Perturbed Angular Correlation (PAC) Spectroscopy in the Fast Reorientation Time Regime: Can Global Molecular Rotational Diffusion and Local Dynamics Be Discriminated?

In PAC spectroscopy, hyperfine interactions of a radioactive probe nucleus with its surroundings are measured, providing information about the local atomic structure and dynamics at the probe site. In the so-called fast reorientation time regime for fluctuating nuclear quadrupole interactions (NQIs), the PAC signal is an exponentially decaying function, with decay constant λ depending on both the hyperfine interaction and dynamics. For a molecular system in solution, dynamics may originate from Brownian molecular tumbling (rotational diffusion) with rotational correlation time τc and from local dynamics at the probe site, occurring at a characteristic time scale τloc. The τc and the τloc cannot be discriminated in a single PAC spectrum; however, assuming that they scale differently with viscosity and temperature, a series of experiments in which these parameters are varied may allow for discrimination of τc and the τloc. Three models are presented for the effect of dynamics on the PAC signal: (1) the Stokes–Einstein–Debye model with linear scaling of λ with viscosity ξ; (2) a more general model presenting a power law scaling of λ with (ξ/ξ0)n; and (3) a model that includes rotational and local dynamics leading to an expression for λ that scales with ξ/(ξ + c), where c is a constant that depends on temperature, molecular volume, and τloc. These models may serve as different approaches to analyze PAC data and their dependence on temperature and solvent viscosity in the fast reorientation time regime, and they can be applied to design experiments for optimal discrimination of global rotational diffusion and local dynamics at the probe site.