Chebyshev-filtered subspace iteration method free of sparse diagonalization for DFT calculations

The Kohn-Sham equation in first-principles density functional theory (DFT) calculations is a nonlinear eigenvalue problem. Solving the nonlinear eigenproblem is usually the most expensive part in DFT calculations. Sparse iterative diagonalization methods that compute explicit eigenvectors can quickly become prohibitive for large scale problems. The Chebyshevfiltered subspace iteration (CheFSI) method avoids most of the explicit computation of eigenvectors, which results in significant speedup over iterative diagonalization methods for the DFT self-consistent field (SCF) calculations. However, the original CheFSI method utilized a sparse iterative diagonalization at the first SCF iteration to provide initial vectors for latter subspace filtering, and this diagonalization is expensive for large scale problems. We develop a new initial filtering step to fully avoid this first step diagonalization, thus making the CheFSI method free of sparse iterative diagonalizations. The new approach saves memory usage and can be two to three times faster than the original CheFSI method.