Example system: IrIn₃

In this example, we're going to demonstrate a DFT-raMO run for an intermetallic binary compound in the iridium-indium system, using data from a VASP 4.6 calculation. This example will follow the scheme outlined in this paper.

Setup

Assuming that you have Julia and DFTraMO.jl installed, download the IrIn₃ VASP 4.6 data, a link to which will be provided in the future. This includes the following files:

• KPOINTS
• OUTCAR
• POSCAR
• POTCAR
• WAVECAR
• step1.yaml - the DFT-raMO input file.
• qdftramo and qdftramo-kestrel - submission scripts for internal use, can be adapted.
• step2.tar
• step3.tar
• step4.tar - tarballs for later steps in the tutorial.

1. Ir $d_{x^2+y^2}$ orbitals

Constructing the YAML input

You'll find that step1.yaml is a blank template. The Usage section of the manual contains information on each of the keys and values in the file.

Since we're starting from scratch, the checkpoint key should be blank. Leave auto_psphere as true, as this will automatically rerun poor reconstructions (less than 15% of the maximum $P_{sphere}$ value).

For the first run, let's reconstruct the Ir $d_{x^2+y^2}$ orbitals, so set type to dx2y2 and sites to Ir. site_file and radius can be blank, as these are not used for AO type runs. For rsphere, as a rule of thumb, you can use the distance from the reconstruction site to the farthest atom in the first coordination sphere, which is 2.65 Å in this case. This does not have to be precise, and overshooting is generally better than undershooting.

The name field can be set at your convenience (here we use 1_Ir_dx2y2) and becomes the name of the directory where the outputs are written.

Your step1.yaml file should look as below:

checkpoint:
auto_psphere: true
runs:
  - name: 1_Ir_dx2y2
    type: dx2y2
    site_file: 
    sites: Ir
    radius:
    rsphere: 2.65

Running DFT-raMO for the first time

In the directory you extracted the tarball, run julia, use the DFTraMO.jl package, and start the run:

julia> using DFTraMO

julia> dftramo_run("step1.yaml")

You should see the beginnings of the DFT-raMO analysis printed to the terminal.

No checkpoint file specified. Run will start from beginning conditions.
Auto-Psphere: true
Number of runs: 1
Run 1:
   name: 1_Ir_dx2y2
   type: dx2y2
   sites: Ir
   rsphere: 2.65 Å
Run: 1_Ir_dx2y2
1, Psphere: 0.905 at site [2.417, 2.417, 0.000]

[ Info: UnicodePlots not loaded: consider loading it for Psphere logging.

Examining the output

After dftramo_run() is finished, you should see lines of $P_{sphere}$ values printed to the terminal.

1, Psphere: 0.905 at site [2.417, 2.417, 0.000]

• 1 - the raMO number in the sequence.
• 0.905 - $P_{sphere}$ value.
• [2.417, 2.417, 0.000] - the site (in Cartesian coordinates) that $P_{sphere}$ is centered on.

The value of $P_{sphere}$ indicates the degree of localization of that raMO function. Though higher values indicate more localization, recall that our setting of rsphere was an arbitrary and estimated value. What is more valuable is the consistency of the $P_{sphere}$ values. Here, the consistent values indicates that the Ir $d_{x^2+y^2}$ orbitals are fully occupied.

See Theory for more details on $P_{sphere}$.

If you check your working directory now, you should see a directory with the name you specified in step1.yaml. Within this directory are four types of files:

1. *.chkpt - checkpoint at that step in the raMO sequence
2. *.raMO - reciprocal space coefficients for the raMO
3. *.xsf - real space electron density grid of the raMO in the supercell
4. *_psphere_*.txt - $P_{sphere}$ information

The .xsf files allow us to visually inspect the raMO functions with software such as VESTA.

2. Ir-Ir isolobal bonds with $sp$ hybrids

Before we reconstruct $sp$-based hybrids, we want to reconstruct all of the Ir $d$ and $s$ orbitals. Skip ahead in the analysis by untarring the step2.tar file, which contains all of the necessary reconstructions.

tar -xf step2.tar

This next section of the raMO sequence will target Ir-Ir isolobal bonding. We want to create multi-center bonding functions between pairs of Ir atoms, with expected contribution from bridging In atoms. For this, we will use the sp type run, which searches for atoms within a specified radius from a central site and creates a target where $s$ and $p$ orbitals are oriented towards the central site.

For this next run, create a new YAML input (step2.yaml) with the following lines:

checkpoint: 6_Ir_s/6_Ir_s_192_192.chkpt
auto_psphere: true
runs:
  - name: 7_Ir-Ir
    type: sp
    site_file: Ir-Ir.txt
    sites: all
    radius: 1.6
    rsphere: 3.5

Our previous analysis ended at the 192nd raMO in the sequence, and we have 192 electrons remaining, (explaining the occurrence of 192 twice in the name of the checkpoint file). The radius parameter is the search radius for automatically including atoms in the target.

The Ir-Ir.txt site file should contain the midpoints of the Ir-Ir bonds in Cartesian coordinates. This can be done by using your preferred molecular modeling software (we've done this by converting the POSCAR to a CIF and adding the dummy atoms into Diamond 3). However, if you'd like to skip the manual creation, the contents of Ir-Ir.txt are given below:

X	  6.99330	  6.99330	 10.78620
X	  0.00000	  6.99330	 10.78620
X	  6.99330	  0.00000	 10.78620
X	  0.00000	  0.00000	 10.78620
X	  6.99330	  6.99330	  3.59540
X	  6.99330	  0.00000	  3.59540
X	  0.00000	  0.00000	  3.59540
X	 10.48995	 10.48995	  7.19080
X	  3.49665	 10.48995	  7.19080
X	 10.48995	  3.49665	  7.19080
X	  0.00000	  6.99330	  3.59540
X	  3.49665	  3.49665	  7.19080
X	 10.48995	 10.48995	  0.00000
X	  3.49665	 10.48995	  0.00000
X	 10.48995	  3.49665	  0.00000
X	  3.49665	  3.49665	  0.00000

The symbol X can be changed arbitrarily.

Now that you have these files, you can just run DFT-raMO again:

julia> dftramo_run("step2.yaml")

As before, have a look at the $P_{sphere}$ values and XSF files to see the reconstructions and validate the electronic assignment.

3. Ir p orbitals with LCAO reconstructions

When working with orbitals with nonzero orbital angular momentum ($p$, $d$, $f$ orbitals) it may be desirable to construct an orbital with an orientation or shape that is not aligned with the coordinate system. To solve this issue, we can use linear combinations of atomic orbitals (LCAOs). LCAOs may also be used to create molecular or multi-center bonding functions, i.e. π-bonding.

To skip to the next step, untar step3.tar in your working directory. You should find two new input files, lcao1.yaml and lcao2.yaml. The contents of lcao1.yaml are given below:

target:
  - px: -1
    py: 1
lcao:
  - [1]
  - [2]
  - [17]
  - [18]
  - [33]
  - [34]
  - [49]
  - [50]
  - [65]
  - [66]
  - [81]
  - [82]
  - [97]
  - [98]
  - [113]
  - [114]

As before, the description of the LCAO sites file is given in the Usage section.

Note that lcao2.yaml file contains reconstructions with different orientations ($p_x$ is positive).

The step3.yaml file contains the information for the LCAO reconstruction, and references both lcao1.yaml and lcao2.yaml for each run. Its contents are below:

checkpoint: 8_Ir_pz/8_Ir_pz_240_96.chkpt
auto_psphere: true
runs:
  - name: 9_Ir_p_pi1
    type: lcao
    site_file: lcao1.yaml
    sites: all
    radius:
    rsphere: 2.65
  - name: 10_Ir_p_pi2
    type: lcao
    site_file: lcao2.yaml
    sites: all
    radius:
    rsphere: 2.65

Run step3.yaml and inspect the $P_{sphere}$ values and XSF files.

julia> dftramo_run("step3.yaml")

4. Remainder analysis of In cage states and In $p$ orbitals

As you complete your DFT-raMO runs, you'll find that the $P_{sphere}$ values of the reconstructed orbitals tends to decrease. To visualize this, untar step4.tar and look at the log for run 11, found at 11_In-In/11_In-In_psphere_4.73.txt:

273     0.6474487830205945       at site [10.490, 3.497, 3.595]
274     0.6429286864719969       at site [0.000, 6.993, 7.191]
275     0.6116188776692522       at site [3.497, 10.490, 3.595]
276     0.6382205090625862       at site [10.490, 10.490, 3.595]
277     0.6504732377051952       at site [6.993, 6.993, 7.191]
278     0.5981010110158822       at site [3.497, 3.497, 10.786]
279     0.5871384506957702       at site [10.490, 3.497, 10.786]
280     0.5162750706706059       at site [3.497, 10.490, 10.786]
281     0.33634765527327326      at site [10.490, 10.490, 10.786]
282     0.6434855799801233       at site [0.000, 0.000, 0.000]
283     0.6433852489950562       at site [6.993, 0.000, 0.000]
284     0.5527474698233648       at site [0.000, 6.993, 0.000]
285     0.49587592534638286      at site [6.993, 6.993, 0.000]
286     0.40417825671730373      at site [0.000, 0.000, 7.191]
287     0.16723350141820606      at site [6.993, 0.000, 7.191]
288     0.1572312564858335       at site [3.497, 3.497, 3.595]

We find that $Psphere$ drops precipitously at some points in this run (raMOs 281, 286-288). In order to complete the analysis, we need to open the XSF files to inspect the character of the raMO functions more closely. For reference and throughness, it is recommended to inspect the raMO functions directly preceding these (raMOs 280, 285).

Upon inspection of these raMOs, we come to the following conclusions:

• raMOs 280, 281, and 286 show delocalization but expected character, so electrons are allocated to these runs.
• raMOs 287 and 288 show delocalization and unexpected p-like character on the In atoms. Electrons are not assigned to these raMOs and the functions are returned to the basis set. However, the $p$-like character informs our next target, as raMO functions are orthogonal to each other.

For the final run, we now target the In $p$ orbitals. Create the last input file, step4.yaml:

checkpoint: 11_In-In/11_In-In_286_4.chkpt
auto_psphere: true
runs:
  - name: 12.1_In_px
    type: px
    site_file: 
    sites: In 1
    radius:
    rsphere: 3.2
  - name: 12.2_In_py
    type: py
    site_file: 
    sites: In 1
    radius:
    rsphere: 3.2
  - name: 12.3_In_pz
    type: pz
    site_file: 
    sites: In 1
    radius:
    rsphere: 3.2

Run DFT-raMO.

julia> dftramo_run("step4.yaml")

The $P_{sphere}$ values are still low, but this is expected. Isosurfaces in the XSFs show delocalized $p$-like functions throughout the In atoms in the cell.