# Why can we know a materials properties by knowing its ground state at 0K - DFT

I have had this doubt ever since I was introduced to DFT. For what I gathered whatever results you obtained with DFT (by using VASP, quantum expresso or any other software) you can say those properties are it, even for temperatures beyond 0K.

I don't understand why. For instance if DFT says it's ferromagnetic at 0K then why would you assume its ferromagnetic properties would stay sufficiently close to the ground state for T>0 as to state that.

I haven't read a theorem that says that excited states are close to the ground state. Does such theorem exist?

Thanks!

Edit: Quoting the book "A chemist's Guide to DFT" at the end of the section about the first Hohenberg-Kohn theorem **

One should note at this point that the ground state density uniquely determines the Hamilton operator, which characterizes all states of the system, ground and excited. Thus, all properties of all states are formally determined by the ground state density (even though we would need functionals other than ∫ρ(r)V dr + F [ρ], which is the functional constructed to deliver E0 but not properties of electronically excited states).

I don't follow it. Seems pretty basic cuz everyone just brushes over but I don't follow it. Why would the ground state characterize excited states?

** The first theorem basically says that the hamiltonian can be defined by the electronic density and can be made a unique functional of it.

• Magnetic properties and such are mostly physics, not chemistry. When one says it is a ferromagnetic ground state, everyone knows she/he talks about the ground state. Chemically relevant electronic excitations are generally high energy, and when we expect low energy ones, generally you explicitly check those.
– Greg
Feb 24, 2019 at 13:55
• It was as an example, I have the same question for the band gap or the resulting structure. As far as I have heard, the answer has to do more with chemistry than physics. Where can I read somewhere that says "Chemically relevant electronic excitations are generally high energy", is that the case if the material is metallic or a semiconductor?
– M.O.
Feb 24, 2019 at 14:06
• Metals and semiconductor band gaps are primarily physics / materials science problems, again. Molecular structures are generally OK with vibrational ground state, and isomerism is generally be described by just another vibrational ground state. You don’t use DFT with 0K for metals, anyways, neither you have many chemists dealing with simulation of metallic systems. “I have heard” sorry, ask them then.
– Greg
Feb 24, 2019 at 16:55
• I think you are asking two different things in your first and second part of your question.
– Greg
Feb 24, 2019 at 17:02
• I might be mistaken but I think they are the same. All the properties of the system are defined by the electronic density, so if the properties of the material can be extrapolated to temperatures beyond 0K, then the reason why has to do with the electronic density's ground state. I am coming here for help in understanding this, so I could be wrong.
– M.O.
Feb 25, 2019 at 0:04