Fast evaluation of spherical harmonics with sphericart
Filippo Bigi1,2, Guillaume Fraux1,2, Nicholas J Browning3
1Laboratory of Computational Science and Modelling, Institute of Materials, École Polytechnique Fédérale de Lausanne, Lausanne 1015, Switzerland.
The Journal of Chemical Physics
|August 8, 2023
Summary
We developed an efficient algorithm for calculating real-valued spherical harmonics and their derivatives. This method is implemented in the sphericart library, enhancing geometric machine learning applications.
Area of Science:
- Physics
- Chemistry
- Computer Science
- Geology
- Atmospheric Sciences
- Signal Processing
- Computer Graphics
Background:
- Spherical harmonics are essential for expanding functions on spheres across various scientific disciplines.
- They are increasingly vital in geometric machine learning for modeling molecules and materials.
Purpose of the Study:
- To present an elegant and efficient algorithm for evaluating real-valued spherical harmonics.
- To enable numerically stable and computationally efficient computation of Cartesian derivatives.
Main Methods:
- Developed a novel algorithm for real-valued spherical harmonic evaluation.
- Implemented the algorithm in a C++ library named sphericart.
- Provided C bindings, a Python API, and a PyTorch implementation with GPU support.
Main Results:
- The algorithm computes real-valued spherical harmonics efficiently.
- Cartesian derivatives are calculated in a numerically stable and efficient manner.
- The sphericart library offers broad accessibility and high performance.
Conclusions:
- The new algorithm and sphericart library offer significant improvements for applications utilizing spherical harmonics.
- This work facilitates advancements in fields ranging from theoretical chemistry to geometric machine learning.
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