Electronic transitions, forbidden systems

Let us begin with the one-mode electron-transfer system. Model IVa, which still exhibits relatively simple oscillatory population dynamics [205]. SimUar to what is found in Fig. 5 for the mean-field description, the SH results shown in Fig. 13 are seen to qualitatively reproduce both diabatic and adiabatic populations, at least for short times. A closer inspection shows that the SH results underestimate the back transfer of the adiabatic population at t 50 and 80 fs. This is because the back reaction would require energetically forbidden electronic transitions which are not possible in the SH algorithm. Figure 13 also shows the SH results for the electronic coherence which are found to... 

In this system with even number N of dimer units a orbitals HOMO and LUMO are nonbonding with zero overlap [9], Therefore, the photo-induced electron transition between these orbitals is forbidden. The first electron transition with lowest energy in optical spectrum of this system proceeds between HOMO and unoccupied molecular orbital next to LUMO [6]. Simple calculations based on formula (9) give the energy AEt of this transition at N 1 as... 

In the application of the exciton theory to transitions that are forbidden or extremely weak in the vapour another result was found that has proved useful in the interpretation of numerous crystal spectra. In these transitions, in the crystal, the intensity appears partly in the vibrationless pure electronic transition, and in part in vibrationally induced transitions as will be described for the benzene 260 nm system (sec 4.1). Other examples are in naphthalene and phenanthrene and in some nitrogen heterocyclic molecules. 

After describing why there is a problem, I will briefly summarize the theoretical description of spin-forbidden reactions. It will be useful at this point to draw parallels with other types of nonadiabatic chemistry, in particular, electron transfer. Then I will review some of the typical contexts in which spin-forbidden behavior occurs in transition metal systems, to try to illustrate how widespread it is. This will be followed by a presentation of strategies used for characterizing and understanding spin-forbidden reactions, based on the use of energies and... 

We now arrive at the major factor which distinguishes the electronic spectra of centrosymmetric M2ALnX6 systems from those of most other lanthanide ion systems. This results from the vanishing of the second bracket of Eq. (22), since rmxr, is odd parity and r(H Cf) is only even parity. Forced dipole pure electronic transitions are thus forbidden for these lanthanide systems. 

Turning now to the intensity of this absorption band in the [Ti(H20)6]3+ ion, we note that it is extremely weak by comparison with absorption bands found in many other systems. The reason for this is that the electron is jumping from one orbital that is centrosymmetric to another that is also centrosymmetric, and that all transitions of this type are nominally forbidden by the rules of quantum mechanics. One-electron transitions which are allowed have intensities that give molar absorbance values at the absorption peaks of 104. If the postulate of the crystal field theory, that in both the ground and the excited states the electrons of the metal ion occupy completely pure d orbitals that have no other interaction than a purely coulombic one with the environment of the ion, were precisely correct, the intensity of this band would be precisely zero. It gains a little intensity because the postulate is not perfectly valid in ways that will be discussed on page 578. It will also be noted that the band is several thousand cm"1 broad, rather than a sharp line at a frequency precisely equivalent to A0. This too is a general phenomenon that will be discussed in detail below. 

The d-d electron transitions for a low-spin iron(II) system cover the spin forbidden Ax = lAx -> TX and A2 = XAX - 3T2 transitions with low intensity, as well as the spin allowed (orbital forbidden) A3 = XAX - XTX and A4 = XAX 1T2 transitions which are well resolved (Fig. 9.20). Typically, Ax 10000cm-1, J3 18000-19 500cm-1 and A4 26000cm-1 so that the LS system is coloured (purple). In contrast, the HS system exhibits only the single spin-allowed d-d transition As = 5T2 -> SE with a typical value of d5 12000 cm-1, which implies that the HS system is colourless (no low-lying metal-to-ligand charge-transfer transitions are assumed). 

The term log (/q/T) is also known as the absorbance (or the optical density in older literature) and may be represented by A. The molar absorptivity (formerly known as the molar extinction coefficient) is a property of the molecule undergoing an electronic transition and is not a function of the variable parameters involved in preparing a solution. The size of the absorbing system and the probability that the electronic transition whl take place control the absorptivity, which ranges from 0 to 10 . Values above 10" are termed high-intensity absorptions, while values below 10 are low-intensity absorptions. Forbidden transitions (see Section 7.1) have absorptivities in the range from 0 to 1000. 

The first pressure-induced excited state electronic crossover in a luminescent transition metal system was reported by Dolan et al. [175] in a study of Cr + K2NaGaFg. Cr + is an excellent candidate for observing an electronic crossover with pressure because, depending on its crystal field strength, it can exhibit either spin allowed T2 A2 emission (low field Cr ) or spin forbidden... 

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