# Biphenyl DFTB torsional PES scan

## Setup

Biphenyl was built from SMILES `c1ccccc1-c2ccccc2` with `ChemicalSystem.from_smiles`. The central inter-ring C-C bond was identified by inspecting `ChemicalSystem.bonds` for the carbon-carbon bond whose removal cuts the molecule.

- Central inter-ring bond, zero-based atom indices: `(5, 6)`
- Central inter-ring bond, AMS one-based atom indices: `(6, 7)`
- Inter-ring dihedral, zero-based atom indices: `(0, 5, 6, 7)`
- Inter-ring dihedral, AMS one-based atom indices: `(1, 6, 7, 8)`

The constrained AMS `PESScan` used DFTB with `Model GFN1-xTB`, scanning the inter-ring dihedral from 0 to 180 degrees in 19 points, i.e. 10 degree spacing. Energies below are reported relative to the lowest scan point.

## Results

![Biphenyl torsional profile](biphenyl_torsion_profile.png)

Minimum-energy scan point: **140.0 degrees**.

Minimum-energy biphenyl twist angle: **40.0 degrees**. This is reported as `min(dihedral, 180 - dihedral)` because the 0 to 180 degree scan has equivalent twisted structures on either side of 90 degrees.

Torsional barrier to the planar structure: **1.8050 kcal/mol**. The 0 and 180 degree planar endpoints are both tabulated below; the quoted planar barrier is the lower of the two endpoint relative energies.

Torsional barrier to the perpendicular structure: **1.7045 kcal/mol**.

## Representative optimized structures

Planar geometry:

![Planar biphenyl](biphenyl_planar.png)

Minimum-energy geometry:

![Minimum-energy biphenyl](biphenyl_minimum.png)

Perpendicular geometry:

![Perpendicular biphenyl](biphenyl_perpendicular.png)

## Scan table

| Dihedral angle (deg)   | Absolute energy (Hartree)   | Relative energy (kcal/mol)   |
|:-----------------------|:----------------------------|:-----------------------------|
| 0.0                    | -30.7270479157              | 1.8050                       |
| 10.0                   | -30.7276375568              | 1.4350                       |
| 20.0                   | -30.7287351168              | 0.7463                       |
| 30.0                   | -30.7296159661              | 0.1936                       |
| 40.0                   | -30.7299151698              | 0.0058                       |
| 50.0                   | -30.7296468314              | 0.1742                       |
| 60.0                   | -30.7289488005              | 0.6122                       |
| 70.0                   | -30.7281162675              | 1.1346                       |
| 80.0                   | -30.7274575254              | 1.5480                       |
| 90.0                   | -30.7272081545              | 1.7045                       |
| 100.0                  | -30.7274586820              | 1.5473                       |
| 110.0                  | -30.7281246087              | 1.1294                       |
| 120.0                  | -30.7289611334              | 0.6045                       |
| 130.0                  | -30.7296515698              | 0.1712                       |
| 140.0                  | -30.7299244088              | 0.0000                       |
| 150.0                  | -30.7296195325              | 0.1913                       |
| 160.0                  | -30.7287447482              | 0.7402                       |
| 170.0                  | -30.7276400215              | 1.4335                       |
| 180.0                  | -30.7270454035              | 1.8066                       |

## AMS input

The PES scan job was loaded from `/home/ubuntu/work/01-run-biphenyl-dftb-pesscan_workdir/biphenyl_dftb_torsion` with `AMSJob.load_external(...)`.

```ams
PESScan
  Optimize True
  ScanCoordinate
    Dihedral 1 6 7 8 0.0 180.0
    nPoints 19
  End
End

Task PESScan

System
  Atoms
              C       1.5436277587      -0.6712511736      -0.8743423895
              C       2.9379238219      -0.6084386430      -0.7895740467
              C       3.5458648903       0.1540229069       0.2101358580
              C       2.7607157299       0.8559722841       1.1272880062
              C       1.3659731986       0.7976348543       1.0467720204
              C       0.7407365542       0.0321748032       0.0438974615
              C      -0.7407365262      -0.0321759898      -0.0438985615
              C      -1.3882544717      -1.2464975341      -0.3418076249
              C      -2.7829651518      -1.3041919267      -0.4233311075
              C      -3.5458647518      -0.1540214568      -0.2101369285
              C      -2.9156742946       1.0566598609       0.0856160895
              C      -1.5213463694       1.1201124254       0.1693765138
              H       1.0941322198      -1.2547297485      -1.6679429353
              H       3.5475041862      -1.1489839049      -1.5021581640
              H       4.6253028921       0.2009111764       0.2741061689
              H       3.2330362523       1.4435115455       1.9039896331
              H       0.7773312479       1.3360188999       1.7788506547
              H      -0.8179456227      -2.1542017782      -0.4938473594
              H      -3.2727104357      -2.2427544850      -0.6487281126
              H      -4.6253028983      -0.2009093371      -0.2741044826
              H      -3.5078300382       1.9482274962       0.2468998516
              H      -1.0535181915       2.0729097247       0.3829394549
  End
  BondOrders
     1 2 1.5
     1 6 1.5
     1 13 1.0
     2 3 1.5
     2 14 1.0
     3 4 1.5
     3 15 1.0
     4 5 1.5
     4 16 1.0
     5 6 1.5
     5 17 1.0
     6 7 1.0
     7 8 1.5
     7 12 1.5
     8 9 1.5
     8 18 1.0
     9 10 1.5
     9 19 1.0
     10 11 1.5
     10 20 1.0
     11 12 1.5
     11 21 1.0
     12 22 1.0
  End
End

Engine dftb
  Model GFN1-xTB
EndEngine


```

## Conclusion

The DFTB scan places the minimum at a scan dihedral of 140.0 degrees, corresponding to a biphenyl twist of 40.0 degrees. Relative to this point, the lower planar endpoint is 1.8050 kcal/mol higher and the perpendicular point is 1.7045 kcal/mol higher.