sphericart documentation¶

The figure shows a plot of the +-1 isosurfaces of the Y^0_3 solid harmonic, colored in orange and blue. Gradients along the surfaces are also shown as black arrows. — A plot of the \(\pm1\) isosurfaces of the \(Y^0_3\) solid harmonic, including its gradient¶

sphericart is a multi-language library for the efficient calculation of spherical harmonics and their derivatives in Cartesian coordinates.

The theory behind this efficient implementation is detailed in this paper.

The core library is implemented in C++ (with OpenMP parallelism) and CUDA. It also provides APIs for C, Python (NumPy), PyTorch and JAX. The torch and JAX implementations provide fast spherical harmonics on GPUs.

A native Julia package is also available, contributed by Christoph Ortner.

This documentation contains an installation guide, an API overview, some examples of how to use the library, and a brief explanation of the mathematics involved.

If you are using sphericart for your academic work, you can cite it as

@article{sphericart,
    title={Fast evaluation of spherical harmonics with sphericart},
    author={Bigi, Filippo and Fraux, Guillaume and Browning, Nicholas J. and Ceriotti, Michele},
    journal={J. Chem. Phys.},
    year={2023},
    number={159},
    pages={064802},
}