How To Simulate The Universe With DFT

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If you used every particle in the observable universe to do a full quantum simulation, how big would that simulation be? At best a large molecule. That’s how insanely information dense the quantum wavefunction really is. And yet we routinely simulate systems with thousands, even millions of particles. How? By cheating. Using the ultimate compression algorithm: Density Functional Theory (DFT). Let’s learn how to cheat the universe.

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Hosted by Matt O'Dowd
Written by Graeme Gossel & Matt O'Dowd
Post Production by Leonardo Scholzer, Yago Ballarini, Pedro Osinski, Adriano Leal & Stephanie Faria
GFX Visualizations: Ajay Manuel
Directed by Andrew Kornhaber
Assistant Producer: Setare Gholipour
Executive Producers: Eric Brown & Andrew Kornhaber
Executives in Charge (PBS): Adam Dylewski, Maribel Lopez
Director of Programming (PBS): Gabrielle Ewing

Spacetime is produced by Kornhaber Brown for PBS Digital Studios.
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[pbsspacetime]

Hey Space Timers! At 10:30 Matt accidentally misspoke and called the Hohenberg-Kohn Theorem, the Kohn-Hohenberg Theorem. We know you're all an incredibly thorough bunch and would never miss a technicality like that, so unfortunately for us it's time to reset our "Days Without An Accident In Explaining the Universe Counter" back to "Big Bang."

[BrownieX]

Thought this was going to be about Discrete Fourier Transforms. Great to learn

[leviathan]

This sounds like the how calculus was invented trying to measure the area under a curve by making a rough estimate with a bunch of rectangles making them smaller and more numerous until you get close enough to reality.

[agentdarkboote]

Wow, finally one that I'm familiar with, I use DFT daily in my job! (Edit: I had said some stuff which was incorrect, deleting that bit. Thanks to John Ferrier for the correction). Anyone interested in reading about all of this can look first at the Hartree Fock method which is the starting point for basically all modern computational chemistry, which then each have various tricks to include the correlation. DFT scales pretty well though, which is why someone has done that virus capsid (although was that strictly DFT? It scales as N^3-N^4 still... Which is unspeakably better than 3^N but still expensive as N gets into the thousands). There are so many interesting methods out there. Semi empirical methods are so cool too, moderately accurate and blazingly fast. And just the way all of these methods actually do the math in the calculations, by stacking up "basis sets" of simpler functions to approximate atomic orbitals but which have really nice properties for calculating the various integrals, is just so cool.

If you want to continue the computational chemistry episodes, you should do an episode on the PPP (Pariser Parr Pople) method - it's simpler than DFT (it came earlier. People actually used to do these by hand), is used to calculate electronic transitions in aromatic molecules and is surprisingly accurate for such a simple method - and this is the real kicker - it was later worked out that it's an approximation to quantum field theory calculations which is why it's so accurate. I've always been super interested to find out how they relate, but the math has gone above my head and I haven't found any sources that attempt to explain it in an approachable way. I think that would tie in really well to this channel!

[jajssblue]

Really love these practical videos that show equations and methods most physicists actually use!

[barbermot]

Really neat that this channel is going places no one else on YouTube is. A lot of interesting things to hear about for the first time for me. Great topic.

[thelocalsage]

as someone whose research uses density functional theory every single day this episode makes me so happy 🥰🥰🥰

[schopenhauer]

I'm poorly educated and I only understand little if anything from this channel, yet I can't miss a single upload and know they'll be inspiring other kids out there to one day become a scientist too.

[shawn]

I did a few different kinds of DFT calculations in grad school. Never thought I'd see it discussed in a video for the lay person.

[otakuribo]

The animator is absolutely _crushing_ it lately; there's a very artful, demoscene vibe to these little animations and there's _so_ much detail 🌌🖥️🌇

[TheBackyardChemist]

One of the most interesting (albeit disappointing) results of DFT is what happens when you apply computational complexity theory to it. As it turns out, whatever the exact functional looks like, it cannot be simple enough to be evaluated in polynomial time, not even by a quantum computer (!!) Paper: 10.1038/nphys1370

[rocketgruntquang]

The deeper discussion of quantum mechanics is much appreciated. Many scientific communicators shy away from talking scientific complexity in front of lay audiences but this channel strikes a great balance between explanation and technicality.

[SlashHarkenUltra]

8:44 He could have said "If you don't get the order right, you're screwed."

[lattice]

Currently using DFT for solid state physics. So happy to see this reach the mainstream community! No surprise that it was PBS Spacetime and that they nailed it :) this channel is great

[mandymouse]

“Make sure you get the order right or it won’t work.” It took me a solid 4 second pause to figure this out. And then I laughed so hard I choked. Well done, guys. 🤓😂😂😂

[Slackermanz]

Ha! I was hoping it was Discrete Fourier Transforms - I work with Cellular Automata to try to understand and simulate artificial life & the conditions for abiogenesis, and DFT/FFT is one of the simulation techniques!
Still, never disappointed by a PBS Space Time video!

[scottthornton]

Yay ... my Ph.D. is on Density Functional Theory (DFT) and Time-Dependent Density Functional Theory (TDDFT)

[manonthedollar]

With the incredible amount of power that would be required to compute even a minuscule number of these interactions... do the ACTUAL interactions also require that much effort from the universe? And is it effort we are able to measure in some form, or is it all still mysterious at this point?

[aniksamiurrahman]

Ah! As a chemist myself, this episode really hit close to home.

[JordanTensor]

Tensor networks are another great method of simulating the low-entanglement subspace of quantum mechanics, informed by quantum information theory. They are more general than DFT, able to support interesting entanglement structures.