Using high-resolution solid-state 15 N cross-polarization magic angle spinning NMR techniques, the proton transfer thermodynamics and dynamics and the proton locations in polycrystalline 15 N-labeled porphycene were studied. Whereas at room temperature only a single 15 N resonance is observed, indicating an equivalence of all nitrogen atoms arising from a quasi-degenerate fast proton transfer, four signals are observed at low temperatures, exhibiting temperature-dependent line positions. Their analysis is consistent with the presence of either (i) two different molecules A and B in the asymmetric unit, each of which is subject to a quasi-degenerate correlated double proton transfer, or (ii) a single molecule exhibiting all four possible near-degenerate tautomeric states, two trans-and two cis-tautomers, interconverting by fast single proton transfers. The average rate constants of the proton transfer processes are found to be in the nanosecond time-scale. These constants were obtained between 228 and 355K by analysis of the longitudinal 9.12 MHz 15 N T 1 relaxation times, which exhibit a minimum around 280 K. The relaxation analysis was performed in terms of a quasi-degenerate two-state proton transfer process which modulates the heteronuclear 1 H-15 N dipole-dipole interaction. From the value of T 1 in the minimum, the crystallographic NN distance of 2.63 Å and the hydrogen bond correlation for N-HÁÁÁN hydrogen bonded systems, the two NÁÁÁH distances of 1.10 and 1.60 Å were obtained, i.e. a hydrogen bond angle of 152°, which are significantly different from the corresponding values of 1.03 and 2.28 Å and 116°found for porphyrin. The analysis of the temperature dependence of the rate constants indicates tunneling as a major reaction pathway, involving a barrier of about 32 kJ mol À1 . The finding of a larger NH distance and a smaller barrier for proton transfer as compared with porphyrin is rationalized in terms of the stronger intramolecular hydrogen bonds in porphycene. A strong coupling between these bonds would indicate that the proton tautomerism in porphycene corresponds to a correlated double proton transfer, in contrast to the stepwise transfer in porphyrin. Finally, a relation between the intrinsic 15 N chemical shifts of porphyrinoids and the NÁÁÁH distance was found, which might be useful for estimating geometries of porphyrinoids.

A theory of magnetic nuclear relaxation, providing a calculation of the correlation functions of complex motion of methyl groups is presented. The complex motion consists of jumps over the barrier (classical motion) and jumps through the barrier (tunneling). The Schrödinger equation has been applied in the calculation of the rate constant of tunneling jumps through the barrier. The equations for the spectral densities (ω), where ω = (ω I ± ωT), and ω = (m ω I), where m = 1 or 2, ω I is the resonance angular frequency, and ωT is the angular frequency of the tunnel splitting, are derived. These spectral densities concern the motion of spin pairs inside methyl groups (“intra”) and outside methyl groups (“inter”). The calculated spectral densities are applied to analyze the temperature dependencies of the spin−lattice relaxation rate in solids containing methyl groups. A wide regime of temperatures from 0 K up to the melting point is considered. The temperature at which the tunneling process ceases is discussed. The theory proposed explains the different temperature dependencies of T 1 for CH3COOK obtained in the experiments caused by small amounts of CH3COOH or water impurities. The theoretical equations derived in this paper are compared to those known in the literature.

ABSTRACT:The calculation of the correlation functions of complex motion consisting of jumps over the barrier (classical motion) and jumps through the barrier (incoherent tunneling) is presented. The Schrö dinger equation has been applied in the calculation of the rate constant of tunneling jumps through the barrier. This rate constant determines directly the temperature at which incoherent tunneling ceases. The calculated spectral densities are applied to analyze the temperature dependencies of the spin-lattice relaxation rate in solids containing a methyl group.

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