS, SEXAFS and XANES, ed. D. C. Koningsberger and R. Prins, Wiley, New York, 1988. 2 D. Bazin, H. Dexpert, N. S. Guyot-Sionnest, J.P. Bournonville and J. Lynch, J. Chim. Phys. Phys. Chim. Biol., 1989, 86, 1707. 3 B. S. Clausen, L. G. Ste†ensen, P. L. Hansen and H. Gra- b~k, Catal. L ett., 1993, 20, 23. Tops‘e, 4 G. Sankar, P. A. Wright, S. Natarajan, J. M. Thomas, G. N. Greaves, A. J. Dent, B. R. Dobson, C. A. Ramsdale and R. H. Jones, J. Phys. Chem., 1993, 97, 9550. 5 H. Bertagnolli and T. S. Ertel, Angew. Chem., 1994, 106, 15. 6 T. Maschmeyer, F. Rey, G. Sankar and J. M. Thomas, Nature (L ondon), 1995, 378, 159. 7 A. Hoser, N. Hilbrandt, M. Martin and M. Denecke, Physica B, 1995, 208/209, 321. 8 P. Andrews, J. M. Corker, J. Evans and M. Webster, J. Chem. Soc., Dalton T rans., 1994, 1337. 9 M. Tabata and K. Ozutsumi, Bull. Chem. Soc. Jpn., 1994, 67, 1608. 10 T. S. Ertel, W. Ho. rner, S. Hu. ckmann, U. Kolb, I. Abraham and H. Bertagnolli, Physica B, 1995, 208/209, 641. 11 N. Yoshida and T. Nagamura, Rev. Sci. Instrum., 1995, 66, 52. 12 A. J. Dent, L. J. Farrugia, A. G. Orpen and S.E. Stratford, J. Chem. Soc., Chem. Commun., 1992, 1456. 13 M. Epple, U. Sazama, A. Reller, N. Hilbrandt, M. Martin and L. Tro. ger, Chem. Commun., 1996, 1755. 14 L. Tro. ger, N. Hilbrandt and M. Epple, J. Phys. Coll., 1997, in press. 15 H. Finkelstein, Chem. Ber., 1910, 43, 1528. 16 S. D. Hamann, Aust. J. Chem., 1975, 28, 693. 17 C. D. Chalk, J. McKenna and I. H. Williams, J. Am. Chem. Soc., 1981, 103, 272. 18 L. Eberston, Acta Chem. Scand., Sect. B, 1982, B36, 533. 19 P.B. D. de la Mare, J. Chem. Soc., 1955, 3169. 20 E. D. Hughes, C. K. Ingold and J. D. H. Mackie, J. Chem. Soc., 1955, 3173. 21 E. D. Hughes, C. K. Ingold and J. D. H. Mackie, J. Chem. Soc., 1955, 3177. 22 P. B. D. de la Mare, J. Chem. Soc., 1955, 3180. 23 L. Fowden, E. D. Hughes and C. K. Ingold, J. Chem. Soc., 1955, 3187. 24 L. Fowden, E. D. Hughes and C. K. Ingold, J. Chem. Soc., 1955, 3193. 25 P. B. D. de la Mare, J. Chem. Soc., 1955, 3196. 26 P. B. D. de la Mare, L. Fowden, E.D. Hughes, C. K. Ingold and J. D. H. Mackie, J. Chem. Soc., 1955, 3200. 27 J. J. Rehr, R. C. Albers and S. I. Zabinsky, Phys. Rev. L ett., 1992, 69, 3397. 28 L. Tro. ger, T. Yokoyama, D. Arvanitis, T. Lederer, M. Tischer and K. Baberschke, Phys. Rev. B, 1994, 49, 888. 29 E. A. Stern, M. Newville, B. Ravel, Y. Yacoby and D. Haskel, Physica B, 1995, 208/209, 117. 30 E. A. Stern, S. M. Heald and B. Bunker, Phys. Rev. L ett., 1979, 42, 1372. 31 G. Li, F. Bridges and G. S.Brown, Phys. Rev. L ett., 1992, 68, 1609. 32 P. DÏAngelo, A. Di Cicco, A. Filipponi and N. V. Pavel, Phys. Rev. A, 1993, 47, 2055. 33 E. Burattini, P. DÏAngelo, A. Di Cicco, A. Filipponi and N. V. Pavel, J. Phys. Chem., 1993, 97, 5486. 34 J. J. Rehr, C. H. Booth, F. Bridges and S. I. Zabinsky, Phys. Rev. B, 1994, 49, 12347. 35 M. Epple, H. Kirschnick, G. N. Greaves, G. Sankar and J. M. Thomas, J. Chem. Soc., Faraday T rans., 1996, 5035. 36 M. Epple and L. Tro. ger, J. Chem.Soc., Dalton T rans., 1996, 11. Paper 7/01433C; Received 28th February, 1997 J. Chem. Soc., Faraday T rans., 1997, V ol. 93 3037pound and d the thickness of the in situ cell]. If an organic solvent of low absorption is used (such as acetone, ethanol or diethyl ether), the necessary concentration increases with increasing X-ray photon energy because the cross-section for X-rays decreases for heavier atoms. XAFS yields quantitative information on short-range order. This requires that the part of the molecule that undergoes a transformation must contain the absorbing element.To facilitate the XAFS analysis, it is advantageous if the monitored element is present only in a few di†erent local environments in the course of the reaction. The fact that the sample is continuously irradiated with X-rays during the experiment does not seem to have a strong inÑuence on the kinetics of the Finkelstein reaction. Were such an e†ect present, one would expect a much faster reaction due to an easier breaking of the BrwC bond.Being aware of these limitations, we believe that in situ XAFS on liquid-state reactions is a valuable tool to obtain structural as well as kinetic information for selected parts of a molecule. Examples could be the study of, e.g., coordination compounds or metalloproteins. Experimental Equal volumes of 1.333 M solutions of 2-bromopropane and NaI in acetone were mixed at room temperature. A tightly closed DSC aluminium crucible was completely �lled with the reaction mixture (ca. 30 ll). The crucible was placed into a Mettler FP 80/84 DSC heat-Ñux calorimeter that was mounted vertically in the synchrotron X-ray beam and heated to 55.0(5) ¡C within 30 s. The experiment was carried out at the Hamburger Synchrotronstrahlungslabor HASYLAB at Deutsches Elektronen-Synchrotron DESY, Germany, at beamline X1 (ROEMO II). This beamline is equipped with a Si(311) double crystal monochromator, yielding approximately 108 photons s~1 mm~2 at the sample.The energy resolution is approximately 2 eV at the bromine K-edge. The DORIS III storage ring was run with positrons of 4.5 GeV at 80È120 mA. Every 8 min 12 s an X-ray absorption spectrum was taken in transmission at the Br K-edge (photon energy ca. 13 475 eV). Reference spectra of crystalline multaneously measured (at room temperature) by use of a third ionization chamber. The sample Br absorption edge jump was limited by the solubility of NaI and the *kd\(It/I0)\0.38, �xed pathlength in the calorimeter.The measured spectra were evaluated with the programs AUTOBK, FEFF and FEFFIT of the University of Washington package.27h29 Multi-electron phenomena lead to a peak at low R in the Br XAFS spectra.30h34 This was corrected by a simpli�ed approach as described in ref. 35. BrieÑy, this peak was isolated in R-space from a NaBr spectrum and back-transformed into k-space. It was then subtracted from all spectra in k-space before evaluation.When quantitatively analysing XAFS spectra of reacting systems, it is important to keep the number of �t-parameters as small as possible to minimize correlation e†ects.13,35,36 By evaluating spectra of pure 2-bromopropane and NaBr at 55 ¡C we determined the following parameters that were kept constant in subsequent �ts of the reaction mixture: p2(BrwCa)\0.0011 ”2, p2(BrwCb)\0.0137 ”2, p2(BrwNa)\0.02593 ”2, R(BrwCb)\2.858 ”, S02(BrwCa)\S02(BrwCb)\1.082, S02(BrwNa)\1.10, eV, E0(BrwCa)\E0(BrwCb)\[0.89 E0(BrwNa)\[1.65 eV.These values are in good agreement with data for similar compounds.13,33,35 was set to Conse- N(BrwCb) 2N(BrwCa). quently, the only �t variables were the mean coordination numbers and N(BrwNa), and the mean distances N(BrwCa) R(BrwNa) and The evaluated XAFS data range R(BrwCa). was k\2.0È7.1 and R\0.8È3.1 throughout all experi- ”~1 ” ments. 2-Bromopropane (99]%), acetone (99.9%; HPLC grade) and NaI (p.a.) were purchased from Aldrich.Hydrate water of NaI was removed before experiments by heating in vacuum. are grateful to HASYLAB for beamtime. We thank A. We Reller and M. Martin for generous support. Financial support was granted by the Deutsche Forschungsgemeinschaft and by the Fonds der Chemischen Industrie. References 1 X-Ray absorption. Principles, applications, techniques of EXAFS, SEXAFS and XANES, ed. D. C. Koningsberger and R. Prins, Wiley, New York, 1988. 2 D. Bazin, H. Dexpert, N. S. Guyot-Sionnest, J. P. Bournonville and J. Lynch, J. Chim. Phys. Phys. Chim. Biol., 1989, 86, 1707. 3 B. S. Clausen, L. G. Ste†ensen, P. L. Hansen and H. Gra- b~k, Catal. L ett., 1993, 20, 23. Tops‘e, 4 G. Sankar, P. A. Wright, S. Natarajan, J. M. Thomas, G. N. Greaves, A. J. Dent, B. R. Dobson, C. A. Ramsdale and R. H. Jones, J. Phys. Chem., 1993, 97, 9550. 5 H. Bertagnolli and T. S. Ertel, Angew. Chem., 1994, 106, 15. 6 T. Maschmeyer, F. Rey, G.Sankar and J. M. Thomas, Nature (L ondon), 1995, 378, 159. 7 A. Hoser, N. Hilbrandt, M. Martin and M. Denecke, Physica B, 1995, 208/209, 321. 8 P. Andrews, J. M. Corker, J. Evans and M. Webster, J. Chem. Soc., Dalton T rans., 1994, 1337. 9 M. Tabata and K. Ozutsumi, Bull. Chem. Soc. Jpn., 1994, 67, 1608. 10 T. S. Ertel, W. Ho. rner, S. Hu. ckmann, U. Kolb, I. Abraham and H. Bertagnolli, Physica B, 1995, 208/209, 641. 11 N. Yoshida and T. Nagamura, Rev. Sci. Instrum., 1995, 66, 52. 12 A. J. Dent, L. J. Farrugia, A. G. Orpen and S. E. Stratford, J. Chem. Soc., Chem. Commun., 1992, 1456. 13 M. Epple, U. Sazama, A. Reller, N. Hilbrandt, M. Martin and L. Tro. ger, Chem. Commun., 1996, 1755. 14 L. Tro. ger, N. Hilbrandt and M. Epple, J. Phys. Coll., 1997, in press. 15 H. Finkelstein, Chem. Ber., 1910, 43, 1528. 16 S. D. Hamann, Aust. J. Chem., 1975, 28, 693. 17 C. D. Chalk, J. McKenna and I. H. Williams, J. Am. Chem. Soc., 1981, 103, 272. 18 L. Eberston, Acta Chem. Scand., Sect. B, 1982, B36, 533. 19 P. B. D. de la Mare, J. Chem. Soc., 1955, 3169. 20 E. D. Hughes, C. K. Ingold and J. D. H. Mackie, J. Chem. Soc., 1955, 3173. 21 E. D. Hughes, C. K. Ingold and J. D. H. Mackie, J. Chem. Soc., 1955, 3177. 22 P. B. D. de la Mare, J. Chem. Soc., 1955, 3180. 23 L. Fowden, E. D. Hughes and C. K. Ingold, J. Chem. Soc., 1955, 3187. 24 L. Fowden, E. D. Hughes and C. K. Ingold, J. Chem. Soc., 1955, 3193. 25 P. B. D. de la Mare, J. Chem. Soc., 1955, 3196. 26 P. B. D. de la Mare, L. Fowden, E. D. Hughes, C. K. Ingold and J. D. H. Mackie, J. Chem. Soc., 1955, 3200. 27 J. J. Rehr, R. C. Albers and S. I. Zabinsky, Phys. Rev. L ett., 1992, 69, 3397. 28 L. Tro. ger, T. Yokoyama, D. Arvanitis, T. Lederer, M. Tischer and K. Baberschke, Phys. Rev. B, 1994, 49, 888. 29 E. A. Stern, M. Newville, B. Ravel, Y. Yacoby and D. Haskel, Physica B, 1995, 208/209, 117. 30 E. A. Stern, S. M. Heald and B. Bunker, Phys. Rev. L ett., 1979, 42, 1372. 31 G. Li, F. Bridges and G. S. Brown, Phys. Rev. L ett., 1992, 68, 1609. 32 P. DÏAngelo, A. Di Cicco, A. Filipponi and N. V. Pavel, Phys. Rev. A, 1993, 47, 2055. 33 E. Burattini, P. DÏAngelo, A. Di Cicco, A. Filipponi and N. V. Pavel, J. Phys. Chem., 1993, 97, 5486. 34 J. J. Rehr, C. H. Booth, F. Bridges and S. I. Zabinsky, Phys. Rev. B, 1994, 49, 12347. 35 M. Epple, H. Kirschnick, G. N. Greaves, G. Sankar and J. M. Thomas, J. Chem. Soc., Faraday T rans., 1996, 5035. 36 M. Epple and L. Tro. ger, J. Chem. Soc., Dalton T rans., 1996, 11. Paper 7/01433C; Received 28th February, 1997 J. Chem. Soc., Faraday T rans., 1997, V o
ISSN:0956-5000
DOI:10.1039/a604618e
出版商:RSC
年代:1997
数据来源: RSC
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Boron dichloride and its cation Geometries, vibrationalfrequencies, ionization energy and excitationenergies |
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Journal of the Chemical Society, Faraday Transactions,
Volume 93,
Issue 1,
1997,
Page 53-61
Oliver Warschkow,
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摘要:
Boron dichloride and its cation Geometries, vibrational frequencies, ionization energy and excitation energies Oliver Warschkow, Edmond P. F. Lee*� and Timothy G. Wright*” Chemistry Department, T he University, High�eld, Southampton, UK SO17 1BJ The geometries and harmonic vibrational frequencies of and have been calculated at various levels of ab initio theory BCl2 BCl2 ` [MP2, MP4(SDQ), CISD and CCSD(T)] and density functional theory (BLYP and B3LYP), using a variety of basis sets.These calculations show the neutral molecule to be bent, with a bond angle of ca. 125¡, and the cation to be linear. Calculated vibrational frequencies were compared with experimental values, where available, including isotopic shifts. The ionization energy of the molecule was calculated to be 7.33 eV at the Gaussian-2 level of theory ; additionally, the heat of formation of the BCl2 cation was calculated to be 160.4 kcal mol~1. Finally, CIS and MRDCI calculations were performed, in order to ascertain the position of excited electronic states for both the cation and the neutral molecule; the calculated excitation energies were then compared with reported energies for transitions in these species.Boron trichloride is used extensively for the etching of various semiconductor surfaces.1 In order to understand and control the chemistry of the plasmas used in such etching procedures, it is necessary to be able to determine the species present and their concentrations and local temperatures, and then to model the plasmas.2,3 Such models depend critically on the accuracy of inputted spectroscopic and thermodynamic data, and so it is of extreme importance to determine such data.Spectroscopic data is useful not only from the modelling point of view, but also with regard to detecting the species present,4 using such techniques as laser-induced Ñuorescence (LIF) and resonance-enhanced multiphoton ionization (REMPI). In the particular case of plasmas, although some BCl3-containing data are available for the parent and the fragment BCl BCl3 species and their cations, almost nothing is known about the other major fragment species or its cation, with even the BCl2 ionization energy having only been estimated, even though it has been noted that is very likely present in plasmas (ref.BCl2 2 and other references noted below). In this work, three areas are considered : the geometry and vibrational frequencies of both the ground neutral and cationic states of the ionization energy of and the BCl2 ; BCl2 ; excitation energies of excited electronic states (relative to the respective ground state) of both the neutral molecule and cation. 1 Geometry and vibrational frequencies of BCl2 and BCl2 ë Theoretical methods Geometry optimizations were performed at various levels of theory for the ground state of both the neutral molecule and the cation. A number of basis sets were used to ascertain that convergence had been obtained for the geometric parameters. The levels of theory used were: MP2/6-31G*, MP2/cc-pVDZ, MP2/cc-pVTZ, MP4(SDQ)/cc-pVTZ, CCSD(T)/cc-pVDZ and CCSD(T)/6-311G(2d).In addition, CISD/cc-pVDZ and CISD/ cc-pVTZ calculations were performed for the ground-state cation. As well as these ab initio methods, density functional theory (DFT) was also used at various levels, to ascertain its accuracy for these species. The levels of DFT theory used were: BLYP/6-31G*, BLYP/cc-pVDZ, BLYP/cc-pVTZ, � E-mail address : epl=soton.ac.uk ” E-mail address : tgw=soton.ac.uk B3LYP/cc-pVDZ and B3LYP/cc-pVTZ. For the neutral ground state, which is a doublet, unrestricted-spin HartreeÈ Fock wavefunctions were used, but spin contamination was found to be small (vide infra).Nevertheless, as an additional check, ROMP2/6-31G* calculations were also performed and compared to the UMP2/6-31G* geometries and vibrational frequencies. Many common acronyms have been used above: MPn is perturbation theory5 carried out to the nth M‘llerÈPlesset order, with SDQ indicating that single, double and quadruple (but not triple) substitutions have been used; ROMP2 implies the use of a restricted open-shell HF wavefunction for the MP2 procedure, using the method of Handy and co-workers;6 CCSD(T)7 is the coupled cluster method, employing single and double substitutions, but using a perturbative method for inclusion of the triple substitutions ; BLYP stands for the Becke88 exchange functional,8 with the Lee, Yang and Parr (LYP) correlation functional ;9 and B3LYP is a hybrid functional which contains some HartreeÈFock exchange energy, it is based on BeckeÏs three-parameter �t10 to Gaussian-1 (G1) energies.The basis sets used are either the standard 6-31G* and 6-311G(2d) split-valence basis sets, or the relatively recent correlation consistent basis sets (cc-pVXZ) of Dunning et al.11 Geometry optimizations were performed using analytic gradient methods, except for the CCSD(T) calculations for which numerical methods were employed.Similarly, analytic secondderivative methods were used to calculate harmonic vibrational frequencies, except for the MP4(SDQ), CISD and CCSD(T) calculations for which numerical methods were utilized. All the above calculations were performed with GAUSSIAN 94,12 except for the ROMP2 calculations, which were performed with CADPAC.13 Background is a 17-electron system, and is therefore expected to be BCl2 bent, on the basis of Walsh diagrams;14 similarly, the 16-electron species is expected to be linear.is valence BCl2 ` (BCl2 ` isoelectronic with the beryllium and magnesium diÑuorides and dichlorides, which are known to be linear.15) The only spectroscopic evidence for the geometry of the neutral species comes from a matrix isolation study by Miller and Andrews16 who derived a bond angle of 125^5¡. The latter estimate is also in agreement with an EPR study,17 where a bond angle of ca. 122¡ was obtained. There is no experimental information available on the ground-state geometry. BCl2 ` J. Chem. Soc., Faraday T rans., 1997, 93(1), 53È61 53With regard to the vibrational frequencies, values for BCl2 of 470, 240 and 990 cm~1 (apparently estimated by comparison with were used by Dessaux et al. to assign a chemi- BCl3) luminescence spectrum obtained by reacting H atoms with however, the reference they quote in that work is an BCl3 ;18 early version of the JANAF Tables.Later JANAF tables19 have the following values : 720, 240 and 980 cm~1, thus there is some doubt as to the assignment of the chemiluminescence spectrum presented in ref. 18. Miller and Andrews obtained IR spectra of the species present after had undergone BCl3 proton radiolysis in an argon matrix.16 They obtained values of 731 and 965.7 cm~1 for assigned to and 11BCl2 , l1 l3 , respectively, with the frequency of the isotopomer l3 10BCl2 being measured at 1004.3 cm~1 (note that the 731 cm~1 value was reassigned later to For the cation, there are HBCl2 20).two pieces of information available : the �rst comes from a synchrotron radiation study21 of the decay processes of the cation from excited electronic states. In that work, BCl3 ` absorption of 17.71 eV energy photons led to Ñuorescence, which was dispersed, leading to the observation of a vibrational progression. Although the assignment of the Ñuorescence (on energetic grounds) to was deemed to be clear, BCl2 ` it could not be unambiguously determined whether this progression was due to vibrational excitation in the upper electronically excited state or the ground state.The progression had a frequency of 650^30 cm~1 and was thought to arise from a progression of with the upper and lower states 2l2 , assumed to be linear, and that the upper state had relaxed to the vibrational ground state (leading to the observation of only even quanta of the bend vibration) ; this assignment then leads to a ground-state bending frequency of ca. 325 cm~1. Further remarks on the assignment of the dispersed Ñuorescence observed in ref. 21 will be made in Section 3 and later in this section. The second source of information on BCl2 ` comes from the JANAF Tables,19 where values of the vibraquencies of 500, 120 and 800 cm~1 were estimated by comparison with these values will be seen to be far from CO2 ; the calculated values obtained here.Results and Discussion The results of the ab initio calculations are given in Tables 1 and 2. It is only possible to compare calculated results with experimental values for the ground-state neutral It is (X3 2A1). clear that, as far as the geometry is concerned, all levels of theory predict a bond angle in the range 125^1¡, in very Table 1 Calculated geometries and vibrational frequencies of BCl2 ` (X 1&g `)a method [energy(]943)/Eh bond length/” bond angle/degrees l1/cm~1 l2/cm~1 l3/cm~1 MP2/6-31G* 0.726 463 1.6112 180 588.4 (0) 282.8 (17) 1504.2 (668) MP2/cc-pVDZ 0.782 140 1.6282 180 574.2 (0) 316.4 (17) 1489.0 (648) MP2/cc-pVTZ 0.932 252 1.6157 180 572.8 (0) 328.4 (15) 1482.1 (621) MP4(SDQ)/cc-pVDZ 0.807 511 1.6320 180 565.1 (0) 315.7 (18) 1463.5 (643) CISD/cc-pVDZ 0.770 285 1.6265 180 573.8 (0) 321.9 (21) 1480.2 (695) CISD/cc-pVTZ 0.908 050 1.6129 180 575.9 (0) 337.1 (19) 1479.7 (680) CCSD(T)/cc-pVDZ 0.819 007 1.6345 180 561.3 (È) 311.6 (È) 1457.6 (È) CCSD(T)/6-311G(2d) 0.877 725 1.6199 180 553.4 (È) 324.3 (È) 1420.0 (È) BLYP/6-31G* 1.932 216 1.6319 180 546.4 (0) 291.0 (14) 1415.8 (478) BLYP/cc-pVDZ 1.977 425 1.6386 180 540.3 (0) 303.4 (12) 1416.8 (492) BLYP/cc-pVTZ 2.020 834 1.6263 180 544.2 (0) 316.6 (12) 1412.7 (479) B3LYP/cc-pVDZ 2.017 520 1.6276 180 558.1 (0) 312.5 (16) 1456.0 (574) B3LYP/cc-pVTZ 2.059 340 1.6163 180 560.6 (0) 326.1 (15) 1449.9 (553) a Values in parentheses in the vibrational frequencies columns are the calculated IR intensities in units of km mol~1.Table 2 Calculated geometries and vibrational frequencies of BCl2 (X3 2A1)a,b method [energy(]943)/Eh bond length/” bond angle/degrees l1/cm~1 l2/cm~1 l3/cm~1 UMP2/6-31G* 0.983 213 1.7225 125.3 741.2 (31) 298.9 (2) 1032.2 (438) SS2T\0.754 ROMP2/6-31G* 1.007 009 1.7201 125.0 744.5 (34) 296.4 (2) 1034.0 (430) UMP2/cc-pVDZ 1.042 754 1.7404 125.0 731.1 (33) 290.2 (1) 1019.0 (443) SS2T\0.755 UMP2/cc-pVTZ 1.195 238 1.7259 125.2 717.2 (26) 288.3 (1) 1007.2 (416) SS2T\0.756 UMP4(SDQ)/cc-pVDZ 1.070 419 1.7451 125.2 721.7 (32) 288.2 (1) 1010.7 (427) SS2T\0.755 CCSD(T)/cc-pVDZ 1.080 569 1.7479 125.1 715.6 (È) 285.7 (È) 1001.9 (È) SS2T\0.755 CCSD(T)/6-311G(2d) 1.143 156 1.7374 125.3 692.5 (È) 287.6 (È) 956.3 (È) SS2T\0.755 BLYP/6-31G* 2.195 825 1.7540 125.2 667.8 (25) 277.9 (1) 925.5 (380) SS2T\0.752 BLYP/cc-pVDZ 2.241 713 1.7594 125.0 668.5 (23) 272.9 (1) 930.7 (378) SS2T\0.752 BLYP/cc-pVTZ 2.283 463 1.7439 125.7 658.7 (19) 273.6 (0) 925.9 (366) SS2T\0.752 B3LYP/cc-pVDZ 2.291 501 1.7456 124.9 695.5 (28) 281.1 (1) 971.0 (408) SS2T\0.752 B3LYP/cc-pVTZ 2.330 485 1.7314 125.6 684.5 (22) 281.4 (1) 964.0 (389) SS2T\0.753 experimental (ref. 16) È È 125^5 731 È 965.7 (matrix isolation) a Values in parentheses in the vibrational frequencies columns are the calculated IR intensities in units of km mol~1. b All calculations employ the frozen core approximation, except for the ROMP2 calculation, which includes all orbitals. 54 J. Chem. Soc., Faraday T rans., 1997, V ol. 93Table 3 Calculated vibrational frequencies for the six iso- BCl2 topomers at the CCSD(T)/cc-pVDZ level isotopomer Cl-B-Cl l1/cm~1 l2/cm~1 l3/cm~1 35-11-35 715.6 285.7 1001.8 37-11-37 709.3 279.3 997.3 35-11-37 712.4 282.5 999.5 35-10-35 739.2 288.2 1042.5 37-10-37 733.2 281.7 1038.2 35-10-37 736.2 285.0 1040.3 good agreement with the experimental estimates.16,17 The bond length has not been obtained experimentally, but the calculations suggest that a value of 1.74^0.01 should be ” reliable ; a value of 1.73 is quoted in the JANAF Tables,19 ” which is an estimated value, intermediate between those for BCl and The vibrational frequencies seem to be a little BCl3 .more sensitive to the level of theory used than the geometry. It appears that, although the frequency is close to con- l2 vergence, there is still some decreasing of the and values, l1 l3 even at the highest levels of theory used here.The computed values are close to the experimental value, but the value l3 l1 is converging to a value signi�cantly lower than the experimental one,16 and perhaps agrees with the fact that this assignment was later20 changed. Comparing now the ab initio calculations and the DFT calculations (Table 2) for the neutral molecule, it can be seen that the B3LYP/cc-pVTZ values are extremely close to the CCSD(T)/6-311G(2d) results but, of course, the DFT calculations are signi�cantly cheaper, computationally. This excellent performance of DFT calculations has been noted previously by Martin et al.,22 amongst others.This good agreement is even more pronounced for the cationic frequencies (Table 1) where the B3LYP/cc-pVTZ results are almost exactly the same as the CCSD(T)/6-311G(2d) values. Clearly, the DFT results in both the cationic and neutral cases appear to be more or less converged.The close agreement of the converged DFT and the CCSD(T)/6-311G(2d) results suggests that these values must be very close to the true experimental harmonic vibrational frequencies. These values are also in fairly close agreement with the estimated values in the JANAF Tables.19 Although the SS2T values for the neutral molecule are very close to the theoretical value (0.75) for the unrestricted calculations, an additional check for lack of spin-contamination e†ects was made by performing ROHF and ROMP2 calculations.As may be seen from Table 2, the agreement between the geometries and vibrational frequencies for UMP2 and ROMP2 is excellent, showing that the small amount of spin contamination is not having a signi�cant e†ect on any calculated properties. For the cation, comparison of the calculated harmonic vibrational frequencies with the estimated values from the JANAF Tables,19 shows that there is very poor agreement here ; only the frequency is close to the calculated value, l1 with the other two being too small by almost a factor of two; this will clearly have implications for the thermodynamic data calculated therein using these values. Considering now the dispersed Ñuorescence spectrum of Biehl et al.,21 where a progression of 650^30 cm~1 was observed and assigned to a progression of in the ground state of the cation.The com- 2l2 puted values of shown in Table 1, suggest that the fre- l2 , l2 quency is ca. 310^20 cm~1, which would be in excellent agreement with the frequency of ca. 325 cm~1 assigned l2 from the Ñuorescence spectrum; however, for the only-even-l2 selection rule to hold (and assuming that the upper state is in its ground vibrational level) there must be a linear excited state of energetically accessible in the synchrotron BCl2 ` studies (vide infra). The structure observed in the dispersed Ñuorescence spectrum of ref. 21 could be due to the upper or lower state of the transition, and so two studies are made in the present work: �rst, to scan the excited states of the cation to see which states are energetically viable candidates for the upper state of the dispersed Ñuorescence; and secondly, to optimize the structure and calculate the vibrational frequencies of the upper state that seems the most likely candidate.These two sets of calculations will be presented in Section 3. Isotopic shifts Miller and Andrews16 obtained an isotopic shift for the l3 mode: for the and isotopomers, the ratio was 11BCl2 10BCl2 965.7 : 1004.3(0.962 : 1.000).For completeness, the isotopic shift was calculated for all six isotopomers at the CCSD(T)/ccpVDZ level (including the 10B and 11B, and the 35Cl and 37Cl isotopes)Èthe results are given in Table 3. The corresponding ratio for the 35-11-35 and 35-10-35 isotopomers is calculated to be 0.961 : 1.000, clearly in excellent agreement with experiment, even though the absolute values are not in such good agreement. 2 Ionization energy of BCl2 Background There has been no direct measurement of the ionization energy of and theonly been three experimental BCl2 , estimates : two based on fragmentation processes in mass spectrometric experiments, the other based on Ñuorescence of ions from dissociative photoionization of BCl3 . Mass spectrometric experiments have allowed the ionisation energy to be determined, and have been performed (Ei) by Osberghaus in 1950,23 with follow-up studies by Marriott and Craggs,24 Koski et al.25 and Dibeler and Walker.26 The study of Marriot and Craggs24 gave an estimate of Ei eV.The later study of Koski et al.25 gave an ion- (BCl2)O9 ization energy of 7.2 eV. Dibeler and Walker26 obtained Ei\ eV. The only other estimate of the ionization energy 7.52 comes from synchrotron studies from Tuckett and coworkers21,27 who obtained an upper limit of 7.71 eV by assuming that the ions they saw “turned onÏ at their BCl2 ` thermodynamic energy.Theoretical method and results Although, in principle, it is possible to calculate the ionization energy for all of these complexes at the levels of theory used in Section 1, the cheapest way of gaining accurate ionization energies is to use the Gaussian-2 (G2) method of Pople and co-workers,28 which is a composite method of obtaining thermochemical data e†ectively at the QCISD(T)/6-311]G(3df, 2p) level, but by only doing single-point calculations at the MP2(FULL)/6-31G* geometry (and including some empirical corrections).Combining the G2 energy at 0 K ([944.274 558 BCl2 Eh) with the G2 energy (0 K) of the cation ([944.007 954 BCl2 ` gives an value of 7.25 eV. It is also possible to calculate Eh) Ei the ionization energy by the di†erence in the calculated Gibbs free energies of and at 298 K (assuming a station- BCl2 BCl2 ` ary electron) ; this gives an ionization energy of 7.33 eV. Although this value is close to the value of 7.52 eV obtained by Dibeler and Walker,26 the value of the heat of formation of obtained by them was [14.7^0.5 kcal mol~1; this BCl2 value compares extremely poorly with the G2 value calculated by Schlegel and Harris29 of [6.79 kcal mol~1.Since G2 energies have been shown to be reliable in the vast majority of cases, it would seen appropriate to calculate the G2 heat of formation of the cation, using the G2 heat of formation of the neutral species. (Note that all Gibbs free energies, enthalpies J.Chem. Soc., Faraday T rans., 1997, V ol. 93 55and entropies are calculated using the simple harmonic oscillator, rigid-rotor approximation and assume ideal gas behaviour.) Doing this yields a heat of formation (298 K) of BCl2 ` of 160.4 kcal mol~1, which is fairly close to the value of 158.6^0.5 kcal mol~1, obtained by Dibeler and Walker.26 In passing, it is worth noting that Bews and Glidewell30 performed semiempirical (MNDO) calculations to investigate the fragmentation processes of boron trichloride, diboron tetrachloride and tetraboron tetrachloride ; in that work, they found to be of symmetry, and calculated its heat BCl2 ` D=h of formation to be ca. 180 kcal mol~1, clearly in poor agreement with the G2 value ; however, this is to be expected with the approximate MNDO method. Note also that values of [20^15 and 148^5 kcal mol~1 are quoted in the JANAF Tables19 for the heats of formation of the neutral molecule and cation (298 K), respectively.These are both in rather poor agreement with the G2 values obtained. 3 Excited states of and BCl2 ë BCl2 Background Cation. As mentioned above, there has been very little information obtained on the excited states of the cation. The only reported work is the Ñuorescence attributed to the cation by Biehl et al.21 This work observed Ñuorescence in the range 280È350 nm (ca. 3.5È4.4 eV), which was assigned to on BCl2 ` the basis of energetics (these considerations led to the exclusion of the possibility that the Ñuorescence was attributable to an excited state of the neutral molecule).Neutral. There have been a number of studies which have reported Ñuorescence that has been attributed to excited states of the neutral molecule. The �rst was the study by BCl2 Dessaux et al.31 who observed the Ñuorescence emanating from the reaction region of a chemiluminescence experiment, which reacted H with this spectrum was later BCl3 ; assigned18 in terms of spinÈorbit splitting and vibrational excitation of Prior to this study, emissions from BCl2 .BCl2 had not been seen, even though they had been looked for in Ñash photolysis experiments32 of and microwave dis- B2Cl4 charge experiments.33 There then followed two synchrotron radiation studies : one in the range 106È190 nm34 and the other in the range 45È106 nm.35 There were a total of four bands seen in these studies, labelled AÈD. Band A had an onset at 380 nm (ca. 3.3 eV) with a maximum at 500 nm (ca. 2.5 eV), with no reproducible structure ; band B consisted of two features, a broad band in the range 280È380 nm (ca. 3.6È4.4 eV) and a sharp band at 360 nm (ca. 3.4 eV); band C was noted as being similar to the chemiluminescent feature of Dessaux et al.18,31 and appeared in the range 240È380 nm (ca. 4.4È5.2 eV); �nally, band D, only seen in the higher energy synchrotron radiation range, and appeared at 200È260 nm (ca. 4.8È6.2 eV). Breitbarth and Ducke36 looked at radiofrequency discharges in and observed three broad, molecular emis- BCl3 sions at 305, 350 and 480 nm from which it was deduced that was the most likely carrier. BCl2 Tokue et al.37 used electron impact to dissociate BCl3 . They observed two emissions in the regions 230È380 nm (ca. 3.3È5.4 eV) and 400È580 nm (ca. 2.1È3.1 eV). The dissociation thresholds observed �tted with calculated thresholds only if the ground state was assumed to be the �nal state of the emission processes.Further synchrotron studies have recently been performed by Tuckett and co-workers.21,27 They observe two main emissions (although they noted that they may not have resolved another emission seen in the previous synchrotron studies), in the ranges 400È650 nm (ca. 1.9È3.1 eV) and 230È500 nm (ca. 2.5È5.4 eV); these were assigned to the following processes : and with the higher energy A3 2B1 ^X3 2A1 B3 2A1 ^X3 2A1 band possibly also containing some contributions from the C3 state (symmetry not noted).Theoretical methods Two approaches were employed: (i) Although the CIS38 method does not, strictly speaking, account for electron correlation, it is the cheapest method that gives both minimum-energy geometries and harmonic vibrational frequencies for excited states. Thus it was used to give an overview of the singlet states that were accessible in the energy ranges indicated by the dispersed Ñuorescence spectra of Biehl et al.21 These calculations also allowed the calculation of oscillator strengths.Single-point CIS(nstate\20)/6- 31G* calculations were �rst performed at the linear MP2/6- 31G* geometry of the state. Further optimisation and X1&g ` frequency calculations on some selected excited states were then made with both and symmetry. Finally, CIS/6- D=h C=v 31G* and CIS/6-311G(2df) geometry optimisation and frequency calculations were performed for the �rst CIS excited state which has a .. . con�guration in (A3 1B2), (7b2)1(9a1)1 C2v symmetry. RHF/6-31G*, MP2/6-31G*, MP2/6-311G(2d), MP4(SDQ)/cc-pVDZ and CCSD(T)/6-311G(2d) calculations were also performed on the state in order to obtain A3 1B2 more reliable equilibrium geometries, harmonic vibrational frequencies, vertical excitation energies (VEE) and adiabatic excitation energies (AEE). Similar CIS and MP2 calculations were carried out for These calculations were performed BCl2 . using GAUSSIAN 94.(ii) MRDCI calculations39 (as implemented in the GAMESS suite of programs40), with threshold selection set at 10 and extrapolation to zero threshold39 were performed. lEh The estimated full CI energy was then obtained by applying the multireference variant of the Davidson correction41 which accounts for quadruple excitations. The energies at each of these stages are denoted and EMRDCI An important quantity in the context of MRDCI calculations is which quanti�es to what extent a state is rep- &ci2, resented by the reference con�gurations; this also has an impact on Strictly speaking the energies of two states, Efull .calculated in this way, are only comparable if their values &ci2 are close and preferably above 0.9. The relative energy between two states with signi�cantly di†erent values con- &ci2 tains rather large di†erential contributions from the application of the Davidson correction. Therefore, the MRDCI calculations were performed in two stages : �rst a relatively small reference set was used in order to obtain a qualitative overview of a large number of low-energy valence states.The reference set was generated by the following approach. With the ground-state con�guration, all singly excited con�gurations of the relevant symmetry within the valence space were generated. Then all singly excited con�gurations (again of the relevant symmetry within the valence space) from each con�guration already generated were also included as reference con�gurations.Although not all doubly excited con�gurations were generated in this strategy, it is a simple way of generating a reference set that is balanced for each symmetry and geometry. For each symmetry, the four lowest CI roots were computed. The calculations on the linear cation are performed in the subgroup. The correlation of the sym- D2h metries in each group is given in Table 4. After this survey of states had indicated which states were the most likely to be the source of the dispersed Ñuorescence spectra, these few states were recalculated using a larger reference set, in order to obtain larger values and thus more &ci2 reliable relative energies.The reference set was extended to include all doubly excited valence con�gurations and all other con�gurations which had a contribution of ci2[0.005. Because of the larger size of the reference set, only the lowest few states of were considered. BCl2 ` 56 J.Chem. Soc., Faraday T rans., 1997, V ol. 93Table 4 Symmetry correlation tablea C2v D=h D2h A1 &g ` Ag B1 &g~ B1g B2 &u ` B1u A2 &u~ Au A2]B2 %g B2g]B3g A1]B1 %u B2u]B3u A1]B1 *g Ag]B1g A2]B2 *u Au]B1u a The axis systems chosen are as follows : for the molecule lies in C2v , the yz plane, with the z axis coinciding with the axis in a right- C2 handed system; for the z-axis lies along the molecular axis as it D2h does in with the molecule in the yz plane.D=h For the cation, single-point MRDCI calculations were performed at the CCSD(T)/6-311G(2d) optimised geometries of the ground state and the bent excited state of X1&g ` A3 1B2 For the neutral, only single-point calculations at the BCl2 `. CCSD(T)/6-311G(2d) optimised geometry of the neutral X3 2A1 state were performed. [Bartlett and co-workers42 have recently shown that CCSD(T) methods are comparable to MRDCI methods and so the use of a CCSD(T) optimised geometry for the MRDCI calculations is not unreasonable. Calculations on the second row dihalide led to the same conclusion.43] A PF2 TZVP basis was used.The natural orbitals from a CISD calculation on the respective ground state, used as the molecular orbital (MO) basis for the MRDCI calculations, are as follows (BCl2 `) . . . (5pg)2(4pu)2(2nu)4(2ng)4(6pg)2(5pu)2(3nu)0(7pg)0(6pu)0 in symmetry and D=h . . . (6a1)2(5b2)2(7a1)2(2b1)2(2a2)2(6b2)2(8a1)2 (7b2)2(9a1)0(3b1)0(8b2)0(10a1)0 in symmetry.For neutral the lowest unoccupied C2v BCl2 , orbital becomes singly occupied. The lowest 11 (core) 9a1 MOs were kept frozen, which results in a CI space involving 12 and 13 valence electrons in 63 active orbitals for the cation and neutral molecule respectively. Results CIS calculations for the cation. At the linear MP2/6-31G* geometry of the ground state of at the BCl2 `, CIS(nstates\20)/6-31G* level, the �rst three excited singlet states arise from a con�guration but have zero oscil- (ng)3(nu)1 lator strength, f.The lowest excited state with a non-zero oscillator strength ( f\1.01) is the seventh excited CIS state, a state, also with a con�guration, and a VEE of &u ` (ng)3(nu)1 10.4 eV. Geometry optimisation in symmetry of the latter D=h state reduced its excitation energy from the ground state to 8.96 eV ( f\0.36) ; however, frequency calculations at the optimised geometry gave one imaginary frequency, which corresponded to the asymmetric stretch.Geometry optimisation in symmetry of this state at the CIS(nstates\20, root\7)/ C=v 6-31G* level, further reduced the excitation energy to 8.45 eV, and produced a minimum on the potential-energy surface, as indicated by the three real frequencies [432.7 cm~1 (p), 221.8 cm~1 (n) and 1133.2 cm~1 (p)]. At the optimised geometry of this linear asymmetric state (BCl bond lengths of 1.6505 and 1.9088 the lowest excited state is a 1% state (corresponding ”), to a n]p excitation) with a VEE of 6.87 eV ( f\0.002).These results make it unlikely that the dispersed Ñuorescence spectrum of Biehl et al.21 could derive from a linear singlet upper state, since the spectrum was seen in the energy range 3.5È4.4 eV. CIS optimisation and frequency calculations for the �rst excited electronic state, employing a bent geometry, gave a state, with the computed VEEs at the 1B2 CIS(nstates\3)/6-31G* and CIS(nstates\20)/6-311G(2df) level of 3.72 and 3.57 eV ( f\0.021 and 0.019), respectively.These VEEs agree very well with the observed Ñuorescence band maximum of 3.76 eV, suggesting that this state is a 1B2 very likely candidate for the upper state of the Ñuorescence process. Its computed minimum-energy geometries and vibrational frequencies at di†erent levels of theory are summarized in Table 5. MRDCI calculations for the cation. The results of the MRDCI survey for the linear states are shown in Table BCl2 ` 6 and Fig. 1. For the bent geometry (Table 7 and Fig. 1) the energy of the ground state is located at ca. 3.5 eV higher in energy than the ground state of the linear cation, in qualitative agreement with the non-MRDCI calculations. An approximate state diagram based on these survey calculations is given in Fig. 1. With the relatively smaller reference set, the value for &ci2 the ground state is ca. 0.91 and for the excited states it is in the range 0.77È0.85. As noted above, this a†ects the reliability of the computed relative energies and they should be considered qualitative.The results of the calculations with the extended reference set are shown in Tables 8 and 9, for the linear and bent states of respectively. BCl2 `, The computed AEEs and VEEs for the state are sum- 1B2 marized in Table 10. Note that the UHF-based calculations have considerable spin contamination (SS2TB1, rather than 0; see Table 5) and so these results should be viewed with caution.However, some deductions can be made (also the MRDCI calculations for this state suggests that single reference methods are adequate). First, although the VEE appears to be in excellent agreement with the experimental spectrum for the CIS calculations, all the correlated calculations are in Table 5 Calculated geometries and vibrational frequencies for the state BCl2 ` (A3 1B2) method [energy(]943)/Eh r/” A/degrees l1 l2 l3 UHF/6-31G* 0.239 680 1.7534 100.0 842.0 272.5 488.8a SS2T\1.027 CIS/6-31G* 0.156 945 1.7316 108.1 793.9 239.2 685.5 SS2T\N/A CIS/6-311G(2d) 0.225 912 1.7263 106.2 798.1 236.7 685.5 SS2T\N/A MP2/6-31G* 0.548 997 1.7409 101.7 834.9 264.4 170.2a SS2T\1.027 MP2/6-311G(2d) 0.658 368 1.7524 99.1 803.8 259.2 240.2a SS2T\1.031 MP4(SDQ)/cc-pVDZ 0.637 899 1.7627 102.1 809.5 249.8 498.2ia SS2T\1.029 CCSD(T)/6-311G(2d) 0.708 271 1.7606 101.1 770.5 240.1 629.1 SS2T\1.034 a These values may possibly be a†ected by symmetry breaking.J. Chem. Soc., Faraday T rans., 1997, V ol. 93 57Table 6 MRDCI survey of states at linear geometry BCl2 ` (D=h) statea relative energy/eVb &ci2 main excitationc X1&g ` (1Ag) 0.00 0.91 reference (0.89) 1*u(1Au) 7.05 0.83 2ng ]3n ]3nu (0.80) 1&u~(1Au) 7.08 0.83 2ng ]3nu (0.81) 1*g(1Ag) 8.51 0.82 2nu ]3nu (0.82) 1*g(1B1g) 8.65 0.83 2nu ]3nu (0.82) 1&u `(1B1u) 8.66 0.82 2ng ]3nu (0.70) 1&g~(1B1g) 8.76 0.82 2nu ]3nu (0.82) 1&g `(1Ag) 10.26 0.81 2nu ]3nu (0.70) 1%g(1B2g) 10.41 0.83 5pu ]3nu (0.46) 2ng ]7pg (0.34) 1%g(1B2g) 10.63 0.83 5pu ]3nu (0.34) 2ng ]7pg (0.45) 1%u(1B2u) 12.45 0.84 6pg ]3nu (0.78) 1&u `(1B1u) 12.46 0.77 5pg ]7pg (0.68) 1%u(1B2u) 12.65 0.81 2nu ]7pg (0.76) a Symmetry species in the subgroup is given in parentheses.Note D2h that the two components of the degenerate * states were obtained in two separate symmetries under b Relative energies are based on D2h .estimated full CI energies (see text) relative to the ground state at c The contribution of the main excitation Efull\[943.835 643 Eh . ci2 to the multireference wavefunction are given in parentheses. poor agreement, except for the MRDCI calculations without extrapolation to zero threshold and the Davidson correction. There is thus no de�nitive agreement with the experimental value ; however, it should be borne in mind that these VEEs have assumed that the upper state was populated at the (000) vibrational level (at the equilibrium geometry).Perhaps the experimental VEE value may be a†ected by, for example, vibrational excitation of the upper electronic state, leading to a dramatically changed FranckÈCondon envelope. The calculated AEE values, on the other hand, are in rather good agreement for most of the methods used. In the case of the MRDCI Table 7 MRDCI survey of states of at the bent BCl2 ` (C2v) geometry of the state 1B2 state relative energy/eVa &ci2 main excitationb 1A1 0.00 0.91 reference (0.88) 1B2 1.20 0.80 6b2 ]9a1 (0.70) 1A2 1.95 0.80 2a2 ]9a1 (0.70) 1A2 4.15 0.81 6b2 ]3b1 (0.76) 1B1 4.24 0.81 2a2 ]9a1 (0.72) 1A1 4.77 0.80 7a1 ]9a1 (0.53) 8a1 ]9a1 (0.13) 1B2 5.03 0.81 7b2 ]9a1 (0.43) 2a2 ]3b1 (0.30) 1B2 5.97 0.78 2a2 ]3b1 (0.41) 7b2 ]9a1 (0.23) 1B1 7.14 0.80 7a1 ]3b1 (0.49) 8a1 ]3b1 (0.29) 1A1 7.20 0.79 2b1 ]3b1 (0.57) a Relative energies are based on estimated full CI energies (see text) relative to the ground state at b The con- Efull\[943.708 419 Eh .ci2 tributions of the main excitation to the multireference wavefunction are given in parentheses. Fig. 1 Energy level diagram indicating the relative positions of the electronic states of in linear and non-linear geometries BCl2 ` calculations, the agreement is getting better with the extra corrections (in contrast to the VEE). Overall, on energetic grounds, the calculated AEEs give qualitative support for the assignment of the dispersed Ñuorescence observed by Biehl et al.21 to the transition.With BCl2 ` A3 1B2 ]X1&g `(1A1) regard to the vibrational frequencies, as was noted above, the observed vibrational structure can possibly be assigned to a progression of in the ground state ; however, if the upper 2l2 state is bent, as seems to be the case, then the non-observation of odd quanta is rather peculiar, especially if the upper state is vibrationally excited. The calculated results shown in Table 5 also suggest that a progression of in the upper state is 2l2 consistent with the observed vibrational spacings but, again, non-observation of odd quanta is difficult to explain.The computed values of the asymmetric stretch [at the CIS and l3 CCSD(T) levels] in the state appear to be consistent A3 1B2 with the observed vibrational structure, and it is at least plausible that this vibration could be excited in some dissociative pathways, following electronic excitation upon irradiation.(The fact that the other methods give rise to vastly Table 8 MRDCI calculation of at the geometry using the extended reference seta BCl2 ` D=h root EMRDCI ET/0 Efull &ci2 1Ag 71 reference con�gurations, 11 355 selected CSFs 1 [943.795 981 [943.812 783 [943.834 040 (0.00) 0.9214 1Au 40 reference con�gurations, 12 235 selected CSFs 1 [943.483 115 [943.530 211 [943.564 865 (7.32) 0.8982 2 [943.482 505 [943.529 188 [943.564 203 (7.34) 0.8974 1B1u 64 reference con�gurations, 15 117 selected CSFs 1 [943.484 183 [943.531 007 [943.566 003 (7.29) 0.8974 a Energies (eV) relative to the ground state are given in parentheses for the results.Efull 58 J. Chem. Soc., Faraday T rans., 1997, V ol. 93Table 9 MRDCI calculation of at the geometry using the extended reference seta BCl2 ` 1B2 C2v root EMRDCI ET/0 Efull &ci2 1A1 108 reference con�gurations, 15 242 selected CSFs 1 [943.663 038 [943.685 824 [943.706 986 (0.00) 0.9213 1A2 89 reference con�gurations, 17 464 selected CSFs 1 [943.518 709 [943.574 675 [943.614 985 (2.50) 0.8890 2 [943.444 943 [943.500 867 [943.539 247 (4.56) 0.8909 1B1 90 reference con�gurations, 20 450 selected CSFs 1 [943.454 504 [943.508 318 [943.549 480 (4.29) 0.8869 1B2 105 reference con�gurations, 16 606 selected CSFs 1 [943.543 117 [943.602 975 [943.643 767 (1.72) 0.8888 a Energies (eV) relative to the ground state are given in parentheses for the results.Efull di†erent values of the frequency, casts some doubt on the l3 reliability of these particular calculated values ; symmetry breaking may well be a†ecting these calculations.) Excited state calculations for neutral Although, BCl2 .similar MRDCI calculations to those on the cation were performed on the neutral states of only the more reliable BCl2 , results with the large reference set are shown in Table 11. CIS(nstates\20)/6-311]G(2df) calculations carried out at the CCSD(T)/6-311G(2d) optimised geometry of X3 2A1 BCl2 give results in generally good agreement with the MRDCI results. The and states are 2.75 and 6.93 eV above 1 2B1 2 2A1 the state, respectively, while the corresponding MRDCI X3 2A1 values are 2.65 and 7.37 eV.CIS geometry optimisation calculations for the �rst excited state, carried out in symmetry, D=h gave a state (which corresponds to the state in 2&g ` X3 2A1 C2v symmetry) with a VEE of ca. 2.0 eV above the lowest 2%u state in symmetry). The optimised BCl bond (1 2B1, 22A1 C2v length for the state is ca. 1.70 at the CIS level. MP2/6- 2%u ” 31G* calculations con�rmed the change of the state ordering of these two lowest states from a linear to bent struc- Table 10 Calculated AEE and VEE (eV) of the BCl2 ` Ñuorescence transition 1B2ÈX3 (1&g `)1A1 method AEE VEE CIS/6-31G* È 3.72 CIS/6-311G(2df) È 3.57 MP2/6-31G* 4.83 (4.43)a 1.51 (1.10)a MP2/6-311G(2d) 5.31 (4.34)a 1.23 (0.76)a MP4(SDQ)/cc-pVDZ 4.62 1.54 CCSD(T)/6-311G(2d) 4.61 1.34 EMRDCI b 6.88 3.26 ET/0 b 5.71 2.25 Efull b 5.18 1.72 experimental21 4.28 3.76 a Values in parentheses are from spin-projected energies ; all other energies are unprojected values.b Calculated using the extended reference set, at the respective CCSD(T)/6-311G(2d) optimised geometry. ture. The MP2/6-31G* VEE for the transition 1 2B1 ^X3 2A1 was calculated to be 2.50 eV, in excellent agreement with the corresponding MRDCI and CIS values. Attempts to assign the various observed emission/ Ñuorescence spectra of the neutral molecule are fraught with uncertainty ; however, some comments will be made.First, as noted above, the assignment18 of the chemiluminescence spectrum (in the energy range 3.4È4.2 eV) of Dessaux et al.31 in terms of a frequency of 470 cm~1 seems uncertain, con- l1 sidering the JANAF estimated value19 of 720 cm~1, the matrix isolation value of 731 cm~1 and the values calculated here (Table 1). Similar bands in this energy region (3.4È5.2 eV) have been seen by Suto et al.34 (labelled bands B and C therein), Lee et al.35, Creasey et al.27 and Biehl et al.21 in their synchrotron experiments.Additionally, the same bands appear to have been seen in electron impact studies by Tokue et al.37 and in the plasma emission studies of Breitbarth and Ducke36 (labelled bands X and Y in the latter work). This feature has been tentatively assigned by Creasey et al.27 to the state, with perhaps contributions from the (unassigned) B3 2A1 state.A broader, lower energy emission is also observed in C3 all the above experiments (labelled band A in the synchrotron studies, unlabelled in the ies, and labelled band Z in the plasma emission study) ; this band is assigned (again tentatively) to the state by Creasey et al.27 The A3 2B1 results of the MRDCI and CIS scans show that there is indeed a state at a VEE energy (from the ground state) of 2.65 eV 2B1 (Table 11) (this is the energy separation at the ground-state optimised geometry), which is the most accurate value here.This is entirely consistent with the experimental observations for band A (1.9È3.1 eV). The higher energy band, which is assigned to the state by Creasey et al.,27 is at an energy A3 2A1 of between 2.5 and 5.4 eV; however, the calculated VEE (from the ground state) is 7.37 eV for the �rst excited state 2A1 (Table 11), and so this is only a plausible assignment for that band.More possible is an assignment to the �rst excited 2B2 state, which has a calculated VEE of 6.4 eV; the AEE will be to lower energy, giving rise to a band similar to that observed. It appears that the and states are the �rst excited and B3 C3 2A1 Table 11 MRDCI calculation of at the geometry of the state using the extended reference seta BCl2 C2v X3 2A1 root EMRDCI ET/0 Efull &ci2 2A1 98 reference con�gurations, 18 459 selected CSFsb 1 [944.038 654 [944.066 512 [944.095 471 (0.00) 0.9075 2 [943.731 749 [943.780 235 [943.824 571 (7.37) 0.8780 2A2 64 reference con�gurations, 17 871 selected CSFs 1 [943.761 941 [943.813 792 [943.850 690 (6.66) 0.8936 2 [943.723 522 [943.806 941 [943.849 865 (6.68) 0.8839 2B1 72 reference con�gurations, 18 946 selected CSFs 1 [943.911 202 [943.963 908 [943.998 222 (2.65) 0.8993 2B2 74 reference con�gurations, 17 984 selected CSFsc 1 [943.772 653c [943.818643c [943.861 971c (6.35c) 0.8795c a Energies (eV) relative to the ground state are given in parentheses for the results.b The reference set for the states is just the full doubly Efull 2A1 excited valence con�gurational space. No further con�gurations were added, as these states did not require further non-valence con�gurations. c The MRDCI calculation on the state using a fully doubly excited valence reference set failed. The energies quoted here are taken from the 2B2 survey calculations using a small reference set.J. Chem. Soc., Faraday T rans., 1997, V ol. 93 59states, but the ordering of these is unclear ; the MRDCI 2B2 calculations suggest the state is the state, in disagree- A3 2B2 ment with the CIS results. Note that the two low-lying 2A2 states are also in this energy region, but that transitions to the ground state from these states should not be allowed under dipole selection rules ; however, if there are any coupling mechanisms, such as vibronic coupling, then these states may become allowed, and indeed may be contributing to this region.Clearly, only qualitative conclusions can be drawn from the calculations as they stand at the moment. Conclusions The geometry and vibrational frequencies of the ground electronic neutral and cationic states of boron dichloride have been calculated. Both ab initio and density functional theory approaches were used, and gave similar results at the highest levels used. The calculated parameters were in very good agreement with experiment, where such values are available.An attempt was then made to assign the dispersed Ñuorescence spectrum obtained by Biehl et al.,21 attributed to the cation. CIS and MRDCI calculations were performed on the cation, in order to ascertain the energy positions of such states. These calculations appeared to exclude any linear singlet cationic states in the energy region of interest. Calculations under symmetry, however, showed that the �rst C2v excited, bent state was probably the most likely candidate 1B2 for the source of the emission.The assignment of the vibrational structure seen in the dispersed Ñuorescence is not straightforward. In order to clarify the assignment, sophisticated FranckÈCondon factor calculations would have to be performed. Finally, a scan of the excited states of the neutral molecule was performed using MRDCI calculations, and some CIS calculations were also carried out; the two sets of calculations were in very good agreement.Some preliminary assignments of Ñuorescent transitions seen in a variety of di†erent experiments were made on the basis of these results. Note added After this work was submitted, a paper appeared by Jacox et al., who studied the results of the interaction of excited neon atoms with Species observed in the matrix were, BCl3 .44 amongst others, and The former had measured BCl2 BCl2 `. values which were in excellent agreement with those of l3 Andrews and co-workers.16,20 An IR absorption of ca. 1436 cm~1 was attributed to the mode of This assign- l3 BCl2 `. ment was aided by ab initio calculation of the harmonic frequencies of this molecule. Calculations were performed at various levels, with the highest being CCSD(T)/6-311G(2df). These calculations give very similar values to those reported in Table 1. The calculated geometry of ref. 44 is also in good agreement with the calculated values presented in Table 1. We gratefully acknowledge the EPSRC for provision of computer time at ULCC.Dr. Julie Altmann (ULCC) is thanked for valuable advice during this work. T.G.W. thanks the LloydÏs Tercentenary Foundation for the award of a two-year fellowship. E.P.F.L. thanks the Hong Kong Polytechnic University for support. References 1 S. Matsumoto, N. Nishida, K. Akashi and K. Sugai, J. Mater. Sci., 1996, 31, 713; A. Salok, O. O. Awadelkarim, F. Preuniger and Y. D. Chan, Appl. Phys. L ett., 1996, 68, 1690; M.W. Cole, W. Y. Han, R. L. Pfe†er, D. W. Eckhart, F. Ren, W-S. Hobson, J. R. Lothian, J. Lopata, J. A. Caballers and S. J. Pearton, J. Appl. Phys., 1996, 79, 3286; C. Chou, K. Saravanan, J. Kava and M. Siegel, J. V ac. Sci. T echnol. B, 1996, 14, 474; G. Franz, C. Hoyler and J. Kaindel, J. V ac. Sci. T echnol. B, 1996, 14, 126; I. W. Rangelow, F. Shi, P. Hudek, I. Kostic, E. Hammel, H. Loschner, G. Stengl and E. Cekan, Microelectron. Eng., 1996, 30, 257. 2 G. R. Scheller, R.A. Gottscho, T. Intrator and D. B. Graves, J. Appl. Phys., 1988, 64, 4384. 3 R. Gottscho, Phys. Rev. A, 1987, 36, 2233; C. E. Gaebe, T. R. Hayes and R. A. Gottscho, Phys. Rev. A, 1987, 35, 2993. 4 B. L. Preppernau and T. A. Miller, in Glow Discharge Spectroscopies, ed. R. K. Marcus, Plenum Press, New York, 1993. 5 C. and M. S. Plesset, Phys. Rev. A, 1934, 46, 618. M‘ller 6 J. S. Andrews, D. Jayatilaka, R. G. A. Bone, N. C. Handy and R. D. Amos, Chem. Phys. L ett., 1991, 183, 423; R.D. Amos, J. S. Andrews, N. C. Handy and P. J. Knowles, Chem. Phys. L ett., 1991, 185, 256; P. J. Knowles, J. S. Andrews, R. D. Amos, N. C. Handy and J. A. Pople, Chem. Phys. L ett., 1991, 186, 130; D. J. Tozer, N. C. Handy, R. D. Amos, J. A. Pople, R. H. Nobes, Y. Xie and H. F. Schaefer, Mol. Phys., 1993, 79, 777. 7 J. Cizek, Adv. Chem. Phys., 1969, 14, 35; G. D. Purvis and R. J. Bartlett, J. Chem. Phys., 1982, 76, 1910; G. E. Scuseria, C. L. Janssen and H. F. Schaefer III, J.Chem. Phys., 1988, 89, 7382; G. E. Scuseria, J. Chem. Phys., 1989, 90, 3700. 8 A. D. Becke, Phys. Rev. A, 1988, 38, 3098. 9 C. Lee, W. Yang and R. G. Parr, Phys. Rev. B, 1988, 37, 785. 10 A. D. Becke, J. Chem. Phys., 1993, 98, 5648. 11 D. E. Woon and T. H. Dunning Jr., J. Chem. Phys., 1993, 98, 1358; T. H. Dunning Jr., J. Chem. Phys., 1989, 90, 1007. 12 GAUSSIAN 94 (Revision C.3), M. J. Frisch, G. W. Trucks, H. B. Schlegel, P. M. W. Gill, B. G. Johnson, M. A. Robb, J.R. Cheesemans, T. W. Keith, G. A. Petersson, J. A. Montgomery, K. Raghavachari, M. A. Al-Laham, V. G. Zakrzewski, J. V. Ortiz, J. B. Foresman, J. Cioslowski, B. B. Stefanov, A. Nanayakkara, M. Challacombe, C. Y. Peng, P. Y. Ayala, W. Chen, M. W. Wong, J. L. Andres, E. S. Replogle, R. Gomperts, R. L. Martin, D. J. Fox, J. S. Binkley, D. J. Defrees, J. Baker, J. P. Stewart, M. Head- Gordon, C. Gonzalez and J. A. Pople, Gaussian Inc., Pittsburgh PA, 1995. 13 CADPAC: The Cambridge Analytic Derivatives Package, Issues 5.0 and 5.2, Cambridge, 1992.A suite of programs developed by R. D. Amos with contributions from: I. L. Alberts, J. S. And. C. Handy, D. Jayatilaka, P. J. Knowles, R. Kobayashi, N. Koga, K. E. Laidig, P. E. Maslen, C. W. Murray, J. E. Rice, J. Sanz, E. D. Simandiras, A. J. Stone and M-D. Su. 14 A. D. Walsh, J. Chem. Soc., 1953, 2266. 15 J. M. Dyke and T. G. Wright, Chem. Phys. L ett., 1990, 169, 138; C. I. Frum, R.Englemann Jr. and P. F. Bernath, J. Chem. Phys., 1991, 95, 1435; Yu. A. Buslaev and Klyagina, Coord. Chem Rev., 1993, 126, 149; J. M. Dyke, D. Haggerston, M. P. Hastings and T. G. Wright, Chem. Phys., 1994, 81, 355; D. M. Hassett and C. J. Marsden, J. Mol. Struct., 1995, 346, 249; N. Vogt, G. V. Girichev, J. Vogt and A. G. Girichev, J. Mol. Struct., 1995, 352/353, 175. 16 J. H. Miller and L. Andrews, J. Am. Chem. Soc., 1980, 102, 4900. 17 R. Franzi, M. Geo†rey, E. A. C. Lucken and N.Leray, J. Chem. Phys., 1983, 78, 708. 18 O. Dessaux, P. Goudmand and G. Pannetier, Bull. Soc. Chim. Fr., 1969, 447. 19 JANAF T hermochemical T ables, ed. D. R. Stull and H. Prophet, National Bureau of Standards, US (NSRDS-NBS 37), 2nd edn., 1971. 20 P. Hassanzadeh and L. Andrews, J. Phys. Chem., 1993, 97, 4910. 21 H. Biehl, J. C. Creasey, D. M. Smith, R. P. Tuckett, K. R. Yoxall, H. Baumgartel, H. W. Jochims and U. Rockland, J. Chem. Soc., Faraday T rans., 1993, 91, 3073. 22 J. M. L. Martin, J. El-Yazal and J. P. Mol. Phys., 1995, FrancÓ ois, 86, 1437. 23 O. Osberghaus, Z. Phys., 1950, 128, 366. 24 J. Marriot and J. D. Craggs, J. Electron. Control, 1957, 3, 194. 25 W. S. Koski, J. J. Kaufman and C. F. Puchucki, J. Am. Chem. Soc., 1959, 81, 1326. 26 V. H. Dibeler and J. A. Walker, Inorg. Chem., 1969, 8, 50. 27 J. C. Creasey, P. A. Hatherley, I. R. Lambert and R. P. Tuckett, Mol. Phys., 1993, 79, 413. 28 L. A. Curtiss, K. Raghavachari, G. W. Trucks and J. A. Pople, J. Chem. Phys., 1993, 98, 1293. 29 H. B. Schlegel and S. J. Harris, J. Phys. Chem., 1994, 98, 11178. 30 J. R. Bews and C. Glidewell, J. Mol. Struct. (T HEOCHEM), 1982, 89, 333. 31 O. Dessaux, P. Goumand and G. Pannetier, C. R. Acad. Sci. Paris C), 1965, 265, 480. (Se� r. 32 A. G. Massey and J. J. Zwolenik, J. Chem. Soc., 1963, 5354. 33 R. T. Holzmann and W. F. Morris, J. Chem. Phys., 1958, 29, 677; A. G. Briggs, M. S. Reason and A. G. Massey, J. Inorg. Nucl. Chem., 1975, 37, 313. 60 J. Chem. Soc., Faraday T rans., 1997, V ol. 9334 M. Suto, C. Ye, J. C. Han and L. C. Lee, J. Chem. Phys., 1988, 89, 6653. 35 L. C. Lee, J. C. Han and M. Suto, J. Chem. Phys., 1989, 91, 2036. 36 F.-W. Breitbarth and E. Ducke, Contrib. Plasma Phys., 1990, 30, 691. 37 I. Tokue, M. Kudo, M. Kasakabe, T. Honda and Y. Ito, J. Chem. Phys., 1992, 96, 8889. 38 J. B. Foresman, M. Head-Gordon and J. A. Pople, J. Phys. Chem., 1992, 96, 135. 39 R. J. Buenker and S. D. Peyerimho†, T heor. Chim. Acta, 1974, 35, 33; 1975, 39, 217; R. J. Buenker and S. D. Peyerimho†, Mol. Phys., 1978, 35, 771. 40 M. F. Guest and J. Kendrick, GAMESS User Manual, SERC Daresbury Laboratory, CCP1/86/1. 41 The single-reference correction is described in : E. R. Davidson in T he W orld of Quantum Chemistry, ed. R. Daudel and B. Pullman, Reidel, Dordrecht, 1974, p. 17. The multireference extension is in : G. Hirsch, P. J. Bruma, S. D. Peyerimho† and R. J. Buenker, Chem. Phys. L ett., 1977, 52, 442. 42 J. Olsen, P. H. Koch, A. Balkova and R. J. Bartlett, J. J‘rgensen, Chem. Phys., 1996, 104, 8007. 43 E. P. F. Lee, D. C. Wang and F. T. Chau, J. Phys. Chem., in the press. 44 M. E. Jacox, K. K. Irikura and W. E. Thompson, J. Chem. Phys., 1996, 104, 8871. Paper 6/03342C; Received 13th May, 1996 J. Chem. Soc., Faraday T rans., 1997, V ol. 93
ISSN:0956-5000
DOI:10.1039/a603342c
出版商:RSC
年代:1997
数据来源: RSC
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Effective rate constant of ferriin reduction in theBelousov–Zhabotinsky reaction |
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Journal of the Chemical Society, Faraday Transactions,
Volume 93,
Issue 1,
1997,
Page 69-71
J. Ungvarai,
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摘要:
pound and d the thickness of the in situ cell]. If an organic solvent of low absorption is used (such as acetone, ethanol or diethyl ether), the necessary concentration increases with increasing X-ray photon energy because the cross-section for X-rays decreases for heavier atoms. XAFS yields quantitative information on short-range order. This requires that the part of the molecule that undergoes a transformation must contain the absorbing element. To facilitate the XAFS analysis, it is advantageous if the monitored element is present only in a few di†erent local environments in the course of the reaction.The fact that the sample is continuously irradiated with X-rays during the experiment does not seem to have a strong inÑuence on the kinetics of the Finkelstein reaction. Were such an e†ect present, one would expect a much faster reaction due to an easier breaking of the BrwC bond. Being aware of these limitations, we believe that in situ XAFS on liquid-state reactions is a valuable tool to obtain structural as well as kinetic information for selected parts of a molecule.Examples could be the study of, e.g., coordination compounds or metalloproteins. Experimental Equal volumes of 1.333 M solutions of 2-bromopropane and NaI in acetone were mixed at room temperature. A tightly closed DSC aluminium crucible was completely �lled with the reaction mixture (ca. 30 ll). The crucible was placed into a Mettler FP 80/84 DSC heat-Ñux calorimeter that was mounted vertically in the synchrotron X-ray beam and heated to 55.0(5) ¡C within 30 s.The experiment was carried out at the Hamburger Synchrotronstrahlungslabor HASYLAB at Deutsches Elektronen-Synchrotron DESY, Germany, at beamline X1 (ROEMO II). This beamline is equipped with a Si(311) double crystal monochromator, yielding approximately 108 photons s~1 mm~2 at the sample. The energy resolution is approximately 2 eV at the bromine K-edge. The DORIS III storage ring was run with positrons of 4.5 GeV at 80È120 mA.Every 8 min 12 s an X-ray absorption spectrum was taken in transmission at the Br K-edge (photon energy ca. 13 475 eV). Reference spectra of crystalline NaBr were simultaneously measured (at room temperature) by use of a third ionization chamber. The sample Br absorption edge jump was limited by the solubility of NaI and the *kd\(It/I0)\0.38, �xed pathlength in the calorimeter. The measured spectra were evaluated with the programs AUTOBK, FEFF and FEFFIT of the University of Washington package.27h29 Multi-electron phenomena lead to a peak at low R in the Br XAFS spectra.30h34 This was corrected by a simpli�ed approach as described in ref. 35. BrieÑy, this peak was isolated in R-space from a NaBr spectrum and back-transformed into k-space. It was then subtracted from all spectra in k-space before evaluation. When quantitatively analysing XAFS spectra of reacting systems, it is important to keep the number of �t-parameters as small as possible to minimize correlation e†ects.13,35,36 By evaluating spectra of pure 2-bromopropane and NaBr at 55 ¡C we determined the following parameters that were kept constant in subsequent �ts of the reaction mixture: p2(BrwCa)\0.0011 ”2, p2(BrwCb)\0.0137 ”2, p2(BrwNa)\0.02593 ”2, R(BrwCb)\2.858 ”, S02(BrwCa)\S02(BrwCb)\1.082, S02(BrwNa)\1.10, eV, E0(BrwCa)\E0(BrwCb)\[0.89 E0(BrwNa)\[1.65 eV.These values are in good agreement with data for similar compounds.13,33,35 was set to Conse- N(BrwCb) 2N(BrwCa).quently, the only �t variables were the mean coordination numbers and N(BrwNa), and the mean distances N(BrwCa) R(BrwNa) and The evaluated XAFS data range R(BrwCa). was k\2.0È7.1 and R\0.8È3.1 throughout all experi- ”~1 ” ments. 2-Bromopropane (99]%), acetone (99.9%; HPLC grade) and NaI (p.a.) were purchased from Aldrich. Hydrate water of NaI was removed before experiments by heating in vacuum. are grateful to HASYLAB for beamtime.We thank A. We Reller and M. Martin for generous support. Financial support was granted by the Deutsche Forschungsgemeinschaft and by the Fonds der Chemischen Industrie. References 1 X-Ray absorption. Principles, applications, techniques of EXAFS, SEXAFS and XANES, ed. D. C. Koningsberger and R. Prins, Wiley, New York, 1988. 2 D. Bazin, H. Dexpert, N. S. Guyot-Sionnest, J. P. Bournonville and J. Lynch, J. Chim. Phys. Phys. Chim. Biol., 1989, 86, 1707. 3 B. S. Clausen, L. G. Ste†ensen, P. L. Hansen and H. Gra- b~k, Catal. L ett., 1993, 20, 23. Tops‘e, 4 G. Sankar, P. A. Wright, S. Natarajan, J. M. Thomas, G. N. Greaves, A. J. Dent, B. R. Dobson, C. A. Ramsdale and R. H. Jones, J. Phys. Chem., 1993, 97, 9550. 5 H. Bertagnolli and T. S. Ertel, Angew. Chem., 1994, 106, 15. 6 T. Maschmeyer, F. Rey, G. Sankar and J. M. Thomas, Nature (L ondon), 1995, 378, 159. 7 A. Hoser, N. Hilbrandt, M. Martin and M. Denecke, Physica B, 1995, 208/209, 321. 8 P. Andrews, J. M. Corker, J. Evans and M. Webster, J. Chem. Soc., Dalton T rans., 1994, 1337. 9 M. Tabata and K. Ozutsumi, Bull. Chem. Soc. Jpn., 1994, 67, 1608. 10 T. S. Ertel, W. Ho. rner, S. Hu. ckmann, U. Kolb, I. Abraham and H. Bertagnolli, Physica B, 1995, 208/209, 641. 11 N. Yoshida and T. Nagamura, Rev. Sci. Instrum., 1995, 66, 52. 12 A. J. Dent, L. J. Farrugia, A. G. Orpen and S. E. Stratford, J. Chem. Soc., Chem. Commun., 1992, 1456. 13 M. Epple, U. Sazama, A. Reller, N.Hilbrandt, M. Martin and L. Tro. ger, Chem. Commun., 1996, 1755. 14 L. Tro. ger, N. Hilbrandt and M. Epple, J. Phys. Coll., 1997, in press. 15 H. Finkelstein, Chem. Ber., 1910, 43, 1528. 16 S. D. Hamann, Aust. J. Chem., 1975, 28, 693. 17 C. D. Chalk, J. McKenna and I. H. Williams, J. Am. Chem. Soc., 1981, 103, 272. 18 L. Eberston, Acta Chem. Scand., Sect. B, 1982, B36, 533. 19 P. B. D. de la Mare, J. Chem. Soc., 1955, 3169. 20 E. D. Hughes, C. K. Ingold and J. D. H. Mackie, J.Chem. Soc., 1955, 3173. 21 E. D. Hughes, C. K. Ingold and J. D. H. Mackie, J. Chem. Soc., 1955, 3177. 22 P. B. D. de la Mare, J. Chem. Soc., 1955, 3180. 23 L. Fowden, E. D. Hughes and C. K. Ingold, J. Chem. Soc., 1955, 3187. 24 L. Fowden, E. D. Hughes and C. K. Ingold, J. Chem. Soc., 1955, 3193. 25 P. B. D. de la Mare, J. Chem. Soc., 1955, 3196. 26 P. B. D. de la Mare, L. Fowden, E. D. Hughes, C. K. Ingold and J. D. H. Mackie, J. Chem. Soc., 1955, 3200. 27 J. J. Rehr, R.C. Albers and S. I. Zabinsky, Phys. Rev. L ett., 1992, 69, 3397. 28 L. Tro. ger, T. Yokoyama, D. Arvanitis, T. Lederer, M. Tischer and K. Baberschke, Phys. Rev. B, 1994, 49, 888. 29 E. A. Stern, M. Newville, B. Ravel, Y. Yacoby and D. Haskel, Physica B, 1995, 208/209, 117. 30 E. A. Stern, S. M. Heald and B. Bunker, Phys. Rev. L ett., 1979, 42, 1372. 31 G. Li, F. Bridges and G. S. Brown, Phys. Rev. L ett., 1992, 68, 1609. 32 P. DÏAngelo, A. Di Cicco, A. Filipponi and N. V.Pavel, Phys. Rev. A, 1993, 47, 2055. 33 E. Burattini, P. DÏAngelo, A. Di Cicco, A. Filipponi and N. V. Pavel, J. Phys. Chem., 1993, 97, 5486. 34 J. J. Rehr, C. H. Booth, F. Bridges and S. I. Zabinsky, Phys. Rev. B, 1994, 49, 12347. 35 M. Epple, H. Kirschnick, G. N. Greaves, G. Sankar and J. M. Thomas, J. Chem. Soc., Faraday T rans., 1996, 5035. 36 M. Epple and L. Tro. ger, J. Chem. Soc., Dalton T rans., 1996, 11. Paper 7/01433C; Received 28th February, 1997 J. Chem. Soc., Faraday T rans., 1997, V ol. 93 3037pound and d the thickness of the in situ cell]. If an organic solvent of low absorption is used (such as acetone, ethanol or diethyl ether), the necessary concentration increases with increasing X-ray photon energy because the cross-section for X-rays decreases for heavier atoms. XAFS yields quantitative information on short-range order. This requires that the part of the molecule that undergoes a transformation must contain the absorbing element. To facilitate the XAFS analysis, it is advantageous if the monitored element is present only in a few di†erent local environments in the course of the reaction.The fact that the sample is continuously irradiated with X-rays during the experiment does not seemtrong inÑuence on the kinetics of the Finkelstein reaction. Were such an e†ect present, one would expect a much faster reaction due to an easier breaking of the BrwC bond. Being aware of these limitations, we believe that in situ XAFS on liquid-state reactions is a valuable tool to obtain structural as well as kinetic information for selected parts of a molecule.Examples could be the study of, e.g., coordination compounds or metalloproteins. Experimental Equal volumes of 1.333 M solutions of 2-bromopropane and NaI in acetone were mixed at room temperature. A tightly closed DSC aluminium crucible was completely �lled with the reaction mixture (ca. 30 ll). The crucible was placed into a Mettler FP 80/84 DSC heat-Ñux calorimeter that was mounted vertically in the synchrotron X-ray beam and heated to 55.0(5) ¡C within 30 s.The experiment was carried out at the Hamburger Synchrotronstrahlungslabor HASYLAB at Deutsches Elektronen-Synchrotron DESY, Germany, at beamline X1 (ROEMO II). This beamline is equipped with a Si(311) double crystal monochromator, yielding approximately 108 photons s~1 mm~2 at the sample. The energy resolution is approximately 2 eV at the bromine K-edge.The DORIS III storage ring was run with positrons of 4.5 GeV at 80È120 mA. Every 8 min 12 s an X-ray absorption spectrum was taken in transmission at the Br K-edge (photon energy ca. 13 475 eV). Reference spectra of crystalline NaBr were simultaneously measured (at room temperature) by use of a third ionization chamber. The sample Br absorption edge jump was limited by the solubility of NaI and the *kd\(It/I0)\0.38, �xed pathlength in the calorimeter. The measured spectra were evaluated with the programs AUTOBK, FEFF and FEFFIT of the University of Washington package.27h29 Multi-electron phenomena lead to a peak at low R in the Br XAFS spectra.30h34 This was corrected by a simpli�ed approach as described in ref. 35. BrieÑy, this peak was isolated in R-space from a NaBr spectrum and back-transformed into k-space. It was then subtracted from all spectra in k-space before evaluation. When quantitatively analysing XAFS spectra of reacting systems, it is important to keep the number of �t-parameters as small as possible to minimize correlation e†ects.13,35,36 By evaluating spectra of pure 2-bromopropane and NaBr at 55 ¡C we determined the following parameters that were kept constant in subsequent �ts of the reaction mixture: p2(BrwCa)\0.0011 ”2, p2(BrwCb)\0.0137 ”2, p2(BrwNa)\0.02593 ”2, R(BrwCb)\2.858 ”, S02(BrwCa)\S02(BrwCb)\1.082, S02(BrwNa)\1.10, eV, E0(BrwCa)\E0(BrwCb)\[0.89 E0(BrwNa)\[1.65 eV. These values are in good agreement with data for similar compounds.13,33,35 was set to Conse- N(BrwCb) 2N(BrwCa).quently, the only �t variables were the mean coordination numbers and N(BrwNa), and the mean distances N(BrwCa) R(BrwNa) and The evaluated XAFS data range R(BrwCa). was k\2.0È7.1 and R\0.8È3.1 throughout all experi- ”~1 ” ments. 2-Bromopropane (99]%), acetone (99.9%; HPLC grade) and NaI (p.a.) were purchased from Aldrich. Hydrate water of NaI was removed before experiments by heating in vacuum.are grateful to HASYLAB for beamtime. We thank A. We Reller and M. Martin for generous support. Financial support was granted by the Deutsche Forschungsgemeinschaft and by the Fonds der Chemischen Industrie. References 1 X-Ray absorption. Principles, applications, techniques of EXAFS, SEXAFS and XANES, ed. D. C. Koningsberger and R. Prins, Wiley, New York, 1988. 2 D. Bazin, H. Dexpert, N. S. Guyot-Sionnest, J. P. Bournonville and J. Lynch, J. Chim. Phys.Phys. Chim. Biol., 1989, 86, 1707. 3 B. S. Clausen, L. G. Ste†ensen, P. L. Hansen and H. Gra- b~k, Catal. L ett., 1993, 20, 23. Tops‘e, 4 G. Sankar, P. A. Wright, S. Natarajan, J. M. Thomas, G. N. Greaves, A. J. Dent, B. R. Dobson, C. A. Ramsdale and R. H. Jones, J. Phys. Chem., 1993, 97, 9550. 5 H. Bertagnolli and T. S. Ertel, Angew. Chem., 1994, 106, 15. 6 T. Maschmeyer, F. Rey, G. Sankar and J. M. Thomas, Nature (L ondon), 1995, 378, 159. 7 A. Hoser, N. Hilbrandt, M. Martin and M.Denecke, Physica B, 1995, 208/209, 321. 8 P. Andrews, J. M. Corker, J. Evans and M. Webster, J. Chem. Soc., Dalton T rans., 1994, 1337. 9 M. Tabata and K. Ozutsumi, Bull. Chem. Soc. Jpn., 1994, 67, 1608. 10 T. S. Ertel, W. Ho. rner, S. Hu. ckmann, U. Kolb, I. Abraham and H. Bertagnolli, Physica B, 1995, 208/209, 641. 11 N. Yoshida and T. Nagamura, Rev. Sci. Instrum., 1995, 66, 52. 12 A. J. Dent, L. J. Farrugia, A. G. Orpen and S. E. Stratford, J. Chem. Soc., Chem. Commun., 1992, 1456. 13 M.Epple, U. Sazama, A. Reller, N. Hilbrandt, M. Martin and L. Tro. ger, Chem. Commun., 1996, 1755. 14 L. Tro. ger, N. Hilbrandt and M. Epple, J. Phys. Coll., 1997, in press. 15 H. Finkelstein, Chem. Ber., 1910, 43, 1528. 16 S. D. Hamann, Aust. J. Chem., 1975, 28, 693. 17 C. D. Chalk, J. McKenna and I. H. Williams, J. Am. Chem. Soc., 1981, 103, 272. 18 L. Eberston, Acta Chem. Scand., Sect. B, 1982, B36, 533. 19 P. B. D. de la Mare, J. Chem. Soc., 1955, 3169. 20 E. D. Hughes, C. K. Ingold and J. D. H. Mackie, J. Chem. Soc., 1955, 3173. 21 E. D. Hughes, C. K. Ingold and J. D. H. Mackie, J. Chem. Soc., 1955, 3177. 22 P. B. D. de la Mare, J. Chem. Soc., 1955, 3180. 23 L. Fowden, E. D. Hughes and C. K. Ingold, J. Chem. Soc., 1955, 3187. 24 L. Fowden, E. D. Hughes and C. K. Ingold, J. Chem. Soc., 1955, 3193. 25 P. B. D. de la Mare, J. Chem. Soc., 1955, 3196. 26 P. B. D. de la Mare, L. Fowden, E. D. Hughes, C. K. Ingold and J. D. H. Mackie, J.Chem. Soc., 1955, 3200. 27 J. J. Rehr, R. C. Albers and S. I. Zabinsky, Phys. Rev. L ett., 1992, 69, 3397. 28 L. Tro. ger, T. Yokoyama, D. Arvanitis, T. Lederer, M. Tischer and K. Baberschke, Phys. Rev. B, 1994, 49, 888. 29 E. A. Stern, M. Newville, B. Ravel, Y. Yacoby and D. Haskel, Physica B, 1995, 208/209, 117. 30 E. A. Stern, S. M. Heald and B. Bunker, Phys. Rev. L ett., 1979, 42, 1372. 31 G. Li, F. Bridges and G. S. Brown, Phys. Rev. L ett., 1992, 68, 1609. 32 P. DÏAngelo, A.Di Cicco, A. Filipponi and N. V. Pavel, Phys. Rev. A, 1993, 47, 2055. 33 E. Burattini, P. DÏAngelo, A. Di Cicco, A. Filipponi and N. V. Pavel, J. Phys. Chem., 1993, 97, 5486. 34 J. J. Rehr, C. H. Booth, F. Bridges and S. I. Zabinsky, Phys. Rev. B, 1994, 49, 12347. 35 M. Epple, H. Kirschnick, G. N. Greaves, G. Sankar and J. M. Thomas, J. Chem. Soc., Faraday T rans., 1996, 5035. 36 M. Epple and L. Tro. ger, J. Chem. Soc., Dalton T rans., 1996, 11. Paper 7/01433C; Received 28th February, 1997 J.Chem. Soc., Faraday T rans., 1997, V ol. 93 3037pound and d the thickness of the in situ cell]. If an organic solvent of low absorption is used (such as acetone, ethanol or diethyl ether), the necessary concentration increases with increasing X-ray photon energy because the cross-section for X-rays decreases for heavier atoms. XAFS yields quantitative information on short-range order. This requires that the part of the molecule that undergoes a transformation must contain the absorbing element.To facilitate the XAFS analysis, it is advantageous if the monitored element is present only in a few di†erent local environments in the course of the reaction. The fact that the sample is continuously irradiated with X-rays during the experiment does not seem to have a strong inÑuence on the kinetics of the Finkelstein reaction. Were such an e†ect present, one would expect a much faster reaction due to an easier breaking of the BrwC bond. Being aware of these limitations, we believe that in situ XAFS on liquid-state reactions is a valuable tool to obtain structural as well as kinetic information for selected parts of a molecule.Examples could be the study of, e.g., coordination compounds or metalloproteins. Experimental Equal volumes of 1.333 M solutions of 2-bromopropane and NaI in acetone were mixed at room temperature. A tightly closed DSC aluminium crucible was completely �lled with the reaction mixture (ca. 30 ll). The crucible was placed into a Mettler Fat-Ñux calorimeter that was mounted vertically in the synchrotron X-ray beam and heated to 55.0(5) ¡C within 30 s. The experiment was carried out at the Hamburger Synchrotronstrahlungslabor HASYLAB at Deutsches Elektronen-Synchrotron DESY, Germany, at beamline X1 (ROEMO II). This beamline is equipped with a Si(311) double crystal monochromator, yielding approximately 108 photons s~1 mm~2 at the sample.The energy resolution is approximately 2 eV at the bromine K-edge. The DORIS III storage ring was run with positrons of 4.5 GeV at 80È120 mA. Every 8 min 12 s an X-ray absorption spectrum was taken in transmission at the Br K-edge (photon energy ca. 13 475 eV). Reference spectra of crystalline NaBr were simultaneously measured (at room temperature) by use of a third ionization chamber. The sample Br absorption edge jump was limited by the solubility of NaI and the *kd\(It/I0)\0.38, �xed pathlength in the calorimeter.The measured spectra were evaluated with the programs AUTOBK, FEFF and FEFFIT of the University of Washington package.27h29 Multi-electron phenomena lead to a peak at low R in the Br XAFS spectra.30h34 This was corrected by a simpli�ed approach as described in ref. 35. BrieÑy, this peak was isolated in R-space from a NaBr spectrum and back-transformed into k-space. It was then subtracted from all spectra in k-space before evaluation.When quantitatively analysing XAFS spectra of reacting systems, it is important to keep the number of �t-parameters as small as possible to minimize correlation e†ects.13,35,36 By evaluating spectra of pure 2-bromopropane and NaBr at 55 ¡C we determined the following parameters that were kept constant in subsequent �ts of the reaction mixture: p2(BrwCa)\0.0011 ”2, p2(BrwCb)\0.0137 ”2, p2(BrwNa)\0.02593 ”2, R(BrwCb)\2.858 ”, S02(BrwCa)\S02(BrwCb)\1.082, S02(BrwNa)\1.10, eV, E0(BrwCa)\E0(BrwCb)\[0.89 E0(BrwNa)\[1.65 eV.These values are in good agreement with data for similar compounds.13,33,35 was set to Conse- N(BrwCb) 2N(BrwCa). quently, the only �t variables were the mean coordination numbers and N(BrwNa), and the mean distances N(BrwCa) R(BrwNa) and The evaluated XAFS data range R(BrwCa). was k\2.0È7.1 and R\0.8È3.1 throughout all experi- ”~1 ” ments. 2-Bromopropane (99]%), acetone (99.9%; HPLC grade) and NaI (p.a.) were purchased from Aldrich.Hydrate water of NaI was removed before experiments by heating in vacuum. are grateful to HASYLAB for beamtime. We thank A. We Reller and M. Martin for generous support. Financial support was granted by the Deutsche Forschungsgemeinschaft and by the Fonds der Chemischen Industrie. References 1 X-Ray absorption. Principles, applications, techniques of EXAFS, SEXAFS and XANES, ed. D. C. Koningsberger and R. Prins, Wiley, New York, 1988. 2 D. Bazin, H. Dexpert, N. S. Guyot-Sionnest, J.P. Bournonville and J. Lynch, J. Chim. Phys. Phys. Chim. Biol., 1989, 86, 1707. 3 B. S. Clausen, L. G. Ste†ensen, P. L. Hansen and H. Gra- b~k, Catal. L ett., 1993, 20, 23. Tops‘e, 4 G. Sankar, P. A. Wright, S. Natarajan, J. M. Thomas, G. N. Greaves, A. J. Dent, B. R. Dobson, C. A. Ramsdale and R. H. Jones, J. Phys. Chem., 1993, 97, 9550. 5 H. Bertagnolli and T. S. Ertel, Angew. Chem., 1994, 106, 15. 6 T. Maschmeyer, F. Rey, G. Sankar and J. M. Thomas, Nature (L ondon), 1995, 378, 159. 7 A. Hoser, N. Hilbrandt, M. Martin and M. Denecke, Physica B, 1995, 208/209, 321. 8 P. Andrews, J. M. Corker, J. Evans and M. Webster, J. Chem. Soc., Dalton T rans., 1994, 1337. 9 M. Tabata and K. Ozutsumi, Bull. Chem. Soc. Jpn., 1994, 67, 1608. 10 T. S. Ertel, W. Ho. rner, S. Hu. ckmann, U. Kolb, I. Abraham and H. Bertagnolli, Physica B, 1995, 208/209, 641. 11 N. Yoshida and T. Nagamura, Rev. Sci. Instrum., 1995, 66, 52. 12 A. J. Dent, L. J. Farrugia, A. G. Orpen and S.E. Stratford, J. Chem. Soc., Chem. Commun., 1992, 1456. 13 M. Epple, U. Sazama, A. Reller, N. Hilbrandt, M. Martin and L. Tro. ger, Chem. Commun., 1996, 1755. 14 L. Tro. ger, N. Hilbrandt and M. Epple, J. Phys. Coll., 1997, in press. 15 H. Finkelstein, Chem. Ber., 1910, 43, 1528. 16 S. D. Hamann, Aust. J. Chem., 1975, 28, 693. 17 C. D. Chalk, J. McKenna and I. H. Williams, J. Am. Chem. Soc., 1981, 103, 272. 18 L. Eberston, Acta Chem. Scand., Sect. B, 1982, B36, 533. 19 P.B. D. de la Mare, J. Chem. Soc., 1955, 3169. 20 E. D. Hughes, C. K. Ingold and J. D. H. Mackie, J. Chem. Soc., 1955, 3173. 21 E. D. Hughes, C. K. Ingold and J. D. H. Mackie, J. Chem. Soc., 1955, 3177. 22 P. B. D. de la Mare, J. Chem. Soc., 1955, 3180. 23 L. Fowden, E. D. Hughes and C. K. Ingold, J. Chem. Soc., 1955, 3187. 24 L. Fowden, E. D. Hughes and C. K. Ingold, J. Chem. Soc., 1955, 3193. 25 P. B. D. de la Mare, J. Chem. Soc., 1955, 3196. 26 P. B. D. de la Mare, L. Fowden, E. D. Hughes, C. K. Ingold and J. D. H. Mackie, J. Chem. Soc., 1955, 3200. 27 J. J. Rehr, R. C. Albers and S. I. Zabinsky, Phys. Rev. L ett., 1992, 69, 3397. 28 L. Tro. ger, T. Yokoyama, D. Arvanitis, T. Lederer, M. Tischer and K. Baberschke, Phys. Rev. B, 1994, 49, 888. 29 E. A. Stern, M. Newville, B. Ravel, Y. Yacoby and D. Haskel, Physica B, 1995, 208/209, 117. 30 E. A. Stern, S. M. Heald and B. Bunker, Phys. Rev. L ett., 1979, 42, 1372. 31 G. Li, F. Bridges and G. S. Brown, Phys. Rev. L ett., 1992, 68, 1609. 32 P. DÏAngelo, A. Di Cicco, A. Filipponi and N. V. Pavel, Phys. Rev. A, 1993, 47, 2055. 33 E. Burattini, P. DÏAngelo, A. Di Cicco, A. Filipponi and N. V. Pavel, J. Phys. Chem., 1993, 97, 5486. 34 J. J. Rehr, C. H. Booth, F. Bridges and S. I. Zabinsky, Phys. Rev. B, 1994, 49, 12347. 35 M. Epple, H. Kirschnick, G. N. Greaves, G. Sankar and J. M. Thomas, J. Chem. Soc., Faraday T rans., 1996, 5035. 36 M. Epple and L. Tro. ger, J. Chem. Soc., Dalton T rans., 1996, 11. Paper 7/01433C; Received 28th February, 1997 J. Chem. Soc., Faraday T rans., 1997, V o
ISSN:0956-5000
DOI:10.1039/a604353d
出版商:RSC
年代:1997
数据来源: RSC
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Velocity of propagation in reaction–diffusion fronts ofthe chlorite–tetrathionate reaction |
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Journal of the Chemical Society, Faraday Transactions,
Volume 93,
Issue 1,
1997,
Page 73-76
Ágota Tóth,
Preview
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摘要:
Velocity of propagation in reaction–di†usion fronts of the chlorite–tetrathionate reaction and Andrea Siska A Š gota To� th,* Dezso° Horva� th* Department of Physical Chemistry, University, P.O. Box 105, Szeged H-6701, Jo� zsef Attila Hungary The e†ect of the initial concentration of reactants on the velocity of chemical fronts in the acid-catalysed chlorite oxidation of tetrathionate was investigated both numerically and experimentally. Based on a simple two-variable model an expression for front velocity as a function of concentration and di†usion coefficient of reactants was developed which can quantitatively describe the observed velocity dependence in slight chlorite excess.Propagating chemical fronts were �rst studied at the beginning of this century by Luther.1,2 Luther assumed that the velocity of a chemical front v is given by v\C)(kD) (1) where C is a constant, k a pseudo-�rst-order rate constant containing the concentrations of reactants and D a di†usion coefficient.Fisher3 and Kolmogorov et al.4 derived a similar expression to eqn. (1) and gave an estimate of C\2 in fronts with quadratic autocatalysis in 1937. The experimental studies of the relationship between the velocity of propagation and the concentration of reactants began in the 1970s when Field and Noyes5 determined a dependence of wave velocity on the reactant concentrations similar to eqn. (1) in the BelousovÈ Zhabotinsky reaction. Since then further investigations have been carried out in di†erent reaction systems with various reaction kinetics.6h8 The chlorite oxidation of tetrathionate shows very complex kinetics ; its stoichiometry and the products change with varying concentrations of the reactants.In slight chlorite excess the reaction is autocatalytic with respect to hydrogen ion with stoichiometry (I) 7ClO2~]2S4O62~]6H2O ]7Cl~]8SO42~]12H` (I) and support propagating acidity fronts in spatially distributed media.9 Recent interest in reactionÈdi†usion fronts of the reaction arose as it became the �rst acidÈcatalysed reaction exhibiting a new type of di†usion-driven instability.10h12 A numerical study and deeper understanding of the phenomenon therefore require a reliable model based on mechanistic considerations and experimental results.Although the kinetics of the reaction is not fully understood, Nagypa� l and Epstein13 determined the following empirical rate law by measuring the initial rate of reaction in solutions containing slight excess of chlorite : r\[ 1 7 d[ClO2~] dt \k[ClO2~][S4O62~][H`]2 (2) with k estimated as k\109 M~3 s~1.They also claimed that deviations from this rate law (including third order with respect to H`) appear at high conversion. In this work we set up a reactionÈdi†usion model based on eqn. (2) as front propagation is mainly determined at early stages of the reaction, where the empirical rate law is strictly valid. Our goal is to examine its ability to describe the experimentally observed behaviour and hence provide a reliable model for further studies of spatiotemporal instabilities. Therefore we consider the velocity of propagation, one of the most important parameters in reactionÈdi†usion systems, in the acid-catalysed reaction [eqn.(1)] and determine its dependence on the initial concentrations of reactants, then �nally compare the numerical results with the experimental observations. Modelling study Propagating reactionÈdi†usion fronts in the tetrathionateÈ chlorite reaction, with the kinetic rate law given in eqn.(2), are governed by L[ClO2~] Lt \DClO2~+2[ClO2~][7r (3) L[S4O62~] Lt \DS4O62~+2[S4O62~][2r (4) L[H`] Lt \DH`+2[H`]]12r (5) where +2 is the Laplacian operator and are the appropriate Di di†usion coefficients. With the exception of H` and OH~ ions, the di†usion coefficients of small hydrated ions are of the same magnitude; therefore, by allowing D4DClO2~\DS4O62~, eqn.(3) can be eliminated upon expressing the concentration of chlorite in terms of that of tetrathionate. By introducing new dimensionless variables and a\[S4O62~]/[S4O62~]0 for a one-spatial dimensional system, b\[H`]/[S4O62~]0 , eqn. (3)È(5) reduce to La Lq \ L2a Lm2 [(i]7a)ab2 (6) Lb Lq \d L2b Lm2 ]6(i]7a)ab2 (7) where and with d\DH`/D i\2[ClO2~]0/[S4O62~]0[7 and being the initial concentrations [ClO2~]0 [S4O62~]0 ahead of the front. The new dimensionless coordinates are de�ned as and m\(k[S4O62~]0 3/D)1@2x q\k[S4O62~]0 3 t.The PDEs in eqn. (6) and (7) were solved using the CVODE package14 on a one-dimensional grid of 2001 points with spacing h\0.05 and no-Ñux boundary conditions at both ends. For initial conditions at q\0 the �rst 100 points were set to a\0.0, b\6.0 and the rest to a\1.0, b\0.0 with the former corresponding to the products behind and the latter the unreacted mixture of reactants ahead of the front. The J. Chem. Soc., Faraday T rans., 1997, 93(1), 73È76 73Fig. 1 Dimensionless concentration pro�les a; b at q\1.5 calculated by eqn. (6) and (7) with i\2 and d\7. The dashed line represents the dimensionless reaction rate u with the front position at mq . solution of eqn. (6) and (7) yielded a propagating front with its position de�ned as coordinate m at the highest dimensionless reaction rate u\(i]7a)ab2 (see Fig. 1). After a short transient period the position of the front varied linearly with integration time representing a constant velocity c.To investigate the e†ect of the parameters d and i on the front velocity, the ratio of the di†usion coefficients d was varied between 1 and 7, and the relative chlorite excess i between 0 and 20. For each set of parameters the dimensionless velocity c of the propagating front was determined. The dimensional form of the velocity v was then calculated via eqn. (8). v\(kD[S4O62~]0 3 )1@2c (8) Experimental All solutions were prepared using analytical grade chemicals (Reanal) without further puri�cation except sodium chlorite (Aldrich, tech.).To almost saturated solution drops NaClO2 of saturated solution were added to remove the carbon- BaCl2 ate content of technical grade sodium chlorite. The excess Ba2` ions were precipitated with saturated solution. Na2SO4 The solution was then recrystallized twice by slowly adding it to four volume ethanol previously cooled to [8 to [10 ¡C and stirred vigorously.The purity of the determined NaClO2 , by iodometry, was [99.5% after two recrystallizations. The solutions containing Congo Red, a pH indicator for making the change in acidity visible, were poured into thin rectangular capillary tubes and chemical fronts were initiated by adding a drop of the product solution to the top of the tubes. The tubes were then positioned so that the fronts were propagating upwards eliminating any hydrodynamic e†ects due to induced convection as the density of the products was higher than that of the reactants.The experiments were carried out at 25^2 ¡C. The chemical fronts were monitored by a video camera connected to a computer. The acquired data were stored digitally and further processed to determine the front velocities. Three sets of experiments were carried out by varying the initial concentration of and/or with constant K2S4O6 NaClO2 ionic strength in each set while keeping the relative chlorite excess (A in Table 1), the concentration of chlorite (B in Table 1) and the concentration of tetrathionate (C in Table 1), respectively, constant within a set.In each set of experiments 9È11 points were considered and for each point six velocity values were averaged. Results and Discussion For di†erent sets of relative chlorite excess i and ratio of dif- Table 1 Reagent concentrations in three sets of experiments; M, [Congo Red]\0.04% [NaOH]0\1]10~3 A B C [NaClO2]0/10~2 M 1.0È2.0 2.0 2.0È6.0 [K2S4O6]0/10~3 M 2.5È5.0 2.5È5.0 5.00 [KNO3]/10~2 M 0.0È1.0 &Egra]/10~3 M 0.0È2.5 0.0È2.5 È fusion coefficients d we have determined the dimensionless front velocities as shown in Fig. 2 by solving eqn. (6) and (7). Based on eqn. (1) the following expression was �tted to the calculated dimensionless velocities at constant i: c\a)d]b (9) yielding a quantitative agreement (see Fig. 2). Parameters a and b are assumed to have a similar dependence on the relative chlorite excess i.Fig. 3 illustrates that the anticipated functionality quantitatively describes the relationship between the parameters: a\a1(i]7)1@2[a2 and b\[a3(i]7)1@2]a4 (10) where a1\6.06^0.03, a2\3.96^0.10, a3\1.36^0.05 and Substituting eqn. (9) and (10) back in a4\0.68^0.20. Fig. 2 Dimensionless front velocity c as a function of the ratio of di†usion coefficients d. Symbols represent values determined from the solutions of eqn. (6) and (7) and solid lines the best �t according to eqn.(9). corresponds to i\0, to i\10 and to i\20. (L) (K) (») Fig. 3 Values of a and b as a function of relative chlorite (L) (K) excess i. Symbols represent the calculated values and solid lines the best �t according to eqn. (10). 74 J. Chem. Soc., Faraday T rans., 1997, V ol. 93Fig. 4 Front velocity v as a function of the initial tetrathionate concentration with Symbols depict the mea- [ClO2~]0/[S4O62~]0\4. sured velocities with the appropriate errors. Dashed line shows the result of the �t based on eqn.(12) and solid line on eqn. (13). eqn. (8) and rearranging the obtained equation we can express the dimensional front velocity in terms of the physical parameters as : v\(2k[ClO2~]0[S4O62~]0 2)1@2(a1)[DH`][a3)D) [(k[S4O62~]0 3 )1@2(a2)[DH`][a4)D) (11) Fig. 5 Front velocity v as a function of the initial tetrathionate concentration with M. Symbols represent the mea- [ClO2~]0\0.0200 sured velocities with the appropriate errors and solid line the result calculated from eqn.(14). Fig. 6 Front velocity v as a function of the initial chlorite concentration with M. Symbols represent the mea- [S4O62~]0\5.00]10~3 sured velocities with the appropriate errors and solid line the result calculated from eqn. (15). Comparing the above equation with eqn. (1), we can realize that the latter is a limiting form of eqn. (11) when the di†usion coefficient of hydrogen ions is greater than that of the reactants and chlorite is in stoichiometric excess. Under these conditions the term containing in eqn.(11) dominates giving a1 rise to an estimate of C\8.6 for eqn. (1) which is well within the range predicted by Luther in 1906. Eqn. (11) is now used to test the reliability of the reactionÈ di†usion model by comparing the calculated velocity relationships with the experimentally measured ones. For constant relative chlorite excess the model yields v\p1[S4O62~]03@2 (12) where cm s~1@2 if p1\0.14)k [ClO2~]0/[S4O62~]0\4 (used in the experiments).The di†usion coefficient of reactants D is taken as the usual value for small hydrated ions (2]10~5 cm2 s~1) with the hydrogen ions di†using approximately seven times faster. The �tting of eqn. (12) to the experimental data (shown by dashed line in Fig. 4) results in cm M~3@2 p1\(35.45^0.10) s~1. A two-parameter �tting of the experimental data v\p2[S4O62~]03@2[p3 (13) with cm M~3@2 s~1 and p2\(38.28^0.45) p3\(8.2^1.3) cm s~1, yielding a negative intercept common in ]10~4 earlier studies of wave velocities,5h7 however, gives a better agreement (see solid line in Fig. 4). The existence of this small negative shift in the front velocity can be rationalized by considering the experimental setup. A constant amount of NaOH is added to the reactant mixture to inhibit spontaneous front initiation by providing a basic solution. This, in turn, slows down the front propagation since ahead of the front hydroxide ions are neutralized by the hydrogen ions formed.The results of the calculations therefore have to be corrected with the negative o†set as the presence of NaOH in the reaction p3 mixture is not incorporated in the reactionÈdi†usion model. From parameter the rate constant can be estimated as p2 k\7.28]104 M~3 s~1 with its error mainly determined by the uncertainty in the values of di†usion coefficients. By decreasing the initial concentration of tetrathionate with constant initial chlorite concentration the velocity of the front varies as v\[p4[S4O62~]03@2]p5[S4O62~]0[p6 (14) where cm M~3@2 s~1, cmM~1 s~1 and p4\11.8 p5\3.54 cm s~1 if M.It is clear p6\8.2]10~4 [ClO2~]0\0.0200 from Fig. 5 that the model is only able to predict the velocities at slight chlorite excess. At higher excess, i.e. at lower tetrathionate concentration, the measured velocities are signi�cantly smaller than the calculated values. By increasing the initial concentration of chlorite and keeping that of tetrathionate constant the front velocity changes according to eqn.(11) as v\p7)([ClO2~]0)[p8 (15) where cm M~1@2 s~1 and cm s~1. p7\0.139 p8\5.44]10~3 The results shown in Fig. 6 are similar to the previous case : the calculated velocities from eqn. (15) agree with the experimentally measured values at slight chlorite excess. At higher concentrations of chlorite, however, decreasing front velocities are observed experimentally suggesting a change in the mechanism of the reaction. Conclusion The dependence of front velocity on the reactant concentrations was determined for the acid-catalysed chlorite oxidation of tetrathionate using a simple rate law suggested by Nagypa� l and Epstein13 for solutions containing slight excess of chlorite.J. Chem. Soc., Faraday T rans., 1997, V ol. 93 75The obtained expression [eqn. (11)] can be simpli�ed to eqn. (1) predicted by Luther in 1906. The numerical results describing front velocity as a function of reactant concentrations are in quantitative agreement with experimental observations only in the validity range of the empirical rate law in eqn.(2). Based on the experiments we give the following estimate of the rate constant k in eqn. (2) as k\7.28]104 M~3 s~1, which appears to be lower than the value reported by Nagypa� l and Epstein.13 This rate constant, however, has worked consistently well throughout the experiments. Finally we conclude that our results con�rm the use of a simple two-variable model [eqn.(6) and (7)] for numerical studies involving di†erent spatiotemporal pattern formations observed in reactionÈdi†usion fronts of this reaction. We are grateful to Andrea Major for carrying out some preliminary experiments. We thank the Hungarian Science Foundation, OTKA (Grant No. F 017264) for �nancial support of this work. Horva� th thanks the Foundation for Hun- Dezs° garian Higher Education and Research for Magyary Zolta� n Fellowship. References 1 R. Luther, Z. Elektrochem., 1906, 12, 596. 2 A. Arnold, K. Showalter and J. J. Tyson, J. Chem. Educ., 1987, 64, 740. 3 R. A. Fisher, Ann. Eugenics, 1937, 7, 355. 4 A. Kolmogorov, I. Petrovsky and N. Piscouno†, Bull. Univ. Moscow, Ser. Int., Sec. A, 1937, 1, 1. 5 R. J. Field and R. M. Noyes, J. Am. Chem. Soc., 1974, 96, 2001. 6 K. Showalter, J. Phys. Chem., 1981, 85, 440. 7 A. Hanna, A. Saul and K. Showalter, J. Am. Chem. Soc., 1982, 104, 3838. 8 Gy. Po� ta, I. Lengyel and Gy. Bazsa, J. Phys. Chem., 1991, 95, 4379. 9 L. Szirovicza, I. Nagypa� l and E. Boga, J. Am. Chem. Soc., 1989, 111, 2842. 10 D. Horva� th, V. Petrov, S. K. Scott and K. Showalter, J. Chem. Phys., 1993, 98, 6332. 11 D. Horva� th and K. Showalter, J. Chem. Phys., 1995, 102, 2471. To� th, I. Lagzi and D. Horva� th, J. Phys. Chem., 1996, 100, 12 AŠ . 14837. 13 I. Nagypa� l and I. R. Epstein, J. Phys. Chem., 1986, 90, 6285. 14 P. N. Brown, G. D. Byrne and A. C. Hindmarsh, SIAM J. Sci. Stat. Comput., 1989, 10, 1038. Paper 6/05450A; Received 5th August, 1996 76 J. C
ISSN:0956-5000
DOI:10.1039/a605450a
出版商:RSC
年代:1997
数据来源: RSC
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Solvatochromic parameters of ethanolamines |
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Journal of the Chemical Society, Faraday Transactions,
Volume 93,
Issue 1,
1997,
Page 77-79
Abdulkarim S. Labban,
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摘要:
pound and d the thickness of the in situ cell]. If an organic solvent of low absorption is used (such as acetone, ethanol or diethyl ether), the necessary concentration increases with increasing X-ray photon energy because the cross-section for X-rays decreases for heavier atoms. XAFS yields quantitative information on short-range order. This requires that the part of the molecule that undergoes a transformation must contain the absorbing element. To facilitate the XAFS analysis, it is advantageous if the monitored element is present only in a few di†erent local environments in the course of the reaction.The fact that the sample is continuously irradiated with X-rays during the experiment does not seem to have a strong inÑuence on the kinetics of the Finkelstein reaction. Were such an e†ect present, one would expect a much faster reaction due to an easier breaking of the BrwC bond. Being aware of these limitations, we believe that in situ XAFS on liquid-state reactions is a valuable tool to obtain structural as well as kinetic information for selected parts of a molecule.Examples could be the study of, e.g., coordination compounds or metalloproteins. Experimental Equal volumes of 1.333 M solutions of 2-bromopropane and NaI in acetone were mixed at room temperature. A tightly closed DSC aluminium crucible was completely �lled with the reaction mixture (ca. 30 ll). The crucible was placed into a Mettler FP 80/84 DSC heat-Ñux calorimeter that was mounted vertically in the synchrotron X-ray beam and heated to 55.0(5) ¡C within 30 s.The experiment was carried out at the Hamburger Synchrotronstrahlungslabor HASYLAB at Deutsches Elektronen-Synchrotron DESY, Germany, at beamline X1 (ROEMO II). This beamline is equipped with a Si(311) double crystal monochromator, yielding approximately 108 photons s~1 mm~2 at the sample. The energy resolution is approximately 2 eV at the bromine K-edge. The DORIS III storage ring was run with positrons of 4.5 GeV at 80È120 mA.Every 8 min 12 s an X-ray absorption spectrum was taken in transmission at the Br K-edge (photon energy ca. 13 475 eV). Reference spectra of crystalline NaBr were simultaneously measured (at room temperature) by use of a third ionization chamber. The sample Br absorption edge jump was limited by the solubility of NaI and the *kd\(It/I0)\0.38, �xed pathlength in the calorimeter. The measured spectra were evaluated with the programs AUTOBK, FEFF and FEFFIT of the University of Washington package.27h29 Multi-electron phenomena lead to a peak at low R in the Br XAFS spectra.30h34 This was corrected by a simpli�ed approach as described in ref. 35. BrieÑy, this peak was isolated in R-space from a NaBr spectrum and back-transformed into k-space. It was then subtracted from all spectra in k-space before evaluation. When quantitatively analysing XAFS spectra of reacting systems, it is important to keep the number of �t-parameters as small as possible to minimize correlation e†ects.13,35,36 By evaluating spectra of pure 2-bromopropane and NaBr at 55 ¡C we determined the following parameters that were kept constant in subsequent �ts of the reaction mixture: p2(BrwCa)\0.0011 ”2, p2(BrwCb)\0.0137 ”2, p2(BrwNa)\0.02593 ”2, R(BrwCb)\2.858 ”, S02(BrwCa)\S02(BrwCb)\1.082, S02(BrwNa)\1.10, eV, E0(BrwCa)\E0(BrwCb)\[0.89 E0(BrwNa)\[1.65 eV.These values are in good agreement with data for similar compounds.13,33,35 was set to Conse- N(BrwCb) 2N(BrwCa).quently, the only �t variables were the mean coordination numbers and N(BrwNa), and the mean distances N(BrwCa) R(BrwNa) and The evaluated XAFS data range R(BrwCa). was k\2.0È7.1 and R\0.8È3.1 throughout all experi- ”~1 ” ments. 2-Bromopropane (99]%), acetone (99.9%; HPLC grade) and NaI (p.a.) were purchased from Aldrich. Hydrate water of NaI was removed before experiments by heating in vacuum. are grateful to HASYLAB for beamtime.We thank A. We Reller and M. Martin for generous support. Financial support was granted by the Deutsche Forschungsgemeinschaft and by the Fonds der Chemischen Industrie. References 1 X-Ray absorption. Principles, applications, techniques of EXAFS, SEXAFS and XANES, ed. D. C. Koningsberger and R. Prins, Wiley, New York, 1988. 2 D. Bazin, H. Dexpert, N. S. Guyot-Sionnest, J. P. Bournonville and J. Lynch, J. Chim. Phys. Phys. Chim. Biol., 1989, 86, 1707. 3 B. S. Clausen, L. G. Ste†ensen, P. L. Hansen and H. Gra- b~k, Catal. L ett., 1993, 20, 23. Tops‘e, 4 G. Sankar, P. A. Wright, S. Natarajan, J. M. Thomas, G. N. Greaves, A. J. Dent, B. R. Dobson, C. A. Ramsdale and R. H. Jones, J. Phys. Chem., 1993, 97, 9550. 5 H. Bertagnolli and T. S. Ertel, Angew. Chem., 1994, 106, 15. 6 T. Maschmeyer, F. Rey, G. Sankar and J. M. Thomas, Nature (L ondon), 1995, 378, 159. 7 A. Hoser, N. Hilbrandt, M. Martin and M. Denecke, Physica B, 1995, 208/209, 321. 8 P. Andrews, J. M. Corker, J. Evans and M. Webster, J. Chem. Soc., Dalton T rans., 1994, 1337. 9 M. Tabata and K. Ozutsumi, Bull. Chem. Soc. Jpn., 1994, 67, 1608. 10 T. S. Ertel, W. Ho. rner, S. Hu. ckmann, U. Kolb, I. Abraham and H. Bertagnolli, Physica B, 1995, 208/209, 641. 11 N. Yoshida and T. Nagamura, Rev. Sci. Instrum., 1995, 66, 52. 12 A. J. Dent, L. J. Farrugia, A. G. Orpen and S. E. Stratford, J. Chem. Soc., Chem. Commun., 1992, 1456. 13 M. Epple, U. Sazama, A. Reller, N.Hilbrandt, M. Martin and L. Tro. ger, Chem. Commun., 1996, 1755. 14 L. Tro. ger, N. Hilbrandt and M. Epple, J. Phys. Coll., 1997, in press. 15 H. Finkelstein, Chem. Ber., 1910, 43, 1528. 16 S. D. Hamann, Aust. J. Chem., 1975, 28, 693. 17 C. D. Chalk, J. McKenna and I. H. Williams, J. Am. Chem. Soc., 1981, 103, 272. 18 L. Eberston, Acta Chem. Scand., Sect. B, 1982, B36, 533. 19 P. B. D. de la Mare, J. Chem. Soc., 1955, 3169. 20 E. D. Hughes, C. K. Ingold and J. D. H. Mackie, J.Chem. Soc., 1955, 3173. 21 E. D. Hughes, C. K. Ingold and J. D. H. Mackie, J. Chem. Soc., 1955, 3177. 22 P. B. D. de la Mare, J. Chem. Soc., 1955, 3180. 23 L. Fowden, E. D. Hughes and C. K. Ingold, J. Chem. Soc., 1955, 3187. 24 L. Fowden, E. D. Hughes and C. K. Ingold, J. Chem. Soc., 1955, 3193. 25 P. B. D. de la Mare, J. Chem. Soc., 1955, 3196. 26 P. B. D. de la Mare, L. Fowden, E. D. Hughes, C. K. Ingold and J. D. H. Mackie, J. Chem. Soc., 1955, 3200. 27 J. J. Rehr, R.C. Albers and S. I. Zabinsky, Phys. Rev. L ett., 1992, 69, 3397. 28 L. Tro. ger, T. Yokoyama, D. Arvanitis, T. Lederer, M. Tischer and K. Baberschke, Phys. Rev. B, 1994, 49, 888. 29 E. A. Stern, M. Newville, B. Ravel, Y. Yacoby and D. Haskel, Physica B, 1995, 208/209, 117. 30 E. A. Stern, S. M. Heald and B. Bunker, Phys. Rev. L ett., 1979, 42, 1372. 31 G. Li, F. Bridges and G. S. Brown, Phys. Rev. L ett., 1992, 68, 1609. 32 P. DÏAngelo, A. Di Cicco, A. Filipponi and N. V.Pavel, Phys. Rev. A, 1993, 47, 2055. 33 E. Burattini, P. DÏAngelo, A. Di Cicco, A. Filipponi and N. V. Pavel, J. Phys. Chem., 1993, 97, 5486. 34 J. J. Rehr, C. H. Booth, F. Bridges and S. I. Zabinsky, Phys. Rev. B, 1994, 49, 12347. 35 M. Epple, H. Kirschnick, G. N. Greaves, G. Sankar and J. M. Thomas, J. Chem. Soc., Faraday T rans., 1996, 5035. 36 M. Epple and L. Tro. ger, J. Chem. Soc., Dalton T rans., 1996, 11. Paper 7/01433C; Received 28th February, 1997 J. Chem. Soc., Faraday T rans., 1997, V ol. 93 3037pound and d the thickness of the in situ cell]. If an organic solvent of low absorption is used (such as acetone, ethanol or diethyl ether), the necessary concentration increases with increasing X-ray photon energy because the cross-section for X-rays decreases for heavier atoms. XAFS yields quantitative information on short-range order. This requires that the part of the molecule that undergoes a transformation must contain the absorbing element. To facilitate the XAFS analysis, it is advantageous if the monitored element is present only in a few di†erent local environments in the course of the reaction.The fact that the sample is continuously irradiated with X-rays during the experiment does not seemtrong inÑuence on the kinetics of the Finkelstein reaction. Were such an e†ect present, one would expect a much faster reaction due to an easier breaking of the BrwC bond. Being aware of these limitations, we believe that in situ XAFS on liquid-state reactions is a valuable tool to obtain structural as well as kinetic information for selected parts of a molecule.Examples could be the study of, e.g., coordination compounds or metalloproteins. Experimental Equal volumes of 1.333 M solutions of 2-bromopropane and NaI in acetone were mixed at room temperature. A tightly closed DSC aluminium crucible was completely �lled with the reaction mixture (ca. 30 ll). The crucible was placed into a Mettler FP 80/84 DSC heat-Ñux calorimeter that was mounted vertically in the synchrotron X-ray beam and heated to 55.0(5) ¡C within 30 s.The experiment was carried out at the Hamburger Synchrotronstrahlungslabor HASYLAB at Deutsches Elektronen-Synchrotron DESY, Germany, at beamline X1 (ROEMO II). This beamline is equipped with a Si(311) double crystal monochromator, yielding approximately 108 photons s~1 mm~2 at the sample. The energy resolution is approximately 2 eV at the bromine K-edge.The DORIS III storage ring was run with positrons of 4.5 GeV at 80È120 mA. Every 8 min 12 s an X-ray absorption spectrum was taken in transmission at the Br K-edge (photon energy ca. 13 475 eV). Reference spectra of crystalline NaBr were simultaneously measured (at room temperature) by use of a third ionization chamber. The sample Br absorption edge jump was limited by the solubility of NaI and the *kd\(It/I0)\0.38, �xed pathlength in the calorimeter. The measured spectra were evaluated with the programs AUTOBK, FEFF and FEFFIT of the University of Washington package.27h29 Multi-electron phenomena lead to a peak at low R in the Br XAFS spectra.30h34 This was corrected by a simpli�ed approach as described in ref. 35. BrieÑy, this peak was isolated in R-space from a NaBr spectrum and back-transformed into k-space. It was then subtracted from all spectra in k-space before evaluation. When quantitatively analysing XAFS spectra of reacting systems, it is important to keep the number of �t-parameters as small as possible to minimize correlation e†ects.13,35,36 By evaluating spectra of pure 2-bromopropane and NaBr at 55 ¡C we determined the following parameters that were kept constant in subsequent �ts of the reaction mixture: p2(BrwCa)\0.0011 ”2, p2(BrwCb)\0.0137 ”2, p2(BrwNa)\0.02593 ”2, R(BrwCb)\2.858 ”, S02(BrwCa)\S02(BrwCb)\1.082, S02(BrwNa)\1.10, eV, E0(BrwCa)\E0(BrwCb)\[0.89 E0(BrwNa)\[1.65 eV. These values are in good agreement with data for similar compounds.13,33,35 was set to Conse- N(BrwCb) 2N(BrwCa).quently, the only �t variables were the mean coordination numbers and N(BrwNa), and the mean distances N(BrwCa) R(BrwNa) and The evaluated XAFS data range R(BrwCa). was k\2.0È7.1 and R\0.8È3.1 throughout all experi- ”~1 ” ments. 2-Bromopropane (99]%), acetone (99.9%; HPLC grade) and NaI (p.a.) were purchased from Aldrich. Hydrate water of NaI was removed before experiments by heating in vacuum.are grateful to HASYLAB for beamtime. We thank A. We Reller and M. Martin for generous support. Financial support was granted by the Deutsche Forschungsgemeinschaft and by the Fonds der Chemischen Industrie. References 1 X-Ray absorption. Principles, applications, techniques of EXAFS, SEXAFS and XANES, ed. D. C. Koningsberger and R. Prins, Wiley, New York, 1988. 2 D. Bazin, H. Dexpert, N. S. Guyot-Sionnest, J. P. Bournonville and J. Lynch, J. Chim. Phys.Phys. Chim. Biol., 1989, 86, 1707. 3 B. S. Clausen, L. G. Ste†ensen, P. L. Hansen and H. Gra- b~k, Catal. L ett., 1993, 20, 23. Tops‘e, 4 G. Sankar, P. A. Wright, S. Natarajan, J. M. Thomas, G. N. Greaves, A. J. Dent, B. R. Dobson, C. A. Ramsdale and R. H. Jones, J. Phys. Chem., 1993, 97, 9550. 5 H. Bertagnolli and T. S. Ertel, Angew. Chem., 1994, 106, 15. 6 T. Maschmeyer, F. Rey, G. Sankar and J. M. Thomas, Nature (L ondon), 1995, 378, 159. 7 A. Hoser, N. Hilbrandt, M. Martin and M.Denecke, Physica B, 1995, 208/209, 321. 8 P. Andrews, J. M. Corker, J. Evans and M. Webster, J. Chem. Soc., Dalton T rans., 1994, 1337. 9 M. Tabata and K. Ozutsumi, Bull. Chem. Soc. Jpn., 1994, 67, 1608. 10 T. S. Ertel, W. Ho. rner, S. Hu. ckmann, U. Kolb, I. Abraham and H. Bertagnolli, Physica B, 1995, 208/209, 641. 11 N. Yoshida and T. Nagamura, Rev. Sci. Instrum., 1995, 66, 52. 12 A. J. Dent, L. J. Farrugia, A. G. Orpen and S. E. Stratford, J. Chem. Soc., Chem. Commun., 1992, 1456. 13 M.Epple, U. Sazama, A. Reller, N. Hilbrandt, M. Martin and L. Tro. ger, Chem. Commun., 1996, 1755. 14 L. Tro. ger, N. Hilbrandt and M. Epple, J. Phys. Coll., 1997, in press. 15 H. Finkelstein, Chem. Ber., 1910, 43, 1528. 16 S. D. Hamann, Aust. J. Chem., 1975, 28, 693. 17 C. D. Chalk, J. McKenna and I. H. Williams, J. Am. Chem. Soc., 1981, 103, 272. 18 L. Eberston, Acta Chem. Scand., Sect. B, 1982, B36, 533. 19 P. B. D. de la Mare, J. Chem. Soc., 1955, 3169. 20 E. D. Hughes, C. K. Ingold and J. D. H. Mackie, J. Chem. Soc., 1955, 3173. 21 E. D. Hughes, C. K. Ingold and J. D. H. Mackie, J. Chem. Soc., 1955, 3177. 22 P. B. D. de la Mare, J. Chem. Soc., 1955, 3180. 23 L. Fowden, E. D. Hughes and C. K. Ingold, J. Chem. Soc., 1955, 3187. 24 L. Fowden, E. D. Hughes and C. K. Ingold, J. Chem. Soc., 1955, 3193. 25 P. B. D. de la Mare, J. Chem. Soc., 1955, 3196. 26 P. B. D. de la Mare, L. Fowden, E. D. Hughes, C. K. Ingold and J. D. H. Mackie, J.Chem. Soc., 1955, 3200. 27 J. J. Rehr, R. C. Albers and S. I. Zabinsky, Phys. Rev. L ett., 1992, 69, 3397. 28 L. Tro. ger, T. Yokoyama, D. Arvanitis, T. Lederer, M. Tischer and K. Baberschke, Phys. Rev. B, 1994, 49, 888. 29 E. A. Stern, M. Newville, B. Ravel, Y. Yacoby and D. Haskel, Physica B, 1995, 208/209, 117. 30 E. A. Stern, S. M. Heald and B. Bunker, Phys. Rev. L ett., 1979, 42, 1372. 31 G. Li, F. Bridges and G. S. Brown, Phys. Rev. L ett., 1992, 68, 1609. 32 P. DÏAngelo, A.Di Cicco, A. Filipponi and N. V. Pavel, Phys. Rev. A, 1993, 47, 2055. 33 E. Burattini, P. DÏAngelo, A. Di Cicco, A. Filipponi and N. V. Pavel, J. Phys. Chem., 1993, 97, 5486. 34 J. J. Rehr, C. H. Booth, F. Bridges and S. I. Zabinsky, Phys. Rev. B, 1994, 49, 12347. 35 M. Epple, H. Kirschnick, G. N. Greaves, G. Sankar and J. M. Thomas, J. Chem. Soc., Faraday T rans., 1996, 5035. 36 M. Epple and L. Tro. ger, J. Chem. Soc., Dalton T rans., 1996, 11. Paper 7/01433C; Received 28th February, 1997 J.Chem. Soc., Faraday T rans., 1997, V ol. 93 3037pound and d the thickness of the in situ cell]. If an organic solvent of low absorption is used (such as acetone, ethanol or diethyl ether), the necessary concentration increases with increasing X-ray photon energy because the cross-section for X-rays decreases for heavier atoms. XAFS yields quantitative information on short-range order. This requires that the part of the molecule that undergoes a transformation must contain the absorbing element.To facilitate the XAFS analysis, it is advantageous if the monitored element is present only in a few di†erent local environments in the course of the reaction. The fact that the sample is continuously irradiated with X-rays during the experiment does not seem to have a strong inÑuence on the kinetics of the Finkelstein reaction. Were such an e†ect present, one would expect a much faster reaction due to an easier breaking of the BrwC bond. Being aware of these limitations, we believe that in situ XAFS on liquid-state reactions is a valuable tool to obtain structural as well as kinetic information for selected parts of a molecule.Examples could be the study of, e.g., coordination compounds or metalloproteins. Experimental Equal volumes of 1.333 M solutions of 2-bromopropane and NaI in acetone were mixed at room temperature. A tightly closed DSC aluminium crucible was completely �lled with the reaction mixture (ca. 30 ll). The crucible was placed into a Mettler Fat-Ñux calorimeter that was mounted vertically in the synchrotron X-ray beam and heated to 55.0(5) ¡C within 30 s. The experiment was carried out at the Hamburger Synchrotronstrahlungslabor HASYLAB at Deutsches Elektronen-Synchrotron DESY, Germany, at beamline X1 (ROEMO II). This beamline is equipped with a Si(311) double crystal monochromator, yielding approximately 108 photons s~1 mm~2 at the sample.The energy resolution is approximately 2 eV at the bromine K-edge. The DORIS III storage ring was run with positrons of 4.5 GeV at 80È120 mA. Every 8 min 12 s an X-ray absorption spectrum was taken in transmission at the Br K-edge (photon energy ca. 13 475 eV). Reference spectra of crystalline NaBr were simultaneously measured (at room temperature) by use of a third ionization chamber. The sample Br absorption edge jump was limited by the solubility of NaI and the *kd\(It/I0)\0.38, �xed pathlength in the calorimeter.The measured spectra were evaluated with the programs AUTOBK, FEFF and FEFFIT of the University of Washington package.27h29 Multi-electron phenomena lead to a peak at low R in the Br XAFS spectra.30h34 This was corrected by a simpli�ed approach as described in ref. 35. BrieÑy, this peak was isolated in R-space from a NaBr spectrum and back-transformed into k-space. It was then subtracted from all spectra in k-space before evaluation.When quantitatively analysing XAFS spectra of reacting systems, it is important to keep the number of �t-parameters as small as possible to minimize correlation e†ects.13,35,36 By evaluating spectra of pure 2-bromopropane and NaBr at 55 ¡C we determined the following parameters that were kept constant in subsequent �ts of the reaction mixture: p2(BrwCa)\0.0011 ”2, p2(BrwCb)\0.0137 ”2, p2(BrwNa)\0.02593 ”2, R(BrwCb)\2.858 ”, S02(BrwCa)\S02(BrwCb)\1.082, S02(BrwNa)\1.10, eV, E0(BrwCa)\E0(BrwCb)\[0.89 E0(BrwNa)\[1.65 eV.These values are in good agreement with data for similar compounds.13,33,35 was set to Conse- N(BrwCb) 2N(BrwCa). quently, the only �t variables were the mean coordination numbers and N(BrwNa), and the mean distances N(BrwCa) R(BrwNa) and The evaluated XAFS data range R(BrwCa). was k\2.0È7.1 and R\0.8È3.1 throughout all experi- ”~1 ” ments. 2-Bromopropane (99]%), acetone (99.9%; HPLC grade) and NaI (p.a.) were purchased from Aldrich.Hydrate water of NaI was removed before experiments by heating in vacuum. are grateful to HASYLAB for beamtime. We thank A. We Reller and M. Martin for generous support. Financial support was granted by the Deutsche Forschungsgemeinschaft and by the Fonds der Chemischen Industrie. References 1 X-Ray absorption. Principles, applications, techniques of EXAFS, SEXAFS and XANES, ed. D. C. Koningsberger and R. Prins, Wiley, New York, 1988. 2 D. Bazin, H. Dexpert, N. S. Guyot-Sionnest, J.P. Bournonville and J. Lynch, J. Chim. Phys. Phys. Chim. Biol., 1989, 86, 1707. 3 B. S. Clausen, L. G. Ste†ensen, P. L. Hansen and H. Gra- b~k, Catal. L ett., 1993, 20, 23. Tops‘e, 4 G. Sankar, P. A. Wright, S. Natarajan, J. M. Thomas, G. N. Greaves, A. J. Dent, B. R. Dobson, C. A. Ramsdale and R. H. Jones, J. Phys. Chem., 1993, 97, 9550. 5 H. Bertagnolli and T. S. Ertel, Angew. Chem., 1994, 106, 15. 6 T. Maschmeyer, F. Rey, G. Sankar and J. M. Thomas, Nature (L ondon), 1995, 378, 159. 7 A. Hoser, N. Hilbrandt, M. Martin and M. Denecke, Physica B, 1995, 208/209, 321. 8 P. Andrews, J. M. Corker, J. Evans and M. Webster, J. Chem. Soc., Dalton T rans., 1994, 1337. 9 M. Tabata and K. Ozutsumi, Bull. Chem. Soc. Jpn., 1994, 67, 1608. 10 T. S. Ertel, W. Ho. rner, S. Hu. ckmann, U. Kolb, I. Abraham and H. Bertagnolli, Physica B, 1995, 208/209, 641. 11 N. Yoshida and T. Nagamura, Rev. Sci. Instrum., 1995, 66, 52. 12 A. J. Dent, L. J. Farrugia, A. G. Orpen and S.E. Stratford, J. Chem. Soc., Chem. Commun., 1992, 1456. 13 M. Epple, U. Sazama, A. Reller, N. Hilbrandt, M. Martin and L. Tro. ger, Chem. Commun., 1996, 1755. 14 L. Tro. ger, N. Hilbrandt and M. Epple, J. Phys. Coll., 1997, in press. 15 H. Finkelstein, Chem. Ber., 1910, 43, 1528. 16 S. D. Hamann, Aust. J. Chem., 1975, 28, 693. 17 C. D. Chalk, J. McKenna and I. H. Williams, J. Am. Chem. Soc., 1981, 103, 272. 18 L. Eberston, Acta Chem. Scand., Sect. B, 1982, B36, 533. 19 P.B. D. de la Mare, J. Chem. Soc., 1955, 3169. 20 E. D. Hughes, C. K. Ingold and J. D. H. Mackie, J. Chem. Soc., 1955, 3173. 21 E. D. Hughes, C. K. Ingold and J. D. H. Mackie, J. Chem. Soc., 1955, 3177. 22 P. B. D. de la Mare, J. Chem. Soc., 1955, 3180. 23 L. Fowden, E. D. Hughes and C. K. Ingold, J. Chem. Soc., 1955, 3187. 24 L. Fowden, E. D. Hughes and C. K. Ingold, J. Chem. Soc., 1955, 3193. 25 P. B. D. de la Mare, J. Chem. Soc., 1955, 3196. 26 P. B. D. de la Mare, L. Fowden, E. D. Hughes, C. K. Ingold and J. D. H. Mackie, J. Chem. Soc., 1955, 3200. 27 J. J. Rehr, R. C. Albers and S. I. Zabinsky, Phys. Rev. L ett., 1992, 69, 3397. 28 L. Tro. ger, T. Yokoyama, D. Arvanitis, T. Lederer, M. Tischer and K. Baberschke, Phys. Rev. B, 1994, 49, 888. 29 E. A. Stern, M. Newville, B. Ravel, Y. Yacoby and D. Haskel, Physica B, 1995, 208/209, 117. 30 E. A. Stern, S. M. Heald and B. Bunker, Phys. Rev. L ett., 1979, 42, 1372. 31 G. Li, F. Bridges and G. S. Brown, Phys. Rev. L ett., 1992, 68, 1609. 32 P. DÏAngelo, A. Di Cicco, A. Filipponi and N. V. Pavel, Phys. Rev. A, 1993, 47, 2055. 33 E. Burattini, P. DÏAngelo, A. Di Cicco, A. Filipponi and N. V. Pavel, J. Phys. Chem., 1993, 97, 5486. 34 J. J. Rehr, C. H. Booth, F. Bridges and S. I. Zabinsky, Phys. Rev. B, 1994, 49, 12347. 35 M. Epple, H. Kirschnick, G. N. Greaves, G. Sankar and J. M. Thomas, J. Chem. Soc., Faraday T rans., 1996, 5035. 36 M. Epple and L. Tro. ger, J. Chem. Soc., Dalton T rans., 1996, 11. Paper 7/01433C; Received 28th February, 1997 J. Chem. Soc., Faraday T rans., 1997, V o
ISSN:0956-5000
DOI:10.1039/a605521d
出版商:RSC
年代:1997
数据来源: RSC
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Silicon-29 NMR self-diffusion and chemical-exchange studiesof concentrated sodium silicate solutions |
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Journal of the Chemical Society, Faraday Transactions,
Volume 93,
Issue 1,
1997,
Page 93-98
Elke K. F. Bahlmann,
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摘要:
Silicon-29 NMR self-di†usion and chemical-exchange studies of concentrated sodium silicate solutions Elke K. F. Bahlmann,a Robin K. Harris,a* Kenneth Metcalfe,b Je†rey W. Rockli†eb and Edward G. Smithb a Department of Chemistry, University of Durham, South Road, Durham, UK DH1 3L E b Unilever Research, Quarry Road East, Bebington, W irral, UK L 63 3JW For the �rst time, self-di†usion of silicate species in a highly condensed silicate solution has been investigated. Self-di†usion coefficients in the range of 5.8]10~11 m2 s~1 (for the Q4 units) to 1.9]10~10 m2 s~1 (for the Q1 units) were obtained.Upper limits to chemical-exchange rates between silicate units have been determined. The exchange processes are not fast enough to average the self-di†usion coefficients between the various units on the timescale of the relevant stimulated echo experiment, though they may reduce the observed di†erences in Dself . Soluble silicates are of considerable technological importance and are among the most widely used inorganic chemicals, with applications falling into three main categories : detergent, adhesive and chemical.Silicates are often employed in detergent products in preference to other alkalis, such as soda ash, because of their corrosion-inhibition properties and detergent attributes.1 Their ability to form �lms on drying gives rise to applications in adhesive and coating technologies. Most silicate applications require the material in the form of an aqueous solution. Compared to all other analytical techniques used to study silicates, NMR methods can provide a greater wealth of microstructural and dynamic information without disturbing the system.The NMR investigations carried out so far, however, mainly focused on silicate solutions with a low degree of condensation and without colloidal particles.2,3 In previous investigations of higher ratio (Rm\SiO2 : Na2O), and more highly condensed silicate solutions, the emphasis has tended to be on silicate speciation, with limited studies of dynamic exchange. Such work has o†ered little in terms of quantitative information on the larger silica aggregates present in silicate solutions.4 The present, quantitative5 29Si NMR studies exploit pulse �eld gradient (PFG) NMR and two-dimensional exchange spectroscopy (EXSY) to study the larger silicate species in a concentrated, (25 wt.% SiO2) Rm\ 4.0, sodium silicate solution.We have investigated the dynamics of such a solution in terms of di†usive motion.Although self-di†usion measurements have been extensively reported for protons and Ñuorine6 in heterogeneous systems, the use of �eld gradients in the measurement of silicon selfdi† usion in simple or highly condensed multicomponent systems is novel. Alkali silicate solutions contain a wide range of anionic species, especially for high concentrations and high ratios of silica to metal oxide. This results in considerable overlapping of 29Si NMR peaks so that only a small number of complex bands can be seen.These bands are generally assigned to di†erent silicon connectivities and indicated by the notation Qn, where Q indicates that silicon has four bonds to oxygen and n represents the number of siloxane bridges, the remaining attached groups being OH or O~Na` (in the case of sodium silicate). Thus an increase in n is expected to be generally associated with increasing particle size.The rates of exchange of silicate groups between the various species present in alkaline silicate solutions have been the subject of discussion for many years.7h12 It seems to be clear that the rates vary according to the species considered and with factors such as pH and concentration. Equilibrium between species is normally established quickly (seconds or minutes) but in some cases it may be reached very slowly, especially in highly concentrated solutions and for large ionic species.We have therefore used two-dimensional exchange (EXSY) NMR to obtain semiquantitative information about exchange rates in the 29Si-enriched solution under study. Previously, EXSY work,13 on relatively dilute potassium silicate solution, was primarily directed to understanding the pathways for exchange between small oligomeric species. The present work is the �rst to monitor successfully the exchange processes in a highly condensed silicate solution semiquantitatively.The purpose of this paper is to report, for a concentrated sodium silicate solution, unique measurements of the di†usion coefficients and the rate of exchange of silicate groups between the di†erent environments. The key points of our strategy are listed below. 1. Use of a sample isotopically enriched in 29Si in order to gain sufficient signal-to-noise to enable the 29Si pulsedgradient spin-echo (PGSE) experiment to be feasible.14h16 2. Selection of the stimulated echo variant of the PGSE technique to overcome the limitation on length of the PFG pulse due to the competing e†ects of transverse relaxation processes on the available echo intensity.17 3.Choosing to vary the duration, d, of the �eld gradient pulse rather than the time, D, between successive �eld gradient pulses in order to avoid additional modulation of the signal attenuation arising from homonuclear spinÈspin coupling e†ects in the enriched sample. (JSi~Si) 4. Fourier transformation of the free induction decay (FID) following the spin-echo maximum to provide an opportunity for selectively measuring di†usion coefficients of di†erent silicate environments giving resolved signals.18 5.Use of EXSY13 to estimate the exchange rates for the di†erent silicate environments. These are required since the di†usion measurements only have meaning for di†erent groups if the species remain intact over the timescale of the di†usion measurement. 6. Consideration of the implications of the di†usion measurements with respect to the particle size of colloidal silica present in the concentrated sodium silicate solution. Rm\4.0 Theory The attenuation of the spin-echo following a 90¡ÈqÈ180¡Èq J. Chem.Soc., Faraday T rans., 1997, 93(1), 93È98 93Fig. 1 The basic PGSE experiment pulse sequence, which arises from di†usive dephasing under the inÑuence of a magnetic �eld gradient, can be used to determine molecular self-di†usion coefficients.The PGSE sequence, �rst used by Stejskal and Tanner,14h16 is illustrated in Fig. 1. The gradient is applied in the form of rectangular pulses inserted in the dephasing and rephasing parts of a spin-echo sequence. The notation used in the �gure is : t1 È inter-pulse time of the echo sequence (equal to the time between the 180¡ pulse and the echo maximum) d Èduration of the pulse gradient delay 1 È period between the end of the 90¡ pulse and the start of the �eld gradient pulse ; D È time between the starts of successive gradient pulses (kept constant in the experiment) ; delay 2 È equals D[d G È�eld gradient strength.Attenuation of the echo arising from spin di†usion can be achieved by varying d, D or G. In the present experiment, d is chosen as the variable in preference to D in order to avoid J-coupling e†ects.18 The measurement of the self-di†usion coefficient by PGSE NMR is limited by the loss of phase coherence due to transverse relaxation during This restricts the maximum usable 2t1.value of d, which obviously has to be less than so that in t1, the case of short spinÈspin relaxation time values and (T2) slow self-di†usion the classical PGSE is not applicable.17 A method of avoiding this problem is to store the transverse magnetisation existing at some point in time after the initial t1 90¡ pulse for later recall thus eliminating the signal attenuation due to dephasing (arising from which would have T2) otherwise occurred during the intervening time This is t2 .done by applying a pulse at time which rotates the 90x ¡ t1, y-component of the magnection (parallel to the static applied magnetic �eld where only B0), spinÈlattice relaxation (which is relatively slow) will occur. Any x-magnetisation will be una†ected by the second pulse, so that only this part of the transverse magnetisation is lost Fig. 2 The stimulated echo sequence during the storage. The magnetisation is recalled after a time using a pulse, which leads to a stimulated echo after a t2 90x ¡ further time The attenuation of this echo has a spinÈlattice t1.relaxation time dependence during the interval between (T1) the second and the third pulse, which is not a problem, however, in the experiments described herein (because is T1 long). The pulse sequence for such a stimulated echo is shown in Fig. 2. The general expression for the attenuation of the spin-echo amplitude with time, taking into account the and relax- T1 T2 ation together with the self-di†usion under the inÑuence of a magnetic �eld gradient, for both the normal and the stimulated echo,11,14,17 is given by: A\f (T1, t1, T2 , t2)expC[c2Dd2G2AD[ d 3BD (1) where D is the self-di†usion coefficient and provided that t1 and are held constant within the experiment.t2 The contributions to the signal attenuation from the relaxation and di†usion processes can be isolated by recording the spin-echo sequence with and without applying the pulsed �eld gradient (PFG).Taking the ratio of these two experiments as a function of increasing d gives : A@\ APFG(on) APFG(off ) \expC[c2Dd2G2AD[ d 3BD (2) Experimental Sodium silicate solutions were prepared by dissolving a source of silica in high purity (BDH Aristar) sodium hydroxide solution in alkali-resistant plastic containers at ca. 75 ¡C. Great care was taken to exclude carbon dioxide and oxygen from the solutions, with preparation and handling conducted under a nitrogen atmosphere.The silica took approximately six weeks to dissolve. The solutions were then allowed to take a further eight weeks to equilibrate at room temperature. Two samples were prepared for this study. Both were sodium silicate solutions with 25 wt.% and One sample SiO2 Rm\4.0. was prepared using silica enriched in 29Si to the 95.65% level (ex. Oakridge National Laboratory), whilst an analogous sample was prepared using fumed silica in which the silicon isotopes were at natural abundance levels.The fumed silica was prepared via the hydrolysis of distilled silicon tetrachloride (BDH). Only a small quantity (ca. 100 mg) of enriched silica was available to us, and so to avoid transfer losses the relevant sodium silicate solution was prepared directly in the 10 mm TeÑon FEP insert used for the NMR measurements. All self-di†usion experiments were carried out on a Bruker MSL300 NMR spectrometer equipped with a custom-built probe head containing anti-Helmholz coils for applying linear �eld gradients (no residual gradients in the G0) B0-direction using the stimulated echo PGSE NMR experiment.The attenuation ratio [eqn. (2)] is measured for the silicate species and compared against a reference of known D while keeping the PFG conditions constant. Since an enriched silicon-29 reference sample of known was not available, water was Dself chosen as the reference. The known dependence of A on c gives validity to this procedure.A semilogarithmic plot of A@ vs. d2[D[(d/3)] yields a slope, S, which can be correlated to that of the water di†usion experiment under equal conditions, using the known di†usion constant of water.6 The self-di†usion constants for the Si units in the silicate solution are calculated with the following equations. 6,17 S\[c2G2D (3) 94 J. Chem. Soc., Faraday T rans., 1997, V ol. 93SSi SH2O cH 2 cSi 2 \ DSi DH2O (4) DSi\25.9 SSi SH2O DH2O (5) The value for the self-di†usion coefficient of water has been reported to be 2.3]10~9 m2 s~1 at 27 ¡C.12 The calibration of the attenuation A@ using the self-di†usion of protons in pure water was carried out under the following conditions : 16 transients were acquired for each value of d; recycle delay\1 s; D\50 ms and ms.This experiment (see Fig. 3) t1\44 resulted in a slope S\[0.543. The self-di†usion constants for the various silicate species were obtained under the following conditions : D\50 ms; d up to 7.0 ms; ms ; number of transients acquired for t1\40 each value of d\32; recycle delay\60 s ; 90¡ pulse duration\18 ms; acquisition time\0.02 s.In many measurements of self di†usion by NMR, only the height of the echo is measured, thus eliminating any information speci�c to given components of the solution. However, we have chosen to Fourier transform the decay of each echo to produce a spectrum. This enables us to monitor the attenuation of the signal for each distinct resonance, i.e., for Q1, Q2, Q3 and Q4 groups, separately.Since larger particles tend to contain a higher proportion of more condensed silicate units, this procedure gives added information regarding self di†usion in the system. Moreover, this implies that separate values for the average radii of particles containing the various units can be obtained. The EXSY technique is useful where exchange rates are relatively slow on the NMR timescale, so that separate resonances are observed for di†erent chemical sites for the nuclei involved. The basic pulse sequence used is as follows : [TdÈ90x ¡ Èt1È90x ¡ ÈtmÈ90x ¡ ÈFID]n where is a delay time ([5 times the longest spinÈlattice Td relaxation time; in this case the longest was 12 s), is a T1 tm mixing time during which exchange takes place and is vari- t1 able.The second variable of the two-dimensional experiment is the running time, of the FID.The sequence is repeated n t2 , times to accumulate an adequate signal-to-noise ratio. During the spins are encoded with their chemical shift, which is also t1 monitored during After double Fourier transformation the t2 . diagonal of the two-dimensional plot relates to spins which have not changed their sites during whereas o†-diagonal tm , peaks give (selectively) information about exchange during tm . The value of can be varied to cover a range of exchange tm Fig. 3 Self-di†usion measurement of protons in water from the attenuation of the half-echo rates, but the minimum rate detectable is governed by the relevant times which limit the usable values of T1, tm .The EXSY experiments were performed on a Bruker AMX500 spectrometer using the same solution as that used for the self-di†usion measurements. Six di†erent mixing times, were used, viz. 0.05, 0.10, 0.20, 0.45, 075 and 2.0 s. The tm , recycle delay was 60 s, the acquisition time 10 ms and 16 transients were accumulated for each value of The number of t1.data points used in each time dimension was 128. The viscosity of the sodium silicate solutions prepared using fumed silica was determined using a Carrimed CSL100 rheometer and was measured as a function of shear rate at constant stress using a thermostatted cone (4¡) and plate (2 cm diameter) which was open to the atmosphere. Results and Discussion The normal 29Si spectrum is shown for both the enriched and normal-abundance sodium silicate solution in Fig. 4, with assignments to the di†erent silicate environments indicated. The concentrations in the solutions were determined SiO2 using a method of quanti�cation described elsewhere5 and were found to be 25.0 and 24.3 wt.% for the enriched and unenriched samples, respectively. The distribution of structural units is shown in Table 1 and indicates that more Q4 units are found in the unenriched sample as compared to the enriched sample. This suggests that the source of silica has in some way a†ected the solution-state speciation and is in line with previous observations that di†erent sources of silica can inÑuence the properties of the resultant silicate solution.19 Clearly, this di†erence in silicate speciation introduces an additionty when we utilise a viscosity measurement made on the unenriched sample in combination with the Fig. 4 Silicon-29 NMR spectrum of a sodium silicate solution with 25 wt.% and a ratio of 4.0.(a) Sample with 29Si at SiO2 SiO2 : Na2O natural abundance (VXR 300 spectrometer, 59.6 MHz). (b) Sample with isotopic enrichment in 29Si (AMX 500 spectrometer, 99.4 MHz). Spectrometer operating conditions : acquisition time 40 ms for (a) and 60 ms for (b), recycle delay 20 s for (a) and 210 s for (b), number of transients 2800 for (a) and 16 for (b). Gated inverse proton decoupling was used. The chemical shift scale is plotted relative to the Q0 signal. J. Chem. Soc., Faraday T rans., 1997, V ol. 93 95Table 1 Distribution of structure units found in the sodium silicate solution 29Si-enriched non-enriched (25 wt.% SiO2 (25 wt.% SiO2 structural unit Rm\4.0) (%) Rm\4.0) (%) Q0 0.2 0.7 Q1 2.8 3.3 Qcyc 2 0.0 0.0 Q2 25.9 21.4 Q3 55.5 52.3 Q4 15.6 22.3 self-di†usion coefficients determined on the enriched sample to consider the implications on the particle size of colloidal silica present in the samples. Self di†usion Fig. 5 shows a stacked plot of spin-echo spectra recorded as a function of the PFG pulse duration, d, and indicates the e†ect of di†usion on peak attenuation for the di†erent Q bands within the spectrum.Notice the poor S/N which is obtained. This is a consequence of the attenuation arising from di†usion. Table 2 and Fig. 6 show the attenuated peak areas for the various Q bands as a function of d. Unfortunately, with the exception of Q1, experimental limitations did not allow us to make measurements extending beyond one decade of peakarea attenuation.Eqn. (5) was used to estimate the self- Fig. 5 Stacked plot of half-echo spectra as a function of d for the 29Si-enriched sample of sodium silicate solution with 25 wt.% SiO2 and a ratio of 4.0 SiO2 : Na2O Table 2 Attenuation of peak areas (arbitrary units) under the inÑuence of a pulsed �eld gradient in a stimulated echo experiment for a sodium silicate solution with 25 wt.% and SiO2 Rm\4.0 d/ms d2[D[(d/3)] Q1 Q2 Q3 Q4 1 50 0.88 0.83 1.0 0.93 3 441 0.60 0.68 0.83 0.89 4 779 0.20 0.47 0.48 0.44 4.5 982 0.30 0.49 0.69 0.22 5.0 1208 0.16 0.47 0.85 0.69 5.5 1457 0.06 0.23 0.47 0.34 6.0 1728 0.03 0.22 0.29 0.21 6.5 2021 0.04 0.18 0.27 0.28 7.0 2336 0.02 0.14 0.24 0.31 di†usion constants for the structural units present in the di†erent Q bands.These are given in Table 3. Clearly there is considerable scatter in the data, but we believe the general trends are clear and the order of magnitude of the results is established.According to the experimental results, the self-di†usion constants of the Q1 units are a factor of two faster than those of the Q2 units. Also, the Q2 units generally di†use slightly faster than the Q3 units, which in turn di†use faster than the Q4 units. However, the likely errors increase from Q1 to Q4 (see Fig. 6), and it should be remembered that all self-di†usion constants are averages for the respective units. This means that all values obtained are averages for all possible connecti- Fig. 6 Dependence of peak attenuation on d2[D[(d/3)] for silicate units : (a) Q1 (b) Q2 (c) Q3 and (d) Q4 (+), (È…È), (ÈLÈ) (ÈËÈ) Table 3 Self-di†usion constants for structural units using the attenuation of peak areas for a sodium silicate solution with 25 wt.% and SiO2 Rm\4.0 Q1 Q2 Q3 Q4 slope [1.76]10~3 [8.20]10~4 [6.57]10~4 [5.54]10~4 correlation 0.969 0.973 0.891 0.717 D/m2 s~1 1.9]10~10 9.0]10~11 7.0]10~11 5.8]10~11 96 J. Chem. Soc., Faraday T rans., 1997, V ol. 93vities of the observed units to other units as well as for a distribution of particle sizes. The units of lower connectivity occur to a more signi�cant extent in the smaller anions and particles, so the signi�cantly faster self-di†usion of Q1 units compared to the others probably arises from the fact that there is a distribution of particle sizes in the silicate systems, as opposed to a single average particle size. Chemical exchange Fig. 7 shows EXSY spectra for mixing times 0.10 and 0.75 s.Table 4 gives the exchange connections observed for tm\0.75 s. All structural units are involved in exchange with units Fig. 7 Two-dimensional EXSY spectra of a sodium silicate solution (enriched in 29Si) containing 25 wt.% with a ratio SiO2 SiO2 : Na2O of 4.0 ; (a) mixing time 0.10 s ; (b) mixing time 0.75 s. The chemical shift scales are plotted relative to the signal for tetramethylsilane. Table 4 Exchange pathways (]) in a sodium silicate solution containing 25 wt.% with as monitored by two- SiO2 Rm\4.0, dimensional exchange spectroscopy with s tm\0.75 Q0 Q1 Q2 Q3 Q4 Q0 ] ] Q1 ] ] ] Q2 ] ] ] Q3 ] ] ] Q4 ] showing the next lower and next higher connectivity.Exchange involving two steps in connectivity can be seen for the Q0/Q2 and Q1/Q3 pairs. At the lower mixing time, however, only cross-peaks Q0/Q1, Q1/Q2 and Q2/Q3 are seen. It is clear that exchange is most signi�cant for the lower connectivities, but the smaller intensities in these sites contribute strongly to this observation.The measurements were signi�cantly simpli�ed by the fact that our silicate solution probably contains insigni�cant amounts of simple three-membered rings (no peak from Q2 in such rings is visible in Fig. 3). Knight et al.13 found three-membered rings to be rather labile. The complexity of the exchange processes in silicate solutions means that derivation of precise exchange rates is not feasible.However, the initial build-up of cross-peak intensities can be used to obtain comparative semi-quantitative data. In particular, the mixing time for which an exchange cross-peak �rst becomes apparent gives a measure of the upper limit for the relevant rate constant. Of course, spinÈlattice relaxation competes with exchange, so that the mixing time for detecting exchange at rate k varies as a function of For kT1. kT1B10, this mixing time is ca. 1.5 k~1, and measurements of sug- T1 gests this is the appropriate regime for our silicate solution.Table 5 gives the observed lower-limit mixing times and the derived maximum rate constants for the various exchange processes. The exchange rate constants, as expected, show an order of magnitude di†erence between processes involving a single step in connectivity and those requiring two steps. The mean lifetimes of individual connectivities are sufficiently long for the spectra to be of the slow-exchange type, as observed, i.e.for exchange-broadening of lines to be small in relation to linewidths (which are, however, mostly dominated by dispersions in chemical shifts). The later appearance of the Q3, Q1 cross peak is of interest because it suggests that it mostly occurs via a true two-step process rather than, for example, by ring closure and opening of the type 2Q2 1 ¢Q2 2Q3Q1. The di†usion measurements involved total times, between initial 90¡ pulse and stimulated echo, of 90 ms.Clearly, during this time exchange may begin to a†ect the result. However, given the fact that the rates in Table 5 are maximum values, it is unlikely that the self-di†usion constants derived from the stimulated echo sequence will be signi�cantly averaged between the various silicate units, and this is borne out by the data in Table 3. That is to say, we believe there are genuine di†erences between D for Q1ÈQ4. Moreover, any exchange e†ects would cause such di†erences to appear less than they in fact are.Particle size implications The self-di†usion coefficients determined in the NMR experiments relate to the di†usion of silicate/silica species in the presence of an undetermined phase volume (/) of colloidal particles on timescales long enough (L) for signi�cant spatial rearrangement of these species, i.e., they are The Dself L (/). average particle radius, a, can be deduced by applying the Table 5 Lower limits for the mixing time and maximum rate constants at 25 &ieural units involved in chemical exchange in a sodium silicate containing 25 wt.% with SiO2 Rm\4.0 mixing time maximum rate constants exchange process (lower limit)/s for exchange/s~1 Q3ÈQ4 0.45 3 Q3ÈQ2 0.1 15 Q3ÈQ1 2.0 1 Q2ÈQ1 0.05 30 Q2ÈQ0 0.45 3 Q1ÈQ0 0.05 30 J.Chem. Soc., Faraday T rans., 1997, V ol. 93 97generalised StokesÈEinstein relationship20 given in eqn. (6) : Dself L (/)\ kT 6ngc?0(/)a (6) In this equation the dependence on volume fraction (/) has been made explicit.The subscript c]0 means that the viscosity is that in the limit of in�nitely small shear rates. The viscosity of the silicate solution made from unen- Rm\4.0 riched, fumed silica was found to be Newtonian (independent of shear rate) and of a value of 0.09 Pa s. This leads to an estimate of particle radius for the Q4 species of 0.8 This ”. value is an order of magnitude smaller than the smallest possible Q4 species. Explanations for this disparity may involve (a) the inaccuracies brought in by linking the di†usion data in the enriched sample with the viscosity data in the unenriched sample, (b) experimental uncertainty in the measure- Rm\4.0 ment of and (c) theoretical shortcomings. Dself L (/) Conclusions For the �rst time, self di†usion of silicate species in a highly condensed silicate solution has been investigated and selfdi† usion coefficients D, in the range of 5.8]10~11 m2 s~1 for the Q4 units to 1.9]10~10 m2 s~1 for the Q1 units, obtained.Upper limits to exchange rates between silicate units have been derived, again for the �rst time, for highly concentrated silicate solutions. These show that all units are involved in exchange and that any two-step change in connectivity is signi�cantly slower than all single connectivity changes. The exchange processes are not fast enough to average the selfdi† usion coefficients between the various units on the timescale of the relevant stimulated echo experiment, though they may reduce the observed di†erences in D.Attempts to combine self-di†usion coefficients and viscosity measurements to yield an estimate of colloidal silica radius were unsuccessful. They yielded a particle radius which was at least an order of magnitude smaller than physical reality. One of us (E.K.F.B.) is grateful to Unilever Research for provision of a Research Studentship. We thank Mr. B. J. Say, Professor H. Barnes and Dr.P. Warren for helpful discussions. We thank Mr. G. Roberts for performing the viscosity measurements. References 1 Soluble Silicates, ed. J. S. Falcone, ACS Symp. Ser. 194, Washington D.C., 1982. 2 G. Engelhardt, D. Zeigin, H. Jancke, D. Hoebbel and W. Wieker, Z. Anorg. Allg. Chem., 1975, 418, 17. 3 R. K. Harris and C. T. G. Knight, J. Chem. Soc., Faraday T rans. 2, 1983, 79, 1525; 1983, 79, 1539. 4 See, for example, G. Engelhardt and D. Michel, High Resolution Solid State NMR of Silicates and Zeolites, John Wiley and Sons, New York 1987, ch. 3. 5 E. K. F. Bahlmann, R. K. Harris and B. J. Say, Magn. Reson. Chem., 1993, 31, 266; R. K. Harris, E. K. F. Bahlmann, K. Metcalfe and E. G. Smith, Magn. Reson. Chem., 1993, 31, 743. 6 E. G. Smith, J. W. Rockli†e and P. I. Riley, J. Colloid Interface Sci., 1989, 131, 29. 7 G. Engelhardt and D. Hoebbel, J. Chem. Soc. Chem. Commun., 1984, 514. 8 R. K. Harris, J. Jones, C. T. G. Knight and R. H. Newman, J. Mol. L iq., 1984, 29, 63. 9 C. T. Creswell, R. K. Harris and P. T. Jageland, J. Chem. Soc., Chem. Commun., 1984, 1261. 10 L. Griffiths, C. S. Cundy and R. J. Plaisted, J. Chem. Soc., Dalton T rans., 1986, 2265. 11 S. D. Kinrade and T. W. Swaddle, J. Chem. Soc., Chem. Commun., 1986, 120. 12 C. T. G. Knight, R. J. Kirkpatrick and E. Old�eld, J. Chem. Soc., Chem. Commun., 1986, 66. 13 C. T. G. Knight, R. J. Kirkpatrick and E. Old�eld, J. Magn. Reson., 1988, 78, 311. 14 E. O. Stejskal and J. E. Tanner, J. Chem. Phys., 1965, 42, 288. 15 J. E. Tanner, Rev. Sci. Instrum., 1965, 36, 1086. 16 E. O. Stejskal and J. E. Tanner, J. Chem. Phys., 1969, 49, 1768. 17 J. E. Tanner, J. Chem. Phys., 1970, 52, 2523. 18 P. Stilbs, J. Colloid Interface Sci., 1982, 87, 385. 19 A. J. Walker and N. Whitehead, J. Appl. Chem., 1966, 16, 230. 20 A. Imhof, A. van Blaaderen, G. Maret, J. Mellema and J. K. G. Dhont, J. Chem. Phys., 1994, 100, 2170. Paper 6/04878A; Received 11th July, 1996 98 J. Chem. Soc., Faraday T rans., 19
ISSN:0956-5000
DOI:10.1039/a604878a
出版商:RSC
年代:1997
数据来源: RSC
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Volume 93 issue 1