Rotational spectra of methane and deuterated methane in helium

We present calculations of the rotational excitations of CH(4) and CD(4) in helium using correlated basis function theory for excited states of spherical top molecules, together with ground state helium density distributions computed by diffusion Monte Carlo simulations. We derive the rotational self-energy for symmetric top molecules, generalizing the previous analysis for linear molecules. The analysis of the self-energy shows that in helium the symmetry of a rigid spherical rotor is lost. In particular, rotational levels with J=2 split into states of E and of F(2) symmetry. This splitting can be analyzed in terms of an effective tetrahedral distortion that is induced by coupling of the molecular rotation to density fluctuations of the helium. Additional splitting occurs within each symmetry group as a result of rotational coupling to the high density of states between the roton and maxon excitations of (4)He, which also results in broad bands in the corresponding rotational absorption spectra. Connecting these pure rotational dynamics of methane to experimental rovibrational spectra, our results imply that the R(1) line of CH(4) is significantly broadened, while the P(2) is not broadened by rotational relaxation, which is consistent with experiment. Comparison of our results for CH(4) and CD(4) shows that the reduction in the moment of inertia in (4)He scales approximately quadratically with the gas phase moment of inertia, as has also been observed experimentally.