[Wien] optics broken symmetry
Peter Blaha
pblaha at theochem.tuwien.ac.at
Thu Sep 6 09:33:52 CEST 2018
Very funny that it works in P1.
I tested a setup with different a,b,c (4 sym.ops.), but this did not help.
Peter
On 09/05/2018 06:49 PM, Oleg Rubel wrote:
> Dear Peter, Laurence, and Xavier:
>
> many thanks for looking into this issue and making suggestions.
>
> The future plan is to go to 128+ atoms supercell for alloys. So the
> computational efficiency will be important at that point.
>
> I also tried to eliminate all symmetry operations except for
> translation, of course. The structure file is at the bottom. There are
> some promising results obtained on a course k-grid.
>
> k-mesh 8x8x8 not shifted, 1 symmetry operation
>
> [oleg at feynman InP-w2k]$ head InP-w2k.epsilon
> #
> # Lorentzian broadening with gamma= 0.100000 [eV]
> # Im(epsilon) shifted by 0.7860 [eV]
> # No intraband contributions added
> #
> # Energy [eV] Re_eps_xx Im_eps_xx Re_eps_yy Im_eps_yy
> #
> 0.013610 0.906000E+01 0.930282E-01 0.906003E+01 0.930290E-01
> 0.040820 0.906072E+01 0.943965E-01 0.906076E+01 0.943973E-01
> 0.068030 0.906217E+01 0.958009E-01 0.906220E+01 0.958016E-01
>
> k-mesh 8x8x8 shifted, 1 symmetry operation
>
> [oleg at feynman InP-w2k]$ head InP-w2k.epsilon
> #
> # Lorentzian broadening with gamma= 0.100000 [eV]
> # Im(epsilon) shifted by 0.7860 [eV]
> # No intraband contributions added
> #
> # Energy [eV] Re_eps_xx Im_eps_xx Re_eps_yy Im_eps_yy
> #
> 0.013610 0.869517E+01 0.842315E-01 0.869517E+01 0.842315E-01
> 0.040820 0.869576E+01 0.853542E-01 0.869576E+01 0.853542E-01
> 0.068030 0.869695E+01 0.865021E-01 0.869695E+01 0.865021E-01
>
> It seems that both shifted and unshifted mesh could work. I lean toward
> an unsifted mesh since the direct gap is at Gamma, so I would prefer to
> have it in the k-mesh. Even without symmetry 16x16x16 mesh might be more
> computationally efficient than the high-density mesh? The alloy
> structure will likely to have no symmetry either.
>
> Going forward, I can try to see how far should the symmetry be reduced.
> Next candidate can be a face-centered orthorhombic structure. Any other
> thoughts?
>
>
> Best regards
> Oleg
>
> P.S. Here is the structure file
>
> [oleg at feynman InP-w2k]$ cat InP-w2k.struct
> InP
> F LATTICE,NONEQUIV.ATOMS: 2
> MODE OF CALC=RELA unit=ang
> 11.090240 11.090240 11.090240 90.000000 90.000000 90.000000
> ATOM -1: X=0.00000000 Y=0.00000000 Z=0.00000000
> MULT= 1 ISPLIT= 8
> In NPT= 781 R0=0.00001000 RMT= 2.0000 Z: 49.000
> LOCAL ROT MATRIX: 1.0000000 0.0000000 0.0000000
> 0.0000000 1.0000000 0.0000000
> 0.0000000 0.0000000 1.0000000
> ATOM -2: X=0.25000000 Y=0.25000000 Z=0.25000000
> MULT= 1 ISPLIT= 8
> P NPT= 781 R0=0.00010000 RMT= 2.0000 Z: 15.000
> LOCAL ROT MATRIX: 1.0000000 0.0000000 0.0000000
> 0.0000000 1.0000000 0.0000000
> 0.0000000 0.0000000 1.0000000
> 1 NUMBER OF SYMMETRY OPERATIONS
> 1 0 0 0.00000000
> 0 1 0 0.00000000
> 0 0 1 0.00000000
> 1
>
> On 2018-09-05 06:10, Peter Blaha wrote:
>> Dear Oleg,
>>
>> I looked into the problem and unfortunately I can offer only a partial
>> solution. I confirm that:
>>
>> a) The scf cycle gives identical results with or without broken symmetry.
>>
>> b) The optics gives "wrong" results with broken symmetry.
>>
>> I inspected the matrix elements and the problem seems to be with
>> degenerate states (eg. the VBM is 3 fold degenerate at Gamma).
>>
>> The corresponding momentum matrix elements in cubic case are all the
>> same (for all 3 eigenvalues and all directions, i.e. Mxx=Myy=Mzz and
>> M10_13 = M11_13 = M_12_13, where the numbers indicate the band indices
>> of the transition).
>> In the non-cubic setup, they are NOT the same, but in my opinion they
>> are still correct (If you sum over the 3 eigenvalues 10-12, you get
>> the same result as in the cubic one, but individually I get (for
>> distortions in z, not in x as you did) M_10_13: (0 0 zz); M_11_13
>> (zz/2 zz/2 0) and the same for M_12_13, while in cubic all 3 matrix
>> elements are (zz/3 zz/3 zz/3).
>> So I concluded the problem is in the tetrahedron method used in joint.
>> However, I was not able to find a "bug" in SRC_joint. It seems to be
>> inherent to the method.
>>
>> The partial fix: Do it "brute force", i.e. increase the number of
>> k-points until convergence: For instance with k-meshes of
>> 27 27 27 eps1-xx/zz(0.0136eV) 0.117709E+02 0.117134E+02
>> 34 34 34 0.118539E+02 0.118216E+02
>> 200000k (58 58 58): 0.119641E+02 0.119573E+02
>>
>> 200000k cubic setup: 0.119618E+02 0.119618E+02
>>
>> Obviously, the error in the tetrahedron method due to degenerate
>> eigenvalues (like at Gamma or other high symmetry points) is reduced
>> the more "general k-points" are in the mesh and the result converges
>> towards the cubic result. In addition, eps-1(0) changes anyway from
>> 11.7 to 11.9 with these k-meshes, so are not yet fully converged.
>>
>> In terms of cpu-time at least for such cells it is not really a
>> problem to use a 100 100 100 grid (or more).
>>
>> Best regards
>> Peter
>>
>> On 09/03/2018 05:33 AM, Oleg Rubel wrote:
>>> Dear Wien2k community,
>>>
>>> I try to compute opto-elastic properties of InP (zinc-blend
>>> structure). It is related to a change of the dielectric constant
>>> (real part) in response to an applied strain. There are no problems
>>> with a response to a hydrostatic strain, and results agree well with
>>> experiments. A problem occurs with a uniaxial strain (strained along
>>> X-axis only by 0.05%). Computed change in the dielectric constant is
>>> too large (~ an order of magnitude).
>>>
>>> Trying to trace back the problem, I did the following:
>>> First, I initialize a tetragonaly-distorted zinc-blend structure
>>> (init_lapw -b -vxc 19 -ecut -6.5 -numk 800) with the following
>>> lattice parameters
>>>
>>> F LATTICE,NONEQUIV.ATOMS: 2
>>> MODE OF CALC=RELA unit=ang
>>> 11.095785 11.090240 11.090240 90.000000 90.000000 90.000000
>>>
>>> Then I set the lattice parameters back to the cubic lattice
>>>
>>> F LATTICE,NONEQUIV.ATOMS: 2
>>> MODE OF CALC=RELA unit=ang
>>> 11.090240 11.090240 11.090240 90.000000 90.000000 90.000000
>>>
>>> and rerun (x dstart). This allows me to preserve the symmetry of a
>>> distorted structure (see the structure file below).
>>>
>>> Next, I run SCF (run_lapw -ec 0.00001 -cc 0.0001) and optics with
>>> 20x20x20 k-mesh. The results for Re and Im parts of the dielectric
>>> constant are here:
>>>
>>> [oleg at feynman InP-w2k]$ head InP-w2k.epsilon
>>> #
>>> # Lorentzian broadening with gamma= 0.100000 [eV]
>>> # Im(epsilon) shifted by 0.7860 [eV]
>>> # No intraband contributions added
>>> #
>>> # Energy [eV] Re_eps_xx Im_eps_xx Re_eps_yy Im_eps_yy
>>> #
>>> 0.013610 0.940850E+01 0.988634E-01 0.947674E+01 0.100908E+00
>>> 0.040820 0.940928E+01 0.100340E+00 0.947756E+01 0.102453E+00
>>> 0.068030 0.941084E+01 0.101855E+00 0.947919E+01 0.104042E+00
>>>
>>> It seems that the symmetry is broken, which causes later problems
>>> with opto-elastic coefficients as change of 0.07 in the second
>>> decimal point of Re_eps for such a small strain is too much.
>>>
>>> Once again, there are no problems when the strain tensor does not
>>> break the zinc-blend cubic symmetry.
>>>
>>> Any thoughts are highly appreciated.
>>>
>>>
>>> Thank you in advance
>>> Oleg
>>>
>>
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--
P.Blaha
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Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060 Vienna
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Email: blaha at theochem.tuwien.ac.at WIEN2k: http://www.wien2k.at
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