Schematic representation of the double proton-transfer process in the formic and benzoic acid dimer.
Arrhenius plot of the rate constants for HH and DD transfers in isolated formic acid dimers. The thick solid lines represent our AIM/DOIT calculations based on MCG3-level potentials and the thin solid lines represent TST calculations with semiclassical tunneling corrections reported in Ref. 32. The broken lines represent our classical TST calculations for the MCG3 potential. The left and right vertical lines denote, respectively, HH and DD crossover temperatures, defined by Eq. (18).
Two antisymmetric (top) and two symmetric modes that are strongly coupled to the tunneling mode in the benzoic acid dimer.
Comparison of spin-lattice correlation rates measured by NMR relaxometry with those calculated by AIM/DOIT for solid benzoic acid isotopomers with mobile HH (top), HD (center), and DD (bottom) pairs. Measurements taken from Ref. 24 are depicted by symbols. The broken and dot-dashed lines represent calculations in which coupled vibrations with (see Sec. II) are treated in the adiabatic and sudden approximation, respectively. The solid curve represents the geometric mean of these two results.
Expansion of the high-temperature part of Fig. 4. The solid lines are the same as in Fig. 4 but the broken lines represent classical TST rate constants calculated for a barrier height of obtained by scaling the B3LYP barrier for the isolated dimer (see Table II) by a compression factor derived for the solid (see Sec. V C). The vertical lines represent crossover temperatures for, from left to right, HH, HD, and DD transfers.
Rotational constants of in .
Principal parameters of the hydrogen bonds relevant to the dynamics of double proton transfer in the benzoic and formic acid dimer. Distances in angstroms, angles in degrees, energies in kcal/mol. Numbers without reference are obtained in the present work at the level and (printed in italics) at the MCG3//MC-QCSD/3 level. Experimental numbers are printed in bold.
Main dynamics parameters of the AIM/DOIT calculations for the benzoic and formic acid dimer calculated at the level.
Main dynamics parameters of the modes most active in the dynamics of double proton transfer in the benzoic and formic acid dimers calculated at the and the MCG3//MC-QCSD/3 level, respectively. The modes of the benzoic acid dimer are depicted in Fig. 3. The mode description is approximate, as the active modes mix between the stationary structures.
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