Together with a group of material scientist, we intend to calculate the atomic and electronic structure of nanoparticles on a quantum-mechanical level. The mathematical core of this modeling is a sequence of large and sparse eigenvalue problems. In this talk, I will present the special requirements of the solutions, the challenges on the computational method, our algorithmic approach and software development. Numerical implementation on the advanced distributed computers will be demonstrated. This work also demonstrates how to efficiently develop special-purpose application code on top of available parallel software packages. At the end of the talk, as a PETSc developer, I will give a short demo on using PETSc as a tool for large scale numerical simulation.