The Quantum Cluster Equilibrium (QCE) model was applied to the liquid phase for the first few members of the homologous series of unbranched aliphatic primary alcohols, methanol, ethanol, propan-1-ol, and butan-1-ol. Cluster structures and energies were calculated by density functional theory [B3LYP/6-311++G(2d,2p)]. For butan-1-ol the dispersion interaction was also considered with the B3LYP-D method. In agreement with previous findings, cyclic cluster structures are the most probable ones. In addition, weak C-H...O interactions as well as dispersion interactions between the longer alkyl chains were found to be important in the cluster formation. The reliability of the model was assessed by the calculated constant pressure heat capacity (C(p)) values. Larger deviations between theory and experiment were found for higher homologes (propan-1-ol, butan-1-ol) with the B3LYP method. When the B3LYP-D method was applied for butan-1-ol, adequate agreement was found between experimental and calculated C(p) values.