https://adambaskerville.github.io/Dr Adam Luke BaskervilleThe personal website of Adam Luke Baskerville Contains information and T>T blog containing mathematics and science content 2026-10-05T17:32:17+01:00 Adam Baskerville https://adambaskerville.github.io/ Jekyll © 2026 Adam Baskerville /assets/img/favicons/favicon.ico /assets/img/favicons/favicon-96x96.png T>T: Helium to 60 Significant Figures with FLAKE, The Full Story2026-08-25T00:00:00+01:00 2026-08-25T00:00:00+01:00 https://adambaskerville.github.io/posts/FLAKE-Helium-Deep-Dive/ Adam Baskerville TLDR: In this post learn how to calculate a rigorous variational upper bound on the non-relativistic ground-state energy of helium, correct to 60 significant figures, computable on your laptop! This surpasses the previous record value (Schwartz, 2006) correct to 44 which stood for 20 years. The result (in hartrees) Schwartz (2006), previous record −2.903724377034119598311159245194404446696... T>T: Exact Cusp–Tail Density Functional for the Bound Two-Electron Coulomb Series2025-11-05T00:00:00+00:00 2025-11-05T00:00:00+00:00 https://adambaskerville.github.io/posts/CuspTailDensityFunctional/ Adam Baskerville My background is in physics and when I entered the weird and wonderful world of chemistry, I remember reading about the Hohenberg and Kohn theorem which has been floating around my head ever since. If you ever see me sitting quietly in a corner, I am probably thinking about this problem, or just staring at the wall but hopefully the former. The TLDR of this theorem is: “the ground-state proper... T>T: Can a Neural Network Predict the Mandelbrot set?2025-09-27T00:00:00+01:00 2026-06-22T23:19:56+01:00 https://adambaskerville.github.io/posts/MandelbrotFourierFeatures/ Adam Baskerville Try the code yourself! Click the following button to launch an ipython notebook on Google Colab which implements the code developed in this post: A few years ago I remember watching a YouTube video where it was tested whether a neural network could be trained to predict the structure of the Mandelbrot set. I cannot find this video and only have vague memories of it (as Bob Mortimer once sa... T>T: The First Solution is Rarely the Best: A Lesson in Numerical Integration2025-07-13T00:00:00+01:00 2026-05-31T22:59:48+01:00 https://adambaskerville.github.io/posts/TwoElectronIntegral/ Adam Baskerville If you spend enough time developing scientific software, you eventually learn that the first solution to a problem is rarely the best one. Science, and the code we write to execute it, is a continual learning process which is one of the things I love most about the field. I have been repeatedly guilty of brute-forcing a mathematical derivation to prove it can be done, only to realise later that... T>T: The Integrals at the Heart of Hartree-Fock Theory2025-05-10T00:00:00+01:00 2026-05-20T16:34:17+01:00 https://adambaskerville.github.io/posts/HFIntegrals/ Adam Baskerville This post is part of a series on Hartree-Fock theory: Restricted Hartree-Fock in 100 Lines: The original post; recommended reading before this one Unrestricted Hartree-Fock in 100 Lines: Extends RHF to open-shell systems The Integrals at the Heart of Hartree-Fock Theory: You are here If you have read the Hartree-Fock post or the UHF post, you will have seen the Roothaan-Hall equation...