2E states

The effects of spin-orbit coupling on geometric phase may be illustrated by imagining the vibronic coupling between the two Kramers doublets arising from a 2E state, spin-orbit coupled to one of symmetry 2A. The formulation given below follows Stone [24]. The four 2E components are denoted by e, a), e a), e+ 3), c p), and those of 2A by coa), cop). The spin-orbit coupling operator has nonzero matrix elements... 

Two configurational coordinate models, presented in Figure 11.13 and 11.14, are sufficient to allow the interpretation of the temperature dependences of the Cr3+ fluorescence in crystal materials qualitatively, even quantitatively to an extent of sufficient precision for thermometric applications, as shown in the cases of CnLiSAF, alexandrite, and ruby. In high-field-strength host crystals, two mechanisms, the thermal repopulation of the 473 and 2E states and the nonradiative process, dominate the... 

The excitation spectrum of neodymium in the doubly doped crystal having 1 per cent chromium and 1.3 per cent neodymium clearly shows chromium bands. From a detailed study of the chromium and neodymium lifetimes, Kiss and Duncan show that energy transfer takes place from the chromium 2E state. This is contrary to the conclusion drawn by Murphy and co-workers on LaA103. 

In two remarkable studies,75-80 Callear and Smith excited, along with the A2S+ and Z)2E+ states, the C2n state of NO in the 0-, 1-, and 2-vibrational levels by irradiation with a xenon source... 

It is immediately apparent that only the 2E states of HRe(CO)5 are split by spin—orbit coupling. However, it is also obvious that subsequent interactions can take place between MOs of the same (E or E") symmetry. Considering only the predominantly metals orbitals, Hall (161) has presented three schemes that differ in the relative energies of the b2 and e MOs. 

The IE differences between the 2T2 and 2E states of the M(PF3)4 compounds, t2,E (Table XXXI), correspond, within the limitations of Koopmans theorem, to the ligand field splitting. The observation that t2,e... 

The pentacoordinate trifluorophosphine complexes behave similarly. Thus the difference in energy between the 2E and 2E" states, Ae e"> increases markedly in going from Fe(PF3)s to Ru(PF3)s. This increase is caused by the change in energy of the 2E state, which, in turn, results from changing from a 3d to a 4d metal orbital. 

The cobalt(II) complexes which undergo spin equilibrium are of several different types. Octahedral high-spin complexes with a T ground state are subject to Jahn-Teller distortion in the low-spin d1 2E state. This effect is best documented in structures of the Co(terpy)22+ spin-equilibrium complex. The high-spin isomer is nearly octahedral, with a difference in Co N bond lengths between the central and distal nitrogens of only 6 pm. In the Jahn-Teller distorted low-spin state this difference has increased to 21 pm (58). 

Such a short spin-equilibrium relaxation time raises the question of whether discrete spin state isomers exist. Their existence is affirmed by two observations. One is the persistence of electronic spectral bands typical of the low-spin 2E state over a wide temperature range in solid samples (98). The other is the observation of EPR signals characteristic of the 2E state in both solids and solutions between 4 and 293 K (98,139). At very low temperatures EPR signals of both spin states can be observed simultaneously (98). At low temperatures hyperfine splitting into eight lines is observed from coupling with the 1 = 7/2 Co nucleus. As the temperature is raised the spectral features broaden and the hyperfine resolution is lost. This implies a relaxation process on the EPR time scale of 1010 sec-1, or a relaxation time of the order 0.1 nsec, consistent with the upper limit set by the ultrasonic experiments. 

The multireference results of Table 5.12 were all based on full valence CASSCF calculations with eleven electrons in twelve active orbitals. This produces a large configuration expansion (about 85 000 CSFs) so it is not possible to perform MRCI(CAS) calculations. Reference configuration lists were selected at the cyclic and linear geometries (taken from MP2 optimized structures) and then merged. The core electrons were not correlated in any of the calculations. One complication in the CASSCF calculations should be pointed out. Since the cyclic state arises as the 2B component, in C3v symmetry, of a 2E state in the D3h symmetry (equilateral triangular) structure, it would be desirable to obtain MOs with D3h symmetry and equivalence restrictions... 

A predissociation, which may or may not be related to the one just discussed, is observed in hot flames147 and in cool atomic flames148. For rotationless states the predissociating curve appears to cross the bound 2E+ state very near v = 2. The corresponding inverse predissociation has been proposed149,150 as an explanation for the observed overpopulation of the first and second vibrational levels of OH(2E+) in flames where there is a considerable excess population (over thermodynamic equilibrium) of O and H atoms. This process may produce a population inversion in nozzle expansion of a dissociated gas 15 x. 

As a result for such levels the inner and outer branches of the Zeeman profile will be interchanged with respect to the normal quartet splitting. For this reason we have denoted this case as an inside out or inverted quartet [72], The pseudoscalar multiplication which relates the two types of quartet splitting corresponds to a Weyl reflection in the root diagram of SO (5). In the center of this reflection we meet a third case of Zeeman isotropy, which we have called a pseudodoublet. Since this case is invariant under the Weyl reflection inner and outer branches of the splitting pattern will coalesce. The V level thus will split in only two sublevels, each of which is pseudo-degenerate. Evidently this case is observed for any 2E state, since the -type orbital component of this state cannot contribute to the Zeeman splitting. It also occurs for a U ( E) state. 

An Attempt to Elucidate the Role of the 2Tt, State. We have some preliminary observations which may bear on the role of the 2Ti excited state in the relaxation process. This state can often be found 200 to 1000 cm- above the (2E) state in simple amine and ammine complexes (22). As the symmetry of the complexes decreases, the 2T state splits into two or three... 

With the exception of a few highly studied states, such as, for example, the redox active lowest metal-to-ligand charge transfer excited state (MLCT) in the [Ru(bipyridine)3]2t cation, or the ligand field active 2E state of Cr(IlI), we know relatively little about these excited states. An enormous body of knowledge is waiting to be explored. 

A schematic energy-level diagram of Cr3+ and Tm3+ in YAG together with the luminescence and absorption spectra of Cr3+ are shown in fig. 18. Three primary Cr3+ - Tm3+ energy transfer pathways can be identified thermally activated energy transfer from the 4T2 state (4T2 ET), thermally activated energy transfer from the 2E anti-Stokes phonon sidebands (2E anti-Stokes ET), and temperature-independent energy transfer from the zero phonon and Stokes phonon sidebands of the 2E state (2E Stokes ET). 

Here Ad(0) is the number of donors excited at t = 0, ITd is the intracenter decay rate of the coupled 4T2-2E states of Cr3+, Ca is equivalent to the acceptor doping concentration, Ns is... 

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