We describe a method for calculating equilibrium properties of liquids by extending the standard quantum statistical thermodynamic treatment of chemical equilibria to the analogous equilibria between molecular clusters, as characterized by modern ab initio techniques. We review the equations of quantum statistical thermodynamics in the canonical ensemble for the case of coupled cluster equilibria, and show how standard treatments of translational and electronic partition functions can be modified to account for excluded-volume and cluster-cluster interaction effects at finite densities. The resulting quantum cluster equilibrium (QCE) model is implemented in a computer program that accepts ab initio input cluster properties and calculates the cluster populations for distinct distributions (phases) satisfying the equilibrium conditions at chosen T, P. We sketch the basic equations and numerical algorithms of the QCE program for neat liquids as well as more general multi-component solution equilibria. The companion paper describes general numerical characteristics of the model, including dependencies on program parameters and cluster input.