Model Extended KIM ID = 
=== Verification check vc-periodicity-support start (2023-05-09 21:29:01) ===
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!!!!!  VERIFICATION CHECK: vc-periodicity-support  !!!!!
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Description: Check that the model supports periodic boundary conditions
             correctly. If the simulation box is increased by an integer factor
             along a periodic direction, the total energy must multiply by that
             factor and the forces on atoms that are periodic copies of each
             other must be the same. The check is performed for a randomly
             distorted non-periodic face-centered cubic (FCC) cube base
             structure. Separate configurations are tested for each species
             supported by the model, as well as one containing a random
             distribution of all species. For each configuration, all possible
             combinations of periodic boundary conditions are tested: TFF, FTF,
             FFT, TTF, TFT, TTF, TTT (where 'T' indicates periodicity along a
             direction, and 'F' indicates no periodicity). The verification
             check passes if the energy of all configurations that the model is
             able to compute support all periodic boundary conditions correctly.
             Configurations used for testing are provided as auxiliary files.

Author: Ellad Tadmor

------------------------------------------------------------------------------------------------------------------------
Results for KIM Model      : MEAM_LAMMPS_KimSeolJi_2017_PtAl__MO_793141037706_002
Supported species          : Al Pt

random seed                = 13
lattice constant (orig)    = 3.000
perturbation amplitude     = 0.300
number unit cells per side = 1
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MONOATOMIC STRUCTURE -- Species = Al, PBC = TTT   (Configuration in file "config-Al-TTT.xyz")
------------------------------------------------------------------------------------------------------------------------

The system is doubled in p=3 periodic directions, which means an increase by a factor n=2^3=8
in the number of atoms and in the energy.

Energy requirement:

V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, 
and DBL_p is an operator that doubles the configuration in p periodic directions.

V(DBL_p(r_1,...,r_N)) = 157.89301819259018
2^p V(r_1,...,r_N)    = 157.8930181925898

Forces requirement:

f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k 
(where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration 
in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator.

  k                 f_k(DBL_p(r_1,...,r_N))                                  f_(k % N)(r_1,...,r_N)
------------------------------------------------------------------------------------------------------------------------
  0    1.28905414e+01   -1.37420439e+01   -2.08827967e+00   |   1.28905414e+01   -1.37420439e+01   -2.08827967e+00   
  1   -2.13285357e+01    9.29450259e+00   -6.44641565e+00   |  -2.13285357e+01    9.29450259e+00   -6.44641565e+00   
  2   -3.20842931e+00   -1.52798212e+00   -2.80594817e+00   |  -3.20842931e+00   -1.52798212e+00   -2.80594817e+00   
  3    1.16464236e+01    5.97552346e+00    1.13406435e+01   |   1.16464236e+01    5.97552346e+00    1.13406435e+01   
  4    1.28905414e+01   -1.37420439e+01   -2.08827967e+00   |   1.28905414e+01   -1.37420439e+01   -2.08827967e+00   
  5   -2.13285357e+01    9.29450259e+00   -6.44641565e+00   |  -2.13285357e+01    9.29450259e+00   -6.44641565e+00   
  6   -3.20842931e+00   -1.52798212e+00   -2.80594817e+00   |  -3.20842931e+00   -1.52798212e+00   -2.80594817e+00   
  7    1.16464236e+01    5.97552346e+00    1.13406435e+01   |   1.16464236e+01    5.97552346e+00    1.13406435e+01   
  8    1.28905414e+01   -1.37420439e+01   -2.08827967e+00   |   1.28905414e+01   -1.37420439e+01   -2.08827967e+00   
  9   -2.13285357e+01    9.29450259e+00   -6.44641565e+00   |  -2.13285357e+01    9.29450259e+00   -6.44641565e+00   
 10   -3.20842931e+00   -1.52798212e+00   -2.80594817e+00   |  -3.20842931e+00   -1.52798212e+00   -2.80594817e+00   
 11    1.16464236e+01    5.97552346e+00    1.13406435e+01   |   1.16464236e+01    5.97552346e+00    1.13406435e+01   
 12    1.28905414e+01   -1.37420439e+01   -2.08827967e+00   |   1.28905414e+01   -1.37420439e+01   -2.08827967e+00   
 13   -2.13285357e+01    9.29450259e+00   -6.44641565e+00   |  -2.13285357e+01    9.29450259e+00   -6.44641565e+00   
 14   -3.20842931e+00   -1.52798212e+00   -2.80594817e+00   |  -3.20842931e+00   -1.52798212e+00   -2.80594817e+00   
 15    1.16464236e+01    5.97552346e+00    1.13406435e+01   |   1.16464236e+01    5.97552346e+00    1.13406435e+01   
 16    1.28905414e+01   -1.37420439e+01   -2.08827967e+00   |   1.28905414e+01   -1.37420439e+01   -2.08827967e+00   
 17   -2.13285357e+01    9.29450259e+00   -6.44641565e+00   |  -2.13285357e+01    9.29450259e+00   -6.44641565e+00   
 18   -3.20842931e+00   -1.52798212e+00   -2.80594817e+00   |  -3.20842931e+00   -1.52798212e+00   -2.80594817e+00   
 19    1.16464236e+01    5.97552346e+00    1.13406435e+01   |   1.16464236e+01    5.97552346e+00    1.13406435e+01   
 20    1.28905414e+01   -1.37420439e+01   -2.08827967e+00   |   1.28905414e+01   -1.37420439e+01   -2.08827967e+00   
 21   -2.13285357e+01    9.29450259e+00   -6.44641565e+00   |  -2.13285357e+01    9.29450259e+00   -6.44641565e+00   
 22   -3.20842931e+00   -1.52798212e+00   -2.80594817e+00   |  -3.20842931e+00   -1.52798212e+00   -2.80594817e+00   
 23    1.16464236e+01    5.97552346e+00    1.13406435e+01   |   1.16464236e+01    5.97552346e+00    1.13406435e+01   
 24    1.28905414e+01   -1.37420439e+01   -2.08827967e+00   |   1.28905414e+01   -1.37420439e+01   -2.08827967e+00   
 25   -2.13285357e+01    9.29450259e+00   -6.44641565e+00   |  -2.13285357e+01    9.29450259e+00   -6.44641565e+00   
 26   -3.20842931e+00   -1.52798212e+00   -2.80594817e+00   |  -3.20842931e+00   -1.52798212e+00   -2.80594817e+00   
 27    1.16464236e+01    5.97552346e+00    1.13406435e+01   |   1.16464236e+01    5.97552346e+00    1.13406435e+01   
 28    1.28905414e+01   -1.37420439e+01   -2.08827967e+00   |   1.28905414e+01   -1.37420439e+01   -2.08827967e+00   
 29   -2.13285357e+01    9.29450259e+00   -6.44641565e+00   |  -2.13285357e+01    9.29450259e+00   -6.44641565e+00   
 30   -3.20842931e+00   -1.52798212e+00   -2.80594817e+00   |  -3.20842931e+00   -1.52798212e+00   -2.80594817e+00   
 31    1.16464236e+01    5.97552346e+00    1.13406435e+01   |   1.16464236e+01    5.97552346e+00    1.13406435e+01   
------------------------------------------------------------------------------------------------------------------------
PASS: Energies and forces are the same to within a relative error of 1e-08
------------------------------------------------------------------------------------------------------------------------

MONOATOMIC STRUCTURE -- Species = Al, PBC = TTF   (Configuration in file "config-Al-TTF.xyz")
------------------------------------------------------------------------------------------------------------------------

The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4
in the number of atoms and in the energy.

Energy requirement:

V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, 
and DBL_p is an operator that doubles the configuration in p periodic directions.

V(DBL_p(r_1,...,r_N)) = 82.49583714626083
2^p V(r_1,...,r_N)    = 82.49583714626091

Forces requirement:

f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k 
(where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration 
in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator.

  k                 f_k(DBL_p(r_1,...,r_N))                                  f_(k % N)(r_1,...,r_N)
------------------------------------------------------------------------------------------------------------------------
  0    2.11313137e+01    2.32806439e+01   -2.02860716e+01   |   2.11313137e+01    2.32806439e+01   -2.02860716e+01   
  1   -2.86912555e+01   -1.66407958e+01   -2.42802364e+01   |  -2.86912555e+01   -1.66407958e+01   -2.42802364e+01   
  2   -1.30962657e+01   -6.78993927e+00    1.69304139e+01   |  -1.30962657e+01   -6.78993927e+00    1.69304139e+01   
  3    2.06562075e+01    1.50091161e-01    2.76358941e+01   |   2.06562075e+01    1.50091161e-01    2.76358941e+01   
  4    2.11313137e+01    2.32806439e+01   -2.02860716e+01   |   2.11313137e+01    2.32806439e+01   -2.02860716e+01   
  5   -2.86912555e+01   -1.66407958e+01   -2.42802364e+01   |  -2.86912555e+01   -1.66407958e+01   -2.42802364e+01   
  6   -1.30962657e+01   -6.78993927e+00    1.69304139e+01   |  -1.30962657e+01   -6.78993927e+00    1.69304139e+01   
  7    2.06562075e+01    1.50091161e-01    2.76358941e+01   |   2.06562075e+01    1.50091161e-01    2.76358941e+01   
  8    2.11313137e+01    2.32806439e+01   -2.02860716e+01   |   2.11313137e+01    2.32806439e+01   -2.02860716e+01   
  9   -2.86912555e+01   -1.66407958e+01   -2.42802364e+01   |  -2.86912555e+01   -1.66407958e+01   -2.42802364e+01   
 10   -1.30962657e+01   -6.78993927e+00    1.69304139e+01   |  -1.30962657e+01   -6.78993927e+00    1.69304139e+01   
 11    2.06562075e+01    1.50091161e-01    2.76358941e+01   |   2.06562075e+01    1.50091161e-01    2.76358941e+01   
 12    2.11313137e+01    2.32806439e+01   -2.02860716e+01   |   2.11313137e+01    2.32806439e+01   -2.02860716e+01   
 13   -2.86912555e+01   -1.66407958e+01   -2.42802364e+01   |  -2.86912555e+01   -1.66407958e+01   -2.42802364e+01   
 14   -1.30962657e+01   -6.78993927e+00    1.69304139e+01   |  -1.30962657e+01   -6.78993927e+00    1.69304139e+01   
 15    2.06562075e+01    1.50091161e-01    2.76358941e+01   |   2.06562075e+01    1.50091161e-01    2.76358941e+01   
------------------------------------------------------------------------------------------------------------------------
PASS: Energies and forces are the same to within a relative error of 1e-08
------------------------------------------------------------------------------------------------------------------------

MONOATOMIC STRUCTURE -- Species = Al, PBC = TFT   (Configuration in file "config-Al-TFT.xyz")
------------------------------------------------------------------------------------------------------------------------

The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4
in the number of atoms and in the energy.

Energy requirement:

V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, 
and DBL_p is an operator that doubles the configuration in p periodic directions.

V(DBL_p(r_1,...,r_N)) = 70.92099047060606
2^p V(r_1,...,r_N)    = 70.92099047060603

Forces requirement:

f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k 
(where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration 
in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator.

  k                 f_k(DBL_p(r_1,...,r_N))                                  f_(k % N)(r_1,...,r_N)
------------------------------------------------------------------------------------------------------------------------
  0    1.32877078e+01   -2.15583149e+01   -1.17334538e+01   |   1.32877078e+01   -2.15583149e+01   -1.17334538e+01   
  1   -1.55247027e+01    2.12418954e+01   -3.49418457e+00   |  -1.55247027e+01    2.12418954e+01   -3.49418457e+00   
  2   -1.50706752e+01   -2.43378329e+01    6.93570096e+00   |  -1.50706752e+01   -2.43378329e+01    6.93570096e+00   
  3    1.73076701e+01    2.46542524e+01    8.29193741e+00   |   1.73076701e+01    2.46542524e+01    8.29193741e+00   
  4    1.32877078e+01   -2.15583149e+01   -1.17334538e+01   |   1.32877078e+01   -2.15583149e+01   -1.17334538e+01   
  5   -1.55247027e+01    2.12418954e+01   -3.49418457e+00   |  -1.55247027e+01    2.12418954e+01   -3.49418457e+00   
  6   -1.50706752e+01   -2.43378329e+01    6.93570096e+00   |  -1.50706752e+01   -2.43378329e+01    6.93570096e+00   
  7    1.73076701e+01    2.46542524e+01    8.29193741e+00   |   1.73076701e+01    2.46542524e+01    8.29193741e+00   
  8    1.32877078e+01   -2.15583149e+01   -1.17334538e+01   |   1.32877078e+01   -2.15583149e+01   -1.17334538e+01   
  9   -1.55247027e+01    2.12418954e+01   -3.49418457e+00   |  -1.55247027e+01    2.12418954e+01   -3.49418457e+00   
 10   -1.50706752e+01   -2.43378329e+01    6.93570096e+00   |  -1.50706752e+01   -2.43378329e+01    6.93570096e+00   
 11    1.73076701e+01    2.46542524e+01    8.29193741e+00   |   1.73076701e+01    2.46542524e+01    8.29193741e+00   
 12    1.32877078e+01   -2.15583149e+01   -1.17334538e+01   |   1.32877078e+01   -2.15583149e+01   -1.17334538e+01   
 13   -1.55247027e+01    2.12418954e+01   -3.49418457e+00   |  -1.55247027e+01    2.12418954e+01   -3.49418457e+00   
 14   -1.50706752e+01   -2.43378329e+01    6.93570096e+00   |  -1.50706752e+01   -2.43378329e+01    6.93570096e+00   
 15    1.73076701e+01    2.46542524e+01    8.29193741e+00   |   1.73076701e+01    2.46542524e+01    8.29193741e+00   
------------------------------------------------------------------------------------------------------------------------
PASS: Energies and forces are the same to within a relative error of 1e-08
------------------------------------------------------------------------------------------------------------------------

MONOATOMIC STRUCTURE -- Species = Al, PBC = TFF   (Configuration in file "config-Al-TFF.xyz")
------------------------------------------------------------------------------------------------------------------------

The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2
in the number of atoms and in the energy.

Energy requirement:

V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, 
and DBL_p is an operator that doubles the configuration in p periodic directions.

V(DBL_p(r_1,...,r_N)) = 24.106911578636474
2^p V(r_1,...,r_N)    = 24.10691157863647

Forces requirement:

f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k 
(where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration 
in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator.

  k                 f_k(DBL_p(r_1,...,r_N))                                  f_(k % N)(r_1,...,r_N)
------------------------------------------------------------------------------------------------------------------------
  0    1.08409694e+01   -2.23078817e+01   -1.68401892e+01   |   1.08409694e+01   -2.23078817e+01   -1.68401892e+01   
  1   -1.34555286e+01    2.05549933e+01   -1.58813709e+01   |  -1.34555286e+01    2.05549933e+01   -1.58813709e+01   
  2   -1.13895197e+01   -1.78687081e+01    1.78967125e+01   |  -1.13895197e+01   -1.78687081e+01    1.78967125e+01   
  3    1.40040789e+01    1.96215964e+01    1.48248477e+01   |   1.40040789e+01    1.96215964e+01    1.48248477e+01   
  4    1.08409694e+01   -2.23078817e+01   -1.68401892e+01   |   1.08409694e+01   -2.23078817e+01   -1.68401892e+01   
  5   -1.34555286e+01    2.05549933e+01   -1.58813709e+01   |  -1.34555286e+01    2.05549933e+01   -1.58813709e+01   
  6   -1.13895197e+01   -1.78687081e+01    1.78967125e+01   |  -1.13895197e+01   -1.78687081e+01    1.78967125e+01   
  7    1.40040789e+01    1.96215964e+01    1.48248477e+01   |   1.40040789e+01    1.96215964e+01    1.48248477e+01   
------------------------------------------------------------------------------------------------------------------------
PASS: Energies and forces are the same to within a relative error of 1e-08
------------------------------------------------------------------------------------------------------------------------

MONOATOMIC STRUCTURE -- Species = Al, PBC = FTT   (Configuration in file "config-Al-FTT.xyz")
------------------------------------------------------------------------------------------------------------------------

The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4
in the number of atoms and in the energy.

Energy requirement:

V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, 
and DBL_p is an operator that doubles the configuration in p periodic directions.

V(DBL_p(r_1,...,r_N)) = 71.1289836468599
2^p V(r_1,...,r_N)    = 71.12898364686004

Forces requirement:

f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k 
(where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration 
in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator.

  k                 f_k(DBL_p(r_1,...,r_N))                                  f_(k % N)(r_1,...,r_N)
------------------------------------------------------------------------------------------------------------------------
  0   -1.75945994e+01    2.36652139e-01   -4.79310888e+00   |  -1.75945994e+01    2.36652139e-01   -4.79310888e+00   
  1    1.78149203e+01   -1.70812107e+01    1.10231234e+01   |   1.78149203e+01   -1.70812107e+01    1.10231234e+01   
  2    1.93131690e+01    1.85043376e+01   -1.72580795e+01   |   1.93131690e+01    1.85043376e+01   -1.72580795e+01   
  3   -1.95334899e+01   -1.65977903e+00    1.10280650e+01   |  -1.95334899e+01   -1.65977903e+00    1.10280650e+01   
  4   -1.75945994e+01    2.36652139e-01   -4.79310888e+00   |  -1.75945994e+01    2.36652139e-01   -4.79310888e+00   
  5    1.78149203e+01   -1.70812107e+01    1.10231234e+01   |   1.78149203e+01   -1.70812107e+01    1.10231234e+01   
  6    1.93131690e+01    1.85043376e+01   -1.72580795e+01   |   1.93131690e+01    1.85043376e+01   -1.72580795e+01   
  7   -1.95334899e+01   -1.65977903e+00    1.10280650e+01   |  -1.95334899e+01   -1.65977903e+00    1.10280650e+01   
  8   -1.75945994e+01    2.36652139e-01   -4.79310888e+00   |  -1.75945994e+01    2.36652139e-01   -4.79310888e+00   
  9    1.78149203e+01   -1.70812107e+01    1.10231234e+01   |   1.78149203e+01   -1.70812107e+01    1.10231234e+01   
 10    1.93131690e+01    1.85043376e+01   -1.72580795e+01   |   1.93131690e+01    1.85043376e+01   -1.72580795e+01   
 11   -1.95334899e+01   -1.65977903e+00    1.10280650e+01   |  -1.95334899e+01   -1.65977903e+00    1.10280650e+01   
 12   -1.75945994e+01    2.36652139e-01   -4.79310888e+00   |  -1.75945994e+01    2.36652139e-01   -4.79310888e+00   
 13    1.78149203e+01   -1.70812107e+01    1.10231234e+01   |   1.78149203e+01   -1.70812107e+01    1.10231234e+01   
 14    1.93131690e+01    1.85043376e+01   -1.72580795e+01   |   1.93131690e+01    1.85043376e+01   -1.72580795e+01   
 15   -1.95334899e+01   -1.65977903e+00    1.10280650e+01   |  -1.95334899e+01   -1.65977903e+00    1.10280650e+01   
------------------------------------------------------------------------------------------------------------------------
PASS: Energies and forces are the same to within a relative error of 1e-08
------------------------------------------------------------------------------------------------------------------------

MONOATOMIC STRUCTURE -- Species = Al, PBC = FTF   (Configuration in file "config-Al-FTF.xyz")
------------------------------------------------------------------------------------------------------------------------

The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2
in the number of atoms and in the energy.

Energy requirement:

V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, 
and DBL_p is an operator that doubles the configuration in p periodic directions.

V(DBL_p(r_1,...,r_N)) = 31.698695456850007
2^p V(r_1,...,r_N)    = 31.69869545685

Forces requirement:

f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k 
(where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration 
in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator.

  k                 f_k(DBL_p(r_1,...,r_N))                                  f_(k % N)(r_1,...,r_N)
------------------------------------------------------------------------------------------------------------------------
  0   -2.63495681e+01   -5.88460141e-01   -2.22191702e+01   |  -2.63495681e+01   -5.88460141e-01   -2.22191702e+01   
  1    1.90733669e+01    6.37043251e+00   -1.87738100e+01   |   1.90733669e+01    6.37043251e+00   -1.87738100e+01   
  2    2.51677516e+01   -1.58684153e-01    2.23247303e+01   |   2.51677516e+01   -1.58684153e-01    2.23247303e+01   
  3   -1.78915504e+01   -5.62328821e+00    1.86682500e+01   |  -1.78915504e+01   -5.62328821e+00    1.86682500e+01   
  4   -2.63495681e+01   -5.88460141e-01   -2.22191702e+01   |  -2.63495681e+01   -5.88460141e-01   -2.22191702e+01   
  5    1.90733669e+01    6.37043251e+00   -1.87738100e+01   |   1.90733669e+01    6.37043251e+00   -1.87738100e+01   
  6    2.51677516e+01   -1.58684153e-01    2.23247303e+01   |   2.51677516e+01   -1.58684153e-01    2.23247303e+01   
  7   -1.78915504e+01   -5.62328821e+00    1.86682500e+01   |  -1.78915504e+01   -5.62328821e+00    1.86682500e+01   
------------------------------------------------------------------------------------------------------------------------
PASS: Energies and forces are the same to within a relative error of 1e-08
------------------------------------------------------------------------------------------------------------------------

MONOATOMIC STRUCTURE -- Species = Al, PBC = FFT   (Configuration in file "config-Al-FFT.xyz")
------------------------------------------------------------------------------------------------------------------------

The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2
in the number of atoms and in the energy.

Energy requirement:

V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, 
and DBL_p is an operator that doubles the configuration in p periodic directions.

V(DBL_p(r_1,...,r_N)) = 51.46600570365805
2^p V(r_1,...,r_N)    = 51.46600570365805

Forces requirement:

f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k 
(where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration 
in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator.

  k                 f_k(DBL_p(r_1,...,r_N))                                  f_(k % N)(r_1,...,r_N)
------------------------------------------------------------------------------------------------------------------------
  0   -2.49645913e+01   -2.28675378e+01    1.34835456e+01   |  -2.49645913e+01   -2.28675378e+01    1.34835456e+01   
  1    2.54102275e+01    2.14912054e+01   -1.39774684e+01   |   2.54102275e+01    2.14912054e+01   -1.39774684e+01   
  2    3.30996398e+01   -2.48918000e+01   -3.46026728e+00   |   3.30996398e+01   -2.48918000e+01   -3.46026728e+00   
  3   -3.35452760e+01    2.62681324e+01    3.95419009e+00   |  -3.35452760e+01    2.62681324e+01    3.95419009e+00   
  4   -2.49645913e+01   -2.28675378e+01    1.34835456e+01   |  -2.49645913e+01   -2.28675378e+01    1.34835456e+01   
  5    2.54102275e+01    2.14912054e+01   -1.39774684e+01   |   2.54102275e+01    2.14912054e+01   -1.39774684e+01   
  6    3.30996398e+01   -2.48918000e+01   -3.46026728e+00   |   3.30996398e+01   -2.48918000e+01   -3.46026728e+00   
  7   -3.35452760e+01    2.62681324e+01    3.95419009e+00   |  -3.35452760e+01    2.62681324e+01    3.95419009e+00   
------------------------------------------------------------------------------------------------------------------------
PASS: Energies and forces are the same to within a relative error of 1e-08
------------------------------------------------------------------------------------------------------------------------

MONOATOMIC STRUCTURE -- Species = Pt, PBC = TTT   (Configuration in file "config-Pt-TTT.xyz")
------------------------------------------------------------------------------------------------------------------------

The system is doubled in p=3 periodic directions, which means an increase by a factor n=2^3=8
in the number of atoms and in the energy.

Energy requirement:

V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, 
and DBL_p is an operator that doubles the configuration in p periodic directions.

V(DBL_p(r_1,...,r_N)) = 870.0401304686891
2^p V(r_1,...,r_N)    = 870.0401304686881

Forces requirement:

f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k 
(where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration 
in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator.

  k                 f_k(DBL_p(r_1,...,r_N))                                  f_(k % N)(r_1,...,r_N)
------------------------------------------------------------------------------------------------------------------------
  0    8.50848154e+00   -8.45707600e+01   -1.00886512e+02   |   8.50848154e+00   -8.45707600e+01   -1.00886512e+02   
  1    8.48438293e+00    4.77409178e+01   -3.48834520e+01   |   8.48438293e+00    4.77409178e+01   -3.48834520e+01   
  2    6.15428710e+00   -3.91206961e+01    4.78062539e+01   |   6.15428710e+00   -3.91206961e+01    4.78062539e+01   
  3   -2.31471516e+01    7.59505383e+01    8.79637103e+01   |  -2.31471516e+01    7.59505383e+01    8.79637103e+01   
  4    8.50848154e+00   -8.45707600e+01   -1.00886512e+02   |   8.50848154e+00   -8.45707600e+01   -1.00886512e+02   
  5    8.48438293e+00    4.77409178e+01   -3.48834520e+01   |   8.48438293e+00    4.77409178e+01   -3.48834520e+01   
  6    6.15428710e+00   -3.91206961e+01    4.78062539e+01   |   6.15428710e+00   -3.91206961e+01    4.78062539e+01   
  7   -2.31471516e+01    7.59505383e+01    8.79637103e+01   |  -2.31471516e+01    7.59505383e+01    8.79637103e+01   
  8    8.50848154e+00   -8.45707600e+01   -1.00886512e+02   |   8.50848154e+00   -8.45707600e+01   -1.00886512e+02   
  9    8.48438293e+00    4.77409178e+01   -3.48834520e+01   |   8.48438293e+00    4.77409178e+01   -3.48834520e+01   
 10    6.15428710e+00   -3.91206961e+01    4.78062539e+01   |   6.15428710e+00   -3.91206961e+01    4.78062539e+01   
 11   -2.31471516e+01    7.59505383e+01    8.79637103e+01   |  -2.31471516e+01    7.59505383e+01    8.79637103e+01   
 12    8.50848154e+00   -8.45707600e+01   -1.00886512e+02   |   8.50848154e+00   -8.45707600e+01   -1.00886512e+02   
 13    8.48438293e+00    4.77409178e+01   -3.48834520e+01   |   8.48438293e+00    4.77409178e+01   -3.48834520e+01   
 14    6.15428710e+00   -3.91206961e+01    4.78062539e+01   |   6.15428710e+00   -3.91206961e+01    4.78062539e+01   
 15   -2.31471516e+01    7.59505383e+01    8.79637103e+01   |  -2.31471516e+01    7.59505383e+01    8.79637103e+01   
 16    8.50848154e+00   -8.45707600e+01   -1.00886512e+02   |   8.50848154e+00   -8.45707600e+01   -1.00886512e+02   
 17    8.48438293e+00    4.77409178e+01   -3.48834520e+01   |   8.48438293e+00    4.77409178e+01   -3.48834520e+01   
 18    6.15428710e+00   -3.91206961e+01    4.78062539e+01   |   6.15428710e+00   -3.91206961e+01    4.78062539e+01   
 19   -2.31471516e+01    7.59505383e+01    8.79637103e+01   |  -2.31471516e+01    7.59505383e+01    8.79637103e+01   
 20    8.50848154e+00   -8.45707600e+01   -1.00886512e+02   |   8.50848154e+00   -8.45707600e+01   -1.00886512e+02   
 21    8.48438293e+00    4.77409178e+01   -3.48834520e+01   |   8.48438293e+00    4.77409178e+01   -3.48834520e+01   
 22    6.15428710e+00   -3.91206961e+01    4.78062539e+01   |   6.15428710e+00   -3.91206961e+01    4.78062539e+01   
 23   -2.31471516e+01    7.59505383e+01    8.79637103e+01   |  -2.31471516e+01    7.59505383e+01    8.79637103e+01   
 24    8.50848154e+00   -8.45707600e+01   -1.00886512e+02   |   8.50848154e+00   -8.45707600e+01   -1.00886512e+02   
 25    8.48438293e+00    4.77409178e+01   -3.48834520e+01   |   8.48438293e+00    4.77409178e+01   -3.48834520e+01   
 26    6.15428710e+00   -3.91206961e+01    4.78062539e+01   |   6.15428710e+00   -3.91206961e+01    4.78062539e+01   
 27   -2.31471516e+01    7.59505383e+01    8.79637103e+01   |  -2.31471516e+01    7.59505383e+01    8.79637103e+01   
 28    8.50848154e+00   -8.45707600e+01   -1.00886512e+02   |   8.50848154e+00   -8.45707600e+01   -1.00886512e+02   
 29    8.48438293e+00    4.77409178e+01   -3.48834520e+01   |   8.48438293e+00    4.77409178e+01   -3.48834520e+01   
 30    6.15428710e+00   -3.91206961e+01    4.78062539e+01   |   6.15428710e+00   -3.91206961e+01    4.78062539e+01   
 31   -2.31471516e+01    7.59505383e+01    8.79637103e+01   |  -2.31471516e+01    7.59505383e+01    8.79637103e+01   
------------------------------------------------------------------------------------------------------------------------
PASS: Energies and forces are the same to within a relative error of 1e-08
------------------------------------------------------------------------------------------------------------------------

MONOATOMIC STRUCTURE -- Species = Pt, PBC = TTF   (Configuration in file "config-Pt-TTF.xyz")
------------------------------------------------------------------------------------------------------------------------

The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4
in the number of atoms and in the energy.

Energy requirement:

V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, 
and DBL_p is an operator that doubles the configuration in p periodic directions.

V(DBL_p(r_1,...,r_N)) = 299.15100216708623
2^p V(r_1,...,r_N)    = 299.1510021670861

Forces requirement:

f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k 
(where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration 
in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator.

  k                 f_k(DBL_p(r_1,...,r_N))                                  f_(k % N)(r_1,...,r_N)
------------------------------------------------------------------------------------------------------------------------
  0    5.82603475e+01   -7.06294505e+01   -8.28570444e+01   |   5.82603475e+01   -7.06294505e+01   -8.28570444e+01   
  1   -5.16292210e+01    6.19569184e+01   -8.06496429e+01   |  -5.16292210e+01    6.19569184e+01   -8.06496429e+01   
  2   -2.47866042e+01   -2.66104706e+01    8.15673688e+01   |  -2.47866042e+01   -2.66104706e+01    8.15673688e+01   
  3    1.81554777e+01    3.52830027e+01    8.19393185e+01   |   1.81554777e+01    3.52830027e+01    8.19393185e+01   
  4    5.82603475e+01   -7.06294505e+01   -8.28570444e+01   |   5.82603475e+01   -7.06294505e+01   -8.28570444e+01   
  5   -5.16292210e+01    6.19569184e+01   -8.06496429e+01   |  -5.16292210e+01    6.19569184e+01   -8.06496429e+01   
  6   -2.47866042e+01   -2.66104706e+01    8.15673688e+01   |  -2.47866042e+01   -2.66104706e+01    8.15673688e+01   
  7    1.81554777e+01    3.52830027e+01    8.19393185e+01   |   1.81554777e+01    3.52830027e+01    8.19393185e+01   
  8    5.82603475e+01   -7.06294505e+01   -8.28570444e+01   |   5.82603475e+01   -7.06294505e+01   -8.28570444e+01   
  9   -5.16292210e+01    6.19569184e+01   -8.06496429e+01   |  -5.16292210e+01    6.19569184e+01   -8.06496429e+01   
 10   -2.47866042e+01   -2.66104706e+01    8.15673688e+01   |  -2.47866042e+01   -2.66104706e+01    8.15673688e+01   
 11    1.81554777e+01    3.52830027e+01    8.19393185e+01   |   1.81554777e+01    3.52830027e+01    8.19393185e+01   
 12    5.82603475e+01   -7.06294505e+01   -8.28570444e+01   |   5.82603475e+01   -7.06294505e+01   -8.28570444e+01   
 13   -5.16292210e+01    6.19569184e+01   -8.06496429e+01   |  -5.16292210e+01    6.19569184e+01   -8.06496429e+01   
 14   -2.47866042e+01   -2.66104706e+01    8.15673688e+01   |  -2.47866042e+01   -2.66104706e+01    8.15673688e+01   
 15    1.81554777e+01    3.52830027e+01    8.19393185e+01   |   1.81554777e+01    3.52830027e+01    8.19393185e+01   
------------------------------------------------------------------------------------------------------------------------
PASS: Energies and forces are the same to within a relative error of 1e-08
------------------------------------------------------------------------------------------------------------------------

MONOATOMIC STRUCTURE -- Species = Pt, PBC = TFT   (Configuration in file "config-Pt-TFT.xyz")
------------------------------------------------------------------------------------------------------------------------

The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4
in the number of atoms and in the energy.

Energy requirement:

V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, 
and DBL_p is an operator that doubles the configuration in p periodic directions.

V(DBL_p(r_1,...,r_N)) = 548.0895818768465
2^p V(r_1,...,r_N)    = 548.0895818768469

Forces requirement:

f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k 
(where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration 
in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator.

  k                 f_k(DBL_p(r_1,...,r_N))                                  f_(k % N)(r_1,...,r_N)
------------------------------------------------------------------------------------------------------------------------
  0    1.50055640e+02   -1.64310320e+02    2.49619039e+01   |   1.50055640e+02   -1.64310320e+02    2.49619039e+01   
  1   -1.01901310e+02    2.11005215e+02    9.34795221e+01   |  -1.01901310e+02    2.11005215e+02    9.34795221e+01   
  2   -6.99598809e+01   -1.34179718e+02   -1.56414583e+02   |  -6.99598809e+01   -1.34179718e+02   -1.56414583e+02   
  3    2.18055506e+01    8.74848231e+01    3.79731569e+01   |   2.18055506e+01    8.74848231e+01    3.79731569e+01   
  4    1.50055640e+02   -1.64310320e+02    2.49619039e+01   |   1.50055640e+02   -1.64310320e+02    2.49619039e+01   
  5   -1.01901310e+02    2.11005215e+02    9.34795221e+01   |  -1.01901310e+02    2.11005215e+02    9.34795221e+01   
  6   -6.99598809e+01   -1.34179718e+02   -1.56414583e+02   |  -6.99598809e+01   -1.34179718e+02   -1.56414583e+02   
  7    2.18055506e+01    8.74848231e+01    3.79731569e+01   |   2.18055506e+01    8.74848231e+01    3.79731569e+01   
  8    1.50055640e+02   -1.64310320e+02    2.49619039e+01   |   1.50055640e+02   -1.64310320e+02    2.49619039e+01   
  9   -1.01901310e+02    2.11005215e+02    9.34795221e+01   |  -1.01901310e+02    2.11005215e+02    9.34795221e+01   
 10   -6.99598809e+01   -1.34179718e+02   -1.56414583e+02   |  -6.99598809e+01   -1.34179718e+02   -1.56414583e+02   
 11    2.18055506e+01    8.74848231e+01    3.79731569e+01   |   2.18055506e+01    8.74848231e+01    3.79731569e+01   
 12    1.50055640e+02   -1.64310320e+02    2.49619039e+01   |   1.50055640e+02   -1.64310320e+02    2.49619039e+01   
 13   -1.01901310e+02    2.11005215e+02    9.34795221e+01   |  -1.01901310e+02    2.11005215e+02    9.34795221e+01   
 14   -6.99598809e+01   -1.34179718e+02   -1.56414583e+02   |  -6.99598809e+01   -1.34179718e+02   -1.56414583e+02   
 15    2.18055506e+01    8.74848231e+01    3.79731569e+01   |   2.18055506e+01    8.74848231e+01    3.79731569e+01   
------------------------------------------------------------------------------------------------------------------------
PASS: Energies and forces are the same to within a relative error of 1e-08
------------------------------------------------------------------------------------------------------------------------

MONOATOMIC STRUCTURE -- Species = Pt, PBC = TFF   (Configuration in file "config-Pt-TFF.xyz")
------------------------------------------------------------------------------------------------------------------------

The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2
in the number of atoms and in the energy.

Energy requirement:

V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, 
and DBL_p is an operator that doubles the configuration in p periodic directions.

V(DBL_p(r_1,...,r_N)) = 91.80094153930452
2^p V(r_1,...,r_N)    = 91.80094153930452

Forces requirement:

f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k 
(where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration 
in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator.

  k                 f_k(DBL_p(r_1,...,r_N))                                  f_(k % N)(r_1,...,r_N)
------------------------------------------------------------------------------------------------------------------------
  0   -5.97312115e+01   -6.31709632e+01   -5.90020779e+01   |  -5.97312115e+01   -6.31709632e+01   -5.90020779e+01   
  1    4.14026803e+01    7.57952504e+01   -7.13009894e+01   |   4.14026803e+01    7.57952504e+01   -7.13009894e+01   
  2    7.22056945e+01   -7.78541926e+01    7.23011736e+01   |   7.22056945e+01   -7.78541926e+01    7.23011736e+01   
  3   -5.38771634e+01    6.52299054e+01    5.80018937e+01   |  -5.38771634e+01    6.52299054e+01    5.80018937e+01   
  4   -5.97312115e+01   -6.31709632e+01   -5.90020779e+01   |  -5.97312115e+01   -6.31709632e+01   -5.90020779e+01   
  5    4.14026803e+01    7.57952504e+01   -7.13009894e+01   |   4.14026803e+01    7.57952504e+01   -7.13009894e+01   
  6    7.22056945e+01   -7.78541926e+01    7.23011736e+01   |   7.22056945e+01   -7.78541926e+01    7.23011736e+01   
  7   -5.38771634e+01    6.52299054e+01    5.80018937e+01   |  -5.38771634e+01    6.52299054e+01    5.80018937e+01   
------------------------------------------------------------------------------------------------------------------------
PASS: Energies and forces are the same to within a relative error of 1e-08
------------------------------------------------------------------------------------------------------------------------

MONOATOMIC STRUCTURE -- Species = Pt, PBC = FTT   (Configuration in file "config-Pt-FTT.xyz")
------------------------------------------------------------------------------------------------------------------------

The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4
in the number of atoms and in the energy.

Energy requirement:

V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, 
and DBL_p is an operator that doubles the configuration in p periodic directions.

V(DBL_p(r_1,...,r_N)) = 287.7844984635111
2^p V(r_1,...,r_N)    = 287.78449846351117

Forces requirement:

f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k 
(where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration 
in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator.

  k                 f_k(DBL_p(r_1,...,r_N))                                  f_(k % N)(r_1,...,r_N)
------------------------------------------------------------------------------------------------------------------------
  0   -7.94766844e+01   -5.60889953e+01   -6.21549712e+01   |  -7.94766844e+01   -5.60889953e+01   -6.21549712e+01   
  1    4.68578741e+01    6.03940803e+01    4.97809341e+01   |   4.68578741e+01    6.03940803e+01    4.97809341e+01   
  2    8.53294079e+01   -7.73442066e+01   -2.35570746e+01   |   8.53294079e+01   -7.73442066e+01   -2.35570746e+01   
  3   -5.27105976e+01    7.30391216e+01    3.59311117e+01   |  -5.27105976e+01    7.30391216e+01    3.59311117e+01   
  4   -7.94766844e+01   -5.60889953e+01   -6.21549712e+01   |  -7.94766844e+01   -5.60889953e+01   -6.21549712e+01   
  5    4.68578741e+01    6.03940803e+01    4.97809341e+01   |   4.68578741e+01    6.03940803e+01    4.97809341e+01   
  6    8.53294079e+01   -7.73442066e+01   -2.35570746e+01   |   8.53294079e+01   -7.73442066e+01   -2.35570746e+01   
  7   -5.27105976e+01    7.30391216e+01    3.59311117e+01   |  -5.27105976e+01    7.30391216e+01    3.59311117e+01   
  8   -7.94766844e+01   -5.60889953e+01   -6.21549712e+01   |  -7.94766844e+01   -5.60889953e+01   -6.21549712e+01   
  9    4.68578741e+01    6.03940803e+01    4.97809341e+01   |   4.68578741e+01    6.03940803e+01    4.97809341e+01   
 10    8.53294079e+01   -7.73442066e+01   -2.35570746e+01   |   8.53294079e+01   -7.73442066e+01   -2.35570746e+01   
 11   -5.27105976e+01    7.30391216e+01    3.59311117e+01   |  -5.27105976e+01    7.30391216e+01    3.59311117e+01   
 12   -7.94766844e+01   -5.60889953e+01   -6.21549712e+01   |  -7.94766844e+01   -5.60889953e+01   -6.21549712e+01   
 13    4.68578741e+01    6.03940803e+01    4.97809341e+01   |   4.68578741e+01    6.03940803e+01    4.97809341e+01   
 14    8.53294079e+01   -7.73442066e+01   -2.35570746e+01   |   8.53294079e+01   -7.73442066e+01   -2.35570746e+01   
 15   -5.27105976e+01    7.30391216e+01    3.59311117e+01   |  -5.27105976e+01    7.30391216e+01    3.59311117e+01   
------------------------------------------------------------------------------------------------------------------------
PASS: Energies and forces are the same to within a relative error of 1e-08
------------------------------------------------------------------------------------------------------------------------

MONOATOMIC STRUCTURE -- Species = Pt, PBC = FTF   (Configuration in file "config-Pt-FTF.xyz")
------------------------------------------------------------------------------------------------------------------------

The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2
in the number of atoms and in the energy.

Energy requirement:

V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, 
and DBL_p is an operator that doubles the configuration in p periodic directions.

V(DBL_p(r_1,...,r_N)) = 45.48848070894493
2^p V(r_1,...,r_N)    = 45.48848070894495

Forces requirement:

f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k 
(where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration 
in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator.

  k                 f_k(DBL_p(r_1,...,r_N))                                  f_(k % N)(r_1,...,r_N)
------------------------------------------------------------------------------------------------------------------------
  0   -5.17052029e+01    1.58580119e+01   -3.55697332e+01   |  -5.17052029e+01    1.58580119e+01   -3.55697332e+01   
  1    5.52314385e+01   -2.50718361e+01   -3.25457308e+01   |   5.52314385e+01   -2.50718361e+01   -3.25457308e+01   
  2    4.32828798e+01   -8.95194159e+00    3.88890570e+01   |   4.32828798e+01   -8.95194159e+00    3.88890570e+01   
  3   -4.68091153e+01    1.81657658e+01    2.92264070e+01   |  -4.68091153e+01    1.81657658e+01    2.92264070e+01   
  4   -5.17052029e+01    1.58580119e+01   -3.55697332e+01   |  -5.17052029e+01    1.58580119e+01   -3.55697332e+01   
  5    5.52314385e+01   -2.50718361e+01   -3.25457308e+01   |   5.52314385e+01   -2.50718361e+01   -3.25457308e+01   
  6    4.32828798e+01   -8.95194159e+00    3.88890570e+01   |   4.32828798e+01   -8.95194159e+00    3.88890570e+01   
  7   -4.68091153e+01    1.81657658e+01    2.92264070e+01   |  -4.68091153e+01    1.81657658e+01    2.92264070e+01   
------------------------------------------------------------------------------------------------------------------------
PASS: Energies and forces are the same to within a relative error of 1e-08
------------------------------------------------------------------------------------------------------------------------

MONOATOMIC STRUCTURE -- Species = Pt, PBC = FFT   (Configuration in file "config-Pt-FFT.xyz")
------------------------------------------------------------------------------------------------------------------------

The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2
in the number of atoms and in the energy.

Energy requirement:

V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, 
and DBL_p is an operator that doubles the configuration in p periodic directions.

V(DBL_p(r_1,...,r_N)) = 286.1983322039724
2^p V(r_1,...,r_N)    = 286.1983322039725

Forces requirement:

f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k 
(where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration 
in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator.

  k                 f_k(DBL_p(r_1,...,r_N))                                  f_(k % N)(r_1,...,r_N)
------------------------------------------------------------------------------------------------------------------------
  0   -1.93133023e+02   -2.01335647e+02   -4.82706917e+01   |  -1.93133023e+02   -2.01335647e+02   -4.82706917e+01   
  1    1.59674195e+02    2.21195242e+02   -8.09082931e+01   |   1.59674195e+02    2.21195242e+02   -8.09082931e+01   
  2    1.09189671e+02   -1.18930420e+02    1.19791599e+02   |   1.09189671e+02   -1.18930420e+02    1.19791599e+02   
  3   -7.57308430e+01    9.90708256e+01    9.38738614e+00   |  -7.57308430e+01    9.90708256e+01    9.38738614e+00   
  4   -1.93133023e+02   -2.01335647e+02   -4.82706917e+01   |  -1.93133023e+02   -2.01335647e+02   -4.82706917e+01   
  5    1.59674195e+02    2.21195242e+02   -8.09082931e+01   |   1.59674195e+02    2.21195242e+02   -8.09082931e+01   
  6    1.09189671e+02   -1.18930420e+02    1.19791599e+02   |   1.09189671e+02   -1.18930420e+02    1.19791599e+02   
  7   -7.57308430e+01    9.90708256e+01    9.38738614e+00   |  -7.57308430e+01    9.90708256e+01    9.38738614e+00   
------------------------------------------------------------------------------------------------------------------------
PASS: Energies and forces are the same to within a relative error of 1e-08
------------------------------------------------------------------------------------------------------------------------

MIXED STRUCTURE -- Species = Al Pt, PBC = TTT   (Configuration in file "config-AlPt-TTT.xyz")
------------------------------------------------------------------------------------------------------------------------

The system is doubled in p=3 periodic directions, which means an increase by a factor n=2^3=8
in the number of atoms and in the energy.

Energy requirement:

V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, 
and DBL_p is an operator that doubles the configuration in p periodic directions.

V(DBL_p(r_1,...,r_N)) = 434.72209514385406
2^p V(r_1,...,r_N)    = 434.72209514385463

Forces requirement:

f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k 
(where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration 
in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator.

  k                 f_k(DBL_p(r_1,...,r_N))                                  f_(k % N)(r_1,...,r_N)
------------------------------------------------------------------------------------------------------------------------
  0    2.58888131e+01    1.72333915e+01    2.07062849e+00   |   2.58888131e+01    1.72333915e+01    2.07062849e+00   
  1    2.85193169e+01   -2.11400512e+01    3.47691565e+01   |   2.85193169e+01   -2.11400512e+01    3.47691565e+01   
  2   -2.39684601e+01    1.11546996e+01    2.13381623e+01   |  -2.39684601e+01    1.11546996e+01    2.13381623e+01   
  3   -3.04396699e+01   -7.24803990e+00   -5.81779472e+01   |  -3.04396699e+01   -7.24803990e+00   -5.81779472e+01   
  4    2.58888131e+01    1.72333915e+01    2.07062849e+00   |   2.58888131e+01    1.72333915e+01    2.07062849e+00   
  5    2.85193169e+01   -2.11400512e+01    3.47691565e+01   |   2.85193169e+01   -2.11400512e+01    3.47691565e+01   
  6   -2.39684601e+01    1.11546996e+01    2.13381623e+01   |  -2.39684601e+01    1.11546996e+01    2.13381623e+01   
  7   -3.04396699e+01   -7.24803990e+00   -5.81779472e+01   |  -3.04396699e+01   -7.24803990e+00   -5.81779472e+01   
  8    2.58888131e+01    1.72333915e+01    2.07062849e+00   |   2.58888131e+01    1.72333915e+01    2.07062849e+00   
  9    2.85193169e+01   -2.11400512e+01    3.47691565e+01   |   2.85193169e+01   -2.11400512e+01    3.47691565e+01   
 10   -2.39684601e+01    1.11546996e+01    2.13381623e+01   |  -2.39684601e+01    1.11546996e+01    2.13381623e+01   
 11   -3.04396699e+01   -7.24803990e+00   -5.81779472e+01   |  -3.04396699e+01   -7.24803990e+00   -5.81779472e+01   
 12    2.58888131e+01    1.72333915e+01    2.07062849e+00   |   2.58888131e+01    1.72333915e+01    2.07062849e+00   
 13    2.85193169e+01   -2.11400512e+01    3.47691565e+01   |   2.85193169e+01   -2.11400512e+01    3.47691565e+01   
 14   -2.39684601e+01    1.11546996e+01    2.13381623e+01   |  -2.39684601e+01    1.11546996e+01    2.13381623e+01   
 15   -3.04396699e+01   -7.24803990e+00   -5.81779472e+01   |  -3.04396699e+01   -7.24803990e+00   -5.81779472e+01   
 16    2.58888131e+01    1.72333915e+01    2.07062849e+00   |   2.58888131e+01    1.72333915e+01    2.07062849e+00   
 17    2.85193169e+01   -2.11400512e+01    3.47691565e+01   |   2.85193169e+01   -2.11400512e+01    3.47691565e+01   
 18   -2.39684601e+01    1.11546996e+01    2.13381623e+01   |  -2.39684601e+01    1.11546996e+01    2.13381623e+01   
 19   -3.04396699e+01   -7.24803990e+00   -5.81779472e+01   |  -3.04396699e+01   -7.24803990e+00   -5.81779472e+01   
 20    2.58888131e+01    1.72333915e+01    2.07062849e+00   |   2.58888131e+01    1.72333915e+01    2.07062849e+00   
 21    2.85193169e+01   -2.11400512e+01    3.47691565e+01   |   2.85193169e+01   -2.11400512e+01    3.47691565e+01   
 22   -2.39684601e+01    1.11546996e+01    2.13381623e+01   |  -2.39684601e+01    1.11546996e+01    2.13381623e+01   
 23   -3.04396699e+01   -7.24803990e+00   -5.81779472e+01   |  -3.04396699e+01   -7.24803990e+00   -5.81779472e+01   
 24    2.58888131e+01    1.72333915e+01    2.07062849e+00   |   2.58888131e+01    1.72333915e+01    2.07062849e+00   
 25    2.85193169e+01   -2.11400512e+01    3.47691565e+01   |   2.85193169e+01   -2.11400512e+01    3.47691565e+01   
 26   -2.39684601e+01    1.11546996e+01    2.13381623e+01   |  -2.39684601e+01    1.11546996e+01    2.13381623e+01   
 27   -3.04396699e+01   -7.24803990e+00   -5.81779472e+01   |  -3.04396699e+01   -7.24803990e+00   -5.81779472e+01   
 28    2.58888131e+01    1.72333915e+01    2.07062849e+00   |   2.58888131e+01    1.72333915e+01    2.07062849e+00   
 29    2.85193169e+01   -2.11400512e+01    3.47691565e+01   |   2.85193169e+01   -2.11400512e+01    3.47691565e+01   
 30   -2.39684601e+01    1.11546996e+01    2.13381623e+01   |  -2.39684601e+01    1.11546996e+01    2.13381623e+01   
 31   -3.04396699e+01   -7.24803990e+00   -5.81779472e+01   |  -3.04396699e+01   -7.24803990e+00   -5.81779472e+01   
------------------------------------------------------------------------------------------------------------------------
PASS: Energies and forces are the same to within a relative error of 1e-08
------------------------------------------------------------------------------------------------------------------------

MIXED STRUCTURE -- Species = Al Pt, PBC = TTF   (Configuration in file "config-AlPt-TTF.xyz")
------------------------------------------------------------------------------------------------------------------------

The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4
in the number of atoms and in the energy.

Energy requirement:

V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, 
and DBL_p is an operator that doubles the configuration in p periodic directions.

V(DBL_p(r_1,...,r_N)) = 224.06288133078962
2^p V(r_1,...,r_N)    = 224.06288133078982

Forces requirement:

f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k 
(where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration 
in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator.

  k                 f_k(DBL_p(r_1,...,r_N))                                  f_(k % N)(r_1,...,r_N)
------------------------------------------------------------------------------------------------------------------------
  0   -9.37455607e+01    7.25234602e+01   -3.21095385e+01   |  -9.37455607e+01    7.25234602e+01   -3.21095385e+01   
  1    7.91058985e+01   -9.60930541e+01   -7.56682681e+01   |   7.91058985e+01   -9.60930541e+01   -7.56682681e+01   
  2    4.57205594e+01    2.40925380e+01    7.16557216e+01   |   4.57205594e+01    2.40925380e+01    7.16557216e+01   
  3   -3.10808971e+01   -5.22944032e-01    3.61220850e+01   |  -3.10808971e+01   -5.22944032e-01    3.61220850e+01   
  4   -9.37455607e+01    7.25234602e+01   -3.21095385e+01   |  -9.37455607e+01    7.25234602e+01   -3.21095385e+01   
  5    7.91058985e+01   -9.60930541e+01   -7.56682681e+01   |   7.91058985e+01   -9.60930541e+01   -7.56682681e+01   
  6    4.57205594e+01    2.40925380e+01    7.16557216e+01   |   4.57205594e+01    2.40925380e+01    7.16557216e+01   
  7   -3.10808971e+01   -5.22944032e-01    3.61220850e+01   |  -3.10808971e+01   -5.22944032e-01    3.61220850e+01   
  8   -9.37455607e+01    7.25234602e+01   -3.21095385e+01   |  -9.37455607e+01    7.25234602e+01   -3.21095385e+01   
  9    7.91058985e+01   -9.60930541e+01   -7.56682681e+01   |   7.91058985e+01   -9.60930541e+01   -7.56682681e+01   
 10    4.57205594e+01    2.40925380e+01    7.16557216e+01   |   4.57205594e+01    2.40925380e+01    7.16557216e+01   
 11   -3.10808971e+01   -5.22944032e-01    3.61220850e+01   |  -3.10808971e+01   -5.22944032e-01    3.61220850e+01   
 12   -9.37455607e+01    7.25234602e+01   -3.21095385e+01   |  -9.37455607e+01    7.25234602e+01   -3.21095385e+01   
 13    7.91058985e+01   -9.60930541e+01   -7.56682681e+01   |   7.91058985e+01   -9.60930541e+01   -7.56682681e+01   
 14    4.57205594e+01    2.40925380e+01    7.16557216e+01   |   4.57205594e+01    2.40925380e+01    7.16557216e+01   
 15   -3.10808971e+01   -5.22944032e-01    3.61220850e+01   |  -3.10808971e+01   -5.22944032e-01    3.61220850e+01   
------------------------------------------------------------------------------------------------------------------------
PASS: Energies and forces are the same to within a relative error of 1e-08
------------------------------------------------------------------------------------------------------------------------

MIXED STRUCTURE -- Species = Al Pt, PBC = TFT   (Configuration in file "config-AlPt-TFT.xyz")
------------------------------------------------------------------------------------------------------------------------

The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4
in the number of atoms and in the energy.

Energy requirement:

V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, 
and DBL_p is an operator that doubles the configuration in p periodic directions.

V(DBL_p(r_1,...,r_N)) = 218.5617734494818
2^p V(r_1,...,r_N)    = 218.56177344948185

Forces requirement:

f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k 
(where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration 
in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator.

  k                 f_k(DBL_p(r_1,...,r_N))                                  f_(k % N)(r_1,...,r_N)
------------------------------------------------------------------------------------------------------------------------
  0   -3.77525708e-01   -5.23825595e+01    9.38858719e+00   |  -3.77525708e-01   -5.23825595e+01    9.38858719e+00   
  1   -5.36737032e+00    8.27708317e+01   -4.94654436e+01   |  -5.36737032e+00    8.27708317e+01   -4.94654436e+01   
  2   -1.31370152e+01   -1.09576976e+02    4.75102103e+01   |  -1.31370152e+01   -1.09576976e+02    4.75102103e+01   
  3    1.88819112e+01    7.91887042e+01   -7.43335384e+00   |   1.88819112e+01    7.91887042e+01   -7.43335384e+00   
  4   -3.77525708e-01   -5.23825595e+01    9.38858719e+00   |  -3.77525708e-01   -5.23825595e+01    9.38858719e+00   
  5   -5.36737032e+00    8.27708317e+01   -4.94654436e+01   |  -5.36737032e+00    8.27708317e+01   -4.94654436e+01   
  6   -1.31370152e+01   -1.09576976e+02    4.75102103e+01   |  -1.31370152e+01   -1.09576976e+02    4.75102103e+01   
  7    1.88819112e+01    7.91887042e+01   -7.43335384e+00   |   1.88819112e+01    7.91887042e+01   -7.43335384e+00   
  8   -3.77525708e-01   -5.23825595e+01    9.38858719e+00   |  -3.77525708e-01   -5.23825595e+01    9.38858719e+00   
  9   -5.36737032e+00    8.27708317e+01   -4.94654436e+01   |  -5.36737032e+00    8.27708317e+01   -4.94654436e+01   
 10   -1.31370152e+01   -1.09576976e+02    4.75102103e+01   |  -1.31370152e+01   -1.09576976e+02    4.75102103e+01   
 11    1.88819112e+01    7.91887042e+01   -7.43335384e+00   |   1.88819112e+01    7.91887042e+01   -7.43335384e+00   
 12   -3.77525708e-01   -5.23825595e+01    9.38858719e+00   |  -3.77525708e-01   -5.23825595e+01    9.38858719e+00   
 13   -5.36737032e+00    8.27708317e+01   -4.94654436e+01   |  -5.36737032e+00    8.27708317e+01   -4.94654436e+01   
 14   -1.31370152e+01   -1.09576976e+02    4.75102103e+01   |  -1.31370152e+01   -1.09576976e+02    4.75102103e+01   
 15    1.88819112e+01    7.91887042e+01   -7.43335384e+00   |   1.88819112e+01    7.91887042e+01   -7.43335384e+00   
------------------------------------------------------------------------------------------------------------------------
PASS: Energies and forces are the same to within a relative error of 1e-08
------------------------------------------------------------------------------------------------------------------------

MIXED STRUCTURE -- Species = Al Pt, PBC = TFF   (Configuration in file "config-AlPt-TFF.xyz")
------------------------------------------------------------------------------------------------------------------------

The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2
in the number of atoms and in the energy.

Energy requirement:

V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, 
and DBL_p is an operator that doubles the configuration in p periodic directions.

V(DBL_p(r_1,...,r_N)) = 60.47286360119509
2^p V(r_1,...,r_N)    = 60.472863601195094

Forces requirement:

f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k 
(where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration 
in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator.

  k                 f_k(DBL_p(r_1,...,r_N))                                  f_(k % N)(r_1,...,r_N)
------------------------------------------------------------------------------------------------------------------------
  0   -1.95620199e+01   -6.20720965e+01   -3.83969173e+01   |  -1.95620199e+01   -6.20720965e+01   -3.83969173e+01   
  1    2.07716981e+01    6.49778115e+01   -4.70823310e+01   |   2.07716981e+01    6.49778115e+01   -4.70823310e+01   
  2    8.11300300e+00   -3.26914965e+01    4.81648980e+01   |   8.11300300e+00   -3.26914965e+01    4.81648980e+01   
  3   -9.32268121e+00    2.97857816e+01    3.73143502e+01   |  -9.32268121e+00    2.97857816e+01    3.73143502e+01   
  4   -1.95620199e+01   -6.20720965e+01   -3.83969173e+01   |  -1.95620199e+01   -6.20720965e+01   -3.83969173e+01   
  5    2.07716981e+01    6.49778115e+01   -4.70823310e+01   |   2.07716981e+01    6.49778115e+01   -4.70823310e+01   
  6    8.11300300e+00   -3.26914965e+01    4.81648980e+01   |   8.11300300e+00   -3.26914965e+01    4.81648980e+01   
  7   -9.32268121e+00    2.97857816e+01    3.73143502e+01   |  -9.32268121e+00    2.97857816e+01    3.73143502e+01   
------------------------------------------------------------------------------------------------------------------------
PASS: Energies and forces are the same to within a relative error of 1e-08
------------------------------------------------------------------------------------------------------------------------

MIXED STRUCTURE -- Species = Al Pt, PBC = FTT   (Configuration in file "config-AlPt-FTT.xyz")
------------------------------------------------------------------------------------------------------------------------

The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4
in the number of atoms and in the energy.

Energy requirement:

V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, 
and DBL_p is an operator that doubles the configuration in p periodic directions.

V(DBL_p(r_1,...,r_N)) = 437.8295640610842
2^p V(r_1,...,r_N)    = 437.82956406108457

Forces requirement:

f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k 
(where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration 
in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator.

  k                 f_k(DBL_p(r_1,...,r_N))                                  f_(k % N)(r_1,...,r_N)
------------------------------------------------------------------------------------------------------------------------
  0   -1.75845296e+02   -8.54393071e+01   -1.21563445e+02   |  -1.75845296e+02   -8.54393071e+01   -1.21563445e+02   
  1    1.41311429e+02    9.98102732e+01   -6.99619125e+01   |   1.41311429e+02    9.98102732e+01   -6.99619125e+01   
  2    1.12106548e+02   -4.42543448e+01    1.27218676e+02   |   1.12106548e+02   -4.42543448e+01    1.27218676e+02   
  3   -7.75726811e+01    2.98833787e+01    6.43066813e+01   |  -7.75726811e+01    2.98833787e+01    6.43066813e+01   
  4   -1.75845296e+02   -8.54393071e+01   -1.21563445e+02   |  -1.75845296e+02   -8.54393071e+01   -1.21563445e+02   
  5    1.41311429e+02    9.98102732e+01   -6.99619125e+01   |   1.41311429e+02    9.98102732e+01   -6.99619125e+01   
  6    1.12106548e+02   -4.42543448e+01    1.27218676e+02   |   1.12106548e+02   -4.42543448e+01    1.27218676e+02   
  7   -7.75726811e+01    2.98833787e+01    6.43066813e+01   |  -7.75726811e+01    2.98833787e+01    6.43066813e+01   
  8   -1.75845296e+02   -8.54393071e+01   -1.21563445e+02   |  -1.75845296e+02   -8.54393071e+01   -1.21563445e+02   
  9    1.41311429e+02    9.98102732e+01   -6.99619125e+01   |   1.41311429e+02    9.98102732e+01   -6.99619125e+01   
 10    1.12106548e+02   -4.42543448e+01    1.27218676e+02   |   1.12106548e+02   -4.42543448e+01    1.27218676e+02   
 11   -7.75726811e+01    2.98833787e+01    6.43066813e+01   |  -7.75726811e+01    2.98833787e+01    6.43066813e+01   
 12   -1.75845296e+02   -8.54393071e+01   -1.21563445e+02   |  -1.75845296e+02   -8.54393071e+01   -1.21563445e+02   
 13    1.41311429e+02    9.98102732e+01   -6.99619125e+01   |   1.41311429e+02    9.98102732e+01   -6.99619125e+01   
 14    1.12106548e+02   -4.42543448e+01    1.27218676e+02   |   1.12106548e+02   -4.42543448e+01    1.27218676e+02   
 15   -7.75726811e+01    2.98833787e+01    6.43066813e+01   |  -7.75726811e+01    2.98833787e+01    6.43066813e+01   
------------------------------------------------------------------------------------------------------------------------
PASS: Energies and forces are the same to within a relative error of 1e-08
------------------------------------------------------------------------------------------------------------------------

MIXED STRUCTURE -- Species = Al Pt, PBC = FTF   (Configuration in file "config-AlPt-FTF.xyz")
------------------------------------------------------------------------------------------------------------------------

The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2
in the number of atoms and in the energy.

Energy requirement:

V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, 
and DBL_p is an operator that doubles the configuration in p periodic directions.

V(DBL_p(r_1,...,r_N)) = 59.72124379058646
2^p V(r_1,...,r_N)    = 59.721243790586456

Forces requirement:

f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k 
(where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration 
in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator.

  k                 f_k(DBL_p(r_1,...,r_N))                                  f_(k % N)(r_1,...,r_N)
------------------------------------------------------------------------------------------------------------------------
  0   -4.30310339e+01   -3.03785394e+01   -5.16908844e+01   |  -4.30310339e+01   -3.03785394e+01   -5.16908844e+01   
  1    2.78690094e+01    1.54086024e+01   -2.34437897e+01   |   2.78690094e+01    1.54086024e+01   -2.34437897e+01   
  2    6.24129367e+01   -3.64643407e+01    5.24971305e+01   |   6.24129367e+01   -3.64643407e+01    5.24971305e+01   
  3   -4.72509122e+01    5.14342777e+01    2.26375436e+01   |  -4.72509122e+01    5.14342777e+01    2.26375436e+01   
  4   -4.30310339e+01   -3.03785394e+01   -5.16908844e+01   |  -4.30310339e+01   -3.03785394e+01   -5.16908844e+01   
  5    2.78690094e+01    1.54086024e+01   -2.34437897e+01   |   2.78690094e+01    1.54086024e+01   -2.34437897e+01   
  6    6.24129367e+01   -3.64643407e+01    5.24971305e+01   |   6.24129367e+01   -3.64643407e+01    5.24971305e+01   
  7   -4.72509122e+01    5.14342777e+01    2.26375436e+01   |  -4.72509122e+01    5.14342777e+01    2.26375436e+01   
------------------------------------------------------------------------------------------------------------------------
PASS: Energies and forces are the same to within a relative error of 1e-08
------------------------------------------------------------------------------------------------------------------------

MIXED STRUCTURE -- Species = Al Pt, PBC = FFT   (Configuration in file "config-AlPt-FFT.xyz")
------------------------------------------------------------------------------------------------------------------------

The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2
in the number of atoms and in the energy.

Energy requirement:

V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, 
and DBL_p is an operator that doubles the configuration in p periodic directions.

V(DBL_p(r_1,...,r_N)) = 52.43847524150688
2^p V(r_1,...,r_N)    = 52.43847524150688

Forces requirement:

f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k 
(where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration 
in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator.

  k                 f_k(DBL_p(r_1,...,r_N))                                  f_(k % N)(r_1,...,r_N)
------------------------------------------------------------------------------------------------------------------------
  0   -3.22222696e+01   -2.41083920e+01   -1.35315321e+01   |  -3.22222696e+01   -2.41083920e+01   -1.35315321e+01   
  1    3.49701979e+01    6.44238764e+01   -3.33218530e+01   |   3.49701979e+01    6.44238764e+01   -3.33218530e+01   
  2    2.14967990e+01   -6.87390396e+01    4.43542167e+01   |   2.14967990e+01   -6.87390396e+01    4.43542167e+01   
  3   -2.42447273e+01    2.84235552e+01    2.49916839e+00   |  -2.42447273e+01    2.84235552e+01    2.49916839e+00   
  4   -3.22222696e+01   -2.41083920e+01   -1.35315321e+01   |  -3.22222696e+01   -2.41083920e+01   -1.35315321e+01   
  5    3.49701979e+01    6.44238764e+01   -3.33218530e+01   |   3.49701979e+01    6.44238764e+01   -3.33218530e+01   
  6    2.14967990e+01   -6.87390396e+01    4.43542167e+01   |   2.14967990e+01   -6.87390396e+01    4.43542167e+01   
  7   -2.42447273e+01    2.84235552e+01    2.49916839e+00   |  -2.42447273e+01    2.84235552e+01    2.49916839e+00   
------------------------------------------------------------------------------------------------------------------------
PASS: Energies and forces are the same to within a relative error of 1e-08
------------------------------------------------------------------------------------------------------------------------
========================================================================================================================

========================================================================================================================
To pass this verification check the model must correctly support periodic boundary conditions for all configurations it was able to compute.

Grade: P

Comment: Periodic boundary conditions were correctly supported for all configurations that the model was able to compute.


=== Verification check vc-periodicity-support end (2023-05-09 21:29:12) ===