= 0.5 eV, a quantum of vibrational stretching, then the rate constant for reaction 2 is V2 106 sec™1 and therefore disallowed. If Ey = £2 0 and both involve translational energy alone it can be estimated that vy = Ay exp(-EyfkT) with Ay s 1013 sec-1 and vy < 1013 sec"1. Since vy = 21r2 for H20, V2 < 5 X 1011 sec-1. This is less than H+-transfer frequency between nearest neighbor acid and base, e.g., by Raman line broadening.7 These considerations indicate that £1 = £2 = 0 and, if so, then H-atom transfer by reaction 2 occurs on the first nearest approach. The average time required is half the vibrational period, or the rate is twice the O-H vibrational stretching frequency.That is, V2 = 2.2 X 1014 sec"1 in H20 and 1.6 x 1014 sec"1 in D20. Since ¡q/V2 is 21 in H20 and 25 in D20, vy = 4.6 X 1015 sec"1 in H20 and 4.0 X 1015 sec"1 in D20. The ratios ¡q/r2, in terms of the model, are the numbers of molecules visited (some twice) by a migrating hole. These values approximate those calculated previously.8The isotope effect on vy suggests interaction of the migrating hole with molecular vibrations. If the hole migrates from oxygen to oxygen along H bridges, the frequency should depend upon the phase angle and, to some extent, upon the vibrational frequency.Acknowledgment. The authors are indebted to Professor Gideon Czapski for helpful comments.
References and Notes(1) The Radiation Laboratory of the University of Notre Dame is operated under contract with the U. S. Atomic Energy Commission. This Is AEG Document No. COO-38-904.(2) M.
The protonation reactions at carbon sites of the anion radicals of certain unsaturated compounds as well as aromatic amino acids and their analogs have been investigated in alkaline and neutral aqueous glasses by electron spin resonance spectroscopy. For the compounds acrylic acid, 3,3-dimethylacrylic acid, crotonic acid, acrylamide, and acrylonitrile protonation or deuteration is found to occur ß to the electronegative group (R3) to form an «-carbon radical: RiR2C=CHR3~+ H20 -* R1R2CH-CHR3 + OH-. The anions were found to be stabilized when Rj (or R2) was a carboxyl (fumaric) or methyl (crotonic and 3,3-dimethylacrylic acid) group. The anions of acetylenedicarboxylic acid and hydrogen cyanide were also found to protonate in these aqueous glasses. The anions of four aromatic amino acids were found to protonate at carbon sites on the aromatic ring. Analogs of these amino acids which contain the aromatic ring were found to protonate at positions equivalent to those found in the amino acids. Molecular orbital calculations of the spin density and free valency show that the magnitude of these parameters can be correlated with the site of protonation and perhaps the tendency to protonate.
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