4.2. Standards and Reference Energies
Contents
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4.2.1. The MedeA Standard 500
MedeA uses a standard for Precision VASP
calculations, automatically applying the directive PREC = Accurate and a plane wave
cutoff of 500 eV (900 eV for hard potentials where the PAW potential
definition in the POTCAR file has ENMAX > 450 eV).
The MedeA VASP GUI option Standard 500 is recommended when an overall precise plane
cutoff and setting is required. Using a standard cutoff of
500 eV within a project facilitates the comparison
of data from compounds containing different elements like, e.g., in the
calculation of heat of formations or defect energies.
VASP parameters covered by Precision Standard 500 :
- VASP precision is set to accurate
- Planewave cutoff energy is set to 500 eV (900 eV for hard PAW potentials which have ENMAX > 450 eV)
VASP parameters recommended to be set in addition, to comply with
Standard 500 :
- Reciprocal space projection
- Convergence criterion for SCF cycle: 10-7 eV
- Convergence criterion for geometry optimization: 0.001 eV/\({\mathring{\mathrm{A}}}\)
- Conjugate gradient algorithm for geometry optimization
For crystalline structures:
- K-spacing of 0.2 \({\mathring{\mathrm{A}}}\)-1, shift origin to \({\Gamma}\)
- For non-local exchange based functionals (e.g. hybrid functionals): k-spacing of 0.5 \({\mathring{\mathrm{A}}}\)-1, shift origin to \({\Gamma}\), and set X, Y, and Z axis components of the k-mesh factors to 2
- K-space integration using the tetrahedron method including Bl\({\ddot{\mathrm o}}\)chl corrections
For molecular structures:
- Box ensuring a minimum of about 8 \({\mathring{\mathrm{A}}}\) empty space between the molecule and its nearest-images over the periodic boundary condition
- \({\Gamma}\)-point only
- K-space integration using Fermi smearing with a 0 eV smearing width
4.2.2. Reference Energies for the Calculation of the Heat of Formation
The computation of the electronic contribution to heats of formation for compounds requires reference energies for all constituent elements in their standard state. Below is a list of model structures for all elements in their standard state, which is applied for calculating the energy of formation as a property from the MedeA VASP 6 GUI. For a few cases, where, e.g., van der Waals interactions have to be included, the standard state structures are replaced by other structures that are correctly covered by standard DFT functionals. Correction energies are then used to obtain the energy of the standard state structures.
In structure optimization calculations for the reference systems, in general a non-magnetic Hamiltonian is used, however, spin-polarization is required for O2, Cr (antiferromagnetic), \({\gamma}\)-Mn (antiferromagnetic), Fe, Co, Ni, and lanthanides heavier than Ce for potentials including f electrons as valence states.
For solids, all cell parameters and internal degrees of freedom need to be relaxed. For atoms and molecules a fixed box of 10 \({\mathring{\mathrm{A}}}\) in each dimension is used (for S8 molecules a cubic box of 15 \({\mathring{\mathrm{A}}}\)), for molecules the atomic positions need to be relaxed.
For computing energies of formation, the application of the Standard 500 setting as outlined above is recommended to obtain a suitable accuracy.
| Elements | Structure | Correction, techn. details |
|---|---|---|
| H | H2 molecule | |
| He | He atom | |
| Li | bcc | |
| Be | \({\alpha}\)-Be, hcp | |
| B | \({\alpha}\)-B, R-3m | |
| C | diamond, Fd-3m | -1.897 kJ/mol, because graphite is the low temperature phase |
| N | N2 molecule | |
| O | O2 molecule | spin-polarized, because molecule exists in triplet state |
| F | F2 molecule | |
| N | Ne atom | |
| Na | bcc | |
| Mg | hcp | |
| Al | fcc | |
| Si | Fd-3m | |
| P | Cmca, black phosphorus | |
| S | S8 molecule | -13.04875 kJ/mol, condensation |
| Cl | Cl2 molecule | |
| Ar | Ar atom | |
| K | bcc | |
| Ca | \({\alpha}\)-Ca, fcc | |
| Sc | \({\alpha}\)-Sc, hcp | |
| Ti | \({\alpha}\)-Ti, hcp | |
| V | bcc | |
| Cr | \({\alpha}\)-Cr, bcc, antiferromagnetic | spin-polarized |
| Mn | \({\gamma}\)-Mn P4/mmm, antiferromagnetic | -4.348 kJ/mol = \({\alpha}\)-Mn, spin-polarized |
| Fe | \({\alpha}\)-Fe, bcc | spin-polarized |
| Co | \({\beta}\)-Co, hcp | spin-polarized |
| Ni | fcc | spin-polarized |
| Cu | fcc | |
| Zn | hcp | |
| Ga | \({\alpha}\)-Ga, Cmca | |
| Ge | Fd-3m | |
| As | R-3m | grey metallic |
| Se | P3121 | grey metallic |
| Br | Br2 molecule | -22.85 kJ/mol, condensation |
| Kr | Kr atom | |
| Rb | bcc | |
| Sr | \({\alpha}\)-Sr, fcc | |
| Y | hcp | |
| Zr | \({\alpha}\)-Zr, hcp | |
| Nb | bcc | |
| Mo | bcc | |
| Tc | hcp | |
| Ru | hcp | |
| Rh | fcc | |
| Pd | fcc | |
| Ag | fcc | |
| Cd | hcp | |
| In | I4/mmm | |
| Sn | \({\alpha}\)-Sn, Fd-3m | transition temperature of 286 K to \({\beta}\)-Sn, I41/amd |
| Sb | R-3m | |
| Te | P3121 | |
| I | Cmca | |
| Xe | Xe atom | |
| Cs | bcc | |
| Ba | bcc | |
| La | \({\alpha}\)-La, dhcp | |
| Ce | \({\gamma}\)-Ce, fcc | |
| Pr | dhcp | |
| Nd | dhcp | |
| Pm | dhcp | |
| Sm | R-3m | |
| Eu | bcc | |
| Gd | hcp | |
| Tb | hcp | |
| Dy | hcp | |
| Ho | hcp | |
| Er | hcp | |
| Tm | hcp | |
| Yb | fcc | |
| Lu | hcp | |
| Hf | hcp | |
| Ta | \({\alpha}\)-Ta, bcc | |
| W | \({\alpha}\)-W, bcc | |
| Re | hcp | |
| Os | hcp | |
| Ir | fcc | |
| Pt | fcc | |
| Au | fcc | |
| Hg | R-3m | 2.3 kJ/mol melting (JANAF) |
| Tl | \({\alpha}\)-Tl, hcp | |
| Pb | fcc | |
| Bi | R-3m | |
| Po | Pm-3m | |
| At | no structure | |
| Rn | Rn atom | |
| Fr | no structure | |
| Ra | bcc | |
| Ac | fcc | |
| Th | \({\alpha}\)-Th, fcc | |
| Pa | I4/mmm | |
| U | \({\alpha}\)-U, Cmcm | |
| Np | Pnma | |
| Pu | \({\alpha}\)-Pu, P121/m1 | |
| Am | dhcp | |
| Cm | dhcp |
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