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Introduction and Motivation

  • Craig S. SlaterEmail author
Chapter
  • 369 Downloads
Part of the Springer Theses book series (Springer Theses)

Abstract

Few experimental techniques have found such a diverse range of applications as has ion imaging. The field of chemical dynamics is constantly advancing, and new applications of ion imaging are being realised with increasing frequency. This thesis is concerned with the application of a fast pixelated imaging sensor, the Pixel Imaging Mass Spectrometry (PImMS) camera, to ion imaging applications. The experimental possibilities of such a marriage are exceptionally broad in scope, and this thesis details with the development of a selection of velocity-map imaging applications within the field of photoinduced molecular dynamics.

Keywords

Coulomb Explosion Torsional Motion Product Fragment Data Readout Parallel Readout 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    W.C.McC. Lewis, J. Chem. Soc. Trans. 113, 471 (1918)Google Scholar
  2. 2.
    W.O. Kermack, R. Robinson, J. Chem. Soc. Trans. 121, 427 (1922)CrossRefGoogle Scholar
  3. 3.
    M.A. Gilbert, J.E. Baggott, Essentials of Molecular Photochemistry (Blackwell Scientific Publications, Oxford, UK, 1991)Google Scholar
  4. 4.
    N.J. Turro, V. Ramamurthy, J.C. Scaiano, Principles of Molecular Photochemistry (University Science Books, Sausalito, CA, USA, 2009)Google Scholar
  5. 5.
    I. Asimov, Photosynthesis (Basic Books, New York, NY, USA, 1968)Google Scholar
  6. 6.
    R.P. Wayne, Chemistry of Atmospheres (Oxford University Press, Oxford, UK, 2000)Google Scholar
  7. 7.
    D. Rogers, Chemistry of Photography (Royal Society of Chemistry, Cambridge, UK, 2007)Google Scholar
  8. 8.
    N.J. Turro, V. Ramamurthy, J.C. Scaiano, Modern Molecular Photochemistry of Organic Molecules (University Science Books, Sausalito, CA, USA, 2010)Google Scholar
  9. 9.
    H.P. Garg, J. Prakash, Solar Energy: Fundamentals and Applications (Tata McGraw-Hill, Noida, UP, India, 1997)Google Scholar
  10. 10.
    K.F. Renk, Basics of Laser Physics: For Students of Science and Engineering (Springer, New York, NY, USA, 2012)CrossRefGoogle Scholar
  11. 11.
    R.G.W. Norrish, G. Porter, Nature 164, 658 (1949)CrossRefGoogle Scholar
  12. 12.
    G. Porter, Proc. R. Soc. Lond. A. 200, 284 (1950)CrossRefGoogle Scholar
  13. 13.
    G. Porter, Nobel Lectures in Chemistry 1963–1970 (Elsevier Publishing Company, Amsterdam, Netherlands, 1972)Google Scholar
  14. 14.
    K. Zhao, Q. Zhang, M. Chini, Y. Wu, X. Wang, Z. Chang, Opt. Lett. 37, 3891 (2012)CrossRefGoogle Scholar
  15. 15.
    G. Herzberg, Molecular Spectra and Molecular Structure: III, Electronic Spectra and Electronic Structure of Polyatomic Molecules (David Van Nostrand Company, Princeton, USA,1967)Google Scholar
  16. 16.
    R. Schinke, Photodissociation Dynamics (Cambridge University Press, Cambridge, UK, 1993)CrossRefGoogle Scholar
  17. 17.
    Mark Brouard, Claire Vallance, Tutorials in Molecular Reaction Dynamics (Royal Society of Chemistry, Cambridge, UK, 2010)Google Scholar
  18. 18.
    R.N. Zare, Faraday Discuss. Chem. Soc. 67, 7 (1979)Google Scholar
  19. 19.
    M. Born, R. Oppenheimer, Zur Quantentheorie der Molekeln 84, 457 (1927)Google Scholar
  20. 20.
    Y. Tang, W.-B. Lee, Z. Hu, B. Zhang, K.-C. Lin, J. Chem. Phys. 126, 064302 (2007)CrossRefGoogle Scholar
  21. 21.
    T.P. Rakitzis, T.N. Kitsopoulos, J. Chem. Phys. 116, 9228 (2002)CrossRefGoogle Scholar
  22. 22.
    A.J. Johnsen, A.B. Alekseyev, G.G. Balint-Kurti, M. Brouard, A. Brown, R.J. Buenker, E.K. Campbell, D.B. Kokh, J. Chem. Phys. 136, 164310 (2012)CrossRefGoogle Scholar
  23. 23.
    T. Seideman, E. Hamilton, Adv. Atom. Mol. Opt. Phy. 52, 289 (2005)CrossRefGoogle Scholar
  24. 24.
    H. Stapelfeldt, T. Seideman, Rev. Mod. Phys. 75, 543 (2003)CrossRefGoogle Scholar
  25. 25.
    Y. Ohshima, H. Hasegawa, Int. Rev. Phys. Chem. 29, 619 (2010)CrossRefGoogle Scholar
  26. 26.
    B. Friedrich, D. Herschbach, Phys. Rev. Lett. 74, 4623 (1995)CrossRefGoogle Scholar
  27. 27.
    P.H. Bucksbaum, A. Zavriyev, H.G. Muller, D.W. Schumacher, Phys. Rev. Lett. 64, 1883 (1990)CrossRefGoogle Scholar
  28. 28.
    H. Niikura, V.R. Bhardwaj, F. Légaré, I.V. Litvinyuk, P.W. Dooley, D.M. Rayner, M. Yu Ivanov, P.B. Corkum, D.M. Villeneuve, Springer Series in Optical Sciences 134, 185 (2009)CrossRefGoogle Scholar
  29. 29.
    J.H. Posthumus, Rep. Prog. Phys. 67, 623 (2004)CrossRefGoogle Scholar
  30. 30.
    M. Schmidt, P. DOliveira, P. Meynadier, D. Normand, C. Cornaggia, J. Nonlinear Opt. Phys. Mat. 4, 817 (1995)Google Scholar
  31. 31.
    K. Codling, L. Frasinski, J. Phys. B 26, 783 (1993)CrossRefGoogle Scholar
  32. 32.
    J. Gagnon, K.F. Lee, D.M. Rayner, P.B. Corkum, V.R. Bhardwaj, J. Phys. B 41, 215104 (2008)CrossRefGoogle Scholar
  33. 33.
    M. Pitzer, M. Kunitski, A.S. Johnson, T. Jahnke, H. Sann, F. Sturm, L.P.H. Schmidt, H. Schmidt-Böcking, R. Dörner, J. Stohner, J. Kiedrowski, M. Reggelin, S. Marquardt, A. Schießer, R. Berger, M.S. Schöffler, Science 341, 1096 (2013)CrossRefGoogle Scholar
  34. 34.
    A. Hishikawa, A. Iwamae, K. Hoshina, M. Kono, K. Yamanouchi, Chem. Phys. Lett. 282, 283 (1998)CrossRefGoogle Scholar
  35. 35.
    J.H. Sanderson et al., Phys. Rev. A 59, R2567 (1999)CrossRefGoogle Scholar
  36. 36.
    T.A. Carlson, R.M. White, J. Chem. Phys. 44, 4510 (1966)CrossRefGoogle Scholar
  37. 37.
    A. Rudenko, Th Ergler, B. Feuerstein, K. Zrost, C.D. Schröter, R. Moshammer, J. Ullrich, Chem. Phys. 329, 193 (2006)CrossRefGoogle Scholar
  38. 38.
    T. Ergler, A. Rudenko, B. Feuerstein, K. Zrost, C.D. Schröter, R. Moshammer, J. Ullrich, Phys. Rev. Lett. 97, 193001 (2006)CrossRefGoogle Scholar
  39. 39.
    F. Légaré, K.F. Lee, I.V. Litvinyuk, P.W. Dooley, S.S. Wesolowski, P.R. Bunker, P. Dombi, F. Krausz, A.D. Bandrauk, D.M. Villeneuve, P.B. Corkum, Phys. Rev. A 71, 013415 (2005)Google Scholar
  40. 40.
    H. Hasegawa, A. Hishikawa, K. Yamanouchi, Chem. Phys. Lett. 349, 57 (2001)CrossRefGoogle Scholar
  41. 41.
    R.L. Fork, B.I. Greene, C.V. Shank, Appl. Phys. Lett., 38, 671 (671)Google Scholar
  42. 42.
    D.E. Spence, P.N. Kean, W. Sibbett, Opt. Lett. 16, 42 (1991)CrossRefGoogle Scholar
  43. 43.
    A.H. Zewail, Science 242, 1645 (1988)CrossRefGoogle Scholar
  44. 44.
    J.A. Davies, R.E. Continetti, D.W. Chandler, C.C. Hayden, Phys. Rev. Lett. 84, 5983 (2000)CrossRefGoogle Scholar
  45. 45.
    A. Zewail, J. Phys. Chem. 100, 12701 (1996)CrossRefGoogle Scholar
  46. 46.
    P. Cheng, D. Zhong, A. Zewail, J. Chem. Phys. 105, 6216 (1996)CrossRefGoogle Scholar
  47. 47.
    J.L. Hansen, J.H. Nielsen, C.B. Madsen, A.T. Lindhardt, M.P. Johansson, T. Skrydstrup, L.B. Madsen, H. Stapelfeldt, J. Chem. Phys. 136, 204310 (2012)CrossRefGoogle Scholar
  48. 48.
    K. Ohmori, Annu. Rev. Phys. Chem. 60, 487 (2009)CrossRefGoogle Scholar
  49. 49.
    J.S. Briggs, J. Phys.: Conf. Ser. 99, 012002 (2008)Google Scholar
  50. 50.
    M. Shapiro, P. Brumer, J. Chem. Phys. 84, 4103 (1986)CrossRefGoogle Scholar
  51. 51.
    D.J. Tannor, S.A. Rice, J. Chem. Phys. 83, 5013 (1985)CrossRefGoogle Scholar
  52. 52.
    L. Zhu, V. Kleiman, X. Li, S.P. Lu, K. Trentelman, R.J. Gordon, Science 270, 77 (1995)CrossRefGoogle Scholar
  53. 53.
    E.D. Potter, J.L. Herek, S. Pedersen, Q. Liu, A.H. Zewail, Nature 355, 66 (1992)CrossRefGoogle Scholar
  54. 54.
    N.F. Scherer, R.J. Carlson, A. Matro, M. Du, A.J. Ruggiero, V. Romero-Rochin, J.A. Cina, G.R. Fleming, S.A. Rice, J. Chem. Phys. 95, 1487 (1991)CrossRefGoogle Scholar
  55. 55.
    R.S. Judson, H. Rabitz, Phys. Rev. Lett. 68, 1500 (1992)CrossRefGoogle Scholar
  56. 56.
    A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Strehle, G. Gerber, Science 282, 919 (1998)CrossRefGoogle Scholar
  57. 57.
    V.I. Prokhorenko, A.M. Nagy, S.A. Waschuk, L.S. Brown, R.R. Birge, R.J.D. Miller, Science 313, 1257 (2006)CrossRefGoogle Scholar
  58. 58.
    T. Seideman, J. Chem. Phys. 103, 7887 (1995)CrossRefGoogle Scholar
  59. 59.
    B. Kohler, V.V. Yakovlev, J. Che, J.L. Krause, M. Messina, K.R. Wilson, N. Schwentner, R.M. Whitnell, Y.J. Yan, Phys. Rev. Lett. 74, 3360 (1995)CrossRefGoogle Scholar
  60. 60.
    Ch. Warmuth, A. Tortschanoff, F. Milota, M. Shapiro, Y. Prior, ISh Averbukh, W. Schleich, W. Jakubetz, H.F. Kauffmann, J. Chem. Phys. 112, 5060 (2000)CrossRefGoogle Scholar
  61. 61.
    H. Katsuki, K. Hosaka, H. Chiba, K. Ohmori, Phys. Rev. A 76, 013403 (2007)CrossRefGoogle Scholar
  62. 62.
    T. Seideman, Phys. Rev. A 56, 17 (1997)CrossRefGoogle Scholar
  63. 63.
    T. Seideman, J. Chem. Phys. 107, 10420 (1997)CrossRefGoogle Scholar
  64. 64.
    M. Artamonov, T. Seideman, Nano Lett. 10, 4908 (2010)CrossRefGoogle Scholar
  65. 65.
    H. Stapelfeldt, H. Sakai, E. Constant, P. Corkum, Phys. Rev. Lett. 79, 2787 (1997)CrossRefGoogle Scholar
  66. 66.
    H. Sakai, A. Tarasevitch, J. Danilov, H. Stapelfeldt, R. Yip, C. Ellert, E. Constant, P. Corkum, Phys. Rev. A 57, 2794 (1998)CrossRefGoogle Scholar
  67. 67.
    T. Seideman, J. Chem. Phys. 111, 4397 (1999)CrossRefGoogle Scholar
  68. 68.
    B. Suk Zhao, H. Sung Chung, K. Cho, S. Hyup Lee, S. Hwang, J. Yu,Y. Ahn, J. Sohn, D. Kim, W. Kyung Kang, D. Chung, Phys. Rev. Lett 85, 2705 (2000)Google Scholar
  69. 69.
    M. Maus, W. Rettig, J. Phys. Chem. A 106, 2104 (2002)CrossRefGoogle Scholar
  70. 70.
    F. Sterpone, R. Martinazzo, A.N. Panda, I. Burghardt, Z. Phys. Chem. 225, 541 (2011)Google Scholar
  71. 71.
    L. Venkataraman, J. Klare, C. Nuckolls, M. Hybertsen, M. Steigerwald, Nature 442, 904 (2006)CrossRefGoogle Scholar
  72. 72.
    D. Vonlanthen, A. Mishchenko, M. Elbing, M. Neuburger, T. Wandlowski, M. Mayor, Angew. Chem. Int. Ed. 48, 8886 (2009)CrossRefGoogle Scholar
  73. 73.
    A. Mishchenko, D. Vonlanthen, V. Meded, M. Burkle, C. Li, I. Pobelov, A. Bagrets, J. Viljas, F. Pauly, F. Evers, M. Mayor, T. Wandlowski, Nano Lett. 10, 156 (2010)CrossRefGoogle Scholar
  74. 74.
    D. Kroner, B. Klaumunzer, T. Klamroth, J. Phys. Chem. A 112, 9924 (2008)CrossRefGoogle Scholar
  75. 75.
    F. Grossmann, L. Feng, G. Schmidt, T. Kunert, R. Schmidt, Europhys. Lett. 60, 201 (2002)CrossRefGoogle Scholar
  76. 76.
    B. Dietzek, B. Brüggemann, T. Pascher, A. Yartsev, Phys. Rev. Lett. 97, 258301 (2006)CrossRefGoogle Scholar
  77. 77.
    S. Belz, T. Grohmann, M. Leibscher, J. Chem. Phys. 131, 034305 (2009)CrossRefGoogle Scholar
  78. 78.
    M. Parker, M.A. Ratner, T. Seideman, Mol. Phys. 110, 1941 (2012)CrossRefGoogle Scholar
  79. 79.
    C.B. Madsen, L.B. Madsen, S.S. Viftrup, M.P. Johansson, T.B. Poulsen, L. Holmegaard, V. Kumarappan, K.A. Jorgensen, H. Stapelfeldt, Phys. Rev. Lett. 102, 073007 (2009)CrossRefGoogle Scholar
  80. 80.
    C.B. Madsen, L.B. Madsen, S.S. Viftrup, M.P. Johansson, T.B. Poulsen, L. Holmegaard, V. Kumarappan, K.A. Jorgensen, H. Stapelfeldt, J. Chem. Phys. 130, 234310 (2009)CrossRefGoogle Scholar
  81. 81.
    W. Bothe, Nobel Lectures in Physics 1942–1962 (Elsevier Publishing Company, Amsterdam, Netherlands, 1964)Google Scholar
  82. 82.
    K. McCulloh, T. Sharp, H. Rosenstock, J. Chem. Phys. 42, 3501 (1965)CrossRefGoogle Scholar
  83. 83.
    A. Hishikawa, A. Iwamae, K. Yamanouchi, J. Chem. Phys. 11, 8871 (1999)CrossRefGoogle Scholar
  84. 84.
    R.K. Kushawaha, S.S. Kumar, I.A. Prajapati, K.P. Subramanian, B. Bapat, J. Phys. B 42, 105201 (2009)CrossRefGoogle Scholar
  85. 85.
    S.D. Price, Int. J. Mass. Spectrom. 260, 1 (2007)CrossRefGoogle Scholar
  86. 86.
    L.J. Frasinski, K. Codling, P.A. Hatherly, Science 246, 1029 (1989)CrossRefGoogle Scholar
  87. 87.
    J. Mikoscha, S. Patchkovskiia, J. Mod. Opt. 60, 1426 (2013)CrossRefGoogle Scholar
  88. 88.
    J. Mikoscha, S. Patchkovskiia, J. Mod. Opt. 60, 1439 (2013)CrossRefGoogle Scholar
  89. 89.
    T.W. Anderson, An Introduction to Multivariate Statistical Analysis (Wiley, New York, NY, USA, 2003)Google Scholar
  90. 90.
    L.J. Frasinski, A.J. Giles, P.A. Hatherly, J.H. Posthumus, M.R. Thompson, K. Codling, J. Electron Spectrosc. Relat. Phenom. 79, 367 (1996)CrossRefGoogle Scholar
  91. 91.
    L.J. Frasinski et al., Phys. Rev. Lett. 111, 073002 (2013)CrossRefGoogle Scholar
  92. 92.
    K. Codling, C. Cornaggia, L.J. Frasinski, P.A. Hatherly, J. Morellec, D. Normand, J. Phys. B: At. Mol. Opt. Phys. 24, L593 (1991)CrossRefGoogle Scholar
  93. 93.
    P.A. Hatherly, M. Stankiewicz, K. Codling, L.J. Frasinski, G.M. Cross, J. Phys. B: At. Mol. Opt. Phys. 27, 2993 (1994)CrossRefGoogle Scholar
  94. 94.
    J.H. Posthumus, A.J. Giles, M.R. Thompson, K. Codling, J. Phys. B: At. Mol. Opt. Phys. 29, 5811 (1996)CrossRefGoogle Scholar
  95. 95.
    V. Zhaunerchyk et al., J. Phys. B: At. Mol. Opt. Phys. 46, 164034 (2013)CrossRefGoogle Scholar
  96. 96.
    D.W. Chandler, P.L. Houston, J. Chem. Phys. 87, 1445 (1987)CrossRefGoogle Scholar
  97. 97.
    A.T. Eppink, D.H. Parker, Rev. Sci. Instrum. 68, 3477 (1997)CrossRefGoogle Scholar
  98. 98.
    M. Brouard, H. Chadwick, C.J. Eyles, B. Hornung, B. Nichols, J.M. Scott, F.J. Aoiz, J. Klos, S. Stolte, X. Zhang, Mol. Phys. 111, 1759 (2013)CrossRefGoogle Scholar
  99. 99.
    L. Holmegaard, J.H. Nielsen, I. Nevo, H. Stapelfeldt, F. Filsinger, J. Kpper, G. Meijer, Phys. Rev. Lett. 102, 023001 (2009)CrossRefGoogle Scholar
  100. 100.
    W.S. Hopkins, A.P. Woodham, R.J. Plowright, T.G. Wright, S.R. Mackenzie, J. Chem. Phys. 132, 214303 (2010)CrossRefGoogle Scholar
  101. 101.
    I. Wilkinson, B.J. Whitaker, J. Chem. Phys. 129, 154312 (2008)CrossRefGoogle Scholar
  102. 102.
    A.I. Chichinin, K.-H. Gericke, S. Kauczok, C. Maul, Int. Rev. Phys. Chem. 28, 607 (2009)CrossRefGoogle Scholar
  103. 103.
    M.N.R. Ashfold, N.H. Nahler, A.J. Orr-Ewing, O.P.J. Vieuxmaire, R.L. Toomes, T.N. Kitsopoulos, I.A. Garcia, D.A. Chestakov, S.-M. Wu, D.H. Parker, Phys. Chem. Chem. Phys. 8, 26 (2006)CrossRefGoogle Scholar
  104. 104.
    C. Martin, P. Jelinsky, M. Lampton, R.F. Malina, H.O. Anger, Rev. Sci. Instrum. 52, 1067 (1981)CrossRefGoogle Scholar
  105. 105.
    O. Jagutzki, J.S. Lapington, L.B.C. Worth, U. Spillman, V. Mergel, H. Schmidt-Böcking, Nucl. Instrum. Meth. Phys. Res. A 477, 256 (2002)CrossRefGoogle Scholar
  106. 106.
    N. Saito, F. Heiser, O. Hemmers, K. Wieliczek, J. Viefhaus, U. Becker, Phys. Rev. A 54, 2004 (1996)CrossRefGoogle Scholar
  107. 107.
    J.H.D. Eland, Meas. Sci. Technol. 1, 36 (1990)CrossRefGoogle Scholar
  108. 108.
    J.H.D. Eland, Meas. Sci. Technol. 5, 1501 (1994)CrossRefGoogle Scholar
  109. 109.
    I. Ali, R. Dörner, O. Jagutzki, S. Nuttgens, V. Mergel, L. Spielberger, K. Khayyat, T. Vogt, H. Bräuning, K. Ullmann, Nucl. Instrum. Methods Phys. Res. B 149, 490 (1999)CrossRefGoogle Scholar
  110. 110.
    O. Jagutzki, V. Mergel, K. Ullmann-Pfleger, L. Spielberger, U. Spillmann, R. Dörner, H. Schmidt-Böcking, Nucl. Instrum. Methods Phys. Res. A 477, 244 (2002)CrossRefGoogle Scholar
  111. 111.
    O. Jagutzki, A. Cerezo, A. Czasch, R. Dorner, M. Hattas, M. Huang, V. Mergel, U. Spillmann, K. Ullmann-Peger, T. Weber, H. Schmidt-Bocking, G. Smith, I.E.E.E.T. Nucl, Sci. 49, 2477 (2002)Google Scholar
  112. 112.
    T.G. Etoh, D. Poggemann, G. Kreider, H. Mutoh, A.J.P. Theuwissen, A. Ruckelshausen, Y. Kondo, H. Maruno, K. Takubo, H. Soya, K. Takehara, T. Okinaka, Y. Takano, I.E.E.E. Trans. Electron. 50, 144 (2003)Google Scholar
  113. 113.
    L. Lazovsky, D. Cismas, G. Allan, D. Given, Proc. SPIE 5787, 184 (2005)CrossRefGoogle Scholar
  114. 114.
    X. Llopart, R. Ballabriga, M. Campbell, L. Tlustos, Nuc.Inst. Meth. Phys. Res., 581, 485 (2007)Google Scholar
  115. 115.
    J.J. John, M. Brouard, A. Clark, J. Crooks, E. Halford, L. Hill, J.W.L. Lee, A. Nomerotski, R. Pisarczyk, I. Sedgwick, C.S. Slater, R. Turchetta, C. Vallance, E. Wilman, B. Winter, W.H. Yuen, J. Inst. 7, C08001 (2012)Google Scholar
  116. 116.
  117. 117.
    W.F. Kosonocky, G. Yang, R.K. Kabra, Z. Pektas C. Ye, J.L. Lowrance,V.J. Mastrocola, F.V. Shallcross, V. Patel, IEEE Trans. Electron. 44, 1617 (1997)Google Scholar
  118. 118.
    D.V.T. Son, T.G. Etoh, M. Tanaka, N.H. Dung, V. Le Cuong, K. Takehara, T. Akino, K. Nishi, H. Aoki, J. Nakai, Sensors 10, 16 (2010)CrossRefGoogle Scholar
  119. 119.
    J. Becker, K. Beckord, U. Werner, H. Lutz, Nucl. Instrum. Meth. Phys. Res. A 337, 409 (1999)CrossRefGoogle Scholar
  120. 120.
    A.T. Clark, J.P. Crooks, I. Sedgwick, R. Turchetta, J.W.L. Lee, J.J. John, E.S. Wilman, L. Hill, E. Halford, C.S. Slater, B. Winter, W.-H. Yuen, S.H. Gardiner, M.L. Lipciuc, M. Brouard, A. Nomerotski, C. Vallance, J. Phys. Chem. A 116, 10897 (2012)CrossRefGoogle Scholar
  121. 121.
    W.H. Yuen, Ion Imaging Mass Spectrometry, PhD thesis, University of Oxford (2012)Google Scholar

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© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Physical and Theoretical Chemistry LaboratoryUniversity of OxfordOxfordUK

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