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

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

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.

Training data

The training_data folder contains the atomic structure, Hamiltonian and overlap matrices stored in HDF5 format with the following schema:

• Data Group : aitb/
• Datasets :
  • H : Real-space Hamiltonian Matrix. Type: Float64. Shape: Tensor(# of TB Cells, # of Rows, # of Columns)
  • S : Real-space Overlap Matrix. Type: Float64. Shape: Tensor(# of TB Cells, # of Rows, # of Columns)
  • energy : Energy. Unit: eV. Type: Float64. Shape: Scalar
  • freeenergy : Free Energy. Unit: eV. Shape: Scalar
  • unitcell : Unit cell vectors. Type: Float64. Shape: Matrix(3,3)
  • positions : Atom positions. Type: Float64. Shape: Array(3)
  • forces : (Optional, if available) Forces. Type: Float64. Shape: Array(3)
  • metadata : 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 onsite_models_ord2 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 (*_H.json) and overlap (*_S.json) 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:

(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

Off-site models

The offsite_models_ord1 and offsite_models_ord2 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:

(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

The optimized model described in the manuscript has the following ID:

Off-site-tuned model -  2606434113214136884

Reference data

Reference electronic structure data computed for the BCC and FCC crystals and along the Bain path is stored in the reference_data folder.

Predicted data

The predicted_data/FCC and predicted_data/BCC folders contain HDF5 files with the results of all model predictions shown in the manuscript on the FCC and BCC crystal structures. predicted_data/FCC-to-BCC contains the results of predictions along the Bain path with the optimized model described in the manuscript.