Thank you very much for the reply Paolo.
a) Yes you are right, I forgot to type the lattice vectors in the
expression for r.
b) Let me put an example so I can make the question clearer. I have
calculated zincblende GaN ground state orbitals. The output of the
calculation is as follows:
1) nr1=nr2=nr3=24 --> 24**3= 13824 points in the real space box
2) "gvectors.dat" has a list of 3119 G vectors within the sphere of
radius 4*Ecut.
As FFT works on a regular grid, i.e. a BOX of nr1 x nr2 x nr3 points, we
take the smallest possible BOX that contains the SPHERE. The difference
between 13824 and 3119 I guess it will be filled with zeros and nl(:) is
the responsible of mapping the sphere into the BOX.
3) Now, if my aim is to fourier transform to real space a particular
orbital, let's say u_(k,n), where (k,n) are wave-vector and band index
respectively. As the expansion of the orbital in G vectors is much
smaller, the file "gkvectors.dat" pointing to gvectors.dat has only
around 400 elements. *Would it be correct to use the following brute
force definition **of**the slides?*
u(m1,m2,m3)=\sum_{h,l,k} u(h,l,k) exp**(i*2pi*(h*m1/nr1 + l*m2/nr2 +
k*m3/nr3))
where *G = h*b_1 + l*b_2 + k*b_3* with (h,l,k) index are taken as they
are written in "gkvectors.dat", i.e. including negative values that
represent the sphere and *r= m1*a_1/nr1+m2*a_2/nr2+m3*a_3/nr3 *belong to
the box. I mean without using FFT.
4) One last question, is there an easy way (a postprocessing tool) that
fourier transforms the wavefunction once the calculation has finished
and is collected? I guess it is done when you ask the PP code to plot
n(r). If you could please address me a subroutine that does this job, I
might be able to use it as a guidance for calculating what I really
need: the fourier transform of density matrix
*rho{n,n'}_{k,k}(r)=**u^{*}_{k,n}(m1,m2,m3) x u_{k,n'}(m1,m2,m3)* at
different bands.
Thank you in advance and sorry for the terribly long email
aritz
On 03/02/2015 06:28 PM, Paolo Giannozzi wrote:
On Tue, 2015-02-24 at 19:08 +0100, Aritz Leonardo Liceranzu wrote:
So if I understood correctly once the Ecutoff is set, the file
"gvectors.dat" contains the complete list of G vectors inside the
sphere with a radius 4*Ecut where magnitudes such like density can be
safely represented.
Starting from here, how is the real-space grid generated? I ask this
because for my particular calculation there are around 3000 G
different vectors for a real space grid that has nr1=nr2=nr3=24
points.
according to the definition:
r= (i-1)/nr1+(j-1)/nr2+(k-1)/nr3
r= (i-1)*a_1/nr1+(j-1)*a_2/nr2+(k-1)*a_3/nr3, where a_1, a_2, a_3 are
the three vectors that generate the lattice
The real space grid is denser than the reciprocal grid, so there has
to be some kind of mapping from one to each other that I am missing.
According to the above transparencies both grids should have equal
amount of points.
G = h*b_1 + k*b_2 + k*b_3, where b_1, b_2, b_3 are the three vectors
that generate the reciprocal lattice. Negative indices (h,k,l) are
refolded to positive one atthe other end of the FFT box. The
correspondence between G vectors and (j,k,l) indices is provided
by array "nl"
Paolo
I could still do (i think) brute force transformations using the
forward and inverse transformations defined in transparency 5 but I if
wanted to use fftw in order to be more efficient, shouldn't they be
the same in size?
As I said, I would appreciate if somebody could address me a reference
or notes to read where these issues are explained. Thanks!
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Aritz Leonardo Liceranzu
Department of Applied Physics II,
Faculty of Science and Technology,
University of the Basque Country (UPV/EHU)
Bº Sarriena s/n, 48940 Leioa, Spain
Mail: [email protected] Phone: +34-946015338
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