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Benzene molecule †

This tutorial explains how to optimize the geometry by using different algorithms. In this tutorial, a benzene molecule is placed in a cubic box with the cell edges of 10 Angstrom. pot_C.pbe1 and pot_H.lda1 are used with the cutoff energies of 36 Ry (GMAX=6) and 400 Ry (GMAXP=20) for the wave functions and the argmentation charge, respectively.

• Input file (nfinp_1)

       0     0     0     0     0     0 : I_CTRL(1:6) (DUMMY)
    6.00 20.00     2    12    12       : GMAX GMAXP NTYP NATM NATM2
      25     0                         : NUM_SPACE_GROUP TYPE_BRAVIS_LATTICE
   18.89726878 18.89726878 18.89726878 90.0 90.0 90.0 : A B C ALPHA BETA GAMMA
       1     1     1     1     1     1 : K_MESH
       1     0                         : NCORD NINV
           0.0000000000        2.6366036317        0.0000000000     1     1     1
          -2.2833569864        1.3182923672        0.0000000000     1     1     1
          -2.2833569864       -1.3182923672        0.0000000000     1     1     1
           0.0000000000       -2.6366036317        0.0000000000     1     1     1
           2.2833569864       -1.3182923672        0.0000000000     1     1     1
           2.2833569864        1.3182923672        0.0000000000     1     1     1
           0.0000000000        4.6909824123        0.0000000000     1     1     2
          -4.0624970473        2.3454912062        0.0000000000     1     1     2
          -4.0624970473       -2.3454912062        0.0000000000     1     1     2
           0.0000000000       -4.6909824123        0.0000000000     1     1     2
           4.0624970473       -2.3454912062        0.0000000000     1     1     2
           4.0624970473        2.3454912062        0.0000000000     1     1     2
    6.00  0.15 28.29     3     1  0.00 : TYPE IATOMN ALFA AMION ILOC IVAN ZETA1
    1.00  0.15 28.29     3     1  0.00 : TYPE IATOMN ALFA AMION ILOC IVAN ZETA1
       0     0     0     0     0       : ICOND INIPOS INIVEL ININOS INIACC
       0     1                         : IPRE IPRI
     300   300     0    28000.00     0 : NMD1 NMD2 LAST_ITER CPUMAX IFSTOP
       6     1                         : WAY_MIX MIMX_WHAT
       0     8  0.80                   : ITER_START KBXMIX  MIX_ALPHA
    0.60  0.50  0.60  0.70  1.00       : DTIM1 DTIM2 DTIM3 DTIM4 DTIM
  500.00     4     1    0.10D-08       : DTIO IMDALG IEXPL EDELTA
  0.0010    0.10D-03     0             : WIDTH FORCCR ISTRESS
  ggapbe           1                   : XCTYPE KSPIN
    1.00                               : DESTM
     101                               : NBZTYP
       4     4     4                   : (DUMMY)
       4     4     4                   : (DUMMY)
      18                               : KEG
       1                               : NEXTST
       0                               : (DUMMY)
       2                               : IMSD
       0                               : EVALUATE_EKO_DIFF
       0                               : NPDOSAO
       0  0.00                         : SM_N DOPPING

  In this example, the GDIIS method is used (IMDALG=4) with the time step of 500 atomic unit. The GDIIS method works fine, when the atomic positions are close to the equilibirium. A rule of thumb is to switch from quenched molecular dynamics (IMDALG=2) to GDIIS when the maximum force becomes smaller than 1.e-2. Note that in the current implementation, GDIIS method does not work when the optimization step exceeds the 3 * N, where N is the number of atoms.

Monitoring the maximum force by using grep as (supposing the output file is "nfout_1")

> grep -A1 f_max nfout_1

we obtain

   NIT     TotalEnergy     f_max     f_rms      edel      vdel      fdel
     1    -40.14215406  0.002809  0.001947  0.10D-08  0.12D-06  0.10D-08
--
   NIT     TotalEnergy     f_max     f_rms      edel      vdel      fdel
     2    -40.14215395  0.005734  0.004041  0.22D-08  0.17D-06  0.22D-08
--
   NIT     TotalEnergy     f_max     f_rms      edel      vdel      fdel
     3    -40.14224266  0.001880  0.001393  0.47D-08  0.13D-06  0.47D-08
--
   NIT     TotalEnergy     f_max     f_rms      edel      vdel      fdel
     4    -40.14225368  0.000871  0.000552  0.11D-08  0.15D-06  0.11D-08
--
   NIT     TotalEnergy     f_max     f_rms      edel      vdel      fdel
     5    -40.14225523  0.000046  0.000030  0.51D-09  0.85D-07  0.51D-09

and we can see that the geometry optimization converges within 5 steps.

Then, let us use the quenched molecular dynamics (QMD) for comparison. In this case we use IMDALG=2 and the time step (DTIO) of 200 atomic unit as

200.00     2     1    0.10D-08       : DTIO IMDALG IEXPL EDELTA

and the resulting maximum forces are

   NIT     TotalEnergy     f_max     f_rms      edel      vdel      fdel
     1    -40.14215406  0.002809  0.001947  0.10D-08  0.12D-06  0.10D-08
--
   NIT     TotalEnergy     f_max     f_rms      edel      vdel      fdel
     2    -40.14218382  0.001971  0.001448  0.22D-08  0.10D-06  0.22D-08
--
...
--
   NIT     TotalEnergy     f_max     f_rms      edel      vdel      fdel
    14    -40.14225511  0.000195  0.000135  0.15D-08  0.66D-07  0.15D-08
--
   NIT     TotalEnergy     f_max     f_rms      edel      vdel      fdel
    15    -40.14225523  0.000071  0.000033  0.21D-09  0.23D-07  0.21D-09

The convergence is achieved with 15 steps and we can see that the GDIIS method is much more efficient than QMD.