Abstract
The results of our recent general analytical-theoretical treatment of completely asymmetric electron-spin-resonance (ESR) hyperfine centers undergoing slow Brownian orientational diffusion are compared with those of the Freed numerical-theoretical treatment based on the stochastic Liouville equation. In agreement with our theoretical results, the dependences of the slow-tumbling dynamic linewidth and line shift on the associated orientational motion correlation time \ensuremath{\tau} we deduced from the Freed theoretical spectra are found to be ${\ensuremath{\tau}}^{\mathrm{\ensuremath{-}}1/2}$ for the ESR external magnetic field B parallel to the ESR principal (x,y,z) axes. The two theories also yield the same absolute signs or directions for various dynamic line shifts. In addition, the magnitudes of slow dynamic linewidths and shifts are in reasonable agreement between the two theories. Except for some unexplainable extra peaks in the Freed theoretical spectra, their overall slow-motional hyperfine structures are similar to those computed by our analytical-theoretical results. It is thereby established that the analytical-theoretical treatment of slow-tumbling anisotropic ESR centers is consistent with all other related slow-tumbling ESR theories, corroborating the general validity of the analytical-theoretical results.
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