!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 = [15, 19, 38, 37, 58, 22, 48, 11, 45, 18, 56, 7, 62, 27, 53, 0, 26, 32, 9, 1, 24, 41, 5, 28, 20, 52, 16, 13, 23, 47, 43, 55, 17, 39, 44, 49, 61, 3, 2, 33, 42, 21, 40, 30, 34, 8, 60, 29, 6, 35, 59, 54, 25, 14, 51, 31, 10, 63, 4, 50, 46, 36, 12, 57] 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)) = -1154.37487473 V(r_1,...,r_N) = -1154.37487473 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 = [4, 52, 27, 13, 0, 17, 50, 61, 62, 26, 38, 33, 16, 3, 35, 45, 12, 5, 36, 54, 40, 31, 59, 46, 34, 58, 9, 2, 44, 49, 47, 21, 60, 11, 24, 14, 18, 55, 10, 48, 20, 43, 57, 41, 28, 15, 23, 30, 39, 29, 6, 63, 1, 56, 19, 37, 53, 42, 25, 22, 32, 7, 8, 51] 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)) = -344.526748692 V(r_1,...,r_N) = -344.526748692 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 3.02109104e-01 2.51356509e+00 2.41917202e+00 | 3.02109104e-01 2.51356509e+00 2.41917202e+00 1 -1.05837934e+01 2.19639380e+01 8.43541038e+00 | -1.05837934e+01 2.19639380e+01 8.43541038e+00 2 4.17845422e+00 -9.26347987e-01 4.33420676e+00 | 4.17845422e+00 -9.26347987e-01 4.33420676e+00 3 1.19067124e+00 -4.78042109e-01 -2.54155826e+00 | 1.19067124e+00 -4.78042109e-01 -2.54155826e+00 4 3.25455727e+00 3.17317611e+00 -3.11627678e+00 | 3.25455727e+00 3.17317611e+00 -3.11627678e+00 5 8.30697194e-02 -4.27444484e+00 2.01461354e+00 | 8.30697194e-02 -4.27444484e+00 2.01461354e+00 6 1.26897458e+01 -2.17088324e+01 -1.11013996e+01 | 1.26897458e+01 -2.17088324e+01 -1.11013996e+01 7 -8.66097180e-01 7.65671340e-01 -1.03407342e+00 | -8.66097180e-01 7.65671340e-01 -1.03407342e+00 8 -3.78308658e+00 2.86897513e+00 3.24027495e+00 | -3.78308658e+00 2.86897513e+00 3.24027495e+00 9 5.61250414e+00 1.67331361e+00 1.55771053e+00 | 5.61250414e+00 1.67331361e+00 1.55771053e+00 10 -1.21460820e+00 2.08179164e+00 5.41646675e+00 | -1.21460820e+00 2.08179164e+00 5.41646675e+00 11 -6.80681394e+00 -1.88136341e+00 -1.59449806e+00 | -6.80681394e+00 -1.88136341e+00 -1.59449806e+00 12 5.90817305e+00 1.22838167e+01 1.12593505e+01 | 5.90817305e+00 1.22838167e+01 1.12593505e+01 13 -6.93375406e+00 -9.28802211e+00 -1.35182140e+01 | -6.93375406e+00 -9.28802211e+00 -1.35182140e+01 14 2.64656614e+00 3.90085259e+00 -2.67942682e+00 | 2.64656614e+00 3.90085259e+00 -2.67942682e+00 15 1.11359213e+01 2.53431513e+01 -3.66454417e+01 | 1.11359213e+01 2.53431513e+01 -3.66454417e+01 16 2.19957333e+00 4.74661557e+00 3.97827051e+00 | 2.19957333e+00 4.74661557e+00 3.97827051e+00 17 8.94160732e+00 1.78106528e+00 2.26231739e+00 | 8.94160732e+00 1.78106528e+00 2.26231739e+00 18 -9.70429331e+00 -3.81449646e+00 6.32664758e-01 | -9.70429331e+00 -3.81449646e+00 6.32664758e-01 19 -1.13253829e+00 -5.38953327e+00 3.41639309e+00 | -1.13253829e+00 -5.38953327e+00 3.41639309e+00 20 -1.51822766e+00 -1.82974810e+00 -2.18814352e+00 | -1.51822766e+00 -1.82974810e+00 -2.18814352e+00 21 1.85558042e+01 3.72986866e+01 -3.53644272e+01 | 1.85558042e+01 3.72986866e+01 -3.53644272e+01 22 3.84909032e+00 1.73631968e-01 -1.06057155e+00 | 3.84909032e+00 1.73631968e-01 -1.06057155e+00 23 2.99866139e+00 -4.46880892e+00 4.06124633e+00 | 2.99866139e+00 -4.46880892e+00 4.06124633e+00 24 -5.66618592e-01 1.23743271e+00 7.19312126e+00 | -5.66618592e-01 1.23743271e+00 7.19312126e+00 25 -2.74479269e+00 7.16774257e-01 3.10742450e+00 | -2.74479269e+00 7.16774257e-01 3.10742450e+00 26 -7.75311235e-01 -1.62358275e+00 1.91915005e+00 | -7.75311235e-01 -1.62358275e+00 1.91915005e+00 27 -9.53997571e-01 -1.18183622e+00 -2.34106832e+00 | -9.53997571e-01 -1.18183622e+00 -2.34106832e+00 28 -1.36266964e+01 -2.82110171e+01 3.56873134e+01 | -1.36266964e+01 -2.82110171e+01 3.56873134e+01 29 -4.02992968e+00 8.12777813e-01 -4.64656846e-01 | -4.02992968e+00 8.12777813e-01 -4.64656846e-01 30 -1.30448567e+01 -3.04961430e+01 3.41104193e+01 | -1.30448567e+01 -3.04961430e+01 3.41104193e+01 31 -3.90863199e+00 -8.23481386e+00 -1.61529419e+00 | -3.90863199e+00 -8.23481386e+00 -1.61529419e+00 32 1.45583060e+01 1.31615413e+01 1.50666777e+01 | 1.45583060e+01 1.31615413e+01 1.50666777e+01 33 -1.34063073e+01 -1.45639505e+01 -9.96969061e+00 | -1.34063073e+01 -1.45639505e+01 -9.96969061e+00 34 1.01090521e-01 -2.27795177e+00 9.24497598e-01 | 1.01090521e-01 -2.27795177e+00 9.24497598e-01 35 -6.51995795e-01 4.38361133e+00 2.35121535e+00 | -6.51995795e-01 4.38361133e+00 2.35121535e+00 36 1.27515061e+00 3.05851620e+00 -4.89436820e+00 | 1.27515061e+00 3.05851620e+00 -4.89436820e+00 37 3.91138456e+00 2.52660251e+00 -2.63304958e+00 | 3.91138456e+00 2.52660251e+00 -2.63304958e+00 38 3.99348703e+00 4.47978453e+00 -2.10388433e+00 | 3.99348703e+00 4.47978453e+00 -2.10388433e+00 39 4.80863641e-01 4.62231678e+00 -6.98926336e+00 | 4.80863641e-01 4.62231678e+00 -6.98926336e+00 40 -3.14831045e+00 4.17893444e+00 1.25530395e+00 | -3.14831045e+00 4.17893444e+00 1.25530395e+00 41 1.74143416e+01 -1.59185660e+01 2.07214163e+01 | 1.74143416e+01 -1.59185660e+01 2.07214163e+01 42 1.66573070e+01 1.03287841e+01 1.98760106e+01 | 1.66573070e+01 1.03287841e+01 1.98760106e+01 43 -2.49891949e+01 -9.87635128e+00 -1.49522661e+01 | -2.49891949e+01 -9.87635128e+00 -1.49522661e+01 44 -1.58013790e+01 2.00449826e+01 -1.91116342e+01 | -1.58013790e+01 2.00449826e+01 -1.91116342e+01 45 -3.57456001e+00 -3.43424772e-02 -2.91793887e+00 | -3.57456001e+00 -3.43424772e-02 -2.91793887e+00 46 2.29520676e+00 -3.18724518e-01 -1.61355469e+00 | 2.29520676e+00 -3.18724518e-01 -1.61355469e+00 47 7.78881106e-01 -7.79782351e-01 -4.69995523e+00 | 7.78881106e-01 -7.79782351e-01 -4.69995523e+00 48 7.76514735e+00 2.17663159e+00 3.46680393e+00 | 7.76514735e+00 2.17663159e+00 3.46680393e+00 49 1.55267518e+01 -1.21501010e+01 2.70448162e+01 | 1.55267518e+01 -1.21501010e+01 2.70448162e+01 50 5.32641809e+00 2.64858157e+00 4.76972858e-01 | 5.32641809e+00 2.64858157e+00 4.76972858e-01 51 -4.05134634e+00 -4.36217559e+00 -3.84536900e+00 | -4.05134634e+00 -4.36217559e+00 -3.84536900e+00 52 -2.26790109e+01 9.03615044e+00 -2.32508178e+01 | -2.26790109e+01 9.03615044e+00 -2.32508178e+01 53 -5.34795697e+00 1.90901498e-01 -5.46652772e+00 | -5.34795697e+00 1.90901498e-01 -5.46652772e+00 54 8.28916054e+00 -1.60650759e+00 -3.08634002e-02 | 8.28916054e+00 -1.60650759e+00 -3.08634002e-02 55 -1.03289674e+00 -6.70593114e+00 -4.12253811e+00 | -1.03289674e+00 -6.70593114e+00 -4.12253811e+00 56 2.24323414e+00 -2.71179203e+00 2.90624053e-01 | 2.24323414e+00 -2.71179203e+00 2.90624053e-01 57 2.14473039e+00 -2.20994435e+00 4.32597146e+00 | 2.14473039e+00 -2.20994435e+00 4.32597146e+00 58 -8.96964409e-01 -6.69183680e-01 -2.57567756e+00 | -8.96964409e-01 -6.69183680e-01 -2.57567756e+00 59 -1.25917121e-01 -7.79723361e-02 -1.44996122e-01 | -1.25917121e-01 -7.79723361e-02 -1.44996122e-01 60 1.36880955e+01 3.62785529e+01 8.81381210e+00 | 1.36880955e+01 3.62785529e+01 8.81381210e+00 61 -2.02692160e+01 -3.93471646e+01 -1.38120290e+01 | -2.02692160e+01 -3.93471646e+01 -1.38120290e+01 62 6.86018640e-01 5.96849398e-01 1.72827280e+00 | 6.86018640e-01 5.96849398e-01 1.72827280e+00 63 -2.51298030e+00 -3.63050304e+00 -2.98844682e+00 | -2.51298030e+00 -3.63050304e+00 -2.98844682e+00 ------------------------------------------------------------------------------------------------------------------------- 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 = [37, 62, 61, 49, 60, 48, 24, 57, 14, 19, 35, 17, 42, 39, 8, 25, 51, 11, 21, 9, 40, 18, 31, 59, 6, 15, 29, 41, 53, 26, 38, 22, 56, 34, 33, 10, 50, 0, 30, 13, 20, 27, 12, 47, 54, 52, 63, 43, 5, 3, 36, 16, 45, 28, 44, 58, 32, 7, 55, 23, 4, 2, 1, 46] 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)) = -2841.25214902 V(r_1,...,r_N) = -2841.25214902 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 3.67038088e+02 5.23196921e+02 5.21924472e+02 | 3.67038088e+02 5.23196921e+02 5.21924472e+02 1 -3.75101648e+02 -5.10218567e+02 -5.17275200e+02 | -3.75101648e+02 -5.10218567e+02 -5.17275200e+02 2 1.75149278e-01 -1.64836117e+00 -3.62578097e+00 | 1.75149278e-01 -1.64836117e+00 -3.62578097e+00 3 -2.21149731e+02 3.24487779e+02 2.73813578e+02 | -2.21149731e+02 3.24487779e+02 2.73813578e+02 4 6.17953224e+00 -4.80031617e+00 2.19153870e+00 | 6.17953224e+00 -4.80031617e+00 2.19153870e+00 5 -5.33633338e-01 -1.22680493e+00 -1.49800185e+00 | -5.33633338e-01 -1.22680493e+00 -1.49800185e+00 6 3.04528873e+00 -7.50937918e+00 -7.76036882e+00 | 3.04528873e+00 -7.50937918e+00 -7.76036882e+00 7 -4.02721537e+02 5.11241366e+02 1.41071213e+02 | -4.02721537e+02 5.11241366e+02 1.41071213e+02 8 -5.60288726e+00 -3.08260609e+00 -3.91672899e+00 | -5.60288726e+00 -3.08260609e+00 -3.91672899e+00 9 1.95095467e+02 3.39644406e+02 -3.23368160e+02 | 1.95095467e+02 3.39644406e+02 -3.23368160e+02 10 -1.83520650e+02 -3.59583338e+02 3.66445065e+02 | -1.83520650e+02 -3.59583338e+02 3.66445065e+02 11 -7.90582470e-01 -3.12425850e-01 2.78733663e-02 | -7.90582470e-01 -3.12425850e-01 2.78733663e-02 12 1.87204482e+02 1.43164693e+02 1.19727397e+02 | 1.87204482e+02 1.43164693e+02 1.19727397e+02 13 -1.88741166e+02 -1.29771550e+02 -1.62842676e+02 | -1.88741166e+02 -1.29771550e+02 -1.62842676e+02 14 -1.95121106e+00 4.32282603e+00 -4.47045246e-01 | -1.95121106e+00 4.32282603e+00 -4.47045246e-01 15 -1.18895365e+02 1.55858902e+02 1.25614579e+02 | -1.18895365e+02 1.55858902e+02 1.25614579e+02 16 -3.45581924e-01 3.89264997e-01 4.77542673e-01 | -3.45581924e-01 3.89264997e-01 4.77542673e-01 17 -5.15527344e+02 4.93590860e+02 3.49579383e+02 | -5.15527344e+02 4.93590860e+02 3.49579383e+02 18 8.67604956e+02 4.14377666e+02 3.09339700e+02 | 8.67604956e+02 4.14377666e+02 3.09339700e+02 19 -8.61171224e+02 -4.09378404e+02 -3.14017264e+02 | -8.61171224e+02 -4.09378404e+02 -3.14017264e+02 20 2.21666441e+02 -3.28105352e+02 -2.73237545e+02 | 2.21666441e+02 -3.28105352e+02 -2.73237545e+02 21 1.30667281e+00 4.21557653e+00 -1.98361146e+00 | 1.30667281e+00 4.21557653e+00 -1.98361146e+00 22 5.24780930e+02 -4.77258309e+02 -3.24945986e+02 | 5.24780930e+02 -4.77258309e+02 -3.24945986e+02 23 -2.22421989e+01 -1.98370983e+01 -2.12496991e+01 | -2.22421989e+01 -1.98370983e+01 -2.12496991e+01 24 7.27754030e-01 -1.73490162e-01 -1.13169385e+00 | 7.27754030e-01 -1.73490162e-01 -1.13169385e+00 25 8.63640822e+02 -1.19147845e+03 1.21231134e+03 | 8.63640822e+02 -1.19147845e+03 1.21231134e+03 26 2.56248163e+02 1.09174644e+02 4.04736301e+02 | 2.56248163e+02 1.09174644e+02 4.04736301e+02 27 -2.55702299e+02 -1.10074801e+02 -4.04521873e+02 | -2.55702299e+02 -1.10074801e+02 -4.04521873e+02 28 -8.60535308e+02 1.18708188e+03 -1.22514407e+03 | -8.60535308e+02 1.18708188e+03 -1.22514407e+03 29 -3.55018748e+01 6.84719792e+01 4.67200208e+01 | -3.55018748e+01 6.84719792e+01 4.67200208e+01 30 3.67869636e+01 4.22203830e+02 1.73841791e+02 | 3.67869636e+01 4.22203830e+02 1.73841791e+02 31 -3.53777086e+01 -4.18889470e+02 -1.70935936e+02 | -3.53777086e+01 -4.18889470e+02 -1.70935936e+02 32 1.65959148e+02 3.14480391e+02 1.90859535e+02 | 1.65959148e+02 3.14480391e+02 1.90859535e+02 33 9.68883053e+01 -1.18375640e+02 -3.37012406e+02 | 9.68883053e+01 -1.18375640e+02 -3.37012406e+02 34 -2.69593023e+02 -1.93012498e+02 1.43034405e+02 | -2.69593023e+02 -1.93012498e+02 1.43034405e+02 35 1.40106008e+02 1.93774341e+02 -1.81353976e+02 | 1.40106008e+02 1.93774341e+02 -1.81353976e+02 36 1.21404283e+00 -9.34203360e+00 -1.46538206e+00 | 1.21404283e+00 -9.34203360e+00 -1.46538206e+00 37 9.18544956e+01 1.99259954e+02 -1.53965163e+02 | 9.18544956e+01 1.99259954e+02 -1.53965163e+02 38 -3.01215084e+00 1.95183487e+00 1.19994913e+00 | -3.01215084e+00 1.95183487e+00 1.19994913e+00 39 1.86926342e+02 3.59653307e+02 -1.94411317e+02 | 1.86926342e+02 3.59653307e+02 -1.94411317e+02 40 1.93536377e+02 1.80168429e+02 1.79638232e+02 | 1.93536377e+02 1.80168429e+02 1.79638232e+02 41 -2.65495638e+02 -5.76709733e+02 5.17010719e+02 | -2.65495638e+02 -5.76709733e+02 5.17010719e+02 42 7.37091794e+02 3.88559314e+02 5.43314048e+02 | 7.37091794e+02 3.88559314e+02 5.43314048e+02 43 -7.34053211e+02 -3.83185657e+02 -5.42038317e+02 | -7.34053211e+02 -3.83185657e+02 -5.42038317e+02 44 -1.77809912e+02 5.49337059e+02 -5.44286437e+02 | -1.77809912e+02 5.49337059e+02 -5.44286437e+02 45 5.87536581e-01 2.77088177e-01 3.84993792e-01 | 5.87536581e-01 2.77088177e-01 3.84993792e-01 46 1.65934366e+02 -3.56185085e+02 1.30442607e+01 | 1.65934366e+02 -3.56185085e+02 1.30442607e+01 47 2.16982336e+02 2.55286655e+02 -1.94661349e+02 | 2.16982336e+02 2.55286655e+02 -1.94661349e+02 48 3.97240691e+02 -5.15105402e+02 -1.47190483e+02 | 3.97240691e+02 -5.15105402e+02 -1.47190483e+02 49 -2.34348938e+02 3.44245962e+02 2.44242955e+02 | -2.34348938e+02 3.44245962e+02 2.44242955e+02 50 5.17236176e+01 8.16933809e+01 5.74084571e+01 | 5.17236176e+01 8.16933809e+01 5.74084571e+01 51 5.25699060e+02 -6.05229783e+02 6.20307699e+02 | 5.25699060e+02 -6.05229783e+02 6.20307699e+02 52 -1.85107634e+02 -3.62996252e+02 1.96882375e+02 | -1.85107634e+02 -3.62996252e+02 1.96882375e+02 53 4.00297988e+00 -4.77637359e+00 9.81860599e+00 | 4.00297988e+00 -4.77637359e+00 9.81860599e+00 54 2.23517971e+02 -3.48703805e+02 -2.41861125e+02 | 2.23517971e+02 -3.48703805e+02 -2.41861125e+02 55 3.83632212e+00 6.81761828e+00 5.15194808e+00 | 3.83632212e+00 6.81761828e+00 5.15194808e+00 56 2.16086010e+01 -2.83134019e+02 1.35449649e+02 | 2.16086010e+01 -2.83134019e+02 1.35449649e+02 57 -5.05510647e+01 -5.96855193e+01 -8.02470374e+01 | -5.05510647e+01 -5.96855193e+01 -8.02470374e+01 58 5.95304432e+01 -5.40283620e+01 -1.83494802e+01 | 5.95304432e+01 -5.40283620e+01 -1.83494802e+01 59 -2.08422457e+01 -9.31025407e+00 -2.35420213e+01 | -2.08422457e+01 -9.31025407e+00 -2.35420213e+01 60 -1.78397451e+02 -2.39637609e+02 2.20672441e+02 | -1.78397451e+02 -2.39637609e+02 2.20672441e+02 61 -3.82286228e+01 -1.69262833e+01 -2.52550664e+01 | -3.82286228e+01 -1.69262833e+01 -2.52550664e+01 62 -5.76274526e+02 5.32359308e+02 -6.82488244e+02 | -5.76274526e+02 5.32359308e+02 -6.82488244e+02 63 3.38521848e+00 4.05787869e-01 -2.12624535e-01 | 3.38521848e+00 4.05787869e-01 -2.12624535e-01 ------------------------------------------------------------------------------------------------------------------------- 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 = [17, 38, 7, 57, 44, 14, 33, 2, 11, 49, 32, 8, 59, 24, 5, 22, 23, 0, 45, 25, 26, 34, 15, 16, 13, 19, 20, 41, 30, 55, 28, 39, 10, 6, 21, 61, 42, 50, 1, 31, 48, 27, 36, 43, 4, 18, 62, 58, 40, 9, 37, 56, 63, 54, 53, 29, 51, 3, 47, 12, 60, 35, 46, 52] 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)) = -1953.20100735 V(r_1,...,r_N) = -1953.20100735 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 6.77146226e+01 5.65714899e+01 3.76616374e+01 | 6.77146226e+01 5.65714899e+01 3.76616374e+01 1 -6.84261353e+01 -5.74952044e+01 -3.63475946e+01 | -6.84261353e+01 -5.74952044e+01 -3.63475946e+01 2 2.63967668e+00 1.83548478e+00 -1.54209564e+00 | 2.63967668e+00 1.83548478e+00 -1.54209564e+00 3 -3.95726249e+00 6.44024587e+00 -3.14361509e+00 | -3.95726249e+00 6.44024587e+00 -3.14361509e+00 4 -4.26453609e-01 -5.54805975e-01 4.16718796e-01 | -4.26453609e-01 -5.54805975e-01 4.16718796e-01 5 2.12048039e+02 -1.12379028e+02 5.53302116e+01 | 2.12048039e+02 -1.12379028e+02 5.53302116e+01 6 1.09484392e+01 8.01532723e+00 9.48036933e+00 | 1.09484392e+01 8.01532723e+00 9.48036933e+00 7 -1.09395289e+01 -3.25807149e+00 -7.74793130e+00 | -1.09395289e+01 -3.25807149e+00 -7.74793130e+00 8 3.54093642e+02 2.65183860e+02 3.62302973e+02 | 3.54093642e+02 2.65183860e+02 3.62302973e+02 9 -3.53669262e+02 -2.65436921e+02 -3.61699463e+02 | -3.53669262e+02 -2.65436921e+02 -3.61699463e+02 10 9.16201797e+02 1.23389594e+03 7.19266403e+02 | 9.16201797e+02 1.23389594e+03 7.19266403e+02 11 -9.14492041e+02 -1.23673045e+03 -7.20965281e+02 | -9.14492041e+02 -1.23673045e+03 -7.20965281e+02 12 -2.54551883e+00 -1.92697523e+00 3.53172315e-01 | -2.54551883e+00 -1.92697523e+00 3.53172315e-01 13 2.83966220e+00 1.87888262e+00 -2.19198570e+00 | 2.83966220e+00 1.87888262e+00 -2.19198570e+00 14 5.40580444e+00 1.70257219e+00 -6.20812236e+00 | 5.40580444e+00 1.70257219e+00 -6.20812236e+00 15 5.59788344e+00 -4.18423302e+00 1.06309893e+00 | 5.59788344e+00 -4.18423302e+00 1.06309893e+00 16 -3.45323377e+00 -2.38327396e+00 -2.44466514e+00 | -3.45323377e+00 -2.38327396e+00 -2.44466514e+00 17 -6.19760735e-01 -3.01974751e+00 7.53106382e+00 | -6.19760735e-01 -3.01974751e+00 7.53106382e+00 18 2.77280464e+01 1.92580443e+01 1.32932104e+01 | 2.77280464e+01 1.92580443e+01 1.32932104e+01 19 -2.26694233e+01 -1.34875278e+01 -1.78725165e+01 | -2.26694233e+01 -1.34875278e+01 -1.78725165e+01 20 1.64796070e-01 -2.28403954e+00 2.35531773e+00 | 1.64796070e-01 -2.28403954e+00 2.35531773e+00 21 -7.62833551e+00 -1.66583990e+00 2.55032014e+00 | -7.62833551e+00 -1.66583990e+00 2.55032014e+00 22 1.03639178e+00 -4.30821972e+00 1.48540209e+00 | 1.03639178e+00 -4.30821972e+00 1.48540209e+00 23 8.81088516e+01 -1.17836046e+02 1.79456723e+02 | 8.81088516e+01 -1.17836046e+02 1.79456723e+02 24 -2.74348746e+00 -3.56987514e+00 3.14291384e+00 | -2.74348746e+00 -3.56987514e+00 3.14291384e+00 25 3.39762139e+00 -4.98446253e-01 1.37666969e+00 | 3.39762139e+00 -4.98446253e-01 1.37666969e+00 26 1.26569761e+01 3.39709503e+01 2.63264256e+01 | 1.26569761e+01 3.39709503e+01 2.63264256e+01 27 -1.43233306e+01 -3.34636797e+01 -2.44575000e+01 | -1.43233306e+01 -3.34636797e+01 -2.44575000e+01 28 -1.29369632e+00 5.77824402e+00 4.86852058e+00 | -1.29369632e+00 5.77824402e+00 4.86852058e+00 29 1.16847771e+00 -3.13449007e+00 -5.39198925e+00 | 1.16847771e+00 -3.13449007e+00 -5.39198925e+00 30 4.32884114e+00 4.37669124e+00 -6.29284481e+00 | 4.32884114e+00 4.37669124e+00 -6.29284481e+00 31 2.87545578e+02 -8.94443188e+02 1.55500156e+02 | 2.87545578e+02 -8.94443188e+02 1.55500156e+02 32 -2.28892293e+00 -3.27478778e+00 -3.44090870e+00 | -2.28892293e+00 -3.27478778e+00 -3.44090870e+00 33 8.54426342e+00 -4.98592725e-01 5.87653841e+00 | 8.54426342e+00 -4.98592725e-01 5.87653841e+00 34 -7.12878876e-01 1.37755125e+00 -2.09195459e+00 | -7.12878876e-01 1.37755125e+00 -2.09195459e+00 35 4.71271471e+01 -9.08081586e+01 5.78043557e+01 | 4.71271471e+01 -9.08081586e+01 5.78043557e+01 36 8.12410732e+01 1.77050692e+02 2.04388619e+02 | 8.12410732e+01 1.77050692e+02 2.04388619e+02 37 -8.68884239e+01 -1.73901606e+02 -2.08756469e+02 | -8.68884239e+01 -1.73901606e+02 -2.08756469e+02 38 -1.83580166e+00 -1.36560801e+00 -3.04530821e-01 | -1.83580166e+00 -1.36560801e+00 -3.04530821e-01 39 -1.74397320e+00 -2.53900238e+00 7.28261115e+00 | -1.74397320e+00 -2.53900238e+00 7.28261115e+00 40 -2.15899185e+02 1.03885384e+02 -4.85103231e+01 | -2.15899185e+02 1.03885384e+02 -4.85103231e+01 41 1.99979609e+02 -8.91092639e+01 -2.83881620e+02 | 1.99979609e+02 -8.91092639e+01 -2.83881620e+02 42 -2.03964762e+02 -1.85388709e+02 4.26191104e+02 | -2.03964762e+02 -1.85388709e+02 4.26191104e+02 43 -1.72858755e+02 3.03553124e+02 6.12117619e+01 | -1.72858755e+02 3.03553124e+02 6.12117619e+01 44 -2.25345944e-02 2.76358267e+02 -1.43298351e+02 | -2.25345944e-02 2.76358267e+02 -1.43298351e+02 45 2.27554955e-02 3.23419280e-01 -6.14342181e-02 | 2.27554955e-02 3.23419280e-01 -6.14342181e-02 46 -4.43644461e+01 9.21036984e+01 -5.69574216e+01 | -4.43644461e+01 9.21036984e+01 -5.69574216e+01 47 -1.22732154e-01 -7.78741611e-01 -2.98737516e-01 | -1.22732154e-01 -7.78741611e-01 -2.98737516e-01 48 3.23056219e+00 -3.03935277e+00 -4.28840909e+00 | 3.23056219e+00 -3.03935277e+00 -4.28840909e+00 49 5.77375372e+02 -9.85205137e+02 3.28274887e+02 | 5.77375372e+02 -9.85205137e+02 3.28274887e+02 50 -8.97616514e+01 1.20525404e+02 -1.78100327e+02 | -8.97616514e+01 1.20525404e+02 -1.78100327e+02 51 1.83180043e+02 -2.08393285e+02 3.66938576e+02 | 1.83180043e+02 -2.08393285e+02 3.66938576e+02 52 -5.80081546e+02 9.94445416e+02 -3.33878096e+02 | -5.80081546e+02 9.94445416e+02 -3.33878096e+02 53 8.61658810e-01 1.09758605e+00 4.81725723e-01 | 8.61658810e-01 1.09758605e+00 4.81725723e-01 54 1.77026572e+02 1.49770779e+02 3.17477567e+01 | 1.77026572e+02 1.49770779e+02 3.17477567e+01 55 -1.71216584e+02 -1.53817149e+02 -3.31271425e+01 | -1.71216584e+02 -1.53817149e+02 -3.31271425e+01 56 1.11214950e+00 2.55597993e+00 1.72253375e+00 | 1.11214950e+00 2.55597993e+00 1.72253375e+00 57 -3.26810842e+00 4.06918222e+00 1.61800272e+00 | -3.26810842e+00 4.06918222e+00 1.61800272e+00 58 -2.91908094e+02 8.95355942e+02 -1.52663006e+02 | -2.91908094e+02 8.95355942e+02 -1.52663006e+02 59 -4.57512902e-01 -5.66385890e-01 -7.64910277e-01 | -4.57512902e-01 -5.66385890e-01 -7.64910277e-01 60 1.75923384e+02 -3.08192215e+02 -6.18263868e+01 | 1.75923384e+02 -3.08192215e+02 -6.18263868e+01 61 -2.92712427e+00 2.52446281e+00 -1.93623234e-01 | -2.92712427e+00 2.52446281e+00 -1.93623234e-01 62 -6.82886835e+01 2.15450428e+02 -2.18783339e+02 | -6.82886835e+01 2.15450428e+02 -2.18783339e+02 63 -1.13450546e+02 -1.04169905e+01 -1.49767187e+02 | -1.13450546e+02 -1.04169905e+01 -1.49767187e+02 ------------------------------------------------------------------------------------------------------------------------- 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.