Eigenvectors hydrogen bonds

Figure 4 The ice XI hydrogen bond BCPs with their easy direction i.e. the 62 eigenvectors are shown (a) 0 kbar, (h) 35 khar, (c)55 kbay (d) 85 kbap and (e) 90 kbar.

The normal-mode calculation produced 597 frequencies and eigenvectors. We represent the former in Fig. 33 by giving a histogram of the calculated frequencies below 1700 cm", plotting the number of normal modes in each 5-cm interval. Such a density of vibrational states, which can be probed by inelastic neutron scattering (Jacrot et al., 1982), is not observed directly by IR or Raman. As we noted, and will consider further below, the IR spectrum is determined by the dji/dQ in each normal mode, which remains to be calculated. Since hydrogen bonding and TDC have also not been included in this calculation, the values of the amide frequencies and the distribution of the low-frequency modes cannot be considered finalized as yet. 

The amide II modes, which are probably at a lower frequency because of the weaker hydrogen bonds, are also split by the TDC interactions in their absence the calculated modes are at 1534 (Ag), 1535 (Au), 1559 (Bg), and 1559 (Bu) cm . The absence of clearly observed high-frequency modes, particularly an IR band near the expected frequency of 1572 cm , raises a very important point it is necessary to be able to predict intensities as well as frequencies. Intensities require knowledge of dipole derivatives (Eq. (5-4)), but since they also depend on eorrect eigenvectors (Eq. (5-5)) they provide an independent test of the force field. Such an IR intensity calculation has been done on PGI [20], and the results show that the B amide II mode is indeed predicted to be very weak, in agreement with observation. 

The role of INS in the study of medium H-bonds is to exploit the advantage of its sensitivity to hydrogen acting as a classical atom. In this it has been successful, the interpretive model is clear and the results are readily understandable. However, where the hydrogen has a developed quantum aspect the interpretive models are inadequately developed, as for strong H-bonds, the situation remains open the H-bond eigenvectors remain insufficiently exploited... 

Fig. 4 Stress tensor analysis of the reactant in the 1,5-sigmatropic hydrogen shift reaction from 5-methylcyclopentadiene to 1-methylcyclopentadiene. The eigenvectors of the stress tensor at the heps of the two active C-H bonds are shown. The stress tensor was computed at the B3LYP/ 6-31 lG(d,p) level. Further details can be found in the paper of Guevara-Gareia et al. [32]...

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