What is matter modeling?

Question

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!

Answer 1

"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 density-functional-theory) 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 mathematical-modeling and algorithms). Some might be using machine-learning, or maybe even doing experimental research but need help in analyzing or interpreting the data, or a modeler might be comparing theory to experiment and may have an experimental question for that reason.

There's a lot of software 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 vasp forum could better be answered by a quantum-espresso 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 high-performance-computing 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 solid-state-physics) which is a bit too specific to describe this community.

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

• Discussion about the name for Materials/Matter Modeling
• What should this site be called?

and then again when the site entered Private Beta:

• Better late than too late: Could a single word substitution in our name, be at least considered?

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!).

Answer 2

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.