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9033 dx.doi.org/10.1021/ja201786y | J. Am. Chem. Soc. 2011, 133, 9023–9035 Journal of the American Chemical Society ARTICLE theoretically some dimers of benzene not yet known and, as we will show, molecules that should be kinetically persistent. Here, in Figure 17, we show just the set of dimers that emerge from this investigation, all local minima on the C 12 H 12 surface.
Of these molecules, 1, 66 2 , 67 3 , 68 11 , 69 and 12 70 are known, as well as derivatives of 4. 71 These molecules lie (calculated) 36 (3) À112 (9) kcal/mol above two benzene molecules. We will give a full account elsewhere 65 of the calculated barriers to the reversion of these dimers to two benzenes, as well as other potential escape routes from their high-energy situation. For the moment, it su ffices to say that, for some of the unknown isomers, activation barriers are likely to be high, and these structures have a very good chance of kinetic persistence, even at room temperature. One approach to simulating irregular polymerization of benzene would be to take this set of dimers and proceed with adding a third and a fourth molecule of benzene. That remains to be done. ’ CONCLUSION In this study benzene has been compressed in a sequence of calculations up to 300 GPa. The computational results show that the phase I f phase II transition occurs at ∼4 GPa, phase II f phase III at ∼7 GPa, and phase IIIf phase V at ∼40 GPa. The agreement with the order of phase transitions found in experimental studies, especially below 10 GPa, is good. Above 50 GPa, hints that molecular structures are unstable with respect to saturated, four- coordinate at C phases —one-, two-, and three-dimensional—led us to examine such phases in detail. We have found that several graphane phases are more stable than any of the molecular phases over the entire range of pressures studied, including P = 1 atm. A qualitative argument for that order of stability is given. But the molecular phases encounter large —sometimes very large
—barriers to rearrangement to a saturated polymer or network of the graphane type. In particular, phonon dispersion calculations show that phase III is dynamically stable up to ∼200
GPa and might become metallic before transformation to a saturated phase. Several simple models for the metallization of benzene are investigated. We also speculate on the possible existence of a phase-coherent Kekul e metal. Finally, in a first approach to nucleated benzene polymerization, we calculate the structures of a number of benzene dimers, some known, some not. ’ ASSOCIATED CONTENT b S Supporting Information. Details of computed ben- zene phase structural parameters; simulated X-ray di ffraction
patterns of benzene phases; “parallel” phase I and II, “C 6 F
” Figure 17. Structures of some benzene dimers.
9034 dx.doi.org/10.1021/ja201786y | J. Am. Chem. Soc. 2011, 133, 9023–9035 Journal of the American Chemical Society ARTICLE phase, and “C 6 H 6 ÀC 6 F 6 ” phases; distance histogram and den- sity of states of polymer I; dynamical analysis for phase III; distance histogram of phase III at various pressures; C ÀC, CÀH, intermolecular H---H, and intramolecular H---H distances in phase III; band structure of phase III at 190 GPa; density of states of polymer II at 210, 250, and 300 GPa; computed total density of states for phase III at 190 and 200 GPa, comparing DFT and eH methods; analysis of the lattice stability of phase III at 190 and 200 GPa; e ffect of rotation on metallization of phase III at 150 GPa; calculated dielectric functions for phase III; phonon dispersion of graphanes; computed total density of states for graphanes; band structure of 1D and 2D benzene models; and three kinds of rotations in 2D benzene models. This material is available free of charge via the Internet at http://pubs.acs.org. ’ AUTHOR INFORMATION Corresponding Author rh34@cornell.edu Present Addresses † Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545 ’ ACKNOWLEDGMENT The four reviews we obtained of this paper were extraordina- rily detailed and useful —we really appreciate the reviewers’ comments. We are grateful to Dr. P. Raiteri for suggesting some benzene phases. Our work at Cornell was supported by the National Science Foundation through Grants CHE-0613306, CHE-0910623, and DMR-0907425, and by EFree, an Energy Frontier Research Center funded by the U.S. Department of Energy, O ffice of Science, Office of Basic Energy Sciences, under Award Number DESC0001057. This research was also sup- ported by the National Science Foundation through TeraGrid resources provided by NCSA. Some calculations were performed in part at the Cornell NanoScale Facility, a member of the National Nanotechnology Infrastructure Network, which is supported by the National Science Foundation. ’ REFERENCES (1) Mujica, A.; Rubio, A.; Mu ~noz, A.; Needs, R. J. Rev. Mod. Phys. 2003
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