Kinetic Isotope Effect on the Photoenolization of o-Methylanthrone. A Microcanonical Transition State Theory Calculation

Abstract

The photoenolization of 1,4-dimethylanthrone (1,4-MAT) and 1,4-dimethylanthrone-d 8 (1,4-DMAT) in the gas phase and in 2,2,2-trifluoroethanol (TFE) has been studied theoretically in this work. An electronic energy profile with minima and saddle-point structures is determined by density functional theory methods in the ground state (S0) and in the triplet state (T1). This study reveals that in the excited state an inversion of stability of the tautomers and a lower energy barrier to overcome makes the proton transfer feasible. Our molecular orbital analysis shows that upon proton transfer, T1 changes from n,π* to π,π* so that a diabatic crossing takes place along the reaction coordinate. This crossing is not influenced by the presence of TFE. Also, upon the photoexcitation to the first excited singlet state (S1) an intersystem crossing must occur to access T1. Pure electronic calculations cannot tell us the exact point of the triplet potential energy surface that will be accessed. For this reason we have performed a microcanonical dynamic calculation taking into account the tunneling effect of the hydrogen and deuterium transfer rate constants (k H and k D, respectively) on T1. After the rate-constant calculation we have also calculated the kinetic isotope effect (KIE) to compare with the experimental value. Our results indicate that the predicted large KIE for this reaction can be explained if the proton transfer takes place through tunneling at an energy slightly below the barrier.

Secondary Kinetic Isotope Effect on the Photoenolization of Triplet O-Methylanthrones. A Microcanonical Transition State Theory Calculation

“…9 At the UB3LYP/ 6-31G(d) level the high-energy barrier for the tautomerization in the ground singlet electronic state (43.11 kcal/ mol) is largely lowered in the first triplet state (7.68 kcal/mol). We have tested these results by reevaluating the energy barrier in the triplet state using the more computational demanding MP4 method (see Theoretical Methods for details).…”

“…We consider the four isotopomers of the scheme even though the MATH3 and MATD3 cases were already studied in our previous work. 9 However, in that work we used the classical density of states for the harmonic oscillator to evaluate the density of states so that direct comparison with the present ones could be somehow biased. In any case it is interesting to have the whole set of results in compact form.…”

“…9,10 Through the use of the well-known RRKM kinetic formalism, modified to take into consideration the possibility of tunneling of the transferring hydrogen, we found that the experimentally measured rate constants for 1,4-MAT when all the methyl-group hydrogens were deuterated were in accordance with the reaction taking place entirely by tunneling at energies shortly below the energy barrier. 9 As expected for a tunneling-dominated reaction, a curved Arrhenius plot was observed at the lowest temperatures, which, in our microcanonical treatment, corresponds to the lowest energies.…”

“…9,10 Through the use of the well-known RRKM kinetic formalism, modified to take into consideration the possibility of tunneling of the transferring hydrogen, we found that the experimentally measured rate constants for 1,4-MAT when all the methyl-group hydrogens were deuterated were in accordance with the reaction taking place entirely by tunneling at energies shortly below the energy barrier. 9 As expected for a tunneling-dominated reaction, a curved Arrhenius plot was observed at the lowest temperatures, which, in our microcanonical treatment, corresponds to the lowest energies. Our results were also in accordance with the absence of phosphorescence observed for the original (nondeuterated) 1,4-MAT as the rate measured at the same energies was high enough (∼10 8 s -1 ) to prevent phosphorescence to compete with triplet decay by hydrogen transfer (this fact poses an experimental lower limit of 10 6 s -1 to the H-atom transfer reaction).…”

Kinetic isotope effects in chemical and biochemical reactions: physical basis and theoretical methods of calculation

“…It is not possible to know the exact point (below the Frank‐Condon 1 K 0 → 1 K 1 transition) where the singlet‐triplet crossing occurs. Then the theoretical study by Casadesús et al had to calculate the rate constants at a wide range of available energies E of 3 K around V AG , the adiabatic vibrational ground‐state energy barrier for the hydrogen transfer in 3 K . To this purpose, the microcanonical rate constants for 1,4‐MAT and 1,4‐DMAT including tunneling in 3 K were calculated using the following equation, which is based on the RRKM theory: with where m is the number of vibrational degrees of freedom, { υ i } and are, respectively, the normal‐mode frequencies at the reactant molecule and transition state, P is the tunneling probability in the reaction coordinate, V ‡ is the classical potential energy barrier, and n = n 1, n 2, …, n m −1 are the vibrational quantum numbers.…”