# Does strain affect on-site energy?

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If I understand what you are asking, the answer is yes. Strain will affect the energy of an individual atom in the lattice. There is no simple formula I know of, it has to be solved with DFT. The typical method is to model the lattice with matched boundary conditions, but your unit cell is actually several unit cells large. You allow the atomic positions to migrate to the lowest energy position. Then take your optimized lattice and model again with one atom popped out, without allowing atoms to migrate. The difference is the "site energy" you're looking for. When you do this kind of modeling, you'll see it converge to a value as you increase the number of unit cells, i.e. 3x3f

TL;DR Summary
Does strain affects on-site energy? Is there any formula which connect strain and on-site energy?
I want to study strain effects on the one material which has non-zero on-site energy . Does strain affects on-site energies?

I guess by “on-site energy”, you mean “internal energy”?

As stress increases, the strain increases, and energy is stored in the elastic material.
There is a yield point, where the stress is partially relieved by plastic deformation.

If the stress is then removed the elastic strain will be reduced, but there will be some energy remaining in plastic strain where adjacent grains in the material have undergone different plastic deformation.

“Work hardening” is associated with remaining internal energy.
https://en.wikipedia.org/wiki/Work_hardening
“Annealing” can relieve the remaining internal energy.

The internal energy that remains will depend on the state of the grains within the material.
What is that material and what do you know about the internal grain structure?

I guess by “on-site energy”, you mean “internal energy”?

As stress increases, the strain increases, and energy is stored in the elastic material.
There is a yield point, where the stress is partially relieved by plastic deformation.

If the stress is then removed the elastic strain will be reduced, but there will be some energy remaining in plastic strain where adjacent grains in the material have undergone different plastic deformation.

“Work hardening” is associated with remaining internal energy.
https://en.wikipedia.org/wiki/Work_hardening
“Annealing” can relieve the remaining internal energy.

The internal energy that remains will depend on the state of the grains within the material.
What is that material and what do you know about the internal grain structure?
Thank you
But I mean exactly on-site energy not internal.
On-site energy is a constant in Hamiltonian matrix

What sort of strain are you referring to here ?
Is this Quantum Theory, or strength of materials ?
If you actually specify the subject, you may get a better answer.

What sort of strain are you referring to here ?
Is this Quantum Theory, or strength of materials ?
If you actually specify the subject, you may get a better answer.
Yes this problem is related to the Quantum mechanic and is about 2D materials.

If I understand what you are asking, the answer is yes. Strain will affect the energy of an individual atom in the lattice. There is no simple formula I know of, it has to be solved with DFT. The typical method is to model the lattice with matched boundary conditions, but your unit cell is actually several unit cells large. You allow the atomic positions to migrate to the lowest energy position. Then take your optimized lattice and model again with one atom popped out, without allowing atoms to migrate. The difference is the "site energy" you're looking for. When you do this kind of modeling, you'll see it converge to a value as you increase the number of unit cells, i.e. 3x3 then 4x4 then 5x5. It doesn't take much to get rid of edge effects.

If I understand what you are asking, the answer is yes. Strain will affect the energy of an individual atom in the lattice. There is no simple formula I know of, it has to be solved with DFT. The typical method is to model the lattice with matched boundary conditions, but your unit cell is actually several unit cells large. You allow the atomic positions to migrate to the lowest energy position. Then take your optimized lattice and model again with one atom popped out, without allowing atoms to migrate. The difference is the "site energy" you're looking for. When you do this kind of modeling, you'll see it converge to a value as you increase the number of unit cells, i.e. 3x3 then 4x4 then 5x5. It doesn't take much to get rid of edge effects.
Thank you so much.
Is there any tight-binding method for calculating on-site energy under strain?

If I understand what you are asking, the answer is yes. Strain will affect the energy of an individual atom in the lattice. There is no simple formula I know of, it has to be solved with DFT. The typical method is to model the lattice with matched boundary conditions, but your unit cell is actually several unit cells large. You allow the atomic positions to migrate to the lowest energy position. Then take your optimized lattice and model again with one atom popped out, without allowing atoms to migrate. The difference is the "site energy" you're looking for. When you do this kind of modeling, you'll see it converge to a value as you increase the number of unit cells, i.e. 3x3 then 4x4 then 5x5. It doesn't take much to get rid of edge effects.
Hi @crashcat , can you provide an example of this from the literature? Whenever I see strain treated via tight binding, I only ever see it entering in the hopping Hamiltonian, rather than the on-site Hamiltonian (example: https://arxiv.org/abs/1511.06254).