Our earlier structural model for binary silicate melts and glasses is extended. More general expressions for the enthalpy and nonconfigurational entropy are given. Expressions for partial thermodynamic properties are derived. A least-squares optimization program permits all available thermodynamic and phase diagram data to be optimized simultaneously within experimental error limits. The model is extended from MO-SiO2 to M2O-SiO2 solutions. Data in acidic melts is well represented for the Na2O-SiO2 system. Examples of optimizations for the MnO-SiO2, CaO-SiO2, and Na2O-SiO2 systems are presented. The model is extended to include sulfide ion. Good predictions of sulfide capacities are obtained. © 1995 The Minerals, Metals & Material Society.