Very Large Electronic StructureCalculations Using an Out-of-CoreFilter-Diagonalization Method

We present an Out-of-Core Filter-Diagonalization method which can be used to solve very large electronic structure problems within the framework of the one-electron pseudopotentialbased methods. The approach is based on the following three steps: First, nonorthogonal states in a desired energy range are generated using the filter-diagonalization method. Next, these states are orthogonalized using the Householder QR orthogonalization method. Finally, the Hamiltonian is diagonalized within the subspace spanned by the orthogonal states generated in the second step. The main limiting step in the calculation is the orthogonalization step, which requires a huge main memory for large systems. To overcome this limitation we have developed and implemented an out-of-core orthogonalization method which allows us to store the states on disks without significantly slowing down the computation. We apply the out-of-core filter-diagonalization method to solve the electronic structure of a quantum dot within the framework of the semiempirical pseudopotential method, and show that problems which require tens of gigabytes to represents the electronic states and electronic density can be solved on a personal computer.