# Ethylene ADF Frontier Orbital Comparison

Ethylene was built from SMILES `C=C`. The geometry was optimized once with a modest ADF GGA setup, then two ADF single-point calculations were run on the optimized geometry: PBE/DZP and B3LYP/DZP. Orbital energies are reported in eV.

## Job provenance

| Role | Method | Job directory | Justification |
|---|---|---|---|
| Geometry optimization | ADF/PBE/DZP | `01-run_workdir/ethylene_opt_pbe_dzp` | Optimized the ethylene geometry once from SMILES C=C. |
| GGA single point | ADF/PBE/DZP | `01-run_workdir/ethylene_sp_pbe_dzp` | Computed frontier orbital energies on the optimized geometry with the GGA setup. |
| Hybrid single point | ADF/B3LYP/DZP | `01-run_workdir/ethylene_sp_b3lyp_dzp` | Computed frontier orbital energies on the same optimized geometry with a hybrid functional. |

## Optimized geometry

The optimized C=C distance is 1.332 angstrom. The mean C-H distance is 1.092 angstrom.

![Optimized ethylene geometry](figures/optimized_ethylene.png)

## HOMO-LUMO comparison

| Method        |   HOMO (eV) |   LUMO (eV) |   Gap (eV) |   HOMO index |   LUMO index |
|:--------------|------------:|------------:|-----------:|-------------:|-------------:|
| ADF/PBE/DZP   |      -7.036 |      -1.235 |      5.801 |            6 |            7 |
| ADF/B3LYP/DZP |      -7.853 |      -0.292 |      7.561 |            6 |            7 |

## Frontier orbital energy windows

### ADF/PBE/DZP

| Orbital   |   Index |   Occupation |   Energy (eV) |
|:----------|--------:|-------------:|--------------:|
| HOMO-3    |       3 |        2.000 |       -11.754 |
| HOMO-2    |       4 |        2.000 |       -10.519 |
| HOMO-1    |       5 |        2.000 |        -8.797 |
| HOMO      |       6 |        2.000 |        -7.036 |
| LUMO      |       7 |        0.000 |        -1.235 |
| LUMO+1    |       8 |        0.000 |         0.886 |
| LUMO+2    |       9 |        0.000 |         2.018 |
| LUMO+3    |      10 |        0.000 |         2.059 |

### ADF/B3LYP/DZP

| Orbital   |   Index |   Occupation |   Energy (eV) |
|:----------|--------:|-------------:|--------------:|
| HOMO-3    |       3 |        2.000 |       -13.120 |
| HOMO-2    |       4 |        2.000 |       -11.871 |
| HOMO-1    |       5 |        2.000 |       -10.026 |
| HOMO      |       6 |        2.000 |        -7.853 |
| LUMO      |       7 |        0.000 |        -0.292 |
| LUMO+1    |       8 |        0.000 |         1.473 |
| LUMO+2    |       9 |        0.000 |         2.696 |
| LUMO+3    |      10 |        0.000 |         2.778 |

## Energy-level diagram

![Frontier orbital energy levels](figures/frontier_energy_levels.png)

## AMSreport orbital isosurfaces

These images were generated by `amsreport` from each single-point `adf.rkf` file.

| Method | HOMO | LUMO |
|---|---|---|
| ADF/PBE/DZP | ![PBE HOMO](figures/pbe_homo_amsreport.jpg) | ![PBE LUMO](figures/pbe_lumo_amsreport.jpg) |
| ADF/B3LYP/DZP | ![B3LYP HOMO](figures/b3lyp_homo_amsreport.jpg) | ![B3LYP LUMO](figures/b3lyp_lumo_amsreport.jpg) |

## Calculation inputs

### Geometry optimization: ADF/PBE/DZP

```ams
Task GeometryOptimization

System
  Atoms
              C       0.6644850805       0.0279879686      -0.0236852009
              C      -0.6644849893      -0.0279879318       0.0236851499
              H       1.2534332310      -0.8786144292       0.0702991539
              H       1.1670384263       0.9805640030      -0.1565753856
              H      -1.2534332920       0.8786143859      -0.0702991171
              H      -1.1670384566      -0.9805639965       0.1565753997
  End
  BondOrders
     1 2 2.0
     1 3 1.0
     1 4 1.0
     2 5 1.0
     2 6 1.0
  End
End

Engine ADF
  Basis
    Type DZP
  End
  NumericalQuality Basic
  XC
    GGA PBE
  End
EndEngine


```

### GGA single point: ADF/PBE/DZP

```ams
Properties
  OrbitalsInfo yes
End

Task SinglePoint

System
  Atoms
              C       0.6651665049       0.0281045107      -0.0235971144
              C      -0.6651713207      -0.0281053452       0.0236173947
              H       1.2802120569      -0.8698054143       0.0685226284
              H       1.1943503882       0.9738532541      -0.1567756217
              H      -1.2801922123       0.8698550678      -0.0682160798
              H      -1.1943654169      -0.9739020730       0.1564487929
  End
  BondOrders
     1 2 2.0
     1 3 1.0
     1 4 1.0
     2 5 1.0
     2 6 1.0
  End
End

Engine ADF
  Basis
    Type DZP
  End
  NumericalQuality Basic
  XC
    GGA PBE
  End
EndEngine


```

### Hybrid single point: ADF/B3LYP/DZP

```ams
Properties
  OrbitalsInfo yes
End

Task SinglePoint

System
  Atoms
              C       0.6651665049       0.0281045107      -0.0235971144
              C      -0.6651713207      -0.0281053452       0.0236173947
              H       1.2802120569      -0.8698054143       0.0685226284
              H       1.1943503882       0.9738532541      -0.1567756217
              H      -1.2801922123       0.8698550678      -0.0682160798
              H      -1.1943654169      -0.9739020730       0.1564487929
  End
  BondOrders
     1 2 2.0
     1 3 1.0
     1 4 1.0
     2 5 1.0
     2 6 1.0
  End
End

Engine ADF
  Basis
    Type DZP
  End
  NumericalQuality Basic
  XC
    Hybrid B3LYP
  End
EndEngine


```

## Conclusion

With this modest DZP setup, the B3LYP single point increases the HOMO-LUMO gap from 5.801 eV for PBE to 7.561 eV. The increase is mainly from a lower HOMO and a higher LUMO relative to the PBE values.