Go-Faster Stripes!

Reducing the cost of each MD step is highly desirable to allow a longer simulation for a given computational cost. In this section we will examine the two methods CASTEP provides for doing this.

Wave-function Extrapolation

A significant speed up is obtained by not throwing away the Kohn-Sham wave-functions from the previous time-step. At the start of each new step, our self-consistent iteration process begins by minimising the electronic Hamiltonian due to the charge density at the previous time-step. If the motion of the atoms over a time-step is small, this will then require fewer subsequent SCF iterations to find the ground state than if we began from scratch.

While this re-use of the wave-functions between time-steps does improve matters, we can go one step further and attempt to extrapolate the old Kohn-Sham wave-functions onto the new ionic positions at each time-step. This will give us an even better starting point for the minimisation process and will therefore require less SCF cycles.

In variable cell calculations, in which either the number or interpretation of plane wave co-efficients changes between time-steps, wave-function extrapolation is somewhat more complex. However a speed-up of 2-3 times can still be gained over unextrapolated calculations in CASTEP.

The extrapolation can be tweaked with the md_extrap parameter. e.g.

md_extrap = none

to disable wave-function extrapolation. The order of the extrapolation scheme can be specified with the value ``first'', ``second'' or ``mixed'' to alternate between the two. Second order extrapolation tends only to be beneficial for systems in which the ionic positions change by very little over an MD step.

Tweaking Electronic Convergence for MD

When minimising the total energy in CASTEP, the convergence criteria is based on a window as indicated in figure 2.3.

Figure 2.3: Convergence of the energy minimisation calculation. The procedure is judged to have converged when the energy has not changed by more than the height of the convergence window during a number of SCF iterations equal to the length of the convergence window.

The default height of the convergence window is $1\times 10^{-5}$eV per atom, and the default length of the window is 3 SCF iterations. For well behaved MD calculations this can lead to more SCF calculations being performed per time-step than is required for accurate calculation of forces. For this reason the ability to specify a different convergence window for use during MD simulations is available.

The length of the convergence window for MD can be reduced to a minimum of 2 SCF iterations, e.g.

md_elec_convergence_win = 2

Similarly the height of the convergence window can be increased so as to ensure the extra iteration inside the window is performing useful minimisation work, e.g.

md_elec_energy_tol      = 1.5E-4 eV

This is the energy tolerance per atom specified in any available energy unit.

These parameters are used entirely at your own risk, and you should always compare results for a number of MD steps both with and without convergence tweaking to ensure convergence is adequate.