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, but it also periodic boundary conditions.

Please use the following citation in any publication using grid library:

“Grid: A Python Library for Molecular Integration, Interpolation, Differentiation and More.”, A. Tehrani, X. D. Yang, M. Martinez-Gonzalez,, L. Pujal, R. Hernandez‐Esparza, M. Chan, E. Vohringer‐Martinez, T. Verstraelen, P. W. Ayers, F. Heidar‐Zadeh

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


  • One-dimensional integration

    • quadratures

    • transformations

  • Multivariate integration

    • Hypercubes:

      • Tensor product of one-dimensional quadratures

      • Rectilinear (a.k.a uniform) and skewed grids

    • Integration over sphere:

      • Lebedev-Laikov grids

      • Symmetric Spherical T-Designs

    • Molecular integration:

      • Atom in molecule weights (nuclear weight functions)

        • Hirshfeld weights

        • Becke weights

  • Interpolation & differentiation

  • General ODE solver and Poisson solver




One-dimensional Grids

Integration of real-valued function over real line.

Radial Transform

Transforming one-dimensional grids from one interval to another.

Angular Grids

Integrating functions over sphere/angular coordinates.


Solving linear ordinary differential equations.


Solving the Poisson equation.

Atomic Grid

Integrating real-valued function over three-dimensional Euclidean space.

Becke Weights

Type of nuclear weight function/atom in molecule weights.

Hirshfield Weights

Type of nuclear weight function/atom in molecule weights.

Molecular Grids

Integration of general functions in three-dimensional space.

Cubic Grids

Hyper-Rectangular Grid in either two or three dimensions.

Periodic Grids

Integrating periodic functions in 1, 2 or 3 dimensions.

API Documentation

Indices and tables