Yet another question about RIM+cutoff technique

[a.ugolotti]

Dear Yamboers,

I am working on optical spectra (RPA level) of 2D monolayers, for which, as far as I have understood, the box cutoff and the RIM integration are mandatory, for improving the vacuum-space convergence and q (G-space) integration. However, even for not fully converged results, I was expecting to find some consistent results, instead for an almost-metallic behaviour I am finding that IP, LF (in e-h space) and ALDA(in e-h space) spectra are in good agreement, while the LF one in G-space, with and without RIM-cut are not. This is for a supercell with 20A vertical separation between two replicated sheets. Increasing that space to 40,80 and further the LF spectrum in G-space not cut converges to the IP one, but the same is not happening when the RIM-cut runlevel is considered, or least more slowly than the uncut one.
Should that cutoff a way to almost avoid increasing the vacuum size (at least not more than required to have the total energy converged at SCF level)?

This reported below is an example of a report:

Code: Select all

                                                                
                                                                
    Y88b    /   e           e    e      888~~\    ,88~-_        
     Y88b  /   d8b         d8b  d8b     888   |  d888   \       
      Y88b/   /Y88b       d888bdY88b    888 _/  88888    |      
       Y8Y   /  Y88b     / Y88Y Y888b   888  \  88888    |      
        Y   /____Y88b   /   YY   Y888b  888   |  Y888   /       
       /   /      Y88b /          Y888b 888__/    `88_-~        
                                                                
                                                                
                GPL Version 4.1.2 Revision 76                   
                          MPI Build                             
                  http://www.yambo-code.org                     
 
 11/27/2017 at 19:12 YAMBO @ jigen117

 [01] CPU structure, Files & I/O Directories
 ===========================================

 * CPU-Threads     :32(CPU)-1(threads)-1(threads@X)-1(threads@DIP)-1(threads@SE)-1(threads@RT)-1(threads@K)
 * MPI CPU         :  32
 * THREADS    (max): 1
 * THREADS TOT(max):  32
 * I/O NODES       : 1
 * Fragmented WFs  :yes

 CORE databases in   .
 Additional I/O in   .
 Communications in   .
 Input file     is   lf_cut.in
 Report file    is   ./r-lf_cut_e100_optics_chi_rim_cut
 Job string(main): lf_cut_e100
 Log files      in ./LOG
  
 [RD./SAVE//ns.db1]------------------------------------------
  Bands                           : 20
  K-points                        :  7
  G-vectors             [RL space]:  453669
  Components       [wavefunctions]:  56961
  Symmetries       [spatial+T-rev]: 12
  Spinor components               : 1
  Spin polarizations              : 1
  Temperature                 [ev]:  0.02585
  Electrons                       : 8.000000
  WF G-vectors                    :  71915
  Max atoms/species               : 2
  No. of atom species             : 1
  Magnetic symmetries             : no
 - S/N 002584 -------------------------- v.04.01.02 r.00076 -

 [02] CORE Variables Setup
 =========================


  [02.01] Unit cells
  ==================

  Unit cell is HCP

  ... containing 2Si atoms

  ... with scaling factors [a.u.]:   7.2571    6.2848  302.3562

  Direct Lattice(DL) unit cell [iru  /  cc(a.u.)]
  A1 = 1.000000  0.000000 -0.000000      7.257094  0.000000 -0.000000
  A2 =-0.500000  1.000000 -0.000000     -3.628547  6.284828 -0.000000
  A3 =-0.000000  0.000000  1.000000     -0.000000  0.000000  302.3562

  DL volume [au]:0.1379E+5

  Reciprocal Lattice(RL) unit cell [iku  /  cc]
  B1 = 1.000000  0.500000  0.000000      0.865799  0.499869  0.000000
  B2 = 0.000000  1.000000  0.000000     -0.000000  0.999739 -0.000000
  B3 = 0.000000  0.000000  1.000000      0.000000  0.000000   0.02078


  [02.02] Symmetries
  ==================

  DL (S)ymmetries [cc]
  [S1] 1.000000  0.000000  0.000000  0.000000  1.000000  0.000000  0.000000  0.000000  1.000000
  [S2]-0.500000  0.866025  0.000000 -0.866025 -0.500000  0.000000  0.000000  0.000000  1.000000
  [S3]-0.500000 -0.866025  0.000000  0.866025 -0.500000  0.000000  0.000000  0.000000  1.000000
  [S4]-1.000000  0.000000  0.000000  0.000000  1.000000  0.000000  0.000000  0.000000  1.000000
  [S5] 0.500000  0.866025  0.000000  0.866025 -0.500000  0.000000  0.000000  0.000000  1.000000
  [S6] 0.500000 -0.866025  0.000000 -0.866025 -0.500000  0.000000  0.000000  0.000000  1.000000

  [SYMs] Time-reversal derived K-space symmetries:  7  12
  [SYMs] Spatial inversion 7 is NOT a symmetry
  [SYMs] Group table built correctly

  [02.03] RL shells
  =================

  Shells, format: [S#] G_RL(mHa)

   [S7202]:126545(0.3325E+5) [S7201]:126533(0.3325E+5) [S7200]:126509(0.3324E+5) [S7199]:126497(0.3324
   [S7198]:126473(0.3324E+5) [S7197]:126461(0.3323E+5) [S7196]:126437(0.3323E+5) [S7195]:126425(0.3322
   [S7194]:126401(0.3322E+5) [S7193]:126377(0.3321E+5) [S7192]:126353(0.3321E+5) [S7191]:126329(0.3321
   [S7190]:126293(0.3321E+5) [S7189]:126281(0.3320E+5) [S7188]:126257(0.3320E+5) [S7187]:126233(0.3320
   [S7186]:126221(0.3319E+5) [S7185]:126197(0.3319E+5) [S7184]:126173(0.3319E+5) [S7183]:126161(0.3318
   [S7182]:126159(0.3318E+5) [S7181]:126147(0.3317E+5) [S7180]:126135(0.3317E+5) [S7179]:126123(0.3317
   [S7178]:126099(0.3317E+5) [S7177]:126087(0.3316E+5) [S7176]:126063(0.3316E+5) [S7175]:126039(0.3315
   ...
   [S12]:23( 26.12627) [S11]:21( 21.59196) [S10]:19( 17.48949) [S9]:17( 13.81886)
   [S8]:15( 10.58006) [S7]:13( 7.773106) [S6]:11( 5.397990) [S5]:9( 3.454714)
   [S4]:7( 1.943276) [S3]:5( 0.863678) [S2]:3( 0.215920) [S1]:1( 0.000000)

  [02.04] K-grid lattice
  ======================

  Compatible Grid is 2D
  B1 [rlu]= 0.000000 -0.166667  0.000000
  B2      =-.1667    0.7451E-8  0.000   
  Grid dimensions               :  6   6
  K lattice UC volume       [au]:0.4996E-3

  [02.05] Energies [ev] & Occupations
  ===================================

  Fermi Level        [ev]: -4.391939
  VBM / CBm          [ev]:  0.00      0.00    
  Electronic Temp. [ev K]: 0.2585E-1  300.0   
  Bosonic    Temp. [ev K]: 0.2585E-1  300.0   
  El. density      [cm-3]: 0.391E+22
  States summary         : Full        Metallic    Empty
                           0001-0003   0004-0005   0006-0020

  [WARNING]Metallic system
   
  N of el / N of met el:  8.000000  2.000000
  Average metallic occ.:             0.500000
  X BZ K-points :  36

  Energy unit is electronVolt [eV]

  *X* K [1] : 0.000000  0.000000  0.000000 ( cc) * Comp.s 56551 * weight   0.02778
              0.000000  0.000000  0.000000 (rlu)
  E -11.13685  -3.21881  -1.18580  -1.18580   2.05075   2.52101   3.06095   3.06095
  E  4.259172  4.379656  4.382413  4.393561  4.417030  4.446243  4.484857  4.504270
  E  4.520288  4.546415  4.589400  4.611929
   
  *X* K [2] : 0.000000  0.166623  0.000000 ( cc) * Comp.s 56745 * weight  0.166667
              0.000000  0.166667  0.000000 (rlu)
  E -10.80924  -3.28399  -2.65791  -1.67138   2.20179   2.70774   4.16826   4.24399
  E  4.630399  4.748819  4.760103  4.763543  4.793969  4.823809  4.830044  4.881876
  E  4.892483  4.922936  4.953001  4.967037
   
  *X* K [3] : 0.000000  0.333246  0.000000 ( cc) * Comp.s 56732 * weight  0.166667
              0.000000  0.333333  0.000000 (rlu)
  E -9.866490 -5.641577 -2.339036 -1.933823  1.353524  2.035668  4.523002  5.738042
  E  5.891289  5.893216  5.907007  5.924979  5.957195  6.001682  6.014680  6.032928
  E  6.053176  6.099071  6.125623  6.169899
   
  *X* K [4] : 0.000000 -0.499869  0.000000 ( cc) * Comp.s 56776 * weight   0.08333
              0.000000 -0.500000  0.000000 (rlu)
  E -8.868067 -7.200621 -2.597208 -1.032574  0.626292  1.174327  5.555747  6.454453
  E  6.658748  7.370589  7.591815  7.777803  7.780208  7.781152  7.781847  7.790524
  E  7.797485  7.803358  7.813529  7.869639
   
  *X* K [5] : 0.144300  0.249935  0.000000 ( cc) * Comp.s 56507 * weight  0.166667
              0.166667  0.250000  0.000000 (rlu)
  E -10.16889  -4.81644  -2.76874  -2.19630   2.38604   3.41593   3.63432   4.51842
  E  5.324536  5.513863  5.515255  5.530766  5.543813  5.579462  5.627053  5.635832
  E  5.656623  5.668358  5.719770  5.749071
   
  *X* K [6] : 0.144300  0.416558  0.000000 ( cc) * Comp.s 56791 * weight  0.333333
              0.166667  0.416667  0.000000 (rlu)
  E -9.009522 -6.730291 -3.609693 -1.108502  1.003830  3.011943  4.852179  5.531888
  E  6.403571  6.918891  7.024345  7.026677  7.039672  7.062471  7.090485  7.133208
  E  7.148602  7.165528  7.191722  7.233830
   
  *X* K [7] : 0.288600  0.499869  0.000000 ( cc) * Comp.s 56961 * weight   0.05556
              0.333333  0.500000  0.000000 (rlu)
  E -7.826    -7.826    -4.483    -.1825E-4 0.1825E-4  3.998     5.745     6.238   
  E  6.237799  7.242211  7.242261  8.265451  8.712445  8.712495  8.878121  8.915612
  E  8.915620  8.915783  8.915830  8.916313

 [03] Transferred momenta grid
 =============================

 [RD./SAVE//ndb.kindx]---------------------------------------
  Fragmentation                    :no
  Polarization last K   :  7
  QP states             :  1   7
  X grid is uniform     :yes
  BS scattering         :no
  COLL scattering       :no
 - S/N 002584 -------------------------- v.04.01.02 r.00076 -

 IBZ Q-points :  7
 BZ  Q-points :  36

 Q [00001] : 0.00      0.00      0.00     (iku) * weight   0.02778
 Q [00002] : 0.000000  0.166667  0.000000 (iku) * weight  0.166667
 Q [00003] : 0.000000  0.333333  0.000000 (iku) * weight  0.166667
 Q [00004] : 0.000000 -0.500000  0.000000 (iku) * weight   0.08333
 Q [00005] : 0.166667  0.250000  0.000000 (iku) * weight  0.166667
 Q [00006] : 0.166667  0.416667  0.000000 (iku) * weight  0.333333
 Q [00007] : 0.333333  0.500000  0.000000 (iku) * weight   0.05556
  
 Q [00001] : 0.00      0.00      0.00     (cc ) * weight   0.02778
 Q [00002] : 0.000000  0.166623  0.000000 (cc ) * weight  0.166667
 Q [00003] : 0.000000  0.333246  0.000000 (cc ) * weight  0.166667
 Q [00004] : 0.000000 -0.499869  0.000000 (cc ) * weight   0.08333
 Q [00005] : 0.144300  0.249935  0.000000 (cc ) * weight  0.166667
 Q [00006] : 0.144300  0.416558  0.000000 (cc ) * weight  0.333333
 Q [00007] : 0.288600  0.499869  0.000000 (cc ) * weight   0.05556

 [04] Coloumb potential Random Integration (RIM)
 ===============================================


  [04.01] RIM initialization
  ==========================

  * Diagonal components only detected *

  8 x (sBL volume)    [au]:   0.0040
  sBZ random points       : 1000000
  Points outside the sBZ  :  8014604
  RL volume           [au]:  0.01799
  Integrated volume   [au]:  0.01795


  [04.02] RIM integrals
  =====================

  Gamma point sphere radius         [au]:  0.02879
  Points outside the sphere             :  896970
  [Int_sBZ(q=0) 1/q^2]*(Vol_sBZ)^(-1/3) = 6.386878
                                 should be < 7.795600
  [WR./lf_cut_e100//ndb.RIM]----------------------------------
   Brillouin Zone Q/K grids (IBZ/BZ):   7   36    7   36
   Coulombian RL components        : 1
   Coulombian diagonal components  :yes
   RIM random points               : 1000000
   RIM  RL volume             [a.u.]:  0.01795
   Real RL volume             [a.u.]:  0.01799
   Eps^-1 reference component       :0
   Eps^-1 components                : 0.00      0.00      0.00    
   RIM anysotropy factor            : 0.000000
  - S/N 002584 -------------------------- v.04.01.02 r.00076 -

  Summary of Coulomb integrals for non-metallic bands |Q|[au] RIM/Bare:

  Q [1]:0.1000E-40.8193 * Q [2]: 0.166623 1.165452
  Q [5]: 0.288600 1.048097 * Q [3]: 0.333246 1.035091
  Q [6]: 0.440843 1.019214 * Q [4]: 0.499869 1.014503
  Q [7]: 0.577199 1.010631

 CpuTiming [Min/Max/Average]: 02s/05s/04s

 [05] Coloumb potential CutOff :box
 ==================================

 Cut directions       :Z
 Box sides        [au]: 300.0000
 Symmetry test passed :yes

 [WR./lf_cut_e100//ndb.cutoff]-------------------------------
  Brillouin Zone Q/K grids (IBZ/BZ):   7   36    7   36
  CutOff Geometry                 :box z
  Coulomb cutoff potential        :box z ******
  Box sides length            [au]:   0.0000    0.0000  300.0000
  Sphere/Cylinder radius      [au]: 0.000000
  Cylinder length             [au]: 0.000000
  RL components                   :  71925
  RL components used in the sum   : 126545
  RIM corrections included        :yes
  RIM RL components               : 1
  RIM random points               : 1000000
 - S/N 002584 -------------------------- v.04.01.02 r.00076 -

 CpuTiming [Min/Max/Average]: 05s/07s/07s

 [06] External corrections
 =========================


 [07] Optics
 ===========

 [RD./SAVE//ns.kb_pp_pwscf]----------------------------------
  Fragmentation                    :yes
 - S/N 002584 -------------------------- v.04.01.02 r.00076 -
 [WF] Performing Wave-Functions I/O from ./SAVE

 [WF loader] Normalization (few states)  min/max  :0.7214E-10 0.9999    

 [WR./lf_cut_e100//ndb.dip_iR_and_P]-------------------------
  Brillouin Zone Q/K grids (IBZ/BZ):   7   36    7   36
  RL vectors                   (WF):  71925
  Fragmentation                    :yes
  Electronic Temperature        [K]: 300.00000
  Bosonic    Temperature        [K]: 300.00000
  X band range           :  1  20
  X band range limits    :  5   4
  X e/h energy range [ev]:-1.0000000 -1.0000000
  RL vectors in the sum  :  71925
  [r,Vnl] included       :yes
  Using shifted grids    :no
  Using covariant dipoles:no
  Using G-space approach :yes
  Using R-space approach :no
  Direct v evaluation    :no
  Field momentum norm    :0.10000E-4
  Wavefunctions          :Perdew, Burke & Ernzerhof(X)+Perdew, Burke & Ernzerhof(C)
 - S/N 002584 -------------------------- v.04.01.02 r.00076 -

 [WARNING] The system is a metal but Drude term not included.
 [WF] Performing Wave-Functions I/O from ./SAVE

 [FFT-X] Mesh size:   15    15   651

 [X-CG] R(p) Tot o/o(of R)  :  20  114  100

 CpuTiming [Min/Max/Average]: 02m-59s/03m-05s/03m-03s

 [08] Game Over & Game summary
 =============================

 11/27/2017 at 19:12 YAMBO @ jigen117 [start]
 11/27/2017 at 19:16                  [end]

 Timing   [Min/Max/Average]: 03m-08s/03m-32s/03m-28s

 .-ACKNOWLEDGMENT
 |
 | The users of YAMBO have little formal obligations with respect to
 | the YAMBO group (those specified in the GNU General Public
 | License, http://www.gnu.org/copyleft/gpl.txt). However, it is
 | common practice in the scientific literature, to acknowledge the
 | efforts of people that have made the research possible. In this
 | spirit, please find below the reference we kindly ask you to use
 | in order to acknowledge YAMBO:
 |
 | Yambo: An ab initio tool for excited state calculations
 | A. Marini, C. Hogan, M. Gr\"uning, D. Varsano
 | Computer Physics Communications  180, 1392 (2009).
 |
  
 .-Input file : lf_cut.in
 | optics                       # [R OPT] Optics
 | chi                          # [R CHI] Dyson equation for Chi.
 | rim_cut                      # [R RIM CUT] Coulomb potential
 | BoseTemp=  0.02585     eV    # Bosonic Temperature
 | FFTGvecs=  71925       RL    # [FFT] Plane-waves
 | X_q_0_CPU= "16.2.1"          # [PARALLEL] CPUs for each role
 | X_q_0_ROLEs= "c.v.k"         # [PARALLEL] CPUs roles (k,c,v)
 | RandQpts= 1000000            # [RIM] Number of random q-points in the BZ
 | RandGvec= 1            RL    # [RIM] Coulomb interaction RS components
 | CUTGeo= "box z"              # [CUT] Coulomb Cutoff geometry: box/cylinder/sphere X/Y/Z/XY..
 | % CUTBox
 |    0.0000 |   0.0000 | 300.0000 |        # [CUT] [au] Box sides
 | %
 | CUTRadius= 0.000000          # [CUT] [au] Sphere/Cylinder radius
 | CUTCylLen= 0.000000          # [CUT] [au] Cylinder length
 | Chimod= "Hartree"            # [X] IP/Hartree/ALDA/LRC/BSfxc
 | NGsBlkXd=  505         RL    # [Xd] Response block size
 | % QpntsRXd
 |  1 | 1 |                     # [Xd] Transferred momenta
 | %
 | % BndsRnXd
 |   1 | 20 |                   # [Xd] Polarization function bands
 | %
 | GrFnTpXd= "R"                # [Xd] Green`s function (T)ordered,(R)etarded,(r)senant,(a)ntiresonant [T, R, r, Ta, Ra]
 | % EnRngeXd
 |   0.00000 | 10.00000 | eV    # [Xd] Energy range
 | %
 | % DmRngeXd
 |   0.10000 |  0.10000 | eV    # [Xd] Damping range
 | %
 | ETStpsXd=  500               # [Xd] Total Energy steps
 | % LongDrXd
 | 0.1000E-4 | 0.000    | 0.000    |        # [Xd] [cc] Electric Field
 | %

At this stage I am not considering any Drude term, and I think I should not need it because anyway there are not partially filled bands.
I guessed that the units for specifying the vertical size of the box are Bohr because in the input one can find [au] and I am almost sure that the code is then considering half of the required side (by comparing cut and uncut potential in test CUT outputs), but for larger supercells that should not be an issue.
Why I am getting such a result is still unclear to me and I am asking for any suggestion to understand it.

Thanks,

Aldo

[Daniele Varsano]

Dear Aldo,

Should that cutoff a way to almost avoid increasing the vacuum size (at least not more than required to have the total energy converged at SCF level)?

Yes, well not as the ground state, in particular for GW, but surely it is meant to mitigate the volume dependence.

while the LF one in G-space, with and without RIM-cut are not.

that's sound strange, as LF in G space an eh space should be the same provided that you include the coupling part in the eh matrix and use the same number of bands and G vector in the response. In any case, being a 2D system, I would expect a difference between IP and LF at least in the direction orthogonal to the plane.

Looking at your report, the only think it is not convincing is the RIM RL components:

Code: Select all

RIM RL components               : 1

Your cell is extremely anisotropic so the RIM at gamma only could be not enough, try to raise that number until convergence (usually 50/100Gs, o may be larger as your cell is very anysotropic)

At this stage I am not considering any Drude term, and I think I should not need it because anyway there are not partially filled bands.

Well, this is not relevant at this stage, but from the report it seems you have 2 metallic bands (partially filled):

Code: Select all

States summary         : Full        Metallic    Empty
                           0001-0003   0004-0005   0006-0020

I guessed that the units for specifying the vertical size of the box are Bohr

Yes, that's correct.

Best,
Daniele

[a.ugolotti]

Dear Daniele,

thanks for your reply. First I still have a doubt:

Yes, well not as the ground state, in particular for GW, but surely it is meant to mitigate the volume dependence.

Reasoning in real space, once I guess the maximum charge-charge distance along z and I check that with such value the supercell is tall enough to avoid the interaction between some charge and the replica of the system, it is still not fully clear to me why the result for system with the cutoff should change with the size of the vacuum region. I mean, the truncated sums should include the same frequencies in reciprocal space (considering the same size of the box). A larger supercell would than allow to include higher frequency components without including terms due to charge-replica coupling?

that's sound strange, as LF in G space an eh space should be the same provided that you include the coupling part in the eh matrix and use the same number of bands and G vector in the response. In any case, being a 2D system, I would expect a difference between IP and LF at least in the direction orthogonal to the plane.

I am referring to the in-plane components of excitation, so the result should be less influenced by the screening. What do you mean by including the coupling part in calculating the spectrum in eh space? I used the same kernel as the G-space case. The input was generated by this command line: yambo -o b -k hartree -y d. The BSENGexx parameter was set as the value converging the exchange-related energy correction (larger than NGsBlkXd)

Your cell is extremely anisotropic so the RIM at gamma only could be not enough, try to raise that number until convergence (usually 50/100Gs, o may be larger as your cell is very anysotropic)

I have tested RandGvec values up to 1000 RL without noticing ant change in the spectrum. Anyway just with 1 RL the ratio between the Bare and RIM integral was close to 1 at the BZ edge, if I was interpreting currectly the output (up to 2*10^-3).

Well, this is not relevant at this stage, but from the report it seems you have 2 metallic bands (partially filled

This is a side question, but if I check the output of scf calculation, no bands ( here read E_KS(k) ) is crossing the Fermi level

[Daniele Varsano]

Ciao Aldo,

Reasoning in real space, once I guess the maximum charge-charge distance along z and I check that with such value the supercell is tall enough to avoid the interaction between some charge and the replica of the system, it is still not fully clear to me why the result for system with the cutoff should change with the size of the vacuum region.

Indeed it should not change, if there is residual change it is due to the numeric construction of the box cutoff which imply an integration of the bare Coulomb potential in the Bz, and the Bz is changing by enlarging the supercell. I observed that box cutoff suffers of this problem. In yambo there is a new implementation of the coulomb cutoff based on a Wigner Seitze cut of the coulomb potential which is surely more stable and robust, but this is not in the GPL version: the reason is that at the moment it works only for othorombic cells> I can give you access to that branch, but looking at your cell it is not useful unless you can resort to an orthorhombic cell.

What do you mean by including the coupling part in calculating the spectrum in eh space?

I mean that the two representation of the reposes function are equivalent only if you include the e->h and h->e transitions and the coupling term between them, this is achieved by setting:

Code: Select all

BSEmod= "coupling"

Anyway just with 1 RL the ratio between the Bare and RIM integral was close to 1 at the BZ edge, if I was interpreting currectly the output (up to 2*10^-3).

Ok, to that's safe.

This is a side question, but if I check the output of scf calculation, no bands ( here read E_KS(k) ) is crossing the Fermi level

Ok, so the metallic character is due to the fact that Yambo adds an electronic temperature by default, you can set it to zero kelvin by adding the variable

Code: Select all

ElecTemp= 0 eV 

in input file: the metallic character should disappear.

Best,

Daniele

[Daniele Varsano]

Dear Aldo,

Indeed it should not change, if there is residual change it is due to the numeric construction of the box cutoff which imply an integration of the bare Coulomb potential in the Bz, and the Bz is changing by enlarging the supercell. I observed that box cutoff suffers of this problem.

I forgot to say that this problem should be mitigated by enhancing the k point sampling, at least this is observed fog GW calculation.
About the equivalence of RPA in eh space and g space, while it has to hold when not using the cutoff, I'm not sure the same old when using the cutoff as the q->0 divergence of the coulomb cutoff is removed.

In any case, without using the cutoff when using such large cess is the calculation converged with respect the vacuum size?

Daniele