The electronic structure of a biexciton is discussed while taking into
account the detailed band structure of CuCl. The fine structure of th
e excitonic molecule is clarified with the effective electron-hole exc
hange effect taken into account beyond the effective mass approximatio
n. The electron-hole exchange interaction mixes the states of opposite
parities with respect to the permutation of electrons and holes. Two
trial envelope functions, symmetric and antisymmetric under the permut
ation of two electrons or two holes, were used in the numerical minimi
zation of the ground state energy of the biexciton. The obtained bindi
ng energy of the biexciton, as well as, the ratio of the mixing of the
trial envelope functions of opposite parities are presented.