Highly correlated ab initio thermodynamics of oxymethylene dimethyl ethers (OME): formation and extension to the liquid phase

Oxymethylene dimethyl ethers, of the structure CH3(OCH2)nOCH3, denoted as OMEn are receiving increasing interest (where n = 2–5) in a range of important applications including as sustainable fuels and solvents (e.g. as derived from green methanol). However, limited thermodynamic information from computational studies exists in the literature regarding their formation in the gas and liquid phases. In this context, this report describes the principal thermodynamic functions of gaseous and liquid phase OME formation derived from B3LYP-D3(BJ)/def2-TZVPP optimised structures and a series of CCSD(T) and MP2 calculations. The generated total energies are almost of CCSD(T)/A′VQZ quality, the “gold standard” of computational chemistry. Thermal corrections to enthalpy and entropy were included on the basis of analytical BP86-D3(BJ)/def-TZVP frequencies and empirical corrections for low anharmonic C–O–C–O torsional vibrations/hindered rotations and due to the neglect of other conformers/enantiomers. This yielded corrected values for the standard entropy S° of gaseous OMEn (n = 2–7). With the well-established experimental formation enthalpies of dimethyl ether (i.e. OME0) and OME1, the formation enthalpies of OME2–7 were obtained from those and the isodesmic reaction enthalpy of nOME1 → OMEn + (n − 1)OME0. Overall, an error bar on those gas phase values of <1 kJ mol−1 is assigned. From the known and extra- or interpolated phase change thermodynamics, the standard formation enthalpy H°, and the standard entropy S°, as well as the heat capacity cp were established for the liquid mixture of OME2–7. The internal consistency of these data was assessed based on the plots of H°/S° vs. n, presenting linear regressions and correlation coefficients very close to unity. Data quality was also evaluated against published combustion energies, suggesting our values are currently the most reliable, internally consistent dataset that should be used in future investigations for the design of sustainable ether-based fuels and chemicals.