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Lattice dynamics codes like phonopy output vibrational frequencies at q-points. Can we get data of vibrational frequencies for each of the atoms in the supercell? (Real and/vs. reciprocal space has always been difficult to grasp.)

I understand that phonons are collective lattice vibrations, but it is after all the individual atoms and bonds that vibrate. If the partial density of states (PDoS) is the answer to this question then how do we know which frequencies will be occupied? Also, can it be said that the total DoS is for phonons (lattice (atoms + bonds)) and the PDoS is for atoms?

Apologies for the multiple questions, but, I suppose, they are the same question asked differently.

Optional (Motivation behind this question): I wish to design a supercell (DFT) representing a random solid solution. I would like for it to be such that most atoms have more phonon density of states at lower frequencies. The procedure I thought of following was to try out different arrangements (supercells) and study the partial density of states for each of those arrangements. From all of that data, I wanted to figure a way to construct a supercell that could be considered optimal with the objective of more low-frequency vibrations in mind.

I thought of two approaches. One, where I explore orbital overlap between atoms which I've to read more about. Another, to somehow figure how much and how far each atom vibrates given the chemical environment in its vicinity. This question was motivated by the second approach.

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    $\begingroup$ +1 but can you please clarify what you mean: do you want to know how a specific atom moves when you only excite a particular phonon? $\endgroup$ – ProfM Feb 5 at 8:23
  • $\begingroup$ Hello @ProfM, I want to know how a specific atom moves at any given temperature, for as many phonons may excite at that temperature. My thoughts are a bit ill-formed at the moment, sorry for that. If it makes it clearer, I've added a section on the motivation behind the question. $\endgroup$ – Hitanshu Sachania Feb 5 at 21:38
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As known [1], the eigenvalues of the dynamical Hessian matrix represent the phonon frequencies, whereas the eigenvectors represent the particular atomic displacement patterns contributing to the vibrations. Therefore you might be interested in analyzing the eigenvectors and building the atomic visualizations based on them. In many cases (especially in the complex systems) you'll find out that the certain phonons are caused by the displacements only of the certain atoms. There are some tools online [2, 3, 4] illustrating this idea.

Concerning your supercell construction, given the types of the atoms and the crystalline symmetry remains the same, your task is unfeasible, since you cannot "shift" the total phonon density of states to the lower frequencies for the same structure, irrelevant of the supercell chosen. However if you can vary the symmetry and the atomic content, this is possible.

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