# What is matter modeling?

Perhaps a stupid question, but.. what is matter modeling?

I've never heard of it, and a google search just returns news articles about this site that seem to assume you already know what it is. I can't even find a Wikipedia article!

• +100 That's a very important question, and we as a community have to figure out the answer! The question is almost identical to: mattermodeling.stackexchange.com/q/110/5, but not a duplicate because our site's name changed since then :) Also: "news articles about the site"? Anything apart from Adam Iaizzi's blog post? Mar 19, 2021 at 20:30
• @NikeDattani So "matter modeling" is the same as "materials modeling"? If the latter is the more common term (based on the fact that my google search for that returns actual results), why was the site name changed? Mar 19, 2021 at 20:39
• They're not the same, and that's why your question is so important. It's also why I've suggested for people not to try to vote to close it as a duplicate. This is the discussion from when we requested to have the name changed. It feels like a decade ago, and I'll probably find myself shocked if I re-read it now, but it describes how we felt at the time: mattermodeling.meta.stackexchange.com/q/96/5 Mar 19, 2021 at 20:43
• Not a full answer, but the idea is basically to cover a wider umbrella. We wanted the site to cover things like modeling of molecules, subatomic particles, and fluid dynamics; none of which are typically classified as "materials" (atleast not as the term is used in chemistry/engineering/material science)
– Tyberius
Mar 19, 2021 at 21:10
• This should have been a meta question. Mar 20, 2021 at 12:55

### "Matter modeling" is a term that was coined by Stack Exchangers!

That's why the words "matter" and "modeling" next to each other, don't seem to exist in any of the results in a Google search of "Matter Modeling", apart from this Stack Exchange site, Adam Iaizzi's blog post about this SE site, and maybe our community's Facebook group but for some reason the last one didn't show up in my Google search just now.

Basically, people trying to model physical matter (materials, molecules, atoms, nuclei, etc.) have so much in common. All of this type of matter is described by the Schrödinger equation, or if modeling on a much more macroscopic scale: by Newton's second law. So we are all basically writing or running computer programs to solve Schrödinger equations (or Kohn-Sham equations for those using the mathematically equivalent ) or Newton's equations to study some phenomena about matter. Some of us might not be coding or computing, but instead are deriving equations (mathematics) or studying the computational complexity of an algorithm (theoretical computer science) for the modeling of matter (see and ). Some might be using , or maybe even doing research but need help in analyzing or interpreting the data, or a modeler might be comparing theory to experiment and may have an question for that reason.

There's a lot of we use (dozens and dozens of software packages), and many of them had their own independent forums requiring users to register a username and password for each one, and sometimes a question on the forum could better be answered by a user because some software can do certain types of calculations which others don't. Physics.SE, Chemistry.SE, QuantumComputing.SE, ComputationalScience.SE, ComputerScience.SE, TheoreticalCS.SE, ArtificialIntelligence.SE, Statistics.SE, Engineering.SE, Mathematics.SE, MathOverflow and others had matter modeling questions sprinkled across them, but it was spread out and never all in one place. We also do a lot of which is on-topic but very "niche" on AskUbuntu, StackOverflow, Linux&Unix, ServerFault, etc. (see this deleted Meta SE question if you have enough reputation there!). This was discussed on Area51.

The name of our site began as "Materials Modeling SE", which does have a Wikipedia page and a little bit of information available online, and while you can argue (for example) that atoms are made of "sub-atomic material", the word material often refers to solid materials (see our tag ) which is a bit too specific to describe this community.

We discussed what we should call ourselves, twice on Area51:

and then again when the site entered Private Beta:

### Did we really just make up a new term?

Even outside of Stack Exchange, pre-cursors started to pop up around the world, as this answer points out that a relatively new journal called "Matter" was launched as a sister journal to "Cell" and "Chem", and Alan Aspuru-Guzik, an always creative and forward-thinking scientist who did computational research for both molecules and solid-state materials, renamed his research group the Matter Lab when he moved from Harvard to Toronto, and he took the domain matter.toronto.edu (we also wanted matter.stackexchange.com but spent all our energy on changing "Materials Modeling" to "Matter Modeling" so we postponed that feature request for later!).

• And the Dirac equation for relativistic matter :). Mar 20, 2021 at 1:41

First of all, we assume the matter is constituted by nuclei and electrons, as illustrated by the following figure:

Mathematically, the matter is mapped into the following Hamiltonian:

$$H=T_e + T_n + V_{ee} + V_{nn} + V_{en} \tag{1}$$

which is called the standard model of condensed matter physics. In principle, all information (ground state/excited state/nonequilibrium state properties) about the matter encoded in this Hamiltonian can be extracted from it just by solving the following Schrodinger equation (SE):

$$H \psi =E \psi \tag{2}$$

In general, you can say matter modeling is to solve the SE of matter to capture the relative properties. Unfortunately, Eq.(2) is a notorious quantum many-body problem and hardly solvable. Therefore, different approximation schemes have been developed.

Based on the mass difference between nucleon and electron, Born and Oppenheimer introduce the BO approximation to separate the nucleon degree of freedom (DOF) and electron DOF:

• Nucleon DOF:

$$H_n=T_{n}+V_{nn} \tag{3}$$

• Electron DOF:

$$H_e=T_{e} + V_{ee} + V_{en} \tag{4}$$

Eq.(3) for nucleon DOF is usually treated classically with the total force are calculated by DFT:

• Molecular dynamics method;
• Density functional perturbation theory;
• .....

Eq.(4) for electron DOF is solved by many first-principles schemes:

• Density Functional Theory (ground-state properties)
• GW method (excited state properties)
• BSE (excited state properties)
• DFT+NEGF (nonequilibrium properties)
• ...

These are what matter modeling is doing in practice! In short, matter modeling means solving the SE with different approximation schemes to decode the information contained in matter Hamiltonian.

Hope it helps.

• +1 you beat me to it! I was writing my answer at the same time but took too long :) You seem to be writing a lot about electronic-structure-theory but what about molecular-dynamics? Mar 20, 2021 at 0:32
• Oops, I meant electronic-structure. Mar 20, 2021 at 0:54
• @NikeDattani We share many similar ideas :). MD is related to nucleon DOF, I just mention it. But I will detail that.
– Jack
Mar 20, 2021 at 4:27