Welcome to Grid’s Documentation!

Welcome to Grid’s Documentation!#

Grid is a free and open-source Python library for numerical integration, interpolation and differentiation of interest for the quantum chemistry community. Grid is intended to support molecular density-functional (DFT) theory calculations, and it also supports periodic boundary conditions.

Citation#

Please use the following citation in any publication using Grid:

Grid: A Python library for molecular integration, interpolation, differentiation, and more. Alireza Tehrani, Xiaotian Derrick Yang, Marco Martínez-González, Leila Pujal, Raymundo Hernández-Esparza, Matthew Chan, Esteban Vöhringer-Martinez, Toon Verstraelen, Paul W. Ayers, Farnaz Heidar-Zadeh. J. Chem. Phys. 160 (17), 172503 (2024). https://doi.org/10.1063/5.0202240

@article{grid,
    author = {Tehrani, Alireza and Yang, Xiaotian Derrick and Martínez-González, Marco and Pujal, Leila and Hernández-Esparza, Raymundo and Chan, Matthew and Vöhringer-Martinez, Esteban and Verstraelen, Toon and Ayers, Paul W. and Heidar-Zadeh, Farnaz},
    title = {Grid: A Python library for molecular integration, interpolation, differentiation, and more},
    journal = {The Journal of Chemical Physics},
    volume = {160},
    number = {17},
    pages = {172503},
    year = {2024},
    month = {05},
    doi = {10.1063/5.0202240},
    url = {https://doi.org/10.1063/5.0202240},
}

License and Contributions#

The Grid source code is hosted on GitHub and is released under the GNU General Public License v3.0. We welcome any contributions to Grid in accordance with our Code of Conduct and Contributing Guidelines. Please report issues on GitHub Issues. For further information and inquiries please contact us at qcdevs@gmail.com.

Key Features#

Integration#

  • One-dimensional integration: quadratures and transformations

  • Multivariate integration:

    • Hypercubes with tensor product grids

    • Integration over spheres with angular grids

    • Molecular integration with various weight functions

Transformations#

  • Radial transformations for converting one-dimensional grids between intervals

  • Support for finite and infinite domains

Analysis#

  • Interpolation on constructed grids

  • Differentiation through grid-based methods

  • ODE solver for linear ordinary differential equations

  • Poisson solver for the Poisson equation

Available Modules#

Module

Purpose

grid.onedgrid

One-dimensional quadrature grids and integration

grid.rtransform

Radial transformations between intervals

grid.angular

Angular grids for spherical integration

grid.atomgrid

Atomic grids for 3D integration

grid.molgrid

Molecular grids with atom-in-molecule weights

grid.becke

Becke weight functions

grid.hirshfeld

Hirshfeld weight functions

grid.cubic

Hyper-rectangular grids in 2D or 3D

grid.periodicgrid

Periodic grids for 1D, 2D, or 3D

grid.ode

ODE solver

grid.poisson

Poisson equation solver

grid.utils

Utility functions for coordinate transformations and spherical harmonics