Not an expert in classical dynamics, but I suppose you could use eq.4.4.2 of Frenkel-Smit ( http://www.dsf.unica.it/~fiore/FS.pdf ) to obtain a local quantity. I am not sure this will be generally appropriate in the quantum case (in that case, I would probably use a stress density, attached).

Hi,

You can consult this paper for more details,

Article Calculation and Visualization of Atomistic Mechanical Stress...

I am far from convinced that this approach is going to be productive, at least right now. My limited experience suggests the problem gets rather complicated, as you have to consider only quantum states. As an example, I once calculated the anharmonicity of some bending vibrational states. The motion is not simple harmonic, because the restoring field at the equilibrium position is along the line of the bond. By assuming the field remained symmetrical, I got very good anharmonicity terms for the excited bending states, relying on the vibrational states had to have quantised action, but this only worked well for a very few molecules, the reason being that the restoring field would not remain symmetrical during excitation.

I also found a relationship to calculate the change of electric field as bonds bend and store the energy as strain. It was reasonably simple, but in the end somewhat empirical because I had to correct for changed bond distances, but it did give interesting predictions of the properties of strained systems. The problem is, it only worked at that level for fixed structures, and it was only useful for situations where a dipole was induced during a reaction, or if wave impedance could restrict bond delocalisation. The problem is, for chemical reactions, there is an awful lot we still do not know about how transition states can be calculated. However, I am reasonably convinced you must concentrate on the energy distribution in quantised states.

Sorry, but I did not find any responses usu-full. I just find the solution from LAMMPS manual.

I finally understood how to calculate it.

(Heyes) Heyes, Phys Rev B 49, 755 (1994),

(Sirk) Sirk, Moore, Brown, J Chem Phys, 138, 064505 (2013).

(Thompson) Thompson, Plimpton, Mattson, J Chem Phys, 131, 154107 (2009).