Geometry relaxation effects

While the CP procedure is exact only in the case of Full Cl wavefimctions, the a priori SCFMI method is always correct and geometry relaxation effects are naturally taken into account. 

For systems of this size, the SCF-MI method is particularly advantageous, as a standard SCF supermolecule CP-corrected approach requires five single point energy evaluations, if geometry relaxation effects are to be included [6, 26]. As will be showed in the following, the SCF-MI algorithm turned out to be particularly efficient one of the main results was that a small basis set, such as the 3-21G basis, could provide structural and energetic results comparable to those obtained by much more expensive standard SCF/6-31G CP-corrected calculations. 

As already mentioned, a direct comparison of vertical excitation energies with experimental data is not possible and such results contain uncertainties due to geometry relaxation effects. A more reliable assessment of theoretical methods can be achieved by a comparison of the values that are... 

Fig. 3.6. Growth shapes of a-Al203 (left) and a-Fe203 (right), according to Mackrodt et al. (1987). The shapes in the upper part of the figure are calculated assuming unrelaxed geometries. Relaxation effects were taken into account to derive the shapes in the lower part of the figure.

Differential relaxation of in-phase and anti-phase operators involving a spin C [10], which are due to additional Tj relaxation effects active only for the anti-phase components and which depend on the geometry of the spin system, can lead to systematic errors of the coupling constant derived from cross-peak multiplets observed in an E. COSY-type experiment [11]. Since these errors depend for a given differential relaxation rate Ap on the frequency difference of the coherences with C in the a or yS state, according to Eq. (1) a remedy to the problem is to maximize the relevant J such that the condition J 3> Ap/2n is fulfilled ... 

The PCM/DFT model failed to predict the intrinsic rotation (i.e. the specific rotation extrapolated to infinite dilution) of (R)-3-methylcyclopentanone dissolved in carbon tetrachloride, methanol and acetonitrile [68], This molecule has been investigated because it exists in both an equatorial and an axial form, allowing researchers to investigate the interplay of solvent and conformational effects. The conformer populations used in the Boltzmann averaging were derived from IR absorption and VCD spectra. The deviation of the calculated optical rotation from experiment was found actually to be larger when IEF-PCM was used to account for direct solvent effects (and geometry relaxation) on the optical rotation than when the gas-phase values were used. 

Table 4.1 Effect of solvent-induced geometry relaxation on dipole moment. As noted in the text, all dipoles were computed using gas phase-like wavefunctions, i.e. neglecting solvent polarization of solute charge distribution...

The effect of geometry relaxation of chemical bonds in solution is small, but not negligible. On average, as the polarity of the solvent increases C - H bonds become shorter, while the polar O - H and N - H bonds elongate (see Table 4.2), suggesting a flux of electrons H -> O/N which will reinforce the bond dipole. Not surprisingly, C = O bonds... 

As we have noted the data reported in Table 7-3 refer to Franck-Condon ICT states it thus becomes interesting to analyze the effects of both the solute and the solvent relaxation. For the apolar cyclohexane, solvent relaxation effects are null whereas they are large for the polar acetonitrile, as shown in Table 7-4 in which we report the evolution of the dipole moment and of the NBO charges of the ICT state of PNA in acetonitrile when we allow both solvent relaxation and solute geometry relaxation. 

Geometry optimizations allowed adsorbates and the central fottr Pt atoms of the first layer to optimize completely while keeping all other Pt-Pt distances fixed to the bulk crystal value of 2.775 A. By doing so, we minimized tmphysical border effects to reproduce the (semi-)irrfinite Pt(lll) surface. This model includes major surface relaxation effects, which were significant for some adsorbates. 

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