Smooth Overlap of Atomic Positions (SOAP), as implemented in DScribe and utilized by ULaMDyn, is a descriptor that captures local atomic geometries by expanding a Gaussian-smeared atomic density using orthonormal functions derived from spherical harmonics and radial basis functions. In this implementation, SOAP requires the atomic coordinates in the form of XYZ data and the corresponding labels for each atom. Additionally, the SOAP constructor accepts various other parameters that allow for further customization, with detailed explanations available in the DScribe library documentation. The SOAP output is represented as the partial power spectrum vector 𝒑, with its elements defined as follows ( )