BayesianOpt4dftu

Determine the Hubbard U parameters in DFT+U using the Bayesian Optimization approach.

Prerequisites

Python Version

• Tested on Python 3.8

Python Dependencies

These will be installed automatically when you install the package via pip:

• numpy
• pandas
• ase
• pymatgen
• bayesian-optimization
• vaspvis

Other Dependencies

These dependencies need to be installed manually:

• Vienna Ab initio Simulation Package (VASP)

Installation

To install BayesianOpt4dftu, use the following command:

pip install git+https://github.com/caizefeng/BayesianOpt4dftu.git

Usage

For the demonstration, let's focus on fitting the Hubbard U values for both elements in indium arsenide (InAs).

The example input and output can be found in the /examples/2d directory:

1. Edit input.json

Navigate to the example directory:

cd examples/2d

Adjust the input.json file with the appropriate vasp_env settings based on your system specifications and the location of your VASP binary.

2. Execute

Run the following command:

bo_dftu

3. Results

Upon reaching the threshold or maximum iterations, two output files are generated:

• u_xxx.txt/formatted_u_xxx.txt: Contains U parameters, band gap, Δgap, Δband, and Δmagnetization (optional) for each iteration.
• 1D_xxx.png or 2D_xxx.png: Provides a visual representation of the Gaussian process predicted mean and acquisition function. This file will be omitted if you set three or more optimizable U parameters.

Example of BO plots:

• 1-D Bayesian Optimization for Ge

  

• 2-D Bayesian Optimization for InAs

  

Optimal U values are automatically deduced from the predicted mean space interpolation. Alternatively, you can use the u_xxx.txt file to select U values with the highest objective value.

Configuration

Before running the program, configure the input.json file. It contains:

• vasp_env: Environment settings for VASP.

  • vasp_run_command:

    • Description: Running command for VASP executable.
    • Example: "vasp_run_command": "mpirun -np 64 /path/to/vasp/executable"

  • out_file_name:

    • Description: The desired name of the VASP output file.
    • Example: "out_file_name": "slurm-vasp.out"

  • vasp_pp_path:

    • Description: Path directing to the VASP pseudopotential. It should be the directory containing the potpaw_PBE folder.
    • Example: "vasp_pp_path": "/path/to/pseudopotentials/"

  • dry_run:

    • Description: Specifies if the run is a dry run (generating files only without actual computation) or not.
    • Default: "dry_run": false

  • dftu_only:

    • Description: Indicates whether only DFT+U is performed. If set to true, completed baseline calculations should be placed in the <working dir>/<baseline> directory.
    • Default: "dftu_only": false

  • get_optimal_band:

    • Description: Indicate if an additional DFT+U using optimal U values is performed after Bayesian optimization. The results of this calculation will be appended to the end of the log file.
    • Default: "get_optimal_band": true

• bo: Settings specific to Bayesian Optimization.

  • resume_checkpoint:

    • Description: Determines whether the Bayesian Optimization resumes from a saved checkpoint, as defined by u_tmp.txt and input_tmp.json.
    • Default: "resume_checkpoint": false

  • baseline:

    • Description: Specifies the baseline calculation for Bayesian Optimization. Currently, only "hse" and "gw" are supported. "gw" must be executed separately, meaning it is only supported when "dftu_only": true.
    • Default: "baseline": "hse"

  • which_u:

    • Description: Specifies which element you'd like to optimize the U for.
    • Format: For a unary substance, it has to be [1,]. For compounds with over 2 elements, you can set each element to 0 or 1 to switch off/on the optimization for that element.
    • Example: For InAs, when optimizing for both In and As, it should be set as "which_u": [1, 1]

  • br:

    • Description: Specifies the band range you'd like to include in your Δband.
    • Format: A list of two integers, defining the number of valence bands and conduction bands from the Fermi level.
    • Default: "br": [5, 5]

  • kappa:

    • Description: Controls the balance between exploration and exploitation when the acquisition function samples the next points. A lower value (nearing 0) indicates a preference for exploitation. A higher value (approaching 10) indicates a preference for exploration.
    • Default: "kappa": 5

  • alpha_gap and alpha_band:

    • Description: Specifies the weight coefficients of Δgap and Δband respectively. So far, there are no constraints on the choice of alphas, meaning they can be arbitrary positive real numbers.
    • Default: "alpha_gap": 0.25 and "alpha_band": 0.75

  • alpha_mag:

    • Description: Specifies the weight coefficients of Δmagnetization. LORBIT must be set in all INCAR files. A alpha_mag of 0 will exclude Δmagnetization from the loss function.
    • Default: "alpha_mag": 0.0

  • mag_axis:

    • Description: Specifies the Cartesian component of the non-collinear magnetic moment used to calculate Δmagnetization. Available options are "x", "y", "z", and "all"(all 3 components). This parameter is only applicable to non-collinear calculations and has no effect on collinear calculations (when LNONCOLLINEAR=.FALSE. and LSORBIT=.FALSE.).
    • Default: "mag_axis": "all"

  • threshold:

    • Description: Specifies the desired accuracy for the objective function, measured as the difference between values from two consecutive iterations, at which you'd like to stop the BO process. A threshold of 0.0 (and threshold_opt_u of 0.0 as well) will disable the convergence assessment, meaning the BO will exit only upon reaching the maximum iterations.
    • Default: "threshold": 0.0001

  • urange:

    • Description: Specifies the U parameter range for optimization. The unit is eV. Defining different U ranges for separate elements is currently unsupported.
    • Default: "urange": [-10, 10]

  • elements:

    • Description: Lists the elements in your system. This is used for plotting the BO results. If it's a unary substance, it has to be ["ele",].
    • Example: "elements": ["In", "As"]

  • iteration:

    • Description: Sets the maximum iterations that BO will perform.
    • Default: "iteration": 50

  • report_optimum_interval:

    • Description: Sets the interval (in iterations) at which the optimal Hubbard U values are calculated and logged.
    • Default: "report_optimum_interval": 10

  • threshold_opt_u:

    • Description: This criterion supplements the original threshold parameter and can be used as the sole convergence criterion or in conjunction with threshold. Specifies the desired accuracy for the optimal Hubbard U values, measured as the difference between values from two iterations separated by report_optimum_interval. A threshold_opt_u of 0.0 will disable this optimal U-based convergence assessment.
    • Default: "threshold_opt_u": 0.0

  • print_magmom:

    • Description: Specifies whether to print the magnetic moment at each iteration.
    • Default: "print_magmom": false

• structure_info : Includes geometry information (such as lattice parameter, lattice vectors, atomic position, etc.) of the target materials.

  An example of InAs:

  • lattice_param and cell: Specify the 2nd to 5th rows in your POSCAR.

    {
        "lattice_param": 6.0584,
        "cell": [
            [
                0.0,
                0.5,
                0.5
            ],
            [
                0.5,
                0.0,
                0.5
            ],
            [
                0.5,
                0.5,
                0.0
            ]
        ]
    }

  • atoms: Specifies the atomic positions of each atom in your system and the initial magnetic moment if there is any.

    Non-collinear magnetism:

    {
        "atoms": [
            [
                "In",
                [
                    0,
                    0,
                    0
                ],
                [
                    0,
                    0,
                    1e-06
                ]
            ],
            [
                "As",
                [
                    0.75,
                    0.75,
                    0.75
                ],
                [
                    0,
                    0,
                    1e-06
                ]
            ]
        ]
    }

    Collinear magnetism:

    {
        "atoms": [
            [
                "In",
                [
                    0,
                    0,
                    0
                ],
                1e-06
            ],
            [
                "As",
                [
                    0.75,
                    0.75,
                    0.75
                ],
                1e-06
            ]
        ]
    }

    In this case, there are two atoms in the primitive cell at positions [0, 0, 0] and [0.75, 0.75, 0.75]. The second term under each atom specifies the initial magnetic moment. For calculations excluding non-collinear magnetization or spin-orbit coupling, this is an integer (or it could be a one-dimensional array with one element). Otherwise, it's a one-dimensional array with three elements, each representing the initial moment in a specific Cartesian direction. To avoid omission errors in the ASE package, the initial moment should be set to a small, non-zero number if it is intended to be 0.

  • kgrid_hse and kgrid_pbe:

    • Description: Set the self-consistent k-point grid for HSE and PBE+U calculations, respectively.
    • Example: "kgrid_pbe": [7, 7, 7] specifies a 7x7x7 k-point grid for PBE+U calculation.

  • num_kpts and kpath:

    • Description: Specify the non-self-consistent (non-SC) k-point path for band structure calculations. num_kpts can be either an integer or a string "auto".
    • Example: "num_kpts": 50 and "kpath": "G X W L G K" set the k-point path to G-X-W-L-G-K and the number of k-points per path segment to 50. Important: In this mode, contributions to Δband are weighted to achieve an approximately uniform density of sampling along the path. "num_kpts": "auto" automatically determines the path and number of k-points based on the HSE or GW baseline calculation.

  • custom_kpoints:

    • Description: Specifies the custom reciprocal coordinates for certain k-points in kpath. If it conflicts with common BZ coordinate conventions for certain k-points, this setting takes higher priority.
    • Example: "custom_kpoints": null (the default) or "custom_kpoints": {"H": [0.5, -0.5, 0.5], "F": [0.5, 0.5, 0]}

  • custom_POTCAR_path:

    • Description: Specifies the path to the custom POTCAR file. This file will be copied to all VASP working directories.
    • Example: "custom_POTCAR_path": null (the default) or "custom_POTCAR_path": "./POTCAR_Pb_sv_Te_sv"

• general_flags: General INCAR tags required in all VASP calculations.

• scf: INCAR tags that will only be added in SCF calculations.

• band: INCAR tags that will only be added in band structure calculations.

• pbe: INCAR tags that will only be added when using PBE as exchange-correlation functional.

• hse: INCAR tags that will only be added when using HSE06 as exchange-correlation functional.

  Check the ASE VASP calculator documentation for additional tag keys. (A large portion of them are simply the lowercase versions of the corresponding INCAR tags.)

Citation

Please cite the following work if you use this code.

[1] M. Yu, S. Yang, C. Wu, N. Marom, Machine learning the Hubbard U parameter in DFT+ U using Bayesian optimization, npj Computational Materials, 6(1):1–6, 2020.