DOI: 10.5281/zenodo.14797131
title: Dataset corresponding to the paper Global atomic structure optimization through machine-learning-enabled barrier circumvention in extra dimensions

description: Paper abstract

We introduce and discuss a method for global optimization of atomic structures based on the introduction of additional degrees of freedom describing: 1) the chemical identities of the atoms, 2) the degree of existence of the atoms, and 3) their positions in a higher-dimensional space (4-6 dimensions). The new degrees of freedom are incorporated in a machine-learning model through a vectorial fingerprint trained using density functional theory energies and forces. The method is shown to enhance global optimization of atomic structures by circumvention of energy barriers otherwise encountered in the conventional energy landscape. The method is applied to clusters as well as to periodic systems with simultaneous optimization of atomic coordinates and unit cell vectors. Finally, we use the method to determine the possible structures of a dual atom catalyst consisting of a Fe-Co pair embedded in nitrogen-doped graphene.

Data explanation

The dataset inludes four main folders with data used to create the figures of the paper.

1) neb_trajectories

Includes 3 xyz files containing a set of atomic paths found using the nudged elastic band method, NEB. The paths are used for traning of Gaussian processes to illustrate energy barrier circumvention using:



Hyperspatial coordinates: "hyperspace_neb.xyz"

Fractional existence: "ghost_neb.xyz"

Interpolation of chemical elements: "ice_neb.xyz"


2) surrogate_relaxations 

Includes two .xyz files containing surrogate relaxations of atomic structures:



Cu12Ni11 cluster: "Cu18Ni5_surrogate_relaxation.xyz" 

FeCo dual atom catalyst on a nitogen doped graphene substrate: "catalyst_surrogate_relaxation.xyz" 


The easiest way to read the files is by using ase.io.read from the Atomic Simulation Environment (ASE), which converts the data into a set of ASE Atoms objects. After this, the full set of three dimensional cartesian coordinates, fractional chemical coordinates, and hyperspatial coordinates can be accessed as atoms.positions, atoms.info['fractions'], and atoms.info['extra_coords'] (last one only for the Cu12Ni11 cluster), respectively. The columns of the fractional chemical coordinates correspond to the different elements in the system and are ordered alphabetically by chemical symbol from left to right. The files also include the data field initial_charges, which has been unconventionally used here to store the total existence of atoms for the sole purpose of plotting and visualization using the ASE GUI. Similarly, the file for the Cu12Ni11 cluster includes the field initial_magmoms, which has also been used unconventionally to store the atomic extensions into the fourth dimension, relative to a chosen center point, not being the same as the unit cell origin. The given fields are only present in the steps of the relaxation process where the corresponding coordinates are active. Potential energy and forces can be accessed as normally from ASE as atoms.get_potential_energy() and atoms.get_forces()

 3) success_curve_and_histogram_data

Includes global optimization runs used to make success curves and energy histograms for the atomic systems studied in the paper. The folder includes four subfolders corresponding to the "Global optimization examples" sections of the results section as specified below. These folders then include a set of folders named after the analyzed atomic system each containing subfolders describing the type of run with the following possibilities: a run in the conventional three dimensional coordinate space (beacon or 3d), a run in more than three dimensions (4d, 5d, 6d), a run with fractionally existing atoms (ghost) or a run with interpolation of chemical elements (ice). If a folder is called e.g. 4d_ghost it means that both extra spatial coordinates and fractional existence was used.  Each of these subfolders include 20 runs named "run0.xyz" to "run19.xyz" each containing 100 DFT calculations of structures found during the global optimization runs.

The four main subfolders and their corresponding paper sections are:



hyperspace: Global optimization examples: hyperspatial coordinates

ice_and_ghost: Global optimization examples: elemental coordinates

method_combinations: Global optimization examples: combinations of hyperspatial and elemental coordinates

dual_atom_catalysts:  Global optimization examples: structure of dual atom catalysts


Note: The subfolders Ni4Pt8Al4/beacon, Ni4Pt8Al4/ice and Ni4Pt8Al4/ghost appear in both ice_and_ghost and method_combinations. These are identical and included in both locations for completeness and clarity.

4) optimum_structures

The folder includes two .xyz files.



"global_minimum_structures.xyz" contain the very lowest identfied global minima for all investigated atomic systems.

"picture_structures.xyz" contain the structures used for showing the structures of the global minima in the figures of the paper. 


The two files may differ for some systems, but correspond to structurally identical systems.  Both are made from structures identified from the files in success_curve_and_histogram_data.