Totally Symmetric Modes

For states of different symmetry, to first order the terms AW and W[2 are independent. When they both go to zero, there is a conical intersection. To connect this to Section III.C, take Qq to be at the conical intersection. The gradient difference vector in Eq. f75) is then a linear combination of the symmetric modes, while the non-adiabatic coupling vector inEq. (76) is a linear combination of the appropriate nonsymmetric modes. States of the same symmetry may also foiiti a conical intersection. In this case it is, however, not possible to say a priori which modes are responsible for the coupling. All totally symmetric modes may couple on- or off-diagonal, and the magnitudes of the coupling determine the topology. 

Fig. 105. TO-LO splitting of totally symmetrical mode A/ (NbO vibration of RbsNbsOFig). Reproduced from [441], A. I. Agulyansky, R. Cavagnat, M. Couzi, J. Ravez, Phys. Stat. Sol. (a) 138 (1993) 327, Copyright 1993, with permission ofWiley-VCH.

The b-polarized absorption bands (see Fig. 6-3b) at 20945 cm 1, 22250 cm-1 and 23535 cm-1 are assigned to a vibronic progression built on the bu Davydov component with the totally symmetric mode at 1275 cm-1. 

At resonance with an electric dipole allowed transition, the Stokes resonance Raman scattering, I(tt/2), associated with a single totally symmetric mode and its overtones is proportional to... 

Kettle, Paul and Stamper33,34) 08 are the only group who have reported intensity data for other than totally symmetric modes. They confined their attention to the i>(CO) region and looked at octahedral M(CO)6, trigonal RM (CO)3 and tetragonal R M(CO)5 species. The measurement of the intensities of several modes may enable... 

This has the very important consequence, as we show in more detail later, that no totally symmetric mode of a mixed-valence compound can contribute to the intervalence bandwidth (in the approximation of equal force constants in both oxidation states). For the moment we therefore drop the terms in Q+ and define the dimensionless variables... 

Totally Symmetric Modes do NOT Contribute Significantly to the Intervalence Bandwidth... 

It has recently been suggested by Hush (13) that the asymmetry on the high energy side of the C T ion intervalence band can be easily rationalized by including contributions from totally symmetric modes of the ion. Day (20) has interpreted the... 

We now demonstrate that, to a good approximation, no totally symmetric mode of the ion can contribute to the intervalence bandwidth. Noting the discussion below eq 6, we reiterate that the potential surfaces W and W are identical in the Q modes. If we explicitly carry t ese terms through to eq 12, tney will appear in identical form on the right hand side for both W ... 

Figure 1. Quantum-mechanical (thick lines) and mean-field-trajectory (thin lines) calculations obtained for Model 1 describing the S2 — Si internal-conversion process in pyrazine. Shown are the time-dependent population probabilities Pf t) and Pf (t) of the initially prepared adiabatic and diabatic electronic state, respectively, as well as the mean momenta pi (t) and P2 t) of the two totally symmetric modes Vi and V( of the model.

Distortions along non-totally symmetric modes may occur in certain excited states. These distortions are non-symmetry preserving the point group of the molecule changes in the excited state. The specific examples in this paper are the linear to bent geometry changes of metal nitrosyls (e.g., from Ci(V to C3 in [Fe(CN)5N0]2+.)... 

The symmetry of the Heilbronner modes of Ceo thus includes just one totally symmetric mode, already implicitly taken into account by the difference in length of the 60 long (pentagon-hexagon) and 30 short (hexagon-hexagon) edges of the a framework. The potentially distortive Heilbronner modes of Ceo span... 

Fig. 4. Doping-induced changes to the totally symmetric modes of vibration of C60. The graphs illustrate the shift in frequency, measured relative to the uncharged molecule, caused by the addition of n electrons. The data points correspond to experimental data collated in Ref. [7] and the lines are least squares fits to the theoretical expression in equation (8).

If all the accepting modes (usually the totally symmetric modes) are displaced oscillators [24], then... 

If the incident radiation is plane-polarized, such as that produced by lasers in Raman spectroscopy, scattering theory predicts that totally symmetric modes... 

TABLE 5. Calculated bond distances Re(A), total bond dissociation energies Do (kcalmol-1) which include ZPE corrections and force constants of the totally symmetric mode ke (Ncm-1) of the molecules EH4 and ECI4, using relativistic gradient-corrected DFT ... 

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