Application of schrodinger equation to study the tunnelling dynamics of proton transfer in the hydrogen bond of 2,5-dinitrobenzoic acid:: Proton T1, T1ρ, and deuteron T1 relaxation methods

Temperature measurements of proton T-1 (24.7 MHz), deuteron (deuterated hydroxyl group) T-1 (55.2 MHz), and proton T-1 rho (B-1 = 9 G) spin-lattice relaxation times of 2,5-dinitrobenzoic acid have been performed. An analysis of present experimental data together with previously published proton T-1 (55.2 MHz) data has revealed the following molecular motions: proton/deuteron transfer in the hydrogen bond and two-site hopping of the whole dimer. It is shown that the proton-transfer dynamics are characterized by two correlation times tau(ov) and tau(tu), describing two fundamentally different motional processes, namely, thermally activated jumps over the barrier and tunneling through the barrier. The temperature dependence of 1/tau(tu) is the solution of Schrodinger's equation, which also yields the temperature T-tun, where begins the tunnel pathway for proton transfer. A new equation for the spectral density function of complex motion consisting of the three motions is derived. The third motion (two-site hopping of the whole dimer characterized by tau(lib) correlation time) is responsible for a proton T-1 rho minimum in high temperatures, just below the melting point. Such a minimum is not reached by T-1 temperature dependencies. The minimum of T-1 rho assigned to the classical hopping of a hydrogen-bonded proton occurs in the same low-temperature regime in which the flattening of the temperature dependencies of T-1 points to the dominance of incoherent tunneling. This experimental fact denies the known theories predicting the intermediate temperature regime where a smooth transition between classical and quantum tunneling dynamics is expected. The fit of the derived theoretical equations to the experimental data T-1 rho and T-1 is satisfactory. The correlation times obtained for deuterons indicate deuteron-transfer dynamics much slower than proton-transfer dynamics. It is concluded that the classical proton transfer takes place over the whole temperature regime, while the incoherent tunneling occurs below 46.5 (hydrogen) or 87.2 K (deuterium) only.