bcal: Program for the calculation of band structure and effective mass for organic semiconductor crystals

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Overview

bcal is a tool for calculating the band structure and effective masses of organic semiconductors. Starting from a crystal structure (CIF), it generates quantum-chemistry inputs, runs DFT calculations, extracts the molecular-orbital matrices, and builds a tight-binding Hamiltonian. From the resulting band dispersion it reports the HOMO and LUMO band edges together with their principal effective masses and axis vectors, and draws the band diagram along a configurable high-symmetry k-path.

Requirements

• Python 3.11 or newer
• NumPy
• Pandas
• SciPy
• Matplotlib
• yu-mcal>=0.7.1
• yu-tcal>=5.0.2

Quantum Chemistry Calculation Tools

At least one of the following is required:

• Gaussian 09 or 16
• PySCF (macOS / Linux / WSL2(Windows Subsystem for Linux))
• GPU4PySCF (macOS / Linux / WSL2(Windows Subsystem for Linux))
• ORCA 6.1.0 or newer

Important notice

• When using Gaussian, the path of the Gaussian executable must be set.
• PySCF is supported on macOS / Linux. Windows users must use WSL2.

Installation

Install from PyPI, choosing the extra that matches the backend you intend to use.

Using Gaussian 09 or 16 (without PySCF)

pip install yu-bcal

Using PySCF (CPU only, macOS / Linux / WSL2)

pip install "yu-bcal[pyscf]"

Using GPU acceleration with PySCF (macOS / Linux / WSL2)

1. Check your installed CUDA Toolkit version

nvcc --version

2. Install the GPU extra that matches your CUDA Toolkit version

If your CUDA Toolkit version is 13.x:

pip install "yu-bcal[gpu4pyscf-cuda13]"

If your CUDA Toolkit version is 12.x:

pip install "yu-bcal[gpu4pyscf-cuda12]"

If your CUDA Toolkit version is 11.x:

pip install "yu-bcal[gpu4pyscf-cuda11]"

Using ORCA 6.1.0 or newer

pip install "yu-bcal[orca]"

Verify Installation

After installation, you can verify by running:

bcal --help

bcal Usage Manual

Basic Usage

bcal <cif_filename> [options]

Required Arguments

• file: Path to the CIF file.

Unlike mobility-tensor tools, bcal does not take a p/n semiconductor type. A single run reports both the HOMO band edge (relevant for p-type transport) and the LUMO band edge (relevant for n-type transport).

Basic Examples

# Compute band structure and effective masses for a crystal
bcal xxx.cif

# Same, using PySCF as the backend
bcal xxx.cif --engine pyscf

Options

Short	Long	Explanation
-h	--help	Show options description.
-M	--method METHOD/BASIS	Calculation method and basis set in "METHOD/BASIS" format. (default: PBEPBE/6-31G(d,p))
-c	--cpu N	Set the number of CPUs. (default: 4)
-m	--mem N	Set the memory size in GB. (default: 10)
-o	--output DIR	Output directory for the results. (default: the directory of the input CIF file)
-r	--read	Read existing log files without executing calculations.
	--engine ENGINE	Quantum-chemistry backend: g16, g09, pyscf, gpu4pyscf, orca. (default: g16)
	--resume	Resume an interrupted calculation from the last incomplete step.
	--num-mo N	Number of MOs per molecule on each side of the frontier; total MOs = 2 * N. (default: 15)
	--band-path PATH	High-symmetry k-path for the band diagram, given as single-character labels (G = Gamma). (default: XGYGZ)
	--bse	Use Basis Set Exchange to obtain basis sets. (PySCF/gpu4pyscf only)

Calculation Settings

-M, --method <method>

Specify the DFT method and basis set used in the quantum-chemistry calculations.

• Default: PBEPBE/6-31G(d,p)
• Example: bcal xxx.cif -M "B3LYP/6-31G(d,p)"

Note: PBEPBE is the Gaussian spelling of the PBE functional. The pyscf, gpu4pyscf, and orca engines do not accept this name, so bcal automatically rewrites a leading PBEPBE to PBE (e.g. PBEPBE/6-31G(d,p) → PBE/6-31G(d,p)) and emits a warning to stderr.

-c, --cpu <number>

Specify the number of CPUs to use.

• Default: 4
• Example: bcal xxx.cif -c 8

-m, --mem <memory>

Specify the amount of memory in GB.

• Default: 10
• Example: bcal xxx.cif -m 16

--engine <engine>

Specify the quantum-chemistry backend.

• Choices: g16, g09, pyscf, gpu4pyscf, orca
• Default: g16 (Gaussian 16)
• Examples:
  • bcal xxx.cif --engine g09 (Gaussian 09)
  • bcal xxx.cif --engine pyscf (PySCF, CPU; requires the pyscf extra)
  • bcal xxx.cif --engine gpu4pyscf (GPU-accelerated PySCF; requires a gpu4pyscf-cudaXX extra)
  • bcal xxx.cif --engine orca (ORCA; requires the orca extra)

ORCA parallel execution

ORCA is driven through the ORCA Python Interface (OPI). To use multiple CPU cores (--cpu N), OpenMPI must be installed and visible to ORCA. First, confirm that mpirun is available:

which mpirun

If OpenMPI is already in $PATH and $LD_LIBRARY_PATH (common on Linux/WSL after apt install), no further configuration is usually needed. Otherwise, point ORCA at the OpenMPI base directory (the directory that contains bin/ and lib/) via the OPI_MPI environment variable:

# Built from source or via a module system
which mpirun
# e.g. /opt/openmpi/bin/mpirun  ->  base: /opt/openmpi
export OPI_MPI=$(dirname $(dirname $(which mpirun)))

# Installed system-wide via apt (Ubuntu/Debian)
export OPI_MPI=/usr/lib/x86_64-linux-gnu/openmpi

Note: ORCA requires a specific version of OpenMPI. The version available via apt may not match. If parallel execution fails, build OpenMPI from source using the version specified in the ORCA documentation.

--bse

Resolve the basis set named in -M, --method through Basis Set Exchange instead of the engine's built-in definition. This is a flag (it takes no value) and only affects the pyscf and gpu4pyscf engines (it uses the basis-set-exchange package bundled with the pyscf extra); it is silently ignored by g16, g09, and orca.

• Default: off
• Example: bcal xxx.cif --engine pyscf --bse

Band-Structure Settings

--num-mo <number>

Number of molecular orbitals (MOs) per molecule kept on each side of the frontier (HOMO side and LUMO side); the total number of MOs used per molecule is 2 * num_mo. Increasing it widens the orbital window included in the tight-binding model.

• Default: 15
• Example: bcal xxx.cif --num-mo 20

--band-path <path>

High-symmetry k-path for the band diagram, given as a sequence of single-character labels (G = Gamma).

• Default: XGYGZ (traces X → Γ → Y → Γ → Z)
• Example: bcal xxx.cif --band-path GXSY

Available high-symmetry points:

Label	Fractional reciprocal coordinates
G	(0.0, 0.0, 0.0) — Gamma
X	(0.5, 0.0, 0.0)
Y	(0.0, 0.5, 0.0)
Z	(0.0, 0.0, 0.5)
S	(0.5, 0.5, 0.0)
T	(0.0, 0.5, 0.5)
U	(0.5, 0.0, 0.5)
R	(0.5, 0.5, 0.5)

The chosen path only affects the band diagram (band.png); the band edges and effective masses are searched over the full Brillouin zone. If a HOMO/LUMO edge does not lie on the requested path, bcal emits a warning to stderr so you can add the corresponding k-point to --band-path.

Output Settings

-o, --output <directory>

Output directory for the results. A per-crystal subdirectory named after the CIF is created inside it.

• Default: the directory containing the input CIF file.
• Example: bcal xxx.cif -o ./results

Calculation Control

-r, --read

Read results from existing log files without executing new DFT calculations. Skips input generation and reuses the logs already present under the crystal's logs/ directory.

• Example: bcal xxx.cif -r

--resume

Resume an interrupted calculation, reusing completed steps and continuing from the last incomplete one (e.g. DFT calculations that already terminated normally are not repeated).

• Example: bcal xxx.cif --resume

Practical Usage Examples

Basic Calculations

# Default run (Gaussian 16, PBEPBE/6-31G(d,p))
bcal xxx.cif

# Use 8 CPUs and 16 GB memory
bcal xxx.cif -c 8 -m 16

Choosing a Backend

# PySCF (CPU)
bcal xxx.cif --engine pyscf

# GPU-accelerated PySCF
bcal xxx.cif --engine gpu4pyscf

# ORCA with 8 CPUs
bcal xxx.cif --engine orca -c 8

# PySCF with basis sets from Basis Set Exchange
bcal xxx.cif --engine pyscf --bse

Tuning the Band Calculation

# Different method / basis set
bcal xxx.cif -M "B3LYP/6-311G(d,p)"

# Wider orbital window
bcal xxx.cif --num-mo 25

# Custom k-path for the band diagram
bcal xxx.cif --band-path GXSYG

Reusing Results

# Read from existing log files (no new DFT)
bcal xxx.cif -r

# Resume an interrupted calculation
bcal xxx.cif --resume

Output

Standard Output

Results are written to stdout, while all warnings and diagnostics are routed to stderr (prefixed with WARNING:, coloured when stderr is an interactive terminal). The two streams can therefore be redirected independently.

At the end of a run, bcal prints to stdout, for each frontier band:

• The band edge: its high-symmetry label (when applicable) and fractional reciprocal-lattice coordinates.
• The three principal effective masses m1, m2, m3 (in units of the electron mass m_e), sorted by |m| in ascending order, each paired with its unit principal-axis vector in Cartesian reciprocal space.

LUMO band edge: G  k=(+0.000, +0.000, +0.000)
  m1 = +0.834 m_e  v=(+0.998, +0.043, +0.000)
  m2 = +1.207 m_e  v=(-0.043, +0.998, +0.000)
  m3 = +3.115 m_e  v=(+0.000, +0.000, +1.000)

HOMO band edge: X  k=(+0.500, +0.000, +0.000)
  m1 = -0.756 m_e  v=(+0.991, +0.000, +0.135)
  m2 = -1.042 m_e  v=(+0.000, +1.000, +0.000)
  m3 = -2.880 m_e  v=(-0.135, +0.000, +0.991)

A warning is printed to stderr if a band edge falls outside the requested --band-path; the path to the saved results and the elapsed time follow on stdout.

Generated Files

bcal writes a self-contained directory per crystal, with the pipeline stages kept in separate subdirectories:

<output>/<NAME>/
├── structure.json     # Crystal topology metadata (lattice, method, engine,
│                      #   sites, dimer_types, pairs) — human-readable
├── inputs/            # Generated QM input files
│   ├── <NAME>_monomer_000.gjf   # .gjf for g16/g09, .xyz for pyscf/gpu4pyscf/orca
│   ├── <NAME>_dimer_000.gjf
│   └── ...
├── logs/              # DFT output logs (.log / .out, .chk)
├── matrices/          # Extracted numerics (NumPy .npz)
│   ├── monomers.npz   # Monomer MO coefficients and energy levels
│   ├── dimers.npz     # Dimer overlap / Fock matrices
│   └── transfer.npz   # Transfer integrals and on-site levels
└── results/           # Final tight-binding results
    ├── band.png       # Band structure diagram along --band-path
    ├── band.npz       # Band energies, k-distances, tick positions and labels
    └── effective_mass.csv  # HOMO/LUMO band-edge effective masses and axis vectors

structure.json

Human-readable record of the generated structure: name, method, engine, generation parameters, the direct lattice vectors, the unique molecular sites, the symmetry-unique dimer_types, and the full pairs table (molecule indices, lattice offsets, and the dimer type each pair maps to). Per-calculation numerics are stored separately under matrices/.

Input file naming

Monomer and dimer inputs are named <NAME>_monomer_{index:03d} and <NAME>_dimer_{type:03d} (with the extension chosen by the engine). The filenames carry only the site/dimer-type identifier; the mapping information needed to reassemble the tight-binding model (central/neighbor molecules, lattice offsets, orbital ordering) lives in structure.json.

Notes

1. Calculation Time: Calculation time depends strongly on the number of molecules per cell, the method/basis set, and the chosen backend.
2. Memory Usage: Ensure sufficient memory for large systems (-m).
3. Gaussian Installation: Gaussian 09 or Gaussian 16 is required for the g09 / g16 engines.
4. Dependencies: Make sure the optional dependencies for your chosen backend are installed (see Installation).

Troubleshooting

If a calculation stops midway

# Resume with the --resume option
bcal xxx.cif --resume

Memory shortage error

# Increase the amount of memory
bcal xxx.cif -m 32

A band edge is not on the band diagram

If bcal warns that a HOMO/LUMO edge is not on --band-path, the band edge and effective masses are still correct (they are found over the full Brillouin zone), but band.png will not show the true extremum. Add the reported k-point's high-symmetry label to --band-path and re-run with -r to redraw without recomputing the DFT.

If a CIF file cannot be read

CIF files come in various formats, and some may not be readable by bcal. Please try the following:

1. Convert the CIF format using another software: Use software such as Mercury to open the CIF file and re-export it, which may resolve the issue.
2. Contact us: If you send the unreadable CIF file to us by email, we will work on adding support for it. Please contact us at the email address listed below.

Authors

Matsui Laboratory, Research Center for Organic Electronics (ROEL), Yamagata University
Tomoharu Okada, Koki Ozawa, Yu Homma, Hiroyuki Matsui
Email: h-matsui[at]yz.yamagata-u.ac.jp
Please replace [at] with @

References

[1] Qiming Sun et al., Recent developments in the PySCF program package, J. Chem. Phys. 2020, 153, 024109.
[2] Benjamin P. Pritchard et al., New Basis Set Exchange: An Open, Up-to-Date Resource for the Molecular Sciences Community, J. Chem. Inf. Model. 2019, 59, 4814-4820.
[3] Frank Neese, The ORCA program system, Wiley Interdiscip. Rev. Comput. Mol. Sci., 2012, 2, 73-78.