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The simulation cell is allowed to vary in shape and volume, driven by the quantum mechanically calculated internal stress (21). The ion-electron interaction is modeled with a fully nonlocal pseudopotential for carbon and a local pseudopotential for hydrogen. Electron-electron interactions are treated within the local density approximation, with gradient corrections as described in (22). A plane-wave basis set with a kinetic energy cutoff of 40 rydberg has been used for the electronic wave functions, which are assumed to have the same periodicity as the (varying) simulation cell.
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10
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1842265761
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note
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4 equation of state at 20 GPa and 2000 K.
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11
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1842392088
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note
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The time scale of our simulations is such that a few hundred C-H stretching oscillations and a few tens of molecular collisions take place in each run. Although this is typically a sufficient time scale for thermalization, and in fact dissociation took place in a fraction of a picosecond, processes like segregation and diffusion occur on a longer time scale. These processes are energetically minor in comparison with dissociation and will not significantly alter the dissociation picture as proposed.
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36549094592
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1842360222
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note
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Mixtures, of course, do not represent a well-defined state at T = 0. Their enthalpy is an upper bound to that of the true low-temperature system, where single phases are likely to prevail.
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17
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1842312040
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note
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4 molecule.
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18
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1842355394
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note
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4 dissociation in forthcoming low-temperature diamond-anvil cell experiments.
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0011454895
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1842309118
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note
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2 do not withstand the pressure conditions of the middle ice layers (23).
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22
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0348042318
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L. Reatto and F. Manghi, Eds. World Scientific, Singapore
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23
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4243553426
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5944261746
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1842399887
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28
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1842388172
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note
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4 and hydrocarbon mixtures were obtained from low-temperature simulations. Results for diamond and hydrogen were obtained from standard total-energy calculations carried out separately, with the same level of accuracy, for carbon (24) and for hydrogen (25).
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29
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1842352444
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note
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We acknowledge useful discussions with J. Kohanoff. The work at SISSA was partly supported by the European Commission and the Italian Research Council.
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