PHYSICAL REVIEW B VOLUME 46, NUMBER 3 15 JULY 1992-I Structural and electronic properties of Ceo N. Troullier and Jose Luis Martins Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55/55 (Received 16 August 1991; revised manuscript received 10 March 1992) We present pseudopotential local-density calculations of the electronic and structural properties of solid Ceo (fullerite). The calculated molecular bond lengths, lattice constant, bulk modulus, enthalpy of formation, and the equation of state for compression are in good agreement with experi- ment. The shape of the theoretical density of states is in excellent agreement with the experimental photoemission and inverse photoemission spectra. We also present the calculated band structure for the states near the fundamental gap. We have made a thorough analysis of the electronic states of C6p and found that they can be conveniently classified according to their angular character, and use it to identify the origin of the peaks in the electronic density of states I. INTRODUCTION In the mid-1980s a cluster containing 60 carbon atoms was observed to be exceptionally stable in a molecu- lar beam. It was proposed that the stability of this molecule, Cso fullerite, was due to a highly symmetric truncated icosahedral shape. With the recent break- through of Kratschmer et al. z the production of Cso in macroscopic amounts has been achieved, and a molecu- lar solid formed by Ceo molecules has been synthesized. Solid Cso is a new crystalline material that is expected to have different properties than the other two more com- mon forms of crystalline carbon, diamond and graphite. With the availability of macroscopic amounts of Ceo, the basic properties of this molecular solid have been de- termined. The early evidence for the cage geometrys was confirmed and the icosahedral symmetry established from Raman and NMR (Refs. 5 — 7) spectra. The molec- ular bond lengths have been obtained from NMR (Ref. 8) and x-ray-scattering spectra. The compressability has been measured. ii The phonon spectra were determined with Raman, 4 iz infrared, is and neutron-scattering' experiments. The electron spectra were observed with photoemissionis and inverse photoemission. is The re- port of the formation of conducting films of Cso by alkali-metal dopingr r was quickly followed by the exciting discovery of superconductivityis in interstitially doped KsCsp with a critical temperature of T, = 18 K. Re- cently, superconductivity was observed in RbsCso, Cs- doped C6o, and Cs~RbC60, withcriticaltemperatures of T, = 28, 30, and 33 K, respectively. We have performed pseudopotential local-density cal- culations of the structural and electronic properties of solid Cso. The calculated molecular bond lengths (1. 382 and 1. 444 A), lattice constant of fullerite (14. 0 A), and cohesive energy (1. 6 eV per molecule) are in good agree- ment with experiment. The calculated pressure versus volume equation of state also agrees with the experimen- tal data. The shape of the theoretical density of states is in excellent agreement with the measured photoemission and inverse photoemission spectra. We have calculated the band structure of fullerite, the band gap is direct at X and is 1. 18 eV wide. The width of the lowest set of conduction bands is 0. 47 eV. Because of the problems with the local-density approximation the true band gap should be larger. From our analysis of the wave functions we can classify them according to their o and vr charac- ter, and their dominant angular momentum component with respect to the center of the C6o molecules. We are able to classify the preeminent features of the density of states, and we show how approximate molecular orbitals with the correct symmetry can be written for the z sys- tem of the molecule. Similar calculations were done for K Ceo crystals and will be discussed elsewhere. In Sec. II we present an outline of the computational procedure. In Sec. III we discuss the calculated struc- tural properties. The electronic structure is presented in Sec. IV, and in Sec. V we discuss the electron wave functions. Atomic units are used throughout this paper unless otherwise noted. II. COMPUTATIONAL PROCEDURE The electronic structure calculations for Cso were performed with the plane-wave pseudopotential local- densityzz method. zs We use the Ceperley and Alderzs form of exchange correlation, as parametrized by Perdew and Zunger. 2s The pseudopotentials were generated us- ing a method proposed by us, z" which has the advantage of producing "soft" pseudopotentials for first-row ele- ments, such as carbon. The carbon pseudopotential used in these calculations was generated in the ground-state valence configuration 2s 2p . The radial cutoffs, i.e. , the radius at which inside this point the pseudo-wave- functions are allowed to deviate from the all-electron wave functions, were r„=r, „= 1. 50ao. We use the p pseudopotential as the local potential and neglect the nonlocality for the d and higher scattering channels. The carbon potential was then made separable using the pro- cedure of Kleinman and Bylander. We checked that 46 1754 1992 The American Physical Society