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! Thi...

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....

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 v...

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 continu...

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: Exten...

Orbitals Are Mathematical Pick up almost any introductory chemistry textbook and you will find an orbital depicted as a tangible object: a lobed shape around an atom, a probability cloud you could...

This post is part of a series on Hartree-Fock theory: Restricted Hartree-Fock in 100 Lines: The original post; start here if new to HF Unrestricted Hartree-Fock in 100 Lines: You are here Th...

The Problem I came across an issue on a project I was working on a few years ago which, for whatever reason, popped into my head yesterday whilst building a shed. I was working on a method for rec...

Try the code yourself! Click the following button to launch an ipython notebook on Google Colab which implements the code developed in this post: In 1950, Chaim L. Pekeris wrote to John von Neu...

Try the code yourself! Click the following button to launch an ipython notebook on Google Colab which implements the code developed in this post: The Problem In computational chemistry, calcul...