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Electronic Spectroscopy and Photoreactivity of Transition Metal Complexes 135 2.6 Non-Adiabatic Processes In an electronically non-adiabatic process the description of the nuclear motion involves more than one PES. Electronic spectroscopy and photochemical reactions involve transitions between two or more PES in critical regions (avoided crossings, conical intersections, crossings) where the nature of the electronic wave function may change rapidly as a function of the nuclear displacement. This is illustrated in Scheme 4 which represents two different Scheme 4 situations, namely an internal conversion (IC) between electronic states of same multiplicity and an intersystem crossing (ISC) process between electronic states of different multiplicity. The efficiency of the transition is governed by the non-zero interaction matrix elements between electronic states, the BO approximation being no longer valid. In order to determine the electronic structure aspects of an electronically non-adiabatic process it is necessary to determine: i) the critical regions of the PES; ii) the coupling between the states in these regions. The first point has been discussed in the previous section whereas the second point will be developed in the next section.
136 C. Daniel 2.6.1 Adiabatic Representation Within the Born-Oppenheimer approximation the adiabatic PES are obtained by calculating the electronic energy and wave function by the standard nonrelativistic methods of quantum chemistry (see above) for a series of fixed nuclear geometries. This leads to avoided crossings (or conical intersections) between electronic states of same spin multiplicity and true crossings between electronic states of different spin multiplicity (Scheme 4). The non-adiabatic coupling between states of same multiplicity is given by the matrix elements of the kinetic energy operator. The calculation of the kinetic coupling terms requires the first and second derivatives of the electronic wave functions with respect to the nuclear coordinates. Although their determination is still delicate for polyatomic molecules, recent developments based on analytical derivatives techniques have allowed a direct computation of non-adiabatic couplings in the case of small triatomic molecules [103]. Apart from the calculation of the kinetic couplings, another difficulty arising in the adiabatic representation is the treatment at the same level of theory of the internal conversions (singlet to singlet or triplet to triplet transitions) and intersystem crossings (singlet to triplet transitions). Indeed, the adiabatic potentials are calculated in the non-relativistic approximation, the spin-orbit interaction being taken into account later on at a perturbational level of theory (see above). The singlet-singlet or triplet-triplet interactions characterized by avoided crossings are given by the matrix elements of the kinetic energy whereas the singlet-triplet interactions occurring at true crossings are determined by the spin-orbit potential coupling. Consequently when the transitions between states of same multiplicity are treated adiabatically the singlet-triplet transitions are described according to a quasi-diabatic picture. 2.6.2 Diabatic Representation The sudden change of the adiabatic wave functions near an avoided crossing and the resultant large non adiabatic coupling elements in a narrow region of the PES make the adiabatic representation rather inconvenient for numerical applications. Moreover the non-adiabaticity of the triplet potentials with respect to the non-relativistic Hamiltonian adds some difficulty in a coherent treatment of various non-radiative transitions. An electronic diabatic basis which changes smoothly across the region of avoided crossing can be obtained by unitary transformation of the electronic adiabatic basis. In the diabatic representation the kinetic couplings vanish exactly within the limit of a complete basis set. Unlike the adiabatic potentials, the diabatic potentials which are not eigenvalues of the electronic Schrödinger equation are allowed to cross (Fig. 1).
Page 1 and 2: 241 Topics in Current Chemistry Edi
Page 3 and 4: Transition Metal and Rare Earth Com
Page 5 and 6: Volume Editor Prof. Dr. Hartmut Yer
Page 7 and 8: Preface For a long time, the proper
Page 9 and 10: Contents Triplet Emitters for OLED
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78 A. Hauser et al. k et D ¼ X A w
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82 A. Hauser et al. The intrinsic l
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86 A. Hauser et al. Fig. 17 Scheme
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88 A. Hauser et al. Fig. 20 a Trans
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94 A. Hauser et al. below 2 K, the
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96 A. Hauser et al. 19. Sugano S, T
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168 P.A. Tanner 14 Conclusions ....
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170 P.A. Tanner ration, the stoichi
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172 P.A. Tanner Fig. 2 a Plot of la
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174 P.A. Tanner with smaller unit c
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176 P.A. Tanner Oh for elpasolites.
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178 P.A. Tanner Fig. 4a-g Infrared,
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180 P.A. Tanner Table 2 (continued)
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182 P.A. Tanner Table 3 Comparison
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184 P.A. Tanner belled. The unit ce
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186 P.A. Tanner sion curve for this
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188 P.A. Tanner so that B ð4Þ 0
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190 P.A. Tanner coordinates. One of
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192 P.A. Tanner
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194 P.A. Tanner where Wl ¼ ½Š l
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196 P.A. Tanner
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198 P.A. Tanner electric dipole mom
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200 P.A. Tanner respectively, where
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202 P.A. Tanner modified form in mo
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204 P.A. Tanner M00;f 1;q ¼ X n ½
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206 P.A. Tanner The sign of the int
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208 P.A. Tanner try notation of Gri
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210 P.A. Tanner Finally, it is note
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212 P.A. Tanner The actual assignme
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214 P.A. Tanner Fig. 13 35 K Raman
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216 P.A. Tanner terial, so that the
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218 P.A. Tanner Fig. 14a-c Electron
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220 P.A. Tanner 2 6 X 6 l;m;n 6 4
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222 P.A. Tanner allowed, and in var
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224 P.A. Tanner Table 7 Calculated
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226 P.A. Tanner Fig. 16 Lowest f-d,
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228 P.A. Tanner Fig. 18a, b 10 K f-
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230 P.A. Tanner It is interesting t
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232 P.A. Tanner Table 9 Selected en
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234 P.A. Tanner Fig. 20 Plots of Sl
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236 P.A. Tanner values are obtained
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238 P.A. Tanner X ½B k qCk q i ð
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240 P.A. Tanner their calculation h
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242 P.A. Tanner 13 Energy Transfer
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244 P.A. Tanner Table 11 (continued
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246 P.A. Tanner Fig. 24a-j Energy t
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248 P.A. Tanner Table 13 Structural
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250 P.A. Tanner s=6, although the c
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252 P.A. Tanner ask 2 ¼ 1 4 h es;a
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256 P.A. Tanner Fig. 25a, b Lumines
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258 P.A. Tanner when excitation is
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260 P.A. Tanner Fig. 26 a Partial e
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262 P.A. Tanner 13.4.3 Upconversion
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264 P.A. Tanner ! 4 I15=2aG8½ŠD 0
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266 P.A. Tanner Fig. 27 a Power dep
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268 P.A. Tanner The study of f-d tr
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270 P.A. Tanner 41. Knudsen GP, Vos
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272 P.A. Tanner 119. Malta OL, Gouv
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274 P.A. Tanner 207. Tanner PA, Mak
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276 P.A. Tanner 290. Hehlen MP, Gü
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278 P.A. Tanner 379. Berry ME, May
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2 H. Yersin trix molecules with sub
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4 H. Yersin into substates, the tot
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6 H. Yersin Fig. 2 Example of an op
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8 H. Yersin 3 Exciton Formation and
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10 H. Yersin gram is simplified and
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12 H. Yersin to-matrix charge trans
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14 H. Yersin triplet excitons, are
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16 H. Yersin tions, but also induce
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18 H. Yersin 5 Photophysical Proper
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20 H. Yersin 5.3 Phosphorescence De
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22 H. Yersin 5.6 Electronic Charge
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24 H. Yersin 3. Tai WP, Inoue K, Oh
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26 H. Yersin 71. Wohlgenannt M, Tan
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280 Author Index Volumes 201-241 Br
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282 Author Index Volumes 201-241 Ga
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284 Author Index Volumes 201-241 Ko
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286 Author Index Volumes 201-241 Mu
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288 Author Index Volumes 201-241 Sh
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290 Author Index Volumes 201-241 Wu
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292 Subject Index DMCT 1, 12 DNA 56
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294 Subject Index Resonant energy t
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