Update required! The differences between dependable computed and experimental enthalpies of formation of larger hydrocarbons, growing systematically with size, are traced to an about 0.5 kJ mol−1 error in the canonical best estimate of the enthalpy of formation of atomic carbon (see figure). The results obtained in this study call for an update of Δf${{{\rm H}_0^{\rm{{\rm o}}} }}$(Cgas).

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Density functional theory (B3LYP-D3, M06-2X) has been used to calculate the structures, interaction energies and vibrational frequencies of a set of 93 methanol-water clusters of different type (cubic, ring, spiro, lasso, bicyclic), size and composition. These interaction energies have been used within the framework of the Quantum Cluster Equilibrium Theory (QCE) to calculate cluster populations as well as thermodynamic properties of binary methanol-water mixtures spanning the whole range from pure water to pure methanol. The necessary parameters amf and bxv of the QCE model were obtained by fitting to experimental isobars of MeOH-H2O mixtures with different MeOH content. The cubic and spiro motifs dominate the distribution of methanol-water clusters in the mixtures with a maximum of mixed clusters at x(MeOH) = 0.365. Reasonable agreement with experimental data as well as earlier molecular dynamics simulations was found for excess enthalpies H(E), entropies S(E) as well as Gibbs free energies of mixing G(E). In contrast, heat capacities Cp and C showed only poor agreement with experimental data.

Benzene-methanol cluster structures were investigated with theoretical chemistry methods to describe the microsolvation of benzene and the benzene-methanol azeotrope. Benzene-methanol (MeOH) clusters containing up to six methanol molecules have been calculated by ab initio [MP2/6-311++G(d,p)//MP2/6-31+G(d,p) + BSSE correction] method. The BSSE was found quite large with this basis set, hence, different extrapolation schemes in combination with the aug-cc-pVxZ basis sets have been used to estimate the complete basis set limit of the MP2 interaction energy [ΔE(MP2/CBS)]. For smaller clusters, n ≤ 3, DFT procedures (DFTB+, MPWB1K, M06-2X) have also been applied. Geometries obtained for these clusters by M06-2X and MP2 calculations are quite similar. Based on the MP2/CBS results, the most stable C(6)H(6)(MeOH)(3) cluster is characterized by a hydrogen bonded MeOH trimer chain interacting with benzene via π···H-O and O···H-C(benzene) hydrogen bonds. Larger benzene-MeOH clusters with n ≥ 4 consist of cyclic (MeOH)(n) subclusters interacting with benzene by dispersive forces, to be denoted by C(6)H(6) + (MeOH)(n). Interaction energies and cooperativity effects are discussed in comparison with methanol clusters. Besides MP2/CBS calculations, for selected larger clusters the M06-2X/6-311++G(d,p)//M06-2X/6-31+G(d,p) procedure including the BSSE correction was also used. Interaction energies obtained thereby are usually close to the MP2/CBS limit. To model the benzene-MeOH azeotrope, several structures for (C(6)H(6))(2)(MeOH)(3) clusters have been calculated. The most stable structures contain a tilted T-shaped benzene dimer interacting by π···H-O and O···H-C (benzene) hydrogen bonds with a (MeOH)(3) chain. A slightly less negative interaction energy results for a parallel displaced benzene sandwich dimer with a (MeOH)(3) chain atop of one of the benzene molecules.