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In the Born-Oppenheimer approximation nuclei are assumed to behave as classical point-like particles. However, in reality the wave-particle duality also applies to them, and so the Schrödinger equation should also be solved for the nuclei $I$ in the potentials $V^I({\bf R})$ generated by the electrons. The harmonic approximation implies not using the full ...


15

This is a difficult question without a straight-forward answer. In general you have to perform a test to decide whether the harmonic approximation is sufficient or whether you need to include higher order anharmonic terms in the potential expansion. Due to the computational cost of including anharmonic terms, very often systems are assumed to be harmonic ...


5

If you have a system without periodicity like your disordered solid solution, then you should use a $1\times1\times1$ $\mathbf{q}$-point grid for a phonon calculation (equivalent to a $1\times1\times1$ supercell). Using a larger supercell will introduce an artificial periodicity in the system. Having said this, it is still really important to converge with ...


4

A "pure harmonic system" does not allow opportunity for evolution. It is the equivalent of a fixed point. In initial consideration, its stability seems appealing, as it appears to be a goal (or “the goal”) of an imperfect system. However, it only embodies that moniker once, and change is the only real constant. Pure harmonics are fragile, brittle, ...


3

The Born-Oppenheimer (BO) approximation works well at high temperatures (far from 0 K), but the quantum nature of the nuclei (i.e. the zero-point energy) is an important consideration at low temperatures. A great example of this is the difference between the Einstein and Debye models of a solid. In the Einstein model, the nuclei are treated as identical ...


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