!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 : Sim_LAMMPS_Polymorphic_ZhouJonesChu_2017_GaInN__SM_887684855692_000 Supported species : Ga In N random seed = 13 lattice constant (orig) = 5.000 perturbation amplitude = 0.500 number unit cells per side = 2 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Ga (Configuration in file "config-Ga.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [3, 51, 32, 0, 62, 27, 31, 46, 48, 43, 53, 49, 41, 17, 52, 60, 37, 13, 45, 34, 55, 24, 30, 63, 21, 42, 54, 5, 33, 59, 22, 6, 2, 28, 19, 50, 56, 16, 47, 61, 58, 12, 25, 9, 57, 18, 7, 38, 8, 11, 35, 1, 14, 10, 26, 20, 36, 44, 40, 29, 15, 39, 4, 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)) = 271.82193827877325 V(r_1,...,r_N) = 271.82193827877364 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 -8.83601480e+00 -4.10623224e+00 -1.30331568e+00 | -8.83601480e+00 -4.10623224e+00 -1.30331568e+00 1 -1.29597007e+01 -1.85285670e+01 7.17583147e+00 | -1.29597007e+01 -1.85285670e+01 7.17583147e+00 2 -3.82043426e+00 1.43145947e+01 -3.19786260e+01 | -3.82043426e+00 1.43145947e+01 -3.19786260e+01 3 1.88428769e+01 1.94049944e+01 7.30700231e+00 | 1.88428769e+01 1.94049944e+01 7.30700231e+00 4 -7.26019372e+00 -1.77779308e+01 9.24636999e+00 | -7.26019372e+00 -1.77779308e+01 9.24636999e+00 5 8.28740036e+00 -1.42065176e+01 3.45907858e+00 | 8.28740036e+00 -1.42065176e+01 3.45907858e+00 6 -1.70219043e+00 -1.38518809e+00 -2.27445839e+00 | -1.70219043e+00 -1.38518809e+00 -2.27445839e+00 7 -2.57974707e+01 5.87805792e+01 -3.55192354e+01 | -2.57974707e+01 5.87805792e+01 -3.55192354e+01 8 -8.71086233e+00 -6.01397324e+00 -1.10730884e+01 | -8.71086233e+00 -6.01397324e+00 -1.10730884e+01 9 -8.82237439e-01 6.86960494e+00 9.32922174e+00 | -8.82237439e-01 6.86960494e+00 9.32922174e+00 10 -7.60241159e+00 -6.77746876e+00 -1.19511718e+01 | -7.60241159e+00 -6.77746876e+00 -1.19511718e+01 11 1.24142446e+01 8.89367433e+00 8.44994429e+00 | 1.24142446e+01 8.89367433e+00 8.44994429e+00 12 -1.41062956e+01 -1.65392336e+01 -1.19211516e+01 | -1.41062956e+01 -1.65392336e+01 -1.19211516e+01 13 2.35187130e+01 5.01246608e+00 1.24626367e+01 | 2.35187130e+01 5.01246608e+00 1.24626367e+01 14 -1.88556094e-01 1.88215161e+01 -2.55059451e+00 | -1.88556094e-01 1.88215161e+01 -2.55059451e+00 15 6.78528334e+00 4.05377697e+00 1.55606770e+00 | 6.78528334e+00 4.05377697e+00 1.55606770e+00 16 -2.25232574e+01 -1.21254249e+01 -1.36781780e+01 | -2.25232574e+01 -1.21254249e+01 -1.36781780e+01 17 1.72638526e+01 3.09623960e+00 1.93609307e+01 | 1.72638526e+01 3.09623960e+00 1.93609307e+01 18 3.23220976e+00 7.22778707e+00 -6.21605248e+00 | 3.23220976e+00 7.22778707e+00 -6.21605248e+00 19 -4.73109257e+01 2.98306774e+01 -3.12648709e+01 | -4.73109257e+01 2.98306774e+01 -3.12648709e+01 20 -1.51875611e+01 -9.46484301e+00 -1.55411518e+01 | -1.51875611e+01 -9.46484301e+00 -1.55411518e+01 21 2.49838512e+01 1.46568912e+01 1.10462407e+01 | 2.49838512e+01 1.46568912e+01 1.10462407e+01 22 -5.02385570e+00 -1.41296710e+01 -2.37177805e+01 | -5.02385570e+00 -1.41296710e+01 -2.37177805e+01 23 5.37615461e+00 1.42508029e+01 2.36482310e+01 | 5.37615461e+00 1.42508029e+01 2.36482310e+01 24 -2.27740946e+01 -1.31473440e+01 -3.08761275e+01 | -2.27740946e+01 -1.31473440e+01 -3.08761275e+01 25 2.68800621e+00 2.82270764e+01 1.57538415e+01 | 2.68800621e+00 2.82270764e+01 1.57538415e+01 26 -2.22531582e+00 -2.07820161e-03 -3.70887511e+00 | -2.22531582e+00 -2.07820161e-03 -3.70887511e+00 27 2.21385544e+00 9.34118758e-01 3.64102328e+00 | 2.21385544e+00 9.34118758e-01 3.64102328e+00 28 3.36998157e+00 -2.42897823e+01 1.01700635e+01 | 3.36998157e+00 -2.42897823e+01 1.01700635e+01 29 1.29865033e+01 6.26180412e+00 1.06030615e+01 | 1.29865033e+01 6.26180412e+00 1.06030615e+01 30 4.46117566e+01 -2.66291316e+01 2.77157819e+01 | 4.46117566e+01 -2.66291316e+01 2.77157819e+01 31 -2.35966799e+01 1.08428763e+01 -1.25118786e+01 | -2.35966799e+01 1.08428763e+01 -1.25118786e+01 32 -6.61413444e+00 -9.05489526e+00 -1.21935542e+01 | -6.61413444e+00 -9.05489526e+00 -1.21935542e+01 33 -1.29370913e+01 3.00566422e+01 -2.08954112e+01 | -1.29370913e+01 3.00566422e+01 -2.08954112e+01 34 2.69642744e+01 -6.87012894e+01 3.69869355e+01 | 2.69642744e+01 -6.87012894e+01 3.69869355e+01 35 -1.73212478e+01 -2.66914310e+01 2.61161559e+01 | -1.73212478e+01 -2.66914310e+01 2.61161559e+01 36 2.12747930e+01 -2.18565577e+01 3.17231435e+01 | 2.12747930e+01 -2.18565577e+01 3.17231435e+01 37 -9.87788701e+00 -9.04501038e+00 5.93567234e+00 | -9.87788701e+00 -9.04501038e+00 5.93567234e+00 38 -1.33267103e+01 -8.47992026e+00 -1.10734135e+01 | -1.33267103e+01 -8.47992026e+00 -1.10734135e+01 39 -9.08053066e+00 -1.05108151e+01 2.33246313e+01 | -9.08053066e+00 -1.05108151e+01 2.33246313e+01 40 2.47406647e-01 -5.99418686e-01 4.98363405e+00 | 2.47406647e-01 -5.99418686e-01 4.98363405e+00 41 -2.04660545e+01 3.58515445e+01 -2.99006171e+01 | -2.04660545e+01 3.58515445e+01 -2.99006171e+01 42 -3.15227120e+01 -2.19223175e+01 -3.06150556e+01 | -3.15227120e+01 -2.19223175e+01 -3.06150556e+01 43 2.79894612e+01 3.07077611e+01 3.37148221e+01 | 2.79894612e+01 3.07077611e+01 3.37148221e+01 44 2.52703840e+01 -4.33801551e+01 2.02026733e+01 | 2.52703840e+01 -4.33801551e+01 2.02026733e+01 45 5.73160159e-01 1.85042242e+00 6.87417732e-01 | 5.73160159e-01 1.85042242e+00 6.87417732e-01 46 -4.08699371e+00 1.22935519e+00 -3.80522990e+00 | -4.08699371e+00 1.22935519e+00 -3.80522990e+00 47 1.42766664e+00 1.12604353e+01 5.92201491e+00 | 1.42766664e+00 1.12604353e+01 5.92201491e+00 48 -1.71381575e+01 -3.04255553e+00 -3.25461726e+00 | -1.71381575e+01 -3.04255553e+00 -3.25461726e+00 49 -4.58209569e-01 2.57791368e-01 1.15214463e+01 | -4.58209569e-01 2.57791368e-01 1.15214463e+01 50 -2.25518607e+00 -1.03281563e+01 -2.06769665e+01 | -2.25518607e+00 -1.03281563e+01 -2.06769665e+01 51 1.11002079e+01 1.90558965e+01 1.64955867e+01 | 1.11002079e+01 1.90558965e+01 1.64955867e+01 52 1.82009881e+01 2.06414973e+01 -1.34016318e+01 | 1.82009881e+01 2.06414973e+01 -1.34016318e+01 53 -4.05610499e+00 -3.33259650e+00 9.41866908e+00 | -4.05610499e+00 -3.33259650e+00 9.41866908e+00 54 -3.80932794e+00 -3.68790348e+00 -3.59377407e+00 | -3.80932794e+00 -3.68790348e+00 -3.59377407e+00 55 4.77462316e+00 2.60053745e+00 2.78489477e+00 | 4.77462316e+00 2.60053745e+00 2.78489477e+00 56 1.93336998e+01 2.30040075e+01 -2.16303408e+01 | 1.93336998e+01 2.30040075e+01 -2.16303408e+01 57 2.23811273e+01 -3.86534346e+01 -4.34588316e+01 | 2.23811273e+01 -3.86534346e+01 -4.34588316e+01 58 2.69063834e+01 -9.78666578e+00 1.42510103e+01 | 2.69063834e+01 -9.78666578e+00 1.42510103e+01 59 6.67195158e-01 -2.73748758e-01 -6.25280399e-01 | 6.67195158e-01 -2.73748758e-01 -6.25280399e-01 60 -9.87819218e+00 -8.06673456e+00 -1.08060842e+01 | -9.87819218e+00 -8.06673456e+00 -1.08060842e+01 61 1.33214028e+01 1.35761609e+01 1.01170914e+01 | 1.33214028e+01 1.35761609e+01 1.01170914e+01 62 -1.35911861e+01 4.05300020e+01 3.52350954e+01 | -1.35911861e+01 4.05300020e+01 3.52350954e+01 63 -7.96792368e-02 4.35458146e-01 1.67114361e+00 | -7.96792368e-02 4.35458146e-01 1.67114361e+00 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = In (Configuration in file "config-In.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [41, 20, 33, 4, 3, 49, 16, 44, 31, 11, 32, 9, 46, 48, 24, 53, 6, 21, 52, 34, 1, 17, 28, 60, 14, 42, 61, 50, 22, 40, 51, 8, 10, 2, 19, 63, 39, 38, 37, 36, 29, 0, 25, 56, 7, 54, 12, 55, 13, 5, 27, 30, 18, 15, 45, 47, 43, 58, 57, 62, 23, 26, 59, 35] 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)) = 307.20881351910083 V(r_1,...,r_N) = 307.20881351910106 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 -1.58054548e+01 -1.72489666e+01 -1.96776982e+01 | -1.58054548e+01 -1.72489666e+01 -1.96776982e+01 1 1.53501841e+01 -3.85413310e+00 -7.50853108e+00 | 1.53501841e+01 -3.85413310e+00 -7.50853108e+00 2 5.76488139e+00 7.50652843e+00 -6.70237253e+00 | 5.76488139e+00 7.50652843e+00 -6.70237253e+00 3 -1.00127815e+01 -6.40900021e+00 3.29883301e+00 | -1.00127815e+01 -6.40900021e+00 3.29883301e+00 4 -1.09753634e+01 -1.10002119e+01 -1.58363741e+01 | -1.09753634e+01 -1.10002119e+01 -1.58363741e+01 5 2.28288193e+01 -7.20202434e+00 2.65146762e+01 | 2.28288193e+01 -7.20202434e+00 2.65146762e+01 6 -2.37574629e+01 1.91133249e+01 2.04831241e+01 | -2.37574629e+01 1.91133249e+01 2.04831241e+01 7 -2.57311631e+00 -3.16860462e+00 5.03802564e+00 | -2.57311631e+00 -3.16860462e+00 5.03802564e+00 8 -5.35093054e+00 -5.02611091e+00 -5.62542457e+00 | -5.35093054e+00 -5.02611091e+00 -5.62542457e+00 9 -6.13992659e+00 1.66013646e+01 -5.25728785e+00 | -6.13992659e+00 1.66013646e+01 -5.25728785e+00 10 -7.45462936e+00 -1.73587497e+01 -2.26764325e+01 | -7.45462936e+00 -1.73587497e+01 -2.26764325e+01 11 1.30548895e+01 8.64381698e+00 1.36225689e+01 | 1.30548895e+01 8.64381698e+00 1.36225689e+01 12 9.87554915e+00 -1.62459614e+01 6.12769735e+00 | 9.87554915e+00 -1.62459614e+01 6.12769735e+00 13 4.91729494e+00 7.90591902e-01 1.46043231e+00 | 4.91729494e+00 7.90591902e-01 1.46043231e+00 14 1.47780102e+00 9.87653474e+00 -1.87837289e-01 | 1.47780102e+00 9.87653474e+00 -1.87837289e-01 15 -1.40923513e-01 -1.62476917e+00 -1.14441978e+01 | -1.40923513e-01 -1.62476917e+00 -1.14441978e+01 16 -3.90668412e-01 -1.78734388e+00 -1.53210432e+00 | -3.90668412e-01 -1.78734388e+00 -1.53210432e+00 17 2.49400842e+01 -1.86677722e+01 -1.98813566e+01 | 2.49400842e+01 -1.86677722e+01 -1.98813566e+01 18 -3.89486687e+00 -7.24750019e-01 -9.15232608e+00 | -3.89486687e+00 -7.24750019e-01 -9.15232608e+00 19 -5.25073488e-01 5.65343909e+00 -2.40480465e+00 | -5.25073488e-01 5.65343909e+00 -2.40480465e+00 20 1.51819638e+01 -1.41520220e+01 6.91317821e+00 | 1.51819638e+01 -1.41520220e+01 6.91317821e+00 21 4.64187088e+00 -9.73097799e+00 4.20793350e+00 | 4.64187088e+00 -9.73097799e+00 4.20793350e+00 22 -4.84540082e+01 2.75997927e+01 7.93801493e+00 | -4.84540082e+01 2.75997927e+01 7.93801493e+00 23 -3.96517084e-01 1.05343581e+01 2.69253056e+00 | -3.96517084e-01 1.05343581e+01 2.69253056e+00 24 -2.73446103e+01 -2.13771710e+01 -4.01679913e+01 | -2.73446103e+01 -2.13771710e+01 -4.01679913e+01 25 2.66014902e+01 2.13305465e+01 3.43425436e+01 | 2.66014902e+01 2.13305465e+01 3.43425436e+01 26 3.32498358e+00 5.27231633e+00 -8.20067014e+00 | 3.32498358e+00 5.27231633e+00 -8.20067014e+00 27 2.64483644e+00 1.91511091e+00 2.93117216e+00 | 2.64483644e+00 1.91511091e+00 2.93117216e+00 28 2.39764261e+00 6.14980372e+00 1.12630370e+01 | 2.39764261e+00 6.14980372e+00 1.12630370e+01 29 7.89900341e+00 -4.85557692e+00 -1.33921872e+00 | 7.89900341e+00 -4.85557692e+00 -1.33921872e+00 30 9.78944005e-01 -5.82690191e+00 -5.72041007e+00 | 9.78944005e-01 -5.82690191e+00 -5.72041007e+00 31 9.05724032e+00 1.43039259e+01 2.90698434e+00 | 9.05724032e+00 1.43039259e+01 2.90698434e+00 32 -3.37428061e+00 -1.10386699e+01 -1.42597525e+01 | -3.37428061e+00 -1.10386699e+01 -1.42597525e+01 33 -7.28053761e+00 2.54526080e+00 7.34441942e+00 | -7.28053761e+00 2.54526080e+00 7.34441942e+00 34 4.01551753e+00 8.08096586e+00 -5.59319971e-01 | 4.01551753e+00 8.08096586e+00 -5.59319971e-01 35 1.90103014e+01 -1.38399521e+01 -3.19556851e+01 | 1.90103014e+01 -1.38399521e+01 -3.19556851e+01 36 5.69576409e+00 -5.02909324e+00 3.59345171e+00 | 5.69576409e+00 -5.02909324e+00 3.59345171e+00 37 -3.86727742e+00 -1.06248256e+01 1.38284438e+01 | -3.86727742e+00 -1.06248256e+01 1.38284438e+01 38 -2.95728758e+01 -8.39542484e+00 -1.62035365e+01 | -2.95728758e+01 -8.39542484e+00 -1.62035365e+01 39 2.24473365e+01 1.09247353e+01 2.81981634e+01 | 2.24473365e+01 1.09247353e+01 2.81981634e+01 40 -1.53189179e+01 -2.15518874e+01 -1.42667192e+01 | -1.53189179e+01 -2.15518874e+01 -1.42667192e+01 41 1.47571417e+01 2.24075993e+01 1.19352857e+01 | 1.47571417e+01 2.24075993e+01 1.19352857e+01 42 -1.94284904e+00 -2.90888611e+00 -9.64487700e-01 | -1.94284904e+00 -2.90888611e+00 -9.64487700e-01 43 9.76486597e+00 -7.50766156e-01 8.02793870e-01 | 9.76486597e+00 -7.50766156e-01 8.02793870e-01 44 -1.29509330e+00 -3.40804422e+00 1.62030676e+00 | -1.29509330e+00 -3.40804422e+00 1.62030676e+00 45 2.51460255e+00 1.73522203e+00 1.00320513e+00 | 2.51460255e+00 1.73522203e+00 1.00320513e+00 46 1.22407760e+01 2.05453325e+00 -1.52869782e+00 | 1.22407760e+01 2.05453325e+00 -1.52869782e+00 47 -2.97108712e+00 -7.75128344e+00 1.33659131e+01 | -2.97108712e+00 -7.75128344e+00 1.33659131e+01 48 -6.74408313e+00 -2.04549380e+01 -1.37016461e+01 | -6.74408313e+00 -2.04549380e+01 -1.37016461e+01 49 2.37247229e+00 1.65906063e+01 -3.68670276e+00 | 2.37247229e+00 1.65906063e+01 -3.68670276e+00 50 -3.20341510e+00 -1.06771704e+00 3.58921230e+00 | -3.20341510e+00 -1.06771704e+00 3.58921230e+00 51 -3.94296146e+01 3.86375117e+01 -2.20063832e+01 | -3.94296146e+01 3.86375117e+01 -2.20063832e+01 52 -2.12721501e+01 2.39060099e+01 2.37524577e+01 | -2.12721501e+01 2.39060099e+01 2.37524577e+01 53 -6.91930900e+00 -8.51774380e+00 9.13527987e+00 | -6.91930900e+00 -8.51774380e+00 9.13527987e+00 54 -1.76846198e+01 -1.24765532e+01 1.25988021e+00 | -1.76846198e+01 -1.24765532e+01 1.25988021e+00 55 1.32918737e+01 1.85977280e+01 8.50492071e+00 | 1.32918737e+01 1.85977280e+01 8.50492071e+00 56 -1.14653101e+01 -3.71481668e+00 -6.56525508e+00 | -1.14653101e+01 -3.71481668e+00 -6.56525508e+00 57 -1.95120074e+01 3.75234594e+01 -1.77966622e+01 | -1.95120074e+01 3.75234594e+01 -1.77966622e+01 58 -3.02995849e+00 2.62787972e+00 6.51074481e+00 | -3.02995849e+00 2.62787972e+00 6.51074481e+00 59 1.05250158e+00 1.02353407e+00 1.84561186e+00 | 1.05250158e+00 1.02353407e+00 1.84561186e+00 60 2.59784426e+01 -1.77636353e+01 2.02791739e+01 | 2.59784426e+01 -1.77636353e+01 2.02791739e+01 61 2.25251299e+00 1.94703014e+00 2.12056884e+00 | 2.25251299e+00 1.94703014e+00 2.12056884e+00 62 4.11477722e+01 -3.89866745e+01 6.54341452e+00 | 4.11477722e+01 -3.89866745e+01 6.54341452e+00 63 1.06203599e+01 1.06484286e+01 1.18358865e+01 | 1.06203599e+01 1.06484286e+01 1.18358865e+01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = N (Configuration in file "config-N.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [16, 23, 60, 49, 56, 20, 51, 26, 22, 34, 40, 27, 41, 59, 44, 57, 0, 19, 61, 17, 5, 42, 8, 1, 39, 43, 7, 11, 47, 62, 33, 63, 35, 30, 9, 32, 37, 36, 55, 24, 10, 12, 21, 25, 14, 58, 48, 28, 46, 3, 54, 6, 53, 52, 50, 38, 4, 15, 45, 13, 2, 18, 29, 31] 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)) = 1010.1861537353906 V(r_1,...,r_N) = 1010.1861537353907 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 -3.12983964e+01 -1.92449862e+01 -3.31936008e+00 | -3.12983964e+01 -1.92449862e+01 -3.31936008e+00 1 -1.19510608e+02 -8.51702604e+01 4.35317738e+01 | -1.19510608e+02 -8.51702604e+01 4.35317738e+01 2 1.32267230e+02 9.49088778e+01 -5.29164088e+01 | 1.32267230e+02 9.49088778e+01 -5.29164088e+01 3 -1.02694707e+02 1.36385390e+02 -1.88309805e+02 | -1.02694707e+02 1.36385390e+02 -1.88309805e+02 4 -6.50433657e+00 -1.75885166e+01 -1.04170988e+01 | -6.50433657e+00 -1.75885166e+01 -1.04170988e+01 5 4.63155532e+01 -3.11025948e+01 -4.64269991e+01 | 4.63155532e+01 -3.11025948e+01 -4.64269991e+01 6 -1.93559254e+00 8.60010039e-01 -2.47759554e+00 | -1.93559254e+00 8.60010039e-01 -2.47759554e+00 7 -4.59824921e+01 7.53188886e+01 -8.29118399e+01 | -4.59824921e+01 7.53188886e+01 -8.29118399e+01 8 -1.30622009e+01 -6.87307265e+00 -1.50195510e+01 | -1.30622009e+01 -6.87307265e+00 -1.50195510e+01 9 -2.32633866e+01 4.78567743e-01 4.40065828e+00 | -2.32633866e+01 4.78567743e-01 4.40065828e+00 10 1.26581391e+01 1.28721784e+01 -1.16816326e+01 | 1.26581391e+01 1.28721784e+01 -1.16816326e+01 11 1.32437298e+02 -9.13784487e+01 -7.24943780e+01 | 1.32437298e+02 -9.13784487e+01 -7.24943780e+01 12 -2.08546343e+00 -2.97844724e+01 1.15792619e+01 | -2.08546343e+00 -2.97844724e+01 1.15792619e+01 13 2.24450025e+01 2.11372865e+01 1.12925706e+01 | 2.24450025e+01 2.11372865e+01 1.12925706e+01 14 1.12282182e+02 -1.24622042e+02 1.94802116e+02 | 1.12282182e+02 -1.24622042e+02 1.94802116e+02 15 -2.61944305e+01 5.17991588e+00 -5.49422933e+01 | -2.61944305e+01 5.17991588e+00 -5.49422933e+01 16 -6.98430635e+00 -4.61734731e+00 -4.74587967e+00 | -6.98430635e+00 -4.61734731e+00 -4.74587967e+00 17 -3.99750819e+01 -1.66009354e+01 2.50684323e+00 | -3.99750819e+01 -1.66009354e+01 2.50684323e+00 18 1.34505397e+01 -8.79067700e+00 -5.67993732e+01 | 1.34505397e+01 -8.79067700e+00 -5.67993732e+01 19 -5.80735232e+01 6.12414369e+01 -2.50770671e+00 | -5.80735232e+01 6.12414369e+01 -2.50770671e+00 20 -5.92494246e+01 -2.24437113e+02 -8.31382839e+01 | -5.92494246e+01 -2.24437113e+02 -8.31382839e+01 21 7.97270544e+01 2.00974614e+02 9.49380730e+01 | 7.97270544e+01 2.00974614e+02 9.49380730e+01 22 -3.89804741e+01 -3.83834646e+01 -6.32959389e+01 | -3.89804741e+01 -3.83834646e+01 -6.32959389e+01 23 4.56216302e+00 4.73181058e+01 5.97956195e+01 | 4.56216302e+00 4.73181058e+01 5.97956195e+01 24 -4.40467581e+01 -5.66162532e+01 -7.05950285e+01 | -4.40467581e+01 -5.66162532e+01 -7.05950285e+01 25 3.03238430e+01 7.03013165e+01 5.31876941e+01 | 3.03238430e+01 7.03013165e+01 5.31876941e+01 26 -1.41380107e+01 -6.02151305e+00 -2.54990868e+01 | -1.41380107e+01 -6.02151305e+00 -2.54990868e+01 27 1.48079983e+01 6.46258874e+00 2.46839579e+01 | 1.48079983e+01 6.46258874e+00 2.46839579e+01 28 -1.39302499e+02 3.88808974e+01 4.17280054e+01 | -1.39302499e+02 3.88808974e+01 4.17280054e+01 29 2.37532442e+01 4.26727490e+01 4.19271043e+01 | 2.37532442e+01 4.26727490e+01 4.19271043e+01 30 2.42179617e+01 -6.78287424e+01 -2.57748985e+01 | 2.42179617e+01 -6.78287424e+01 -2.57748985e+01 31 5.19256051e+01 4.93296271e+01 5.43235637e+01 | 5.19256051e+01 4.93296271e+01 5.43235637e+01 32 -3.52078517e+01 -2.67000430e+01 -2.01798382e+01 | -3.52078517e+01 -2.67000430e+01 -2.01798382e+01 33 1.88208094e+01 -1.12926651e+01 1.28589427e+01 | 1.88208094e+01 -1.12926651e+01 1.28589427e+01 34 3.10060027e+01 -7.73273069e+01 9.32603247e+01 | 3.10060027e+01 -7.73273069e+01 9.32603247e+01 35 3.79082379e+00 -5.26914945e+00 -4.10187601e+01 | 3.79082379e+00 -5.26914945e+00 -4.10187601e+01 36 7.66803788e+00 -4.63552452e+00 5.93388491e+00 | 7.66803788e+00 -4.63552452e+00 5.93388491e+00 37 -3.12847984e+00 -2.82037062e+00 4.53158574e+00 | -3.12847984e+00 -2.82037062e+00 4.53158574e+00 38 -1.21183683e+01 1.60769995e+01 7.61578619e+00 | -1.21183683e+01 1.60769995e+01 7.61578619e+00 39 -1.66984006e-02 7.44967835e+00 1.13502455e+01 | -1.66984006e-02 7.44967835e+00 1.13502455e+01 40 1.06347879e+01 -1.79236171e+01 -1.81523850e+00 | 1.06347879e+01 -1.79236171e+01 -1.81523850e+00 41 -5.08210816e+00 -4.77953931e+01 -1.47529761e+00 | -5.08210816e+00 -4.77953931e+01 -1.47529761e+00 42 5.55652308e+01 -6.20662721e+00 2.93139028e+01 | 5.55652308e+01 -6.20662721e+00 2.93139028e+01 43 6.52166052e+01 -7.40707768e+01 -3.01559794e+01 | 6.52166052e+01 -7.40707768e+01 -3.01559794e+01 44 1.75605352e+00 -2.87729710e+00 -1.43241808e+00 | 1.75605352e+00 -2.87729710e+00 -1.43241808e+00 45 -3.74667282e-01 2.40827871e+00 1.58156849e-01 | -3.74667282e-01 2.40827871e+00 1.58156849e-01 46 -1.93487980e+02 -9.48499281e+01 -2.11980383e+02 | -1.93487980e+02 -9.48499281e+01 -2.11980383e+02 47 1.80792682e+02 1.32817268e+02 2.39229392e+02 | 1.80792682e+02 1.32817268e+02 2.39229392e+02 48 -4.11260252e+01 5.51956811e+01 2.04703272e+00 | -4.11260252e+01 5.51956811e+01 2.04703272e+00 49 2.35324977e+01 -7.04679798e+01 -1.02328876e+02 | 2.35324977e+01 -7.04679798e+01 -1.02328876e+02 50 1.48224688e+01 -1.09688626e+01 -5.71548563e+00 | 1.48224688e+01 -1.09688626e+01 -5.71548563e+00 51 5.62402222e+00 2.60246853e+01 1.92121562e+01 | 5.62402222e+00 2.60246853e+01 1.92121562e+01 52 -2.22274536e-01 1.23757605e+01 6.37888009e+01 | -2.22274536e-01 1.23757605e+01 6.37888009e+01 53 6.46962246e-01 2.11677930e+00 6.68835764e+00 | 6.46962246e-01 2.11677930e+00 6.68835764e+00 54 -3.48138526e+01 5.74095780e+01 9.39786990e+01 | -3.48138526e+01 5.74095780e+01 9.39786990e+01 55 1.37030614e+01 1.51294655e+01 9.93382611e+00 | 1.37030614e+01 1.51294655e+01 9.93382611e+00 56 1.70498203e+00 1.73023314e+01 2.94448094e+00 | 1.70498203e+00 1.73023314e+01 2.94448094e+00 57 -3.14707574e+01 -4.77279649e+01 1.38863018e+01 | -3.14707574e+01 -4.77279649e+01 1.38863018e+01 58 -5.75843150e+00 3.64349165e+01 -5.76297810e+01 | -5.75843150e+00 3.64349165e+01 -5.76297810e+01 59 2.29685645e+01 1.42304790e+01 1.67414729e+01 | 2.29685645e+01 1.42304790e+01 1.67414729e+01 60 -1.83013790e+01 5.30149516e+01 4.07411993e+01 | -1.83013790e+01 5.30149516e+01 4.07411993e+01 61 -6.02745031e-01 1.36099247e+01 1.72557973e+01 | -6.02745031e-01 1.36099247e+01 1.72557973e+01 62 -7.77517529e+00 -8.20778417e-01 1.04997437e+01 | -7.77517529e+00 -8.20778417e-01 1.04997437e+01 63 3.34108039e+00 4.89549644e+00 6.33788374e+00 | 3.34108039e+00 4.89549644e+00 6.33788374e+00 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MIXED STRUCTURE -- Species = Ga In N (Configuration in file "config-GaInN.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [28, 21, 31, 32, 5, 4, 58, 62, 20, 49, 14, 61, 39, 25, 10, 42, 24, 57, 29, 23, 8, 1, 33, 19, 16, 13, 40, 35, 0, 18, 44, 2, 3, 22, 36, 27, 34, 54, 45, 12, 26, 50, 15, 63, 30, 38, 59, 55, 51, 9, 41, 48, 56, 53, 37, 47, 52, 17, 6, 46, 60, 11, 7, 43] 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)) = 172.5986650997508 V(r_1,...,r_N) = 172.59866509975086 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 -3.37667525e+00 -2.51405704e+00 -2.67764691e+00 | -3.37667525e+00 -2.51405704e+00 -2.67764691e+00 1 -5.66048038e+00 6.10494741e+00 -1.11638717e+01 | -5.66048038e+00 6.10494741e+00 -1.11638717e+01 2 -2.56964443e+01 -3.60851542e+01 -3.46286373e+01 | -2.56964443e+01 -3.60851542e+01 -3.46286373e+01 3 1.83755476e+01 3.44636283e+01 2.36263889e+01 | 1.83755476e+01 3.44636283e+01 2.36263889e+01 4 9.41070496e+00 -1.28985780e+01 1.30684396e+01 | 9.41070496e+00 -1.28985780e+01 1.30684396e+01 5 8.47201877e+00 -1.75337357e+01 -1.48018301e+01 | 8.47201877e+00 -1.75337357e+01 -1.48018301e+01 6 -1.06279425e+01 -4.38056178e+00 -6.69890342e+00 | -1.06279425e+01 -4.38056178e+00 -6.69890342e+00 7 -1.24090334e+01 1.56162916e+01 -1.31952636e+01 | -1.24090334e+01 1.56162916e+01 -1.31952636e+01 8 1.03021243e+00 -3.29223352e-01 -1.32704206e+00 | 1.03021243e+00 -3.29223352e-01 -1.32704206e+00 9 -9.21746632e-01 1.22100048e+00 -4.49109333e-01 | -9.21746632e-01 1.22100048e+00 -4.49109333e-01 10 -1.49861612e+01 -6.45866610e+00 -1.16318483e+01 | -1.49861612e+01 -6.45866610e+00 -1.16318483e+01 11 1.63146938e+01 3.28585498e+00 9.67643921e+00 | 1.63146938e+01 3.28585498e+00 9.67643921e+00 12 -1.73511273e+00 5.93532585e-01 -2.23031302e-01 | -1.73511273e+00 5.93532585e-01 -2.23031302e-01 13 1.02942667e+00 1.04489643e-01 -3.51367388e-01 | 1.02942667e+00 1.04489643e-01 -3.51367388e-01 14 9.50432047e+00 2.94167830e-01 7.94136689e+00 | 9.50432047e+00 2.94167830e-01 7.94136689e+00 15 2.54398386e+00 -4.41666037e+00 4.61248329e+00 | 2.54398386e+00 -4.41666037e+00 4.61248329e+00 16 4.45499071e-01 -1.01536465e+00 7.03582703e-01 | 4.45499071e-01 -1.01536465e+00 7.03582703e-01 17 -9.81430413e+00 2.71433222e+00 6.85953477e-02 | -9.81430413e+00 2.71433222e+00 6.85953477e-02 18 5.67156627e-01 1.49588328e+00 -7.05113252e-01 | 5.67156627e-01 1.49588328e+00 -7.05113252e-01 19 -1.20969661e-01 7.55027293e-01 1.30690273e+00 | -1.20969661e-01 7.55027293e-01 1.30690273e+00 20 -3.28124293e+01 -1.72565536e+01 -2.34807245e+01 | -3.28124293e+01 -1.72565536e+01 -2.34807245e+01 21 2.33193133e+01 1.13725552e+01 3.12981622e+01 | 2.33193133e+01 1.13725552e+01 3.12981622e+01 22 2.30850250e-01 -1.61973840e+00 -7.90012140e-01 | 2.30850250e-01 -1.61973840e+00 -7.90012140e-01 23 -4.09647720e+00 3.81457392e+00 -3.03732193e+00 | -4.09647720e+00 3.81457392e+00 -3.03732193e+00 24 5.52082134e+00 -1.39269384e+00 -7.71919905e+00 | 5.52082134e+00 -1.39269384e+00 -7.71919905e+00 25 7.34043416e+00 -4.84854459e+00 -1.26515241e+00 | 7.34043416e+00 -4.84854459e+00 -1.26515241e+00 26 -9.20266764e-01 3.31700555e-01 -1.09029284e+01 | -9.20266764e-01 3.31700555e-01 -1.09029284e+01 27 2.06439961e+00 3.14876938e+00 1.98387144e+00 | 2.06439961e+00 3.14876938e+00 1.98387144e+00 28 -2.41745905e+00 -4.39278211e+00 5.14302815e-01 | -2.41745905e+00 -4.39278211e+00 5.14302815e-01 29 1.15478409e+01 4.14669887e+00 -1.26333085e+01 | 1.15478409e+01 4.14669887e+00 -1.26333085e+01 30 -2.30311643e+00 4.33221717e+00 -2.16720177e+00 | -2.30311643e+00 4.33221717e+00 -2.16720177e+00 31 3.79573644e+00 4.57099579e+00 4.93622876e+00 | 3.79573644e+00 4.57099579e+00 4.93622876e+00 32 -8.18730959e-01 -6.87182525e-01 -1.74502393e+00 | -8.18730959e-01 -6.87182525e-01 -1.74502393e+00 33 -4.31948614e+00 -9.91625908e-01 -2.94087715e+00 | -4.31948614e+00 -9.91625908e-01 -2.94087715e+00 34 -3.05503340e+00 -4.66003548e+00 1.15992698e+01 | -3.05503340e+00 -4.66003548e+00 1.15992698e+01 35 -3.04508227e+01 2.69403782e+01 -5.53816766e+01 | -3.04508227e+01 2.69403782e+01 -5.53816766e+01 36 -4.52330541e+01 -4.94574395e+01 -2.18982381e+01 | -4.52330541e+01 -4.94574395e+01 -2.18982381e+01 37 4.93314842e+01 4.82780370e+01 2.69331357e+01 | 4.93314842e+01 4.82780370e+01 2.69331357e+01 38 -3.37686144e+00 -3.86873400e+00 4.85810419e+00 | -3.37686144e+00 -3.86873400e+00 4.85810419e+00 39 7.10872333e-01 -3.41780623e-01 -1.92812439e-01 | 7.10872333e-01 -3.41780623e-01 -1.92812439e-01 40 -1.25332942e+00 -1.42530644e+01 -2.90904217e+01 | -1.25332942e+00 -1.42530644e+01 -2.90904217e+01 41 7.59709753e+00 8.70204258e+00 2.78041762e+01 | 7.59709753e+00 8.70204258e+00 2.78041762e+01 42 -2.09004089e+01 -2.12845053e+01 -1.69528830e+01 | -2.09004089e+01 -2.12845053e+01 -1.69528830e+01 43 2.17985690e+01 2.22346988e+01 1.72713058e+01 | 2.17985690e+01 2.22346988e+01 1.72713058e+01 44 -9.98544471e-01 1.31759525e+00 -4.05694540e-01 | -9.98544471e-01 1.31759525e+00 -4.05694540e-01 45 -5.07932058e-01 3.09383075e-01 -4.78423831e-01 | -5.07932058e-01 3.09383075e-01 -4.78423831e-01 46 4.71810995e+01 -6.28945902e+01 7.21893296e+01 | 4.71810995e+01 -6.28945902e+01 7.21893296e+01 47 1.14684934e+00 -2.42444495e+00 9.94752264e+00 | 1.14684934e+00 -2.42444495e+00 9.94752264e+00 48 -2.56302560e+00 1.01505145e+01 8.43033002e-01 | -2.56302560e+00 1.01505145e+01 8.43033002e-01 49 -7.13191751e+00 -5.54929128e+00 -1.00595586e+01 | -7.13191751e+00 -5.54929128e+00 -1.00595586e+01 50 1.89806251e+00 -1.03826793e+01 -1.09745615e+00 | 1.89806251e+00 -1.03826793e+01 -1.09745615e+00 51 -2.55524344e-02 1.13566101e+01 1.22337758e+00 | -2.55524344e-02 1.13566101e+01 1.22337758e+00 52 -2.70476697e+01 2.78449493e+01 2.63152123e+01 | -2.70476697e+01 2.78449493e+01 2.63152123e+01 53 -2.46300964e-01 -3.51520904e+00 7.95770080e-01 | -2.46300964e-01 -3.51520904e+00 7.95770080e-01 54 1.11629785e+00 6.35375458e-01 2.07702893e-01 | 1.11629785e+00 6.35375458e-01 2.07702893e-01 55 2.43445899e+00 9.24244750e+00 9.46811246e+00 | 2.43445899e+00 9.24244750e+00 9.46811246e+00 56 2.46153999e+01 2.14285889e+01 -2.44895015e+01 | 2.46153999e+01 2.14285889e+01 -2.44895015e+01 57 -3.16720564e+01 1.69276870e+01 -2.53757937e+01 | -3.16720564e+01 1.69276870e+01 -2.53757937e+01 58 -8.91741530e+00 2.89928063e+00 1.83689066e+01 | -8.91741530e+00 2.89928063e+00 1.83689066e+01 59 2.80534487e+00 4.51886885e+00 -1.83529065e+00 | 2.80534487e+00 4.51886885e+00 -1.83529065e+00 60 1.72120471e+01 -1.43074768e+01 7.37531444e+00 | 1.72120471e+01 -1.43074768e+01 7.37531444e+00 61 1.52032115e+01 -4.70623644e+00 1.36309506e+01 | 1.52032115e+01 -4.70623644e+00 1.36309506e+01 62 -4.52014619e+00 1.95920470e+00 1.54054321e+00 | -4.52014619e+00 1.95920470e+00 1.54054321e+00 63 6.37315194e+00 1.35428123e+00 1.68463449e+00 | 6.37315194e+00 1.35428123e+00 1.68463449e+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.