In the framework of the binary quantum cluster equilibrium theory, we introduce a cluster approach to access activity coefficients of binary mixtures. This approach allows derivation of activity coefficients based on quantum chemically calculated clusters. The cluster sets in this work comprise clusters ranging in size from one to six molecules of either a single or two species. For each cluster size up to five conformers if detectable are considered such that important liquid motifs are included. Via self-consistent-field calculations the binary quantum cluster equilibrium theory gives the Gibbs energies and thus the excess Gibbs energies of mixing. Derivation with respect to the particle number allows access to activity coefficients. To achieve an analytical expression, we apply the standard approach of fitting a Redlich-Kister polynomial to the excess Gibbs energy and calculate its derivative, which leads to good results for the binary mixture cases of acetonitrile/benzene and methanol/ethanol, as well as satisfying results for acetone/chloroform. Very good results for vaporization enthalpies are obtained for the pure substances.