!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 : IMD_EAM_Schopf_AlNiCo_B__MO_128037485276_002 Supported species : Al Co Ni 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 = [51, 52, 28, 27, 11, 36, 19, 15, 59, 30, 50, 4, 49, 18, 53, 7, 42, 45, 13, 6, 62, 55, 43, 56, 39, 44, 58, 3, 2, 47, 9, 38, 60, 40, 46, 41, 5, 57, 31, 24, 33, 35, 16, 22, 25, 17, 34, 29, 54, 12, 10, 0, 1, 14, 48, 21, 23, 37, 26, 8, 32, 63, 20, 61] 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)) = 192.251621924 V(r_1,...,r_N) = 192.251621924 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 -7.77577390e+00 -3.92225647e+00 -1.21202370e+01 | -7.77577390e+00 -3.92225647e+00 -1.21202370e+01 1 -4.63817777e-01 -1.23822167e+00 6.42632261e+00 | -4.63817777e-01 -1.23822167e+00 6.42632261e+00 2 -8.50030794e+00 -1.82172158e+00 -1.93414439e+01 | -8.50030794e+00 -1.82172158e+00 -1.93414439e+01 3 3.66371199e+01 -3.96803855e+01 -1.08142548e+02 | 3.66371199e+01 -3.96803855e+01 -1.08142548e+02 4 -1.06603901e+02 -7.91490362e+01 -8.54790820e+00 | -1.06603901e+02 -7.91490362e+01 -8.54790820e+00 5 4.41169813e+01 -5.43725368e+01 2.48615864e+01 | 4.41169813e+01 -5.43725368e+01 2.48615864e+01 6 -2.18662294e+01 -7.23583668e+00 -1.13567481e+01 | -2.18662294e+01 -7.23583668e+00 -1.13567481e+01 7 -7.33897694e+01 2.41031896e+02 -1.12089179e+02 | -7.33897694e+01 2.41031896e+02 -1.12089179e+02 8 2.19938714e+00 -3.74844543e+00 -7.64327692e+00 | 2.19938714e+00 -3.74844543e+00 -7.64327692e+00 9 2.31622639e+01 -6.66317712e+00 -1.34354767e+01 | 2.31622639e+01 -6.66317712e+00 -1.34354767e+01 10 -2.69416517e+01 -8.76003938e+00 -1.96659551e+01 | -2.69416517e+01 -8.76003938e+00 -1.96659551e+01 11 2.89054384e+01 9.76249210e+00 1.72611326e+01 | 2.89054384e+01 9.76249210e+00 1.72611326e+01 12 -6.81835069e+00 -2.10850903e+01 -2.46777489e+01 | -6.81835069e+00 -2.10850903e+01 -2.46777489e+01 13 2.11186368e+01 2.06817627e+01 9.81522657e+00 | 2.11186368e+01 2.06817627e+01 9.81522657e+00 14 5.09412463e+01 4.44383983e+01 -6.36899618e+01 | 5.09412463e+01 4.44383983e+01 -6.36899618e+01 15 5.13837047e+01 3.52633502e+01 2.82771550e+01 | 5.13837047e+01 3.52633502e+01 2.82771550e+01 16 -9.36465426e+00 -1.66726281e+00 -8.60931223e+00 | -9.36465426e+00 -1.66726281e+00 -8.60931223e+00 17 -1.35288613e+01 1.31015048e+01 -8.77128405e+00 | -1.35288613e+01 1.31015048e+01 -8.77128405e+00 18 -5.30679828e+00 -7.63283771e-01 -1.14976659e+01 | -5.30679828e+00 -7.63283771e-01 -1.14976659e+01 19 -5.60630611e+00 1.53135008e+01 5.64406144e-01 | -5.60630611e+00 1.53135008e+01 5.64406144e-01 20 -3.66002113e+01 1.83062154e+01 4.95108322e+01 | -3.66002113e+01 1.83062154e+01 4.95108322e+01 21 4.23657830e+01 2.91104945e+01 1.17206363e+01 | 4.23657830e+01 2.91104945e+01 1.17206363e+01 22 -7.15654336e+00 -3.15141259e-01 -1.50384359e+01 | -7.15654336e+00 -3.15141259e-01 -1.50384359e+01 23 2.39703820e+00 8.82158116e+00 1.42720476e+01 | 2.39703820e+00 8.82158116e+00 1.42720476e+01 24 7.90372436e+00 1.17196247e+01 -2.28140020e+01 | 7.90372436e+00 1.17196247e+01 -2.28140020e+01 25 9.68735941e+00 3.81581238e+00 -5.87622218e-01 | 9.68735941e+00 3.81581238e+00 -5.87622218e-01 26 -3.37050185e+00 -1.25148417e+00 -4.72354732e+00 | -3.37050185e+00 -1.25148417e+00 -4.72354732e+00 27 3.87726875e+00 2.97007110e+00 4.64762135e+00 | 3.87726875e+00 2.97007110e+00 4.64762135e+00 28 -1.33016562e+01 -7.22078211e+00 -2.08528804e+01 | -1.33016562e+01 -7.22078211e+00 -2.08528804e+01 29 1.82578449e+01 3.05213356e+00 2.26903639e+01 | 1.82578449e+01 3.05213356e+00 2.26903639e+01 30 1.23132183e+01 2.02279909e+00 2.12009228e+00 | 1.23132183e+01 2.02279909e+00 2.12009228e+00 31 -8.98435983e+00 7.19915978e+00 -4.50159050e+00 | -8.98435983e+00 7.19915978e+00 -4.50159050e+00 32 -1.47789851e+01 -1.16748261e+01 -3.26056496e+00 | -1.47789851e+01 -1.16748261e+01 -3.26056496e+00 33 -7.64415654e+00 -1.45441531e+01 1.47307153e+01 | -7.64415654e+00 -1.45441531e+01 1.47307153e+01 34 5.57043593e+00 -2.33555563e+02 1.47317004e+02 | 5.57043593e+00 -2.33555563e+02 1.47317004e+02 35 -2.96619898e+01 -3.49544456e+01 3.94929023e+01 | -2.96619898e+01 -3.49544456e+01 3.94929023e+01 36 -4.45215579e+00 -5.78734424e+00 5.48276421e+00 | -4.45215579e+00 -5.78734424e+00 5.48276421e+00 37 -5.59067418e+01 -6.96344876e+01 5.87784972e+01 | -5.59067418e+01 -6.96344876e+01 5.87784972e+01 38 -1.14371715e+01 -6.89236171e+00 1.45114057e+00 | -1.14371715e+01 -6.89236171e+00 1.45114057e+00 39 -2.26479620e+02 -3.81845439e+01 8.69581326e+01 | -2.26479620e+02 -3.81845439e+01 8.69581326e+01 40 -6.09917377e+01 -3.78725475e+01 -1.54276386e+01 | -6.09917377e+01 -3.78725475e+01 -1.54276386e+01 41 -3.31132331e+02 1.49681158e+02 -2.65908735e+02 | -3.31132331e+02 1.49681158e+02 -2.65908735e+02 42 2.60869605e+01 2.24898767e+01 -1.64167254e+01 | 2.60869605e+01 2.24898767e+01 -1.64167254e+01 43 8.98179387e+00 1.26154519e+01 -1.97531904e+00 | 8.98179387e+00 1.26154519e+01 -1.97531904e+00 44 4.14885277e+02 -2.28552710e+02 2.61763893e+02 | 4.14885277e+02 -2.28552710e+02 2.61763893e+02 45 1.61536126e+01 -4.46652331e-01 1.87076692e+01 | 1.61536126e+01 -4.46652331e-01 1.87076692e+01 46 2.08352454e+01 6.86494643e+01 9.21645906e+00 | 2.08352454e+01 6.86494643e+01 9.21645906e+00 47 1.90847705e+01 8.74959492e+00 1.65389505e+01 | 1.90847705e+01 8.74959492e+00 1.65389505e+01 48 -1.62212601e+01 8.23406452e+00 2.94818780e+00 | -1.62212601e+01 8.23406452e+00 2.94818780e+00 49 -2.80548163e+00 1.08023129e+01 -2.21688368e-01 | -2.80548163e+00 1.08023129e+01 -2.21688368e-01 50 -1.13823848e+01 2.74040560e+01 1.37782641e+01 | -1.13823848e+01 2.74040560e+01 1.37782641e+01 51 -3.96092940e+00 8.69407472e+00 -6.53410784e-01 | -3.96092940e+00 8.69407472e+00 -6.53410784e-01 52 1.66822664e+02 4.10378861e+01 -4.72746238e+01 | 1.66822664e+02 4.10378861e+01 -4.72746238e+01 53 2.71338247e+01 2.68131136e+01 1.77871019e+01 | 2.71338247e+01 2.68131136e+01 1.77871019e+01 54 -6.02383899e+00 -1.90806741e+00 4.01285615e-01 | -6.02383899e+00 -1.90806741e+00 4.01285615e-01 55 5.01068016e+00 2.56641651e+00 4.10415220e-01 | 5.01068016e+00 2.56641651e+00 4.10415220e-01 56 4.90978116e+01 5.61259546e+01 -4.70677589e+01 | 4.90978116e+01 5.61259546e+01 -4.70677589e+01 57 1.67958624e+01 -2.85832153e+00 -1.80184961e+01 | 1.67958624e+01 -2.85832153e+00 -1.80184961e+01 58 9.81770128e+00 -2.56235767e+00 2.31774196e+00 | 9.81770128e+00 -2.56235767e+00 2.31774196e+00 59 6.71963500e-01 7.50304429e-01 1.25034978e+00 | 6.71963500e-01 7.50304429e-01 1.25034978e+00 60 -2.72244473e+00 -1.71271827e+00 -4.97511092e+00 | -2.72244473e+00 -1.71271827e+00 -4.97511092e+00 61 3.94856997e+00 3.73409377e+00 7.80121826e+00 | 3.94856997e+00 3.73409377e+00 7.80121826e+00 62 -5.38288805e+00 1.50461761e+01 1.97002491e+01 | -5.38288805e+00 1.50461761e+01 1.97002491e+01 63 3.99622279e-01 3.10046000e-02 3.06530919e-01 | 3.99622279e-01 3.10046000e-02 3.06530919e-01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Co (Configuration in file "config-Co.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [17, 10, 59, 37, 8, 19, 32, 53, 4, 56, 1, 49, 26, 34, 61, 33, 46, 0, 20, 5, 18, 41, 43, 60, 62, 52, 12, 38, 57, 58, 31, 30, 6, 15, 13, 44, 48, 3, 27, 45, 42, 21, 40, 22, 35, 39, 16, 55, 36, 11, 54, 63, 25, 7, 50, 47, 9, 28, 29, 2, 23, 14, 24, 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)) = -18.8766723331 V(r_1,...,r_N) = -18.8766723331 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 -5.01557512e+00 -9.43074741e+00 -1.24021720e+01 | -5.01557512e+00 -9.43074741e+00 -1.24021720e+01 1 7.43942089e+00 2.49441900e-01 7.15439731e+00 | 7.43942089e+00 2.49441900e-01 7.15439731e+00 2 -5.06140493e+00 -7.93167188e+00 -3.76757974e+00 | -5.06140493e+00 -7.93167188e+00 -3.76757974e+00 3 -2.06325312e+00 3.75523281e+00 8.47134416e+00 | -2.06325312e+00 3.75523281e+00 8.47134416e+00 4 -9.06544367e-01 -7.10544638e-01 -1.71720457e+00 | -9.06544367e-01 -7.10544638e-01 -1.71720457e+00 5 -5.65912245e+00 2.96772513e+01 -4.84164571e+01 | -5.65912245e+00 2.96772513e+01 -4.84164571e+01 6 -1.88084840e+01 -5.42520322e+01 -6.14572837e+00 | -1.88084840e+01 -5.42520322e+01 -6.14572837e+00 7 1.92579714e+01 5.77865469e+01 8.27821244e+00 | 1.92579714e+01 5.77865469e+01 8.27821244e+00 8 -5.05995159e+00 -7.83863742e+00 -4.70802115e+00 | -5.05995159e+00 -7.83863742e+00 -4.70802115e+00 9 -2.38565993e+01 6.55165761e+00 1.34479595e+01 | -2.38565993e+01 6.55165761e+00 1.34479595e+01 10 1.85152154e+01 7.52641705e+00 -1.64992477e+01 | 1.85152154e+01 7.52641705e+00 -1.64992477e+01 11 2.67605360e+00 -1.97855566e+00 8.73555530e-01 | 2.67605360e+00 -1.97855566e+00 8.73555530e-01 12 5.94138111e+00 -6.80229287e+00 4.66180192e+00 | 5.94138111e+00 -6.80229287e+00 4.66180192e+00 13 3.16839696e+00 -2.74370852e-01 -1.06889928e+00 | 3.16839696e+00 -2.74370852e-01 -1.06889928e+00 14 -1.11335208e+01 -1.16213114e+01 4.30793575e+00 | -1.11335208e+01 -1.16213114e+01 4.30793575e+00 15 1.22445483e+01 1.16586079e+01 -3.46648895e+00 | 1.22445483e+01 1.16586079e+01 -3.46648895e+00 16 1.08152614e+00 -7.51014236e-02 1.91391145e-01 | 1.08152614e+00 -7.51014236e-02 1.91391145e-01 17 -3.91121869e+00 -8.46954380e+00 -9.30257904e+00 | -3.91121869e+00 -8.46954380e+00 -9.30257904e+00 18 1.15415980e+00 -2.01914564e+00 4.75290077e-01 | 1.15415980e+00 -2.01914564e+00 4.75290077e-01 19 -6.79992069e+00 6.62868548e+00 -1.73752083e+00 | -6.79992069e+00 6.62868548e+00 -1.73752083e+00 20 -5.62283334e-01 -6.01539711e-01 -5.90167012e+00 | -5.62283334e-01 -6.01539711e-01 -5.90167012e+00 21 -3.62807561e+00 -4.19396127e+00 1.11730579e+01 | -3.62807561e+00 -4.19396127e+00 1.11730579e+01 22 -7.42521723e+00 1.07788326e+01 5.17051689e+00 | -7.42521723e+00 1.07788326e+01 5.17051689e+00 23 1.24820433e+00 2.31005662e-01 1.41702662e+00 | 1.24820433e+00 2.31005662e-01 1.41702662e+00 24 -1.92988181e+01 -3.24744710e+01 -1.96820389e+01 | -1.92988181e+01 -3.24744710e+01 -1.96820389e+01 25 2.30297776e+01 3.39763906e+01 1.43103034e+01 | 2.30297776e+01 3.39763906e+01 1.43103034e+01 26 -4.08686767e+00 -2.10767630e+01 -1.75143629e+01 | -4.08686767e+00 -2.10767630e+01 -1.75143629e+01 27 6.75432496e+00 2.00910640e+01 1.78405595e+01 | 6.75432496e+00 2.00910640e+01 1.78405595e+01 28 -1.33450949e+01 4.19673893e+00 -8.04428053e+00 | -1.33450949e+01 4.19673893e+00 -8.04428053e+00 29 1.48938114e+01 2.03747850e+00 8.73960461e+00 | 1.48938114e+01 2.03747850e+00 8.73960461e+00 30 1.61872599e+01 1.67258929e+00 -5.08700556e+00 | 1.61872599e+01 1.67258929e+00 -5.08700556e+00 31 -1.07577599e+00 3.53574669e-01 9.48071704e-01 | -1.07577599e+00 3.53574669e-01 9.48071704e-01 32 2.09033313e+00 9.07411425e-01 -5.01037592e-02 | 2.09033313e+00 9.07411425e-01 -5.01037592e-02 33 -4.28894515e+01 -3.18496064e+01 4.60427352e+01 | -4.28894515e+01 -3.18496064e+01 4.60427352e+01 34 3.84744908e+01 3.14075358e+01 -4.89319218e+01 | 3.84744908e+01 3.14075358e+01 -4.89319218e+01 35 9.04276625e+00 -1.98784538e-01 -7.01019374e+00 | 9.04276625e+00 -1.98784538e-01 -7.01019374e+00 36 -3.71456176e-01 -2.28557792e+00 7.44577735e-01 | -3.71456176e-01 -2.28557792e+00 7.44577735e-01 37 -9.73747889e-01 -1.07792642e+01 7.18160055e+00 | -9.73747889e-01 -1.07792642e+01 7.18160055e+00 38 -2.44219354e+00 -2.31956694e-01 3.89750439e-01 | -2.44219354e+00 -2.31956694e-01 3.89750439e-01 39 -1.96955104e+00 3.75639945e-01 4.92015849e+00 | -1.96955104e+00 3.75639945e-01 4.92015849e+00 40 6.70598203e+00 -3.20418583e+01 5.18518944e+01 | 6.70598203e+00 -3.20418583e+01 5.18518944e+01 41 -2.08132167e+01 -1.28312618e+01 2.35160873e+01 | -2.08132167e+01 -1.28312618e+01 2.35160873e+01 42 1.48768937e+01 1.18392970e+01 -2.31231126e+01 | 1.48768937e+01 1.18392970e+01 -2.31231126e+01 43 4.27019296e+00 7.26986138e-01 -3.72378049e+00 | 4.27019296e+00 7.26986138e-01 -3.72378049e+00 44 -4.32647109e+00 -9.30283210e+00 -4.43697946e+00 | -4.32647109e+00 -9.30283210e+00 -4.43697946e+00 45 5.16628332e+00 9.38129386e+00 3.80728210e+00 | 5.16628332e+00 9.38129386e+00 3.80728210e+00 46 -7.68640188e-01 6.75864749e+00 -3.68925968e+00 | -7.68640188e-01 6.75864749e+00 -3.68925968e+00 47 3.98329831e-01 2.07922044e+00 8.26665657e-01 | 3.98329831e-01 2.07922044e+00 8.26665657e-01 48 -3.43760237e+00 3.55285646e+00 3.22746601e-01 | -3.43760237e+00 3.55285646e+00 3.22746601e-01 49 3.68047959e+00 -1.85411351e+00 4.79280989e-01 | 3.68047959e+00 -1.85411351e+00 4.79280989e-01 50 -5.92538399e-01 -4.55879218e+00 -1.38369695e-01 | -5.92538399e-01 -4.55879218e+00 -1.38369695e-01 51 2.68131459e+00 5.24295733e+00 2.92212379e+00 | 2.68131459e+00 5.24295733e+00 2.92212379e+00 52 -4.88459751e-01 1.29295272e+00 1.60963520e+00 | -4.88459751e-01 1.29295272e+00 1.60963520e+00 53 -6.60813645e+00 -3.52287299e+00 2.74575930e+00 | -6.60813645e+00 -3.52287299e+00 2.74575930e+00 54 -4.56511025e+00 3.07019714e+00 4.89712715e-01 | -4.56511025e+00 3.07019714e+00 4.89712715e-01 55 9.95491054e-01 -7.30615720e-02 -1.60259303e-01 | 9.95491054e-01 -7.30615720e-02 -1.60259303e-01 56 -1.72510312e+00 -2.73603315e+00 -4.82229606e-01 | -1.72510312e+00 -2.73603315e+00 -4.82229606e-01 57 -2.71531032e+01 -6.12744766e+00 2.09205339e+01 | -2.71531032e+01 -6.12744766e+00 2.09205339e+01 58 2.96355422e+01 8.67124918e+00 -1.83988148e+01 | 2.96355422e+01 8.67124918e+00 -1.83988148e+01 59 -1.18805127e-01 1.29883943e+00 1.43433362e-01 | -1.18805127e-01 1.29883943e+00 1.43433362e-01 60 -9.09083686e-01 7.88614166e-01 1.39372082e+00 | -9.09083686e-01 7.88614166e-01 1.39372082e+00 61 -6.14141198e-01 2.07169749e-01 9.46804115e-01 | -6.14141198e-01 2.07169749e-01 9.46804115e-01 62 3.38121613e+00 -1.33549883e+01 -5.94591208e+00 | 3.38121613e+00 -1.33549883e+01 -5.94591208e+00 63 3.47317180e+00 1.67267580e+01 2.83666241e+00 | 3.47317180e+00 1.67267580e+01 2.83666241e+00 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Ni (Configuration in file "config-Ni.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [33, 62, 46, 16, 19, 53, 50, 14, 52, 25, 39, 58, 59, 22, 7, 23, 3, 30, 44, 4, 61, 47, 13, 15, 51, 9, 55, 40, 37, 56, 17, 45, 60, 0, 63, 42, 41, 28, 49, 10, 27, 36, 35, 48, 18, 31, 2, 21, 43, 38, 6, 24, 8, 5, 57, 26, 29, 54, 11, 12, 32, 20, 1, 34] 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)) = -120.020210439 V(r_1,...,r_N) = -120.020210439 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 2.32720772e+00 2.66166599e+00 3.86804384e-01 | 2.32720772e+00 2.66166599e+00 3.86804384e-01 1 2.35140488e+00 -7.76478834e+00 3.36401571e+00 | 2.35140488e+00 -7.76478834e+00 3.36401571e+00 2 -7.82826813e+00 7.71599363e+00 -2.31778462e+00 | -7.82826813e+00 7.71599363e+00 -2.31778462e+00 3 3.61078665e-01 -1.27007219e+01 -3.79410878e+00 | 3.61078665e-01 -1.27007219e+01 -3.79410878e+00 4 6.77230937e-01 -3.48766815e-02 1.96347821e+00 | 6.77230937e-01 -3.48766815e-02 1.96347821e+00 5 1.54083681e+01 -1.47793237e+00 -4.33056296e+00 | 1.54083681e+01 -1.47793237e+00 -4.33056296e+00 6 -1.44418683e+00 -7.27227089e-01 3.32706877e+00 | -1.44418683e+00 -7.27227089e-01 3.32706877e+00 7 2.61596457e+00 3.19310471e+00 -5.65003586e-01 | 2.61596457e+00 3.19310471e+00 -5.65003586e-01 8 -1.20692798e+01 -2.22382143e+00 -7.36141007e+00 | -1.20692798e+01 -2.22382143e+00 -7.36141007e+00 9 1.01583952e+01 -2.81242653e+00 4.08026041e+00 | 1.01583952e+01 -2.81242653e+00 4.08026041e+00 10 -3.86079358e+00 -1.23973876e+00 -8.17272385e+00 | -3.86079358e+00 -1.23973876e+00 -8.17272385e+00 11 7.64649007e+00 5.35953278e+00 -1.08448582e+00 | 7.64649007e+00 5.35953278e+00 -1.08448582e+00 12 3.24585596e-01 -8.71311059e+00 -7.32270988e+00 | 3.24585596e-01 -8.71311059e+00 -7.32270988e+00 13 3.47546449e+00 6.44219803e+00 3.02284041e-01 | 3.47546449e+00 6.44219803e+00 3.02284041e-01 14 3.16044798e+00 3.46098785e+00 4.66856269e+00 | 3.16044798e+00 3.46098785e+00 4.66856269e+00 15 -7.28368160e-02 -5.57367420e-03 -1.13782607e+00 | -7.28368160e-02 -5.57367420e-03 -1.13782607e+00 16 -7.85704241e-03 -3.37563462e-01 -1.57783828e+00 | -7.85704241e-03 -3.37563462e-01 -1.57783828e+00 17 -6.22331094e-01 -4.99449050e+00 1.69915868e+00 | -6.22331094e-01 -4.99449050e+00 1.69915868e+00 18 -8.10407211e+00 3.10782295e+00 -1.09287818e+01 | -8.10407211e+00 3.10782295e+00 -1.09287818e+01 19 1.88539832e+00 1.57984353e+00 1.02519969e+01 | 1.88539832e+00 1.57984353e+00 1.02519969e+01 20 1.35509941e+00 3.57670614e+00 -3.31360295e+00 | 1.35509941e+00 3.57670614e+00 -3.31360295e+00 21 2.95369039e+00 4.47493235e-01 -4.43095438e+00 | 2.95369039e+00 4.47493235e-01 -4.43095438e+00 22 -7.13478179e+00 2.38616458e+00 -2.03935707e+00 | -7.13478179e+00 2.38616458e+00 -2.03935707e+00 23 -4.62995937e+00 7.00205530e+00 -1.64749944e+00 | -4.62995937e+00 7.00205530e+00 -1.64749944e+00 24 8.28356387e+00 -1.05336276e+00 4.84472531e+00 | 8.28356387e+00 -1.05336276e+00 4.84472531e+00 25 5.37742028e+00 5.07077244e-01 5.43332550e+00 | 5.37742028e+00 5.07077244e-01 5.43332550e+00 26 1.65026031e+00 -4.84174250e+00 -3.58506164e+00 | 1.65026031e+00 -4.84174250e+00 -3.58506164e+00 27 -1.09089173e+00 1.81266973e-01 1.27592089e+00 | -1.09089173e+00 1.81266973e-01 1.27592089e+00 28 -2.10747899e+00 4.75326519e+00 -6.60065202e+00 | -2.10747899e+00 4.75326519e+00 -6.60065202e+00 29 3.01193232e+00 4.14932038e+00 -6.88196718e+00 | 3.01193232e+00 4.14932038e+00 -6.88196718e+00 30 6.53609745e+00 8.37067253e-02 1.90173047e+00 | 6.53609745e+00 8.37067253e-02 1.90173047e+00 31 -2.07165307e+00 -2.35056845e+00 -2.88767199e+00 | -2.07165307e+00 -2.35056845e+00 -2.88767199e+00 32 -5.61429518e+00 -8.33046706e+00 -1.86093039e+00 | -5.61429518e+00 -8.33046706e+00 -1.86093039e+00 33 6.74773973e+00 4.81234092e+00 -5.76185788e+00 | 6.74773973e+00 4.81234092e+00 -5.76185788e+00 34 -1.19548617e+01 -5.12695471e+00 1.24345671e+00 | -1.19548617e+01 -5.12695471e+00 1.24345671e+00 35 9.90504496e+00 1.02550866e+01 8.78764449e-01 | 9.90504496e+00 1.02550866e+01 8.78764449e-01 36 -1.23719704e+01 -3.28930937e+00 -3.89929981e+00 | -1.23719704e+01 -3.28930937e+00 -3.89929981e+00 37 2.58343260e+00 -8.50759665e-01 1.37192190e+01 | 2.58343260e+00 -8.50759665e-01 1.37192190e+01 38 -5.38299172e+00 -3.22521139e-01 1.07341117e+01 | -5.38299172e+00 -3.22521139e-01 1.07341117e+01 39 1.65039004e+00 -4.82194864e+00 2.69412440e+00 | 1.65039004e+00 -4.82194864e+00 2.69412440e+00 40 -6.40186276e+00 -8.42604838e+00 -5.13389459e+00 | -6.40186276e+00 -8.42604838e+00 -5.13389459e+00 41 2.90596240e+00 1.43668988e+01 -3.79115342e+00 | 2.90596240e+00 1.43668988e+01 -3.79115342e+00 42 -2.73460177e+00 -1.04120932e+01 6.14718737e+00 | -2.73460177e+00 -1.04120932e+01 6.14718737e+00 43 7.98113110e+00 -6.38622015e-01 -3.18415227e+00 | 7.98113110e+00 -6.38622015e-01 -3.18415227e+00 44 -2.63987536e+00 -5.64502569e+00 7.92280098e+00 | -2.63987536e+00 -5.64502569e+00 7.92280098e+00 45 1.46392071e-01 6.05509517e+00 1.90781458e+00 | 1.46392071e-01 6.05509517e+00 1.90781458e+00 46 2.35290441e+00 5.42477566e-01 -1.26712731e+01 | 2.35290441e+00 5.42477566e-01 -1.26712731e+01 47 3.69452471e-01 5.24805451e+00 8.17952801e+00 | 3.69452471e-01 5.24805451e+00 8.17952801e+00 48 -1.06134006e+01 -3.14219357e+00 -2.13683413e+00 | -1.06134006e+01 -3.14219357e+00 -2.13683413e+00 49 -8.31802871e-01 2.14436655e+00 -2.74984399e+00 | -8.31802871e-01 2.14436655e+00 -2.74984399e+00 50 6.94552966e+00 -5.03859592e+00 5.27774404e+00 | 6.94552966e+00 -5.03859592e+00 5.27774404e+00 51 1.48522777e+00 4.05105322e+00 -3.87063115e+00 | 1.48522777e+00 4.05105322e+00 -3.87063115e+00 52 -2.21462505e-01 1.19947831e-01 -2.68206500e+00 | -2.21462505e-01 1.19947831e-01 -2.68206500e+00 53 -7.38763148e+00 -1.03468932e+01 4.09189243e+00 | -7.38763148e+00 -1.03468932e+01 4.09189243e+00 54 -1.48808711e+01 5.52392480e+00 5.14673986e-02 | -1.48808711e+01 5.52392480e+00 5.14673986e-02 55 8.29957353e+00 2.06755333e+00 6.33252506e+00 | 8.29957353e+00 2.06755333e+00 6.33252506e+00 56 -7.73810139e+00 3.28832866e+00 1.22683157e+01 | -7.73810139e+00 3.28832866e+00 1.22683157e+01 57 9.93949950e-01 -2.95241996e+00 1.03294176e+00 | 9.93949950e-01 -2.95241996e+00 1.03294176e+00 58 -1.34282538e+00 -3.61612038e+00 -1.00841408e+00 | -1.34282538e+00 -3.61612038e+00 -1.00841408e+00 59 -2.11051820e+00 -1.21426671e+00 4.69682043e+00 | -2.11051820e+00 -1.21426671e+00 4.69682043e+00 60 -1.20106867e+01 -4.87938116e+00 -5.59296489e+00 | -1.20106867e+01 -4.87938116e+00 -5.59296489e+00 61 5.37573227e+00 1.58397826e+01 2.04792096e+00 | 5.37573227e+00 1.58397826e+01 2.04792096e+00 62 1.68951376e+01 -4.29988224e+00 -1.34382211e+00 | 1.68951376e+01 -4.29988224e+00 -1.34382211e+00 63 1.08444833e+00 3.70833224e+00 2.94117210e+00 | 1.08444833e+00 3.70833224e+00 2.94117210e+00 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MIXED STRUCTURE -- Species = Al Co Ni (Configuration in file "config-AlCoNi.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [7, 37, 12, 4, 3, 39, 36, 0, 17, 49, 46, 42, 2, 18, 30, 48, 54, 8, 13, 38, 44, 63, 31, 25, 53, 23, 50, 59, 35, 33, 14, 22, 57, 29, 47, 28, 6, 1, 19, 5, 56, 52, 11, 61, 20, 55, 10, 34, 15, 9, 26, 51, 41, 24, 16, 45, 40, 32, 58, 27, 62, 43, 60, 21] 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)) = -8.04911798081 V(r_1,...,r_N) = -8.04911798081 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 2.45522949e+00 -1.81562129e+00 7.23412288e-01 | 2.45522949e+00 -1.81562129e+00 7.23412288e-01 1 -1.17743552e+01 -7.08115076e-01 -1.78883382e+01 | -1.17743552e+01 -7.08115076e-01 -1.78883382e+01 2 1.45848986e+01 -3.17434124e+00 -4.65782991e+00 | 1.45848986e+01 -3.17434124e+00 -4.65782991e+00 3 -4.25346143e+00 -2.98481947e+00 1.81281719e+00 | -4.25346143e+00 -2.98481947e+00 1.81281719e+00 4 -4.55491730e+00 6.21022561e-01 -1.37262610e+00 | -4.55491730e+00 6.21022561e-01 -1.37262610e+00 5 -1.27188906e+00 3.98809360e-01 -1.12773847e+00 | -1.27188906e+00 3.98809360e-01 -1.12773847e+00 6 1.37479982e+00 -4.35412328e-01 2.40886096e+01 | 1.37479982e+00 -4.35412328e-01 2.40886096e+01 7 2.91920690e+00 1.11827863e+00 -4.91495790e+00 | 2.91920690e+00 1.11827863e+00 -4.91495790e+00 8 -2.29550374e+00 2.02978521e+00 5.78302953e+00 | -2.29550374e+00 2.02978521e+00 5.78302953e+00 9 -4.52768621e+00 1.33743003e+01 -9.43980695e+00 | -4.52768621e+00 1.33743003e+01 -9.43980695e+00 10 -1.25110657e+00 -3.49246620e+00 -3.69011626e+00 | -1.25110657e+00 -3.49246620e+00 -3.69011626e+00 11 8.78769954e+00 -6.67613243e+00 4.24687278e-01 | 8.78769954e+00 -6.67613243e+00 4.24687278e-01 12 -3.18633132e+00 -1.54700024e+01 4.49373847e+00 | -3.18633132e+00 -1.54700024e+01 4.49373847e+00 13 4.15583309e+00 2.18090370e+00 1.54902677e+00 | 4.15583309e+00 2.18090370e+00 1.54902677e+00 14 1.30657102e+00 -1.82519530e+00 1.82881116e-01 | 1.30657102e+00 -1.82519530e+00 1.82881116e-01 15 -1.07437862e+01 -8.64982895e-01 -1.04777568e+01 | -1.07437862e+01 -8.64982895e-01 -1.04777568e+01 16 2.42863159e+00 2.07442698e+00 4.15769690e+00 | 2.42863159e+00 2.07442698e+00 4.15769690e+00 17 8.98989722e+00 -5.18317558e+00 1.38427674e-02 | 8.98989722e+00 -5.18317558e+00 1.38427674e-02 18 -2.09218025e+00 -2.19011815e+00 -1.00242052e+00 | -2.09218025e+00 -2.19011815e+00 -1.00242052e+00 19 -1.92126008e+00 -7.95082239e-01 1.70794382e+00 | -1.92126008e+00 -7.95082239e-01 1.70794382e+00 20 -4.89505602e+00 1.92085000e+00 4.29637439e+00 | -4.89505602e+00 1.92085000e+00 4.29637439e+00 21 -5.82395455e+00 1.67951394e+01 -2.07936200e+01 | -5.82395455e+00 1.67951394e+01 -2.07936200e+01 22 -8.61365169e+00 1.66644334e+00 -8.79202267e+00 | -8.61365169e+00 1.66644334e+00 -8.79202267e+00 23 2.38054249e+00 1.09142146e+01 4.19530965e+00 | 2.38054249e+00 1.09142146e+01 4.19530965e+00 24 6.72968358e-01 7.21865253e+00 -2.86892554e+00 | 6.72968358e-01 7.21865253e+00 -2.86892554e+00 25 -1.95712531e+01 4.85680438e+01 -4.31205513e+00 | -1.95712531e+01 4.85680438e+01 -4.31205513e+00 26 -7.75625192e-01 1.77615667e+00 -4.64843083e+00 | -7.75625192e-01 1.77615667e+00 -4.64843083e+00 27 -2.03123971e+00 -2.76126546e+00 5.71119017e+00 | -2.03123971e+00 -2.76126546e+00 5.71119017e+00 28 9.09082513e+00 -3.59437705e+01 2.36148574e+01 | 9.09082513e+00 -3.59437705e+01 2.36148574e+01 29 2.32952579e+00 -4.29603902e+00 -2.39870646e+00 | 2.32952579e+00 -4.29603902e+00 -2.39870646e+00 30 6.99786975e+00 -8.17160391e+00 -7.20993723e-01 | 6.99786975e+00 -8.17160391e+00 -7.20993723e-01 31 -7.09302457e+00 6.91108022e-01 2.27453587e+00 | -7.09302457e+00 6.91108022e-01 2.27453587e+00 32 3.88435483e+00 -1.13794328e-01 -2.41141803e+00 | 3.88435483e+00 -1.13794328e-01 -2.41141803e+00 33 -5.56009277e+00 3.32329419e+00 3.49452725e+00 | -5.56009277e+00 3.32329419e+00 3.49452725e+00 34 2.69475065e+00 3.80441954e+00 -5.11790864e+00 | 2.69475065e+00 3.80441954e+00 -5.11790864e+00 35 4.54639898e+00 -2.76129059e+00 1.61071578e+00 | 4.54639898e+00 -2.76129059e+00 1.61071578e+00 36 8.83032371e+00 -3.37319621e+00 2.54515962e+00 | 8.83032371e+00 -3.37319621e+00 2.54515962e+00 37 -8.99995279e+01 -5.29539006e+01 3.57362565e+01 | -8.99995279e+01 -5.29539006e+01 3.57362565e+01 38 -4.92895463e+01 -8.77884731e+00 -7.84528917e+01 | -4.92895463e+01 -8.77884731e+00 -7.84528917e+01 39 5.14464640e+01 7.72187104e+00 7.63239031e+01 | 5.14464640e+01 7.72187104e+00 7.63239031e+01 40 5.29504059e-01 6.10727848e-01 8.65365057e-01 | 5.29504059e-01 6.10727848e-01 8.65365057e-01 41 -9.68139963e+00 1.51118964e+01 -1.58024100e+01 | -9.68139963e+00 1.51118964e+01 -1.58024100e+01 42 -1.88383146e+00 4.26224512e+00 3.62508438e+00 | -1.88383146e+00 4.26224512e+00 3.62508438e+00 43 7.33419360e+00 -2.80646015e+00 8.80654705e+00 | 7.33419360e+00 -2.80646015e+00 8.80654705e+00 44 7.36548380e+00 -1.10674309e+01 1.40491195e+01 | 7.36548380e+00 -1.10674309e+01 1.40491195e+01 45 4.69165854e-01 2.05614091e+00 2.62166250e-01 | 4.69165854e-01 2.05614091e+00 2.62166250e-01 46 8.43076289e+01 4.71470632e+01 -4.14285058e+01 | 8.43076289e+01 4.71470632e+01 -4.14285058e+01 47 2.40435716e+00 4.51334325e+00 1.31002906e+00 | 2.40435716e+00 4.51334325e+00 1.31002906e+00 48 -3.18595335e+00 -1.41354807e+00 2.12711309e+00 | -3.18595335e+00 -1.41354807e+00 2.12711309e+00 49 -1.08349935e+01 -9.25677580e+00 1.73027127e+01 | -1.08349935e+01 -9.25677580e+00 1.73027127e+01 50 7.34854215e+00 -1.33504459e+01 -3.18348461e+01 | 7.34854215e+00 -1.33504459e+01 -3.18348461e+01 51 1.30655069e+01 1.35391247e+01 1.57684460e+01 | 1.30655069e+01 1.35391247e+01 1.57684460e+01 52 -1.13092306e+01 5.00912514e+00 8.40598465e+00 | -1.13092306e+01 5.00912514e+00 8.40598465e+00 53 -4.25394041e+00 -1.16265586e+00 -1.09669747e+00 | -4.25394041e+00 -1.16265586e+00 -1.09669747e+00 54 2.87308367e+00 -1.36190146e+00 -1.46319425e+00 | 2.87308367e+00 -1.36190146e+00 -1.46319425e+00 55 1.12882958e+00 -1.82515520e+00 -2.29779060e+00 | 1.12882958e+00 -1.82515520e+00 -2.29779060e+00 56 1.39605147e+01 -1.20361554e+01 9.22877609e+00 | 1.39605147e+01 -1.20361554e+01 9.22877609e+00 57 -6.74514137e+01 4.20026298e+01 -3.99735289e+01 | -6.74514137e+01 4.20026298e+01 -3.99735289e+01 58 1.67692073e+00 4.12088267e+00 6.06009563e-01 | 1.67692073e+00 4.12088267e+00 6.06009563e-01 59 9.09473298e-01 -1.80643444e+00 -3.29262249e+00 | 9.09473298e-01 -1.80643444e+00 -3.29262249e+00 60 6.42497185e+01 -4.55318570e+01 2.36627494e+01 | 6.42497185e+01 -4.55318570e+01 2.36627494e+01 61 4.53993571e+00 5.82537398e+00 1.09855621e+01 | 4.53993571e+00 5.82537398e+00 1.09855621e+01 62 -1.13198548e-01 -2.10462659e+00 -1.22473009e+00 | -1.13198548e-01 -2.10462659e+00 -1.22473009e+00 63 -1.80023919e+00 -1.90365354e+00 1.75670913e+00 | -1.80023919e+00 -1.90365354e+00 1.75670913e+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.