Why does BURAI give the correct output file but wrong graph?

Question

Edit3: HemanthHaridas' answer explained why BURAI gave me the result. However, when I opened the same output file using XCrySDen, I got a completely different result (the correct one). So, even though I accepted the answer, I am opening this question again. Since XCrySDen is maintained in a more regular manner than BURAI, I trust the result of XCrySDen cannot understand the discrepancy between XCrySDen result and BURAI result (or alternatively, the result obtained using @HemanthHaridas' explanation).

I was following a youtube tutorial for finding the lattice constant of Si crystal: Project: 3.1 Si crystal constant and density | Quantum Espresso Tutorial 2019. The input file I used is the following:

&control
    calculation = 'vc-relax'
    prefix = 'si'
    etot_conv_thr = 1e-5
    forc_conv_thr = 1e-4
/
&system
    ibrav=2 
    celldm(1) =14 
    nat=2 
    ntyp=1
    ecutwfc=30
/
&electrons
    conv_thr=1e-7
/
&ions
/
&cell
    cell_dofree='all'
/
ATOMIC_SPECIES
 Si  28.0855  Si.pbe-n-rrkjus_psl.1.0.0.UPF
ATOMIC_POSITIONS (alat)
 Si 0.00 0.00 0.00 0 0 0 
 Si 0.25 0.25 0.25 0 0 0
K_POINTS (automatic)
  4 4 4 0 0 0

When I run this, I got the output file which gave me the (almost) correct value for the lattice constant of the Si which I found from the output/log file (5.48 Å). However, inside BURAI GUI, there is a window to view the convergence for geometric convergence which indicates a wrong result as can be seen from the image below.

My question is why is the lattice constant converging to a different (wrong) value in the graph, while the output file gives the correct lattice constant (within an error of 1%) after the end of the SCF iteration?

Edit1: The output file espresso.log.opt can be found here. The cell parameters in each step and the volume can be found inside denoted by CELL_PARAMETERS and new unit-cell volume, respectively. To find the cell parameter in Bohr radius, I first divided the cell parameter by 0.5 and then multiplied by alat=14. To convert it to Å, one needs to multiply the Bohr radius by 0.529

Edit2: alat multiplier and the x, y and z axes lengths at each step

 13.999998  0.696568  0.696568  0.696568
 13.999998  0.680759  0.680759  0.680759
 13.999998  0.657046  0.657046  0.657046
 13.999998  0.644397  0.644397  0.644397
 13.999998  0.625422  0.625422  0.625422
 13.999998  0.611748  0.611748  0.611748
 13.999998  0.591238  0.591238  0.591238
 13.999998  0.560472  0.560472  0.560472
 13.999998  0.514324  0.514324  0.514324
 13.999998  0.526698  0.526698  0.526698
 13.999998  0.523420  0.523420  0.523420
 13.999998  0.523121  0.523121  0.523121
 13.999998  0.523121  0.523121  0.523121

Answer 1

TL;DR

The results obtained by OP from BURAI has been independently verified to be correct using the attached Python script, and by redoing the calculation with cell vectors and positions set explicitly in units of angstrom. The results from both the calculations converged to the same final structure, as it should.

Unfortunately, OP got confused between primitive and conventional cells. The main issue was that OP is trying to compare the cell parameters from the optimized primitive cell to the cell parameters of the conventional cell. If we transform the optimized primitive cell to a conventional cell, we get a cell parameter of 5.50929172400000 Å which is the value that OP is after (0.5% error compared to the value of 5.48 Å).

Longer answer

Gist of the answer that I had previously written:

The cell parameters that were extracted from the output file that OP had posted are as follows:

The values for celldm(1) and cell parameters in x, y and z in units of angstrom are given below:

  7.408477  5.160506  5.160506  5.160506
  7.408477  5.043389  5.043389  5.043389
  7.408477  4.867713  4.867713  4.867713
  7.408477  4.773997  4.773997  4.773997
  7.408477  4.633422  4.633422  4.633422
  7.408477  4.532122  4.532122  4.532122
  7.408477  4.380172  4.380172  4.380172
  7.408477  4.152247  4.152247  4.152247
  7.408477  3.810360  3.810360  3.810360
  7.408477  3.902034  3.902034  3.902034
  7.408477  3.877742  3.877742  3.877742
  7.408477  3.875530  3.875530  3.875530
  7.408477  3.875530  3.875530  3.875530

The code that was used for the analysis is

from numpy.linalg   import  norm

with open("raw") as f: # give your output file name instead
    fileContents    =   f.readlines()
    for index, line in enumerate(fileContents):
        if "CELL_PARAMETERS" in line:
            reqdlines   =   fileContents[index:index+4]
            multiplier  =   float(reqdlines[0].split()[-1].strip(")"))
            x_axis      =   [float(x) for x in reqdlines[1].split()]
            y_axis      =   [float(x) for x in reqdlines[2].split()]
            z_axis      =   [float(x) for x in reqdlines[3].split()]
            print("{:10.6f}{:10.6f}{:10.6f}{:10.6f}".format(multiplier*0.529177, norm(x_axis)*multiplier*0.529, norm(y_axis)*multiplier*0.529, norm(z_axis)*multiplier*0.529))

Thus, in the previous iteration of question and answer, it was made clear that BURAI is giving the correct answer, and the tutorial that OP was following was wrong.

Since OP is not convinced with the results, I redid the optimization of the Si cell using the same input file, but with the coordinates and cell vectors explicitly provided in units of angstrom.

The cell vectors in x, y and z that were obtained by are as follows:

  5.158930  5.158930  5.158930
  5.039445  5.039445  5.039445
  4.860218  4.860218  4.860218
  4.764030  4.764030  4.764030
  4.619749  4.619749  4.619749
  4.516518  4.516518  4.516518
  4.361672  4.361672  4.361672
  4.129403  4.129403  4.129403
  3.780998  3.780998  3.780998
  3.932265  3.932265  3.932265
  3.900708  3.900708  3.900708
  3.895402  3.895402  3.895402
  3.895658  3.895658  3.895658
  3.895658  3.895658  3.895658

It is clear that the optimization converges to the same structure regardless of whether we use alat or angstrom (which it must ideally).

Just to drive the point home, reproduced below is the output from AFlow.org showing that BURAI output is the correct one.

Input

EXAMPLE POSCAR
1.000000
   0.000000000   2.754645862   2.754645862
   2.754645862   0.000000000   2.754645862
   2.754645862   2.754645862   0.000000000
Si
2 
Cartesian(2) [Si2]
0.000000000   0.000000000   0.000000000
4.131968792   1.377322931   4.131968792

Output

REAL LATTICE
 Real space lattice:
   0.0000e+00  2.7546e+00  2.7546e+00
   2.7546e+00  0.0000e+00  2.7546e+00
   2.7546e+00  2.7546e+00  0.0000e+00
 a b c alpha beta gamma: 3.895657538 3.895657538 3.895657538 60 60 60
 a b c alpha beta gamma: 7.361725291 7.361725291 7.361725291 60 60 60   Bohrs/Degs 
 Volume: 41.8
 c/a = 1
BRAVAIS LATTICE OF THE CRYSTAL (pgroup_xtal)
 Bravais Lattice Primitive        = FCC
 Lattice Variation                = FCC
 Lattice System                   = cubic
 Pearson Symbol                   = cF8

Endnote: I strongly suspect that OP is making some mistake in measuring the cell parameters manually, and that is the origin for the confusion.

Edit: I have now identified the origin of the confusion for OP. OP did the calculations in primitive cell, and has the cell parameter value for the conventional cell. Once that transformation is made, we get a value of 5.50929172400000 which is the value that OP is after.