  A well-known cluster expansion, which leads to virial expansion for the free
energy of low density systems, is modified in such a way that it becomes
applicable to the description of condensed state of matter. To this end, the
averaging of individual clusters over the states of an ideal gas is replaced by
the averaging over the states of a non-correlated crystal using single-particle
cell potentials. As a result, we arrive at the expansion of the partition
function in correlations on the basis of single-particle functions
corresponding to the multiplicative approximation. The cell potentials defining
these functions are found from the condition of the minimum of the remainder in
the constructed decomposition.
