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Photophysics of Organometallics pp 193–235Cite as

Organometallic Pt(II) and Ir(III) Triplet Emitters for OLED Applications and the Role of Spin–Orbit Coupling: A Study Based on High-Resolution Optical Spectroscopy

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Part of the book series: Topics in Organometallic Chemistry ((TOPORGAN,volume 29))

Abstract

High-resolution optical spectroscopy of organometallic triplet emitters reveals detailed insights into the lowest triplet states and the corresponding electronic and vibronic transitions to the singlet ground state. As case studies, the blue-light emitting materials Pt(4,6-dFppy)(acac) and Ir(4,6-dFppy)2(acac) are investigated and characterized in detail. The compounds’ photophysical properties, being markedly different, are largely controlled by spin–orbit coupling (SOC). Therefore, we study the impact of SOC on the triplet state and elucidate the dominant SOC and state-mixing paths. These depend distinctly on the compounds’ coordination geometry. Relatively simple rules and relations are pointed out. The combined experimental and theoretical results lead us towards structure-efficiency rules and guidelines for the design of new organic light emitting diode (OLED) emitter materials.

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Notes

  1. 1.

    For Pt(4,6-dFppy)(acac) in a PMMA film, a distinctly higher quantum yield of 40% is found. This can be explained with a destabilization of quenching dd* states in the rigid PMMA host compared to fluid solutions.

  2. 2.

    Librations are hindered rotational modes of the doped complex in its matrix cage.

  3. 3.

    The radial average of the function \( \xi ({r_A}) \) \( {\hbar^2} \) can be written as \( hc\zeta (A) \) [119].

  4. 4.

    This rule is frequently addressed in the discussion of intersystem crossing (ISC) and SOC between 1(ππ*) and 3(ππ*) states of purely organic molecules (compare [113]). For these molecules, SOC is very weak. In this case, the matrix elements as expressed in (12) involve equal p-orbitals that are located on one C atom. The angular momentum operator acts on a p-orbital by rotating it by 90°. Thus, a matrix element of two orthogonal p-orbitals results, and this integral vanishes. A corresponding situation is discussed below by use of the example shown in Fig. 12b.

  5. 5.

    It is remarked that for a quantitative description, a significant LC (ππ*) contribution cannot be ignored (e.g., compare [110]).

References

  1. Yersin H (ed) (2008) Highly efficient OLEDs with phosphorescent materials. Wiley, Weinheim

    Google Scholar 

  2. Müllen K, Scherf U (eds) (2006) Organic light emitting devices − synthesis, properties and applications. Wiley, Weinheim

    Google Scholar 

  3. Kafafi ZH (ed) (2005) Organic electroluminescence. CRC Taylor & Francis, Boca Raton

    Google Scholar 

  4. Shinar J (ed) (2004) Organic light emitting devices. Springer, New York

    Google Scholar 

  5. Kalinowski J (2004) Organic light emitting diodes: principles, characteristics and processes. Marcel Dekker, New York

    Book  Google Scholar 

  6. Hirani B, Li J, Djurovich PI, Yousufuddin M, Oxgaard J, Persson P, Wilson SR, Bau R, Goddard WA III, Thompson ME (2007) Inorg Chem 46:3865

    Article  CAS  Google Scholar 

  7. Chou PT, Chi Y (2007) Chem Eur J 13:380

    Article  CAS  Google Scholar 

  8. Borek C, Hanson K, Djurovich PI, Thompson ME, Aznavour K, Bau R, Sun Y, Forrest SR, Brooks J, Michalski L, Brown J (2007) Angew Chem Int Ed 46:1109

    Article  CAS  Google Scholar 

  9. Evans RC, Douglas P, Winscom CJ (2006) Coord Chem Rev 250:2093

    Article  CAS  Google Scholar 

  10. Adachi C, Baldo MA, Thompson ME, Forrest SR (2001) J Appl Phys 90:5048

    Article  CAS  Google Scholar 

  11. Ikai M, Tokito S, Sakamoto Y, Suzuki T, Taga Y (2001) Appl Phys Lett 79:156

    Article  CAS  Google Scholar 

  12. Yersin H (2004) Top Curr Chem 241:1

    CAS  Google Scholar 

  13. Baldo MA, O’Brien DF, Thompson ME, Forrest SR (1999) Phys Rev B 60:14422

    Article  CAS  Google Scholar 

  14. Flamigni L, Barbieri A, Sabatini C, Ventura B, Barigelletti F (2007) Top Curr Chem 281:143

    Article  CAS  Google Scholar 

  15. Tamayo AB, Garon S, Sajoto T, Djurovich PI, Tsyba IM, Bau R, Thompson ME (2005) Inorg Chem 44:8723

    Article  CAS  Google Scholar 

  16. Yang CH, Cheng YM, Chi Y, Hsu CJ, Fang FC, Wong KT, Chou PT, Chang CH, Tsai MH, Wu CC (2007) Angew Chem Int Ed 46:2418

    Article  CAS  Google Scholar 

  17. Su SJ, Gonmori E, Sasabe H, Kido J (2008) Adv Mater 20:4189

    CAS  Google Scholar 

  18. Sasabe H, Gonmori E, Chiba T, Li YJ, Tanaka D, Su SJ, Takeda T, Pu YJ, Nakayama KI, Kido J (2008) Chem Mater 20:5951

    Article  CAS  Google Scholar 

  19. You Y, Park SY (2009) Dalton Trans 8:1267

    Article  CAS  Google Scholar 

  20. Kawamura Y, Sasabe H, Adachi C (2004) Jpn J Appl Phys 43:7729

    Article  CAS  Google Scholar 

  21. Kawamura Y, Goushi K, Brooks J, Brown JJ, Sasabe H, Adachi C (2005) Appl Phys Lett 86:071104

    Article  CAS  Google Scholar 

  22. a) Hofbeck T, Yersin H (2009) submitted; b) Hofbeck T, Yersin H (2008) 3rd International Symposium on Molecular Materials - MOLMAT, Book of Abstracts. Toulouse, France, p.157

    Google Scholar 

  23. Williams JAG, Beeby A, Davies ES, Weinstein JA, Wilson C (2003) Inorg Chem 42:8609

    Article  CAS  Google Scholar 

  24. Farley SJ, Rochester DL, Thompson AL, Howard JAK, Williams JAG (2005) Inorg Chem 44:9690

    Article  CAS  Google Scholar 

  25. Kui SCF, Sham IHT, Cheung CCC, Ma CW, Yan B, Zhu N, Che CM, Fu WF (2007) Chem Eur J 13:417

    Article  CAS  Google Scholar 

  26. Williams JAG (2007) Top Curr Chem 281:205

    Article  CAS  Google Scholar 

  27. Yang X, Wang Z, Madakuni S, Li J, Jabbour GE (2008) Adv Mater 20:2405

    Article  CAS  Google Scholar 

  28. Lin YY, Chan SC, Chan MCW, Hou YJ, Zhu N, Che CM, Liu Y, Wang Y (2003) Chem Eur J 9:1263

    Article  CAS  Google Scholar 

  29. Connick WB, Geiger D, Eisenberg R (1999) Inorg Chem 38:3264

    Article  CAS  Google Scholar 

  30. Pettijohn CN, Jochnovitz EB, Chuong B, Nagle JK, Vogler A (1998) Coord Chem Rev 171:85

    Article  CAS  Google Scholar 

  31. Adamovich V, Brooks J, Tamayo A, Alexander AM, Djurovich PI, D’Andrade BW, Adachi C, Forrest SR, Thompson ME (2002) New J Chem 26:1171

    Article  CAS  Google Scholar 

  32. Yersin H, Donges D, Humbs W, Strasser J, Sitters R, Glasbeek M (2002) Inorg Chem 41:4915

    Article  CAS  Google Scholar 

  33. Lu W, Chan MCW, Zhu N, Che CM, Li C, Hui Z (2004) J Am Chem Soc 126:7639

    Article  CAS  Google Scholar 

  34. Mdleleni MM, Bridgewater JS, Watts RJ, Ford PC (1995) Inorg Chem 34:2334

    Article  CAS  Google Scholar 

  35. Yersin H, Monkowius U, Fischer T, Finkenzeller WJ, Czerwieniec R (2008) WO 2008/003464 A1

    Google Scholar 

  36. Yersin H, Monkowius U, Czerwieniec R (2007) WO2007/118671 A1

    Google Scholar 

  37. D’Andrade BW, Brooks J, Adamovich V, Thompson ME, Forrest SR (2002) Adv Mater 14:1032

    Article  Google Scholar 

  38. D’Andrade BW, Forrest SR (2003) J Appl Phys 94:3101

    Article  CAS  Google Scholar 

  39. Adamovich VI, Cordero SR, Djurovich PI, Tamayo A, Thompson ME, D’Andrade BW, Forrest SR (2003) Org Electron 4:77

    Article  CAS  Google Scholar 

  40. Williams EL, Haavisto K, Li J, Jabbour GE (2007) Adv Mater 19:197

    Article  CAS  Google Scholar 

  41. Cocchi M, Kalinowski J, Virgili D, Fattori V, Develay S, Williams JAG (2007) Appl Phys Lett 90:163508

    Article  CAS  Google Scholar 

  42. Kalinowski J, Cocchi M, Virgili D, Fattori V, Williams JAG (2007) Adv Mater 19:4000

    Article  CAS  Google Scholar 

  43. Cocchi M, Kalinowski J, Fattori V, Williams JAG, Murphy L (2009) Appl Phys Lett 94:073309

    Article  CAS  Google Scholar 

  44. Brooks J, Babayan Y, Lamansky S, Djurovich PI, Tsyba I, Bau R, Thompson ME (2002) Inorg Chem 41:3055

    Article  CAS  Google Scholar 

  45. Li J, Djurovich PI, Alleyne BD, Tsyba I, Ho NN, Bau R, Thompson ME (2004) Polyhedron 23:419

    Article  CAS  Google Scholar 

  46. Yersin H, Huber P, Wiedenhofer H (1994) Coord Chem Rev 132:35

    Article  CAS  Google Scholar 

  47. Colombo MG, Brunold TC, Riedener T, Güdel H, Förtsch M, Bürgi HB (1994) Inorg Chem 33:545

    Article  CAS  Google Scholar 

  48. Finkenzeller WJ, Yersin H (2003) Chem Phys Lett 377:299

    Article  CAS  Google Scholar 

  49. Yersin H, Finkenzeller WJ (2008) In: Yersin H (ed) Highly efficient OLEDs with phosphorescent materials. Wiley, Weinheim, p 1

    Google Scholar 

  50. Rausch AF, Thompson ME, Yersin H (2009) J Phys Chem A 113:5927

    Article  CAS  Google Scholar 

  51. Ma B, Djurovich PI, Thompson ME (2005) Coord Chem Rev 249:1501

    Article  CAS  Google Scholar 

  52. D’Andrade B, Forrest SR (2003) Chem Phys 286:321

    Article  Google Scholar 

  53. Rausch AF, Thompson ME, Yersin H (2009) Inorg Chem 48:1928

    Article  CAS  Google Scholar 

  54. Adachi C, Kwong RC, Djurovich PI, Adamovich V, Baldo MA, Thompson ME, Forrest SR (2001) Appl Phys Lett 79:2082

    Article  CAS  Google Scholar 

  55. Su SJ, Sasabe H, Takeda T, Kido J (2008) Chem Mater 20:1691

    Article  CAS  Google Scholar 

  56. Vecchi PA, Padmaperuma AB, Qiao H, Sapochak LS, Burrows PE (2006) Org Lett 8:4211

    Article  CAS  Google Scholar 

  57. Li J, Djurovich PI, Alleyne BD, Yousufuddin M, Ho NN, Thomas JC, Peters JC, Bau R, Thompson ME (2005) Inorg Chem 44:1713

    Article  CAS  Google Scholar 

  58. Coppo P, Plummer EA, De Cola L (2004) Chem Commun 15:1774

    Article  CAS  Google Scholar 

  59. Yersin H, Schützenmeier S, Wiedenhofer H, von Zelewsky A (1993) J Phys Chem 97:13496

    Article  CAS  Google Scholar 

  60. Yersin H, Donges D, Nagle JK, Sitters R, Glasbeek M (2000) Inorg Chem 39:770

    Article  CAS  Google Scholar 

  61. Schmidt J, Wiedenhofer H, von Zelewsky A, Yersin H (1995) J Phys Chem 99:226

    Article  CAS  Google Scholar 

  62. Becker D, Yersin H, von Zelewsky A (1995) Chem Phys Lett 235:490

    Article  CAS  Google Scholar 

  63. Yersin H, Donges D (2001) Top Curr Chem 214:81

    Article  CAS  Google Scholar 

  64. Donges D, Nagle JK, Yersin H (1997) Inorg Chem 36:3040

    Article  CAS  Google Scholar 

  65. Kozhevnikov DM, Kozhevnikov VN, Ustinova MM, Santoro A, Bruce DW, König B, Czerwieniec R, Fischer T, Zabel M, Yersin H (2009) Inorg Chem 48:4179

    Article  CAS  Google Scholar 

  66. Shpol’skii EV (1960) Sov Phys Usp 3:372 Engl Transl

    Article  Google Scholar 

  67. Murao T, Azumi T (1979) J Chem Phys 70:4460

    Article  CAS  Google Scholar 

  68. Jansen G, Noort M, van Dijk N, van der Waals JH (1980) Mol Phys 39:865

    Article  CAS  Google Scholar 

  69. Komada Y, Yamauchi S, Hirota N (1985) J Chem Phys 82:1651

    Article  CAS  Google Scholar 

  70. Dick B, Nickel B (1986) Chem Phys 110:131

    Article  CAS  Google Scholar 

  71. Rausch AF, Thompson ME, Yersin H (2009) Chem Phys Lett 468:46

    Article  CAS  Google Scholar 

  72. Finkenzeller WJ, Hofbeck T, Thompson ME, Yersin H (2007) Inorg Chem 46:5076

    Article  CAS  Google Scholar 

  73. Van Dijk N, Noort M, Voelker S, Canters GW, van der Waals JH (1980) Chem Phys Lett 71:415

    Article  Google Scholar 

  74. Chen WH, Rieckhoff KE, Voigt EM (1985) Chem Phys 95:123

    Article  CAS  Google Scholar 

  75. Huang SC, Chen WH (1996) J Chem Phys 104:8210

    Article  CAS  Google Scholar 

  76. Gliemann G (1986) Comments Inorg Chem 5:263

    Article  CAS  Google Scholar 

  77. Czerwieniec R, Finkenzeller WJ, Hofbeck T, Starukhin A, Wedel A, Yersin H (2009) Chem Phys Lett 468:205

    Article  CAS  Google Scholar 

  78. Baker DC, Crosby GA (1974) Chem Phys 4:428

    Article  CAS  Google Scholar 

  79. Gallhuber E, Hensler G, Yersin H (1987) J Am Chem Soc 109:4818

    Article  CAS  Google Scholar 

  80. Yersin H, Kratzer C (2002) Chem Phys Lett 362:365

    Article  CAS  Google Scholar 

  81. Yersin H, Humbs W, Strasser J (1997) Top Curr Chem 191:153

    Article  CAS  Google Scholar 

  82. Yersin H, Kratzer C (2002) Coord Chem Rev 229:75

    Article  CAS  Google Scholar 

  83. Carrigan RW, Crosby GA (1973) J Chem Phys 59:3468

    Article  Google Scholar 

  84. Azumi T, O’Donnell CM, McGlynn SP (1966) J Chem Phys 45:2735

    Article  CAS  Google Scholar 

  85. Pentlehner D, Grau I, Yersin H (2008) Chem Phys Lett 455:72

    Article  CAS  Google Scholar 

  86. Yersin H, Strasser J (2000) Coord Chem Rev 208:331

    Article  CAS  Google Scholar 

  87. Strasser J, Homeier HHH, Yersin H (2000) Chem Phys 255:301

    Article  CAS  Google Scholar 

  88. Wiedenhofer H, Schützenmeier S, von Zelewsky A, Yersin H (1995) J Phys Chem 99:13385

    Article  CAS  Google Scholar 

  89. Albrecht AC (1963) J Chem Phys 38:354

    Article  CAS  Google Scholar 

  90. Fischer G (1984) Vibronic coupling. Academic Press, London

    Google Scholar 

  91. Flint CD (ed) (1989) Vibronic processes in inorganic chemistry. NATO ASI Series C, vol 288. Kluwer Academic, Dordrecht

    Google Scholar 

  92. Hochstrasser RM (1966) Molecular aspects of symmetry. Benjamin Inc WA, New York

    Google Scholar 

  93. Braun D, Hensler G, Gallhuber E, Yersin H (1991) J Phys Chem 95:1067

    Article  CAS  Google Scholar 

  94. Ballhausen CJ (1979) Molecular electronic structures of transition metal complexes. McGraw-Hill, New York

    Google Scholar 

  95. Wilson RB, Solomon EI (1980) J Am Chem Soc 102:4085

    Article  CAS  Google Scholar 

  96. Henderson B, Imbusch GF (1989) Optical spectroscopy of inorganic solids. Clarendon, Oxford

    Google Scholar 

  97. Solomon EI (1984) Comments Inorg Chem 3:225

    CAS  Google Scholar 

  98. Seiler R, Kensy U, Dick B (2001) Phys Chem Chem Phys 3:5373

    Article  CAS  Google Scholar 

  99. Humbs W, Yersin H (1997) Inorg Chim Acta 265:139

    Article  CAS  Google Scholar 

  100. Humbs W, Yersin H (1996) Inorg Chem 35:2220

    Article  CAS  Google Scholar 

  101. Finkenzeller WJ, Thompson ME, Yersin H (2007) Chem Phys Lett 444:273

    Article  CAS  Google Scholar 

  102. Marchetti AP, Deaton JC, Young RH (2006) J Phys Chem A 110:9828

    Article  CAS  Google Scholar 

  103. Wang X, Li J, Thompson ME, Zink JI (2007) J Phys Chem A 111:3256

    Article  CAS  Google Scholar 

  104. Liu T, Xia BH, Zhou Y, Zheng QC, Pan QJ, Zhang HX (2008) Theor Chem Account 121:155

    Article  CAS  Google Scholar 

  105. Rebane KK (1988) In: Sild O, Haller K (eds) Zero-phonon lines and spectral hole burning in spectroscopy and photochemistry. Springer, Berlin

    Google Scholar 

  106. Bauer R, Finkenzeller WJ, Bogner U, Thompson ME, Yersin H (2008) Org Electron 9:641

    Article  CAS  Google Scholar 

  107. Rausch AF, Phd thesis, in preparation

    Google Scholar 

  108. Rausch AF, Homeier HHH, Djurovich PI, Thompson ME, Yersin H (2007) In: Kafafi Z, So F (eds) Proceedings of SPIE optics and photonics – organic light emitting materials and devices XI, vol 6655. San Diego, USA, p 66550F

    Google Scholar 

  109. Gu X, Fei T, Zhang H, Xu H, Yang B, Ma Y, Liu X (2008) J Phys Chem A 112:8387

    Article  CAS  Google Scholar 

  110. Nozaki K (2006) J Chin Chem Soc 53:101

    CAS  Google Scholar 

  111. Jansson E, Minaev B, Schrader S, Ågren H (2007) Chem Phys 333:157

    Article  CAS  Google Scholar 

  112. Minaev B, Minaeva V, Ågren H (2009) J Phys Chem A 113:726

    Article  CAS  Google Scholar 

  113. Mc Glynn SP, Kinoshita M, Azumi T (1969) Molecular spectroscopy of the triplet state. Prentice Hall, Englewood Cliffs

    Google Scholar 

  114. Yagi M, Schlyer D, Maki AH (1991) Chem Phys 157:209

    Article  CAS  Google Scholar 

  115. Miki H, Azumi T (1994) J Phys Chem 98:6059

    Article  CAS  Google Scholar 

  116. Azumi T, Miki H (1997) Top Curr Chem 191:1

    Article  CAS  Google Scholar 

  117. Vanhelmont FWM, Güdel HU, Förtsch M, Bürgi HB (1997) Inorg Chem 36:5512

    Article  CAS  Google Scholar 

  118. Funayama T, Kato M, Kosugi H, Yagi M, Higuchi J, Yamauchi S (2000) Bull Chem Soc Jpn 73:1541

    Article  CAS  Google Scholar 

  119. Atkins PW (1997) Molecular quantum mechanics. Oxford University Press, Oxford, p 208

    Google Scholar 

  120. Sakurai JJ (1994) Modern quantum mechanics. Addison-Wesley, Reading, p 239

    Google Scholar 

  121. Szabo A, Ostlund NS (1989) Modern quantum chemistry: introduction to advanced electronic structure theory. McGraw-Hill, New York

    Google Scholar 

  122. Roos BO (ed) (1992) Lecture notes in quantum chemistry (Lecture notes in chemistry), vol 58. Springer, Berlin

    Google Scholar 

  123. Miki H, Shimada M, Azumi T, Brozik JA, Crosby GA (1993) J Phys Chem 97:11175

    Article  CAS  Google Scholar 

  124. Giesbergen C, Glasbeek M (1993) J Phys Chem 97:9942

    Article  CAS  Google Scholar 

  125. Komada Y, Yamauchi S, Hirota N (1986) J Phys Chem 90:6425

    Article  CAS  Google Scholar 

  126. Glasbeek M, Sitters R, van Veldhoven E, von Zelewsky A, Humbs W, Yersin H (1998) Inorg Chem 37:5159

    Article  CAS  Google Scholar 

  127. Finkenzeller WJ, Stößel P, Yersin H (2004) Chem Phys Lett 397:289

    Google Scholar 

  128. Schläfer HL, Gliemann G (1967) Einführung in die Ligandenfeldtheorie. AkadVerlagsgesellschaft, Wiesbaden

    Article  CAS  Google Scholar 

  129. Ikeela S, Yamamto S, Nozaki K, Ikeyama T, Azumi T, Burt JA, Crosley GA (1991) J Phys Chem 95:8583

    Google Scholar 

  130. Abedin-Siddique Z, Ohno T, Nozaki K, Tsubomura T (2004) Inorg Chem 43:663

    Article  CAS  Google Scholar 

  131. Figgis BN (1987) Ligand field theory. Comprehensive coordination chemistry. Pergamon, Oxford, p 213

    Google Scholar 

  132. Ceulemans A, Vanquickenborne LG (1981) J Am Chem Soc 103:2238

    Article  CAS  Google Scholar 

  133. Kober EM, Meyer TJ (1982) Inorg Chem 21:3967

    Article  CAS  Google Scholar 

  134. Daul C, Baerends EJ, Vernooijs P (1994) Inorg Chem 33:3538

    Article  CAS  Google Scholar 

  135. Ziegler T, Nagle JK, Snijders JG, Baerends EJ (1989) J Am Chem Soc 111:5631

    Article  CAS  Google Scholar 

  136. Murov SL, Carmichael J, Hug GL (1993) Handbook of photochemistry, 2nd edn. Marcel Dekker, New York

    Google Scholar 

  137. Griffith JS (1964) The theory of transition metal ions. Cambridge University Press, London

    Google Scholar 

  138. Chen P, Meyer TJ (1998) Chem Rev 98:1439

    Article  CAS  Google Scholar 

  139. Ulstrup J (1979) Processes in condensed media (Lecture notes in chemistry), vol 10. Springer, New York

    Google Scholar 

  140. Colombo MG, Hauser A, Güdel HU (1993) Inorg Chem 32:3088

    Article  CAS  Google Scholar 

  141. Colombo MG, Hauser A, Güdel HU (1994) Top Curr Chem 171:143

    CAS  Google Scholar 

Download references

Acknowledgments

The Bundesministerium für Bildung und Forschung (BMBF) is gratefully acknowledged for providing the funding of our research. We thank Prof. Dr. Mark E. Thompson (University of Southern California) for a fruitful cooperation with respect to the studied compounds.

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Authors and Affiliations

  1. Institut für Physikalische und Theoretische Chemie, Universität Regensburg, 93053, Regensburg, Germany

    Andreas F. Rausch, Herbert H. H. Homeier & Hartmut Yersin

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  1. Andreas F. Rausch
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  2. Herbert H. H. Homeier
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  3. Hartmut Yersin
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Correspondence to Hartmut Yersin .

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Editors and Affiliations

  1. Dept. Chemistry, State University of New York, Binghamton, Binghamton, 13902-6016, U.S.A.

    Alistair J. Lees

Appendix

Appendix

Here, we discuss how Rule E is related to the fact that angular momentum operators are purely imaginary. It further depends on the fact that, without magnetic field, the spatial orbitals are real. It is claimed that the diagonal matrix elements of the angular momentum operators vanish. For instance, in the case of l z , we have for any real orbital \( \chi = \chi (\vec r) \)

$ \left\langle \chi \right|{l_z}\left| \chi \right\rangle = \left\langle \chi \right|{l_z}{\left| \chi \right\rangle^*}, $

since l z is Hermitian. On the other hand, performing the complex conjugation explicitly, we have

$ \left\langle \chi \right|{l_z}{\left| \chi \right\rangle^*} = {\left( {\int {\int {\int {\chi (\vec r)\frac{1}{i}\frac{\partial }{{\partial \varphi }}\chi (\vec r){r^2}{{\rm d}}r{{\rm d}}\Omega } } } } \right)^* } = - \left\langle \chi \right|{l_z}\left| \chi \right\rangle, $

where \( {{\rm d}}\Omega = \sin \vartheta {{\rm d}}\vartheta {{\rm d}}\varphi \) is the usual surface element in spherical coordinates \( r,\vartheta, \varphi \) and the integration is over all space. Combining the two equations yields that the matrix element can only be zero.

This proves the assertion, since the other components of \( \vec l \) can be treated similarly.

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Rausch, A.F., Homeier, H.H.H., Yersin, H. (2010). Organometallic Pt(II) and Ir(III) Triplet Emitters for OLED Applications and the Role of Spin–Orbit Coupling: A Study Based on High-Resolution Optical Spectroscopy. In: Lees, A. (eds) Photophysics of Organometallics. Topics in Organometallic Chemistry, vol 29. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3418_2009_6

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