--Opium-- tutorial

Lesson 0 : Hydrogen - basic operation
The rest of the tutorials are in pdf form for now:
Lesson 1 : Carbon - next steps
Lesson 2 : Aluminum - transferability
Lesson 3 : Copper - ghost states, local potential
Lesson 4 : Titanium - semicore states
Lesson 5 : Iron - core correction
Lesson 6 : Platinum - scalar relativistic potential

Hydrogen

Getting help Using the following param file, h.param we will go through the construction of a hydrogen pseudopotential. The first thing to note is that entering "opium -h" or just "opium" with no argument will display a help screen:

<~/prompt->./opium -h ===========================Opium help============================ version: 1.0.2 ================================================================= usage: opium <parameterfile> <logfile> <command line options> Opium can be executed interactively or non-interactively To enter an interactive session just enter: opium <parameterfile> <logfile> In an interactive session... enter "comm" for command line help enter "plot" for plotting help enter "keys" for keyblock help To run Opium non-interactively enter: opium <parameterfile> <logfile> <commands> In a non-interactive session... enter "opium -c" or "opium comm" for command line help enter "opium -p" or "opium plot" for plotting help enter "opium -k" or "opium keys" for keyblock help =================================================================

Command, keyblock, and plotting help can also be obtained via the command-line.

Constructing the parameter file

Before continuing, lets analyze the parameter file:

[Atom] H 1 100 1.00 - [Pseudo] 1 1.80 opt [Optinfo] 3.00 4 [Configs] 3 100 0.75 - 100 0.50 - 100 0.35 -

The [Atom] keyblock indicates that the atomic symbol is 'H' for hydrogen, that there is one orbital, and this orbital is "1s" with occupation 1.0. The "-" means that an eigenvalue guess should be generated by Opium. The configuration specified in the [Atom] keyblock is the reference configuration . It is used to construct the pseudopotential and will reproduce the valence electron properties of the all-electron atom in this configuration.

The [Pseudo] keyblock lists the number of valence orbitals, 1, and the cut-off radius ("rc") for the pseudopotential (here 1.80 au). Also, opt indicates that we want to use the optimized pseudopotential method.

The [Optinfo] keyblock is used to indicate the inputs necessary for the optimized pseudopotential method. These are the cut-off wavevector ("qc") and the number of bessel fucntions used in the pseudopotential construction.

The last keyblock is the [Configs] section. This keyblock contains the number of test configurations and their definitions. Here we are testing the gradual removal of the 1s electron.

Creating the hydrogen pseudopotential

Now, the hydrogen pseudopotential can be generated and tested via this command line:

<~/prompt->./opium h h.log ae ps nl tc rpt

This runs the all-electron (ae), pseudopotential generation (ps), non-local calculation (nl) and configuration testing (tc). The rpt command indicates that the results should be summarized in a report file.

Running the command generates the 'h.log' and 'h.rpt' files. The h.log file contains all of the output from the commands and indicates any errors or warnings. It is important to look through the log file for any errors.

For such a simple system, there are no problems in the log, so we can concentrate on the report file.

The first problem to notice in the report file is the size of the convergence error :

### PS report ######################################## Orbital Conv. error: [mRy/e] [mRy] [meV] Ghost -------------------------------------------------------------------------- 100 18.5486952500 18.5486952500 252.3698378324 no Tot. error = 18.5486952500 252.3698378324

The convergence error is much too large. This states that this pseudopotential would have on the order of 250 meV when run at a converged cut-off energy. This potential is being designed and tested at a 9.0 Ry cut-off energy ('qc'^2 == Ecut). We need to reduce the convergence energy before proceeding.

There are two direct ways to reduce the convergence error, by increasing rc or qc. Increasing rc leads to a less transferable potential, while increasing qc leads to a larger cut-off energy. So, lets plot the all-electron wavefunctions and see where rc is relative to to the 1s peak.

The cut-off radius is at 1.80 au and is pretty far from the peak. Therefore, it is probably better to increase qc.

Increasing qc to 4.75 gives the following result:

### PS report ######################################## Orbital Conv. error: [mRy/e] [mRy] [meV] Ghost -------------------------------------------------------------------------- 100 0.1718933923 0.1718933923 2.3387471167 no Tot. error = 0.1718933923 2.3387471167

A convergence error of 2 meV/atom is a significant improvement over 252 meV/atom. Of course, qc could be increased further if even higher accuracy is desired.

Now that the convergence error is fixed, we can now analyze the transferability. Here, we list the lines that begin with 'AE-NL' which is the difference between the all-electron and psuedopotential results:

AE-NL:Orbital Filling Eigenvalues[mRy] Norm[1e-3] AE-NL- -------------------------------------------------------------- AE-NL- 100 0.750 -0.9201432489 -1.4704986312 AE-NL- total error = 0.9201432489 1.4704986312 AE-NL:Orbital Filling Eigenvalues[mRy] Norm[1e-3] AE-NL- -------------------------------------------------------------- AE-NL- 100 0.500 -3.2455119043 -3.2095046059 AE-NL- total error = 3.2455119043 3.2095046059 AE-NL:Orbital Filling Eigenvalues[mRy] Norm[1e-3] AE-NL- -------------------------------------------------------------- AE-NL- 100 0.350 -5.3718978139 -4.2422160466 AE-NL- total error = 5.3718978139 4.2422160466 AE-NL- i j DD[mRy] DD[meV] AE-NL- ------------------------------------------ AE-NL- 0 1 -0.090566 -1.232220 AE-NL- 0 2 -0.578335 -7.868648 AE-NL- 0 3 -1.218700 -16.581266 AE-NL- 1 2 -0.487768 -6.636428 AE-NL- 1 3 -1.128133 -15.349046 AE-NL- 2 3 -0.640365 -8.712618

The transferability is quite good, but if we wanted to make it better, we could try by reducing rc. Lets pull it back to 1.4 au and retest the transferability:

AE-NL:Orbital Filling Eigenvalues[mRy] Norm[1e-3] AE-NL- -------------------------------------------------------------- AE-NL- 100 0.750 -0.3792913715 -0.7511997938 AE-NL- total error = 0.3792913715 0.7511997938 AE-NL:Orbital Filling Eigenvalues[mRy] Norm[1e-3] AE-NL- -------------------------------------------------------------- AE-NL- 100 0.500 -1.3891149867 -1.7356415420 AE-NL- total error = 1.3891149867 1.7356415420 AE-NL:Orbital Filling Eigenvalues[mRy] Norm[1e-3] AE-NL- -------------------------------------------------------------- AE-NL- 100 0.350 -2.3418063212 -2.3655590767 AE-NL- total error = 2.3418063212 2.3655590767 AE-NL- i j DD[mRy] DD[meV] AE-NL- ------------------------------------------ AE-NL- 0 1 -0.036849 -0.501362 AE-NL- 0 2 -0.242634 -3.301207 AE-NL- 0 3 -0.519554 -7.068902 AE-NL- 1 2 -0.205785 -2.799844 AE-NL- 1 3 -0.482705 -6.567539 AE-NL- 2 3 -0.276920 -3.767695

Now the transferability is even better. But, remember, making rc smaller makes a harder pseudopotential which requires a larger qc. Lets recheck the convergence error:

### PS report ######################################## Orbital Conv. error: [mRy/e] [mRy] [meV] Ghost -------------------------------------------------------------------------- 100 1.9344081672 1.9344081672 26.3191706410 no Tot. error = 1.9344081672 26.3191706410

As suspected, the smaller rc increases the convergence error. So, we can increase qc again to get back to a reasonable level of convergence. Lets try 4.75:

Pretty good, but how is the transferability?:

AE-NL:Orbital Filling Eigenvalues[mRy] Norm[1e-3] AE-NL- -------------------------------------------------------------- AE-NL- 100 0.750 -0.3178702858 -0.6330880156 AE-NL- total error = 0.3178702858 0.6330880156 AE-NL:Orbital Filling Eigenvalues[mRy] Norm[1e-3] AE-NL- -------------------------------------------------------------- AE-NL- 100 0.500 -1.1673939074 -1.4641105002 AE-NL- total error = 1.1673939074 1.4641105002 AE-NL:Orbital Filling Eigenvalues[mRy] Norm[1e-3] AE-NL- -------------------------------------------------------------- AE-NL- 100 0.350 -1.9696295215 -1.9959511662 AE-NL- total error = 1.9696295215 1.9959511662 AE-NL- i j DD[mRy] DD[meV] AE-NL- ------------------------------------------ AE-NL- 0 1 -0.030837 -0.419562 AE-NL- 0 2 -0.203612 -2.770278 AE-NL- 0 3 -0.436448 -5.938186 AE-NL- 1 2 -0.172774 -2.350716 AE-NL- 1 3 -0.405611 -5.518624 AE-NL- 2 3 -0.232837 -3.167908

Very good! This potential is ready to be written to a file. Lets use the .fhi format:

<~/prompt->./opium all fhi rpt

The command "all" is an abbreviation for "ae ps nl tc " and we repeat all of the steps to ensure that all steps of the generation and testing are in the log and report file and to make sure that no steps were skipped.

Last updated: Apr 10, 2018