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I have a Si slab of thickness 0.5nm for which I want to calculate the phonon dispersion. The unitcell has 5 atomic layers and 10 Si atoms with vacuum of 10A in z-direction (a 2x2 supercell is shown below)

enter image description here

The dispersion (calculated with phonopy and alamode) has large negative frequencies [THz]:

enter image description here

Visualizing the phonon modes reveals that those negative frequencies are largely associated with the vibration of the surface atoms (surface phonons).

The structure is tightly relaxed before carrying out the calculations. I use VASP with tight criteria (EDIFFG=-1e-3, EDIFF=1e-8, PREC = ACCURATE, LREAL = .FALSE.). I followed two different strategies which gave the same result for lattice constant (a=5.36A in x and y directions):

  1. Volume relaxation: (isif = 4) with high ENCUT (~1.3*ENMAX) to avoid Pulay stress.
  2. Equation of state approach: only relaxation of positions (isif = 2) with varying lattice constant in a step of 0.01A and finding the lattice constant that gives the minimum energy.

I even tried relaxation without symmetry (isym=0) starting from a rattled structure.

The forces of the displaced structure are also calculated accurately (EDIFF=1e-8, PREC = ACCURATE, LREAL = .FALSE., with and without ADDGRID)

I am not sure whether the structure is at a saddle point of the potential energy surface. I know I can get the direction in which the frequency is negative and move the associated atom in that direction to get out of the saddle point (if any). However, this will break the symmetry. The structure is very symmetric and simple; you just control the lattice constant (which is the same in the x and y directions), and the fractional atoms' positions are constant. As mentioned, I tried different relaxation strategies.

I am now stuck and do not know how to proceed. Thanks for your help.

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    $\begingroup$ Some questions/suggestions. 1) Did you converge the forces with respect to the KPOINT grid? Gamma point sampling might not be enough. 2) Did you inspect the maximum force components and stress components in the planar and perpendicular direction for the relaxed structure? The perpendicular stress might be useful for checking if the vacuum is converged. $\endgroup$
    – CW Tan
    Commented Feb 14 at 15:42
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    $\begingroup$ The structure was really at a local minimum $\endgroup$ Commented Feb 25 at 9:26

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Just because the structure is simple with high symmetry doesn't mean it's the correct ground state. More often that not, symmetry breaking leads to interesting physics (e.g. the surface reconstruction affects thermal transport, see the ACS ref below). I encourage you to relax along the soft modes, or create a slightly randomized version of your structure and relax from there with e.g. simulated annealing.

Also note that your structure and many other variations have most likely been extensively studied before. Silicon is probably the most widely studied materials that exists! You can likely find papers that have already done what you are trying to do. You can save yourself some work and read those or try to reproduce their results for practice.

In any case, your structure is a saddle point. People have studied surface reconstruction of silicon in the past! See e.g. here https://doi.org/10.1103/PhysRevB.14.588 and here https://doi.org/10.1021/nn506792d Your structure may have a different orientation, I am not sure. I remember these refs from some old work I did, but I am sure there are many other related papers that cite or are cited by these. Hopefully these are a good starting point for you!

Cheers! Ty

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  • $\begingroup$ Oops, I see that you tried starting from a rattled structure already. Good idea! I missed that before I posted my answer. $\endgroup$ Commented Feb 14 at 18:29

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