  In a recently developed microscopic mean field theory, we have shown that the
dynamics of a system, when described only in terms of its pair structure, can
predict the correct dynamical transition temperature. Further, the theory
predicted the difference in dynamics of two systems (the Lennard-Jones and the
WCA) despite them having quite similar structures. This is in contrast to the
Schweizer-Saltzman (SS) formalism which predicted the dynamics of these two
systems to be similar. The two theories although similar in spirit have certain
differences. Here we present a comparative study of these two formalisms to
find the origin of the difference in their predictive power. We show that not
only the dynamics in the potential energy surface, as described by our earlier
study, but also that in the free energy surface, like in the SS theory, can
predict the correct dynamical transition temperature. Even an approximate one
component version of our theory, similar to the system used in the SS theory,
can predict the transition temperature reasonably well. According to our
analysis, the absence of the Vineyard approximation in the SS formalism led it
to predict similar dynamics for the two systems. Interestingly, we show here
that despite the above mentioned shortcomings the SS theory can actually
predict the correct transition temperatures. Thus microscopic mean field
theories of this class which express dynamics in terms of the pair structure of
the liquid while being unable to predict the actual dynamics of the system are
successful in predicting the correct dynamical transition temperature.
