Controlling adiabaticity for CP-dynamics in practice

Running meaningful Car-Parrinello dynamics simulation requires adiabaticity conditions to be met. The problem is widely discussed in the literature (e.g. see Marx and Hutter, NIC Series, 2000). Here a ``difficult'' example is given together with practical hints how to overcome the difficulties.

Theoretically the separation of the electronic and ionic degrees of freedom can be achieved by separating the power spectrum of the orbital classical fields from the phonon spectrum of the ions (the gap between the lowest electronic frequency and the highest ionic frequency should be large enough). Since the electronic frequencies depend on the fictitious electron mass $\mu$ one can optimize the value of $\mu$ and rise the lowest frequency appropriately. This however might turn out difficult in practice.

The adiabaticity can be observed by running test simulations and looking at the energy components. In particular the fictitious kinetic energy of the electronic degrees of freedom ( $E_{\mathrm {KINC}}$ ) might have a tendency to grow. However, after an initial transfer of a little kinetic energy, the electrons should be much ``colder'' than the ions, since only then will the electronic structure remain close to the Born-Oppenheimer surface and thus the wavefunction and forces derived from it meaningful.

Ensuring adiabaticity of CP dynamics consists of decoupling the two subsystems and thus minimizing the energy transfer from ionic degrees of freedom to electronic ones. In this sense the system during CP dynamics simulation should be kept in a metastable state.

A good practice in running advanced simulations is to start with the simplest case for a given system and then turning on additional features gradually.

Figure 8: Conserved energy $E_{\mathrm {HAM}}$ from microcanonical simulation with different time step, functional: BLYP, pseudopotentials: Vanderbilt, R $_{\mathrm {cut}}$ =30 Ry, $\mu$ =400 a.u.