The electronic structure of the ternary silver compound Ag3SI has been studied in order to clarify the microscopic origin of the structural phase transition and the fast ionic conduction. The present LMTO band calculations show that beta-Ag3SI (cubic antiperovskite structure) has a direct gap at M=(1/2, 1/2, 0), while the low-temperature gamma-Ag3SI has an indirect gap from M to Gamma (0, 0, 0). The total energy is estimated as functions of atomic coordinates. The contour map of beta-Ag3SI, where Ag ions are assumed to move within the (001) plane, is found to reproduce the experimental results showing four energy minima at (1/2+0.14, 1/2, 0). The present calculations also show that the saddle point of the Ag diffusion path, between the points (1/2, 0, 1/2) and (0, 1/2, 1/2), appears around (0.155, 0.155, 0.555). (C) 2004 Elsevier B.V. All rights reserved.