DOI: 10.5281/zenodo.6561452
title: Equivariant analytical mapping of first principles Hamiltonians to accurate and transferable materials models

description: Supporting data for https://arxiv.org/abs/2111.13736. ACEhamiltonians.jl code This is an archived copy of the ACEhamiltonians.jl code to accompany the paper arXiv:2111.13736. See https://github.com/ACEsuit/ACEhamiltoniansExamples for examples of how to use this code. The code is written in Julia and requires v1.6 or later. To install the Julia depenendencies: <pre><code><code>$ cd ACEhamiltonians.jl $ julia julia&gt; import Pkg julia&gt; Pkg.activate(".") julia&gt; Pkg.instantiate() </code></code></pre> The scripts <code>test/plots.jl</code>, <code>test/fcc-to-bcc.jl</code> and <code>test/vacancy.jl</code> which produce all the plots in the paper can then run as, e.g. <pre><code><code>julia --project=. test/plots.jl </code></code></pre> Training data 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. On-site models 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 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> Off-site models 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> FCC only Onsite models: <pre><code><code>2 6 5311732756869418284 2 7 13030014632886405308 2 8 5820099621734447846 2 9 10161014511878227635 2 10 11298425190201843107 2 11 9932031839231628354 2 12 9447261873515969583 </code></code></pre> Optimised FCC model <code>16110190062237887798</code> BCC only Onsite models: <pre><code><code>2 6 8949023800586845770 2 7 8045797268444730200 2 8 6919809282139600809 2 9 9935027806122780319 2 10 6376963380608532713 2 11 5001375576268070883 2 12 9678585765722197901 </code></code></pre> Optimised BCC model <code>10293566074413000591</code> FCC+BCC optimised models Onsite models <pre><code><code>2 6 2154760103892646619 2 7 6450474921309693835 2 8 14227277988574899288 2 9 476820595195218567 2 10 5364136683220082110 2 11 14619519825012606580 2 12 14181614899005838824 </code></code></pre> Offsite FCC+BCC optimised model - <code>4570230078043807257</code> Model errors The <code>model_errors</code> directory contains summarised model errors for the training and testing errors for the models listed above. Reference data Reference electronic structure data computed for the BCC and FCC crystals, along the Bain path and for the relaxed vacancy is stored in the <code>reference_data</code> folder. The Hamiltonian and overlap matrices are stored as compressed binary HDF5 files. The format and metadata can be viewed with the <code>h5dump</code> utility, or read in using the supplied Julia code (or indeed from other languages). Predicted data 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 and <code>predicted_data/vacancy</code> contains the vacancy calculations.