Thermally Averaged Magnetic Anisotropy Tensors via Machine Learning Based on Gaussian Moments

• D-Tensor Data

The reference data for 3500 configurations of [Co(N₂S₂O₄C₈H₁₀)₂]²⁻ (CoSar), [Fe(tpa)^Ph]⁻ (FeTPAPh), and [Ni(HIM₂−py)₂NO₃]⁺ (NiComplex) is generated employing Molpro package [1]. For more details see the original publication [2]. The data is stored in python compressed array format (.npz) with the D-Tensor in cm^-1. The data set contains four \(np.ndarray\)

import numpy as np
data = np.load('CoSar.npz')
R = data['R']     # Cartesian coordinates of nuclei in Ang.
D = data['MAT']   # D-Tensor values in cm-1, D = (D11, D12, D13, D22, D23, D33)
N = data['N']     # Number of atoms in each structure
Z = data['Z']     # Nuclear charges

• AIMD Data

To propagate the periodic cell containing four CoSar molecules, for which D-Tensor was computed above, a data set containing total energies as well as atomic forces of 3500 structures was generated employing VASP package [3-6]. For more details see the original publication [2]. The data is stored in python compressed array format (.npz) with the total energy in kcal/mol and atomic forces in kcal/mol/Ang. The data set contains six \(np.ndarray\)

import numpy as np
data = np.load('CoSar_bulk.npz')
R = data['R']   # Cartesian coordinates of nuclei in Ang.
C = data['C']   # Cell vectors in Ang.
E = data['E']   # Total energy in kcal/mol
F = data['F']   # Atomic forces in kcal/mol/Ang.
N = data['N']   # Number of atoms in each structure
Z = data['Z']   # Nuclear charges

• References

[1] H.-J. Werner, P. J. Knowles, G. Knizia, F. R. Manby, M. Schütz,et al.,“Molpro, version 2020.0, a package of ab initio programs,” (2020), see https://www.molpro.net.

[2] V. Zaverkin, J. Netz, F. Zills, A. Köhn, and J. Kästner, “Thermally Averaged Magnetic Anisotropy Tensors via Machine Learning Based on Gaussian Moments,” submitted (2021).

[3] P. E. Blöchl, “Projector augmented-wave method,” Phys. Rev. B 50, 17953 (1994).

[4] G. Kresse and J. Hafner, “Ab initio molecular dynamics for liquid metals,” Phys. Rev. B 47, 558 (1993).

[5] G. Kresse and J. Furthmüller, “Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set,” Comput. Mater. Sci. 6, 15 – 50 (1996).

[6] G. Kresse and J. Furthmüller, “Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set,” Phys. Rev. B 54, 11169 (1996).