!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! VERIFICATION CHECK: vc-permutation-symmetry !!!!! !!!!! !!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Description: Check whether a model is invariant with respect to atom permutations that preserve species, i.e. swapping any two atoms with the same species must not change the energy or forces. This must be true for all models. The check is performed for a randomly distorted non-periodic diamond 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. The energy and forces of each configuration are compared with one where each atom is randomly swapped with another atom of the same species. The energy and forces must remain unchanged. The verification check will pass if these conditions are satisfied for all configurations that the model is able to compute. Configurations used for testing are provided as auxiliary files. Author: Ellad Tadmor ------------------------------------------------------------------------------------------------------------------------- Results for KIM Model : EAM_Dynamo_FarkasCaro_2018_FeNiCrCoCu__MO_803527979660_000 Supported species : Co Cr Cu Fe Ni random seed = 13 lattice constant (orig) = 5.000 perturbation amplitude = 0.500 number unit cells per side = 2 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Co (Configuration in file "config-Co.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [38, 55, 35, 16, 32, 44, 25, 21, 56, 14, 19, 63, 24, 20, 9, 62, 3, 50, 39, 10, 13, 7, 36, 30, 12, 6, 33, 60, 40, 31, 23, 29, 4, 26, 37, 2, 22, 34, 0, 18, 28, 49, 51, 58, 5, 47, 59, 45, 61, 41, 17, 42, 57, 54, 53, 1, 8, 52, 43, 46, 27, 48, 15, 11] Energy requirement: V(r_(PI 1),...,r_(PI N)) = V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). V(r_(PI 1),...,r_(PI N)) = -68.27056343718402 V(r_1,...,r_N) = -68.27056343718404 Forces requirement: f_(PI i)(r_(PI 1),...,r_(PI N)) = f_i(r_1,...,r_N), where r_i is the position of atom i, f_i is the force on atom i and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). i f_(PI i)(r_(PI 1),...,r_(PI N)) f_i(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------- 0 -8.05713160e-01 4.31789821e-01 4.78657350e-01 | -8.05713160e-01 4.31789821e-01 4.78657350e-01 1 1.19912847e+00 -4.40625421e+00 1.53476708e+00 | 1.19912847e+00 -4.40625421e+00 1.53476708e+00 2 -3.98745478e+00 2.09048267e+00 -1.80600627e+00 | -3.98745478e+00 2.09048267e+00 -1.80600627e+00 3 2.65032833e+00 9.29666152e-01 -1.83544969e+00 | 2.65032833e+00 9.29666152e-01 -1.83544969e+00 4 -1.79018010e+00 7.25360885e-01 -5.77306736e-01 | -1.79018010e+00 7.25360885e-01 -5.77306736e-01 5 2.02175210e-01 9.85666570e-01 -5.31904737e-01 | 2.02175210e-01 9.85666570e-01 -5.31904737e-01 6 5.03270172e-02 -1.20051995e+00 -8.83501039e-01 | 5.03270172e-02 -1.20051995e+00 -8.83501039e-01 7 -7.90236649e+00 2.35869769e+01 -1.18095916e+01 | -7.90236649e+00 2.35869769e+01 -1.18095916e+01 8 -3.05368526e+00 -2.01480025e+00 -3.00400042e+00 | -3.05368526e+00 -2.01480025e+00 -3.00400042e+00 9 1.02604304e+00 8.30944848e-01 7.70471602e+00 | 1.02604304e+00 8.30944848e-01 7.70471602e+00 10 -7.18008566e-01 -1.05974306e+00 -5.56059403e+00 | -7.18008566e-01 -1.05974306e+00 -5.56059403e+00 11 2.59174235e+00 2.57748323e+00 2.81428766e+00 | 2.59174235e+00 2.57748323e+00 2.81428766e+00 12 -2.23786426e+00 -1.79843346e-01 1.27681917e-01 | -2.23786426e+00 -1.79843346e-01 1.27681917e-01 13 3.10866793e+00 -4.51688043e-01 -4.07860578e+00 | 3.10866793e+00 -4.51688043e-01 -4.07860578e+00 14 -1.49488006e+00 1.03502742e+00 -4.75991825e+00 | -1.49488006e+00 1.03502742e+00 -4.75991825e+00 15 1.85642768e+00 1.48638826e+00 1.70832507e+00 | 1.85642768e+00 1.48638826e+00 1.70832507e+00 16 -2.55997909e+00 -2.58698938e+00 -2.51874063e+00 | -2.55997909e+00 -2.58698938e+00 -2.51874063e+00 17 4.31526520e+00 1.32849440e+00 4.05054175e+00 | 4.31526520e+00 1.32849440e+00 4.05054175e+00 18 -3.11926067e+00 -1.66856381e+00 -1.59440561e+00 | -3.11926067e+00 -1.66856381e+00 -1.59440561e+00 19 -8.24105023e+00 7.17670272e+00 -4.15677576e+00 | -8.24105023e+00 7.17670272e+00 -4.15677576e+00 20 -1.26356847e+00 2.16982801e-01 2.40142232e+00 | -1.26356847e+00 2.16982801e-01 2.40142232e+00 21 4.25041220e+00 5.72566649e-01 4.27214608e+00 | 4.25041220e+00 5.72566649e-01 4.27214608e+00 22 -1.59072907e+00 -2.74236160e+00 -3.70866473e+00 | -1.59072907e+00 -2.74236160e+00 -3.70866473e+00 23 1.93016498e+00 2.51877027e+00 2.98075734e+00 | 1.93016498e+00 2.51877027e+00 2.98075734e+00 24 -5.90174863e-01 -7.68879672e-02 6.70927918e-01 | -5.90174863e-01 -7.68879672e-02 6.70927918e-01 25 1.02944902e+00 -4.10295066e-01 -1.53239703e+00 | 1.02944902e+00 -4.10295066e-01 -1.53239703e+00 26 -1.16254066e-02 5.49709294e-02 1.34463518e-01 | -1.16254066e-02 5.49709294e-02 1.34463518e-01 27 -6.29193570e-01 -5.92076813e-01 -9.77164212e-02 | -6.29193570e-01 -5.92076813e-01 -9.77164212e-02 28 5.45937252e-02 -2.93206184e+00 7.74789445e-01 | 5.45937252e-02 -2.93206184e+00 7.74789445e-01 29 1.04764595e+00 7.29567914e-01 1.27166089e+00 | 1.04764595e+00 7.29567914e-01 1.27166089e+00 30 6.81732880e+00 -9.97619188e-01 5.72155873e+00 | 6.81732880e+00 -9.97619188e-01 5.72155873e+00 31 -4.80030439e-01 -1.36215958e+00 9.48573076e-01 | -4.80030439e-01 -1.36215958e+00 9.48573076e-01 32 -7.04212349e-01 -6.55273781e-01 -4.94214237e+00 | -7.04212349e-01 -6.55273781e-01 -4.94214237e+00 33 -6.15628851e-01 5.58037615e+00 1.63574432e+00 | -6.15628851e-01 5.58037615e+00 1.63574432e+00 34 6.94572188e+00 -2.40508212e+01 9.51659320e+00 | 6.94572188e+00 -2.40508212e+01 9.51659320e+00 35 -4.57856905e-01 -3.85893638e+00 4.43225814e+00 | -4.57856905e-01 -3.85893638e+00 4.43225814e+00 36 3.58365494e+00 -2.24627497e+00 1.89256898e+00 | 3.58365494e+00 -2.24627497e+00 1.89256898e+00 37 -1.94890530e-01 -1.94912238e+00 -1.33858882e+00 | -1.94890530e-01 -1.94912238e+00 -1.33858882e+00 38 -4.01830596e-01 -7.93600449e-02 -2.60186861e+00 | -4.01830596e-01 -7.93600449e-02 -2.60186861e+00 39 -1.10233153e+00 -3.21124390e+00 2.24248049e+00 | -1.10233153e+00 -3.21124390e+00 2.24248049e+00 40 1.88079242e-01 -1.67144833e+00 4.95510938e+00 | 1.88079242e-01 -1.67144833e+00 4.95510938e+00 41 -5.72927846e+00 5.50325066e+00 -1.63969527e+00 | -5.72927846e+00 5.50325066e+00 -1.63969527e+00 42 -1.12542032e+00 -3.22496574e-02 -1.64100459e+00 | -1.12542032e+00 -3.22496574e-02 -1.64100459e+00 43 -6.83207961e-01 3.03452793e+00 3.03667791e+00 | -6.83207961e-01 3.03452793e+00 3.03667791e+00 44 1.96435800e-01 -7.57827081e+00 -4.88249700e-02 | 1.96435800e-01 -7.57827081e+00 -4.88249700e-02 45 1.81099473e+00 2.14877021e+00 2.48836064e+00 | 1.81099473e+00 2.14877021e+00 2.48836064e+00 46 -1.58514466e+00 -2.42603463e+00 -3.10218424e-01 | -1.58514466e+00 -2.42603463e+00 -3.10218424e-01 47 8.15114673e-02 2.26492342e+00 4.27390126e-01 | 8.15114673e-02 2.26492342e+00 4.27390126e-01 48 -1.59916181e-01 -1.80372350e+00 8.54931547e-02 | -1.59916181e-01 -1.80372350e+00 8.54931547e-02 49 1.13654054e+00 1.69550994e-01 8.41632733e-01 | 1.13654054e+00 1.69550994e-01 8.41632733e-01 50 -2.52434312e+01 -3.06001991e+01 -3.26945360e+01 | -2.52434312e+01 -3.06001991e+01 -3.26945360e+01 51 2.99391995e+01 2.76217416e+01 3.08026029e+01 | 2.99391995e+01 2.76217416e+01 3.08026029e+01 52 -2.03626770e+00 4.81803916e+00 -3.93403022e+00 | -2.03626770e+00 4.81803916e+00 -3.93403022e+00 53 5.15560224e+00 6.76701338e-01 1.25766945e+00 | 5.15560224e+00 6.76701338e-01 1.25766945e+00 54 -2.90324752e-01 3.78184189e-01 9.53418965e-01 | -2.90324752e-01 3.78184189e-01 9.53418965e-01 55 -5.53402165e-01 -7.96669797e-01 -1.13989481e+00 | -5.53402165e-01 -7.96669797e-01 -1.13989481e+00 56 -1.58902416e+00 -1.16820412e-01 -2.16043010e+00 | -1.58902416e+00 -1.16820412e-01 -2.16043010e+00 57 6.64595501e+00 -5.19239093e+00 -8.83790609e+00 | 6.64595501e+00 -5.19239093e+00 -8.83790609e+00 58 -3.21721394e+00 -2.57965752e+00 -1.56897716e+00 | -3.21721394e+00 -2.57965752e+00 -1.56897716e+00 59 1.87841671e+00 1.59464448e+00 2.61040309e+00 | 1.87841671e+00 1.59464448e+00 2.61040309e+00 60 -1.21480154e+00 1.46669625e+00 -3.27847141e+00 | -1.21480154e+00 1.46669625e+00 -3.27847141e+00 61 2.19517189e+00 2.32809103e+00 1.33213055e+00 | 2.19517189e+00 2.32809103e+00 1.33213055e+00 62 -5.40792433e+00 5.56994184e+00 7.45694531e+00 | -5.40792433e+00 5.56994184e+00 7.45694531e+00 63 9.00888703e-01 1.09707975e+00 1.02941205e+00 | 9.00888703e-01 1.09707975e+00 1.02941205e+00 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Cr (Configuration in file "config-Cr.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [29, 50, 44, 61, 20, 24, 47, 33, 9, 8, 45, 16, 26, 59, 46, 55, 11, 54, 49, 37, 4, 25, 35, 32, 5, 21, 12, 39, 31, 0, 38, 28, 23, 7, 60, 22, 42, 19, 30, 27, 43, 52, 36, 40, 2, 10, 14, 6, 63, 18, 1, 62, 41, 56, 17, 15, 53, 58, 57, 13, 34, 3, 51, 48] Energy requirement: V(r_(PI 1),...,r_(PI N)) = V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). V(r_(PI 1),...,r_(PI N)) = -42.108688444464825 V(r_1,...,r_N) = -42.10868844446477 Forces requirement: f_(PI i)(r_(PI 1),...,r_(PI N)) = f_i(r_1,...,r_N), where r_i is the position of atom i, f_i is the force on atom i and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). i f_(PI i)(r_(PI 1),...,r_(PI N)) f_i(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------- 0 -9.03783651e-01 2.46727815e-01 -1.68267193e+00 | -9.03783651e-01 2.46727815e-01 -1.68267193e+00 1 1.83299683e-01 3.07852371e+00 1.20537701e+00 | 1.83299683e-01 3.07852371e+00 1.20537701e+00 2 -1.04174620e+00 -1.52224790e+00 -1.13355215e+00 | -1.04174620e+00 -1.52224790e+00 -1.13355215e+00 3 1.18398677e+00 5.63656532e+00 -1.90723637e+00 | 1.18398677e+00 5.63656532e+00 -1.90723637e+00 4 1.80355689e+00 -1.01605532e+00 3.53835707e+00 | 1.80355689e+00 -1.01605532e+00 3.53835707e+00 5 -9.13390595e+01 6.17737795e+00 4.87148452e+01 | -9.13390595e+01 6.17737795e+00 4.87148452e+01 6 -3.37106207e+00 -3.76116185e+00 -2.76866409e+00 | -3.37106207e+00 -3.76116185e+00 -2.76866409e+00 7 1.53088290e+00 3.23550793e-02 3.25648876e+00 | 1.53088290e+00 3.23550793e-02 3.25648876e+00 8 -3.72550241e-02 1.37515122e+00 1.23484703e+00 | -3.72550241e-02 1.37515122e+00 1.23484703e+00 9 1.49091632e+00 8.26616102e-05 3.40521198e-02 | 1.49091632e+00 8.26616102e-05 3.40521198e-02 10 -1.78202960e+00 -2.42476531e+00 -2.44792014e+00 | -1.78202960e+00 -2.42476531e+00 -2.44792014e+00 11 -1.35563931e-01 2.38419063e+00 4.46894480e+00 | -1.35563931e-01 2.38419063e+00 4.46894480e+00 12 -1.15503610e+00 1.78076939e+00 2.42048057e-01 | -1.15503610e+00 1.78076939e+00 2.42048057e-01 13 -7.18788559e-01 -1.58088869e+00 -3.40030024e+00 | -7.18788559e-01 -1.58088869e+00 -3.40030024e+00 14 9.57050774e+01 -1.61578909e+01 -5.58400597e+01 | 9.57050774e+01 -1.61578909e+01 -5.58400597e+01 15 6.26140624e-01 -1.33685280e-01 6.40832132e-01 | 6.26140624e-01 -1.33685280e-01 6.40832132e-01 16 -1.63564764e+00 -7.31206385e-02 -1.63772623e+00 | -1.63564764e+00 -7.31206385e-02 -1.63772623e+00 17 -6.07121131e+00 1.09602161e+01 -1.19326887e+01 | -6.07121131e+00 1.09602161e+01 -1.19326887e+01 18 7.57244934e-01 7.68183891e-01 1.21157108e+00 | 7.57244934e-01 7.68183891e-01 1.21157108e+00 19 -2.92927322e+00 1.60928400e+00 -2.12461991e+00 | -2.92927322e+00 1.60928400e+00 -2.12461991e+00 20 9.50500248e+00 -5.88698709e+00 1.66611175e+01 | 9.50500248e+00 -5.88698709e+00 1.66611175e+01 21 -6.74128278e+00 -3.58570170e+00 3.78218602e-01 | -6.74128278e+00 -3.58570170e+00 3.78218602e-01 22 -1.51191484e+00 -3.76803854e+00 -2.62610753e+00 | -1.51191484e+00 -3.76803854e+00 -2.62610753e+00 23 3.93245187e+00 1.25496741e+00 9.70543309e-01 | 3.93245187e+00 1.25496741e+00 9.70543309e-01 24 -3.89168368e+00 -1.32987518e+00 8.55259074e-01 | -3.89168368e+00 -1.32987518e+00 8.55259074e-01 25 3.14178787e+00 3.78120919e+00 -1.49866398e-01 | 3.14178787e+00 3.78120919e+00 -1.49866398e-01 26 -8.84710844e+00 -9.37806573e+00 -1.52518179e+01 | -8.84710844e+00 -9.37806573e+00 -1.52518179e+01 27 8.25011907e+00 8.71568648e+00 1.62079017e+01 | 8.25011907e+00 8.71568648e+00 1.62079017e+01 28 -4.80980793e-02 -1.50492534e+00 3.74540772e+00 | -4.80980793e-02 -1.50492534e+00 3.74540772e+00 29 -2.41775170e+00 -2.38825800e-01 -3.16634572e-01 | -2.41775170e+00 -2.38825800e-01 -3.16634572e-01 30 5.36785593e+00 -3.77546053e-01 -2.05215096e+00 | 5.36785593e+00 -3.77546053e-01 -2.05215096e+00 31 -2.11522198e+01 3.19586156e+01 -2.77223011e+01 | -2.11522198e+01 3.19586156e+01 -2.77223011e+01 32 5.83541084e-01 -8.25745239e-01 -1.85001535e+00 | 5.83541084e-01 -8.25745239e-01 -1.85001535e+00 33 5.98075157e+00 -8.63555406e+00 -1.10156444e+01 | 5.98075157e+00 -8.63555406e+00 -1.10156444e+01 34 -3.90147590e+00 3.38668164e+00 1.09552465e+01 | -3.90147590e+00 3.38668164e+00 1.09552465e+01 35 -3.84027232e+00 7.51183996e+00 -4.89198083e+00 | -3.84027232e+00 7.51183996e+00 -4.89198083e+00 36 -2.20953405e+00 -3.64179170e-01 -1.41798770e+00 | -2.20953405e+00 -3.64179170e-01 -1.41798770e+00 37 -1.67881238e+01 -1.62476160e+01 1.36124249e+01 | -1.67881238e+01 -1.62476160e+01 1.36124249e+01 38 -2.42021863e+00 7.93889737e+00 1.06166121e+01 | -2.42021863e+00 7.93889737e+00 1.06166121e+01 39 2.93248741e+00 1.70403778e+00 1.91970772e-01 | 2.93248741e+00 1.70403778e+00 1.91970772e-01 40 -2.88885734e+00 9.39138124e-01 -4.18463763e+00 | -2.88885734e+00 9.39138124e-01 -4.18463763e+00 41 1.74582375e+00 2.37543971e+00 2.99457674e+00 | 1.74582375e+00 2.37543971e+00 2.99457674e+00 42 -8.54770705e-01 -4.26522323e+00 -3.90351194e+00 | -8.54770705e-01 -4.26522323e+00 -3.90351194e+00 43 -1.00953119e+00 4.81192667e+00 2.50436944e+00 | -1.00953119e+00 4.81192667e+00 2.50436944e+00 44 -1.86139260e+00 -3.55186092e+00 -4.72621363e-01 | -1.86139260e+00 -3.55186092e+00 -4.72621363e-01 45 1.23056801e+00 3.96239823e+00 -9.85163651e-02 | 1.23056801e+00 3.96239823e+00 -9.85163651e-02 46 2.05148430e+01 1.21743155e+01 -1.01267436e+01 | 2.05148430e+01 1.21743155e+01 -1.01267436e+01 47 -2.28716492e+00 1.63690166e-01 -1.34721205e+00 | -2.28716492e+00 1.63690166e-01 -1.34721205e+00 48 2.73009448e-01 -6.66400726e-01 -3.30300869e+00 | 2.73009448e-01 -6.66400726e-01 -3.30300869e+00 49 3.16835949e+00 -2.62763786e+00 3.11194900e+00 | 3.16835949e+00 -2.62763786e+00 3.11194900e+00 50 -6.20042171e-01 -7.22967582e-01 -1.54952756e+00 | -6.20042171e-01 -7.22967582e-01 -1.54952756e+00 51 -1.76508900e+00 1.69852743e+00 -3.28795463e+00 | -1.76508900e+00 1.69852743e+00 -3.28795463e+00 52 -1.91762839e+00 -7.02719932e+00 -3.88355679e-01 | -1.91762839e+00 -7.02719932e+00 -3.88355679e-01 53 6.65247594e-01 5.36481164e+00 1.56278178e+00 | 6.65247594e-01 5.36481164e+00 1.56278178e+00 54 4.08595334e-01 1.24264621e+00 -4.85017657e-01 | 4.08595334e-01 1.24264621e+00 -4.85017657e-01 55 1.71530019e+00 -3.55443252e-01 1.30910398e-01 | 1.71530019e+00 -3.55443252e-01 1.30910398e-01 56 6.49563881e-01 -5.19835580e+00 -4.33850132e+00 | 6.49563881e-01 -5.19835580e+00 -4.33850132e+00 57 2.43637647e+00 3.88618989e+00 7.35242283e+00 | 2.43637647e+00 3.88618989e+00 7.35242283e+00 58 2.28719334e+01 -3.31600345e+01 2.87260029e+01 | 2.28719334e+01 -3.31600345e+01 2.87260029e+01 59 -2.77267620e+00 1.24388161e+00 -2.05560214e+00 | -2.77267620e+00 1.24388161e+00 -2.05560214e+00 60 -1.12405576e+00 3.16636017e+00 1.97410167e+00 | -1.12405576e+00 3.16636017e+00 1.97410167e+00 61 -9.93239465e-01 -2.68142554e+00 1.41031098e+00 | -9.93239465e-01 -2.68142554e+00 1.41031098e+00 62 1.69401451e+00 -2.49816027e+00 -1.74211648e+00 | 1.69401451e+00 -2.49816027e+00 -1.74211648e+00 63 2.63585066e+00 2.36896282e-01 9.43782302e-01 | 2.63585066e+00 2.36896282e-01 9.43782302e-01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Cu (Configuration in file "config-Cu.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [48, 35, 45, 13, 38, 57, 31, 41, 33, 32, 46, 14, 62, 3, 11, 52, 22, 25, 23, 53, 21, 20, 16, 18, 39, 17, 56, 59, 50, 36, 34, 6, 9, 8, 30, 1, 29, 60, 4, 24, 61, 7, 51, 58, 54, 2, 10, 55, 0, 63, 28, 42, 15, 19, 44, 47, 26, 5, 43, 27, 37, 40, 12, 49] Energy requirement: V(r_(PI 1),...,r_(PI N)) = V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). V(r_(PI 1),...,r_(PI N)) = -82.1444602001729 V(r_1,...,r_N) = -82.1444602001729 Forces requirement: f_(PI i)(r_(PI 1),...,r_(PI N)) = f_i(r_1,...,r_N), where r_i is the position of atom i, f_i is the force on atom i and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). i f_(PI i)(r_(PI 1),...,r_(PI N)) f_i(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------- 0 -9.49250782e-01 -9.44456579e-01 -1.30085923e+00 | -9.49250782e-01 -9.44456579e-01 -1.30085923e+00 1 1.26870551e+01 -1.06837264e+01 -1.06819700e+01 | 1.26870551e+01 -1.06837264e+01 -1.06819700e+01 2 -3.59928548e+00 -1.17170666e+00 -6.02659742e-01 | -3.59928548e+00 -1.17170666e+00 -6.02659742e-01 3 2.44400568e+00 1.14730741e-01 -1.18305571e+00 | 2.44400568e+00 1.14730741e-01 -1.18305571e+00 4 -1.46366852e+00 -4.96697309e-01 1.61513318e-01 | -1.46366852e+00 -4.96697309e-01 1.61513318e-01 5 -8.03965680e-01 4.11522461e+00 -2.79527731e+00 | -8.03965680e-01 4.11522461e+00 -2.79527731e+00 6 -1.20177267e+01 1.10517927e+01 1.20319528e+01 | -1.20177267e+01 1.10517927e+01 1.20319528e+01 7 5.32853833e-01 9.21774287e-01 7.39702499e-01 | 5.32853833e-01 9.21774287e-01 7.39702499e-01 8 -2.08409432e+01 -6.12402969e+00 -8.38646159e+00 | -2.08409432e+01 -6.12402969e+00 -8.38646159e+00 9 2.02368618e+01 3.10620740e+00 8.33116990e+00 | 2.02368618e+01 3.10620740e+00 8.33116990e+00 10 1.88855075e+00 1.81628830e+00 -1.60175901e-01 | 1.88855075e+00 1.81628830e+00 -1.60175901e-01 11 1.18692439e+00 -2.78901920e+00 -1.69011378e+00 | 1.18692439e+00 -2.78901920e+00 -1.69011378e+00 12 -1.14346821e+00 -1.23387489e+00 -2.03982849e+00 | -1.14346821e+00 -1.23387489e+00 -2.03982849e+00 13 1.12242814e+00 2.23305565e+00 3.40841159e+00 | 1.12242814e+00 2.23305565e+00 3.40841159e+00 14 -2.03491193e+00 -5.94596570e-01 -1.88854769e+00 | -2.03491193e+00 -5.94596570e-01 -1.88854769e+00 15 1.71631790e+00 2.38161023e+00 -4.85131075e-01 | 1.71631790e+00 2.38161023e+00 -4.85131075e-01 16 -1.06403867e+00 -3.08563630e+00 -5.50911343e-01 | -1.06403867e+00 -3.08563630e+00 -5.50911343e-01 17 2.26275167e+00 2.19397262e+00 1.11940760e+00 | 2.26275167e+00 2.19397262e+00 1.11940760e+00 18 -2.92400194e+00 -1.04627453e+00 -2.06045251e+00 | -2.92400194e+00 -1.04627453e+00 -2.06045251e+00 19 6.02145814e-01 1.46095206e+00 1.66383037e+00 | 6.02145814e-01 1.46095206e+00 1.66383037e+00 20 -2.15899041e+00 3.25029012e+00 1.58177407e+00 | -2.15899041e+00 3.25029012e+00 1.58177407e+00 21 2.25533558e+00 1.34991272e+00 -7.53224515e-01 | 2.25533558e+00 1.34991272e+00 -7.53224515e-01 22 -8.38300596e-03 -8.29744475e-01 8.05363466e-01 | -8.38300596e-03 -8.29744475e-01 8.05363466e-01 23 -4.58561160e-01 2.23586221e+00 -1.03131880e+00 | -4.58561160e-01 2.23586221e+00 -1.03131880e+00 24 -8.47224780e+00 -1.36419909e+01 -1.40638318e+01 | -8.47224780e+00 -1.36419909e+01 -1.40638318e+01 25 5.98215290e+00 1.17282766e+01 1.33120998e+01 | 5.98215290e+00 1.17282766e+01 1.33120998e+01 26 -2.73373192e+00 -1.48354639e+00 -9.03134308e-01 | -2.73373192e+00 -1.48354639e+00 -9.03134308e-01 27 1.64290679e+00 -1.16622626e-02 2.45212165e+00 | 1.64290679e+00 -1.16622626e-02 2.45212165e+00 28 -1.72843278e+00 2.10702598e+00 1.17398756e+00 | -1.72843278e+00 2.10702598e+00 1.17398756e+00 29 3.52170089e-01 3.08448100e-02 2.49394006e+00 | 3.52170089e-01 3.08448100e-02 2.49394006e+00 30 1.98655552e+00 -3.22721307e+00 7.80665696e-02 | 1.98655552e+00 -3.22721307e+00 7.80665696e-02 31 -1.54922049e-01 1.74958179e+00 1.90988528e+00 | -1.54922049e-01 1.74958179e+00 1.90988528e+00 32 9.42607370e-01 1.24181072e+00 -6.78648219e-01 | 9.42607370e-01 1.24181072e+00 -6.78648219e-01 33 -1.72122035e-01 -3.79765864e+00 -1.24567170e+00 | -1.72122035e-01 -3.79765864e+00 -1.24567170e+00 34 -2.15350737e+00 2.83076443e-01 -9.97780692e+00 | -2.15350737e+00 2.83076443e-01 -9.97780692e+00 35 4.66391663e+00 2.81059697e+00 7.17168357e+00 | 4.66391663e+00 2.81059697e+00 7.17168357e+00 36 1.16120314e-01 2.08025335e+00 -7.67198141e-01 | 1.16120314e-01 2.08025335e+00 -7.67198141e-01 37 -2.00683314e+00 -2.71837603e+00 2.20049307e+00 | -2.00683314e+00 -2.71837603e+00 2.20049307e+00 38 -1.26956545e+00 1.10302966e+00 2.57043652e+00 | -1.26956545e+00 1.10302966e+00 2.57043652e+00 39 -1.88665566e+00 -1.17030196e+00 6.86535749e-01 | -1.88665566e+00 -1.17030196e+00 6.86535749e-01 40 2.54985254e+00 -5.28099572e-01 2.70744350e+00 | 2.54985254e+00 -5.28099572e-01 2.70744350e+00 41 3.93930728e-01 -3.05122629e+00 5.71780955e-01 | 3.93930728e-01 -3.05122629e+00 5.71780955e-01 42 -6.90427774e-01 -6.68490220e-01 -2.25239181e+00 | -6.90427774e-01 -6.68490220e-01 -2.25239181e+00 43 3.52508341e+00 -3.26658697e+00 4.70080214e-01 | 3.52508341e+00 -3.26658697e+00 4.70080214e-01 44 -8.05557682e-01 -1.11202371e+00 -1.76927129e+00 | -8.05557682e-01 -1.11202371e+00 -1.76927129e+00 45 1.52836435e-01 2.18692859e+00 6.38430865e-01 | 1.52836435e-01 2.18692859e+00 6.38430865e-01 46 -8.56994628e-01 -3.16731268e+00 -4.57939487e+00 | -8.56994628e-01 -3.16731268e+00 -4.57939487e+00 47 3.45593533e+00 5.50568851e+00 3.04349812e+00 | 3.45593533e+00 5.50568851e+00 3.04349812e+00 48 9.63169752e-01 -8.09421157e-01 -1.07819211e+00 | 9.63169752e-01 -8.09421157e-01 -1.07819211e+00 49 3.72498313e-01 -3.11070890e+00 -4.07812663e-01 | 3.72498313e-01 -3.11070890e+00 -4.07812663e-01 50 2.09840135e+00 -1.62295173e+00 1.93654883e+00 | 2.09840135e+00 -1.62295173e+00 1.93654883e+00 51 -1.42338255e-01 -1.51859796e+00 -3.70550637e-01 | -1.42338255e-01 -1.51859796e+00 -3.70550637e-01 52 2.36454213e-01 1.01753786e+00 -3.37370085e+00 | 2.36454213e-01 1.01753786e+00 -3.37370085e+00 53 1.01714882e-01 1.50134165e+00 2.61408804e-01 | 1.01714882e-01 1.50134165e+00 2.61408804e-01 54 -2.34494683e+00 5.05328652e-01 2.90097982e-01 | -2.34494683e+00 5.05328652e-01 2.90097982e-01 55 2.61963650e+00 1.03174651e+00 1.63445307e+00 | 2.61963650e+00 1.03174651e+00 1.63445307e+00 56 -7.91731727e-01 6.58073800e-01 8.12268522e-01 | -7.91731727e-01 6.58073800e-01 8.12268522e-01 57 8.69983218e-02 -2.25085910e+00 5.62366512e-01 | 8.69983218e-02 -2.25085910e+00 5.62366512e-01 58 2.62405731e+00 -1.55582246e+00 -4.03334039e+00 | 2.62405731e+00 -1.55582246e+00 -4.03334039e+00 59 -3.27085284e-02 1.23404998e+00 2.63403234e+00 | -3.27085284e-02 1.23404998e+00 2.63403234e+00 60 -2.93340249e+00 2.51910416e+00 -3.57153794e-01 | -2.93340249e+00 2.51910416e+00 -3.57153794e-01 61 -2.76792226e-01 2.36072040e+00 9.28244170e-01 | -2.76792226e-01 2.36072040e+00 9.28244170e-01 62 -5.02300456e+00 -2.30155662e+00 6.56741215e-01 | -5.02300456e+00 -2.30155662e+00 6.56741215e-01 63 2.14088929e+00 2.12747918e+00 4.28316642e-01 | 2.14088929e+00 2.12747918e+00 4.28316642e-01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Fe (Configuration in file "config-Fe.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [62, 38, 29, 24, 34, 33, 14, 56, 15, 50, 31, 53, 41, 44, 6, 8, 25, 46, 45, 63, 27, 49, 23, 22, 3, 16, 55, 20, 59, 2, 61, 10, 42, 5, 4, 54, 48, 40, 1, 43, 37, 12, 32, 39, 13, 18, 17, 52, 36, 21, 9, 60, 47, 11, 35, 26, 7, 58, 57, 28, 51, 30, 0, 19] Energy requirement: V(r_(PI 1),...,r_(PI N)) = V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). V(r_(PI 1),...,r_(PI N)) = 50.485170400113205 V(r_1,...,r_N) = 50.485170400113184 Forces requirement: f_(PI i)(r_(PI 1),...,r_(PI N)) = f_i(r_1,...,r_N), where r_i is the position of atom i, f_i is the force on atom i and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). i f_(PI i)(r_(PI 1),...,r_(PI N)) f_i(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------- 0 3.83861292e+00 8.53888914e+00 8.28882927e+00 | 3.83861292e+00 8.53888914e+00 8.28882927e+00 1 -1.70067880e-01 3.72907221e+00 -1.67971447e+00 | -1.70067880e-01 3.72907221e+00 -1.67971447e+00 2 -2.83094188e+00 -2.09581506e+00 8.13615200e+00 | -2.83094188e+00 -2.09581506e+00 8.13615200e+00 3 -4.66878145e+00 -8.43054837e-01 2.15914587e+00 | -4.66878145e+00 -8.43054837e-01 2.15914587e+00 4 -3.23420653e+00 5.49443253e+00 2.47150076e+00 | -3.23420653e+00 5.49443253e+00 2.47150076e+00 5 -2.57848830e+00 -2.92093060e+00 -4.09838032e+00 | -2.57848830e+00 -2.92093060e+00 -4.09838032e+00 6 1.04752470e+01 -4.48853624e+00 -7.51116975e+00 | 1.04752470e+01 -4.48853624e+00 -7.51116975e+00 7 -6.24049487e-01 4.94236470e-01 -1.18768607e+00 | -6.24049487e-01 4.94236470e-01 -1.18768607e+00 8 -3.43984802e+00 4.08909946e+00 2.96430495e-01 | -3.43984802e+00 4.08909946e+00 2.96430495e-01 9 4.96553018e+01 -4.36407108e+01 -3.84395444e+01 | 4.96553018e+01 -4.36407108e+01 -3.84395444e+01 10 -6.26074768e+00 -1.42271144e+00 1.64490964e+00 | -6.26074768e+00 -1.42271144e+00 1.64490964e+00 11 2.28682869e+00 -3.57339587e+00 2.15384532e+00 | 2.28682869e+00 -3.57339587e+00 2.15384532e+00 12 -3.40286276e+00 6.24350876e+00 -4.14854946e-01 | -3.40286276e+00 6.24350876e+00 -4.14854946e-01 13 -7.77646121e+00 7.72501253e+00 7.07079193e-01 | -7.77646121e+00 7.72501253e+00 7.07079193e-01 14 -4.44207752e+01 3.99345168e+01 4.33968873e+01 | -4.44207752e+01 3.99345168e+01 4.33968873e+01 15 -1.74572721e+00 -2.07884626e+00 -3.99703426e+00 | -1.74572721e+00 -2.07884626e+00 -3.99703426e+00 16 9.23171612e+00 -2.44106476e+00 6.08519869e+00 | 9.23171612e+00 -2.44106476e+00 6.08519869e+00 17 -1.29928102e+01 1.83369451e+01 -1.47315338e+01 | -1.29928102e+01 1.83369451e+01 -1.47315338e+01 18 1.68587100e+00 5.23504320e-01 1.72316305e+00 | 1.68587100e+00 5.23504320e-01 1.72316305e+00 19 -2.08408296e-01 -6.47743637e+00 2.50267786e+00 | -2.08408296e-01 -6.47743637e+00 2.50267786e+00 20 5.81643294e+00 -2.06414579e+01 1.33933294e+01 | 5.81643294e+00 -2.06414579e+01 1.33933294e+01 21 -1.51334807e+01 1.88491989e+00 8.47696408e+00 | -1.51334807e+01 1.88491989e+00 8.47696408e+00 22 4.72688888e+00 -8.10044639e+00 1.49692942e-01 | 4.72688888e+00 -8.10044639e+00 1.49692942e-01 23 8.86723119e+00 -1.14976398e+00 1.85378862e+00 | 8.86723119e+00 -1.14976398e+00 1.85378862e+00 24 3.61867946e+00 -3.72188716e+00 -3.30812850e+00 | 3.61867946e+00 -3.72188716e+00 -3.30812850e+00 25 1.03585471e+00 1.24304186e+00 1.38165481e+00 | 1.03585471e+00 1.24304186e+00 1.38165481e+00 26 -1.31316881e+00 1.46145131e+00 4.66859217e+00 | -1.31316881e+00 1.46145131e+00 4.66859217e+00 27 -2.05000535e+00 -1.75311058e+00 -6.91681233e-01 | -2.05000535e+00 -1.75311058e+00 -6.91681233e-01 28 -2.10004337e+00 3.94966676e+00 3.06214784e-01 | -2.10004337e+00 3.94966676e+00 3.06214784e-01 29 -4.12095285e-01 -1.72325019e+00 3.30727231e+00 | -4.12095285e-01 -1.72325019e+00 3.30727231e+00 30 5.80492258e+00 5.08962984e+00 -8.88785892e+00 | 5.80492258e+00 5.08962984e+00 -8.88785892e+00 31 2.29351991e+00 3.64758748e+00 3.75127378e-01 | 2.29351991e+00 3.64758748e+00 3.75127378e-01 32 7.78902804e+00 5.64606861e+00 3.65865061e+00 | 7.78902804e+00 5.64606861e+00 3.65865061e+00 33 -8.73232110e-01 -7.61129667e+00 4.90989456e-01 | -8.73232110e-01 -7.61129667e+00 4.90989456e-01 34 -1.76796868e-01 3.28012377e+00 1.70441468e+00 | -1.76796868e-01 3.28012377e+00 1.70441468e+00 35 -5.50411986e-01 -4.05255342e-01 1.08420555e+00 | -5.50411986e-01 -4.05255342e-01 1.08420555e+00 36 -4.18165027e+00 6.47851517e+00 -7.63305002e+00 | -4.18165027e+00 6.47851517e+00 -7.63305002e+00 37 -7.25809681e-01 2.36538121e+00 -1.12134760e+00 | -7.25809681e-01 2.36538121e+00 -1.12134760e+00 38 4.96237952e+00 4.29325676e+00 1.51172490e-02 | 4.96237952e+00 4.29325676e+00 1.51172490e-02 39 2.30388700e+00 -4.13917111e+00 -4.65767376e+00 | 2.30388700e+00 -4.13917111e+00 -4.65767376e+00 40 6.74799568e+00 -3.18113168e-01 5.85492466e-01 | 6.74799568e+00 -3.18113168e-01 5.85492466e-01 41 -2.85548790e+00 7.81558990e-01 2.98673485e-01 | -2.85548790e+00 7.81558990e-01 2.98673485e-01 42 4.88362575e+00 -3.73988599e+00 1.34040044e+00 | 4.88362575e+00 -3.73988599e+00 1.34040044e+00 43 -4.19272509e+00 -1.37342627e+00 -3.55142637e+00 | -4.19272509e+00 -1.37342627e+00 -3.55142637e+00 44 -1.37824852e-01 6.61130534e+00 3.12612070e+00 | -1.37824852e-01 6.61130534e+00 3.12612070e+00 45 -5.64153879e+00 -7.79739579e-01 -5.68402566e+00 | -5.64153879e+00 -7.79739579e-01 -5.68402566e+00 46 -5.31566958e+00 -5.34694189e-01 -6.30028474e+00 | -5.31566958e+00 -5.34694189e-01 -6.30028474e+00 47 4.57760044e+00 -5.27921492e+00 6.67918430e+00 | 4.57760044e+00 -5.27921492e+00 6.67918430e+00 48 -2.01105298e+01 -1.06783939e+01 -2.01631819e+01 | -2.01105298e+01 -1.06783939e+01 -2.01631819e+01 49 1.93362414e+01 6.46491665e+00 2.11378538e+01 | 1.93362414e+01 6.46491665e+00 2.11378538e+01 50 -1.00992548e+00 3.57473653e+00 -2.63360885e+00 | -1.00992548e+00 3.57473653e+00 -2.63360885e+00 51 -9.94073525e-01 -7.48355759e+00 -1.04050631e+01 | -9.94073525e-01 -7.48355759e+00 -1.04050631e+01 52 1.21746617e+00 3.06325393e+00 2.32274179e+00 | 1.21746617e+00 3.06325393e+00 2.32274179e+00 53 -7.50365879e-01 -3.81330094e+00 -1.72919722e+00 | -7.50365879e-01 -3.81330094e+00 -1.72919722e+00 54 -5.16812673e-01 1.11472028e+00 5.65162939e-01 | -5.16812673e-01 1.11472028e+00 5.65162939e-01 55 -1.20510139e+00 -6.58884817e-01 -4.81456044e-02 | -1.20510139e+00 -6.58884817e-01 -4.81456044e-02 56 1.39761602e+00 -1.70460596e+00 2.27123840e+00 | 1.39761602e+00 -1.70460596e+00 2.27123840e+00 57 -6.30586423e+01 -5.49535184e+01 3.52024213e+01 | -6.30586423e+01 -5.49535184e+01 3.52024213e+01 58 6.52677241e+01 5.45366307e+01 -3.34791744e+01 | 6.52677241e+01 5.45366307e+01 -3.34791744e+01 59 -1.60807862e+00 -2.52462298e+00 1.06262190e+00 | -1.60807862e+00 -2.52462298e+00 1.06262190e+00 60 4.86362842e+00 3.17295285e+00 -4.19190256e+00 | 4.86362842e+00 3.17295285e+00 -4.19190256e+00 61 -3.59882395e+00 2.38353688e+00 -4.52283994e+00 | -3.59882395e+00 2.38353688e+00 -4.52283994e+00 62 -1.45338976e+00 -2.62740313e+00 -5.23334784e+00 | -1.45338976e+00 -2.62740313e+00 -5.23334784e+00 63 1.63556030e+00 -4.54968707e-01 1.27811115e+00 | 1.63556030e+00 -4.54968707e-01 1.27811115e+00 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Ni (Configuration in file "config-Ni.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [19, 6, 54, 8, 45, 56, 1, 17, 3, 47, 21, 58, 25, 62, 52, 33, 20, 7, 41, 0, 16, 10, 37, 31, 32, 12, 53, 39, 34, 61, 35, 23, 24, 15, 28, 30, 51, 22, 60, 27, 50, 18, 44, 49, 42, 4, 48, 9, 46, 43, 40, 36, 14, 26, 2, 57, 5, 55, 11, 63, 38, 29, 13, 59] Energy requirement: V(r_(PI 1),...,r_(PI N)) = V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). V(r_(PI 1),...,r_(PI N)) = -6.485764051246654 V(r_1,...,r_N) = -6.485764051246722 Forces requirement: f_(PI i)(r_(PI 1),...,r_(PI N)) = f_i(r_1,...,r_N), where r_i is the position of atom i, f_i is the force on atom i and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). i f_(PI i)(r_(PI 1),...,r_(PI N)) f_i(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------- 0 8.44293980e-01 5.00876930e-01 8.23679949e-01 | 8.44293980e-01 5.00876930e-01 8.23679949e-01 1 -2.91595837e+01 1.68311556e+01 -2.72690715e+01 | -2.91595837e+01 1.68311556e+01 -2.72690715e+01 2 1.24518908e+00 3.94343356e-01 1.39326199e+00 | 1.24518908e+00 3.94343356e-01 1.39326199e+00 3 4.23916113e+00 -3.39925929e+00 -1.41102641e+01 | 4.23916113e+00 -3.39925929e+00 -1.41102641e+01 4 2.85261411e+01 -1.54287901e+01 2.81573068e+01 | 2.85261411e+01 -1.54287901e+01 2.81573068e+01 5 -5.99107971e-01 -1.07839677e+00 -1.19692804e+00 | -5.99107971e-01 -1.07839677e+00 -1.19692804e+00 6 4.30582703e-01 -4.26112035e+00 -1.82651491e+00 | 4.30582703e-01 -4.26112035e+00 -1.82651491e+00 7 3.36697796e+00 2.57990958e+00 -9.52510331e-01 | 3.36697796e+00 2.57990958e+00 -9.52510331e-01 8 -3.01182203e+00 1.06589163e-01 -1.54427445e+00 | -3.01182203e+00 1.06589163e-01 -1.54427445e+00 9 -7.06712525e-01 3.83762774e+00 3.27784236e+00 | -7.06712525e-01 3.83762774e+00 3.27784236e+00 10 3.00693666e-01 1.48567425e+00 -1.97070808e-01 | 3.00693666e-01 1.48567425e+00 -1.97070808e-01 11 2.98981831e+01 -1.67362792e+01 -1.23556482e+01 | 2.98981831e+01 -1.67362792e+01 -1.23556482e+01 12 1.68327362e+00 -1.40518497e+00 9.87626735e-01 | 1.68327362e+00 -1.40518497e+00 9.87626735e-01 13 3.21901955e+00 -3.71163253e+00 -7.13713631e-01 | 3.21901955e+00 -3.71163253e+00 -7.13713631e-01 14 -2.16566224e+00 -8.54770137e+00 -4.01160220e+00 | -2.16566224e+00 -8.54770137e+00 -4.01160220e+00 15 4.33858941e+00 9.32263881e+00 2.12659359e+00 | 4.33858941e+00 9.32263881e+00 2.12659359e+00 16 1.58658954e+00 5.77558831e-01 3.37203937e-01 | 1.58658954e+00 5.77558831e-01 3.37203937e-01 17 -4.12209044e+00 2.05855566e+00 8.46110748e-01 | -4.12209044e+00 2.05855566e+00 8.46110748e-01 18 7.21435669e-01 -1.30108274e+00 2.02918174e+00 | 7.21435669e-01 -1.30108274e+00 2.02918174e+00 19 -2.66802808e+00 5.78116900e-01 -2.40233785e+00 | -2.66802808e+00 5.78116900e-01 -2.40233785e+00 20 -6.38915802e-01 -1.08468161e+00 1.56820843e+01 | -6.38915802e-01 -1.08468161e+00 1.56820843e+01 21 1.39557316e+00 -1.91141518e+00 -1.07966769e+00 | 1.39557316e+00 -1.91141518e+00 -1.07966769e+00 22 -7.00598419e-01 -4.14408592e+00 -1.75439838e+00 | -7.00598419e-01 -4.14408592e+00 -1.75439838e+00 23 2.35388992e+00 3.23523991e+00 2.54403638e+00 | 2.35388992e+00 3.23523991e+00 2.54403638e+00 24 1.49643533e+00 1.21196180e+00 1.03369078e+00 | 1.49643533e+00 1.21196180e+00 1.03369078e+00 25 -9.25944584e+01 -5.85961087e+01 7.34235793e+01 | -9.25944584e+01 -5.85961087e+01 7.34235793e+01 26 9.10378726e+01 5.66779793e+01 -7.20290404e+01 | 9.10378726e+01 5.66779793e+01 -7.20290404e+01 27 -5.07751700e-01 -4.75544384e-01 2.91858194e-01 | -5.07751700e-01 -4.75544384e-01 2.91858194e-01 28 -3.23887166e+01 1.63735857e+01 1.20907369e+01 | -3.23887166e+01 1.63735857e+01 1.20907369e+01 29 9.19244407e-01 -4.04868047e+00 -4.36317879e-01 | 9.19244407e-01 -4.04868047e+00 -4.36317879e-01 30 1.86240370e+00 -3.21204910e+00 1.96438597e+00 | 1.86240370e+00 -3.21204910e+00 1.96438597e+00 31 -1.56300171e+01 1.42905510e+01 -5.68067773e+00 | -1.56300171e+01 1.42905510e+01 -5.68067773e+00 32 1.33071815e-01 -3.25193228e-02 -2.50549146e+00 | 1.33071815e-01 -3.25193228e-02 -2.50549146e+00 33 -3.72728114e+01 2.34802355e+01 -2.63372518e+01 | -3.72728114e+01 2.34802355e+01 -2.63372518e+01 34 -2.79964158e+00 -2.48201301e+00 -1.90815166e+00 | -2.79964158e+00 -2.48201301e+00 -1.90815166e+00 35 -1.61410423e+00 7.02373128e-01 1.31228791e+00 | -1.61410423e+00 7.02373128e-01 1.31228791e+00 36 3.99919717e+01 -1.98293304e+01 2.70751968e+01 | 3.99919717e+01 -1.98293304e+01 2.70751968e+01 37 -7.91360616e+00 -1.00860830e+00 5.88967806e+00 | -7.91360616e+00 -1.00860830e+00 5.88967806e+00 38 4.80670755e-01 -2.32334444e+00 -1.17179240e+00 | 4.80670755e-01 -2.32334444e+00 -1.17179240e+00 39 2.23885307e+00 3.11979053e+00 -1.27133766e+00 | 2.23885307e+00 3.11979053e+00 -1.27133766e+00 40 -2.06953765e+00 1.82702962e+00 2.22906235e-01 | -2.06953765e+00 1.82702962e+00 2.22906235e-01 41 -3.38048065e+00 2.11151564e-01 4.72533221e+00 | -3.38048065e+00 2.11151564e-01 4.72533221e+00 42 -2.53896790e+00 6.70407633e+00 -4.32401506e+00 | -2.53896790e+00 6.70407633e+00 -4.32401506e+00 43 3.30066563e+00 -1.42165750e+00 -5.18987465e-01 | 3.30066563e+00 -1.42165750e+00 -5.18987465e-01 44 -2.29169712e+00 -2.50748872e+00 -2.38302652e+00 | -2.29169712e+00 -2.50748872e+00 -2.38302652e+00 45 -7.88273387e-01 4.80970133e+00 1.32194390e+00 | -7.88273387e-01 4.80970133e+00 1.32194390e+00 46 8.54203864e+00 1.57041408e+00 -8.37035501e+00 | 8.54203864e+00 1.57041408e+00 -8.37035501e+00 47 -1.37241133e+00 -2.18811607e+00 7.61322320e-01 | -1.37241133e+00 -2.18811607e+00 7.61322320e-01 48 -8.92710803e-01 9.97955234e-01 2.08776716e+00 | -8.92710803e-01 9.97955234e-01 2.08776716e+00 49 -5.02811708e+01 2.94266983e+01 -1.97045259e+01 | -5.02811708e+01 2.94266983e+01 -1.97045259e+01 50 -3.32509509e+00 2.63018000e+00 -5.38700885e-01 | -3.32509509e+00 2.63018000e+00 -5.38700885e-01 51 -2.38440609e+01 3.66426523e+01 -1.94615078e+01 | -2.38440609e+01 3.66426523e+01 -1.94615078e+01 52 5.48353422e+01 -3.11663682e+01 2.05368238e+01 | 5.48353422e+01 -3.11663682e+01 2.05368238e+01 53 -2.30795891e+00 -1.24596731e+00 2.14223047e+00 | -2.30795891e+00 -1.24596731e+00 2.14223047e+00 54 -3.66858546e-01 -3.56113409e-01 -5.74563156e-01 | -3.66858546e-01 -3.56113409e-01 -5.74563156e-01 55 2.04454312e+00 -3.88025282e-01 -4.15220976e-01 | 2.04454312e+00 -3.88025282e-01 -4.15220976e-01 56 2.27449419e+00 -1.39345671e+00 2.20973661e+00 | 2.27449419e+00 -1.39345671e+00 2.20973661e+00 57 4.05173167e+00 1.80346495e+00 -2.12533203e+00 | 4.05173167e+00 1.80346495e+00 -2.12533203e+00 58 1.28674322e+01 -1.19041117e+01 8.51341813e+00 | 1.28674322e+01 -1.19041117e+01 8.51341813e+00 59 -1.94068135e+00 -1.91230282e+00 -5.97142222e-01 | -1.94068135e+00 -1.91230282e+00 -5.97142222e-01 60 -1.20934091e+00 1.29554362e+00 -1.91586369e+00 | -1.20934091e+00 1.29554362e+00 -1.91586369e+00 61 -1.33808063e+00 1.03470174e+00 1.13089784e-01 | -1.33808063e+00 1.03470174e+00 1.13089784e-01 62 2.18327737e+01 -3.51599963e+01 2.01356692e+01 | 2.18327737e+01 -3.51599963e+01 2.01356692e+01 63 3.81816092e-01 -1.65690047e+00 -2.37327836e+00 | 3.81816092e-01 -1.65690047e+00 -2.37327836e+00 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MIXED STRUCTURE -- Species = Co Cr Cu Fe Ni (Configuration in file "config-CoCrCuFeNi.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [27, 36, 19, 30, 45, 15, 61, 46, 10, 41, 8, 26, 18, 49, 40, 5, 44, 53, 12, 2, 35, 22, 21, 63, 28, 33, 11, 0, 24, 50, 3, 54, 38, 25, 43, 20, 1, 60, 32, 47, 14, 9, 57, 34, 16, 4, 7, 39, 51, 13, 29, 48, 52, 17, 31, 59, 56, 42, 58, 55, 37, 6, 62, 23] Energy requirement: V(r_(PI 1),...,r_(PI N)) = V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). V(r_(PI 1),...,r_(PI N)) = -51.69584683617079 V(r_1,...,r_N) = -51.69584683617076 Forces requirement: f_(PI i)(r_(PI 1),...,r_(PI N)) = f_i(r_1,...,r_N), where r_i is the position of atom i, f_i is the force on atom i and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). i f_(PI i)(r_(PI 1),...,r_(PI N)) f_i(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------- 0 -2.01450058e+00 -1.37415174e+00 8.62441939e-01 | -2.01450058e+00 -1.37415174e+00 8.62441939e-01 1 1.11706641e+00 5.15791318e+00 1.92920860e+00 | 1.11706641e+00 5.15791318e+00 1.92920860e+00 2 -2.27938112e+00 -2.28980677e+00 -1.14622061e+00 | -2.27938112e+00 -2.28980677e+00 -1.14622061e+00 3 3.43500998e+00 -2.23357515e+00 6.33378595e+00 | 3.43500998e+00 -2.23357515e+00 6.33378595e+00 4 -7.04933120e+00 3.72398846e-01 9.57500768e-01 | -7.04933120e+00 3.72398846e-01 9.57500768e-01 5 -5.52135406e-01 7.25309765e-01 5.15898928e-01 | -5.52135406e-01 7.25309765e-01 5.15898928e-01 6 2.04984419e+00 -5.37139551e+00 -4.20238627e+00 | 2.04984419e+00 -5.37139551e+00 -4.20238627e+00 7 2.12931699e+00 3.06525202e+00 -8.22064060e-01 | 2.12931699e+00 3.06525202e+00 -8.22064060e-01 8 1.27262804e+00 1.06911335e+00 -1.39825115e+00 | 1.27262804e+00 1.06911335e+00 -1.39825115e+00 9 -4.86726714e-01 -2.93876882e+00 2.41269227e+00 | -4.86726714e-01 -2.93876882e+00 2.41269227e+00 10 -2.35699657e+00 4.81904650e+00 5.03250946e+00 | -2.35699657e+00 4.81904650e+00 5.03250946e+00 11 -3.51662761e+00 -2.04234988e+00 -3.29486825e-01 | -3.51662761e+00 -2.04234988e+00 -3.29486825e-01 12 -4.41047152e+00 -6.69603575e-01 -2.16016402e+00 | -4.41047152e+00 -6.69603575e-01 -2.16016402e+00 13 4.03740890e+00 -1.01271013e+00 1.82835230e+00 | 4.03740890e+00 -1.01271013e+00 1.82835230e+00 14 1.34457991e+00 3.08201329e+00 -2.96173546e+00 | 1.34457991e+00 3.08201329e+00 -2.96173546e+00 15 -1.68117165e+00 1.06861298e+00 1.74020658e+00 | -1.68117165e+00 1.06861298e+00 1.74020658e+00 16 -3.19916607e+00 -1.90145211e+00 -1.30505988e+00 | -3.19916607e+00 -1.90145211e+00 -1.30505988e+00 17 2.00914007e+00 6.63065876e-01 4.22628319e+00 | 2.00914007e+00 6.63065876e-01 4.22628319e+00 18 2.12126005e+00 2.15084379e+00 -3.91704543e-01 | 2.12126005e+00 2.15084379e+00 -3.91704543e-01 19 3.04175125e-01 -1.64300947e+00 8.05479987e-01 | 3.04175125e-01 -1.64300947e+00 8.05479987e-01 20 -1.41802480e+00 -3.02727792e+00 -2.14374652e+00 | -1.41802480e+00 -3.02727792e+00 -2.14374652e+00 21 2.03801317e+00 2.32225958e+00 3.33511465e+00 | 2.03801317e+00 2.32225958e+00 3.33511465e+00 22 -2.65998405e+00 -2.35074337e+00 -1.58711923e+00 | -2.65998405e+00 -2.35074337e+00 -1.58711923e+00 23 1.56493176e+00 2.46743291e+00 -1.55201810e+00 | 1.56493176e+00 2.46743291e+00 -1.55201810e+00 24 -4.73690864e-01 8.94755114e-01 -4.66984237e+00 | -4.73690864e-01 8.94755114e-01 -4.66984237e+00 25 -4.90407934e-01 1.27339013e+00 3.45328822e+00 | -4.90407934e-01 1.27339013e+00 3.45328822e+00 26 8.83022491e-01 -5.84005705e-01 -4.72390863e-01 | 8.83022491e-01 -5.84005705e-01 -4.72390863e-01 27 -5.45833918e-01 2.43815358e-01 1.74552970e+00 | -5.45833918e-01 2.43815358e-01 1.74552970e+00 28 1.53681240e+00 1.65076420e+00 -4.04377474e+00 | 1.53681240e+00 1.65076420e+00 -4.04377474e+00 29 -1.28769885e+00 3.22359489e-01 5.75447157e-01 | -1.28769885e+00 3.22359489e-01 5.75447157e-01 30 -1.75569013e+00 -1.06534616e+00 -6.44059447e+00 | -1.75569013e+00 -1.06534616e+00 -6.44059447e+00 31 -1.70010375e-01 1.46777000e+00 -1.23309282e-01 | -1.70010375e-01 1.46777000e+00 -1.23309282e-01 32 1.83345350e+00 2.46355524e+00 -8.83897917e-01 | 1.83345350e+00 2.46355524e+00 -8.83897917e-01 33 -8.38334285e+00 -9.93933180e+00 2.65853001e+00 | -8.38334285e+00 -9.93933180e+00 2.65853001e+00 34 8.19481901e+00 7.18831669e+00 -2.55665997e+00 | 8.19481901e+00 7.18831669e+00 -2.55665997e+00 35 -1.90450964e+00 -2.92409363e+00 6.57530280e-01 | -1.90450964e+00 -2.92409363e+00 6.57530280e-01 36 -4.37674538e-01 3.63266904e-01 -3.47450461e+00 | -4.37674538e-01 3.63266904e-01 -3.47450461e+00 37 2.91247570e+00 3.18739694e+00 2.40143131e+00 | 2.91247570e+00 3.18739694e+00 2.40143131e+00 38 4.29730139e+00 9.22907722e-01 1.13448273e+00 | 4.29730139e+00 9.22907722e-01 1.13448273e+00 39 7.05764209e-01 1.90209604e+00 -3.11311601e+00 | 7.05764209e-01 1.90209604e+00 -3.11311601e+00 40 2.92874627e+00 -1.11239534e+00 3.55798574e+00 | 2.92874627e+00 -1.11239534e+00 3.55798574e+00 41 6.87730573e-01 5.77377000e-01 5.32712899e-01 | 6.87730573e-01 5.77377000e-01 5.32712899e-01 42 -1.59830501e+00 1.78356221e+00 1.07020707e-01 | -1.59830501e+00 1.78356221e+00 1.07020707e-01 43 1.96095191e+00 -2.19249362e+00 -7.74624705e-01 | 1.96095191e+00 -2.19249362e+00 -7.74624705e-01 44 -2.14110219e+00 1.07999547e-01 -1.07687761e+00 | -2.14110219e+00 1.07999547e-01 -1.07687761e+00 45 8.30693100e-01 1.80754321e+00 -9.96700355e-03 | 8.30693100e-01 1.80754321e+00 -9.96700355e-03 46 -1.43061051e+00 -6.18266032e-01 -2.11630032e+00 | -1.43061051e+00 -6.18266032e-01 -2.11630032e+00 47 2.67303112e+00 8.36080032e-01 -1.15730912e+00 | 2.67303112e+00 8.36080032e-01 -1.15730912e+00 48 1.37691185e+00 5.09715291e-01 9.93729355e-01 | 1.37691185e+00 5.09715291e-01 9.93729355e-01 49 1.73462199e+00 -1.55311459e+00 -3.69732238e-01 | 1.73462199e+00 -1.55311459e+00 -3.69732238e-01 50 1.09499374e+00 -1.06191512e+00 3.46016302e+00 | 1.09499374e+00 -1.06191512e+00 3.46016302e+00 51 -2.62881501e+00 2.21871830e+00 -3.00138301e+00 | -2.62881501e+00 2.21871830e+00 -3.00138301e+00 52 -4.44937856e+00 5.10086265e+00 1.09992952e+00 | -4.44937856e+00 5.10086265e+00 1.09992952e+00 53 -5.31857448e+00 -5.76978599e+00 2.05449692e-01 | -5.31857448e+00 -5.76978599e+00 2.05449692e-01 54 1.75658438e+00 -2.78116165e+00 -8.33380199e-01 | 1.75658438e+00 -2.78116165e+00 -8.33380199e-01 55 9.83826624e-01 7.28023296e-01 4.31383804e-01 | 9.83826624e-01 7.28023296e-01 4.31383804e-01 56 5.02362170e+00 -1.46211771e+00 -5.31508742e-01 | 5.02362170e+00 -1.46211771e+00 -5.31508742e-01 57 2.95998488e-01 1.63516339e-01 -3.52289868e-01 | 2.95998488e-01 1.63516339e-01 -3.52289868e-01 58 -5.97611917e-01 -1.85387670e+00 1.47778853e+00 | -5.97611917e-01 -1.85387670e+00 1.47778853e+00 59 1.88265668e+00 2.10150087e-01 1.61117848e+00 | 1.88265668e+00 2.10150087e-01 1.61117848e+00 60 -2.56890094e+01 -9.66402549e+00 -2.97877089e+01 | -2.56890094e+01 -9.66402549e+00 -2.97877089e+01 61 1.96553638e+01 9.61140765e+00 3.11111353e+01 | 1.96553638e+01 9.61140765e+00 3.11111353e+01 62 -1.34132341e-01 -3.92251874e+00 -2.68932011e-01 | -1.34132341e-01 -3.92251874e+00 -2.68932011e-01 63 4.38816024e+00 8.60681186e-01 -1.13613037e+00 | 4.38816024e+00 8.60681186e-01 -1.13613037e+00 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- ========================================================================================================================= To pass this verification check the model must be invariant with respect to perumutation symmetry for all configurations it was able to compute. Grade: P Comment: Model energy has permutation symmetry for all configurations the model was able to compute.