DFT characterization of the first step of methyl acrylate polymerization: Performance of modern functionals in the complete basis limit

Abstract

We obtain values of the reaction barrier for the reaction of methyl acrylate CH 2 CHCOOCH 3 (MA) with the radical CH 3CHCOOCH 3 (HMA ) by density functional theory (DFT) using a variety of functionals and basis sets. Structures for the reactants and the transition state are optimized in B3LYP/cc-pVTZ. We extrapolate energies for these structures to the complete basis set (CBS) limit for each of the functionals B3LYP, PBE, TPSS, BMK, HSE2PBE, mPW1PW91, B97-1, wB97-XD, and M06-2X. The extrapolation follows the energies obtained by the basis sets cc-pVnZ with n = 2, 3, and 4. The estimate of the barrier height is sensitive to the basis and the choice of functional. In order to recover the rate constant for the radical addition we require partition functions as well as the barrier height. To obtain the partition functions for internal rotation in MA, the radical HMA , and the transition state for their addition HMAMA (TS), we trace one-dimensional torsional potentials in B3LYP/cc-pVTZ. Using this data we employ a range of approximations to the partition function ranging from the harmonic oscillator limit, interpolation schemes linking the harmonic oscillator and free rotor limits, and semi-classical expressions. Comparison with the partition functions obtained by direct sum of Boltzmann factors with energy eigenvalues obtained by solution of the Schrödinger equations (total eigenvalue sum or TES) for the one-dimensional torsional potentials show that Mielke and Truhlar’s TDPPI-HS approximation is very accurate. Estimates of activation energies and rate constants for the addition reaction based on the modern functionals wB97-XD and M06-2X in the CBS limit and the TES partition functions reproduce the best experimental measurement.