[Pw_forum] IFCs and supercell
stefano de gironcoli
degironc at sissa.it
Fri Nov 7 17:18:47 CET 2014
Dear Alexader
you are right that the vector separating two atoms includes also
the difference between their position inside the cell but they are
uniquely defined by this difference (well defined when the two atoms are
chosen) and a direct lattice vector R.
this is the vector r(i) = (n1-1)*at(i,1)+(n2-1)*at(i,2)+(n3-1)*at(i,3)
we are talking about.
then the actual vector is computed as r_ws(i) = r(i) +
tau(i,na)-tau(i,nb)
and its relation with respect to the WS super-cell of the system
is computed by wsweight(r_ws,rws,nrws)
why the summation goes from -2*N to +2*N ? One wants to include
in the summation all the R that would lead to a point inside the WS
supercell. For a simple cubic lattice this would be just from -N to N.
For Bravais lattices with small angles between the fundamental lattice
vectors this is might not be enough.
One could/should actually compute what is the safe range needed
include all relevant points... this was not done but we just included a
"VERY VERY SAFE RANGE!" of +/-2*N that proved safe for all system
examined so far.
stefano
On 11/07/2014 11:23 AM, Kvasov Alexander wrote:
>
> Dear Stefano,
>
> thanks a lot for your kind reply! One thing is still not clear for me.
> Could you please clarify it? Please see below.
>
> > the corresponding relevant real space vectors vectors are
> therefore given by
> > r(i) = (n1-1)*at(i,1)+(n2-1)*at(i,2)+(n3-1)*at(i,3) + their
> periodic refolding to points nearest the origin
> > a few examples should clarify:
> > 1 1 1 -> r = 0
> > 2 1 1 -> r = a1
> > 8 1 1 -> r = -a1
>
> It’s true for the same atoms, for example
>
> 8 8 8
>
> 1 1 1 1 (atom1=atom2=1)
>
> 1 1 1 5.72142674655E-02
>
> 2 1 1 -1.06343912107E-02
>
> 3 1 1 1.01649714042E-04
>
> 4 1 1 4.15611567060E-06
>
> 5 1 1 -6.46046533014E-06
>
> 6 1 1 4.15611567060E-06
>
> 7 1 1 1.01649714042E-04
>
> 8 1 1 -1.06343912107E-02
>
> and indeed
>
> 1 1 1 -> r = 0
> 2 1 1 -> r = a1
> 8 1 1 -> r = -a1
>
> However, if we take
>
> 3 5 0 7.3434758 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
>
> 1.000000000 0.000000000 0.000000000
>
> 0.000000000 1.000000000 0.000000000
>
> 0.000000000 0.000000000 1.000000000
>
> 1 'Sr ' 79860.7444956297
>
> 2 'Ti ' 43628.1015381455
>
> 3 'O ' 14582.5610075711
>
> 1 1 0.0000000000 0.0000000000 0.0000000000
>
> 2 2 0.5000000000 0.5000000000 0.5000000000
>
> 3 3 0.5000000000 0.5000000000 0.0000000000
>
> 4 3 0.5000000000 0.0000000000 0.5000000000
>
> 5 3 0.0000000000 0.5000000000 0.5000000000
>
> T
>
> 6.2439081 0.0000000 0.0000000
>
> 0.0000000 6.2439081 0.0000000
>
> 0.0000000 0.0000000 6.2439081
>
> 1
>
> 2.4363133 0.0000000 0.0000000
>
> 0.0000000 2.4363133 0.0000000
>
> 0.0000000 0.0000000 2.4363133
>
> 2
>
> 7.3260124 0.0000000 0.0000000
>
> 0.0000000 7.3260124 0.0000000
>
> 0.0000000 0.0000000 7.3260124
>
> 3
>
> -2.0082996 0.0000000 0.0000000
>
> 0.0000000 -2.0082996 0.0000000
>
> 0.0000000 0.0000000 -5.7457266
>
> 4
>
> -2.0082996 0.0000000 0.0000000
>
> 0.0000000 -5.7457266 0.0000000
>
> 0.0000000 0.0000000 -2.0082996
>
> 5
>
> -5.7457266 0.0000000 0.0000000
>
> 0.0000000 -2.0082996 0.0000000
>
> 0.0000000 0.0000000 -2.0082996
>
> 8 8 8
>
> …..
>
> …..
>
> 1 1 1 2 (*atom1(atom of origin)=2, atoms2=1*)
>
> 1 1 1 -1.52661521097E-03
>
> 2 1 1 -1.52661520884E-03
>
> 3 1 1 -2.40826237874E-04
>
> 4 1 1 -1.56748657082E-04
>
> 5 1 1 -9.53993420913E-05
>
> 6 1 1 -9.53993442291E-05
>
> 7 1 1 -1.56748429042E-04
>
> 8 1 1 -2.40826009834E-04
>
> and R-R0 is not anymore (n1-1)*a+(n2-1)*b+(n3-1)*c, but should include
> difference between atoms like
>
> R-R0=(n1-1)*a+(n2-1)*b+(n3-1)*c+( R_cell(atom1) – R_cell(atom2))
>
> this way
>
> 1 1 1 -1.52661521097E-03 R-R0=-a/2
>
> 2 1 1 -1.52661520884E-03 R-R0= a/2
>
> 3 1 1 -2.40826237874E-04 R-R0= 3a/2
>
> 4 1 1 -1.56748657082E-04
>
> 5 1 1 -9.53993420913E-05
>
> 6 1 1 -9.53993442291E-05
>
> 7 1 1 -1.56748429042E-04
>
> 8 1 1 -2.40826009834E-04 R-R0=-3a/2
>
> Moreover in SUBROUTINE frc_blk i don’t find the place where the
> difference between atoms is taken into account
>
> …
>
> r(i) = n1*at(i,1)+n2*at(i,2)+n3*at(i,3)
>
> …
>
> arg = tpi*(q(1)*r(1) + q(2)*r(2) + q(3)*r(3))
>
> DO ipol=1, 3
>
> DO jpol=1, 3
>
> dyn(ipol,jpol,na,nb) = &
>
> dyn(ipol,jpol,na,nb) + &
>
> (frc(m1,m2,m3,ipol,jpol,na,nb)+f_of_q(ipol,jpol,na,nb)) &
>
> *CMPLX(COS(arg),-SIN(arg),kind=DP)*weight
>
> …
>
> another small question why in SUBROUTINE frc_blk the summation goes
> from -2N to 2N ???
>
> DO n1=-2*nr1,2*nr1
>
> DO n2=-2*nr2,2*nr2
>
> DO n3=-2*nr3,2*nr3
>
> Alexander
>
> From: pw_forum-bounces at pwscf.org [mailto:pw_forum-bounces at pwscf.org]
> On Behalf Of stefano de gironcoli
> Sent: 06 November 2014 18:55
> To: PWSCF Forum
> Subject: Re: [Pw_forum] IFCs and supercell
>
> dear Alexander,
>
> the grid correspond to a 8x8x8 supercell (or rather to the FFT of
> a 8x8x8 q-point grid ... which is the same)
>
> atomic pairs are specified by the indices of the two atoms in the
> unit cell plus the direct lattice vector connecting the two cells in
> which they are located with two important details to be considered
> 1) the origin is the 1,1,1 element of the list
> 2) the IFC are obtained by a FFT from the dynamical matrices of
> the q-point grid and are therefore written assuming 8 8 8 periodicity
> (in the present case)
> the corresponding relevant real space vectors vectors are
> therefore given by
> r(i) = (n1-1)*at(i,1)+(n2-1)*at(i,2)+(n3-1)*at(i,3) + their
> periodic refolding to points nearest the origin
> a few examples should clarify:
> 1 1 1 -> r = 0
> 2 1 1 -> r = a1
> 8 1 1 -> r = -a1
>
> the routine weight play the fundamental role of trimming the
> vector in such a way the only the points inside the wigner-seitze
> cell of the supercell contribute
> weight (r) = 1 if r is inside the WS cell
> weight (r) = 0 if r is ouside the WS cell
> weight (r) = 1/(n+1) if r is on the surface of the WS cell where
> n is the number of planes that pass through it
>
> stefano
>
> On 11/06/2014 06:14 PM, Kvasov Alexander wrote:
>
> Dear All,
>
> My question is: how the supercell (which is used by q2r and matdyn) is
> specified? If anybody has any information about this I would highly
> appreciate.
>
> “fltau” option of matdyn gives atomic positions only for 1 cell and
> not for N1xN2xN3 supercell.
>
> Apparently, there are some tricks… for example, here one has some IFCs
> for 8x8x8 grid of SrTiO3
>
> ...
>
> 8 8 8
>
> 1 1 1 1
>
> 1 1 1 5.72142674655E-02
>
> 2 1 1 -1.06343912107E-02
>
> 3 1 1 1.01649714042E-04
>
> 4 1 1 4.15611567060E-06
>
> 5 1 1 -6.46046533014E-06
>
> 6 1 1 4.15611567060E-06
>
> 7 1 1 1.01649714042E-04
>
> 8 1 1 -1.06343912107E-02
>
> ...
>
> 1. first, IFC values decries with N1 and then increase, so they have
> to be shuffled
>
> 2. second, it seems SUBROUTINE setupmat and frc_blk is the right place
> to look for this
>
> …
>
> DO na=1, nat
>
> DO nb=1, nat
>
> total_weight=0.0d0
>
> DO n1=-2*nr1,2*nr1
>
> DO n2=-2*nr2,2*nr2
>
> DO n3=-2*nr3,2*nr3
>
> !
>
> ! SUM OVER R VECTORS IN THE SUPERCELL - VERY VERY SAFE RANGE!
>
> !
>
> DO i=1, 3
>
> r(i) = n1*at(i,1)+n2*at(i,2)+n3*at(i,3)
>
> END DO
>
> …
>
> but summation goes from -2N to 2N, which is not clear for me.
>
> 3. what is “weight” in SUBROUTINE setupmat and frc_blk
>
> If anybody could explain what is going on here it would be great!
>
> Sincerely yours,
>
> Alexander Kvasov
>
> Scientist
>
> Ceramics Laboratory (LC)
>
> École Polytechnique Fédérale de Lausanne (EPFL)
>
> Phone: +41 21 693 5805
>
> Address:
>
> EPFL STI IMX LC
>
> MXD 220 (Bâtiment MXD) Station 12
>
> 1015 Lausanne, Switzerland
>
>
>
>
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