APPLICATION OF GENERALIZED GRADIENT APPROXIMATIONS - THE DIAMOND-BETA-TIN PHASE-TRANSITION IN SI AND GE

Generalized gradient approximations (GGA) for the exchange-correlation energy have been suggested to improve upon the local-density approxim ation (LDA) in density-functional theory. It has been demonstrated by various authors that the gradient correction suggested by Becke for th e exchange functional and Perdew for the correlation energy, as well a s the recent GGA by Perdew and Wang (1991), yield improved cohesive en ergies for solids, correcting for the overbinding in LDA. In this pape r we focus on a structural phase transition of Si, which under pressur e transforms from the diamond structure to the beta-tin structure. The coexistence pressure calculated within the LDA is 80 kbar, smaller th an the experimental values (103 - 125 kbar). Both gradient-corrected s chemes yield a coexistence pressure which is larger than the LDA value (146 kbar for the Becke-Perdew and 122 kbar for the Perdew-Wang excha nge-correlation functional). Ge undergoes a similar transition at arou nd 105 kbar. The LDA result for the coexistence pressure is 73 kbar, i t amounts to 118 kbar when calculated within the Becke-Perdew GGA, and 98 kbar within the Perdew-Wang GGA.