# Graphite c-axis PES scans with QuantumESPRESSO

This report combines two non-optimizing PES scan segments per functional for graphite, scanning the c lattice parameter and plotting the relative energy against the interlayer distance c/2.

## Conclusion

All curves are referenced to the energy at the longest sampled c value for each functional. The plot order is the reverse order of minimum energy so the legend follows the visible stacking order of the plotted curves.

## Relative-energy plot

![Relative energy versus interlayer distance](relative_energy_vs_interlayer_distance.png)

## Summary table

| Functional                  |   Min at c/2 (A) |   Min rel. energy (meV/atom) |   Ref. point c/2 (A) |
|:----------------------------|-----------------:|-----------------------------:|---------------------:|
| r2SCAN-D4 / Dojo            |         3.350000 |                   -57.165492 |             8.000000 |
| B86bPBE-XDM / pslibrary-PAW |         3.350000 |                   -53.810884 |             8.000000 |
| r2SCAN / Dojo               |         3.550000 |                   -20.923848 |             8.000000 |
| PBE / pslibrary-PAW         |         4.250000 |                    -1.820954 |             8.000000 |

## Provenance

- `pbe_psl_paw_seg1`: Short-range scan for PBE with pslibrary-PAW.
- `pbe_psl_paw_seg2`: Long-range continuation for PBE with pslibrary-PAW.
- `b86bpbe_xdm_psl_paw_seg1`: Short-range scan for B86bPBE with QE XDM dispersion and pslibrary-PAW.
- `b86bpbe_xdm_psl_paw_seg2`: Long-range continuation for B86bPBE with QE XDM dispersion and pslibrary-PAW.
- `r2scan_dojo_seg1`: Short-range scan for r2SCAN with Dojo pseudopotentials.
- `r2scan_dojo_seg2`: Long-range continuation for r2SCAN with Dojo pseudopotentials.
- `r2scan_d4_dojo_seg1`: Short-range scan for r2SCAN with Dojo pseudopotentials and the AMS D4 add-on.
- `r2scan_d4_dojo_seg2`: Long-range continuation for r2SCAN with Dojo pseudopotentials and the AMS D4 add-on.

## Calculation inputs

### `pbe_psl_paw_seg1`

Reason: Short-range scan for PBE with pslibrary-PAW.

```ams
PESScan
  CalcPropertiesAtPESPoints no
  Optimize no
  ScanCoordinate
    LatticeCRange 6 9
    nPoints 31
  End
End

Task PESScan

System
  Atoms
              C       0.0000000000       0.0000000000       1.5000000000
              C       0.0000000000       0.0000000000       4.5000000000
              C       0.0000000000       1.4202816622       1.5000000000
              C       1.2300000000       0.7101408311       4.5000000000
  End
  Lattice
         2.4600000000     0.0000000000     0.0000000000
        -1.2300000000     2.1304224933     0.0000000000
         0.0000000000     0.0000000000     6.0000000000
  End
End

Engine QuantumESPRESSO
  K_Points automatic
     12 12 4 0 0 0
  End
  Pseudopotentials
    Family pslibrary-PAW
    Functional PBE
  End
  System
    degauss 0.001
    ecutrho 1000.0
    ecutwfc 100.0
    input_dft pbe
    occupations Smearing
    smearing Gaussian
  End
EndEngine
```
### `pbe_psl_paw_seg2`

Reason: Long-range continuation for PBE with pslibrary-PAW.

```ams
PESScan
  CalcPropertiesAtPESPoints no
  Optimize no
  ScanCoordinate
    LatticeCRange 9 16
    nPoints 15
  End
End

Task PESScan

System
  Atoms
              C       0.0000000000       0.0000000000       1.5000000000
              C       0.0000000000       0.0000000000       4.5000000000
              C       0.0000000000       1.4202816622       1.5000000000
              C       1.2300000000       0.7101408311       4.5000000000
  End
  Lattice
         2.4600000000     0.0000000000     0.0000000000
        -1.2300000000     2.1304224933     0.0000000000
         0.0000000000     0.0000000000     6.0000000000
  End
End

Engine QuantumESPRESSO
  K_Points automatic
     12 12 4 0 0 0
  End
  Pseudopotentials
    Family pslibrary-PAW
    Functional PBE
  End
  System
    degauss 0.001
    ecutrho 1000.0
    ecutwfc 100.0
    input_dft pbe
    occupations Smearing
    smearing Gaussian
  End
EndEngine
```
### `b86bpbe_xdm_psl_paw_seg1`

Reason: Short-range scan for B86bPBE with QE XDM dispersion and pslibrary-PAW.

```ams
PESScan
  CalcPropertiesAtPESPoints no
  Optimize no
  ScanCoordinate
    LatticeCRange 6 9
    nPoints 31
  End
End

Task PESScan

System
  Atoms
              C       0.0000000000       0.0000000000       1.5000000000
              C       0.0000000000       0.0000000000       4.5000000000
              C       0.0000000000       1.4202816622       1.5000000000
              C       1.2300000000       0.7101408311       4.5000000000
  End
  Lattice
         2.4600000000     0.0000000000     0.0000000000
        -1.2300000000     2.1304224933     0.0000000000
         0.0000000000     0.0000000000     6.0000000000
  End
End

Engine QuantumESPRESSO
  K_Points automatic
     12 12 4 0 0 0
  End
  Pseudopotentials
    Family pslibrary-PAW
    Functional PBE
  End
  System
    degauss 0.001
    ecutrho 1000.0
    ecutwfc 100.0
    input_dft b86bpbe
    occupations Smearing
    smearing Gaussian
    vdw_corr XDM
  End
EndEngine
```
### `b86bpbe_xdm_psl_paw_seg2`

Reason: Long-range continuation for B86bPBE with QE XDM dispersion and pslibrary-PAW.

```ams
PESScan
  CalcPropertiesAtPESPoints no
  Optimize no
  ScanCoordinate
    LatticeCRange 9 16
    nPoints 15
  End
End

Task PESScan

System
  Atoms
              C       0.0000000000       0.0000000000       1.5000000000
              C       0.0000000000       0.0000000000       4.5000000000
              C       0.0000000000       1.4202816622       1.5000000000
              C       1.2300000000       0.7101408311       4.5000000000
  End
  Lattice
         2.4600000000     0.0000000000     0.0000000000
        -1.2300000000     2.1304224933     0.0000000000
         0.0000000000     0.0000000000     6.0000000000
  End
End

Engine QuantumESPRESSO
  K_Points automatic
     12 12 4 0 0 0
  End
  Pseudopotentials
    Family pslibrary-PAW
    Functional PBE
  End
  System
    degauss 0.001
    ecutrho 1000.0
    ecutwfc 100.0
    input_dft b86bpbe
    occupations Smearing
    smearing Gaussian
    vdw_corr XDM
  End
EndEngine
```
### `r2scan_dojo_seg1`

Reason: Short-range scan for r2SCAN with Dojo pseudopotentials.

```ams
PESScan
  CalcPropertiesAtPESPoints no
  Optimize no
  ScanCoordinate
    LatticeCRange 6 9
    nPoints 31
  End
End

Task PESScan

System
  Atoms
              C       0.0000000000       0.0000000000       1.5000000000
              C       0.0000000000       0.0000000000       4.5000000000
              C       0.0000000000       1.4202816622       1.5000000000
              C       1.2300000000       0.7101408311       4.5000000000
  End
  Lattice
         2.4600000000     0.0000000000     0.0000000000
        -1.2300000000     2.1304224933     0.0000000000
         0.0000000000     0.0000000000     6.0000000000
  End
End

Engine QuantumESPRESSO
  K_Points automatic
     12 12 4 0 0 0
  End
  Pseudopotentials
    Family Dojo
    Functional PBE
  End
  System
    degauss 0.001
    ecutrho 1000.0
    ecutwfc 100.0
    input_dft r2scan
    occupations Smearing
    smearing Gaussian
  End
EndEngine
```
### `r2scan_dojo_seg2`

Reason: Long-range continuation for r2SCAN with Dojo pseudopotentials.

```ams
PESScan
  CalcPropertiesAtPESPoints no
  Optimize no
  ScanCoordinate
    LatticeCRange 9 16
    nPoints 15
  End
End

Task PESScan

System
  Atoms
              C       0.0000000000       0.0000000000       1.5000000000
              C       0.0000000000       0.0000000000       4.5000000000
              C       0.0000000000       1.4202816622       1.5000000000
              C       1.2300000000       0.7101408311       4.5000000000
  End
  Lattice
         2.4600000000     0.0000000000     0.0000000000
        -1.2300000000     2.1304224933     0.0000000000
         0.0000000000     0.0000000000     6.0000000000
  End
End

Engine QuantumESPRESSO
  K_Points automatic
     12 12 4 0 0 0
  End
  Pseudopotentials
    Family Dojo
    Functional PBE
  End
  System
    degauss 0.001
    ecutrho 1000.0
    ecutwfc 100.0
    input_dft r2scan
    occupations Smearing
    smearing Gaussian
  End
EndEngine
```
### `r2scan_d4_dojo_seg1`

Reason: Short-range scan for r2SCAN with Dojo pseudopotentials and the AMS D4 add-on.

```ams
EngineAddons
  D4Dispersion
    Enabled yes
    Functional R2SCAN
  End
End

PESScan
  CalcPropertiesAtPESPoints no
  Optimize no
  ScanCoordinate
    LatticeCRange 6 9
    nPoints 31
  End
End

Task PESScan

System
  Atoms
              C       0.0000000000       0.0000000000       1.5000000000
              C       0.0000000000       0.0000000000       4.5000000000
              C       0.0000000000       1.4202816622       1.5000000000
              C       1.2300000000       0.7101408311       4.5000000000
  End
  Lattice
         2.4600000000     0.0000000000     0.0000000000
        -1.2300000000     2.1304224933     0.0000000000
         0.0000000000     0.0000000000     6.0000000000
  End
End

Engine QuantumESPRESSO
  K_Points automatic
     12 12 4 0 0 0
  End
  Pseudopotentials
    Family Dojo
    Functional PBE
  End
  System
    degauss 0.001
    ecutrho 1000.0
    ecutwfc 100.0
    input_dft r2scan
    occupations Smearing
    smearing Gaussian
  End
EndEngine
```
### `r2scan_d4_dojo_seg2`

Reason: Long-range continuation for r2SCAN with Dojo pseudopotentials and the AMS D4 add-on.

```ams
EngineAddons
  D4Dispersion
    Enabled yes
    Functional R2SCAN
  End
End

PESScan
  CalcPropertiesAtPESPoints no
  Optimize no
  ScanCoordinate
    LatticeCRange 9 16
    nPoints 15
  End
End

Task PESScan

System
  Atoms
              C       0.0000000000       0.0000000000       1.5000000000
              C       0.0000000000       0.0000000000       4.5000000000
              C       0.0000000000       1.4202816622       1.5000000000
              C       1.2300000000       0.7101408311       4.5000000000
  End
  Lattice
         2.4600000000     0.0000000000     0.0000000000
        -1.2300000000     2.1304224933     0.0000000000
         0.0000000000     0.0000000000     6.0000000000
  End
End

Engine QuantumESPRESSO
  K_Points automatic
     12 12 4 0 0 0
  End
  Pseudopotentials
    Family Dojo
    Functional PBE
  End
  System
    degauss 0.001
    ecutrho 1000.0
    ecutwfc 100.0
    input_dft r2scan
    occupations Smearing
    smearing Gaussian
  End
EndEngine
```