Model Extended KIM ID =
=== Verification check vc-periodicity-support start (2023-05-09 23:14:57) ===
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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
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Results for KIM Model : MEAM_LAMMPS_WuLeeSu_2017_NiCr__MO_880803040302_002
Supported species : Cr Ni
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 = Cr, PBC = TTT (Configuration in file "config-Cr-TTT.xyz")
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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)) = 123.67372349145059
2^p V(r_1,...,r_N) = 123.67372349145064
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)
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0 2.53845267e+01 -2.86559413e+01 -8.86913995e+00 | 2.53845267e+01 -2.86559413e+01 -8.86913995e+00
1 -4.17865001e+01 2.46865204e+01 -1.70595768e+01 | -4.17865001e+01 2.46865204e+01 -1.70595768e+01
2 -6.04631719e+00 -9.35486275e+00 -3.33312397e+00 | -6.04631719e+00 -9.35486275e+00 -3.33312397e+00
3 2.24482906e+01 1.33242836e+01 2.92618407e+01 | 2.24482906e+01 1.33242836e+01 2.92618407e+01
4 2.53845267e+01 -2.86559413e+01 -8.86913995e+00 | 2.53845267e+01 -2.86559413e+01 -8.86913995e+00
5 -4.17865001e+01 2.46865204e+01 -1.70595768e+01 | -4.17865001e+01 2.46865204e+01 -1.70595768e+01
6 -6.04631719e+00 -9.35486275e+00 -3.33312397e+00 | -6.04631719e+00 -9.35486275e+00 -3.33312397e+00
7 2.24482906e+01 1.33242836e+01 2.92618407e+01 | 2.24482906e+01 1.33242836e+01 2.92618407e+01
8 2.53845267e+01 -2.86559413e+01 -8.86913995e+00 | 2.53845267e+01 -2.86559413e+01 -8.86913995e+00
9 -4.17865001e+01 2.46865204e+01 -1.70595768e+01 | -4.17865001e+01 2.46865204e+01 -1.70595768e+01
10 -6.04631719e+00 -9.35486275e+00 -3.33312397e+00 | -6.04631719e+00 -9.35486275e+00 -3.33312397e+00
11 2.24482906e+01 1.33242836e+01 2.92618407e+01 | 2.24482906e+01 1.33242836e+01 2.92618407e+01
12 2.53845267e+01 -2.86559413e+01 -8.86913995e+00 | 2.53845267e+01 -2.86559413e+01 -8.86913995e+00
13 -4.17865001e+01 2.46865204e+01 -1.70595768e+01 | -4.17865001e+01 2.46865204e+01 -1.70595768e+01
14 -6.04631719e+00 -9.35486275e+00 -3.33312397e+00 | -6.04631719e+00 -9.35486275e+00 -3.33312397e+00
15 2.24482906e+01 1.33242836e+01 2.92618407e+01 | 2.24482906e+01 1.33242836e+01 2.92618407e+01
16 2.53845267e+01 -2.86559413e+01 -8.86913995e+00 | 2.53845267e+01 -2.86559413e+01 -8.86913995e+00
17 -4.17865001e+01 2.46865204e+01 -1.70595768e+01 | -4.17865001e+01 2.46865204e+01 -1.70595768e+01
18 -6.04631719e+00 -9.35486275e+00 -3.33312397e+00 | -6.04631719e+00 -9.35486275e+00 -3.33312397e+00
19 2.24482906e+01 1.33242836e+01 2.92618407e+01 | 2.24482906e+01 1.33242836e+01 2.92618407e+01
20 2.53845267e+01 -2.86559413e+01 -8.86913995e+00 | 2.53845267e+01 -2.86559413e+01 -8.86913995e+00
21 -4.17865001e+01 2.46865204e+01 -1.70595768e+01 | -4.17865001e+01 2.46865204e+01 -1.70595768e+01
22 -6.04631719e+00 -9.35486275e+00 -3.33312397e+00 | -6.04631719e+00 -9.35486275e+00 -3.33312397e+00
23 2.24482906e+01 1.33242836e+01 2.92618407e+01 | 2.24482906e+01 1.33242836e+01 2.92618407e+01
24 2.53845267e+01 -2.86559413e+01 -8.86913995e+00 | 2.53845267e+01 -2.86559413e+01 -8.86913995e+00
25 -4.17865001e+01 2.46865204e+01 -1.70595768e+01 | -4.17865001e+01 2.46865204e+01 -1.70595768e+01
26 -6.04631719e+00 -9.35486275e+00 -3.33312397e+00 | -6.04631719e+00 -9.35486275e+00 -3.33312397e+00
27 2.24482906e+01 1.33242836e+01 2.92618407e+01 | 2.24482906e+01 1.33242836e+01 2.92618407e+01
28 2.53845267e+01 -2.86559413e+01 -8.86913995e+00 | 2.53845267e+01 -2.86559413e+01 -8.86913995e+00
29 -4.17865001e+01 2.46865204e+01 -1.70595768e+01 | -4.17865001e+01 2.46865204e+01 -1.70595768e+01
30 -6.04631719e+00 -9.35486275e+00 -3.33312397e+00 | -6.04631719e+00 -9.35486275e+00 -3.33312397e+00
31 2.24482906e+01 1.33242836e+01 2.92618407e+01 | 2.24482906e+01 1.33242836e+01 2.92618407e+01
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PASS: Energies and forces are the same to within a relative error of 1e-08
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MONOATOMIC STRUCTURE -- Species = Cr, PBC = TTF (Configuration in file "config-Cr-TTF.xyz")
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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)) = 33.3949415454248
2^p V(r_1,...,r_N) = 33.39494154542481
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)
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0 -1.44945225e+01 -7.02098039e+00 -3.43329590e+01 | -1.44945225e+01 -7.02098039e+00 -3.43329590e+01
1 4.82755318e+00 2.26430238e+00 -1.98092518e+01 | 4.82755318e+00 2.26430238e+00 -1.98092518e+01
2 2.69857412e+01 -1.24027738e+01 2.91226452e+01 | 2.69857412e+01 -1.24027738e+01 2.91226452e+01
3 -1.73187719e+01 1.71594518e+01 2.50195656e+01 | -1.73187719e+01 1.71594518e+01 2.50195656e+01
4 -1.44945225e+01 -7.02098039e+00 -3.43329590e+01 | -1.44945225e+01 -7.02098039e+00 -3.43329590e+01
5 4.82755318e+00 2.26430238e+00 -1.98092518e+01 | 4.82755318e+00 2.26430238e+00 -1.98092518e+01
6 2.69857412e+01 -1.24027738e+01 2.91226452e+01 | 2.69857412e+01 -1.24027738e+01 2.91226452e+01
7 -1.73187719e+01 1.71594518e+01 2.50195656e+01 | -1.73187719e+01 1.71594518e+01 2.50195656e+01
8 -1.44945225e+01 -7.02098039e+00 -3.43329590e+01 | -1.44945225e+01 -7.02098039e+00 -3.43329590e+01
9 4.82755318e+00 2.26430238e+00 -1.98092518e+01 | 4.82755318e+00 2.26430238e+00 -1.98092518e+01
10 2.69857412e+01 -1.24027738e+01 2.91226452e+01 | 2.69857412e+01 -1.24027738e+01 2.91226452e+01
11 -1.73187719e+01 1.71594518e+01 2.50195656e+01 | -1.73187719e+01 1.71594518e+01 2.50195656e+01
12 -1.44945225e+01 -7.02098039e+00 -3.43329590e+01 | -1.44945225e+01 -7.02098039e+00 -3.43329590e+01
13 4.82755318e+00 2.26430238e+00 -1.98092518e+01 | 4.82755318e+00 2.26430238e+00 -1.98092518e+01
14 2.69857412e+01 -1.24027738e+01 2.91226452e+01 | 2.69857412e+01 -1.24027738e+01 2.91226452e+01
15 -1.73187719e+01 1.71594518e+01 2.50195656e+01 | -1.73187719e+01 1.71594518e+01 2.50195656e+01
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PASS: Energies and forces are the same to within a relative error of 1e-08
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MONOATOMIC STRUCTURE -- Species = Cr, PBC = TFT (Configuration in file "config-Cr-TFT.xyz")
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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)) = 59.123321812716675
2^p V(r_1,...,r_N) = 59.12332181271674
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)
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0 2.13923408e+01 -3.44236055e+01 -2.19790182e+01 | 2.13923408e+01 -3.44236055e+01 -2.19790182e+01
1 -2.78967448e+01 2.54027273e+01 -4.98455759e+00 | -2.78967448e+01 2.54027273e+01 -4.98455759e+00
2 -2.94860545e+01 -3.34730244e+01 1.20565396e+01 | -2.94860545e+01 -3.34730244e+01 1.20565396e+01
3 3.59904586e+01 4.24939027e+01 1.49070362e+01 | 3.59904586e+01 4.24939027e+01 1.49070362e+01
4 2.13923408e+01 -3.44236055e+01 -2.19790182e+01 | 2.13923408e+01 -3.44236055e+01 -2.19790182e+01
5 -2.78967448e+01 2.54027273e+01 -4.98455759e+00 | -2.78967448e+01 2.54027273e+01 -4.98455759e+00
6 -2.94860545e+01 -3.34730244e+01 1.20565396e+01 | -2.94860545e+01 -3.34730244e+01 1.20565396e+01
7 3.59904586e+01 4.24939027e+01 1.49070362e+01 | 3.59904586e+01 4.24939027e+01 1.49070362e+01
8 2.13923408e+01 -3.44236055e+01 -2.19790182e+01 | 2.13923408e+01 -3.44236055e+01 -2.19790182e+01
9 -2.78967448e+01 2.54027273e+01 -4.98455759e+00 | -2.78967448e+01 2.54027273e+01 -4.98455759e+00
10 -2.94860545e+01 -3.34730244e+01 1.20565396e+01 | -2.94860545e+01 -3.34730244e+01 1.20565396e+01
11 3.59904586e+01 4.24939027e+01 1.49070362e+01 | 3.59904586e+01 4.24939027e+01 1.49070362e+01
12 2.13923408e+01 -3.44236055e+01 -2.19790182e+01 | 2.13923408e+01 -3.44236055e+01 -2.19790182e+01
13 -2.78967448e+01 2.54027273e+01 -4.98455759e+00 | -2.78967448e+01 2.54027273e+01 -4.98455759e+00
14 -2.94860545e+01 -3.34730244e+01 1.20565396e+01 | -2.94860545e+01 -3.34730244e+01 1.20565396e+01
15 3.59904586e+01 4.24939027e+01 1.49070362e+01 | 3.59904586e+01 4.24939027e+01 1.49070362e+01
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PASS: Energies and forces are the same to within a relative error of 1e-08
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MONOATOMIC STRUCTURE -- Species = Cr, PBC = TFF (Configuration in file "config-Cr-TFF.xyz")
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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)) = 16.364105832879396
2^p V(r_1,...,r_N) = 16.364105832879403
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)
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0 1.91932003e+01 -3.08824218e+01 -2.02195861e+01 | 1.91932003e+01 -3.08824218e+01 -2.02195861e+01
1 -2.36371200e+01 2.62440068e+01 -2.14599282e+01 | -2.36371200e+01 2.62440068e+01 -2.14599282e+01
2 -2.03300364e+01 -2.65881540e+01 1.92181746e+01 | -2.03300364e+01 -2.65881540e+01 1.92181746e+01
3 2.47739560e+01 3.12265690e+01 2.24613397e+01 | 2.47739560e+01 3.12265690e+01 2.24613397e+01
4 1.91932003e+01 -3.08824218e+01 -2.02195861e+01 | 1.91932003e+01 -3.08824218e+01 -2.02195861e+01
5 -2.36371200e+01 2.62440068e+01 -2.14599282e+01 | -2.36371200e+01 2.62440068e+01 -2.14599282e+01
6 -2.03300364e+01 -2.65881540e+01 1.92181746e+01 | -2.03300364e+01 -2.65881540e+01 1.92181746e+01
7 2.47739560e+01 3.12265690e+01 2.24613397e+01 | 2.47739560e+01 3.12265690e+01 2.24613397e+01
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PASS: Energies and forces are the same to within a relative error of 1e-08
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MONOATOMIC STRUCTURE -- Species = Cr, PBC = FTT (Configuration in file "config-Cr-FTT.xyz")
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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)) = 60.680598043774346
2^p V(r_1,...,r_N) = 60.68059804377434
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)
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0 -2.32980670e+01 -9.54221718e+00 -1.10625031e+01 | -2.32980670e+01 -9.54221718e+00 -1.10625031e+01
1 2.37860472e+01 -3.42275122e+01 2.77623839e+01 | 2.37860472e+01 -3.42275122e+01 2.77623839e+01
2 2.13542345e+01 3.84072114e+01 -3.80841242e+01 | 2.13542345e+01 3.84072114e+01 -3.80841242e+01
3 -2.18422147e+01 5.36251803e+00 2.13842434e+01 | -2.18422147e+01 5.36251803e+00 2.13842434e+01
4 -2.32980670e+01 -9.54221718e+00 -1.10625031e+01 | -2.32980670e+01 -9.54221718e+00 -1.10625031e+01
5 2.37860472e+01 -3.42275122e+01 2.77623839e+01 | 2.37860472e+01 -3.42275122e+01 2.77623839e+01
6 2.13542345e+01 3.84072114e+01 -3.80841242e+01 | 2.13542345e+01 3.84072114e+01 -3.80841242e+01
7 -2.18422147e+01 5.36251803e+00 2.13842434e+01 | -2.18422147e+01 5.36251803e+00 2.13842434e+01
8 -2.32980670e+01 -9.54221718e+00 -1.10625031e+01 | -2.32980670e+01 -9.54221718e+00 -1.10625031e+01
9 2.37860472e+01 -3.42275122e+01 2.77623839e+01 | 2.37860472e+01 -3.42275122e+01 2.77623839e+01
10 2.13542345e+01 3.84072114e+01 -3.80841242e+01 | 2.13542345e+01 3.84072114e+01 -3.80841242e+01
11 -2.18422147e+01 5.36251803e+00 2.13842434e+01 | -2.18422147e+01 5.36251803e+00 2.13842434e+01
12 -2.32980670e+01 -9.54221718e+00 -1.10625031e+01 | -2.32980670e+01 -9.54221718e+00 -1.10625031e+01
13 2.37860472e+01 -3.42275122e+01 2.77623839e+01 | 2.37860472e+01 -3.42275122e+01 2.77623839e+01
14 2.13542345e+01 3.84072114e+01 -3.80841242e+01 | 2.13542345e+01 3.84072114e+01 -3.80841242e+01
15 -2.18422147e+01 5.36251803e+00 2.13842434e+01 | -2.18422147e+01 5.36251803e+00 2.13842434e+01
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PASS: Energies and forces are the same to within a relative error of 1e-08
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MONOATOMIC STRUCTURE -- Species = Cr, PBC = FTF (Configuration in file "config-Cr-FTF.xyz")
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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)) = 25.49055780923622
2^p V(r_1,...,r_N) = 25.490557809236215
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)
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0 -3.07996708e+01 1.06935737e+01 -2.60900597e+01 | -3.07996708e+01 1.06935737e+01 -2.60900597e+01
1 2.27818170e+01 -2.76680886e+01 -3.94886551e+01 | 2.27818170e+01 -2.76680886e+01 -3.94886551e+01
2 3.38551851e+01 2.88090128e+01 4.70026785e+01 | 3.38551851e+01 2.88090128e+01 4.70026785e+01
3 -2.58373313e+01 -1.18344979e+01 1.85760362e+01 | -2.58373313e+01 -1.18344979e+01 1.85760362e+01
4 -3.07996708e+01 1.06935737e+01 -2.60900597e+01 | -3.07996708e+01 1.06935737e+01 -2.60900597e+01
5 2.27818170e+01 -2.76680886e+01 -3.94886551e+01 | 2.27818170e+01 -2.76680886e+01 -3.94886551e+01
6 3.38551851e+01 2.88090128e+01 4.70026785e+01 | 3.38551851e+01 2.88090128e+01 4.70026785e+01
7 -2.58373313e+01 -1.18344979e+01 1.85760362e+01 | -2.58373313e+01 -1.18344979e+01 1.85760362e+01
------------------------------------------------------------------------------------------------------------------------
PASS: Energies and forces are the same to within a relative error of 1e-08
------------------------------------------------------------------------------------------------------------------------
MONOATOMIC STRUCTURE -- Species = Cr, PBC = FFT (Configuration in file "config-Cr-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)) = 62.15494956026225
2^p V(r_1,...,r_N) = 62.15494956026226
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 -5.45165691e+01 -3.02732125e+01 3.45307955e+01 | -5.45165691e+01 -3.02732125e+01 3.45307955e+01
1 3.38204778e+01 3.44894574e+01 -3.04802654e+01 | 3.38204778e+01 3.44894574e+01 -3.04802654e+01
2 7.66831286e+01 -4.74939507e+01 -1.29732947e+01 | 7.66831286e+01 -4.74939507e+01 -1.29732947e+01
3 -5.59870373e+01 4.32777059e+01 8.92276460e+00 | -5.59870373e+01 4.32777059e+01 8.92276460e+00
4 -5.45165691e+01 -3.02732125e+01 3.45307955e+01 | -5.45165691e+01 -3.02732125e+01 3.45307955e+01
5 3.38204778e+01 3.44894574e+01 -3.04802654e+01 | 3.38204778e+01 3.44894574e+01 -3.04802654e+01
6 7.66831286e+01 -4.74939507e+01 -1.29732947e+01 | 7.66831286e+01 -4.74939507e+01 -1.29732947e+01
7 -5.59870373e+01 4.32777059e+01 8.92276460e+00 | -5.59870373e+01 4.32777059e+01 8.92276460e+00
------------------------------------------------------------------------------------------------------------------------
PASS: Energies and forces are the same to within a relative error of 1e-08
------------------------------------------------------------------------------------------------------------------------
MONOATOMIC STRUCTURE -- Species = Ni, PBC = TTT (Configuration in file "config-Ni-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)) = 0.6268070736446965
2^p V(r_1,...,r_N) = 0.626807073644847
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 -5.59216850e+00 -1.88512502e+01 -2.22957648e+01 | -5.59216850e+00 -1.88512502e+01 -2.22957648e+01
1 4.44651045e+00 5.08853921e+00 -1.58313378e+01 | 4.44651045e+00 5.08853921e+00 -1.58313378e+01
2 4.54090712e+00 -4.72696964e+00 1.40525073e+01 | 4.54090712e+00 -4.72696964e+00 1.40525073e+01
3 -3.39524907e+00 1.84896807e+01 2.40745953e+01 | -3.39524907e+00 1.84896807e+01 2.40745953e+01
4 -5.59216850e+00 -1.88512502e+01 -2.22957648e+01 | -5.59216850e+00 -1.88512502e+01 -2.22957648e+01
5 4.44651045e+00 5.08853921e+00 -1.58313378e+01 | 4.44651045e+00 5.08853921e+00 -1.58313378e+01
6 4.54090712e+00 -4.72696964e+00 1.40525073e+01 | 4.54090712e+00 -4.72696964e+00 1.40525073e+01
7 -3.39524907e+00 1.84896807e+01 2.40745953e+01 | -3.39524907e+00 1.84896807e+01 2.40745953e+01
8 -5.59216850e+00 -1.88512502e+01 -2.22957648e+01 | -5.59216850e+00 -1.88512502e+01 -2.22957648e+01
9 4.44651045e+00 5.08853921e+00 -1.58313378e+01 | 4.44651045e+00 5.08853921e+00 -1.58313378e+01
10 4.54090712e+00 -4.72696964e+00 1.40525073e+01 | 4.54090712e+00 -4.72696964e+00 1.40525073e+01
11 -3.39524907e+00 1.84896807e+01 2.40745953e+01 | -3.39524907e+00 1.84896807e+01 2.40745953e+01
12 -5.59216850e+00 -1.88512502e+01 -2.22957648e+01 | -5.59216850e+00 -1.88512502e+01 -2.22957648e+01
13 4.44651045e+00 5.08853921e+00 -1.58313378e+01 | 4.44651045e+00 5.08853921e+00 -1.58313378e+01
14 4.54090712e+00 -4.72696964e+00 1.40525073e+01 | 4.54090712e+00 -4.72696964e+00 1.40525073e+01
15 -3.39524907e+00 1.84896807e+01 2.40745953e+01 | -3.39524907e+00 1.84896807e+01 2.40745953e+01
16 -5.59216850e+00 -1.88512502e+01 -2.22957648e+01 | -5.59216850e+00 -1.88512502e+01 -2.22957648e+01
17 4.44651045e+00 5.08853921e+00 -1.58313378e+01 | 4.44651045e+00 5.08853921e+00 -1.58313378e+01
18 4.54090712e+00 -4.72696964e+00 1.40525073e+01 | 4.54090712e+00 -4.72696964e+00 1.40525073e+01
19 -3.39524907e+00 1.84896807e+01 2.40745953e+01 | -3.39524907e+00 1.84896807e+01 2.40745953e+01
20 -5.59216850e+00 -1.88512502e+01 -2.22957648e+01 | -5.59216850e+00 -1.88512502e+01 -2.22957648e+01
21 4.44651045e+00 5.08853921e+00 -1.58313378e+01 | 4.44651045e+00 5.08853921e+00 -1.58313378e+01
22 4.54090712e+00 -4.72696964e+00 1.40525073e+01 | 4.54090712e+00 -4.72696964e+00 1.40525073e+01
23 -3.39524907e+00 1.84896807e+01 2.40745953e+01 | -3.39524907e+00 1.84896807e+01 2.40745953e+01
24 -5.59216850e+00 -1.88512502e+01 -2.22957648e+01 | -5.59216850e+00 -1.88512502e+01 -2.22957648e+01
25 4.44651045e+00 5.08853921e+00 -1.58313378e+01 | 4.44651045e+00 5.08853921e+00 -1.58313378e+01
26 4.54090712e+00 -4.72696964e+00 1.40525073e+01 | 4.54090712e+00 -4.72696964e+00 1.40525073e+01
27 -3.39524907e+00 1.84896807e+01 2.40745953e+01 | -3.39524907e+00 1.84896807e+01 2.40745953e+01
28 -5.59216850e+00 -1.88512502e+01 -2.22957648e+01 | -5.59216850e+00 -1.88512502e+01 -2.22957648e+01
29 4.44651045e+00 5.08853921e+00 -1.58313378e+01 | 4.44651045e+00 5.08853921e+00 -1.58313378e+01
30 4.54090712e+00 -4.72696964e+00 1.40525073e+01 | 4.54090712e+00 -4.72696964e+00 1.40525073e+01
31 -3.39524907e+00 1.84896807e+01 2.40745953e+01 | -3.39524907e+00 1.84896807e+01 2.40745953e+01
------------------------------------------------------------------------------------------------------------------------
PASS: Energies and forces are the same to within a relative error of 1e-08
------------------------------------------------------------------------------------------------------------------------
MONOATOMIC STRUCTURE -- Species = Ni, PBC = TTF (Configuration in file "config-Ni-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)) = -4.076060788147118
2^p V(r_1,...,r_N) = -4.076060788147037
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 1.31655149e+00 -3.73990004e+00 -1.19716787e+01 | 1.31655149e+00 -3.73990004e+00 -1.19716787e+01
1 -7.20079485e-01 6.24311925e+00 -1.52928143e+01 | -7.20079485e-01 6.24311925e+00 -1.52928143e+01
2 1.69107072e+01 -2.17873605e+01 1.40130439e+01 | 1.69107072e+01 -2.17873605e+01 1.40130439e+01
3 -1.75071792e+01 1.92841413e+01 1.32514491e+01 | -1.75071792e+01 1.92841413e+01 1.32514491e+01
4 1.31655149e+00 -3.73990004e+00 -1.19716787e+01 | 1.31655149e+00 -3.73990004e+00 -1.19716787e+01
5 -7.20079485e-01 6.24311925e+00 -1.52928143e+01 | -7.20079485e-01 6.24311925e+00 -1.52928143e+01
6 1.69107072e+01 -2.17873605e+01 1.40130439e+01 | 1.69107072e+01 -2.17873605e+01 1.40130439e+01
7 -1.75071792e+01 1.92841413e+01 1.32514491e+01 | -1.75071792e+01 1.92841413e+01 1.32514491e+01
8 1.31655149e+00 -3.73990004e+00 -1.19716787e+01 | 1.31655149e+00 -3.73990004e+00 -1.19716787e+01
9 -7.20079485e-01 6.24311925e+00 -1.52928143e+01 | -7.20079485e-01 6.24311925e+00 -1.52928143e+01
10 1.69107072e+01 -2.17873605e+01 1.40130439e+01 | 1.69107072e+01 -2.17873605e+01 1.40130439e+01
11 -1.75071792e+01 1.92841413e+01 1.32514491e+01 | -1.75071792e+01 1.92841413e+01 1.32514491e+01
12 1.31655149e+00 -3.73990004e+00 -1.19716787e+01 | 1.31655149e+00 -3.73990004e+00 -1.19716787e+01
13 -7.20079485e-01 6.24311925e+00 -1.52928143e+01 | -7.20079485e-01 6.24311925e+00 -1.52928143e+01
14 1.69107072e+01 -2.17873605e+01 1.40130439e+01 | 1.69107072e+01 -2.17873605e+01 1.40130439e+01
15 -1.75071792e+01 1.92841413e+01 1.32514491e+01 | -1.75071792e+01 1.92841413e+01 1.32514491e+01
------------------------------------------------------------------------------------------------------------------------
PASS: Energies and forces are the same to within a relative error of 1e-08
------------------------------------------------------------------------------------------------------------------------
MONOATOMIC STRUCTURE -- Species = Ni, PBC = TFT (Configuration in file "config-Ni-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)) = 58.94888737944323
2^p V(r_1,...,r_N) = 58.94888737944321
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 2.75931592e+00 -3.84210685e+01 -3.02501861e+01 | 2.75931592e+00 -3.84210685e+01 -3.02501861e+01
1 1.23706916e+01 1.75917834e+01 -9.25175686e+00 | 1.23706916e+01 1.75917834e+01 -9.25175686e+00
2 -3.18321932e+01 -3.85996630e+01 1.60346444e+01 | -3.18321932e+01 -3.85996630e+01 1.60346444e+01
3 1.67021857e+01 5.94289481e+01 2.34672986e+01 | 1.67021857e+01 5.94289481e+01 2.34672986e+01
4 2.75931592e+00 -3.84210685e+01 -3.02501861e+01 | 2.75931592e+00 -3.84210685e+01 -3.02501861e+01
5 1.23706916e+01 1.75917834e+01 -9.25175686e+00 | 1.23706916e+01 1.75917834e+01 -9.25175686e+00
6 -3.18321932e+01 -3.85996630e+01 1.60346444e+01 | -3.18321932e+01 -3.85996630e+01 1.60346444e+01
7 1.67021857e+01 5.94289481e+01 2.34672986e+01 | 1.67021857e+01 5.94289481e+01 2.34672986e+01
8 2.75931592e+00 -3.84210685e+01 -3.02501861e+01 | 2.75931592e+00 -3.84210685e+01 -3.02501861e+01
9 1.23706916e+01 1.75917834e+01 -9.25175686e+00 | 1.23706916e+01 1.75917834e+01 -9.25175686e+00
10 -3.18321932e+01 -3.85996630e+01 1.60346444e+01 | -3.18321932e+01 -3.85996630e+01 1.60346444e+01
11 1.67021857e+01 5.94289481e+01 2.34672986e+01 | 1.67021857e+01 5.94289481e+01 2.34672986e+01
12 2.75931592e+00 -3.84210685e+01 -3.02501861e+01 | 2.75931592e+00 -3.84210685e+01 -3.02501861e+01
13 1.23706916e+01 1.75917834e+01 -9.25175686e+00 | 1.23706916e+01 1.75917834e+01 -9.25175686e+00
14 -3.18321932e+01 -3.85996630e+01 1.60346444e+01 | -3.18321932e+01 -3.85996630e+01 1.60346444e+01
15 1.67021857e+01 5.94289481e+01 2.34672986e+01 | 1.67021857e+01 5.94289481e+01 2.34672986e+01
------------------------------------------------------------------------------------------------------------------------
PASS: Energies and forces are the same to within a relative error of 1e-08
------------------------------------------------------------------------------------------------------------------------
MONOATOMIC STRUCTURE -- Species = Ni, PBC = TFF (Configuration in file "config-Ni-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)) = -8.797943098667494
2^p V(r_1,...,r_N) = -8.7979430986675
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 7.39840338e+00 -5.12566230e+00 -1.35184154e+01 | 7.39840338e+00 -5.12566230e+00 -1.35184154e+01
1 1.09609471e+01 3.55878328e+00 -1.51804631e+01 | 1.09609471e+01 3.55878328e+00 -1.51804631e+01
2 -8.72483474e+00 -3.19219882e+00 1.19903680e+01 | -8.72483474e+00 -3.19219882e+00 1.19903680e+01
3 -9.63451571e+00 4.75907783e+00 1.67085105e+01 | -9.63451571e+00 4.75907783e+00 1.67085105e+01
4 7.39840338e+00 -5.12566230e+00 -1.35184154e+01 | 7.39840338e+00 -5.12566230e+00 -1.35184154e+01
5 1.09609471e+01 3.55878328e+00 -1.51804631e+01 | 1.09609471e+01 3.55878328e+00 -1.51804631e+01
6 -8.72483474e+00 -3.19219882e+00 1.19903680e+01 | -8.72483474e+00 -3.19219882e+00 1.19903680e+01
7 -9.63451571e+00 4.75907783e+00 1.67085105e+01 | -9.63451571e+00 4.75907783e+00 1.67085105e+01
------------------------------------------------------------------------------------------------------------------------
PASS: Energies and forces are the same to within a relative error of 1e-08
------------------------------------------------------------------------------------------------------------------------
MONOATOMIC STRUCTURE -- Species = Ni, PBC = FTT (Configuration in file "config-Ni-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)) = 29.578889003636885
2^p V(r_1,...,r_N) = 29.57888900363689
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 -2.60006351e+01 -5.13555209e+00 -1.92843027e+01 | -2.60006351e+01 -5.13555209e+00 -1.92843027e+01
1 1.79541503e+01 -1.98058966e+01 -7.81804331e+00 | 1.79541503e+01 -1.98058966e+01 -7.81804331e+00
2 2.54624755e+01 1.32287857e+01 2.32845412e+01 | 2.54624755e+01 1.32287857e+01 2.32845412e+01
3 -1.74159907e+01 1.17126630e+01 3.81780483e+00 | -1.74159907e+01 1.17126630e+01 3.81780483e+00
4 -2.60006351e+01 -5.13555209e+00 -1.92843027e+01 | -2.60006351e+01 -5.13555209e+00 -1.92843027e+01
5 1.79541503e+01 -1.98058966e+01 -7.81804331e+00 | 1.79541503e+01 -1.98058966e+01 -7.81804331e+00
6 2.54624755e+01 1.32287857e+01 2.32845412e+01 | 2.54624755e+01 1.32287857e+01 2.32845412e+01
7 -1.74159907e+01 1.17126630e+01 3.81780483e+00 | -1.74159907e+01 1.17126630e+01 3.81780483e+00
8 -2.60006351e+01 -5.13555209e+00 -1.92843027e+01 | -2.60006351e+01 -5.13555209e+00 -1.92843027e+01
9 1.79541503e+01 -1.98058966e+01 -7.81804331e+00 | 1.79541503e+01 -1.98058966e+01 -7.81804331e+00
10 2.54624755e+01 1.32287857e+01 2.32845412e+01 | 2.54624755e+01 1.32287857e+01 2.32845412e+01
11 -1.74159907e+01 1.17126630e+01 3.81780483e+00 | -1.74159907e+01 1.17126630e+01 3.81780483e+00
12 -2.60006351e+01 -5.13555209e+00 -1.92843027e+01 | -2.60006351e+01 -5.13555209e+00 -1.92843027e+01
13 1.79541503e+01 -1.98058966e+01 -7.81804331e+00 | 1.79541503e+01 -1.98058966e+01 -7.81804331e+00
14 2.54624755e+01 1.32287857e+01 2.32845412e+01 | 2.54624755e+01 1.32287857e+01 2.32845412e+01
15 -1.74159907e+01 1.17126630e+01 3.81780483e+00 | -1.74159907e+01 1.17126630e+01 3.81780483e+00
------------------------------------------------------------------------------------------------------------------------
PASS: Energies and forces are the same to within a relative error of 1e-08
------------------------------------------------------------------------------------------------------------------------
MONOATOMIC STRUCTURE -- Species = Ni, PBC = FTF (Configuration in file "config-Ni-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)) = -0.7870695379987331
2^p V(r_1,...,r_N) = -0.7870695379987301
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 -9.74787851e+00 -1.78414582e+01 -2.06390573e+01 | -9.74787851e+00 -1.78414582e+01 -2.06390573e+01
1 1.79038465e+01 6.81102833e+00 -6.75370194e+00 | 1.79038465e+01 6.81102833e+00 -6.75370194e+00
2 9.88253881e+00 1.71414101e+00 1.01999000e+01 | 9.88253881e+00 1.71414101e+00 1.01999000e+01
3 -1.80385068e+01 9.31628889e+00 1.71928592e+01 | -1.80385068e+01 9.31628889e+00 1.71928592e+01
4 -9.74787851e+00 -1.78414582e+01 -2.06390573e+01 | -9.74787851e+00 -1.78414582e+01 -2.06390573e+01
5 1.79038465e+01 6.81102833e+00 -6.75370194e+00 | 1.79038465e+01 6.81102833e+00 -6.75370194e+00
6 9.88253881e+00 1.71414101e+00 1.01999000e+01 | 9.88253881e+00 1.71414101e+00 1.01999000e+01
7 -1.80385068e+01 9.31628889e+00 1.71928592e+01 | -1.80385068e+01 9.31628889e+00 1.71928592e+01
------------------------------------------------------------------------------------------------------------------------
PASS: Energies and forces are the same to within a relative error of 1e-08
------------------------------------------------------------------------------------------------------------------------
MONOATOMIC STRUCTURE -- Species = Ni, PBC = FFT (Configuration in file "config-Ni-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)) = 1.4867852252405118
2^p V(r_1,...,r_N) = 1.486785225240514
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 -1.25289737e+01 -1.97225242e+01 -8.92148557e+00 | -1.25289737e+01 -1.97225242e+01 -8.92148557e+00
1 6.73104873e+00 9.37395618e+00 -2.75194707e+00 | 6.73104873e+00 9.37395618e+00 -2.75194707e+00
2 2.48638717e+01 -1.15323335e+01 7.50855559e+00 | 2.48638717e+01 -1.15323335e+01 7.50855559e+00
3 -1.90659467e+01 2.18809015e+01 4.16487706e+00 | -1.90659467e+01 2.18809015e+01 4.16487706e+00
4 -1.25289737e+01 -1.97225242e+01 -8.92148557e+00 | -1.25289737e+01 -1.97225242e+01 -8.92148557e+00
5 6.73104873e+00 9.37395618e+00 -2.75194707e+00 | 6.73104873e+00 9.37395618e+00 -2.75194707e+00
6 2.48638717e+01 -1.15323335e+01 7.50855559e+00 | 2.48638717e+01 -1.15323335e+01 7.50855559e+00
7 -1.90659467e+01 2.18809015e+01 4.16487706e+00 | -1.90659467e+01 2.18809015e+01 4.16487706e+00
------------------------------------------------------------------------------------------------------------------------
PASS: Energies and forces are the same to within a relative error of 1e-08
------------------------------------------------------------------------------------------------------------------------
MIXED STRUCTURE -- Species = Cr Ni, PBC = TTT (Configuration in file "config-CrNi-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)) = 144.3385455476088
2^p V(r_1,...,r_N) = 144.33854554760921
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 1.59671098e+01 -1.27599391e+01 -1.86714043e+01 | 1.59671098e+01 -1.27599391e+01 -1.86714043e+01
1 -2.16181149e+01 -5.04293554e+01 5.23855201e+01 | -2.16181149e+01 -5.04293554e+01 5.23855201e+01
2 -1.52924790e+01 4.01055690e+01 -4.65712114e+01 | -1.52924790e+01 4.01055690e+01 -4.65712114e+01
3 2.09434841e+01 2.30837255e+01 1.28570956e+01 | 2.09434841e+01 2.30837255e+01 1.28570956e+01
4 1.59671098e+01 -1.27599391e+01 -1.86714043e+01 | 1.59671098e+01 -1.27599391e+01 -1.86714043e+01
5 -2.16181149e+01 -5.04293554e+01 5.23855201e+01 | -2.16181149e+01 -5.04293554e+01 5.23855201e+01
6 -1.52924790e+01 4.01055690e+01 -4.65712114e+01 | -1.52924790e+01 4.01055690e+01 -4.65712114e+01
7 2.09434841e+01 2.30837255e+01 1.28570956e+01 | 2.09434841e+01 2.30837255e+01 1.28570956e+01
8 1.59671098e+01 -1.27599391e+01 -1.86714043e+01 | 1.59671098e+01 -1.27599391e+01 -1.86714043e+01
9 -2.16181149e+01 -5.04293554e+01 5.23855201e+01 | -2.16181149e+01 -5.04293554e+01 5.23855201e+01
10 -1.52924790e+01 4.01055690e+01 -4.65712114e+01 | -1.52924790e+01 4.01055690e+01 -4.65712114e+01
11 2.09434841e+01 2.30837255e+01 1.28570956e+01 | 2.09434841e+01 2.30837255e+01 1.28570956e+01
12 1.59671098e+01 -1.27599391e+01 -1.86714043e+01 | 1.59671098e+01 -1.27599391e+01 -1.86714043e+01
13 -2.16181149e+01 -5.04293554e+01 5.23855201e+01 | -2.16181149e+01 -5.04293554e+01 5.23855201e+01
14 -1.52924790e+01 4.01055690e+01 -4.65712114e+01 | -1.52924790e+01 4.01055690e+01 -4.65712114e+01
15 2.09434841e+01 2.30837255e+01 1.28570956e+01 | 2.09434841e+01 2.30837255e+01 1.28570956e+01
16 1.59671098e+01 -1.27599391e+01 -1.86714043e+01 | 1.59671098e+01 -1.27599391e+01 -1.86714043e+01
17 -2.16181149e+01 -5.04293554e+01 5.23855201e+01 | -2.16181149e+01 -5.04293554e+01 5.23855201e+01
18 -1.52924790e+01 4.01055690e+01 -4.65712114e+01 | -1.52924790e+01 4.01055690e+01 -4.65712114e+01
19 2.09434841e+01 2.30837255e+01 1.28570956e+01 | 2.09434841e+01 2.30837255e+01 1.28570956e+01
20 1.59671098e+01 -1.27599391e+01 -1.86714043e+01 | 1.59671098e+01 -1.27599391e+01 -1.86714043e+01
21 -2.16181149e+01 -5.04293554e+01 5.23855201e+01 | -2.16181149e+01 -5.04293554e+01 5.23855201e+01
22 -1.52924790e+01 4.01055690e+01 -4.65712114e+01 | -1.52924790e+01 4.01055690e+01 -4.65712114e+01
23 2.09434841e+01 2.30837255e+01 1.28570956e+01 | 2.09434841e+01 2.30837255e+01 1.28570956e+01
24 1.59671098e+01 -1.27599391e+01 -1.86714043e+01 | 1.59671098e+01 -1.27599391e+01 -1.86714043e+01
25 -2.16181149e+01 -5.04293554e+01 5.23855201e+01 | -2.16181149e+01 -5.04293554e+01 5.23855201e+01
26 -1.52924790e+01 4.01055690e+01 -4.65712114e+01 | -1.52924790e+01 4.01055690e+01 -4.65712114e+01
27 2.09434841e+01 2.30837255e+01 1.28570956e+01 | 2.09434841e+01 2.30837255e+01 1.28570956e+01
28 1.59671098e+01 -1.27599391e+01 -1.86714043e+01 | 1.59671098e+01 -1.27599391e+01 -1.86714043e+01
29 -2.16181149e+01 -5.04293554e+01 5.23855201e+01 | -2.16181149e+01 -5.04293554e+01 5.23855201e+01
30 -1.52924790e+01 4.01055690e+01 -4.65712114e+01 | -1.52924790e+01 4.01055690e+01 -4.65712114e+01
31 2.09434841e+01 2.30837255e+01 1.28570956e+01 | 2.09434841e+01 2.30837255e+01 1.28570956e+01
------------------------------------------------------------------------------------------------------------------------
PASS: Energies and forces are the same to within a relative error of 1e-08
------------------------------------------------------------------------------------------------------------------------
MIXED STRUCTURE -- Species = Cr Ni, PBC = TTF (Configuration in file "config-CrNi-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)) = 20.414671851992654
2^p V(r_1,...,r_N) = 20.41467185199265
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 1.45740913e+01 1.75232118e+01 -1.56725210e+01 | 1.45740913e+01 1.75232118e+01 -1.56725210e+01
1 -4.26118822e+01 -4.89847866e+00 -3.58674686e+01 | -4.26118822e+01 -4.89847866e+00 -3.58674686e+01
2 -1.20798536e+00 -2.25370101e+00 4.11061304e+00 | -1.20798536e+00 -2.25370101e+00 4.11061304e+00
3 2.92457763e+01 -1.03710321e+01 4.74293766e+01 | 2.92457763e+01 -1.03710321e+01 4.74293766e+01
4 1.45740913e+01 1.75232118e+01 -1.56725210e+01 | 1.45740913e+01 1.75232118e+01 -1.56725210e+01
5 -4.26118822e+01 -4.89847866e+00 -3.58674686e+01 | -4.26118822e+01 -4.89847866e+00 -3.58674686e+01
6 -1.20798536e+00 -2.25370101e+00 4.11061304e+00 | -1.20798536e+00 -2.25370101e+00 4.11061304e+00
7 2.92457763e+01 -1.03710321e+01 4.74293766e+01 | 2.92457763e+01 -1.03710321e+01 4.74293766e+01
8 1.45740913e+01 1.75232118e+01 -1.56725210e+01 | 1.45740913e+01 1.75232118e+01 -1.56725210e+01
9 -4.26118822e+01 -4.89847866e+00 -3.58674686e+01 | -4.26118822e+01 -4.89847866e+00 -3.58674686e+01
10 -1.20798536e+00 -2.25370101e+00 4.11061304e+00 | -1.20798536e+00 -2.25370101e+00 4.11061304e+00
11 2.92457763e+01 -1.03710321e+01 4.74293766e+01 | 2.92457763e+01 -1.03710321e+01 4.74293766e+01
12 1.45740913e+01 1.75232118e+01 -1.56725210e+01 | 1.45740913e+01 1.75232118e+01 -1.56725210e+01
13 -4.26118822e+01 -4.89847866e+00 -3.58674686e+01 | -4.26118822e+01 -4.89847866e+00 -3.58674686e+01
14 -1.20798536e+00 -2.25370101e+00 4.11061304e+00 | -1.20798536e+00 -2.25370101e+00 4.11061304e+00
15 2.92457763e+01 -1.03710321e+01 4.74293766e+01 | 2.92457763e+01 -1.03710321e+01 4.74293766e+01
------------------------------------------------------------------------------------------------------------------------
PASS: Energies and forces are the same to within a relative error of 1e-08
------------------------------------------------------------------------------------------------------------------------
MIXED STRUCTURE -- Species = Cr Ni, PBC = TFT (Configuration in file "config-CrNi-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)) = -13.012907665016991
2^p V(r_1,...,r_N) = -13.012907665017002
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 1.24387540e+01 -1.05570269e+01 -1.43730769e+01 | 1.24387540e+01 -1.05570269e+01 -1.43730769e+01
1 -1.68646656e+00 1.21461418e+01 -3.38149438e+00 | -1.68646656e+00 1.21461418e+01 -3.38149438e+00
2 -8.63826068e+00 -1.31531976e+01 1.45853932e+01 | -8.63826068e+00 -1.31531976e+01 1.45853932e+01
3 -2.11402678e+00 1.15640827e+01 3.16917813e+00 | -2.11402678e+00 1.15640827e+01 3.16917813e+00
4 1.24387540e+01 -1.05570269e+01 -1.43730769e+01 | 1.24387540e+01 -1.05570269e+01 -1.43730769e+01
5 -1.68646656e+00 1.21461418e+01 -3.38149438e+00 | -1.68646656e+00 1.21461418e+01 -3.38149438e+00
6 -8.63826068e+00 -1.31531976e+01 1.45853932e+01 | -8.63826068e+00 -1.31531976e+01 1.45853932e+01
7 -2.11402678e+00 1.15640827e+01 3.16917813e+00 | -2.11402678e+00 1.15640827e+01 3.16917813e+00
8 1.24387540e+01 -1.05570269e+01 -1.43730769e+01 | 1.24387540e+01 -1.05570269e+01 -1.43730769e+01
9 -1.68646656e+00 1.21461418e+01 -3.38149438e+00 | -1.68646656e+00 1.21461418e+01 -3.38149438e+00
10 -8.63826068e+00 -1.31531976e+01 1.45853932e+01 | -8.63826068e+00 -1.31531976e+01 1.45853932e+01
11 -2.11402678e+00 1.15640827e+01 3.16917813e+00 | -2.11402678e+00 1.15640827e+01 3.16917813e+00
12 1.24387540e+01 -1.05570269e+01 -1.43730769e+01 | 1.24387540e+01 -1.05570269e+01 -1.43730769e+01
13 -1.68646656e+00 1.21461418e+01 -3.38149438e+00 | -1.68646656e+00 1.21461418e+01 -3.38149438e+00
14 -8.63826068e+00 -1.31531976e+01 1.45853932e+01 | -8.63826068e+00 -1.31531976e+01 1.45853932e+01
15 -2.11402678e+00 1.15640827e+01 3.16917813e+00 | -2.11402678e+00 1.15640827e+01 3.16917813e+00
------------------------------------------------------------------------------------------------------------------------
PASS: Energies and forces are the same to within a relative error of 1e-08
------------------------------------------------------------------------------------------------------------------------
MIXED STRUCTURE -- Species = Cr Ni, PBC = TFF (Configuration in file "config-CrNi-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)) = 22.678631219906357
2^p V(r_1,...,r_N) = 22.67863121990635
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 -1.04157899e+01 -3.11569497e+01 -3.88895742e+01 | -1.04157899e+01 -3.11569497e+01 -3.88895742e+01
1 -3.57957982e+00 1.52351374e+01 -1.73868161e+01 | -3.57957982e+00 1.52351374e+01 -1.73868161e+01
2 2.82647130e+01 -2.89732125e+01 2.58802751e+01 | 2.82647130e+01 -2.89732125e+01 2.58802751e+01
3 -1.42693433e+01 4.48950248e+01 3.03961152e+01 | -1.42693433e+01 4.48950248e+01 3.03961152e+01
4 -1.04157899e+01 -3.11569497e+01 -3.88895742e+01 | -1.04157899e+01 -3.11569497e+01 -3.88895742e+01
5 -3.57957982e+00 1.52351374e+01 -1.73868161e+01 | -3.57957982e+00 1.52351374e+01 -1.73868161e+01
6 2.82647130e+01 -2.89732125e+01 2.58802751e+01 | 2.82647130e+01 -2.89732125e+01 2.58802751e+01
7 -1.42693433e+01 4.48950248e+01 3.03961152e+01 | -1.42693433e+01 4.48950248e+01 3.03961152e+01
------------------------------------------------------------------------------------------------------------------------
PASS: Energies and forces are the same to within a relative error of 1e-08
------------------------------------------------------------------------------------------------------------------------
MIXED STRUCTURE -- Species = Cr Ni, PBC = FTT (Configuration in file "config-CrNi-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)) = 34.681063516432936
2^p V(r_1,...,r_N) = 34.68106351643299
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 -4.22996987e+01 -6.78846054e+00 -1.80400951e+01 | -4.22996987e+01 -6.78846054e+00 -1.80400951e+01
1 2.70307457e+01 2.81966113e+01 -1.32039572e+01 | 2.70307457e+01 2.81966113e+01 -1.32039572e+01
2 3.10846262e+01 -2.31828654e+00 2.14237310e+01 | 3.10846262e+01 -2.31828654e+00 2.14237310e+01
3 -1.58156731e+01 -1.90898643e+01 9.82032133e+00 | -1.58156731e+01 -1.90898643e+01 9.82032133e+00
4 -4.22996987e+01 -6.78846054e+00 -1.80400951e+01 | -4.22996987e+01 -6.78846054e+00 -1.80400951e+01
5 2.70307457e+01 2.81966113e+01 -1.32039572e+01 | 2.70307457e+01 2.81966113e+01 -1.32039572e+01
6 3.10846262e+01 -2.31828654e+00 2.14237310e+01 | 3.10846262e+01 -2.31828654e+00 2.14237310e+01
7 -1.58156731e+01 -1.90898643e+01 9.82032133e+00 | -1.58156731e+01 -1.90898643e+01 9.82032133e+00
8 -4.22996987e+01 -6.78846054e+00 -1.80400951e+01 | -4.22996987e+01 -6.78846054e+00 -1.80400951e+01
9 2.70307457e+01 2.81966113e+01 -1.32039572e+01 | 2.70307457e+01 2.81966113e+01 -1.32039572e+01
10 3.10846262e+01 -2.31828654e+00 2.14237310e+01 | 3.10846262e+01 -2.31828654e+00 2.14237310e+01
11 -1.58156731e+01 -1.90898643e+01 9.82032133e+00 | -1.58156731e+01 -1.90898643e+01 9.82032133e+00
12 -4.22996987e+01 -6.78846054e+00 -1.80400951e+01 | -4.22996987e+01 -6.78846054e+00 -1.80400951e+01
13 2.70307457e+01 2.81966113e+01 -1.32039572e+01 | 2.70307457e+01 2.81966113e+01 -1.32039572e+01
14 3.10846262e+01 -2.31828654e+00 2.14237310e+01 | 3.10846262e+01 -2.31828654e+00 2.14237310e+01
15 -1.58156731e+01 -1.90898643e+01 9.82032133e+00 | -1.58156731e+01 -1.90898643e+01 9.82032133e+00
------------------------------------------------------------------------------------------------------------------------
PASS: Energies and forces are the same to within a relative error of 1e-08
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MIXED STRUCTURE -- Species = Cr Ni, PBC = FTF (Configuration in file "config-CrNi-FTF.xyz")
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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)) = 18.606330617151265
2^p V(r_1,...,r_N) = 18.606330617151254
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 -2.00025586e+01 -1.58783812e+01 -1.51489940e+01 | -2.00025586e+01 -1.58783812e+01 -1.51489940e+01
1 1.83875787e+01 1.42633379e+01 -1.06841853e+01 | 1.83875787e+01 1.42633379e+01 -1.06841853e+01
2 5.13739464e+01 -3.75555700e+01 7.93015439e+00 | 5.13739464e+01 -3.75555700e+01 7.93015439e+00
3 -4.97589666e+01 3.91706133e+01 1.79030249e+01 | -4.97589666e+01 3.91706133e+01 1.79030249e+01
4 -2.00025586e+01 -1.58783812e+01 -1.51489940e+01 | -2.00025586e+01 -1.58783812e+01 -1.51489940e+01
5 1.83875787e+01 1.42633379e+01 -1.06841853e+01 | 1.83875787e+01 1.42633379e+01 -1.06841853e+01
6 5.13739464e+01 -3.75555700e+01 7.93015439e+00 | 5.13739464e+01 -3.75555700e+01 7.93015439e+00
7 -4.97589666e+01 3.91706133e+01 1.79030249e+01 | -4.97589666e+01 3.91706133e+01 1.79030249e+01
------------------------------------------------------------------------------------------------------------------------
PASS: Energies and forces are the same to within a relative error of 1e-08
------------------------------------------------------------------------------------------------------------------------
MIXED STRUCTURE -- Species = Cr Ni, PBC = FFT (Configuration in file "config-CrNi-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)) = 24.247981103204
2^p V(r_1,...,r_N) = 24.24798110320402
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 -1.95756480e+01 -5.01465964e+01 -4.56129064e+01 | -1.95756480e+01 -5.01465964e+01 -4.56129064e+01
1 9.00318907e+00 1.09566428e+01 -4.99514783e+00 | 9.00318907e+00 1.09566428e+01 -4.99514783e+00
2 3.78886195e+01 -1.84280877e+01 2.30087133e+01 | 3.78886195e+01 -1.84280877e+01 2.30087133e+01
3 -2.73161606e+01 5.76180413e+01 2.75993409e+01 | -2.73161606e+01 5.76180413e+01 2.75993409e+01
4 -1.95756480e+01 -5.01465964e+01 -4.56129064e+01 | -1.95756480e+01 -5.01465964e+01 -4.56129064e+01
5 9.00318907e+00 1.09566428e+01 -4.99514783e+00 | 9.00318907e+00 1.09566428e+01 -4.99514783e+00
6 3.78886195e+01 -1.84280877e+01 2.30087133e+01 | 3.78886195e+01 -1.84280877e+01 2.30087133e+01
7 -2.73161606e+01 5.76180413e+01 2.75993409e+01 | -2.73161606e+01 5.76180413e+01 2.75993409e+01
------------------------------------------------------------------------------------------------------------------------
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 23:15:15) ===