Pseudo potentials
A pseudopotential is an approximation used in electronic structure calculations that replaces the strong Coulomb potential of the nucleus and the effect of tightly-bound core electrons with a weaker, effective potential acting only on the valence electrons . This approach is based on the chemical observation that core electrons are essentially "frozen" and do not participate in bonding, allowing the valence electrons to be described by smoother pseudo-wavefunctions . In Quantum ESPRESSO, a plane-wave pseudopotential code , this approximation is fundamental as it makes calculations computationally feasible by drastically reducing the required number of plane waves and eliminating the need to describe rapid wavefunction oscillations near the nucleus . The code supports modern norm-conserving and ultrasoft pseudopotentials, with ultrasoft types being particularly valuable as they allow for even lower plane-wave energy cutoffs, speeding up calculations without sacrificing accuracy.
You may try my Pseudos Web-App, where you can look for pseudopotentials by element name, and download them. Currently, Standard Solid State Pseudopotentials (SSSP) and GBRV pseudopotentials are included.
We can choose form various pseudopotential libraries. Choice of pseudopotential depends on the problem we are investigating, e.g., if there is a heavy element present in our system and we are interested in the spin-orbit coupling effects, we should choose a full relativistic pseudopotential. We need to be careful whether our chosen pseudopotential correctly reproduces physical properties. Various pseudopotential libraries:
- https://www.quantum-espresso.org/pseudopotentials
- https://www.materialscloud.org/discover/sssp/table/efficiency
- http://www.pseudo-dojo.org
- https://www.physics.rutgers.edu/gbrv/
- https://nninc.cnf.cornell.edu
- http://www.quantum-simulation.org/potentials/
- BLYP pseudopotentials
- SCAN pseudopotentials
Pseudopotential naming conventions in PSLibrary: an example pseudopotential
filename is O.rel-pbe-n-rrkjus_psl.1.0.0.UPF.
O → denotes the atomic species
rel → full relativistic (optional)
pbe → exchange correlation functional
n → non-linear core correction (optional)
rrkjus → pseudopotential type
Exchange correlation functionals:
| Identifier | Functional |
|---|---|
| pz | Perdew-Zunger (LDA) |
| pbe | Perdew-Burke-Ernzerhof (GGA) |
| pw91 | Perdew-Wang 91 (GGA) |
| blyp | Becke-Lee-Yang-Parr (GGA) |
Pseudopotential types:
| Identifier | PP types |
|---|---|
| ae | all-electron |
| rrkj | Rappe-Rabe-Kaxiras-Joannopoulos (Norm conserving) |
| rrkjus | Rappe-Rabe-Kaxiras-Joannopoulos (Ultrasoft) |
| kjpaw | Kresse-Joubert (PAW) |
Ultra soft pseudopotentials are computationally efficient than the norm
conserving pseudopotentials. You will find the recommended ecutwfc in the
header of each pseudopotential file. If you choose an ultra-soft
pseudopotential, you will need ecutrho about 8 times the value of ecutwfc.
The default ecutrho is 4 times ecutwfc in Quantum Espresso code, which is a
good choice for norm conserving pseudopotentials. You should check energy
convergence against ecutwfc for your system.
By using pseudopotential, we want to get rid of the core electrons that do not participate in the chemical properties of material. This is known also as rigid core approximation. Instead of accounting the nucleus and core electrons separately, we want to have a pseudopotential that interacts in a similar way with the valence electrons.
-
We can mix different types of pseudo potentials (e.g., norm conserving, ultra-soft, or PAW), but we cannot mix different exchange correlation functional (e.g., PBE and LDA). Exchange correlation functional can be read from the pseudopotential file or be provided via
input_dftparameter in Quantum Espresso. -
"sol" in PBE-sol stands for solid. For bulk systems PBE-sol should be used, while PBE is appropriate for molecules. In case of 2D materials generally PBE is chosen, but one can check PBE-sol.
If you mix PBE with PBE-sol type, it results in Error: conflicting values for
igcx. However, it is allowed to mix those two types of pseudo. We can set
desired exchange correlation functional via input_dft instead of reading from
the pseudopotential file.