!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 : MEAM_LAMMPS_DoShinLee_2009_GaInN__MO_815057898706_001 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 = [35, 22, 27, 49, 11, 19, 55, 31, 38, 54, 15, 4, 50, 46, 40, 10, 17, 16, 58, 5, 53, 39, 1, 44, 52, 63, 28, 2, 26, 32, 45, 7, 29, 43, 37, 0, 59, 34, 8, 21, 14, 56, 57, 33, 23, 30, 13, 61, 51, 3, 12, 48, 24, 20, 9, 6, 41, 42, 18, 36, 62, 47, 60, 25] 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)) = 29.633045421431184 V(r_1,...,r_N) = 29.6330454214311 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 -1.12637220e+00 -7.88243774e-01 -1.41155054e+00 | -1.12637220e+00 -7.88243774e-01 -1.41155054e+00 1 -1.61645755e+01 -1.84300065e+01 1.04798031e+01 | -1.61645755e+01 -1.84300065e+01 1.04798031e+01 2 -6.80936353e-01 8.17540582e+00 -3.42870073e+01 | -6.80936353e-01 8.17540582e+00 -3.42870073e+01 3 5.72449095e+00 1.92526051e+01 7.97011121e+00 | 5.72449095e+00 1.92526051e+01 7.97011121e+00 4 2.51865853e+00 -7.95873312e+00 7.00539325e+00 | 2.51865853e+00 -7.95873312e+00 7.00539325e+00 5 -8.96912508e+00 9.74054632e+00 -2.61229652e+01 | -8.96912508e+00 9.74054632e+00 -2.61229652e+01 6 -7.25837679e-01 -1.17290519e+01 -1.35901700e+01 | -7.25837679e-01 -1.17290519e+01 -1.35901700e+01 7 -1.63488979e+01 6.23079193e+01 -3.16357958e+01 | -1.63488979e+01 6.23079193e+01 -3.16357958e+01 8 -1.28062639e+00 -1.41619579e+00 -1.25560087e+00 | -1.28062639e+00 -1.41619579e+00 -1.25560087e+00 9 -1.92245173e+01 1.59642876e+01 -1.53506745e+01 | -1.92245173e+01 1.59642876e+01 -1.53506745e+01 10 -6.94620993e-01 -1.85606272e+00 -2.28886725e+00 | -6.94620993e-01 -1.85606272e+00 -2.28886725e+00 11 1.93196336e+00 2.55733964e+00 1.52641525e+00 | 1.93196336e+00 2.55733964e+00 1.52641525e+00 12 1.81685621e+01 -1.63458049e+01 1.73233243e+01 | 1.81685621e+01 -1.63458049e+01 1.73233243e+01 13 2.06430482e+01 -5.97460016e+00 -1.71358094e+01 | 2.06430482e+01 -5.97460016e+00 -1.71358094e+01 14 -1.50959014e+01 -6.60474847e+00 -2.35693397e+01 | -1.50959014e+01 -6.60474847e+00 -2.35693397e+01 15 2.61010546e+01 2.01006496e+00 2.93346871e+01 | 2.61010546e+01 2.01006496e+00 2.93346871e+01 16 -1.64626714e+00 -2.61397049e+00 -1.26058433e+00 | -1.64626714e+00 -2.61397049e+00 -1.26058433e+00 17 -1.53901167e+00 7.07890329e+00 -1.86122101e+00 | -1.53901167e+00 7.07890329e+00 -1.86122101e+00 18 -2.62698807e+00 -4.59186834e+00 -3.08416795e+00 | -2.62698807e+00 -4.59186834e+00 -3.08416795e+00 19 -3.54741484e+01 2.85370147e+01 -2.15800827e+01 | -3.54741484e+01 2.85370147e+01 -2.15800827e+01 20 -1.71768267e+01 -1.55351340e+01 -6.27663924e+00 | -1.71768267e+01 -1.55351340e+01 -6.27663924e+00 21 1.66659606e+01 1.39587573e+01 1.00334622e+01 | 1.66659606e+01 1.39587573e+01 1.00334622e+01 22 -5.28161286e+00 -6.18351168e+00 -1.06373559e+01 | -5.28161286e+00 -6.18351168e+00 -1.06373559e+01 23 5.25795375e+00 5.70081100e+00 1.10301140e+01 | 5.25795375e+00 5.70081100e+00 1.10301140e+01 24 -1.10502415e-01 -2.94026605e-01 4.99012017e-01 | -1.10502415e-01 -2.94026605e-01 4.99012017e-01 25 -1.42519218e+01 1.54604292e+01 -1.50387846e+01 | -1.42519218e+01 1.54604292e+01 -1.50387846e+01 26 -6.61714345e-02 5.93593370e-01 -2.69112277e-01 | -6.61714345e-02 5.93593370e-01 -2.69112277e-01 27 -1.17028054e-01 -5.71592423e-01 5.52000983e-01 | -1.17028054e-01 -5.71592423e-01 5.52000983e-01 28 1.40825597e+01 -1.79083395e+01 1.39488746e+01 | 1.40825597e+01 -1.79083395e+01 1.39488746e+01 29 -2.35928061e-01 7.10454257e-01 -2.99555431e-01 | -2.35928061e-01 7.10454257e-01 -2.99555431e-01 30 3.73072223e+01 -2.48538096e+01 2.26201535e+01 | 3.73072223e+01 -2.48538096e+01 2.26201535e+01 31 -1.91170721e+01 1.05958681e+01 -8.76653017e+00 | -1.91170721e+01 1.05958681e+01 -8.76653017e+00 32 -4.98844768e+00 -4.07651579e+00 -3.79714277e+00 | -4.98844768e+00 -4.07651579e+00 -3.79714277e+00 33 -3.73526822e+00 -6.33475168e+00 1.11098727e+01 | -3.73526822e+00 -6.33475168e+00 1.11098727e+01 34 3.39865549e+01 -4.92855269e+01 2.72360478e+01 | 3.39865549e+01 -4.92855269e+01 2.72360478e+01 35 -8.20794571e+00 -8.53878598e+00 8.98057170e+00 | -8.20794571e+00 -8.53878598e+00 8.98057170e+00 36 -3.04621414e-01 -3.16772611e-01 -1.28880842e+00 | -3.04621414e-01 -3.16772611e-01 -1.28880842e+00 37 -7.02984213e+00 -9.25152452e+00 7.40036989e+00 | -7.02984213e+00 -9.25152452e+00 7.40036989e+00 38 -2.05095452e+00 -2.50718234e+00 -3.68570208e+00 | -2.05095452e+00 -2.50718234e+00 -3.68570208e+00 39 -1.39432278e+01 -1.24350293e+01 1.36549763e+01 | -1.39432278e+01 -1.24350293e+01 1.36549763e+01 40 1.08178397e+01 -8.81977332e+00 2.72687982e+01 | 1.08178397e+01 -8.81977332e+00 2.72687982e+01 41 -1.81160569e+01 3.24499691e+01 -1.82651556e+01 | -1.81160569e+01 3.24499691e+01 -1.82651556e+01 42 -2.69936603e+01 -2.03567772e+00 1.06094350e+01 | -2.69936603e+01 -2.03567772e+00 1.06094350e+01 43 7.70959040e+00 9.81513988e+00 7.06608652e+00 | 7.70959040e+00 9.81513988e+00 7.06608652e+00 44 1.91067611e+01 -3.20327205e+01 1.69838694e+01 | 1.91067611e+01 -3.20327205e+01 1.69838694e+01 45 2.18865169e-02 7.16997622e-02 4.12943499e-02 | 2.18865169e-02 7.16997622e-02 4.12943499e-02 46 5.69782465e+00 8.61907260e+00 -8.31792274e+00 | 5.69782465e+00 8.61907260e+00 -8.31792274e+00 47 5.70214620e+00 -4.75956040e+00 3.22404756e+00 | 5.70214620e+00 -4.75956040e+00 3.22404756e+00 48 -9.42565572e+00 9.72233487e+00 1.38404941e+01 | -9.42565572e+00 9.72233487e+00 1.38404941e+01 49 1.21059116e+00 -2.32213360e+00 -7.67762094e-01 | 1.21059116e+00 -2.32213360e+00 -7.67762094e-01 50 -1.07007818e+01 -1.27903886e+01 -1.29815429e+01 | -1.07007818e+01 -1.27903886e+01 -1.29815429e+01 51 1.02555582e+01 1.28890367e+01 1.25057229e+01 | 1.02555582e+01 1.28890367e+01 1.25057229e+01 52 1.69016820e+01 1.51806313e+01 -1.28313746e+01 | 1.69016820e+01 1.51806313e+01 -1.28313746e+01 53 -4.34781062e+00 6.86110426e+00 -7.27817353e-01 | -4.34781062e+00 6.86110426e+00 -7.27817353e-01 54 -4.34105878e+00 -1.76474689e-02 -2.08397220e+00 | -4.34105878e+00 -1.76474689e-02 -2.08397220e+00 55 3.78207147e+00 1.29300150e+00 2.89804752e+00 | 3.78207147e+00 1.29300150e+00 2.89804752e+00 56 6.74310685e+00 7.46475070e+00 -7.83551873e+00 | 6.74310685e+00 7.46475070e+00 -7.83551873e+00 57 2.37355561e+01 -2.92391904e+01 -3.59298618e+01 | 2.37355561e+01 -2.92391904e+01 -3.59298618e+01 58 2.00894831e+01 -8.71559096e+00 1.31516907e+01 | 2.00894831e+01 -8.71559096e+00 1.31516907e+01 59 -1.04682778e+00 -2.16964966e-01 6.93835497e-02 | -1.04682778e+00 -2.16964966e-01 6.93835497e-02 60 -4.51490471e+00 -5.14720405e+00 -4.36036980e+00 | -4.51490471e+00 -5.14720405e+00 -4.36036980e+00 61 3.81699502e+00 4.12358470e+00 4.09108884e+00 | 3.81699502e+00 4.12358470e+00 4.09108884e+00 62 -2.15061581e+01 3.12131706e+01 3.65639982e+01 | -2.15061581e+01 3.12131706e+01 3.65639982e+01 63 1.22898988e+00 1.51145044e-01 -4.24381178e-01 | 1.22898988e+00 1.51145044e-01 -4.24381178e-01 ------------------------------------------------------------------------------------------------------------------------- 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 = [8, 37, 50, 52, 20, 14, 13, 38, 0, 39, 44, 32, 36, 6, 5, 59, 34, 22, 56, 46, 4, 51, 17, 30, 45, 28, 55, 42, 25, 35, 23, 40, 11, 47, 16, 29, 12, 1, 7, 9, 31, 43, 27, 41, 10, 24, 19, 33, 58, 57, 2, 21, 3, 54, 53, 26, 18, 49, 48, 15, 62, 63, 60, 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)) = 252.74623371490833 V(r_1,...,r_N) = 252.74623371490839 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 -1.99160854e+01 -1.98624508e+01 -1.85667930e+01 | -1.99160854e+01 -1.98624508e+01 -1.85667930e+01 1 9.92034490e+00 -2.20740361e+01 4.54901358e+01 | 9.92034490e+00 -2.20740361e+01 4.54901358e+01 2 9.58248403e-01 4.37670856e+01 -3.39118170e+01 | 9.58248403e-01 4.37670856e+01 -3.39118170e+01 3 -1.28054975e+01 -1.93527544e+01 9.48503528e+00 | -1.28054975e+01 -1.93527544e+01 9.48503528e+00 4 4.74903125e+00 -4.94413012e+00 3.91184109e+00 | 4.74903125e+00 -4.94413012e+00 3.91184109e+00 5 -2.53465264e+01 3.13804972e+01 -9.12617256e+00 | -2.53465264e+01 3.13804972e+01 -9.12617256e+00 6 -4.97811005e+01 -2.87612621e+01 -2.07682857e+01 | -4.97811005e+01 -2.87612621e+01 -2.07682857e+01 7 1.82377152e+01 -2.87896906e+01 4.93795230e+01 | 1.82377152e+01 -2.87896906e+01 4.93795230e+01 8 -1.11248516e+00 -6.88190794e-01 -2.08120038e+00 | -1.11248516e+00 -6.88190794e-01 -2.08120038e+00 9 -6.59167289e+00 2.03741090e+00 -6.92327104e-01 | -6.59167289e+00 2.03741090e+00 -6.92327104e-01 10 -7.51273894e+00 -1.33793793e+01 -1.31794116e+01 | -7.51273894e+00 -1.33793793e+01 -1.31794116e+01 11 1.03720291e+01 1.43017802e+01 1.03085994e+01 | 1.03720291e+01 1.43017802e+01 1.03085994e+01 12 3.13879073e+00 -2.93897559e+01 -2.23684479e+00 | 3.13879073e+00 -2.93897559e+01 -2.23684479e+00 13 2.52759737e+01 -1.12899937e+00 -2.13088529e+01 | 2.52759737e+01 -1.12899937e+00 -2.13088529e+01 14 -2.93472319e+01 -2.47918972e+01 -5.43637422e+01 | -2.93472319e+01 -2.47918972e+01 -5.43637422e+01 15 2.55304655e+01 2.73085360e+01 5.51129166e+01 | 2.55304655e+01 2.73085360e+01 5.51129166e+01 16 -6.40721161e+00 -2.87879332e+00 -5.37853923e+00 | -6.40721161e+00 -2.87879332e+00 -5.37853923e+00 17 -2.29746393e+00 3.98323286e-01 7.59554000e+00 | -2.29746393e+00 3.98323286e-01 7.59554000e+00 18 6.00932171e+00 3.27893792e+00 -7.15586487e+00 | 6.00932171e+00 3.27893792e+00 -7.15586487e+00 19 -3.22700773e-01 3.29309709e+00 6.54730308e-01 | -3.22700773e-01 3.29309709e+00 6.54730308e-01 20 3.17104947e+01 5.83369377e+01 -2.66823515e+01 | 3.17104947e+01 5.83369377e+01 -2.66823515e+01 21 -1.76445876e+01 1.96123021e+01 -2.15743297e+01 | -1.76445876e+01 1.96123021e+01 -2.15743297e+01 22 -2.81912151e+00 -3.79667913e+00 -6.98142333e+00 | -2.81912151e+00 -3.79667913e+00 -6.98142333e+00 23 2.03909747e+00 5.47625262e+00 3.94805080e+00 | 2.03909747e+00 5.47625262e+00 3.94805080e+00 24 1.56924219e+01 2.23644285e+01 -1.00319151e+01 | 1.56924219e+01 2.23644285e+01 -1.00319151e+01 25 -4.78841559e-01 -8.74184343e-01 -7.42728079e-01 | -4.78841559e-01 -8.74184343e-01 -7.42728079e-01 26 -7.58828691e+00 -7.81561609e+00 -1.21218728e+01 | -7.58828691e+00 -7.81561609e+00 -1.21218728e+01 27 1.01223883e+01 1.22166301e+01 4.82545683e+00 | 1.01223883e+01 1.22166301e+01 4.82545683e+00 28 -4.45501862e+01 -5.23967434e+01 -6.78012326e+00 | -4.45501862e+01 -5.23967434e+01 -6.78012326e+00 29 4.79803613e+01 4.82009762e+01 1.15535958e+01 | 4.79803613e+01 4.82009762e+01 1.15535958e+01 30 -3.39592052e+01 -3.85777242e+01 -2.86366683e+01 | -3.39592052e+01 -3.85777242e+01 -2.86366683e+01 31 2.75016263e+01 5.73703146e+01 1.07766431e+01 | 2.75016263e+01 5.73703146e+01 1.07766431e+01 32 -4.08226040e+00 -4.20004983e+00 -3.51773575e+00 | -4.08226040e+00 -4.20004983e+00 -3.51773575e+00 33 -2.19475441e+00 1.32511661e+01 -7.43826539e+00 | -2.19475441e+00 1.32511661e+01 -7.43826539e+00 34 -3.09807413e+01 -1.60170997e+01 -3.31377596e+01 | -3.09807413e+01 -1.60170997e+01 -3.31377596e+01 35 2.77593594e+01 2.03730426e+01 3.23882152e+01 | 2.77593594e+01 2.03730426e+01 3.23882152e+01 36 2.51511260e+00 -1.34319556e+01 9.88629992e+00 | 2.51511260e+00 -1.34319556e+01 9.88629992e+00 37 2.46932208e+00 3.15329536e+00 1.92264397e+00 | 2.46932208e+00 3.15329536e+00 1.92264397e+00 38 -1.21045173e+01 -6.15952298e+00 -1.13726747e+01 | -1.21045173e+01 -6.15952298e+00 -1.13726747e+01 39 7.95648771e+00 8.37608524e-01 1.45977627e+01 | 7.95648771e+00 8.37608524e-01 1.45977627e+01 40 2.29187116e+01 -3.29228460e+01 7.92983170e+00 | 2.29187116e+01 -3.29228460e+01 7.92983170e+00 41 2.79960038e+01 -3.94397560e+01 -4.13856940e+01 | 2.79960038e+01 -3.94397560e+01 -4.13856940e+01 42 -1.71496120e+01 2.10706968e+01 2.75314627e+01 | -1.71496120e+01 2.10706968e+01 2.75314627e+01 43 3.27715751e+00 1.86690113e+00 1.72009766e+00 | 3.27715751e+00 1.86690113e+00 1.72009766e+00 44 -6.15064152e-01 -7.96727759e+00 -2.31202508e-01 | -6.15064152e-01 -7.96727759e+00 -2.31202508e-01 45 4.38699585e+00 3.31440713e+00 2.82029069e+00 | 4.38699585e+00 3.31440713e+00 2.82029069e+00 46 -2.94532814e+01 3.98686718e+01 3.85930065e+01 | -2.94532814e+01 3.98686718e+01 3.85930065e+01 47 6.75996946e-01 -5.32441918e+00 8.57310288e+00 | 6.75996946e-01 -5.32441918e+00 8.57310288e+00 48 -1.85868343e+01 -1.05749741e+01 -1.44917047e+01 | -1.85868343e+01 -1.05749741e+01 -1.44917047e+01 49 3.56698750e+01 -1.15912409e+01 7.35209624e-01 | 3.56698750e+01 -1.15912409e+01 7.35209624e-01 50 -6.37932434e+00 -4.20497395e+01 -3.20935662e+01 | -6.37932434e+00 -4.20497395e+01 -3.20935662e+01 51 2.23252111e+00 4.57063246e+01 3.34026590e+01 | 2.23252111e+00 4.57063246e+01 3.34026590e+01 52 -1.54361307e+00 -3.40635600e+00 -8.27471924e+00 | -1.54361307e+00 -3.40635600e+00 -8.27471924e+00 53 4.12190327e+00 6.43379586e+00 4.62707256e+00 | 4.12190327e+00 6.43379586e+00 4.62707256e+00 54 -1.61411687e+01 2.14321734e+01 1.55322438e+01 | -1.61411687e+01 2.14321734e+01 1.55322438e+01 55 2.62183459e-01 8.48332766e-03 8.39186007e-01 | 2.62183459e-01 8.48332766e-03 8.39186007e-01 56 1.97884205e+01 -2.37086827e+01 2.02192657e+01 | 1.97884205e+01 -2.37086827e+01 2.02192657e+01 57 -4.13300094e+00 3.97487238e+00 -3.26563233e+00 | -4.13300094e+00 3.97487238e+00 -3.26563233e+00 58 7.97105111e-01 -1.77497784e+01 2.15414628e+01 | 7.97105111e-01 -1.77497784e+01 2.15414628e+01 59 1.53431832e+00 4.24684493e+00 -5.54833314e+00 | 1.53431832e+00 4.24684493e+00 -5.54833314e+00 60 -1.88973644e+01 -6.27634000e+01 -4.81032033e+00 | -1.88973644e+01 -6.27634000e+01 -4.81032033e+00 61 2.47137890e+01 6.17520231e+01 9.84617736e+00 | 2.47137890e+01 6.17520231e+01 9.84617736e+00 62 -4.41643590e+00 -5.38053808e+00 -9.81949601e+00 | -4.41643590e+00 -5.38053808e+00 -9.81949601e+00 63 6.84534297e+00 5.55610696e+00 1.19603085e+01 | 6.84534297e+00 5.55610696e+00 1.19603085e+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 = [14, 41, 50, 34, 52, 17, 55, 16, 38, 22, 44, 58, 32, 30, 0, 61, 7, 5, 62, 21, 39, 19, 9, 31, 56, 47, 37, 53, 45, 49, 13, 23, 12, 40, 3, 60, 57, 26, 8, 20, 33, 1, 59, 63, 10, 28, 51, 25, 54, 29, 2, 46, 4, 27, 48, 6, 24, 36, 11, 42, 35, 15, 18, 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)) = 82.37262371116329 V(r_1,...,r_N) = 82.37262371116326 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 5.55174965e+00 2.90878193e+00 5.71824806e+00 | 5.55174965e+00 2.90878193e+00 5.71824806e+00 1 -8.78726938e+00 -5.03252878e+00 -7.03152960e+00 | -8.78726938e+00 -5.03252878e+00 -7.03152960e+00 2 -1.17077291e-01 3.72803477e+00 1.87785250e-02 | -1.17077291e-01 3.72803477e+00 1.87785250e-02 3 -4.95949591e-01 -4.69444469e+00 -7.80149923e-01 | -4.95949591e-01 -4.69444469e+00 -7.80149923e-01 4 1.88117864e+00 -6.02819828e-01 1.49117175e+00 | 1.88117864e+00 -6.02819828e-01 1.49117175e+00 5 5.94958570e-01 1.95050774e+00 -4.31910864e+00 | 5.94958570e-01 1.95050774e+00 -4.31910864e+00 6 -1.23051048e-01 2.03568670e-02 2.95584154e-01 | -1.23051048e-01 2.03568670e-02 2.95584154e-01 7 -6.06271155e+00 3.29558075e+00 1.88771256e+00 | -6.06271155e+00 3.29558075e+00 1.88771256e+00 8 1.77051973e+00 -1.85200892e+00 4.61320063e-01 | 1.77051973e+00 -1.85200892e+00 4.61320063e-01 9 -5.06471344e+00 4.24778026e+00 5.21370195e-01 | -5.06471344e+00 4.24778026e+00 5.21370195e-01 10 1.62577507e+00 -3.65723697e+00 4.09060544e-01 | 1.62577507e+00 -3.65723697e+00 4.09060544e-01 11 -1.10726213e+00 1.21324863e+00 -3.81108778e+00 | -1.10726213e+00 1.21324863e+00 -3.81108778e+00 12 7.39906207e+00 1.14800555e+00 1.20936295e+00 | 7.39906207e+00 1.14800555e+00 1.20936295e+00 13 -2.66161009e+00 -6.64300377e+00 -1.27694052e+00 | -2.66161009e+00 -6.64300377e+00 -1.27694052e+00 14 6.42347774e-01 -4.03618980e+00 -3.07925675e+00 | 6.42347774e-01 -4.03618980e+00 -3.07925675e+00 15 -5.08873828e+00 4.83283664e+00 3.04510343e+00 | -5.08873828e+00 4.83283664e+00 3.04510343e+00 16 -1.43212153e+00 -6.58037346e-01 -1.65986979e+00 | -1.43212153e+00 -6.58037346e-01 -1.65986979e+00 17 4.16128744e+00 5.86275680e+00 -2.95330024e+00 | 4.16128744e+00 5.86275680e+00 -2.95330024e+00 18 -6.82830464e+00 -8.48323328e-01 3.02267876e+00 | -6.82830464e+00 -8.48323328e-01 3.02267876e+00 19 -2.77784229e+00 2.11587594e+00 -1.29560167e+00 | -2.77784229e+00 2.11587594e+00 -1.29560167e+00 20 8.13647843e+00 5.71439549e+00 6.17851239e+00 | 8.13647843e+00 5.71439549e+00 6.17851239e+00 21 -5.01671908e+00 -2.94409672e+00 -6.50458710e+00 | -5.01671908e+00 -2.94409672e+00 -6.50458710e+00 22 -1.01149292e+00 7.48095081e-01 -3.36093189e+00 | -1.01149292e+00 7.48095081e-01 -3.36093189e+00 23 -5.32186896e+00 -8.66672873e+00 1.07314572e+00 | -5.32186896e+00 -8.66672873e+00 1.07314572e+00 24 8.03165696e+00 3.22380970e+00 -4.93887018e-01 | 8.03165696e+00 3.22380970e+00 -4.93887018e-01 25 -2.69721485e+00 1.09741562e+00 -5.15955995e-01 | -2.69721485e+00 1.09741562e+00 -5.15955995e-01 26 2.61019395e+00 -1.43669372e+00 2.06476611e+00 | 2.61019395e+00 -1.43669372e+00 2.06476611e+00 27 3.70434341e-01 1.45213764e-01 -2.79759887e+00 | 3.70434341e-01 1.45213764e-01 -2.79759887e+00 28 -5.55593681e-01 -8.67395970e-01 -1.87387383e+00 | -5.55593681e-01 -8.67395970e-01 -1.87387383e+00 29 -4.00425367e+00 9.66176669e+00 5.79779866e+00 | -4.00425367e+00 9.66176669e+00 5.79779866e+00 30 1.66193991e+00 9.57929188e+00 1.83801317e-01 | 1.66193991e+00 9.57929188e+00 1.83801317e-01 31 -4.91756460e+00 -7.22170494e+00 -2.72624067e+00 | -4.91756460e+00 -7.22170494e+00 -2.72624067e+00 32 3.96738454e+00 4.16420167e+00 2.10767664e+00 | 3.96738454e+00 4.16420167e+00 2.10767664e+00 33 -7.26768816e+00 -3.48565275e+00 -1.46273278e+00 | -7.26768816e+00 -3.48565275e+00 -1.46273278e+00 34 6.97734974e-01 -2.61405737e+00 2.28477993e-02 | 6.97734974e-01 -2.61405737e+00 2.28477993e-02 35 2.07528481e+00 -7.15086844e-01 -5.07659096e-01 | 2.07528481e+00 -7.15086844e-01 -5.07659096e-01 36 9.86850588e-01 2.20631384e+00 1.92038000e+00 | 9.86850588e-01 2.20631384e+00 1.92038000e+00 37 1.34345217e+01 -7.99125256e+00 -4.03067493e+00 | 1.34345217e+01 -7.99125256e+00 -4.03067493e+00 38 -6.50569917e-01 -2.89759779e+00 -2.28739737e+00 | -6.50569917e-01 -2.89759779e+00 -2.28739737e+00 39 8.46996028e-01 4.38012716e+00 -2.94706461e+00 | 8.46996028e-01 4.38012716e+00 -2.94706461e+00 40 2.32550652e+00 4.57819727e-01 6.53561114e+00 | 2.32550652e+00 4.57819727e-01 6.53561114e+00 41 -3.12811356e+00 -3.79177794e+00 -5.07147543e+00 | -3.12811356e+00 -3.79177794e+00 -5.07147543e+00 42 5.65143036e+00 3.00709113e+00 9.52759956e+00 | 5.65143036e+00 3.00709113e+00 9.52759956e+00 43 3.46141129e-01 3.17034846e-01 -8.24102184e+00 | 3.46141129e-01 3.17034846e-01 -8.24102184e+00 44 4.38120389e+00 4.80563206e+00 1.14452764e+00 | 4.38120389e+00 4.80563206e+00 1.14452764e+00 45 -4.55855126e+00 -1.09966439e+01 -1.05292588e+00 | -4.55855126e+00 -1.09966439e+01 -1.05292588e+00 46 -1.50708523e+01 3.10818369e+00 9.71200356e+00 | -1.50708523e+01 3.10818369e+00 9.71200356e+00 47 -1.71859865e+00 1.03292362e-01 2.27046929e+00 | -1.71859865e+00 1.03292362e-01 2.27046929e+00 48 1.81743045e+00 -6.33657167e+00 -6.71630651e-01 | 1.81743045e+00 -6.33657167e+00 -6.71630651e-01 49 9.38533153e+00 2.94675506e+00 -1.59004019e+00 | 9.38533153e+00 2.94675506e+00 -1.59004019e+00 50 -7.82399648e+00 1.40810969e+01 2.64801598e+00 | -7.82399648e+00 1.40810969e+01 2.64801598e+00 51 2.91575057e+00 -1.18441340e+00 1.73690920e+00 | 2.91575057e+00 -1.18441340e+00 1.73690920e+00 52 2.50741238e+00 6.68656719e+00 1.09342625e+01 | 2.50741238e+00 6.68656719e+00 1.09342625e+01 53 -4.72181213e+00 -1.06681392e+01 -7.36483405e+00 | -4.72181213e+00 -1.06681392e+01 -7.36483405e+00 54 6.12389709e+00 5.22591789e+00 5.42540994e+00 | 6.12389709e+00 5.22591789e+00 5.42540994e+00 55 -1.01933787e+01 -4.88428945e+00 -4.18562023e+00 | -1.01933787e+01 -4.88428945e+00 -4.18562023e+00 56 8.15493073e+00 -4.10141666e+00 -8.44643525e-01 | 8.15493073e+00 -4.10141666e+00 -8.44643525e-01 57 3.88910787e+00 -2.51904916e+00 2.43062262e+00 | 3.88910787e+00 -2.51904916e+00 2.43062262e+00 58 8.79526548e+00 -6.16333534e+00 -3.83909963e+00 | 8.79526548e+00 -6.16333534e+00 -3.83909963e+00 59 2.11905138e+00 -1.94535473e+00 -1.41770382e+00 | 2.11905138e+00 -1.94535473e+00 -1.41770382e+00 60 -4.59834491e+00 4.43248445e+00 -2.98923923e+00 | -4.59834491e+00 4.43248445e+00 -2.98923923e+00 61 1.35957218e+00 -4.23359490e-01 4.92487670e-01 | 1.35957218e+00 -4.23359490e-01 4.92487670e-01 62 2.41080541e+00 3.84851480e+00 1.27858327e+01 | 2.41080541e+00 3.84851480e+00 1.27858327e+01 63 -4.82592705e+00 -1.38557515e+00 -1.00893879e+01 | -4.82592705e+00 -1.38557515e+00 -1.00893879e+01 ------------------------------------------------------------------------------------------------------------------------- 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 = [4, 48, 34, 46, 0, 42, 32, 63, 37, 20, 51, 19, 13, 12, 49, 27, 26, 50, 28, 11, 9, 53, 23, 22, 60, 36, 16, 15, 18, 44, 38, 33, 6, 31, 2, 52, 25, 8, 30, 55, 45, 47, 5, 59, 29, 40, 3, 41, 1, 14, 17, 10, 35, 21, 56, 39, 54, 62, 58, 43, 24, 61, 57, 7] 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)) = 369.5765697510431 V(r_1,...,r_N) = 369.57656975104305 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 8.78513291e-01 1.69234335e+00 -4.84630366e-01 | 8.78513291e-01 1.69234335e+00 -4.84630366e-01 1 -2.18536269e+01 7.65037166e+00 -1.29647117e+01 | -2.18536269e+01 7.65037166e+00 -1.29647117e+01 2 6.52308539e+00 6.77877448e+00 -5.86967241e+00 | 6.52308539e+00 6.77877448e+00 -5.86967241e+00 3 -2.25161960e+00 -2.61116271e+00 -1.56845829e+00 | -2.25161960e+00 -2.61116271e+00 -1.56845829e+00 4 1.64439757e+01 -1.53554004e+01 1.67279350e+01 | 1.64439757e+01 -1.53554004e+01 1.67279350e+01 5 -1.86933879e+01 1.54417456e+01 -2.06569171e+01 | -1.86933879e+01 1.54417456e+01 -2.06569171e+01 6 1.20981384e+00 2.96713996e-02 -2.65612979e+00 | 1.20981384e+00 2.96713996e-02 -2.65612979e+00 7 -5.60991525e+00 -4.06606869e+00 4.39635506e+00 | -5.60991525e+00 -4.06606869e+00 4.39635506e+00 8 -6.54470872e+00 -5.42079297e+00 -1.01921474e+01 | -6.54470872e+00 -5.42079297e+00 -1.01921474e+01 9 1.99278990e-01 9.34926401e+00 4.20989322e+00 | 1.99278990e-01 9.34926401e+00 4.20989322e+00 10 -9.90162730e+00 -2.02357644e+01 -3.14521943e+01 | -9.90162730e+00 -2.02357644e+01 -3.14521943e+01 11 1.22645107e+01 1.86516108e+01 2.72737668e+01 | 1.22645107e+01 1.86516108e+01 2.72737668e+01 12 6.92642678e+00 -4.64773403e+00 5.15327844e+00 | 6.92642678e+00 -4.64773403e+00 5.15327844e+00 13 2.89186897e+00 -6.68692390e+00 -1.28032060e+00 | 2.89186897e+00 -6.68692390e+00 -1.28032060e+00 14 -2.82952769e+00 -5.95652968e-01 -7.46104101e-01 | -2.82952769e+00 -5.95652968e-01 -7.46104101e-01 15 -4.38409430e+02 -6.20072795e+02 2.22189979e+02 | -4.38409430e+02 -6.20072795e+02 2.22189979e+02 16 -1.83890883e+00 1.57495483e+00 1.73590791e+00 | -1.83890883e+00 1.57495483e+00 1.73590791e+00 17 9.34421530e+00 -2.16104521e+01 -2.28818209e+01 | 9.34421530e+00 -2.16104521e+01 -2.28818209e+01 18 -2.75622098e-01 1.19260825e+00 1.89669715e+00 | -2.75622098e-01 1.19260825e+00 1.89669715e+00 19 2.16936553e+00 -2.21052998e+00 -2.92040731e+00 | 2.16936553e+00 -2.21052998e+00 -2.92040731e+00 20 5.19459932e+00 3.29554156e+00 9.90345623e-01 | 5.19459932e+00 3.29554156e+00 9.90345623e-01 21 1.10337005e+02 -1.08639388e+02 -6.75931051e+01 | 1.10337005e+02 -1.08639388e+02 -6.75931051e+01 22 -3.37823569e+01 -1.70905249e+01 -9.11756866e+00 | -3.37823569e+01 -1.70905249e+01 -9.11756866e+00 23 2.37393590e+01 3.84808775e+01 3.15187789e+01 | 2.37393590e+01 3.84808775e+01 3.15187789e+01 24 -9.58416359e-01 -7.93969250e-02 -3.49256388e+00 | -9.58416359e-01 -7.93969250e-02 -3.49256388e+00 25 4.61940377e+00 4.69712006e+00 -1.14568951e+01 | 4.61940377e+00 4.69712006e+00 -1.14568951e+01 26 -2.73955896e+00 -7.51991601e-01 7.69922937e+00 | -2.73955896e+00 -7.51991601e-01 7.69922937e+00 27 -7.66844942e-01 -1.46111107e+00 -7.59474232e-01 | -7.66844942e-01 -1.46111107e+00 -7.59474232e-01 28 4.46718015e+02 6.15608501e+02 -2.25485494e+02 | 4.46718015e+02 6.15608501e+02 -2.25485494e+02 29 1.52209286e+00 2.74334525e-01 3.48940338e-01 | 1.52209286e+00 2.74334525e-01 3.48940338e-01 30 -8.79690302e+00 -1.21105365e+01 -6.08642228e+00 | -8.79690302e+00 -1.21105365e+01 -6.08642228e+00 31 7.48333998e+00 1.61992385e+01 4.93108891e+00 | 7.48333998e+00 1.61992385e+01 4.93108891e+00 32 -1.35869683e+00 -5.29860797e-01 6.74792404e-01 | -1.35869683e+00 -5.29860797e-01 6.74792404e-01 33 -7.00631650e+01 -4.13456085e+01 2.93169915e+01 | -7.00631650e+01 -4.13456085e+01 2.93169915e+01 34 6.68841150e+01 4.50061605e+01 -2.58699227e+01 | 6.68841150e+01 4.50061605e+01 -2.58699227e+01 35 1.03110107e+01 -1.12699508e+01 -1.44344513e+01 | 1.03110107e+01 -1.12699508e+01 -1.44344513e+01 36 -1.00087900e+02 -3.26566258e+00 -3.40933477e+02 | -1.00087900e+02 -3.26566258e+00 -3.40933477e+02 37 9.94955418e+01 2.40184619e+00 3.41495308e+02 | 9.94955418e+01 2.40184619e+00 3.41495308e+02 38 1.43213360e+00 -2.37920291e+00 -3.62551852e+00 | 1.43213360e+00 -2.37920291e+00 -3.62551852e+00 39 -2.39679735e+00 -3.54551612e+00 3.93099300e+00 | -2.39679735e+00 -3.54551612e+00 3.93099300e+00 40 1.57535816e+01 -2.02667807e+01 1.54250230e+01 | 1.57535816e+01 -2.02667807e+01 1.54250230e+01 41 4.73855666e+00 4.18791606e+00 6.97048035e+00 | 4.73855666e+00 4.18791606e+00 6.97048035e+00 42 -3.86276351e+00 -3.17387870e+01 -3.09827529e+01 | -3.86276351e+00 -3.17387870e+01 -3.09827529e+01 43 3.00531352e+00 3.57096027e+01 3.48228457e+01 | 3.00531352e+00 3.57096027e+01 3.48228457e+01 44 -3.08500501e+00 -6.13218202e+00 -8.60186292e+00 | -3.08500501e+00 -6.13218202e+00 -8.60186292e+00 45 3.92719235e+00 4.82258510e+00 9.35153378e+00 | 3.92719235e+00 4.82258510e+00 9.35153378e+00 46 -1.82873677e+01 -5.47535106e+00 -4.48193911e+01 | -1.82873677e+01 -5.47535106e+00 -4.48193911e+01 47 1.92554163e+01 5.54257275e+00 4.51631772e+01 | 1.92554163e+01 5.54257275e+00 4.51631772e+01 48 6.27206576e-01 8.78444648e-01 -3.40460186e-01 | 6.27206576e-01 8.78444648e-01 -3.40460186e-01 49 5.20779850e+00 -1.33736094e+01 -7.51625017e+00 | 5.20779850e+00 -1.33736094e+01 -7.51625017e+00 50 -1.12101048e+02 1.09113002e+02 7.26936319e+01 | -1.12101048e+02 1.09113002e+02 7.26936319e+01 51 -9.38041676e-01 -5.05192140e-01 -5.15576185e+00 | -9.38041676e-01 -5.05192140e-01 -5.15576185e+00 52 -1.89816245e+01 1.18348528e+01 4.07042518e+00 | -1.89816245e+01 1.18348528e+01 4.07042518e+00 53 1.53252121e+01 1.03179127e+01 6.19872969e+00 | 1.53252121e+01 1.03179127e+01 6.19872969e+00 54 -1.48856643e+02 -4.70116784e+01 -5.31163269e+01 | -1.48856643e+02 -4.70116784e+01 -5.31163269e+01 55 1.41535755e+02 5.84078682e+01 6.00614228e+01 | 1.41535755e+02 5.84078682e+01 6.00614228e+01 56 -7.79545568e+00 6.31940167e+00 7.56935783e+00 | -7.79545568e+00 6.31940167e+00 7.56935783e+00 57 -1.93801976e+01 -1.34593584e+01 9.34390188e+00 | -1.93801976e+01 -1.34593584e+01 9.34390188e+00 58 2.17511698e+01 1.12054142e+01 -1.19505176e+01 | 2.17511698e+01 1.12054142e+01 -1.19505176e+01 59 -2.51667148e-02 1.37820783e-01 2.25884154e-01 | -2.51667148e-02 1.37820783e-01 2.25884154e-01 60 -1.11714233e+00 1.85761980e+00 1.97434703e+00 | -1.11714233e+00 1.85761980e+00 1.97434703e+00 61 9.80772476e-01 4.56817710e-01 9.82501722e-01 | 9.80772476e-01 4.56817710e-01 9.82501722e-01 62 -4.45085209e+00 -3.87276044e+00 5.70574385e+00 | -4.45085209e+00 -3.87276044e+00 5.70574385e+00 63 -6.55323662e-01 -1.29906816e+00 -3.75555747e-02 | -6.55323662e-01 -1.29906816e+00 -3.75555747e-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.