[Pw_forum] the difference between the linear response method and finite differences of the atomic forces

[degironc]

numerical derivative vs analytic ones.
If well done they agree.
Advantages of numerical derivatives: relative simplicity of coding,
access to non-linear anharminic terms.
Disadvantages of numerical derivatives: needs care in order to isolate
the harmonic terms from the anharmonic one, limited to zone-center modes
(electric fields require extra coding/care), non-zone center modes
requires supercells which imply extra computational effort, especially
for small/low symmetry q-points.
Advantages of analytical derivates: direct access to harmonic terms, not
limited to zone-center modes, used to be the only way to deal properly
with macroscopic electric fields but this is not so much true nowadays.
Disadvantage of anaylital derivatves: anharmonic terms require extra coding.
hope this helps.
Stefano de Gironcoli, SISSA and DEMOCRITOS

li niu wrote:
> dear all,
> I found there are two methods to obtain the vibarational modes and
> frequencies by diagonalizing the dymamical matrix. One is the linear
> response method and the other other is finite differences of the
> atomic forces by displacing each atom and computing the resulting forces.
> My question is that what's the difference between these two methods?
> And what's the advantage of respective method?
>
> Thank you in advance!
>
> Best wishes,
>
> Niu Li
>
> Harbin Institue of Technology
>
> China
>
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