What can clusters tell us about the bulk? {sc Peacemaker}: extended quantum cluster equilibrium calculations The quantum cluster equilibrium theory and its implementation into the freely available Peacemaker program are described in this paper. The important equations of the quantum cluster equilibrium with a constant mean field potential and an excluded volume are derived. The scheme of the consecutive iterations to obtain both natural variables (volume and particle number) is presented, as well. Further, we describe the implemented method to solve the polynomials arising in each iteration. Additionally, we deal with the question: Which kinds of particles are important for a physically meaningful description of a system. In order to arrive at a systematic classification of these particles, we discuss the important term of a cluster motif. We propose how to determine whether a particle is important for the investigated system and describe the implementation of this method into Peacemaker. Finally, in a case study the thermodynamic properties computed with Peacemaker and the corresponding experimental data are compared with each other.

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