Equivariant analytical mapping of first principles Hamiltonians to accurate and transferable materials models

<strong>Equivariant analytical mapping of first principles Hamiltonians to accurate and transferable materials models</strong> Liwei Zhang, Berk Onat, Genevieve Dusson, Gautam Anand, Reinhard J. Maurer, Christoph Ortner and James R. Kermode Supporting data for https://arxiv.org/abs/2111.13736. <strong>Training data</strong> The <code>training_data</code> folder contains the atomic structure, Hamiltonian and overlap matrices stored in HDF5 format with the following schema: Data Group : <strong>aitb/</strong> Datasets : <strong>H</strong> : Real-space Hamiltonian Matrix. Type: Float64. Shape: Tensor(# of TB Cells, # of Rows, # of Columns) <strong>S</strong> : Real-space Overlap Matrix. Type: Float64. Shape: Tensor(# of TB Cells, # of Rows, # of Columns) <strong>energy</strong> : Energy. Unit: eV. Type: Float64. Shape: Scalar <strong>freeenergy</strong> : Free Energy. Unit: eV. Shape: Scalar <strong>unitcell</strong> : Unit cell vectors. Type: Float64. Shape: Matrix(3,3) <strong>positions</strong> : Atom positions. Type: Float64. Shape: Array(3) <strong>forces</strong> : (Optional, if available) Forces. Type: Float64. Shape: Array(3) <strong>metadata</strong> : JSON String including dictionary of information of FHIaims calculation (k-points, basis sets), TB Cells, Cutoff, Orbital definitions., The molecular dynamics and FHI-aims parameters are described in the manuscript. <strong>On-site models</strong> The <code>onsite_models_ord2</code> folder contains our correlation order 2 models for the on site blocks of the Hamiltonian, in a JSON format readable by the ACE.jl and ACEhamiltonians.jl (not yet publically available) Julia packages. There are separate files for the Hamiltonian (<code>*_H.json</code>) and overlap (<code>*_S.json</code>) models. The JSON files also contain training and test sets and associated errors as plotted in Figure 3 in our manuscript. Models have a unique identifier (UUID) which is a hash of the input parameters and training data. The mapping from (order, max_degree) to UUID is as follows: <pre><code><code>(2,4) - 13427527590286463256 (2,5) - 10538156191357510769 (2,6) - 1646489440533135164 (2,7) - 12130775482127724115 (2,8) - 12487060958610974041 (2,9) - 2653067664384673997 (2,10) - 1143382251563115664 (2,11) - 4564001820340015372 (2,12) - 9474261500251782658 </code></code></pre> <strong>Off-site models</strong> The <code>offsite_models_ord1</code> and <code>offsite_models_ord2</code> folders contain our order 1 and order 2 offsite models for Hamiltonian and overlap matrices. The mapping from (H_order, H_max_degree) + (S_order, S_max_degree) to UUID is as follows: <pre><code><code>(1,6) + (1,8) - 7014526518680934587 (1,7) + (1,9) - 8594416159488562244 (1,8) + (1,10) - 10204186688118368371 (1,9) + (1,11) - 13078304848585360574 (1,10)+ (1,12) - 14750835312950641338 (1,11)+ (1,13) - 9883802224093245794 (1,12)+ (1,14) - 3907899412408606585 (1,13)+ (1,15) - 201683837542179657 (1,14)+ (1,16) - 277744202775070779 (2,6) + (1,8) - 4699475053563592071 (2,7) + (1,9) - 489637409713831432 (2,8) + (1,10) - 18034631670613263469 (2,9) + (1,11) - 720654516759450160 (2,10)+ (1,12) - 15214900801060024044 (2,11)+ (1,13) - 13798832597295943078 (2,12)+ (1,14) - 13162803789413134473 </code></code></pre> The optimized model described in the manuscript has the following ID: <pre><code><code>Off-site-tuned model - 2606434113214136884 </code></code></pre> <strong>Reference data</strong> Reference electronic structure data computed for the BCC and FCC crystals and along the Bain path is stored in the <code>reference_data</code> folder. <strong>Predicted data</strong> The <code>predicted_data/FCC</code> and <code>predicted_data/BCC</code> folders contain HDF5 files with the results of all model predictions shown in the manuscript on the FCC and BCC crystal structures. <code>predicted_data/FCC-to-BCC</code> contains the results of predictions along the Bain path with the optimized model described in the manuscript.