HORTON-PART

HORTON-PART is a computational chemistry package that supports different partition schemes. It is based on the sub-module part of HORTON2, which is written and maintained by Toon Verstraelen (2). In HORTON3, all sub-modules have been rewritten using the pure Python programming language to support Python 3+. See more details on this website. It should be noted that HORTON2 also supports Python 3+ now. The part module has also been rewritten and is now called the denspart module. However, the algorithm implemented in denspart only uses one-step optimization, which can be computationally expensive for large systems. Additionally, denspart only supports the MBIS partitioning scheme. Another part module has been rewritten in pure Python by Farnaz Heidar-Zadeh (2). However, the integration grid implemented in this module still uses the old 'grid' from Horton2. HORTON-PART with version 0.0.X is based on this module. Starting from version 1.X.X, HORTON-PART only supports the new integration qc-grid. The molecular density can be prepared using IOData and GBasis packages.

This version contains contributions from: YingXing Cheng (1), Toon Verstraelen (2), Pawel Tecmer (3), Farnaz Heidar-Zadeh (3), Cristina E. González-Espinoza (3), Matthew Chan (3), Taewon D. Kim (3), Katharina Boguslawski (3), Stijn Fias (4), Steven Vandenbrande (2), Diego Berrocal (3), and Paul W. Ayers (3).

• (1) Numerical Mathematics for High Performance Computing (NMH), University of Stuttgart, Stuttgart, Germany.
• (2) Center for Molecular Modeling (CMM), Ghent University, Ghent, Belgium.
• (3) The Ayers Group, McMaster University, Hamilton, Ontario, Canada.
• (4) General Chemistry (ALGC), Free University of Brussels, Brussels, Belgium.

The Horton-Part source code is hosted on GitHub and is released under the GNU General Public License v3.0 or later. Please report any issues you encounter while using the Horton-Part library on GitHub Issues. For further information and inquiries, please contact us at yxcheng2buaa@gmail.com.

About

This package implements partitioning schemes described in three papers: a mathematical perspective, a numerical perspective and Approximations of the Iterative Stockholder Analysis scheme using exponential basis functions, including:

• Becke method
• Mulliken method
• Hirshfeld partitioning scheme
• Iterative Hirshfeld (Hirshfeld-I) partitioning scheme
• Iterative stockholder approach (ISA)
• Gaussian iterative stockholder approach (GISA)
• Minimal Basis Iterative Stockholder (MBIS)
• Alternating Linear approximation of the ISA (aLISA) method
• Global version of Linear approximation of the ISA (gLISA) method
• Generalized Minimal Basis Iterative Stockholder (GMBIS)
• Non-linear approximation of the ISA (NLIS) method

Periodic real-space grids

The periodic API provides a shared qc-grid engine for Hirshfeld, Hirshfeld-I, MBIS, LISA, and AVH-A/B/M. It accumulates translated local grid images and can return both atomic charges and full AIM weights. Fixed LISA, Hirshfeld, and AVH basis functions and active Hirshfeld-I charge states are cached only on their local grids. Periodic MBIS similarly reuses shell-local grids, expanding a grid only when its optimized shell becomes more diffuse. All-electron DensPart-style NPZ files, including uniform and PAW augmentation grid blocks, can be used directly:

part-from-gpaw calculation.gpw density.npz  # run in a legacy GPAW environment
part-periodic density.npz mbis.npz --method mbis
part-periodic density.npz mbis-sc.npz --method mbis --solver sc
part-periodic density.npz hi.npz --method hirshfeld-i \
  --basis pbe-6311pgdp-sapporo-dkh3tzp-dkh2.json

GPAW remains optional and is not installed with HORTON-Part. The converter runs serially and preserves the all-electron PAW augmentation blocks required for the article calculations.

Periodic LISA, AVH, and MBIS provide both the default SciPy optimizer and a finite-system-style self-consistent route selected with --solver sc. The result archive records the solver used; performance should be benchmarked for each system.

Hirshfeld, Hirshfeld-I, and AVH use a shared aim-proatom-spline-v1 library; finite and periodic LISA both accept aim-lisa-basis-v1 in addition to the bundled basis. See the periodic guide for the input schema, Python API, output fields, and method-specific basis requirements. Executable examples are provided in the periodic quick start and five-method comparison notebooks.

License

horton-part is distributed under the GNU General Public License version 3 or later. Third-party source-code acknowledgements are listed in NOTICE.

Dependencies

The following dependencies will be necessary for horton-part to build properly,

• quadprog>=0.1.11 : https://github.com/quadprog/quadprog
• cvxopt>=1.3.1 : https://github.com/cvxopt/cvxopt
• qc-grid : https://github.com/theochem/grid
• qc-iodata : https://github.com/theochem/iodata
• gbasis : https://github.com/theochem/gbasis

Installation

To install the latest version of horton-part:

pip install horton-part

To install horton-part with version 0.0.x:

pip install horton-part==0.0.x

To install latest horton-part:

git clone https://github.com/LISA-partitioning-method/horton-part.git
cd horton-part
pip install .

To run test, one needs to add tests dependencies for tests:

pip install .[tests]

For developers, one could need all dependencies:

pip install -e .[dev,tests]

Citations

Please use the following citations in any publication using horton-part library:

[1] Cheng, Y. and Stamm, B. Approximations of the Iterative Stockholder Analysis scheme using exponential basis functions.

[2] Cheng, Y.; Cancès, E.; Ehrlacher, V.; Misquitta, A. J.; Stamm, B. Multi-center decomposition of molecular densities: A numerical perspective. J. Chem. Phys. 2025, 162, 074101,

[3] Benda, R.; Cancès, E.; Ehrlacher, V.; Stamm, B. Multi-center decomposition of molecular densities: A mathematical perspective. J. Chem. Phys. 2022, 156, 164107.

[4] Chan, M.; Verstraelen, T.; Tehrani, A.; Richer, M.; Yang, X. D.; Kim, T. D.; Vöhringer-Martinez, E.; Heidar-Zadeh, F.; Ayers, P. W. The tale of HORTON: Lessons learned in a decade of scientific software development. J. Chem. Phys. 2024, 160, 162501.

[5] Tehrani, A.; Yang, X. D.; Martínez-González, M.; Pujal, L.; Hernández-Esparza, R.; Chan, M.; Vöhringer-Martinez, E.; Verstraelen, T.; Ayers, P. W.; Heidar-Zadeh, F. Grid: A Python library for molecular integration, interpolation, differentiation, and more. J. Chem. Phys. 2024, 160, 172503.

[6] Kim, T. D.; Pujal, L.; Richer, M.; van Zyl, M.; Martínez-González, M.; Tehrani, A.; Chuiko, V.; Sánchez-Díaz, G.; Sanchez, W.; Adams, W.; Huang, X.; Kelly, B. D.; Vöhringer-Martinez, E.; Verstraelen, T.; Heidar-Zadeh, F.; Ayers, P. W. GBasis: A Python library for evaluating functions, functionals, and integrals expressed with Gaussian basis functions. J. Chem. Phys. 2024, 161, 042503.

[7] Verstraelen, T.; Adams, W.; Pujal, L.; Tehrani, A.; Kelly, B. D.; Macaya, L.; Meng, F.; Richer, M.; Hernández-Esparza, R.; Yang, X. D.; Chan, M.; Kim, T. D.; Cools-Ceuppens, M.; Chuiko, V.; Vöhringer-Martinez, E.; Ayers, P. W.; Heidar-Zadeh, F. IOData: A python library for reading, writing, and converting computational chemistry file formats and generating input files. J. Comput. Chem. 2021, 42, 458–464.