The phonon density of states of CO2, calculated at the PBE-XDM equilibrium geometry using a 4 × 4 × 4 sampling grid, Fourier-reinterpolated to 503.
The vibrational Helmholtz energy of carbon dioxide against volume is shown, together with a quartic fit (black, full line), a parabolic fit to the equilibrium volume and two points on compression (red, stippled line), and the line tangent to the vibrational energy curve at the equilibrium volume (blue, dotted line). The arrow marks the equilibrium geometry.
Graphical representation of the lattice energy errors relative to the reference value for all the functionals used. The black crosses mark single experimental results and give an idea of the spread and quality of the reference.
The column labels are, in order: the average over experimental sublimation enthalpy measurements corrected to room temperature (via C p calculated by group additivity37), the relaxation energies (Eq. (15)), the deviation of the intermolecular vibrational contribution of the solid from the Dulong-Petit value (6RT), the intermolecular zero-point vibrational contribution of the solid, the difference between our correction to the lattice energy (ΔE vib + 4RT in Eq. (14)) and −2RT (Eq. (17)), and the total thermal correction on sublimation enthalpies (, T 0 = 298.15 K) . The last two columns are the reference data for the benchmark: experimental lattice energies and thermal pressures. Units are kJ/mol (energies) and GPa (pressures).
Lattice energies of the C21 crystals compared to the experimental reference data. The mean absolute errors (MAE) and mean absolute relative errors (MA%E) are indicated. The last two lines show the MA%E when no thermal correction and the 2RT term are used. Units are kJ/mol.
Mean absolute and relative deviations of cell lengths, angles, and atomic positions. The coordinates of hydrogen atoms have not been included in the statistics. Length units are bohr.
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