Pressure dependent stability and structure of carbon dioxide—A density functional study including long-range corrections

Abstract

First-principles density functional theory (DFT) is used to study the solid-state modifications of carbon dioxide up to pressures of 60 GPa. All known molecular CO2 structures are investigated in this pressure range, as well as three non-molecular modifications. To account for long-range van der Waals interactions, the dispersion corrected DFT method developed by Grimme and co-workers (DFT-D3) is applied. We find that the DFT-D3 method substantially improves the results compared to the uncorrected DFT methods for the molecular carbon dioxide crystals. Enthalpies at 0 K and cohesive energies support only one possibility of the available experimental solutions for the structure of phase IV: the R3c modification, proposed by Datchi and co-workers [Phys. Rev. Lett. 103, 185701 (2009)]. Furthermore, comparing bulk moduli with experimental values, we cannot reproduce the quite large--rather typical for covalent crystal structures--experimental values for the molecular phases II and III.

Structure and compressibility of the high-pressure molecular phase II of carbon dioxide

“…They found that the elongated molecules were unstable, and when relaxed, the C=O bond distance reverted to a value similar to that of the free CO 2 molecule. This result was later confirmed by other theoretical studies [21][22][23]. The computed Raman spectra of the optimized tetragonal structure reproduced very well the experimental one, including the frequency splitting of the internal ν + mode, showing that the crystal field alone is sufficient to explain it [20].…”

“…The latter includes a London dispersion two-body correction to the DFT-PBE approximation in order to take into account the long-range interaction effects of van der Waals type. The PBE-D3 EOS [23] predicts lower volumes than the PBE EOS [20] TABLE I. Lattice parameters and volume of phase II as a function of pressure determined in the present work. Average uncertainties are 0.2 GPa for P , 0.002Å for a and c, and 0.09Å 3 /molecule for V .…”

“…Note that, as for the lower pressure, we only performed Le Bail refinements of the patterns collected on compression, as the sample remained highly textured. Figure 10 also shows the 0 K P-V EOS predicted by DFT calculations [20,23] using either the Perdew-Burke-Emzerhof (PBE) functional [47] or the more recent PBE-D3 functional [48]. The latter includes a London dispersion two-body correction to the DFT-PBE approximation in order to take into account the long-range interaction effects of van der Waals type.…”

“…In the fit to the P-V data, B 0 was fixed to the theoretical value (6.29) of Ref. [23], giving V 0 = 44.4(4)Å 3 /molecule and B 0 = 8.5(3) GPa (see text and Table II). The green and blue lines are the EOS of phase II predicted by DFT with either the PBE [20] or PBE-D3 functional [23], and the purple circles are the experimental data from Ref.…”

Second-Order Many-Body Perturbation Study on Thermal Expansion of Solid Carbon Dioxide

“…29 The volume collapse at about 11 GPa is caused by a solid−solid phase transition, and the data above that pressure correspond to phase III. 21 dispersion interactions is added, 35 a reasonable value of B 0 is obtained. In short, it seems exceedingly difficult to determine B 0 accurately either computationally or experimentally.…”