Materials Project is funded by the US Department of Energy and uses supercomputing to simulate hundreds of thousands of different crystal structures on the quantum mechanical level to try and find those which have useful properties for practical applications.
This line of research is broadly called “materials discovery”, “materials design” (often “high throughput”) or even “materials genomics” depending on who you ask. These terms are provided in case anyone wants to search and read more about it.
A truly periodic substrate lets you wrap it in a closed universe just big enough for what you hope to make live in it.
Besides it's been fairly recent that simulations for classical thermodynamics with a decent number of particles became somewhat feasible. And even then it often uses lots of approximations as well as statistical tricks to get decent results for sizeable systems. For quantum mechanics quite a few tricks to explore the state-space stop working because the state-space is unimaginably huge, so I'm not even sure how to begin to do similar simulations, but I reckon they'll be disastrously slow for all but the simplest of systems.
The level of detail you need for a simulation that allows you to see cooper pairs come into existence is downright insane, you might be better of trying to predict next years weather.
[0] https://iopscience.iop.org/article/10.1088/0953-8984/23/5/05...
Create a simulation, down to the quantum states, of a lattice of molecules at a certain simulated temperature (say, room temperature), and induce a simulated current through the lattice, and see if it superconducts. Proceed by iterating through billions of permutations of compounds in the simulated lattice, until the simulation finds a room-temperature superconductor.
Assuming this is feasible, does anyone know of organizations that are doing this?