Charge density due to doping atom in Si
This example shows how to use c2x to display the change in charge density caused by replacing an atom of Si with P in bulk silicon. The calculations are performed in Quantum Espresso, but Abinit, Castep, Siesta or VASP could have been used instead. The minimum version of c2x for this example is 2.40.
Running the calculations
The starting point was the eight atom silicon
si8.cell, given on
the crystals page. This was then
expanded to 2x2x2 64-atom supercell.
$ c2x -x=2x2x2 -Q --cell si8.cell si64.cell
By sorting the atomic co-ordinates (
-Q) it is easy to
edit the file to replace the central Si atom with P.
$ cp si64.cell si63p.cell $ emacs si63p.cell
Separate subdirectories were prepared for the two QE runs. The bulk Si run is the easiest.
run_si64$ c2x --qe ../si64.cell si64.in run_si64$ curl -o Si.UPF https://pseudopotentials.quantum-espresso.org/upf_files/Si.pbe-nl-rrkjus_psl.1.0.0.UPF run_si64$ pw.x -in si64.in > si64.log
The doped system is slightly harder, as QE defaults to assuming the
system is insulating, and does not switch automatically to partial
occupancies if there is an odd number of electrons. So one must edit
.in file produced by c2x and add to
SYSTEM namelist the lines:
occupations = 'smearing', degauss = 0.2,
So the full sequence is
run_si63p$ c2x --qe ../si63p.cell si63p.in run_si63p$ emacs si63p.in run_si63p$ curl -o Si.UPF https://pseudopotentials.quantum-espresso.org/upf_files/Si.pbe-nl-rrkjus_psl.1.0.0.UPF run_si63p$ curl -o P.UPF https://pseudopotentials.quantum-espresso.org/upf_files/P.pbe-nl-rrkjus_psl.1.0.0.UPF run_si63p$ pw.x -in si63p.in > si63p.log
Calculating the Density Difference
As the same cutoff was used in both calculations, the grid sizes are the same, and it suffices to use
$ c2x -cv --diff run_si63p/pwscf.xml run_si64/pwscf.xml diff.xsf [...] Found 3D data for Charge min=-0.0619541 max=0.330954 sum=69.9793 int=1
Had the grid sizes been different, it would have been necessary to
-i=0x0x0 to cause the coarser grid to be
interpolated to the finer.
Note that the integral of charge difference is a single electron, as expected, and the there are places where there is less charge than before, as well as places where there is more.
(The images below use XCrysDen. In order to show the bonds, it was necessary to increase the "connectivity factor" for Si using Modify|Atomic Radii|Chemical connectivity factor. It was set to 1.15.)
The charge density isosurface at 0.045e/A3 for P substitutionally doping Si in bulk Si. The extra charge (red) is localised around the single P atom at the centre of the image, and there is a slight reduction in charge (blue) in the bonds between the P and its Si neighbours.
The charge density isosurface at 0.010e/A3. Now it can be seen that the effect of the addition of the P is not entirely localised, but that all the Si-Si bonds have lost a small amount of charge. It would seem credible that this system is now conducting (which, of course, P-doped Si is).
The above is a demonstration of how to use c2x, not of how to do good science. No relaxation of the atoms around the phosphorous was performed, and no thought was given to convergence with respect to k-point density, basis set cut-off, or smearing width.