Ask The Doctor!

• Q. When all else fails … a.k.a. “I'm doing everything right, but it still messes up” ..

Wien is modular - it's the weakness and the strength - and sometimes it just takes too long to figure out which file has been overwritten by what process. Start again in a completely new folder. Often, it takes just a few minutes to get back to the point that took you two days to reach!

• Q. How does Wien calculate band structure?

Wien2k implements a method called FLAPW (Full potential Linearized Augmented Plane Wave) - actually a specific variant called: APW+LO (APW + Local Orbitals). It is different from a pseudopotential method, which is also commonly found in the literature. Here is a talk by Prof Blaha, one of Wien's developers, on the program and some of its uses.

• Q. What is a Ry? And a Bohr? What does Wien use?

A. The are commonly-used units in atomic systems. A Rydberg (Ry) is an energy unit equal to 13.6 eV. A Bohr is a distance unit equal to 0.5 Å.

Wien does all its internal calculations in Ry, so many of the numbers you can enter in the files are in Ry. However, it will display in eV if you want it to (select this option in the DoS under tasks). You can select Å or bohr in the structgen program.

• Q. Wien uses a cutoff energy“ What is this? Is -6.0 Ry (Wien's default) always a good estimate? Should the value be based on the elements present?

A. (GS) In Wien2K, electrons are treated either as valence electrons or core electrons. Core electrons are assumed to not interact. The -6.0 Ry in Wien2K specifies the energy below which states are treated as core states. It is a relative energy (wrt to Energy = 0 Ry used in Wien2K, which is arbitrary). What is NOT arbitrary is the energy of typical valence states, which are approximately in the range -1 Ry … +1 Ry. The specific value of -6 Ry comes from experience and there is almost never a reason to change it. Usually the division between core and valence states can be done by looking at the periodic table. For example Ti has an electronic configuration of 1s2 2s2 2p6 3s2 3p6 4s2 3d2 = [Ar] 4s2 3d2, where [Ar] specifies the closed electrons shells of Argon. The electrons in closed shells are usually treated as core electrons. However, for certain atoms, some of electrons in a closed shell are sufficiently delocalized that they do interact with the valence electrons and treating them as core electrons introduces an unacceptable error. For example, this is the case for the Ti 3p6 states. In Wien2k, the energy cutoff of -6 Ry relative to typical valence state energies of -1 Ry … 1 Ry is used an indicator that enough interaction between electron states takes place to warrant treating them ALL as valence electrons.

• Q. I have read that well-converged calculations of 3d transition metals and f-electron systems require plane wave cutoffs ranging from 10-20 Ry. What does this mean and is this the same cutoff as the cutoff energy, but without the minus sign?

A. (GS) It is NOT the same as the cutoff energy that separates core and valence states. The plane wave cutoff energy describes how many plane waves are used in the basis set to describe the valence electrons. All plane waves with energy less than this energy Ecut are included in the basis set. Historically, the plane wave cutoff in pseudopotential methods is specified as an energy (Ecut), while in FLAPW methods it is specified as the maximum value of |k| for a plane wave (kmax). They are connected by Ecut = (hbar^2*kmax^2)/(2*m_e). If the units for Ecut and kmax are [Ry] and [1/bohr] than hbar=1 and m_e=1/2. Ecut=10 Ry is approx. equivalent to kmax=6. That doesn't mean you need to use kmax = 6.0 in Wien2k for a transition metal. In general the FLAPW in Wien2k requires fewer plane waves than ultra-soft pseudo-potential methods.

• Q. What is a good convergence criterion? Energy, Charge, Force?

A. (GS) Energy convergence is easiest to understand. We are mostly interested in material properties at room temperature: kT = 300K = 25meV = 0.002Ry. The choice 0.0001 Ry is simply an order of magnitude smaller just to be on the safe side.

• Q. What is gmax?

A. (GS) gmax is related to kmax. gmax specifies which plane waves are used as a basis set for describing the electron density. Since n( r) = sum k int dr e*Phi^*(k,r) * Phi(k,r), in the electron density plane waves appear with g >= 2*kmax, hence gmax must be >= 2*kmax.

• Q. If I start out with a lower gmax and then continue to iterate with increasing gmax (and therefore number of plane waves), would this help to speed up the final calculations using the largest gmax or would the calculation with gmax at 14 still take just as long as setting it to 14 on the very first SCF cycle?

A. (GS) Your idea is correct and you potentially can save computer time this way. Not much however, since computer time in Wien2k is mostly determined by kmax and not gmax. In general gmax is kept constant at 13 or 14. Using a certain number of plane waves with g < = gmax corresponds to a real space grid on which certain things like density gradients are calculated. The real-space grid and the k-space grid are connected by a fast fourier transform.

• Q. The paper I am reading says “final zone sampling for the DOS consisted of 32 X 32 X 8 mesh.” I was thinking this means that the number of k-space points was set to 32 X 32 X 8 = 8192 points, does this sound correct? What mesh do you suppose they are talking about? I also believe it might be related back to gmax which, I read, “determines the mesh on which the “gradients” (what gradients?) are calculated numerically”

A. (GS) Yes, this is a mesh in k-space mesh. Is not related to gmax. It is a mesh in reciprocal space on which the electron density is calculated (The sum k in n( r) = …, which really is an int dk). The “gradients” are mostly electron density gradients.

• Q. If a material is not 3d structure, but 1-D like a carbon nanotube or linear polymer, can Wien calculate the band structure of that material? We need to input a space group of the material but nanotube materials are described by a line group, not a space group.

A. (GS) Wien2k does not know about 1D (line) or 2D symmetries. To treat low-dimensional systems, one creates a 3D cell which is artificially large in 1 dimension for 2D systems and artificially large in 2 dimensions for a 1D system like a CNT. The size of this extra space depends on the system you plan to study. An important point is that even though you just add empty space to separate the periodic images of your low dimensional system, you still have to fill this space with plane waves (the basis functions of Wien2k) and calculations of that sort can take a long time. The choice of symmetry is in fact yours. For a linear system it is best to choose a hexagonal space group compatible with your line group. This choice minimizes the empty space. Overall, a low dimensional system is much more work than a starting project should be!

• Q. Can I calculate piezoelectric response in Wien/Flair?

A. (GS) Unfortunately polarization calculations are not obvious and involve a so-called topological phase or Berry phase in quantum mechanics. It is not implemented in either Wien2K or flair. Those interested in the theory might consult the standard reference, R. Resta, Rev. Mod. Phys. 66, 899­915 (1994), and the original articles R. D. King-Smith and David Vanderbilt, Phys. Rev. B 47, 1651­1654 (1993) & David Vanderbilt and R. D. King-Smith , Phys. Rev. B 48, 4442­4455 (1993).

• Q. Why does Wien get the band gap of Si wrong?

A. Density Functional Theory underestimates the band gaps of insulators and semiconductors. This is a well-known shortcoming, and there are ways to estimate the gap better, but they are computationally more expensive. Theories that take account of many-body interactions in the solid, including the “exchange interaction”, can be expected to reproduce the excited state structure of the solid far more accurately. The “GW” approximation is one such. Many papers address the topic. One that uses Si as an example is Yakovkin et al., Surface Review and Letters 14 (2007) 481. There is another discussion at the Materials Project bandstructure webpage.

• Q. Why are rhombohedral spacegroups troublesome?

A. Rhombohedral spacegroups (those that start with R, like R3m for example) are tricky because there are 2 ways to describe a material with rhombohedral symmetry. One way is the true rhombohedral coordinates: a=b=c, and alpha=beta=gamma, and the associated positions for that system. Another way is to create a hexagonal unit cell with 3 times the volume with a'=b' not= c' and alpha'=beta'=90˚ and gamma'=120˚ and use the positions for those. Google “hexagonal to rhombohedral conversion” and look here. In Bi2Te3, for example (SG = R3barm = #166), using the hexagonal lattice parameters and placing Bi at (u,u,u) x=0.4 and Te1 and (0,0,0) and Te2 at (v,v,v) v=0.792 generates the correct 5-atom cell.