Finite-temperature properties of the muonium substituted ethyl radical CH2MuCH2: nuclear degrees of freedom and hyperfine splitting constants*

Abstract

The finite-temperature (T) properties of the muonium substituted ethyl radical CH2MuCH2 have been theoretically studied by Feynman path integral quantum Monte Carlo (PIMC) simulations. To derive the ensemble averaged expectation values we have combined the PIMC formalism with an efficient tight-binding (TB) Hamiltonian and a density functional operator of the B3LYP type in the EPRIII basis. The TB operator has been used to calculate the potential energy surface (PES) of the ethyl radical in the doublet ground state, the harmonic and anharmonic vibrational wave numbers as well as several probability density functions of the nuclei. The harmonic linear response approximation, which makes use of the Feynman centroid density, has been adopted to evaluate the anharmonic wave numbers. The large anharmonicities in the nuclear potential lead to bond lengths in thermal equilibrium which exceed the vibrationless parameters at the PES minimum. This enhancement is particularly strong for the C–Mu bond. It is responsible for the suppression of the intramolecular rotation for temperatures below room temperature. In C2 H5 the rotation is allowed down to 10 K. The dissimilar rotational dynamics for H2MuCH2 and C2 H5 has been studied with the help of TB-based probability density functions. The nuclear configurations of CH2MuCH2 and C2 H5, which are populated in thermal equilibrium, have been used to evaluate the isotropic and anisotropic hyperfine splitting (hfs) constants under explicit consideration of the nuclear vibrations and the internal rotation. The hfs constants have been determined with the help of the B3LYP-EPRIII Hamiltonian. The hindered low-temperature rotation in the Mu isomer is responsible for roto-vibrational corrections to the isotropic hfs constants which are smaller than the corrections in C2 H5. The shortcomings of single-configuration approaches for the evaluation of isotropic hfs constants have been demonstrated for both radicals. The ensemble corrections to the isotropic hfs parameters are correlated with fluctuations in the atomic spin densities. Differences in the absolute values of the isotropic hfs parameters in CH2MuCH2 and C2 H5 can be traced back to differences in the nuclear degrees of freedom. The ensemble shift for each isotropic hfs parameter can be explained by characteristic nuclear motions. For this discussion we make use of the distribution functions of the isotropic hfs constants. Roto-vibrational corrections to the anisotropic hfs constants are rather small. PIMC simulations have been performed between 25 and 1000 K, i.e. in a T interval that is large enough to consider nuclear effects beyond zero-point motions. The TB and B3LYP-EPRIII based physical quantities of CH2MuCH2 and C2 H5 have been compared with experimental findings whenever possible.