  On the basis of microscopic statistical mechanics of simple liquids the
orientational interaction between clusters consisting of a particle and its
nearest neighbors is estimated. It is shown that there are ranges of density
and temperature where the interaction changes sign as a function of a radius of
a cluster. The model of interacting cubic and icosahedral clusters is proposed
and solved in mean-field replica symmetric approximation. It is shown that the
glass order parameter grows smoothly upon cooling, the transition temperature
being identified with the temperature of the replica symmetry breaking. It is
shown that upon cooling a Lennard-Jones system, cubic clusters freeze first.
The transition temperature for icosahedral clusters is about ten per cent
lower. So the local structure of Lennard-Jones glass in the vicinity of glass
transition should be most probably cubic.
