In this paper, a service-oriented framework for running quantum mechanical simulation of material properties over Grids is proposed, and a prototype framework has been developed. The framework consists of portal and workflow systems, a set of class libraries and application programming interfaces, defined service specifications, schemas, and configuration files. The framework can be instantiated to submit specific quantum mechanical simulation (e.g., CASTEP) jobs to a Grid from a Web browser with the required tasks managed and coordinated by the workflow without human interaction. The paper details analysis, design, and implementation of a prototype framework. In the test case, the prototype framework is instantiated to submit a CASTEP simulation job to available Grid resources in order to calculate the equation of state of a material.