~ ) Solid State Communications, Vol. 87, No. 11, 1009-1012, 1993. PP. Printed in Great Britain. 0038-1098/9356.00+.00 Pergamon Press Ltd SCREENING TRENDS IN C60 SOLIDS D. P. Joubert Physics Department, University of the Witwatersrand, P.O. Wits, Johannesburg 2050, South Africa (Received4May1993, m revisedform 21June1993, accepwdforpublication23Ju~ 1993) by R. T. Phillips The dielectric function for solid C60 is calculated within the RPA. The screened coulomb interaction shows a remarkable spatial and orientation dependence. Inter-molecular screening is considerably better than intra-molecular screening and inter-molecular screening increases with separation of molecules. Since the discovery of Cs0,1 and especially after it was realised that Cs0 doped with certain alkali metals 2 becomes superconducting, there has been an ongoing ex- perimental and theoretical effort to understand its mi- croscopic properties. It has been suggested that many- body properties may play an important role in the be- haviour of Cs0 solids,a An understanding of the screened electron-electron interaction is therefore of crucial impor- tance. Gunnarson, Rainer and Zwicknagl4 investigated the screening in C6o using a simple model within the Ran- dom Phase Approximation (RPA). s Screening properties of Cs0 systems were also studied by Gonzalez, Guinea and Vozmediano s in a continuum approximation using the wave functions of planar graphite as starting point. For an isolated molecule this approach gives a reduction of the bare coulomb interaction between two electrons in the lowest unoccupied triplet of ~ 50%, but gives no in- formation about the spatial dependence of the screened interaction. In this paper an investigation of the screening proper- ties of fcc-T~, Cso (figure 1) is reported. C60 crystallizes with the molecules situated at fcc lattice sites with a nearest neighbour distance of ,,, 10.04 ,~..~ The structure with the highest symmetry (T~) consistent with this ob- servation is depicted in figure 1. The lattice parameter used here is 14.198 ~i and the nearest neighbour atomic bond lengths are 1.369 ~.(between pentagons) and 1.453 ~,(on pentagons), s This solid is a semiconductor with a calculated direct bandgap of ~ 1.8 eV. The static dielec- tric function in RPA (in Rydberg atomic units) is given by 4r eGG' (q) = 6GG' lq+ G]2'XGG'(q)' (i) where the polarizability, XGG'(q), can be expressed as XGG'(q) = 4 ~v,c <~(r)le-qq÷G)rl'~><'~q'~(q÷G')'rl'~'> (2) (~-e c ) with ~b~,~b¢ the valence and conduction band wave func- tions and ~, c, the corresponding eigenenergies. The electronic structure was calculated within Local Density Functional Theory (DFT) ~ using the non-local pseudopo- tential of Bachelet, Harnaan and Schlfter w and exchange- correlation function of Ceperley and Alder n as param- eterized by Perdew and Zunger. n Basis functions were constructed from a contracted gaussian basis for the 2s and 2p carbon wave functions. The calculated long-wavelength limit of the dielectric function c00(0) = 4.84. This value agrees very well with that calculated by Ching et al Is using a similar approach. The average, or macroscopic, response of the system, de- fined as c,~(q + G) = 1/cfilG(q), (3) however, is determined by the diagonal elements of ~-1 not c. In particular, the macroscopic dielectric function, co = lirrk,o CM(q), since it comes from the inverse of c, Figure 1: Atomic positions for nearest neighbours of solid fcc-T~, C60 projected on the (100) plane. 1009