  The elusive connection between dynamics and local structure in supercooled
liquids is an important piece of the puzzle in the unsolved problem of the
glass transition. The Johari-Goldstein beta relaxation, ubiquitous in
glass-forming liquids, exhibits mean properties that are strongly correlated to
the long-time alpha dynamics. However, the former comprises simpler, more
localized motion, and thus has perhaps a more straightforward connection to
structure. Molecular dynamics simulations were carried out on a
two-dimensional, rigid diatomic molecule (the simplest structure exhibiting a
distinct beta process) to assess the role of the local liquid structure on both
the Johari-Goldstein beta and the alpha relaxation. Although the average
properties for these two relaxations are correlated, there is no connection
between the beta and alpha properties of a given (single) molecule. The
propensity for motion at long times is independent of the rate or strength of a
molecule's beta relaxation. The mobility of a molecule averaged over many
initial energies, a measure of the influence of structure, was found to be
heterogeneous, with clustering at both the beta and alpha timescales. This
heterogeneity is less extended spatially for the beta than for the alpha
dynamics, as expected; however, the local structure is the more dominant
control parameter for the beta prcoess. In the glassy state, the arrangement of
neighboring molecules determines entirely the relaxation properties, with no
discernible effect from the particle momenta.
