Bulk systems tutorial for SeqQuest: Hexagonal GaN

Introduction
Examples:

Introduction

The purpose of this tutorial is to introduce the user to the effective use of the code for three-dimensional bulk problems. This tutorial uses the example of hexagonal gallium nitride to illustrate the use of the code for bulk problems. The input is rather flexible, and can use a very basic input file, but has options that lead to easier manipulation of the calculation in increasingly more sophisticated input files. This tutorial is presented in the form of a sequence of input files that illustrate the use of various features available in the code: how to take advantage of symmetries in the system to reduce the size of the calculation, how to create Brillouin Zone sampling appropriate to the symmetry of the system, how to use scaling functions in the input to simplify the description of the atom coordinates, etc.

Units

The default units for energy are Rydberg (1 Rydberg = 0.5 Hartree = 13.605 eV), and for distances are bohr (1 bohr = 0.52918 Ang = 0.052918 nm). All input coordinates will be in these units, though one can use the scaling functions in the code to aid in the conversions.

Input files

The code uses one main input file that the user must construct. Atom files (potential+basis), which will need to be listed in the input file, can be obtained from the atom libraries. The input file is a text-rich keyword-driven document that, once constructed, is self-documenting. The input is a sequence of keyword lines with the indicated data on following lines. Only the first few (6 or 8) characters of the keyword line are significant. The remainder of a keyword line can be used for additional documentation. The data itself, in general, is free-format. The input in the setup data section is highly structured, and requires its input in a very specific order. Other sections take their data in any order. If you miss putting something in the right place in the input, not to worry. The code will very happily process the input file, and stop when it cannot find required input in the right place. It echoes the input file as it reads it, and will politely tell you what it was looking for when it runs into a problem. Interspersed among the required inputs, are a variety of usually invisible optional input sections. The code uses a variety of defaults that can be overridden in the input file. The use of many optional inputs will be illustrated in the tutorial.

Example: A basic input file

Illustrated in this first example is a very basic file for doing a bulk hexagonal GaN calculation.

Important: While a calculation with this input file will run to completion, this input file is flawed and would not be a viable production calculation because of an incorrect use of the Brillouin Zone sampling, which will be discussed in the next example.

Command options

The input file begins with a sequence of instructions to the code about the sort of calculation it will be doing. In this example, we will “do” a “setup” (the iteration independent integrals), and “do iters” (self-consistency), but “no force” and no relaxation. The “setup data” is the instruction to the code to read the data that describes the system. Please do not try to “do iters” with “no setup”!

Setup phase data

This section begins with a title line(s). The keyword “notes” signals the beginning of the title/notes section that describes the nature of the problem. The keyword “end_notes” marks the end of the title/notes section The notes keyword and title lines are optional, but highly encouraged. Since the entire input file will be echoed into the output listing file, this provides a useful output record of the nature of the calculation. In this case, we are setting up a bulk hexagonal GaN problem, with a=6.13, and a c/a ratio of 1.630714474.

The “dimension” statement is the first required data in the input. We are doing a 3-dimensional bulk problem. If we were doing a molecular problem, we would enter a “0”, or if we were doing a surface problem using a 2-dimensional slab, we would have entered a “2” here.

The next required input is “primitive lattice” – supercell vectors. Here, we define a unit cell that is hexagonal in the x-y plane with a lattice parameter a=6.13 bohr (=3.24 A), and an orthogonal repeat vector in the z-direction with c=6.13*c/a.

The next required input is “grid dimensions”. The code evaluates many of its integrals on a regular space (fft) grid. This regular grid is defined by taking the primitive lattice vectors, and dividing them into grid intervals. Here we use a 24×24 grid in the hexagonal plane, and put 36 grid intervals along the z-direction. The more grid intervals, the more accurately the integrals are evaluated, but, also, the more expensive the calculation. A general rule of thumb: you want spacing between points of 0.30-0.40 bohr for most systems, and 0.20-0.30 for finer accuracy in systems containing “hard” atoms. Hard atoms include late first row atoms like N, O, F, or late 3d atoms. We have nitrogen in our system, and this example has a spacing of slightly less than 0.3 bohr. This can be tuned to the problem. If I wanted to compute an energy, a coarser grid might suffice. If I wished to evaluate a force or stress, a finer grid might be required. For a hexagonal system, it is a good idea to use a grid dimension in the plane that is divisible by three, so that the various high-symmetry points in the surface (i.e.), atop, hcp and fcc hollows) are at the same position with respect to the grid.

The next required input is number of “atom types”. Here, we have only two (Ga and N), and the code requires input to specify the “atom file” to be used to obtain the atomic potential and basis information for each atom type. Here, we will read from files “n.atm” and “ga.atm” for nitrogen and gallium, respectively.

Next, the input requires the number of atoms in the unit cell (4), and then a list of each “atom, type, and position”. The arguments for an atom input are the atom index (the order of the atom in the list, #1-#4 here), which type (in the order in which the types were listed above), and the positions of the atoms in Cartesian coordinates (in bohr). Atom 1 is of the first atom type (i.e., from “n.atm”), and is at (3.539,0.0,0.0257), and then next atom is the second atom type (i.e., from “ga.atm”), etc.

The final required input in the setup section (for a periodic calculation) is definition of the Brillouin Zone sampling. For molecular calculations this is unnecessary – one has only real integrals, or the “gamma-point”, to worry about. In a (periodic) bulk calculation, the Schroedinger equation generally needs to be solved for a sampling of points in reciprocal space. It is possible to input the k-point sampling as an explicit list of k-vectors and their weights (using a different keyword/data sequence than shown here), but this example takes advantage of an optional feature to automatically generate a simple k-point sample. The “kgrid ” keyword tells the code to generate a regular mesh in reciprocal space, and here we specify a 4x4x2 grid in the BZ. A k-sample with just the gamma-point would be specified as 0x0x0. The kgrid command generates this grid, and offsets this grid from the reciprocal space origin (i.e., the gamma point) by (1/2,1/2,1/2) in the reciprocal space mesh, i.e., the body-centered position.

The final, required statement in the setup phase section is the “end setup phase” line.

Run phase data

The next section begins with the line “run phase” and ends with the line “end run phase”, and allows you to modify parameters that affect the run (SCF) phase of the calculation. In this example, we modify the convergence criterion to be 0.0005. This criterion does NOT refer to the convergence of the energy in the SCF cycle, but rather refers to the maximum change in an Hamiltonian matrix element (integrals between basis functions over potentials). The value specified here will converge the total energy to roughly 1.d-6 Ry for this problem, but this will vary between different systems (e.g., a covalent system with a big energy gap will converge differently than a metallic system). Note that the convergence criterion is an optional parameter, and that the code will provide a default if you do not override it with this input.

do setup
do iters
no force
no relax
setup data
notes
 GaN bulk wurzite: a=6.13 bohr, c/a=1.630714474, GaN(Z)=3.755109729
end_notes
dimension of system (0=cluster ... 3=bulk)
 3
primitive lattice vectors
  5.308735725    -3.0650     0.000000000
  0.000000000     6.1300     0.000000000
  0.000000000     0.0000     9.996279726
grid dimensions
  24  24  36
atom types
  2
atom file
 n.atm
atom file
 ga.atm
number of atoms in unit cell
   4
atom, type, position vector
   1    1    3.539157150     0.0000     0.025788046
   2    2    1.769578575     3.0650     1.268818179
   3    1    1.769578575     3.0650     5.023927909
   4    2    3.539157150     0.0000     6.266958042
kgrid
 4 4 2
end setup phase data
run phase input data
convergence criterion
 0.000500
end run phase data

Bulk systems tutorial for SeqQuest: Hexagonal GaN

Introduction

Units

Input files

Example: A basic input file

Command options

Setup phase data

Run phase data

Hexagonal symmetries and BZ sampling

Picking a density functional (and spin)

Symmetry I: Point groups

Scaling functions I: global scaling

Scaling functions II: direction-specific

Shift coordinates

Symmetry II: non-symmorphic groups

SCF parameters

Atomic relaxation

Relaxation parameters

Lattice coordinates

Calculations with strain

Cell optimization

Aliasing atom types

Labeling atom names