[QE-users] A DFPT equation

[Paolo Giannozzi]

Insert Eq.61 into Eq.59. You will get Eq.62, plus a higher-order term.

Paolo

On Fri, Feb 19, 2021 at 12:52 AM Andrew Xu <andrewaccount at gmail.com> wrote:

> Hi users,
>
> I had a question about one of the DFPT equations in Baroni et al. "Phonons
> and related crystal properties from DFPT." I was unsure about posting this
> question here because most of the questions here are about using QE, but I
> choose to do so since DFPT is implemented in QE, the authors are on this
> mailing list, and in case someone else had the same question.
>
> I'm curious how we arrive at the LHS of equation 62 (H - epsilon) |Delta
> psi>. It appears that we started from equation 59 and rearranged the RHS to
> arrive at equation 62, so I would expect the LHS to remain the same. Yet
> the LHS of both equations differ ((H - epsilon) |Delta psi> and H |Delta
> psi> - sum(Lambda |\Delta psi>).
>
> My initial thought was do to the same thing done in equation 52 in moving
> to the canonical KS equations, but it is not obvious to me how that might
> change H |Delta psi> - sum(Lambda |\Delta psi>) to (H - epsilon) |Delta
> psi> because they are acting on the perturbed wavefunctions, whereas the
> unitary was defined based on linear combinations on the KS wavefunctions.
>
> Best regards,
> Andrew
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-- 
Paolo Giannozzi, Dip. Scienze Matematiche Informatiche e Fisiche,
Univ. Udine, via delle Scienze 206, 33100 Udine, Italy
Phone +39-0432-558216, fax +39-0432-558222
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