.. _dihedral_scan:

Dihedral scan
=============

Purpose
-------

This benchmark evaluates the **MLIP**'s ability to reproduce torsional energy profiles of rotatable bonds in small molecules,
aiming to approach the quantum-mechanical **QM** reference quality.

Description
-----------

For each molecule, the benchmark leverages the `mlip <https://github.com/instadeepai/mlip>`_ library library for model inference, comparing
the predicted energies along a dihedral scan to quantum mechanical **QM** reference energy profiles. The reference profile is
shifted so that its global minimum is zero, and the **MLIP** profile is aligned to the same conformer.
Performance is quantified using the following metrics:

- **MAE (Mean Absolute Error)** and **RMSE (Root Mean Square Error)** between the **MLIP** and reference energy profiles.
- **Pearson correlation coefficient** between the **MLIP**-predicted and reference datapoints.
- **Mean barrier height error**: For each energy profile, the maximum energy relative to the energy minimum is calculated as the barrier height.
  The absolute error between **MLIP** and reference barrier heights is computed, and the mean over the full dataset is reported.

.. list-table::
   :widths: 25 45
   :header-rows: 0

   * - .. figure:: img/dihedral_example.png
          :width: 100%
          :align: center
          :figclass: align-center

     - .. figure:: img/dihedral_scan.png
          :width: 100%
          :align: center
          :figclass: align-center

These metrics assess the **MLIP**'s ability to accurately reproduce quantum mechanical torsional energy landscapes,
which is critical for modeling conformational energetics and barriers in small molecules.

Dataset
-------

The **TorsionNet500** \ [#f1]_ dataset consists of 500 drug-like organic molecules with systematically sampled dihedral angles.

Interpretation
--------------

The correct representation of energetic barriers along conformational changes, like dihedral rotation, is important for
simulation-based methods and also to correctly represent transition states of any reaction involving conformational changes.
The **MAE (Mean Absolute Error)** and **RMSE (Root Mean Square Error)** should be **as low as possible** and match the expectations from
training and testing of the energy inference. The **Pearson correlation** should be **close to 1**, but since energy differences between
conformers along a dihedral scan may be small, this criterion can be considered a bit less strict than the criterion given for
conformational sampling. The mean barrier height error should also be **as low as possible** and match the expectations about
the **MLIP**'s energy inference.


References
----------

.. [#f1] Brajesh K. Rai [...] A. Bakken, Journal of Chemical Information and Modeling 2022 62 (4), 785-800. DOI: 10.1021/acs.jcim.1c01346