Interesting! H2 is relatively straight forward since you can assume opposite spin, so can skip exchange and just run an integral (read: 3D grid) over space and have the two electrons repel each other (Via modifying the potential) using a fractional charge at each point. You can model each electron as a handful of STOs or GTOs. (And they are identical)
H2 also has large amplitude motions. Becomes a quantum solid where one can obtain single-photon absorption spectra which would normally be forbidden. Among other very interesting phenomena.
The solid molecular hydrogens in the condensed phase:
Fundamentals and static properties
Isaac F. Silvera
Rev. Mod. Phys. 52, 393 – Published 1 April 1980
"Abstract
The molecular hydrogens (H2, D2, HD, etc.) form the simplest of all molecular solids. The combination of the light mass, small moment of inertia, weak interactions, and the quasi-metastable ortho-para species result in a fascinating low-temperature behavior that can be understood to a large extent from considerations of first principles. After discussing single molecule properties and intermolecular interactions we discuss in detail the ortho-para properties, conversion and diffusion. This is followed by a description of the crystal structures and the orientational ordering phenomena. The thermodynamic properties are reviewed. The article is concluded with a discussion of the translational ground state of the solid and the effect of the large zero-point motion on the solid state properties. A large number of data are collected in tables and graphs to provide a reference source."
Quantum chemistry in this context refers to numerical simulations of how atoms and their electrons behave. The paper says that they used density functional theory as implemented in VASP (Vienna Ab initio Simulation Package), a common way to approximate electron-atom and electron-electron interactions:
Another common way to simulate behavior of materials dissolved in water is "classical" molecular dynamics, using only Newtonian physics and a set of lumped empirical parameterizations to model molecules as a collection of "balls and springs." This is much faster than ab initio molecular dynamics but less usable for exotic materials like promethium complexes, where it is unlikely that anyone has ever generated/validated a good set of parameters.
Solving the Schrodinger equation for multiple electrons in a molecule. This becomes very computationally intensive as you add more electrons.
For example, there’s not enough energy in the universe to simulate a human with the full Schrodinger equation with our existing technology for a meaningful amount of time.
I was just struggling to find any significance in prime numbered elements and thought that the fine structure constant's appearance in a bunch of equations was a bit more interesting of a topic.
I would have to spend a few hours in review to comment any further.
Actual paper in Nature: https://www.nature.com/articles/s41586-024-07267-6