Potential double minimum

In (87BBPC941), Limbach made a major contribution to understanding crystalline and amorphous environments using compounds that in the gas phase show symmetric double minimum potentials. Several compounds were used to illustrate the periodic (crystal) and random (glass) distortions of the potential surface, among them H2P and porphycene. Tlie seminal paper on the tautomerism of porphyrins in the solid state is that of Limbach... 

Fig. 5 Potential energy hypersurfaces as a function of the reaction coordinate for adiabatic (A, single-minimum potential B, double-minimum potential) and non-adiabatic (C) electron-transfer reactions.

If we consider ET in the ground state, we shall deal with an adiabatic case where the occurrence of charge transfer depends on the activation energy between the double-minimum potential (Meyer, 1978). When defining the activation energy AG+, one typically uses the approximations of harmonic... 

Hence for this complex the proton is held roughly equally between the carboxylate and amine bases in a double-minimum potential well. 

The AS value for pentane-2,4-dione in Table 3 is compatible with a double-minimum potential for the intramolecular hydrogen bond in the enol. This was also the conclusion reached from the microwave and photoelectron spectra. For unsymmetrically substituted diketones, for example 1,1,1-trifluoropentane-2,4-dione, measurement of 13C chemical shifts has been used to estimate values for the equilibrium constant K = [R]/[L] in (38)... 

The presence or absence of a homoaromatic interaction is often based solely on the distance between the non-bonded atoms. Distances greatly over 2.0 A are thought to lead to a p-p overlap that is too small to make any significant contribution. This simplistic approach is not necessarily reliable as shown by Cremer et al. (1991). Their calculations on the homotropylium cation [12] indicate a double-minimum potential energy surface with respect to variations of the C(l)-C(7) distance at the Hartree-Fock level of theory. At the MP4(SDQ) level of theory, only a single-minimum curve was found with the minimum at 2.03 A. The calculated potential energy curves are quite flat in this region. 

Figure 2. Proposed double-minimum potential surface for gas-phase nucleophilic...

Fig. 7. The tunneling paths in a double minimum potential like that of Fig. 5 may be classified as having one or more (odd) numbers of instantons, or tunneling segments. Three such traverses of the classically forbidden region are shown above. The classification of all paths according to the number N of instantons is the basis for evaluating the path integral as the sum in Eq. 29 note however that the therein is constructed to include non-harmonic (beyond semiclassical) fluctuations around the minimum action instanton paths, which are evaluable by Metropolis Monte Carlo...

Values of A[5( H) — 5( H)] for a large number of enols have been determined. The results are close to +0.6 ppm and point to double minimum potentials and strong hydrogen bonds. Low values are found for l,l,l,5,5,5-hexafluoropentane-2,4-dione (0.30 ppm) and 3-(4-methoxy-phenyl)pentane-2,4-dione (0.31 ppm), but these two species are of the same double minimum hydrogen-bond type and the O O bond length in 3-(4-methoxyphenyl)pentane-2,4-dione (i = 245pm Emsley et al., 1988a) is similar to that for other enols. 

The O—H N hydrogen bond in the phenylazoresorcinol monoanion is strong, giving a large and positive value of A[S( H) — 8( H)], characteristic of a double minimum potential (Hibbert and Phillips, 1989). Two examples of intermolecularly hydrogen-bonded species for which the isotope effect on the chemical shift has been measured are also given in Table 5. 

The proton sponges are exceptionally strong bases (see Section 4, p. 321 for a discussion) and one of the reasons for this is the strong hydrogen bonds with double-minimum potentials (A[8( H) — 8( H)] 0.5 present in the... 

The ir spectrum of bis(phenolate) complexes has been interpreted in terms of a double minimum potential function (Kreevoy et ai, 1977 Kreevoy and Liang, 1980). With values of (p of ca. 0.3-0.4, points for these species probably lie close to the centre in Fig. 10. The point for the enol of 1, 1,1,5,5,5-hexafluoropentanedione with tp = 0.6 (Kreevoy and RidI, 1981)... 

Since these early X-ray diffraction experiments, several other crystals have been subjected to analysis by X-ray and neutron diffraction and the F bond length has remained virtually unchanged. The location of the proton has been the point at issue. Early ir studies on KHF2 were interpreted as evidence for a double minimum potential well (Ketelaar, 1941 Glocker and Evans, 1942), but later studies questioned this (Pitzer and Westrum, 1947 Cote and Thompson, 1951 Newman and Badger, 1951) and led to a revision of earlier opinions (Ketelaar and Vedder, 1951). 

Other structural analyses of crystals in which the bifluoride is present are listed in Table 7. One compound, p-toluidinium fluoride [C7H,oN ][HF2 ], is worthy of further comment. The first X-ray diffraction study reported a symmetrical anion (Denne and MacKay, 1971), but a later analysis showed that the proton was not centred between the two fluorines and 7 f h values were 102.5 and 123.5 pm (Williams and Schneemeyer, 1973). This can be explained not by a double minimum potential energy well but by asymmetry due to other forces, such as secondary hydrogen bonding between one end of the bifluoride anion and the N—H group of the cation. An alternative explanation attributes the asymmetry of the bifluoride hydrogen bond to an unsymmetrical crystal field caused by the cation (Ostlund and Bellenger, 1975). 

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