[Pw_forum] possible bug in scatter_forw.f90
Manoj Srivastava
manoj at phys.ufl.edu
Tue Oct 21 00:01:34 CEST 2008
Dear Alexander,
Thank you very much for your answer. I have one more question, it seems
my list of questions is never gonna end :(
this is about init_gper.f90 subroutine. where you calculate
|G+k|^2<Ecut2d.
the expression -
norm2=(((il+xyk(1,ik))*bg(1,1)+(jl+xyk(2,ik))*bg(1,2))**2+ &
((il+xyk(1,ik))*bg(2,1)+(jl+xyk(2,ik))*bg(2,2))**2)* &
i believe is |G+k|^2. How do you get above expression in the code for
this? I tried to work it out but could not get this. You even have g.k
term! I guess i would have more understanding once i understand how did
you define Gper in the fourier transform,
V(rper,z)=sum(gper)[exp(i*gper*rper) V(gper,z)
Is gper just gx and gy, and then you rotate your axis to get
bg(1,1),bg(1,2), bg(2,1) and bg(2,2)? Would you mind explaining?
Regards,
Manoj
On Mon, 20 Oct 2008, Alexander wrote:
> Dear Manoj
>
> On Thursday 16 October 2008 23:15, Manoj Srivastava wrote:
> > Dear Alexandar,
> > Thank you very much. Your answers make sense and now i have better
> > understanding of the subroutine scatter_forw.f90. I have one question
> > about poten.f90 subroutine, where you calculate the V(p,gper) in each
> > slices of the slab(equation 15). I have a question about Gz, which is
> > 2*pi*q/L, with [-N/2]+1<=q>=[N/2]. Now in the code at the line at the line
> > 60, you have Gz multiplied with bg(3,3). I kind of understand this is
> > because 3rd direction is perpendicular to xy plane,
> Exactly. As it is implemented now pwcond deals with systems
> having monoclinic unit cell, i.e. such that a3 is perpendicular to both a1 and
> a2 (a1 and a2 are not necessary orthogonal one to another) and the direction
> of transport is a3. This seems to us the most general setup for transport and
> I do not think we should consider at the moment the situation where the a3 is
> not perpendicular to the xy plane.
>
> Best regards,
> Alexander
>
> > but not totally clear
> > about it. Would you mind explaining? my other question is when reciprocal
> > space vectors b1, b2 and b3 are not orhogonal to each other, which is
> > more general case, then should not we take bg(1,3) and bg(2,3) in there
> > too?
> > Thank you once again for listening to my questions and i hope i am
> > not bothering you too much.
> >
> > Regards,
> > Manoj Srivastava
> > Physics Graduate Student
> > Department of Physics
> > Gainesville, FL, USA.
> >
> > have On Wed, 15 Oct 2008, Alexander wrote:
> > > Dear Manoj
> > >
> > > On Tuesday 14 October 2008 17:49, Manoj Srivastava wrote:
> > > > Dear Alexader,
> > > >
> > > > Thank you very much for your reply. I was out of town and could not
> > > > see the message till yesterday. I have some questions on it, it would
> > > > be great if you could answer them.
> > > >
> > > > On Fri, 10 Oct 2008, Alexander wrote:
> > > > > Dear Manoj
> > > > >
> > > > > On Friday 10 October 2008 05:20, Manoj Srivastava wrote:
> > > > > > Any follow ups on the message below? Alexander?
> > > > > >
> > > > > > Regards,
> > > > > > Manoj
> > > > > >
> > > > > > On Wed, 8 Oct 2008, Manoj Srivastava wrote:
> > > > > > > Dear All,
> > > > > > > Is any body familiar with the scatter_forw.f90 subroutine of
> > > > > > > PWCOND? I think there is a bug in this subroutine at the place
> > > > > > > where you calculate intw2, which is z integration of nonlocal
> > > > > > > wavefunction with beta function. I have looked up the necessary
> > > > > > > formulae in the Choi & Ihm's paper (PRB 59, 2267, Jan 1999). In
> > > > > > > the paper, nonlocal wavefunction has 3 terms, one of which
> > > > > > > contains beta function, say W. The other two parts dont have any
> > > > > > > W in them, rather they are just plane wave solution. (Please have
> > > > > > > a look at equation 24 and 26 of the paper ). So, when we are
> > > > > > > doing z integration of nonlocal wavefunction with beta function
> > > > > > > W, we should have three terms, one of which should contain two W,
> > > > > > > but rest should just have one W. On the other hand in the code
> > > > > > > all three terms contain two beta functions!! (please have a look
> > > > > > > at line 228 of scatter_forw.f90). I am wondering if my
> > > > > > > understanding is right?
> > > > >
> > > > > Your understanding is wrong. On the line 228 you add to the integral
> > > > > ONLY contribution with two beta functions (from the 1st term in the
> > > > > nonlocal function, see Eq. 24) but on the line 393 the contribution
> > > > > from the 2nd term is added too. There is no 3rd term since every step
> > > > > you rotate your local solutions \psi_n in such a way that b_{\lambda
> > > > > \alpha lm} vanish (see the paragraph after Eq. 37).
> > > >
> > > > I believe that the equations 40, 41 and 42 implemented in the code
> > > > are in the momentum space. In the code, intw2 has 3 terms. We can tell
> > > > this by looking at the subroutine integrals.f90, where int2d is
> > > > defined. Now, by looking at the choi& Ihm 's paper, the very first term
> > > > of psi{alpha,l,m} has f{lambda,alpha,l,m}(equation26).And, if we
> > > > substitute this in equation 40, we should just get one term. I am just
> > > > confuesd on the fact that how come this one term in paper gets
> > > > transformed into 3 terms of the code!
> > >
> > > intw2(alpha,beta) is the integral of nonlocal solution (24) with w
> > > functions, intw2(alpha,beta) = \int_{0,d} w_{alpha}(r)*psi_{beta}(r)dr,
> > > where alpha,beta={alpha,l,m} in the paper. In each slab it will have TWO
> > > contributions from the first and second terms of (24), the one from the
> > > third term vanishes as I explained before. These two contributions are
> > > calculated on the lines 228 and 393 of the code. The integrals intw1
> > > (alpha,n)=\int_{0,d} w_{alpha}(r)*psi_{n}(r)dr are the integrals of local
> > > solutions (17) with the same projector functions w.
> > > The integrals intw2 and intw1 have nothing to do with boundary conditions
> > > (40). They enter in (11) and are needed to construct the final solutions
> > > according to Eq.(10). Substituting the form of this solution (10) in the
> > > boundary conditions (40) you will be led to the generalized eigenvalue
> > > problem, AX=exp(ikd) BX, with known matrices A and B and unknown
> > > coefficients X={a_n,C_{alpha,l,m}} defining the resulting solution (10).
> > >
> > > > Would you mind explaining? Also, the integrals that are defined in the
> > > > code are only in the slabs (nz1), so how are you taking the integration
> > > > in the region (0,d), which we need according to equations 40, 41 and 42
> > > > ?
> > >
> > > When you go over slabs you add new contributions to the integrals intw1
> > > and intw2 (see the line 228 for the first contribution to intw2 and the
> > > part "add to the integrals" for another contribution to intw2 and
> > > contributions to intw1) so at the end you obtain integrals over all the
> > > region.
> > >
> > > Regards,
> > > Alexander
> > >
> > > > > > > I have one more question in the later part of the same
> > > > > > > subroutine. What
> > > > > > >
> > > > > > > does the lapack subroutine
> > > > > > > ZGESV(2*n2d,2*n2d+norb*npol,amat,2*n2d,ipiv,xmat,2*n2d,info)
> > > > > > > do?
> > > > > > > I tried to look it up and i got the idea that it is trying to
> > > > > > > solve amat*x=xmat, with amat and xmat known and x unknown, and at
> > > > > > > the end of calculation it stores x in xmat.
> > > > > > > so, basically it does-- x=[(amat)^(-1)]*xmat. Am i right? So, it
> > > > > > > changes the structure of xmat from what is defined in 'constructs
> > > > > > > matrices' part. Is it correct?
> > > > >
> > > > > Here, you are right.
> > > > >
> > > > > > > Also, afterwards in this code where it 'rotates integrals' is
> > > > > > > not very clear to me.
> > > > > > > Could somebody please tell me in little detail, what is going on
> > > > > > > here?
> > > > >
> > > > > As I explained before rotation means that every step (at each slab)
> > > > > you make a linear combination of local solutions \psi_n with the
> > > > > transformation matrix h_{nn'} (see the last paragraph on the p.
> > > > > 2270). so that the new solutions have the property:
> > > > > b_{\lambda n} = \delta_{\lambda n} and the new nonlocal solutions
> > > > > have b_{\lambda \alpha lm}=0. Doing this transformation of local and
> > > > > nonlocal solutions you should also perform the corresponding
> > > > > transformations of the integrals.
> > > > >
> > > > > > > Also, is this subroutine written just on the basis of Choi and
> > > > > > > Ihm paper, or are there more reference to it? If yes, would
> > > > > > > someone mind mentioning them?
> > > > >
> > > > > Unfortunately, the paper of Choi and Ihm is very detail, and in the
> > > > > PWCOND code we followed it very closely, so no more references
> > > > > are needed. In our papers we just extended those ideas to ultrasoft
> > > > > pseudopotentials, magnetism, spin-orbit coupling and so on.
> > > > >
> > > > > Hope this helped you,
> > > > > regards, Alexander
> > > > >
> > > > > > > Regards,
> > > > > > > Manoj Srivastava
> > > > > > > Physics Graduate Student
> > > > > > > University of Florida,
> > > > > > > Gainesville,FL, USA
> > > > > >
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> > > >
> > > > Once again thank you very much for your help. I appreciate it.
> > > >
> > > > Regards,
> > > > Manoj Srivastava
> > > >
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