  Wavefunction extrapolation greatly reduces the number of self-consistent
field (SCF) iterations and thus the overall computational cost of
Born-Oppenheimer molecular dynamics (BOMD) that is based on the Kohn-Sham
density functional theory. Going against the intuition that the higher order of
extrapolation possesses a better accuracy, we demonstrate, from both
theoretical and numerical perspectives, that the extrapolation accuracy firstly
increases and then decreases with respect to the order, and an optimal
extrapolation order in terms of minimal number of SCF iterations always exists.
We also prove that the optimal order tends to be larger when using larger MD
time steps or more strict SCF convergence criteria. By example BOMD simulations
of a solid copper system, we show that the optimal extrapolation order covers a
broad range when varying the MD time step or the SCF convergence criterion.
Therefore, we suggest the necessity for BOMD simulation packages to open the
user interface and to provide more choices on the extrapolation order. Another
factor that may influence the extrapolation accuracy is the alignment scheme
that eliminates the discontinuity in the wavefunctions with respect to the
atomic or cell variables. We prove the equivalence between the two existing
schemes, thus the implementation of either of them does not lead to essential
difference in the extrapolation accuracy.

Computational Physics;Chemical Physics