  In the classic implementation of the LOBPCG method, orthogonalization and the
R-R (Rayleigh-Ritz) procedure cost nonignorable CPU time. Especially this
consumption could be very expensive to deal with situations with large block
sizes. In this paper, we propose an orthogonalization-free framework of
implementing the LOBPCG method for SCF (self-consistent field) iterations in
solving the Kohn-Sham equation. In this framework, orthogonalization is avoided
in calculations, which can decrease the computational complexity. And the R-R
procedure is implemented parallelly through OpenMP, which can further reduce
computational time. During numerical experiments, an effective preconditioning
strategy is designed, which can accelerate the LOBPCG method remarkably.
Consequently, the efficiency of the LOBPCG method can be significantly
improved. Based on this, the SCF iteration can solve the Kohn-Sham equation
efficiently. A series of numerical experiments are inducted to demonstrate the
effectiveness of our implementation, in which significant improvements in
computational time can be observed.
