# ADF optimization and vibrational analysis of formaldehyde

## Calculation

Formaldehyde was built from the SMILES string `C=O`, symmetrized, and optimized as a neutral closed-shell molecule. The optimized structure has C(2V) symmetry. ADF used PBE-D3(BJ), the all-electron DZP basis, and default numerical and SCF settings. Harmonic normal modes and IR intensities were calculated at the final optimized geometry.

Job directory: `01-run_workdir/formaldehyde_adf_pbe_dzp`

Provenance: Combined ADF geometry optimization, harmonic frequencies, IR intensities, and PES-point characterization.

## Optimized geometry

| Quantity   |      Value | Unit     |
|:-----------|-----------:|:---------|
| C=O        |   1.212143 | angstrom |
| C-H(1)     |   1.115562 | angstrom |
| C-H(2)     |   1.115562 | angstrom |
| mean C-H   |   1.115562 | angstrom |
| H-C-H      | 115.943895 | degree   |

![Optimized formaldehyde structure](figures/optimized_structure.png)

## Minimum verification

AMS PES-point classification: `local minimum`.

Negative harmonic frequencies: 0.

The optimized formaldehyde structure is a local minimum. AMS classified the PES point as local minimum, and all 6 vibrational frequencies are positive.

## Vibrational modes

The assignments use changes in C=O distance, the two C-H distances, H-C-H angle, and displacement normal to the molecular plane. They are qualitative harmonic-mode descriptions.

|   Mode |   Frequency (cm^-1) |   IR intensity (km mol^-1) | Symmetry   | Qualitative assignment    |
|-------:|--------------------:|---------------------------:|:-----------|:--------------------------|
|      1 |             1157.06 |                      4.682 | B1         | CH2 out-of-plane bend     |
|      2 |             1226.38 |                      8.786 | B2         | CH2 in-plane rocking bend |
|      3 |             1487.73 |                     14.647 | A1         | H-C-H scissoring bend     |
|      4 |             1743.28 |                     88.378 | A1         | C=O stretch               |
|      5 |             2797.14 |                     60.003 | A1         | symmetric C-H stretch     |
|      6 |             2850.66 |                    133.912 | B2         | asymmetric C-H stretch    |

## Broadened IR spectrum

The blue curve applies Gaussian broadening with a width of 20 cm^-1 to the calculated sticks. Red lines mark the unbroadened modes. The wavenumber axis follows the usual IR convention.

![Broadened harmonic IR spectrum](figures/ir_spectrum.png)

## Normal-mode displacement pictures

The maximum atomic displacement in each outer structure is 0.25 angstrom. All views use `along_pca3`.

### Mode 1: 1157.06 cm^-1, B1

Assignment: CH2 out-of-plane bend. The left and right structures use equal displacements along the normal coordinate.

![Mode 1 displacement grid](figures/mode_01_grid.png)
### Mode 2: 1226.38 cm^-1, B2

Assignment: CH2 in-plane rocking bend. The left and right structures use equal displacements along the normal coordinate.

![Mode 2 displacement grid](figures/mode_02_grid.png)
### Mode 3: 1487.73 cm^-1, A1

Assignment: H-C-H scissoring bend. The left and right structures use equal displacements along the normal coordinate.

![Mode 3 displacement grid](figures/mode_03_grid.png)
### Mode 4: 1743.28 cm^-1, A1

Assignment: C=O stretch. The left and right structures use equal displacements along the normal coordinate.

![Mode 4 displacement grid](figures/mode_04_grid.png)
### Mode 5: 2797.14 cm^-1, A1

Assignment: symmetric C-H stretch. The left and right structures use equal displacements along the normal coordinate.

![Mode 5 displacement grid](figures/mode_05_grid.png)
### Mode 6: 2850.66 cm^-1, B2

Assignment: asymmetric C-H stretch. The left and right structures use equal displacements along the normal coordinate.

![Mode 6 displacement grid](figures/mode_06_grid.png)

## AMS input

```ams
Properties
  NormalModes yes
  PESPointCharacter yes
End

Task GeometryOptimization

System
  Atoms
              C       0.0000000000       0.0000000000       0.0337596501
              O       0.0000000000       0.0000000000      -1.1856950809
              H       0.0000000000       0.9391319492       0.5759677154
              H       0.0000000000      -0.9391319492       0.5759677154
  End
  BondOrders
     1 2 2.0
     1 3 1.0
     1 4 1.0
  End
End

Engine adf
  Basis
    Core None
    Type DZP
  End
  XC
    Dispersion GRIMME3 BJDAMP
    GGA PBE
  End
EndEngine
```

## Conclusion

The optimized formaldehyde structure is a local minimum. AMS classified the PES point as local minimum, and all 6 vibrational frequencies are positive. The optimized bond metrics are C=O 1.212143 angstrom, mean C-H 1.115562 angstrom, and H-C-H 115.9439 degrees.