five-membered ring (108 ") and in an ideal tetrahedron (1 09.47 ',) accounts for the stability. An ideal structure composed of sp3 C atoms would therefore contain solely facesharing pentagonal dodecahedra. However, as it is impossible to build an infinite structure from pentagonal dodecahedra alone, six-membered rings are required even though they introduce greater ring strain. With this general building principle, namely face-sharing fullerene-like cages, it is possible to construct a large class of polymorphic solids that are expected to be similar in energy to the ones we have studied. Recently Guo et al. proposed structures for transition metal carbide clusters forming face-sharing pentagonal dodecahedrd."81 The structures of C,,, and C, , , can be considered extensions of these clusters to bulk structures (cf. Figs. 2,3). C,,, and C,,, exhibit large band gaps that are even 6 and 23 o/ o smaller than that of diamond. (These numbers should be taken with a grain of salt as the LDA does not in principle allow the prediction of excitation energies. Trends, however, are usually well reproduced.) These hypothetical carbon modifications have a number of interesting characteristics. The large cages might accommodate interstitial dopant atoms providing a means to engineer their electronic and optical properties. The nearest-neighbor distances for the interstitial sites within the various fullerene-like cages are 207 and 255 pm for C,,, and 215 and 223 pm for C,,,, compared to 153 pm in diamond. The first value always refers to the nearest-neighbor distance in pentagonal dodecahedron. The average volume per atom is increased by about 25% over diamond but considerably less than in graphite (1 53 Yo) and in solid C,, (205 YO).We expect C,,, and C,,, to exhibit high mechanical stability once they are formed, as a result of their low energy difference compared t o C,,, , the large energy required to break a C-C bond, and the three-dimensional linkage of the network C atoms.Currently we are investigating whether the new structures can be identified in the products formed by the Kratschmer process. High-pressure experiments on C,, are being performed as ~e 1 l .