Transformed Cubic Grids

Description

One disadvantage of Becke-style molecular grids is that, due to overlapping atomic grids, there are numerous grid points that have very small, but nonnegligible, weights. Our strategy to overcome this issue is to use a cubic grid, but transform it to real space in such a way that points are concentrated where the integrands of interest are large and/or rapidly changing. The goal of this project is add this functionality to Grid. One nice facet of this approach is that it is easy to adaptively refine a cubic grid, and ergo a transformed cubic grid. This allows for adaptive quadrature to be implemented without too much pain.

📚 Package Description and Impact

Grid is a pure Python library for numerical integration, interpolation and differentiation of interest for the quantum chemistry community.

👷 What will you do?

A more detailed description of this project is available in issue #15 . The basic idea is to take a cubic grid, and then perform a transformation based on a probability distribution function, using the conditional distribution method.

🏁 Expected Outcomes

1. Refresh pull request #96 and merge it.
2. Implement adaptive transformed cubic grid.
3. Write comprehensive tests and documentation for all new functionality.
4. Write tutorial Jupyter notebooks that show how to use the new functionality.

🙋 Mentors

Start with the Grid entry point, then read issue #15 and review pull request #96 for the existing transformed-grid work. Done means adaptive transformed cubic-grid functionality is implemented, with comprehensive tests, documentation, and tutorial Jupyter notebooks.