[Pw_forum] Interpolation method used in getting projector in k-space

[Paolo Giannozzi]

The Fourier-Bessel transformation was tested once upon a time, but it
had a funny behavior sometimes and it was finally abandoned; the
Fourier transforms of the radial parts are done in a rather dumb way,
by computing the integrals \beta_l(q_i) = \int 4\pi r^2 \beta(r)
j_l(q_ir) dr  on a uniform grid of q_i, interpolating them (optionally
with splines, with a simple interpolation formula otherwise) for the
required q=|k+G|

Paolo

On Fri, Jun 17, 2016 at 1:49 PM, Ryky Nelson <nelson.ryky at gmail.com> wrote:
> Hello Paolo,
>
> I just want to know what kind of algorithm (method) used to
> 3D-Fourier-transform and interpolate the projectors (beta functions). Does
> it use the Fourier-Bessel transformation and Spline interpolation,
> respectively? And thank you for the information of the subroutines.
>
> Ryky Nelson
> Institut für Anorganische Chemie
> RWTH Aachen University
>
> On Fri, Jun 17, 2016 at 12:20 PM, Paolo Giannozzi <p.giannozzi at gmail.com>
> wrote:
>>
>> I am not sure I understand your questions. Projectors, aka "beta
>> functions", are computed in reciprocal space (variable "vkb") by
>> routine "init_us_2", using interpolation from a table computed by
>> routine "init_us_1"
>>
>> Paolo
>>
>> On Thu, Jun 16, 2016 at 2:33 PM, Ryky Nelson <nelson.ryky at gmail.com>
>> wrote:
>> > Hello QE users and developers,
>> >
>> > in the PAW scheme, there's a step to calculate wave-function characters
>> > at a
>> > given k-point, i.e. <p_tilde (k) | psi_tilde(k)>. However, projectors
>> > (p_tilde) are given in real-space in UPF files whereas the smooth
>> > wave-functions are expanded in G(reciprocal)-space. Could someone tell
>> > me
>> > how and in what subroutine(s) this wave-function character is calculated
>> > in
>> > Espresso? Also, is there any interpolation method used in this
>> > calculation?
>> >
>> > Thank you!
>> >
>> > Ryky Nelson
>> > Institut für Anorganische Chemie
>> > RWTH Aachen University
>> >
>> > _______________________________________________
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>>
>>
>>
>> --
>> Paolo Giannozzi, Dip. Scienze Matematiche Informatiche e Fisiche,
>> Univ. Udine, via delle Scienze 208, 33100 Udine, Italy
>> Phone +39-0432-558216, fax +39-0432-558222
>>
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>
>
>
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-- 
Paolo Giannozzi, Dip. Scienze Matematiche Informatiche e Fisiche,
Univ. Udine, via delle Scienze 208, 33100 Udine, Italy
Phone +39-0432-558216, fax +39-0432-558222