Theoretical models of hydrogen bonding and proton transfer in the ground (So) and lowest excited '1T7T* singlet (S 1) states oftropolone are developed in terms of the localized OH"'O fragment model and ab initio three-dimensional potential energy surfaces (PESs). The PESs for proton transfer in the So and S 1 states are calculated using ab initio SCF and CIS methods, respectively, with a 6-31G basis set which includes polarization functions on the atoms involved in the internal H bond. The Schrodinger equation for nuclear vibrations is solved numerically using adiabatic separation of the variables. The calculated values for the So state (geometry, relaxed barrier height, vibrational frequencies, tunnel splittings and HID isotope effects) agree fairly well with available experimental and theoretical data. The calculated data for the S 1 state reproduce the principal experimental trends, established for S 1 +-S 0 excitation in tropolone, but are less successful with other features of the dynamics of the excited state, e.g., the comparatively large value of vibrationless level tunnel splitting and its irregular increase with 0"·0 excitation in S l ' In order to oVercome these discrepancies, a model 2-D PES is constructed by fitting an analytical approximation of the CIS calculation to the experimental vibrationless level tunnel splitting and 0···0 stretch frequency of tropolone-OH. It is found that the specifics of the proton transfer in the S 1 state ar~determined by a relatively low barrier (only one doublet of the OH stretch lies under the barrier peak). Bending vibrations playa minor role in modulation of the proton transfer barrier, so correct description of tunnel splitting of the proton stretch levels in both electronic states can be obtained in terms of the two-dimensional stretching model, which includes 0···0 and O-H stretching vibration coordinates only.
Temperature dependence of the proton spin-lattice relaxation time (T1) in powdered benzoic acid dimer and in its deuterated analog is calculated. The model assumes that two protons (deuterons) synchronously move in the double-minimum potential of the dimer. The two-dimensional potential energy surface was constructed previously, which adequately describes the static properties of the hydrogen-bonded complex. The important characteristics of this potential are a very strong mode coupling and a very high proton potential barrier (≳25 kcal/mol), whereas the experimental activation energy for the proton transfer is known to be on the order of 1 kcal/mol only. This apparent discrepancy is removed by our suggestion that the proton transfer is driven by the transitions between OHO fragment vibrational levels under the action of random forces of the surrounding. The excitation of the low-frequency intermolecular vibrations assists such transfer mechanism strongly. Using four fitting parameters to allow for the medium repolarization, the calculated T1 temperature dependence is found to be in good agreement with the experiments in the natural and deuterated benzoic acid dimer. The agreement is best at high temperature where the apparent activation energy for proton transfer was found to be 2.3 kcal/mol.
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