Shortly after this experimental work, Serra et al. (2) reported a total energy calculation of several possible phases of CO₂ using plane wave pseudopotential density functional theory (PWP-DFT). They concluded that there should be a transition from a molecular phase to a phase isostructural to SiO₂ -quartz in the range of 35 to 60 GPa. Their results support the work of Iota et al.

We concurrently investigated polymeric phases of CO₂ theoretically (3) and concluded that the observed structure is not quartz, but cristobalite-like at pressures of at least up to many tens of gigapascals. We find that the -cristobalite phase (I2d) is lower in energy than -quartz (P3₂21) by 0.4 eV/CO₂. These results are obtained by using the local density approximation (LDA) and a plane wave cutoff of 29 Ry. A generalized gradient approximation (GGA) (4) was also used to evaluate the energies of the optimized structures, and was found to have little effect on the relative energetics of the polymeric phases. This energy difference is substantial and we expect that the theoretical technique of PWP-DFT that we used (5) can reliably predict the relative energetics of these structures.

To further substantiate this conclusion, we computed the vibration modes and their pressure dependence, and compared them with the Raman spectrum of Iota et al. Compared to that of -quartz, our calculated Raman spectrum for -cristobalite is far more consistent with the experimental data. The signature A₁ mode at about 790 cm¹ (at 40 GPa) has an average pressure derivative of 3.2 cm¹/GPa, while our calculations give 3.5 cm¹/GPa and 2.0 cm¹/GPa for -cristobalite and -quartz, respectively. This mode in cristobalite is a bond stretching mode of oxygen with motionless carbon. The pressure derivatives of the other modes show a more striking contrast. In particular, the E mode near 900 cm¹ (at 40 GPa) has little dependence on pressure (10 to 20 cm¹) in the Iota et al. experiments; the same pressure insensitivity of this mode is seen in our calculated spectrum of -cristobalite, whereas in -quartz we find a shift of over 150 cm¹. We believe that this and similar analyses of the other Raman modes, along with our total energy calculations, eliminate -quartz as a possible candidate.

Serra et al. (2) also considered cristobalite, but did not favor it as a possible candidate. They chose a linear C-O-C bond angle in cristobalite (effectively transforming the I2d structure to the "special case" Fdm C9 structure). This would cause a mild energy increase in SiO₂. However, unlike SiO₂, CO₂ has a deep energy minimum at the C-O-C bond angle near 124° (3). The energy difference between the linear system and one with an optimized C-O-C angle is nearly 2 eV/CO₂. Thus, Serra et al. incorrectly concluded that cristobalite is a high energy structure. The other extreme of a C-O-C bond angle of 109° (defective chalcopyrite) also yields a high energy structure. These considerations underscore that assumptions about the properties of CO₂ based on the behavior of SiO₂ will likely be incorrect. The small energy difference between the wide range of SiO₂ polymorphs is largely a result of SiO₂'s tolerance for a wide range of Si-O-Si inter-tetrahedron angles, while the C-O-C bond angle is quite stiff about the 124° minimum.

Jianjun Dong
John K. Tomfohr
Otto F. Sankey
Department of Physics and Astronomy
and Materials Research Center
Arizona State University
Tempe, AZ 85287-1504, U.S.A.

REFERENCES AND NOTES

1. V. Iota, C. S. Yoo, H. Cynn, Science 283, 1510 (1999) [Abstract/Free Full Text] .
2. S. Serra, C. Cavazzoni, G. L. Chiarotti, S. Scandolo, E. Tosatti, Science 284, 788 (1999) [Abstract/Free Full Text] .
3. J. Dong, J. K. Tomfohr, O. F. Sankey, Phys. Rev. B, in press.
4. J. P. Perdew in Electronic Structure of Solids '91, P. Ziesche and H. Eschrig, Eds. (Akademie Verlag, Berlin, 1999), p. 11.
5. The calculations have been performed with the use of Vienna Ab initio Simulation Program (VASP); G. Kresse and J. Furthmüller, Comput. Mat. Sci. 6, 15 (1996) .

Response: Dong et al. discuss the results of structural refinement calculations that they made on some of the non-molecular CO₂ phases that we proposed in our work (1). They find that 42d -cristobalite is favored over -quartz, at unspecified pressure.

Predicting that non-molecular CO₂ phases can be produced under high pressure and temperature was the main point of our report. This prediction was simultaneously confirmed by the experiments of Iota et al. (2). The comment by Dong et al. reinforces this prediction.

Moreover, as recognized by Dong et al., we, too, considered the 42d -cristobalite structure as a possible candidate for the ground state, although only in its extremal cases: a C-O-C bond angle of 180° as in "ideal cristobalite" (referred to simply as "cristobalite" in our report) and a C-O-C bond angle of 109° cristobalite (referred to as "m-chalcopyrite" in our report). We reported that the ideal cristobalite is very high in enthalpy and thus unlikely to be a good candidate for the ground-state structure. We also reported that, at 100 GPa, the 109° cristobalite only has a slightly higher enthalpy than does -quartz. It is likely that the optimal C-O-C bond angle in 42d -cristobalite will vary with pressure. Some additional preliminary results indicate the possibility of a pressure window of stability for 42d -cristobalite between the molecular crystal and the -quartz structures, with a C-O-C bond angle somewhat larger than 109°. This seems to agree with recent experimental findings (3), showing that the product of the transformation of CO₂ observed upon increasing pressure up to about 40 GPa and heating up to 1800 K may indeed be a mixture of the SiO₂-like structures trydimite and cristobalite.

C. Cavazzoni
G. L. Chiarotti
S. Scandolo
S. Serra
E. Tosatti
International School for Advanced Studies
Via Beirut 2-4, I-34100
Trieste, Italy

REFERENCES

1. S. Serra, C. Cavazzoni, G. L. Chiarotti, S. Scandolo, E. Tosatti, Science 284, 788 (1999) .
2. V. Iota, C. S. Yoo, H. Cynn, Science 283, 1510 (1999) .
3. C.-S. Yoo, XVIII Congress of the International Union of Crystallography, Glasgow, UK (August 1999), invited talk M08.OC.004.

Response: Dong et al. state that the structure of polymeric CO₂ discovered in recent high-pressure experiments (1) is cristobalite-like rather than quartz-like (2). Dong et al. used the same theoretical framework as Serra et al. (2) with different results and interpretations, with which I agree. The calculated (vibrational and total energies) properties by Dong et al. seem to better describe Iota et al.'s experimental results (1).

However, there are many other polymorphs of SiO₂ with similar energetic stabilities, many of whose structures have not been considered in either this or previous calculations (2). For example, none of the many polymorphs of tridymites have been considered, despite their structural and energetic similarities to -quartz and crystoballite (4). I believe that, because of the complexity in those crystal structures and the similarity in their energetics (particularly of quartz, crystobalite and many forms of tridymites), it is difficult to entirely rule out any one structure without experimental verification of the structure of polymeric CO₂ by x-ray diffraction. Our recent x-ray results (4) show that the diffraction pattern of CO₂-V is more closely related to those of tridymite polymorphs. There seems no obvious reason to consider polymeric CO₂ to be one of the structures found in SiO₂.

Nevertheless, the work underlying this exchange (3) is important and deserves recognition for pointing out other SiO₂ structures (cristobalite and tridymite as candidate structures for the extended carbon dioxide).

C. S. Yoo
Lawrence Livermore National Laboratory
Livermore, California 94551, U.S.A.
E-mail: yool{at}llnl.gov

REFERENCES

1. V. Iota, C. Cavazzoni, G. L. Chiarrotti, S. Scandolo, E. Tosatti, Science 283, 1510 (1999) .
2. S. Serra, C. S. Yoo, H. Cynn, Science 284, 788 (1999) .
3. J. Dong et al., Phys. Rev. Lett., in press.
4. C. S. Yoo et al., Phys. Rev. Lett., in press.