GSoC 2026: Integration of the Sphere with Maximum Determinant Points

[PaulWAyers]

Description

Add functionality to the Grid library for integration over the surface of a sphere. Currently we support Lebedev quadrature (nonequal weights, sometimes negative weights) and spherical t-designs (equal positive weights). An alternative, with nonequal but always positive weights, is the maximum determinant stategy.

📚 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?

Following the style of the spherical t-design grids, you will add functionality for the maximum determinant strategy. Up to a degree of 200, the points/weights are available here.
Incidentally, the same web page has one spherical design beyond what we have right now, for degree 325. It would be good to add this to our list.

🏁 Expected Outcomes

1. Add functionality for the maximum determinant strategy spherical integration.
2. Add the $\ell=325$ spherical t-design.
3. Write comprehensive tests and documentation for all new functionality.
4. Write tutorial Jupyter notebooks that show how to use the new functionality.

Required skills	Python, OOP
Preferred skills	Be comfortable with math and numerical algorithms. Experience with scientific programming can help
Project size	90 hours, Small
Difficulty	Easy ☺️

🙋 Mentors

Marco Martínez-González	mmg870630_at_gmail_dot_com	@marco-2023
Farnaz Heidar-Zadeh	farnaz.heidarzadeh_at_queensu_dot_ca	@FarnazH
Paul Ayers	ayers_at_mcmaster_dot_ca	@PaulWAyers
Ali Tehrani	19at27_at_queensu_dot_ca	@Ali-Tehrani

📝 Notes

• A stretch goal would be to implement yet another angular integration method, where the grid points are rigorously nested. One possibility would be to polish and merge Created Nested_Angluar_Grid.ipynb #274.
• See the discussion in Issue Integration of the Sphere with Maximum Determinant Points #237 .

[dhruvDev23]

Hi @PaulWAyers ,

My Name is Dhruv Kumar, and I am a third year engineering undergraduate at IIT Kanpur. I have been learning the Grid library and making contributions for past few months.

I am very interested in working on the project GSoC 2026: Integration of the Sphere with Maximum Determinant Points. I am comfortable working with Python and OOP, and I have been working with numerical methods and scientific Python.

I am currently exploring the current Lebedev and spherical t-design implementations and testing methodology and I have also started learning the maximum determinant strategy. I am also interested in working on the stretch goal and have started looking through the related discussion.

Could you please let me know if there are any specific parts of the codebase or prerequisite topics you would recommend learning first? and Also is there any Slack, Discord or any other communication channel of theochem where i can discuss the project and ask questions?

Thanks for your time.

[PaulWAyers]

I've invited you to the key orgs and the (private) discussion forum.

[dhruvDev23]

Thanks for the invitation. I really appreciate it.

[ShivamSukhija]

Hello @PaulWAyers ,

I’m Shivam Sukhija, a second-year engineering undergraduate at NSUT.

I’m very interested in contributing to this project for GSoC. I have experience working with Python and object-oriented programming, and I’m keen to apply those skills here. I’ve set up the repository locally and have started familiarizing myself with the codebase so I can begin contributing soon.

Looking forward to contributing to Grid.

[dhruvDev23]

Hi @PaulWAyers ,

I have made a good progress studying the codebase specially the angular.py file. I have gone through angular.py to understand how Lebedev and spherical t-designs are implemented, particularly the caching mechanism, degree/size mapping with bisect_left, and the weight normalization.

I have a quick question about the MaxDet data format: I have downloaded one of the points/weights file from here , and noticed they're plain text files, not .npz.

When I tried loading them with np.load() I get a pickle error because the file isn't actually a numpy archive.

Should I :

1. Create a conversion script to convert all MaxDet text files to .npz format?

2. Alternatively, is there an existing conversion script/different data source you'd recommend?

Thanks for your help!

[PaulWAyers]

I'd go with workflow #1.

[ShivamSukhija]

Hi @PaulWAyers ,

I wanted to share a progress update on the project. I've been working through understanding the maximum determinant method and the codebase structure.

I've downloaded all the maximum determinant data from the UNSW website for degrees 1 to 200. I then wrote a Python script which converts all the raw text data files into the .npz format. I've verified that all the converted data files pass basic checks, the weights sum to 4π as expected for the surface area of a unit sphere, all points lie exactly on the unit sphere surface, and all weights are positive.

I've organized the data files following the same naming pattern as the existing spherical design grids and placed them in the data directory to maintain consistency with the current repository structure. My next steps are to implement the MaximumDeterminant class itself, and then write a comprehensive test suite to validate the implementation.