Electronic symmetry

The above results mainly apply to the Longuet-Higgins E x e problem, but this historical survey would be incomplete without reference to early work on the much more challenging problems posed by threefold or higher electronic degeneracies in molecules with tetrahedral or octahedral symmetry [3]. For example, tetrahedral species, with electronic symmetry T or T2, have at least five Jahn-Teller active vibrations belonging to the representations E and T with individual coordinates (Qa,Qb) and (Qx. Qx. Q ) say. The linear terms in the nine Hamiltonian matrix elements were shown in 1957 [3] to be... 

We have recently developed a new symmetry correlation scheme that connects symmetry-distinct rovibronic states of the isolated reactants with distinct electronic symmetries of the system in the interaction region independent of the detailed geometry of the collision complex. Briefly, the approach can be logically divided into four steps. First, the appropriate PI group for describing the isolated reactants is chosen. Second, P rvet reactant supermolecule system and the electronic... 

In a chemical bond in a bound molecule at its equilibrium configuration, there are values of p of momentum which are more probable, i.e., which correspond to local maxima of II(p). Those values are determined by both the geometric and electronic symmetries of the molecule. For momenta, p = Pm + 8p, near a maximum it is more likely that 8p is perpendicular rather than parallel to the bond axis. 

Beyond such electronic symmetry analysis, it is also possible to derive vibrational and rotational selection rules for electronic transitions that are El allowed. As was done in the vibrational spectroscopy case, it is conventional to expand i j (R) in a power series about the equilibrium geometry of the initial electronic state (since this geometry is more characteristic of the molecular structure prior to photon absorption) ... 

For polyatomic molecules, (7.2) and (7.6) give the wave numbers and transition moment for an electronic transition. Besides the S selection rule (7.7), there are electronic selection rules stating between which electronic symmetry species transitions are allowed these are derived using group theory (Section 9.11). Equation (7.13) applies to polyatomics, except that Pei is now a function of the 3N —6 (or 3Af —5) normal coordinates Qr... 

In the unsymmetrical cyanines such as (122) the direction of the spectral shift compared with the two possible symmetrical dyes depends upon the electron releasing ability of the two nitrogen atoms. The dye (122) can be regarded as a hybrid of the two dyes (123) and (124), which absorb at 490 and 610 nm respectively. The unsymmetrical cyanine (122) absorbs at 553 nm in the same solvent (nitromethane) which is close to the average of the two former values and indicates the electronic symmetry of the dye. In cases where the basicity of the terminal nitrogens differs markedly then electronic symmetry,is lost and the dyes exhibit an absorption maximum deviation to shorter wavelength than the averaged value of the two parent symmetrical dyes. This difference is known as the Brooker deviation. 

The photodissociation of H2S in the 195 nm band has already been discussed in Chapters 9 and 14 in relation to vibrational excitation and Raman spectroscopy. At first glance, one might be tempted to think that it evolves similarly to the dissociation of H2O in the first absorption band. That is not the case, however While the fragmentation of H2O proceeds via a single electronic state, with electronic symmetry B in -configuration, the dissociation of H2S involves two states, 1B and xA<2. (Weide, Staemmler, and Schinke 1990 Theodorakopoulos and Pet-salakis 1991 Heumann, Diiren, and Schinke 1991). 

The representation of the A-electron symmetry group generated by a given configuration is block-diagonalized into irreducible representations indexed by A, with subspecies index M. In general there will be some number m independent functions with the same symmetry indices. If the configuration basis is < >,, i = 1, / , then a set of m < n unnormalized projected determinants = 0j = l 5Z"=1 are to be constructed, where O is a projector onto the symmetry species A, M. The function j j is normalized if j = YH=i yp I2 and yjj = 1. The projected determinants can be transformed into an orthonormal set 4V = k fi Ya=i xtu >where kn = E = i xm I2- Alternatively, as an expansion in... 

The first and second electronic states are in perfect juxtaposition, and it is only their electronic symmetries that prevent the onset of an S2 — Sj IC. The matrix element connecting these electronic states, (S2(Ai) Qp Si(A2)), however,... 

Figure 11. Time-resolved PADs from ionization of DABCO for linearly polarized pump and probe pulses. Here, the optically bright S E state internally converts to the dark 5i state on picosecond time scales, (a) PADs at 200 fs time delay for pump and probe polarization vector both parallel to the spectrometer axis. The difference in electronic symmetry between S2 and Si leads to significant changes in the form of the PAD. (b) The PADs at 200 fs time delay for pump polarization parallel and probe polarization perpendicular to the spectrometer axis, showing the effects of lab frame molecular alignment, (c) and (d) The PADs evolve as a function of time due to molecular axis rotational wavepacket dynamics. Taken with permission from C. C. Hayden, unpublished.

Besides electronic symmetry, other factors that can affect NMR line widths, such as chemical exchange, viscosity and temperature, can often preclude the detection of 33S NMR signals. 

For the S20 dianion, Tf is significantly shorter than for SO - because of the lower electron symmetry around the sulphur nucleus. 

The first study of Cr in natural abundance and in the liquid phase was reported by Egozy and Loewenstein (206) in 1969 from which the rate constant for the chromate-dichromate equilibrium was derived. Although the quadrupole moment of Cr is small (0-03 barn) no chromium signal could be detected for the dichromate anion in which the valence electron symmetry is only slightly perturbed relative to the tetrahedral CrO. ... 

Because of the square dependence of the relaxation rate on the electric field gradient tensor invariant minor alterations of valence electron symmetry may give rise to sizeable relaxation differentials. Thanks to this amplification effect the binding of ions can be studied at low substrate concentration provided that the resulting complex is kinetically labile. The relaxation rate thus emerges as a complementary experimental observable, at least as informative as the chemical shift. 

Although the quadrupole moment is relatively small, N NMR spectroscopy is dominated by quadrupolar relaxation. The linewidths of the signals vary greatly because they depend on the nitrogen bond type and the molecular mobility. High-resolution work is possible only if the local electronic symmetry and the mobility are both high. 

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