Laporte forbidden

To the writer s knowledge, it has not been pointed out that moderate deviations from the highest symmetry available to the chromophore, producing comparatively high intensities of Laporte-forbidden transitions and a variety of observable effects, are characteristic for soft central atoms. At an instantaneous picture, Cu(H20) 2 and other instances of Cu(II)06 are not cubic, i.e. having three equivalent Cartesian axes. 

Table 1. Wave-numbers o (in the unit 1000 cm-1) and oscillator strengths P (in the unit 10—S) of spin-allowed (but Laporte-forbidden) transitions in nickel(II), copper(II) and palladium(II) complexes of water, ammonia, ethylenediamine (en), diethylenetriamine (den) and pyridine (py). Shoulders in parentheses...

As mentioned earlier, in a centrosymmetric complex, d-d transitions are Laporte forbidden. The fact that they are observed at all is due to a mechanism called vibronic interaction, which is a mixing of the vibrational and electronic wave-functions. Qualitatively, we may imagine that an electronic transition occurs at the very moment some vibrational modes of the complex distort the molecule in such a way that the center of symmetry is destroyed. When such a vibration takes place, the g character of the state is lost and the transition becomes (very slightly) allowed. Figure 8.10.1 shows two vibrations, with u symmetry, of an octahedral complex which remove the inversion center. 

This is in disagreement with all absorption spectra observed (cf. Fig. 3) except perhaps of cases such as Cr(CO)6, because low-lying Laporte-forbidden bands usually are observed well before the strong Laporte-allowed bands, whereas this theory would predict transitions tzg - tiu at nearly the same wavenumber as t2g - eg and further on, complexes such as Cr(NH3)e+3 not having the t2g sub-shell completely occupied by six electrons would also show transitions tiu - t2g at low wavenumber. 

The actual mixing of rcd and (n + l)p orbitals is, of course, of crucial importance in providing a mechanism by which the Laporte forbidden d-d transitions in transition metal complexes may gain in intensity. This may occur in the static situation (e.g., tetrahedral complexes), where the p orbitals and one set of the d orbitals transform as t2 or in the dynamic situation (as in octahedral complexes) where such mixing is only possible when the point symmetry has been reduced by an asymmetric vibration (vibronic coupling). 

Because of the orbital singlet nature of high-spin Fe111 there are no excited states of the same spin multiplicity and all d-d transitions are therefore spin forbidden as well as Laporte forbidden. The free-ion ground state 65 becomes 6A, in a cubic field while the first excited state 4G splits into two T states,4 Ti and 4 T2, and into a degenerate pair, At and 4E (Figure 2). The first four ligand field... 

In Fe + ions, d-d transitions are both multiplicity- and Laporte-forbidden. Splitting of S is possible due to a second-order spin-orbit coupling of the S manifold with excited quartet spin states or due to higher order effects of the crystal field. ... 

Unless (v iG)spin = ( i E)spin. then the spin component is zero and the transition is spin-forbidden. Nevertheless, spin-forbidden transitions are observed as weak features (as in Fig. 2.18) typically with 10 -10 the intensity of fully allowed transitions. This is because of the interaction between the electron spin magnetic moment and the magnetic moment due to the orbital motion of the electron (spin-orbit coupling). The La-porte selection rule, furthermore, states that only transitions between wave functions with one having gerade and the other ungerade character are allowed (hence all d-d transitions are Laporte forbidden). This arises since the spatial component can be further broken down ... 

The dipole moment operator ( x) has associated with it ungerade character so the integral will be zero if v i[ and v g are both either gerade or ungerade. Again, Laporte-forbidden transitions do occur (with 10 -10 the intensity of fully allowed transitions) because of mixing of the orbitals in the excited state in noncentrosymmetric sites, and even in centrosym-metric sites as a result of vibrations of the metal atoms away from the center of symmetry (vibronic coupling). 

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