Adiabatic frequencies, experimental

Ab initio frequencies of normal vibrational modes and, by this also, adiabatic frequencies suffer from the harmonic approximation used in the calculation. Even when applying efficient scaling procedures, there is no guarantee that ab initio frequencies accurately reproduce the exact fundamental frequencies of the experiment. Therefore, one has to ask whether the adiabatic internal frequencies might not be much more meaningful if they would be based on experimental frequencies rather than frequencies calculated within the harmonic approximation. 

Figure 11. Comparison of directly calculated adiabatic frequencies (HF/6-31G(d,p) calculations) and adiabatic frequencies derived from experimental vibrational frequencies (see text).

Once adiabatic modes are known either from calculations or experimental data, adiabatic frequencies can be used to characterize chemical bonds. For example, it is easy to verify a McKean relationship [30] between adiabatic CH or CC stretching frequencies and the corresponding bond lengths (Section 11). It can... 

Naturally, neither of these approximations is valid near the border between the two regions. Physically sensible are only such parameters, for which b < 1. Note that even for a low vibration frequency Q, the adiabatic limit may hold for large enough coupling parameter C (see the bill of the adiabatic approximation domain in fig. 30). This situation is referred to as strong-fiuctuation limit by [Benderskii et al. 1991a-c], and it actually takes place for heavy particle transfer, as described in the experimental section of this review. In the section 5 we shall describe how both the sudden and adiabatic limits may be viewed from a unique perspective. 

Distances Ce are in A, dissociation energies in eV (calculated values are not corrected for the 2ero-point vibrational energy, harmonic frequencies Oe in cm , and adiabatic ionization potentials AEip and electron affinities AEea in eV. Experimental values are from Refs. [94, 159-162]. 

An inverse correlation occurs between the experimental value < i.expi and the theoretical values of the standard rate constant k,caic when the latter is computed from Eq. (1) using the adiabatic value of the transmission coefficient(i.e.,/c= 1), the solvent-independent frequency factorv = A 77/i (see solid circles in Fig. 18), and the solvent dependence is taken into account only via continuum A., (het) values obtained from Eq. (3). 

The analysis of the curvature of the experimental parabola led to very reasonable determinations of the intrinsic barrier. The measured values are relatively large, ca. 10-13 kcal moP, i.e. larger than usually found in stepwise dissociative processes but still not as large as found with other dissociative-type acceptors, such as halides. On the other hand, if the intrinsic barriers are calculated by the Eyring equation (equation 4) the values are larger by a few kcal mol (using the collision frequency factor Z). This is because the heterogeneous ET is actually non-adiabatic (which means that the actual pre-exponential factor is smaller). This is a very important aspect, which will be covered below. 

Fig. 20. Experimental setup for applications of the SPECIFIC CP experiment in the context of triple-resonance solid-state NMR experiments. After an initial broadband adiabatic CP step from protons to the I nuclei, SPECIFIC transfer to the observed 5 nucleus occurs during the mixing time tm. The resulting signal represents a dipolar and chemical shift-filtered spectrum and can be controlled by variation of the carrier frequencies and the radiofrequency during the SPECIFIC transfer. A conventional HETCOR experiment is obtained by the introduction of an evolution time t. (Adapted from Baldus et al.215 with permission.)...

Figure 13-7. Adiabatic energies of the lowest tttt transitions calculated of the most stable tautomers of guanine at several levels of theory (a-d) compared to experimental origin transitions [18]. Lower panel absolute values for the 7AHi species Upper panel relative values. Labels a-d refer to the following references a, b) [38] c) [30] and d) [24]. In this latter case, frequency values corrected for zero-point vibrational energies are also given when available...

---