!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_SchopfBrommerFrigan_2012_AlMnPd__MO_137572817842_000 Supported species : Al Mn Pd random seed = 13 lattice constant (orig) = 5.000 perturbation amplitude = 0.500 number unit cells per side = 2 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Al (Configuration in file "config-Al.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [31, 17, 21, 57, 44, 54, 45, 36, 28, 29, 25, 18, 19, 30, 20, 32, 46, 1, 11, 12, 14, 2, 27, 61, 39, 10, 58, 22, 8, 9, 13, 0, 15, 47, 38, 41, 7, 63, 34, 24, 52, 35, 59, 48, 4, 6, 16, 33, 43, 60, 51, 50, 40, 62, 5, 56, 55, 3, 26, 42, 49, 23, 53, 37] 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)) = -1154.3748747252805 V(r_1,...,r_N) = -1154.374874725282 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 -4.91245131e+00 -3.19563380e+00 -4.21157456e+00 | -4.91245131e+00 -3.19563380e+00 -4.21157456e+00 1 9.45749157e+01 2.15589664e+02 -1.19748480e+02 | 9.45749157e+01 2.15589664e+02 -1.19748480e+02 2 -7.08831015e+00 -9.70455342e+01 2.23370730e+02 | -7.08831015e+00 -9.70455342e+01 2.23370730e+02 3 -8.41604397e+01 -1.14587127e+02 -1.02882338e+02 | -8.41604397e+01 -1.14587127e+02 -1.02882338e+02 4 1.02626954e+00 -5.86443167e-01 6.14068003e-01 | 1.02626954e+00 -5.86443167e-01 6.14068003e-01 5 -1.32496335e+00 -2.66161976e+00 1.94036077e+00 | -1.32496335e+00 -2.66161976e+00 1.94036077e+00 6 -3.54398197e+00 -1.70473676e+00 -1.85440124e+00 | -3.54398197e+00 -1.70473676e+00 -1.85440124e+00 7 2.83608329e+02 -6.86853279e+02 4.02039579e+02 | 2.83608329e+02 -6.86853279e+02 4.02039579e+02 8 -4.87902430e+00 -1.65513618e+00 -5.22386062e+00 | -4.87902430e+00 -1.65513618e+00 -5.22386062e+00 9 1.06284455e+00 1.11214855e-01 -2.51266551e-01 | 1.06284455e+00 1.11214855e-01 -2.51266551e-01 10 4.00576677e-01 4.97414141e-01 -1.09895546e+00 | 4.00576677e-01 4.97414141e-01 -1.09895546e+00 11 -1.34389483e+00 2.36875747e+00 2.33656840e+00 | -1.34389483e+00 2.36875747e+00 2.33656840e+00 12 5.18209773e+02 1.17131924e+02 3.12970257e+02 | 5.18209773e+02 1.17131924e+02 3.12970257e+02 13 -5.08542002e+02 -1.26096133e+02 -3.18043642e+02 | -5.08542002e+02 -1.26096133e+02 -3.18043642e+02 14 5.60738007e+01 5.57560586e+01 9.37465118e+01 | 5.60738007e+01 5.57560586e+01 9.37465118e+01 15 -5.32625200e+01 -5.22034296e+01 -9.59612253e+01 | -5.32625200e+01 -5.22034296e+01 -9.59612253e+01 16 8.57256921e+01 8.48416870e+01 7.75044488e+01 | 8.57256921e+01 8.48416870e+01 7.75044488e+01 17 -8.55746217e+01 -8.48856866e+01 -7.75088301e+01 | -8.55746217e+01 -8.48856866e+01 -7.75088301e+01 18 -9.20698180e-01 -6.71328344e-01 -7.81762355e-01 | -9.20698180e-01 -6.71328344e-01 -7.81762355e-01 19 4.42018709e+02 -2.68515299e+02 3.00283032e+02 | 4.42018709e+02 -2.68515299e+02 3.00283032e+02 20 2.98995945e+02 2.21949886e+02 7.77773984e+00 | 2.98995945e+02 2.21949886e+02 7.77773984e+00 21 -2.96215755e+02 -2.20035412e+02 -1.40194435e+01 | -2.96215755e+02 -2.20035412e+02 -1.40194435e+01 22 -2.66398725e+00 -7.11833719e-01 -6.32543828e+00 | -2.66398725e+00 -7.11833719e-01 -6.32543828e+00 23 1.17767510e+02 -4.84557308e+01 -7.21267289e+00 | 1.17767510e+02 -4.84557308e+01 -7.21267289e+00 24 -1.12679977e+00 -5.10441466e-01 -1.02699465e+00 | -1.12679977e+00 -5.10441466e-01 -1.02699465e+00 25 7.79856964e+01 -8.40382421e+01 7.30292294e+01 | 7.79856964e+01 -8.40382421e+01 7.30292294e+01 26 1.85157089e+02 1.23607796e+02 1.24151492e+02 | 1.85157089e+02 1.23607796e+02 1.24151492e+02 27 -1.84367799e+02 -1.22054172e+02 -1.25606530e+02 | -1.84367799e+02 -1.22054172e+02 -1.25606530e+02 28 -7.96925534e+01 7.59600904e+01 -7.58577357e+01 | -7.96925534e+01 7.59600904e+01 -7.58577357e+01 29 4.85699401e+00 2.77152185e+00 2.85983591e+00 | 4.85699401e+00 2.77152185e+00 2.85983591e+00 30 -4.49083404e+02 2.70966165e+02 -3.09843012e+02 | -4.49083404e+02 2.70966165e+02 -3.09843012e+02 31 2.20667724e+02 -3.58005065e+00 1.35834946e+02 | 2.20667724e+02 -3.58005065e+00 1.35834946e+02 32 -8.14741630e+00 -4.37769185e+00 -6.92813967e+00 | -8.14741630e+00 -4.37769185e+00 -6.92813967e+00 33 1.29348060e+02 -6.95595121e+01 1.95868661e+02 | 1.29348060e+02 -6.95595121e+01 1.95868661e+02 34 -2.84246009e+02 6.84124698e+02 -3.97687322e+02 | -2.84246009e+02 6.84124698e+02 -3.97687322e+02 35 1.38156683e-02 -4.46426092e+00 7.06369595e+00 | 1.38156683e-02 -4.46426092e+00 7.06369595e+00 36 -1.29241506e+02 7.29148913e+01 -1.90673712e+02 | -1.29241506e+02 7.29148913e+01 -1.90673712e+02 37 5.19175328e+00 -1.97607853e+00 3.67626776e+00 | 5.19175328e+00 -1.97607853e+00 3.67626776e+00 38 -3.48557153e+00 -2.89099142e+00 -5.41106083e+00 | -3.48557153e+00 -2.89099142e+00 -5.41106083e+00 39 8.36125784e+00 7.15374121e+00 1.18270990e+00 | 8.36125784e+00 7.15374121e+00 1.18270990e+00 40 -2.97112503e+00 -2.07320928e+00 -1.08109216e+00 | -2.97112503e+00 -2.07320928e+00 -1.08109216e+00 41 2.13915923e+02 -3.43229707e+02 1.80159966e+02 | 2.13915923e+02 -3.43229707e+02 1.80159966e+02 42 6.45679622e+01 2.64787827e+02 1.07909805e+02 | 6.45679622e+01 2.64787827e+02 1.07909805e+02 43 -6.79842523e+01 -2.54877357e+02 -9.81964188e+01 | -6.79842523e+01 -2.54877357e+02 -9.81964188e+01 44 -2.12035771e+02 3.42652496e+02 -1.79040634e+02 | -2.12035771e+02 3.42652496e+02 -1.79040634e+02 45 -1.02088701e-01 3.74863331e-01 -3.82903949e-02 | -1.02088701e-01 3.74863331e-01 -3.82903949e-02 46 3.38364200e+02 5.53748167e+02 5.11818301e+02 | 3.38364200e+02 5.53748167e+02 5.11818301e+02 47 -3.35115431e+02 -5.51957466e+02 -5.09820078e+02 | -3.35115431e+02 -5.51957466e+02 -5.09820078e+02 48 -3.75864023e+00 -1.42500659e+00 -1.62648237e-01 | -3.75864023e+00 -1.42500659e+00 -1.62648237e-01 49 7.43539045e+00 -1.17295271e+01 -6.26647615e-01 | 7.43539045e+00 -1.17295271e+01 -6.26647615e-01 50 3.45564752e+01 2.05814966e+02 4.30130513e+02 | 3.45564752e+01 2.05814966e+02 4.30130513e+02 51 -1.46716168e+02 -1.47207536e+02 -4.23083535e+02 | -1.46716168e+02 -1.47207536e+02 -4.23083535e+02 52 -8.30316351e+00 -2.54398773e+00 6.19157190e+00 | -8.30316351e+00 -2.54398773e+00 6.19157190e+00 53 -8.50841466e-01 -5.18083312e-01 2.71058959e+00 | -8.50841466e-01 -5.18083312e-01 2.71058959e+00 54 -1.45335693e+01 1.10982926e+00 1.96774607e+00 | -1.45335693e+01 1.10982926e+00 1.96774607e+00 55 5.81701965e+00 4.36084638e+00 6.19095457e+00 | 5.81701965e+00 4.36084638e+00 6.19095457e+00 56 2.46887282e+00 1.75512156e+00 -4.43447191e+00 | 2.46887282e+00 1.75512156e+00 -4.43447191e+00 57 -1.93278280e+02 3.39962939e+02 3.87657202e+02 | -1.93278280e+02 3.39962939e+02 3.87657202e+02 58 -2.13038834e+02 7.04491215e+00 -1.26083141e+02 | -2.13038834e+02 7.04491215e+00 -1.26083141e+02 59 -1.61945552e-01 -2.71861220e-01 -2.21469230e-01 | -1.61945552e-01 -2.71861220e-01 -2.21469230e-01 60 3.51394356e+02 1.28778877e+02 4.92913192e+02 | 3.51394356e+02 1.28778877e+02 4.92913192e+02 61 -3.50145692e+02 -1.29555681e+02 -4.92092306e+02 | -3.50145692e+02 -1.29555681e+02 -4.92092306e+02 62 1.93265970e+02 -3.37523023e+02 -3.90873828e+02 | 1.93265970e+02 -3.37523023e+02 -3.90873828e+02 63 -1.34160355e-02 9.18960325e-02 1.29846176e-02 | -1.34160355e-02 9.18960325e-02 1.29846176e-02 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Mn (Configuration in file "config-Mn.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [24, 54, 20, 36, 61, 23, 17, 34, 58, 31, 38, 32, 27, 15, 45, 13, 25, 6, 35, 33, 2, 59, 55, 5, 0, 16, 42, 12, 46, 62, 51, 9, 11, 19, 7, 18, 3, 63, 10, 40, 39, 44, 26, 60, 41, 14, 28, 56, 52, 57, 53, 30, 48, 50, 1, 22, 47, 49, 8, 21, 43, 4, 29, 37] 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)) = -306.38249270113147 V(r_1,...,r_N) = -306.3824927011314 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 4.36217532e+00 5.28955197e-01 2.97273411e+00 | 4.36217532e+00 5.28955197e-01 2.97273411e+00 1 -4.58766937e+00 -4.91498005e+00 1.22836436e+01 | -4.58766937e+00 -4.91498005e+00 1.22836436e+01 2 4.06795039e+01 2.48995013e+01 3.57406478e+01 | 4.06795039e+01 2.48995013e+01 3.57406478e+01 3 -1.94248160e+01 -2.06628983e+01 -1.63213871e+01 | -1.94248160e+01 -2.06628983e+01 -1.63213871e+01 4 2.01942155e+00 7.69363437e+00 -1.37731056e+01 | 2.01942155e+00 7.69363437e+00 -1.37731056e+01 5 6.79077654e+00 -1.62552738e+01 2.71859690e+01 | 6.79077654e+00 -1.62552738e+01 2.71859690e+01 6 2.95678836e+00 3.12194762e+00 4.50612741e+00 | 2.95678836e+00 3.12194762e+00 4.50612741e+00 7 -6.31686891e+00 -2.32528201e+00 5.17848815e-01 | -6.31686891e+00 -2.32528201e+00 5.17848815e-01 8 1.44740568e+01 8.56407298e+00 1.13518238e+01 | 1.44740568e+01 8.56407298e+00 1.13518238e+01 9 -8.49322310e+00 -1.12305749e+01 -1.00855683e+01 | -8.49322310e+00 -1.12305749e+01 -1.00855683e+01 10 1.62935771e+00 1.27632155e+01 7.14273646e+00 | 1.62935771e+00 1.27632155e+01 7.14273646e+00 11 -5.06928633e-01 -1.15044729e+01 -8.12331456e+00 | -5.06928633e-01 -1.15044729e+01 -8.12331456e+00 12 -2.31330854e+00 2.84706163e+00 -1.65226824e+00 | -2.31330854e+00 2.84706163e+00 -1.65226824e+00 13 -4.62926457e-02 1.59139569e-01 1.37207175e+00 | -4.62926457e-02 1.59139569e-01 1.37207175e+00 14 -1.56559545e+01 5.13765106e+00 -2.22874811e+01 | -1.56559545e+01 5.13765106e+00 -2.22874811e+01 15 1.59718609e-02 2.30907951e-01 1.51515791e+00 | 1.59718609e-02 2.30907951e-01 1.51515791e+00 16 1.88250426e+01 1.09307539e+01 1.75209526e+01 | 1.88250426e+01 1.09307539e+01 1.75209526e+01 17 2.39728125e+01 -1.04129722e+01 1.13508782e+01 | 2.39728125e+01 -1.04129722e+01 1.13508782e+01 18 1.21337073e+01 5.37483106e+00 1.21143251e+01 | 1.21337073e+01 5.37483106e+00 1.21143251e+01 19 -1.32887095e+01 -1.23553758e+01 -8.76103728e+00 | -1.32887095e+01 -1.23553758e+01 -8.76103728e+00 20 -3.91859316e+01 6.23843892e+00 -2.97991168e+01 | -3.91859316e+01 6.23843892e+00 -2.97991168e+01 21 -1.65267499e+00 9.82632541e-01 6.09727241e-01 | -1.65267499e+00 9.82632541e-01 6.09727241e-01 22 2.71812130e+00 5.13544174e-01 -2.01052144e+00 | 2.71812130e+00 5.13544174e-01 -2.01052144e+00 23 -8.42032465e-02 -3.93519497e+00 3.20581886e+00 | -8.42032465e-02 -3.93519497e+00 3.20581886e+00 24 -3.92790310e+00 -5.74843870e+00 7.56351136e+00 | -3.92790310e+00 -5.74843870e+00 7.56351136e+00 25 -2.13730321e+01 1.75225543e+01 1.89172924e+01 | -2.13730321e+01 1.75225543e+01 1.89172924e+01 26 -1.21634241e+00 1.52953340e+00 4.91774209e+00 | -1.21634241e+00 1.52953340e+00 4.91774209e+00 27 -1.92613261e-01 -3.07994628e+00 -4.47460494e+00 | -1.92613261e-01 -3.07994628e+00 -4.47460494e+00 28 -3.21267119e+00 1.98310474e+00 -3.38714342e+00 | -3.21267119e+00 1.98310474e+00 -3.38714342e+00 29 -3.06169588e+00 2.63169944e+00 5.17889293e-01 | -3.06169588e+00 2.63169944e+00 5.17889293e-01 30 2.27214068e+01 -1.97838850e+01 -1.69126812e+01 | 2.27214068e+01 -1.97838850e+01 -1.69126812e+01 31 2.57789347e+00 -2.41843633e+00 2.57689275e+00 | 2.57789347e+00 -2.41843633e+00 2.57689275e+00 32 2.05784407e+00 4.43796937e+00 4.69113766e+00 | 2.05784407e+00 4.43796937e+00 4.69113766e+00 33 -5.43247709e+00 8.97926220e+00 3.71074563e+00 | -5.43247709e+00 8.97926220e+00 3.71074563e+00 34 9.65640796e+00 -4.51492079e+00 -4.57536840e+00 | 9.65640796e+00 -4.51492079e+00 -4.57536840e+00 35 1.10496660e+00 -2.19301792e+00 -2.80890302e+00 | 1.10496660e+00 -2.19301792e+00 -2.80890302e+00 36 -3.20314920e+00 4.00394586e+00 3.08819249e-01 | -3.20314920e+00 4.00394586e+00 3.08819249e-01 37 -3.04554318e+00 1.87475697e+00 -4.16174240e+00 | -3.04554318e+00 1.87475697e+00 -4.16174240e+00 38 9.71994990e+00 -1.00020413e+01 -3.36225994e+00 | 9.71994990e+00 -1.00020413e+01 -3.36225994e+00 39 -3.19483681e-01 7.56916716e-01 -3.60391444e+00 | -3.19483681e-01 7.56916716e-01 -3.60391444e+00 40 -1.69425722e+01 2.18836454e+01 -2.16929273e+01 | -1.69425722e+01 2.18836454e+01 -2.16929273e+01 41 -7.10768598e+00 3.18165535e+00 8.42690674e+00 | -7.10768598e+00 3.18165535e+00 8.42690674e+00 42 4.50008704e+00 1.29407829e+01 6.46137277e+00 | 4.50008704e+00 1.29407829e+01 6.46137277e+00 43 -6.01287661e+00 -1.05830187e+01 -9.85437602e+00 | -6.01287661e+00 -1.05830187e+01 -9.85437602e+00 44 -2.77202674e-01 3.83934770e+00 7.10071067e-01 | -2.77202674e-01 3.83934770e+00 7.10071067e-01 45 -6.87909007e-01 -2.29450440e+00 -8.28812843e-01 | -6.87909007e-01 -2.29450440e+00 -8.28812843e-01 46 5.44186132e+00 -5.73377886e+00 -7.04520432e+00 | 5.44186132e+00 -5.73377886e+00 -7.04520432e+00 47 -1.04888249e+00 -2.42879564e+00 -2.61188058e+00 | -1.04888249e+00 -2.42879564e+00 -2.61188058e+00 48 4.62148354e+00 -5.22200833e+00 9.32360430e-01 | 4.62148354e+00 -5.22200833e+00 9.32360430e-01 49 1.42046858e+00 -5.83906262e-02 4.73781613e-01 | 1.42046858e+00 -5.83906262e-02 4.73781613e-01 50 2.94020514e+00 1.60606724e+00 5.71515848e-01 | 2.94020514e+00 1.60606724e+00 5.71515848e-01 51 -2.82552579e+00 -3.01414494e+00 -5.30612673e+00 | -2.82552579e+00 -3.01414494e+00 -5.30612673e+00 52 1.88708984e-01 -8.65954605e-01 4.93358589e-01 | 1.88708984e-01 -8.65954605e-01 4.93358589e-01 53 1.34994453e+00 -1.41239893e+00 -4.82673374e+00 | 1.34994453e+00 -1.41239893e+00 -4.82673374e+00 54 3.36931509e+00 2.38180759e+00 4.39981769e+00 | 3.36931509e+00 2.38180759e+00 4.39981769e+00 55 -3.21959467e+00 -2.45256459e+00 -4.08635813e+00 | -3.21959467e+00 -2.45256459e+00 -4.08635813e+00 56 -1.33665614e+00 3.89928701e+00 -2.83914352e-02 | -1.33665614e+00 3.89928701e+00 -2.83914352e-02 57 -2.43902926e+00 -3.25655925e+00 3.34794452e+00 | -2.43902926e+00 -3.25655925e+00 3.34794452e+00 58 2.93433193e+00 1.87278053e+00 -5.51954405e-02 | 2.93433193e+00 1.87278053e+00 -5.51954405e-02 59 -3.33041881e+00 -1.99961813e+00 -5.57862721e+00 | -3.33041881e+00 -1.99961813e+00 -5.57862721e+00 60 2.41144265e-01 5.72064013e-01 1.74182040e+00 | 2.41144265e-01 5.72064013e-01 1.74182040e+00 61 -6.51723304e-01 -4.05842272e+00 -1.74677179e+00 | -6.51723304e-01 -4.05842272e+00 -1.74677179e+00 62 2.91890710e-01 1.02937151e+00 -3.96600856e-01 | 2.91890710e-01 1.02937151e+00 -3.96600856e-01 63 -3.29407644e+00 -2.19496896e+00 4.98184127e-03 | -3.29407644e+00 -2.19496896e+00 4.98184127e-03 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Pd (Configuration in file "config-Pd.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [38, 10, 29, 28, 46, 55, 33, 27, 17, 18, 1, 39, 16, 36, 30, 63, 12, 8, 9, 59, 31, 45, 34, 51, 40, 50, 41, 7, 3, 2, 14, 20, 54, 6, 22, 49, 13, 60, 0, 11, 24, 26, 44, 47, 42, 21, 4, 43, 62, 35, 25, 23, 57, 58, 32, 5, 61, 52, 53, 19, 37, 56, 48, 15] 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)) = -6144.590233612022 V(r_1,...,r_N) = -6144.590233612032 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 2.09465785e+00 1.48697940e+00 1.19121802e+00 | 2.09465785e+00 1.48697940e+00 1.19121802e+00 1 2.57054406e+02 -7.02728468e+01 -1.28950728e+03 | 2.57054406e+02 -7.02728468e+01 -1.28950728e+03 2 -2.58268913e+02 7.25042898e+01 1.28761929e+03 | -2.58268913e+02 7.25042898e+01 1.28761929e+03 3 -7.81056656e+02 1.06451878e+03 1.04601186e+03 | -7.81056656e+02 1.06451878e+03 1.04601186e+03 4 -2.73701201e+00 -7.70115031e+00 -2.42149031e+00 | -2.73701201e+00 -7.70115031e+00 -2.42149031e+00 5 -1.03607027e+03 6.00674059e+02 5.86968867e+02 | -1.03607027e+03 6.00674059e+02 5.86968867e+02 6 -2.61992399e+00 -2.95475002e+00 -1.46263251e+00 | -2.61992399e+00 -2.95475002e+00 -1.46263251e+00 7 7.65077554e+02 -1.26054939e+03 2.25652203e+02 | 7.65077554e+02 -1.26054939e+03 2.25652203e+02 8 5.04361674e+02 1.57577481e+02 6.10762812e+02 | 5.04361674e+02 1.57577481e+02 6.10762812e+02 9 -6.59755798e+02 3.15097622e+02 -4.37155714e+02 | -6.59755798e+02 3.15097622e+02 -4.37155714e+02 10 -3.20790222e+00 -4.13891672e+00 -2.20311803e+00 | -3.20790222e+00 -4.13891672e+00 -2.20311803e+00 11 2.91566207e+00 3.26599593e+00 2.13125000e+00 | 2.91566207e+00 3.26599593e+00 2.13125000e+00 12 2.69683445e+00 -4.63197281e-01 1.44523161e+00 | 2.69683445e+00 -4.63197281e-01 1.44523161e+00 13 -9.03652836e-01 6.43692739e-02 -7.12492189e-01 | -9.03652836e-01 6.43692739e-02 -7.12492189e-01 14 1.52809857e+02 -4.70927896e+02 -1.74564817e+02 | 1.52809857e+02 -4.70927896e+02 -1.74564817e+02 15 3.78812200e+01 2.03512154e+02 3.62099293e+00 | 3.78812200e+01 2.03512154e+02 3.62099293e+00 16 1.00005140e+02 5.61476160e+01 3.48675616e+01 | 1.00005140e+02 5.61476160e+01 3.48675616e+01 17 3.85738198e+02 2.43084882e+02 -5.21052478e+02 | 3.85738198e+02 2.43084882e+02 -5.21052478e+02 18 -4.95177025e+02 -2.98177186e+02 4.79103015e+02 | -4.95177025e+02 -2.98177186e+02 4.79103015e+02 19 8.57103029e+01 -1.56871815e+02 9.08667638e+01 | 8.57103029e+01 -1.56871815e+02 9.08667638e+01 20 7.81315131e+02 -1.07237541e+03 -1.04153702e+03 | 7.81315131e+02 -1.07237541e+03 -1.04153702e+03 21 1.66758162e+03 -1.48803675e+03 9.35636387e+02 | 1.66758162e+03 -1.48803675e+03 9.35636387e+02 22 3.45476634e+02 4.94518934e+02 7.00717019e+02 | 3.45476634e+02 4.94518934e+02 7.00717019e+02 23 -3.45453427e+02 -4.95575974e+02 -6.99436830e+02 | -3.45453427e+02 -4.95575974e+02 -6.99436830e+02 24 3.17817122e+02 1.20434675e+03 6.33139087e+02 | 3.17817122e+02 1.20434675e+03 6.33139087e+02 25 -4.38038133e+02 -1.08811871e+03 -5.24512308e+02 | -4.38038133e+02 -1.08811871e+03 -5.24512308e+02 26 1.02841399e+02 2.54506972e+01 1.50774995e+02 | 1.02841399e+02 2.54506972e+01 1.50774995e+02 27 -1.02649939e+02 -2.52577070e+01 -1.50214455e+02 | -1.02649939e+02 -2.52577070e+01 -1.50214455e+02 28 1.26242500e+00 -2.62413717e+02 1.73785676e+02 | 1.26242500e+00 -2.62413717e+02 1.73785676e+02 29 -5.03354020e-01 -4.33428600e-01 -2.89456932e-01 | -5.03354020e-01 -4.33428600e-01 -2.89456932e-01 30 4.39237170e+01 4.92273029e+01 -2.02081838e+02 | 4.39237170e+01 4.92273029e+01 -2.02081838e+02 31 -2.35575315e-01 2.14698210e-01 -7.75343703e-01 | -2.35575315e-01 2.14698210e-01 -7.75343703e-01 32 8.81182690e-01 1.73647870e+00 -4.85317051e-01 | 8.81182690e-01 1.73647870e+00 -4.85317051e-01 33 1.37858888e+02 2.02562079e+02 -3.25901681e+02 | 1.37858888e+02 2.02562079e+02 -3.25901681e+02 34 1.35101258e+02 4.64268617e+02 -4.84221799e+02 | 1.35101258e+02 4.64268617e+02 -4.84221799e+02 35 2.56292150e+03 -8.62699165e+02 2.49541807e+03 | 2.56292150e+03 -8.62699165e+02 2.49541807e+03 36 -7.16238263e-01 -1.88807216e+00 1.61609259e-02 | -7.16238263e-01 -1.88807216e+00 1.61609259e-02 37 3.71296216e+00 1.36523500e+01 -5.66768888e+00 | 3.71296216e+00 1.36523500e+01 -5.66768888e+00 38 3.48439568e+02 4.07884946e+02 1.31441743e+02 | 3.48439568e+02 4.07884946e+02 1.31441743e+02 39 -3.16137247e+02 -3.99902700e+02 -1.64721596e+02 | -3.16137247e+02 -3.99902700e+02 -1.64721596e+02 40 -2.05368048e+00 -7.08355101e+00 -4.05814013e+00 | -2.05368048e+00 -7.08355101e+00 -4.05814013e+00 41 8.37295539e+00 -6.18983332e+00 1.31278499e-01 | 8.37295539e+00 -6.18983332e+00 1.31278499e-01 42 -4.07450739e+01 5.51414396e+01 -1.75501923e+02 | -4.07450739e+01 5.51414396e+01 -1.75501923e+02 43 4.35734437e+00 3.49594770e+00 3.07913598e+00 | 4.35734437e+00 3.49594770e+00 3.07913598e+00 44 2.39835815e+02 4.46283739e+02 1.58780642e+02 | 2.39835815e+02 4.46283739e+02 1.58780642e+02 45 -2.40291952e+02 -4.45986546e+02 -1.58915615e+02 | -2.40291952e+02 -4.45986546e+02 -1.58915615e+02 46 -2.57454720e+03 8.57108883e+02 -2.49004440e+03 | -2.57454720e+03 8.57108883e+02 -2.49004440e+03 47 1.04298813e+00 -2.48696621e+00 9.37889984e+00 | 1.04298813e+00 -2.48696621e+00 9.37889984e+00 48 5.48579712e+01 2.77274384e+01 4.60586379e+00 | 5.48579712e+01 2.77274384e+01 4.60586379e+00 49 3.88309790e+02 -6.61191863e+02 9.57037956e+02 | 3.88309790e+02 -6.61191863e+02 9.57037956e+02 50 3.36820573e+02 1.26983999e+02 2.86152362e+02 | 3.36820573e+02 1.26983999e+02 2.86152362e+02 51 -1.65302787e+02 -1.47035340e+02 -1.15470484e+02 | -1.65302787e+02 -1.47035340e+02 -1.15470484e+02 52 -4.79818091e+02 6.23012903e+02 -9.30604616e+02 | -4.79818091e+02 6.23012903e+02 -9.30604616e+02 53 1.90694425e+00 2.61885225e+00 3.17175534e+00 | 1.90694425e+00 2.61885225e+00 3.17175534e+00 54 -1.59181093e+00 -2.46546802e+00 -1.64293064e+00 | -1.59181093e+00 -2.46546802e+00 -1.64293064e+00 55 2.28879233e+00 2.02290530e+00 1.88078795e-01 | 2.28879233e+00 2.02290530e+00 1.88078795e-01 56 -1.67036115e+03 1.48465913e+03 -9.38833519e+02 | -1.67036115e+03 1.48465913e+03 -9.38833519e+02 57 4.01528881e+02 1.94223308e+02 -2.44314915e+02 | 4.01528881e+02 1.94223308e+02 -2.44314915e+02 58 -3.96786468e+02 -1.98427510e+02 2.52372415e+02 | -3.96786468e+02 -1.98427510e+02 2.52372415e+02 59 3.53205416e+00 3.44426091e+00 2.75277186e+00 | 3.53205416e+00 3.44426091e+00 2.75277186e+00 60 1.49627069e+02 1.99266031e+01 8.32113401e+01 | 1.49627069e+02 1.99266031e+01 8.32113401e+01 61 -1.50738913e+02 -1.13182539e+01 -9.30079292e+01 | -1.50738913e+02 -1.13182539e+01 -9.30079292e+01 62 1.93038887e+02 9.92703824e+01 1.21487847e+02 | 1.93038887e+02 9.92703824e+01 1.21487847e+02 63 -3.65230784e+02 -7.67727620e+01 -2.92200724e+02 | -3.65230784e+02 -7.67727620e+01 -2.92200724e+02 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MIXED STRUCTURE -- Species = Al Mn Pd (Configuration in file "config-AlMnPd.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [19, 48, 23, 52, 47, 57, 32, 61, 44, 15, 11, 10, 14, 49, 12, 9, 42, 29, 35, 0, 36, 41, 37, 2, 53, 50, 31, 54, 34, 17, 58, 26, 6, 59, 28, 18, 20, 22, 40, 55, 38, 21, 16, 60, 8, 51, 62, 4, 1, 13, 25, 45, 3, 24, 27, 39, 56, 5, 30, 33, 43, 7, 46, 63] 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)) = -957.9447227117752 V(r_1,...,r_N) = -957.9447227117756 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 -3.37328642e+00 -2.93698516e+00 -1.59951212e+00 | -3.37328642e+00 -2.93698516e+00 -1.59951212e+00 1 6.09383997e+01 -9.88570420e+01 1.04205670e+02 | 6.09383997e+01 -9.88570420e+01 1.04205670e+02 2 2.04130203e+02 1.34923346e+02 1.65844287e+02 | 2.04130203e+02 1.34923346e+02 1.65844287e+02 3 -1.87130294e+02 -1.26961736e+02 -1.57541838e+02 | -1.87130294e+02 -1.26961736e+02 -1.57541838e+02 4 1.22524899e+02 2.50010612e+02 1.34005136e+02 | 1.22524899e+02 2.50010612e+02 1.34005136e+02 5 -1.76731474e+02 -1.35345753e+02 -2.36747712e+02 | -1.76731474e+02 -1.35345753e+02 -2.36747712e+02 6 -4.25362171e+00 5.66632289e-01 3.70009327e+00 | -4.25362171e+00 5.66632289e-01 3.70009327e+00 7 4.14529432e+01 -4.48376207e+01 1.51032878e+01 | 4.14529432e+01 -4.48376207e+01 1.51032878e+01 8 4.89562340e+00 -9.46950584e-01 -2.66594654e-01 | 4.89562340e+00 -9.46950584e-01 -2.66594654e-01 9 -2.14977476e+02 2.52583158e+02 3.33197074e+02 | -2.14977476e+02 2.52583158e+02 3.33197074e+02 10 6.44256552e+01 1.72359270e+02 1.13227318e+02 | 6.44256552e+01 1.72359270e+02 1.13227318e+02 11 -6.63652958e+01 -1.74451049e+02 -1.13923081e+02 | -6.63652958e+01 -1.74451049e+02 -1.13923081e+02 12 -7.85720680e-01 -1.07180221e+00 6.94233585e-02 | -7.85720680e-01 -1.07180221e+00 6.94233585e-02 13 3.10247334e+00 -3.02739021e+00 -9.07877198e+00 | 3.10247334e+00 -3.02739021e+00 -9.07877198e+00 14 2.15887293e+02 -2.37238102e+02 -3.23646529e+02 | 2.15887293e+02 -2.37238102e+02 -3.23646529e+02 15 5.63159337e+01 2.02435966e+01 -3.14911396e+01 | 5.63159337e+01 2.02435966e+01 -3.14911396e+01 16 2.60984755e+00 -9.49218689e-01 1.85458181e+00 | 2.60984755e+00 -9.49218689e-01 1.85458181e+00 17 -5.79768094e-01 1.11722279e+00 -4.63273061e-01 | -5.79768094e-01 1.11722279e+00 -4.63273061e-01 18 -2.96114602e+00 -6.83717535e+00 -2.00072631e+00 | -2.96114602e+00 -6.83717535e+00 -2.00072631e+00 19 3.01040506e+00 5.12699927e+00 4.17951527e+00 | 3.01040506e+00 5.12699927e+00 4.17951527e+00 20 3.65916080e+00 1.04964212e+01 8.99744625e+00 | 3.65916080e+00 1.04964212e+01 8.99744625e+00 21 -1.32012030e+01 -1.18885418e+01 -1.10866891e+01 | -1.32012030e+01 -1.18885418e+01 -1.10866891e+01 22 -6.39926901e+00 -2.32821454e+00 -4.47031282e+00 | -6.39926901e+00 -2.32821454e+00 -4.47031282e+00 23 1.92723658e+01 -3.90159509e+01 7.24660616e+01 | 1.92723658e+01 -3.90159509e+01 7.24660616e+01 24 -5.51663574e+00 -1.26580103e+01 2.68410309e+00 | -5.51663574e+00 -1.26580103e+01 2.68410309e+00 25 -2.68778001e+00 -8.31747482e-01 3.32473072e-01 | -2.68778001e+00 -8.31747482e-01 3.32473072e-01 26 3.91068814e+00 3.50132155e+00 1.69783072e+00 | 3.91068814e+00 3.50132155e+00 1.69783072e+00 27 -4.98610950e+00 -2.56619302e+00 -3.00457337e+00 | -4.98610950e+00 -2.56619302e+00 -3.00457337e+00 28 -6.42916307e+01 -3.77229025e+01 2.71871554e+01 | -6.42916307e+01 -3.77229025e+01 2.71871554e+01 29 -1.56106446e+00 2.47954882e+00 4.64216095e+00 | -1.56106446e+00 2.47954882e+00 4.64216095e+00 30 3.58365502e+00 3.00947592e+00 2.74567896e+00 | 3.58365502e+00 3.00947592e+00 2.74567896e+00 31 1.72267235e+00 -1.80790555e+00 -4.20663582e-01 | 1.72267235e+00 -1.80790555e+00 -4.20663582e-01 32 1.26765801e+02 7.85632523e+01 1.62291509e+02 | 1.26765801e+02 7.85632523e+01 1.62291509e+02 33 -1.29474421e+02 -7.92886619e+01 -1.61176435e+02 | -1.29474421e+02 -7.92886619e+01 -1.61176435e+02 34 -3.57451911e+01 4.19915540e+01 -2.21186163e+01 | -3.57451911e+01 4.19915540e+01 -2.21186163e+01 35 3.15163442e+01 -3.93989951e+01 3.29769572e+01 | 3.15163442e+01 -3.93989951e+01 3.29769572e+01 36 -2.34519206e+00 -4.06884551e+00 -3.17310030e+00 | -2.34519206e+00 -4.06884551e+00 -3.17310030e+00 37 6.79321883e+01 5.20710495e+01 -1.36548550e+02 | 6.79321883e+01 5.20710495e+01 -1.36548550e+02 38 1.14116649e+02 1.59828540e+02 6.59111941e+01 | 1.14116649e+02 1.59828540e+02 6.59111941e+01 39 -1.14271424e+02 -1.59934691e+02 -6.52083820e+01 | -1.14271424e+02 -1.59934691e+02 -6.52083820e+01 40 -4.93583762e+00 3.51525006e+00 -3.86387502e+00 | -4.93583762e+00 3.51525006e+00 -3.86387502e+00 41 -3.08711587e+02 1.00766050e+02 2.18139605e+02 | -3.08711587e+02 1.00766050e+02 2.18139605e+02 42 -6.17828528e+00 5.20302746e+00 7.15688545e+00 | -6.17828528e+00 5.20302746e+00 7.15688545e+00 43 -1.70843101e+02 3.17349282e+01 3.32264194e+02 | -1.70843101e+02 3.17349282e+01 3.32264194e+02 44 1.11619243e+00 1.21220039e+00 4.58085905e-01 | 1.11619243e+00 1.21220039e+00 4.58085905e-01 45 -1.25318968e+00 -1.95686659e-01 -1.27583451e+00 | -1.25318968e+00 -1.95686659e-01 -1.27583451e+00 46 2.17519951e+02 -1.13297615e+02 -1.17289833e+02 | 2.17519951e+02 -1.13297615e+02 -1.17289833e+02 47 1.14551695e+02 5.16716500e+01 -1.11698041e+02 | 1.14551695e+02 5.16716500e+01 -1.11698041e+02 48 1.84048434e+01 4.29189175e+01 3.04638337e+01 | 1.84048434e+01 4.29189175e+01 3.04638337e+01 49 -2.41319506e+01 -3.92668964e+01 -1.60371522e+01 | -2.41319506e+01 -3.92668964e+01 -1.60371522e+01 50 1.48759033e+02 9.34940800e+01 1.49262651e+01 | 1.48759033e+02 9.34940800e+01 1.49262651e+01 51 -1.58391647e+02 -4.97125360e+01 -8.50267107e+01 | -1.58391647e+02 -4.97125360e+01 -8.50267107e+01 52 -5.30671304e+00 4.14869616e+00 6.42462818e-03 | -5.30671304e+00 4.14869616e+00 6.42462818e-03 53 1.95709894e+02 3.13497117e+02 -1.58288832e+02 | 1.95709894e+02 3.13497117e+02 -1.58288832e+02 54 2.87710948e+00 -5.20315740e+00 -1.31409909e+01 | 2.87710948e+00 -5.20315740e+00 -1.31409909e+01 55 -3.70671075e-01 -9.66458657e-01 -6.93616124e-01 | -3.70671075e-01 -9.66458657e-01 -6.93616124e-01 56 5.28626592e+00 -2.81568391e+00 -1.51912774e+00 | 5.28626592e+00 -2.81568391e+00 -1.51912774e+00 57 -2.49200240e+00 -6.61926348e+00 3.09439164e+00 | -2.49200240e+00 -6.61926348e+00 3.09439164e+00 58 9.27204847e+00 4.91484758e-01 -1.51839742e+01 | 9.27204847e+00 4.91484758e-01 -1.51839742e+01 59 -4.07751313e-01 -4.68590129e-01 5.66281127e-01 | -4.07751313e-01 -4.68590129e-01 5.66281127e-01 60 5.40988827e+01 -8.67560280e+01 -2.24639046e+02 | 5.40988827e+01 -8.67560280e+01 -2.24639046e+02 61 1.51865066e+00 3.95463422e+00 3.72462433e+00 | 1.51865066e+00 3.95463422e+00 3.72462433e+00 62 -6.79346484e+01 -1.96132033e+02 1.89922981e+02 | -6.79346484e+01 -1.96132033e+02 1.89922981e+02 63 -1.32292380e+02 -1.15074604e+02 -2.54189955e+01 | -1.32292380e+02 -1.15074604e+02 -2.54189955e+01 ------------------------------------------------------------------------------------------------------------------------- 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.