Theoretical study of the nuclear degrees of freedom in the isotropic and anisotropic hyperfine coupling constants of the C2H5 radical: a Feynman path integral–density functional approach

The isotropic and anisotropic hyperfine coupling (hfs) constants of the C₂H₅ radical have been theoretically studied under the conditions of thermal equilibrium, i.e. under the explicit consideration of the nuclear degrees of freedom. For this purpose the Feynman path integral quantum Monte Carlo (PIMC) formalism has been combined with an electronic Hamiltonian of the B3LYP–EPRIII type. The density functional operator has been used to derive both the distribution functions for the isotropic and anisotropic hfs constants of the ethyl radical as well as the thermal mean values. The electron paramagnetic resonance (EPR) timescale enables only the measurement of the thermal averages. The underlying distribution functions of these mean values, however, offer insight into the nature and strength of the nuclear degrees of freedom contributing to the observable thermal averages. The EPR parameters of C₂H₅ have been studied between 25 and 1000?K. This temperature (T?) window is large enough to consider nuclear fluctuations beyond zero-point effects. The deviations between the thermally averaged hfs constants and the values at the minimum of the potential energy surface (PES) are caused by (i) enlargements of the bond lengths in thermal equilibrium under the influence of anharmonicities in the internuclear potential, and (ii) by the intramolecular methylene rotation. The latter degree of freedom leads to a planar CH₂ unit in thermal equilibrium. At the minimum of the PES the methylene fragment exhibits a certain pyramidalization. The ensemble corrections as well as the T dependence of the isotropic hfs constants are larger than the ensemble shifts and T dependence of the anisotropic parameters. The non-validity of the crude Born–Oppenheimer approximation for the theoretical evaluation of physically meaningful isotropic hfs constants of the ethyl radical has been explained on the basis of specific nuclear degrees of freedom. Theoretical results of the ensemble averaged Monte Carlo type as well as single-nuclear configuration data are compared with experiment whenever available.