!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! VERIFICATION CHECK: vc-forces-numerical-derivative !!!!! !!!!! !!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Description: Comparison of the analytical forces obtained from the model with forces computed by numerical differentiation using Richardson extrapolation for a randomly distorted non-periodic structure based off the equilibrium face-centered cubic (fcc) structure. Separate configurations are tested for each species supported by the model, as well as one containing a random distribution of all species. Configurations used for testing are provided as auxiliary files. Author: Ellad Tadmor ----------------------------------------------------------------------------------------------------- Results for KIM Model : MEAM_LAMMPS_SaLee_2008_NbFe__MO_162036141261_001 Supported species : Fe Nb random seed = 13 perturbation amplitude = 0.250 number unit cells per side = 2 ----------------------------------------------------------------------------------------------------- Comparison of analytical forces obtained from the model, the force computed as a numerical derivative of the energy, the difference between them, and the uncertainty in the numerical estimate of the force. The computed equilibrium lattice constant for the crystal (a0) is given in the heading. MONOATOMIC STRUCTURE -- Species = Fe | a0 = 3.611098289489746 | (Configuration in file "config-Fe.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Fe 1 3.605565097578760e-01 3.605565096523897e-01 1.05486e-10 9.69693e-11 2 -5.251217466400691e-02 -5.251217469545885e-02 3.14519e-11 1.78472e-10 3 -4.185755648434410e-01 -4.185755647592944e-01 8.41466e-11 2.70801e-10 ----------------------------------------------------------------------------------------------------- 2 Fe 1 -5.848068085059370e-01 -5.848068086185231e-01 1.12586e-10 2.91618e-11 2 3.299962547871352e-01 3.299962547864236e-01 7.11597e-13 2.96854e-10 3 9.219258901951279e-01 9.219258902048038e-01 9.67582e-12 1.38621e-10 ----------------------------------------------------------------------------------------------------- 3 Fe 1 1.455453993201445e+00 1.455453993217768e+00 1.63225e-11 1.60193e-08 * 2 2.390684151641953e-01 2.390684151637482e-01 4.47031e-13 5.16861e-10 3 -1.418158935592065e+00 -1.418158935612162e+00 2.00973e-11 3.16083e-10 ----------------------------------------------------------------------------------------------------- 4 Fe 1 6.591937296356217e-01 6.591937296542537e-01 1.86320e-11 1.29281e-10 2 3.477510574601759e-01 3.477510574397512e-01 2.04247e-11 3.23646e-10 3 5.346519353652516e-01 5.346519354065424e-01 4.12909e-11 3.57396e-10 ----------------------------------------------------------------------------------------------------- 5 Fe 1 9.583721530916987e-02 9.583721536246484e-02 5.32950e-11 2.92045e-10 2 2.981737567568553e-01 2.981737567552765e-01 1.57879e-12 1.18583e-10 3 6.515382111153076e-01 6.515382111049000e-01 1.04077e-11 1.68254e-09 ----------------------------------------------------------------------------------------------------- 6 Fe 1 -7.841188404721965e-01 -7.841188404718223e-01 3.74145e-13 1.45381e-10 2 5.580859282320410e-01 5.580859282194548e-01 1.25862e-11 2.28891e-10 3 4.862243491162534e-01 4.862243490821931e-01 3.40603e-11 1.44657e-10 ----------------------------------------------------------------------------------------------------- 7 Fe 1 4.215223134005134e-01 4.215223133950637e-01 5.44975e-12 5.67254e-10 2 -2.492701083925867e+00 -2.492701083941083e+00 1.52163e-11 4.27289e-11 3 -2.740352950099295e+00 -2.740352950099461e+00 1.65645e-13 2.48454e-10 ----------------------------------------------------------------------------------------------------- 8 Fe 1 -1.829420260416214e+00 -1.829420260364979e+00 5.12341e-11 1.23485e-08 * 2 -2.189356892541623e+00 -2.189356892505979e+00 3.56439e-11 6.39103e-10 3 -8.916608121328964e-01 -8.916608121543915e-01 2.14951e-11 1.10056e-09 ----------------------------------------------------------------------------------------------------- 9 Fe 1 1.906240463273637e-01 1.906240463030075e-01 2.43562e-11 3.14720e-10 2 -1.667627145628084e+00 -1.667627145555750e+00 7.23339e-11 1.23237e-09 3 -1.468850589898598e+00 -1.468850589880871e+00 1.77265e-11 1.31353e-09 ----------------------------------------------------------------------------------------------------- 10 Fe 1 -1.353616415891610e+00 -1.353616415897949e+00 6.33849e-12 1.53839e-09 2 1.084616358187516e+00 1.084616358214942e+00 2.74254e-11 4.33252e-10 3 -1.486886855699967e+00 -1.486886855619020e+00 8.09468e-11 5.95151e-10 ----------------------------------------------------------------------------------------------------- 11 Fe 1 -8.589261059321988e-01 -8.589261058920878e-01 4.01109e-11 8.93779e-11 2 -1.392420884030786e+00 -1.392420884145766e+00 1.14980e-10 1.06841e-09 3 1.268570248848372e+00 1.268570248873464e+00 2.50919e-11 1.28053e-08 * ----------------------------------------------------------------------------------------------------- 12 Fe 1 4.246646633761584e-01 4.246646633625738e-01 1.35846e-11 1.63209e-10 2 1.557589322558504e+00 1.557589322640271e+00 8.17666e-11 1.63999e-10 3 1.157023420683108e+00 1.157023420741154e+00 5.80456e-11 1.97742e-09 * ----------------------------------------------------------------------------------------------------- 13 Fe 1 -1.031471956698021e+00 -1.031471956668036e+00 2.99856e-11 4.99965e-10 2 -2.238060165713909e+00 -2.238060165703425e+00 1.04841e-11 4.87765e-11 3 -3.168660359908114e+00 -3.168660359883613e+00 2.45013e-11 4.21259e-10 ----------------------------------------------------------------------------------------------------- 14 Fe 1 3.934934593453962e-01 3.934934593228261e-01 2.25701e-11 2.37513e-10 2 6.177594577810908e-01 6.177594578206544e-01 3.95637e-11 6.88209e-11 3 1.645737887388684e-01 1.645737886258591e-01 1.13009e-10 9.82127e-11 ----------------------------------------------------------------------------------------------------- 15 Fe 1 3.131262574115241e+00 3.131262574067020e+00 4.82214e-11 1.96409e-10 2 2.852998560905395e-01 2.852998560818825e-01 8.65702e-12 4.47907e-10 3 1.080787433290424e+00 1.080787433343355e+00 5.29314e-11 3.89462e-10 ----------------------------------------------------------------------------------------------------- 16 Fe 1 1.279256254427384e+00 1.279256254417321e+00 1.00628e-11 2.74180e-10 2 2.095066614751360e+00 2.095066614757438e+00 6.07825e-12 3.29356e-10 3 1.396268793850125e+00 1.396268793802848e+00 4.72771e-11 2.22087e-11 ----------------------------------------------------------------------------------------------------- 17 Fe 1 -2.067441300856477e+00 -2.067441300941464e+00 8.49867e-11 8.03437e-11 2 -5.579894166018795e-01 -5.579894166256720e-01 2.37925e-11 2.83810e-10 3 3.625332621409308e-01 3.625332621932991e-01 5.23683e-11 6.55027e-10 ----------------------------------------------------------------------------------------------------- 18 Fe 1 1.605345152715979e+00 1.605345152696246e+00 1.97329e-11 2.19259e-09 * 2 1.556784044591724e+00 1.556784044569635e+00 2.20892e-11 2.84729e-10 3 5.378713789220061e-01 5.378713788833427e-01 3.86634e-11 4.24473e-10 ----------------------------------------------------------------------------------------------------- 19 Fe 1 4.481153291858679e-01 4.481153291885311e-01 2.66315e-12 6.81472e-10 2 6.526801808944079e-02 6.526801809043212e-02 9.91332e-13 3.19830e-10 3 9.255514987481421e-02 9.255514985384222e-02 2.09720e-11 2.65069e-10 ----------------------------------------------------------------------------------------------------- 20 Fe 1 6.715571132018773e-01 6.715571132116974e-01 9.82014e-12 2.60401e-10 2 4.707268292754717e-01 4.707268293072714e-01 3.17997e-11 5.11974e-09 * 3 -4.760086306928830e-01 -4.760086306840418e-01 8.84126e-12 2.20093e-10 ----------------------------------------------------------------------------------------------------- 21 Fe 1 -1.071355921355640e+00 -1.071355921361957e+00 6.31650e-12 2.12955e-09 * 2 4.583815598646940e-01 4.583815598225879e-01 4.21060e-11 2.65237e-10 3 7.811767716253177e-01 7.811767716349282e-01 9.61042e-12 3.85731e-10 ----------------------------------------------------------------------------------------------------- 22 Fe 1 1.534528585535936e-01 1.534528585382777e-01 1.53159e-11 5.13449e-10 2 2.405370016482884e+00 2.405370016465071e+00 1.78124e-11 1.38058e-10 3 2.723853107315407e+00 2.723853107221850e+00 9.35576e-11 4.78906e-11 ----------------------------------------------------------------------------------------------------- 23 Fe 1 -6.272652100285239e-01 -6.272652100184627e-01 1.00612e-11 1.49524e-11 2 6.519283188411483e-01 6.519283188507115e-01 9.56313e-12 1.50314e-10 3 -4.603577780430228e-01 -4.603577780149168e-01 2.81060e-11 2.04698e-10 ----------------------------------------------------------------------------------------------------- 24 Fe 1 3.754765835823801e-01 3.754765836230486e-01 4.06686e-11 2.89116e-10 2 4.738696793487941e-01 4.738696793602761e-01 1.14820e-11 3.18634e-10 3 -8.731204525923939e-01 -8.731204526167390e-01 2.43451e-11 1.28132e-09 ----------------------------------------------------------------------------------------------------- 25 Fe 1 -3.964379209639017e-01 -3.964379209554597e-01 8.44208e-12 2.64572e-10 2 -7.151461852468661e-01 -7.151461852559561e-01 9.08995e-12 8.80879e-11 3 7.433521414592237e-01 7.433521414718162e-01 1.25925e-11 5.76083e-10 ----------------------------------------------------------------------------------------------------- 26 Fe 1 -1.468469793920032e+00 -1.468469793900510e+00 1.95219e-11 1.03940e-10 2 7.105156537943915e-01 7.105156537795877e-01 1.48038e-11 6.45994e-10 3 -1.173601794369697e+00 -1.173601794320861e+00 4.88358e-11 5.16240e-11 ----------------------------------------------------------------------------------------------------- 27 Fe 1 1.495477737640010e+00 1.495477737661050e+00 2.10398e-11 1.64094e-10 2 -3.139751329446602e+00 -3.139751329452148e+00 5.54667e-12 2.33526e-10 3 4.315219965625262e-02 4.315219963224551e-02 2.40071e-11 1.74494e-10 ----------------------------------------------------------------------------------------------------- 28 Fe 1 -1.544662030182580e+00 -1.544662030181194e+00 1.38578e-12 1.82643e-10 2 1.437343641352877e+00 1.437343641360684e+00 7.80642e-12 1.36091e-09 3 -3.876698293470214e-01 -3.876698293041307e-01 4.28906e-11 1.04757e-10 ----------------------------------------------------------------------------------------------------- 29 Fe 1 -3.779532567691532e-01 -3.779532567497196e-01 1.94336e-11 6.67381e-11 2 -8.702665536798356e-01 -8.702665536932594e-01 1.34238e-11 8.47201e-11 3 1.428620985620916e+00 1.428620985611790e+00 9.12603e-12 3.49622e-10 ----------------------------------------------------------------------------------------------------- 30 Fe 1 -5.378851830423581e-01 -5.378851830275541e-01 1.48040e-11 6.52023e-11 2 5.582702851748544e-02 5.582702863899421e-02 1.21509e-10 4.86772e-10 3 -4.543697324171287e-02 -4.543697327251536e-02 3.08025e-11 5.04917e-09 * ----------------------------------------------------------------------------------------------------- 31 Fe 1 8.192339379220839e-02 8.192339381820110e-02 2.59927e-11 1.97721e-10 2 -9.845969156393330e-01 -9.845969156568923e-01 1.75593e-11 8.42715e-11 3 -7.912754767428118e-02 -7.912754769996164e-02 2.56805e-11 2.99391e-10 ----------------------------------------------------------------------------------------------------- 32 Fe 1 1.290618077466755e+00 1.290618077394988e+00 7.17670e-11 1.34181e-10 2 6.010069351904674e-01 6.010069352248910e-01 3.44236e-11 2.08994e-10 3 7.137900063176809e-01 7.137900063295043e-01 1.18234e-11 9.06870e-09 * ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as discontinuities. Maximum error obtained for particle = 30, direction = 2: |F_model - F_numer| error = ----------------------- = 2.17652e-09 max{|F_numer|, eps} Comparison of analytical forces obtained from the model, the force computed as a numerical derivative of the energy, the difference between them, and the uncertainty in the numerical estimate of the force. The computed equilibrium lattice constant for the crystal (a0) is given in the heading. MONOATOMIC STRUCTURE -- Species = Nb | a0 = 4.165855407714844 | (Configuration in file "config-Nb.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Nb 1 1.591131146621564e+00 1.591131146600651e+00 2.09137e-11 5.35669e-11 2 1.355400239027714e+00 1.355400239021631e+00 6.08225e-12 4.65995e-10 3 1.562386105372986e+00 1.562386105387382e+00 1.43963e-11 3.49700e-11 ----------------------------------------------------------------------------------------------------- 2 Nb 1 -7.964219295523156e-01 -7.964219295491063e-01 3.20932e-12 4.42241e-10 2 -6.976463863679681e-01 -6.976463863784853e-01 1.05173e-11 4.91180e-11 3 1.485368926765092e+00 1.485368926751900e+00 1.31921e-11 4.60898e-11 ----------------------------------------------------------------------------------------------------- 3 Nb 1 -6.112078231258030e-01 -6.112078231245549e-01 1.24811e-12 1.46859e-09 2 1.575214368932903e+00 1.575214368935843e+00 2.93965e-12 1.00898e-09 3 -1.078297522610458e+00 -1.078297522607227e+00 3.23030e-12 4.64493e-11 ----------------------------------------------------------------------------------------------------- 4 Nb 1 1.330374962585502e+00 1.330374962589940e+00 4.43778e-12 1.32830e-09 2 -5.488267724268251e-01 -5.488267724404573e-01 1.36322e-11 6.87399e-11 3 -9.247215897458750e-01 -9.247215897219943e-01 2.38808e-11 2.85231e-09 ----------------------------------------------------------------------------------------------------- 5 Nb 1 4.919080797251221e-01 4.919080797021683e-01 2.29538e-11 9.78635e-11 2 1.778615084537424e+00 1.778615084565975e+00 2.85509e-11 9.03797e-11 3 1.679497878216296e+00 1.679497878146184e+00 7.01121e-11 1.22335e-09 ----------------------------------------------------------------------------------------------------- 6 Nb 1 -1.591845855442572e+00 -1.591845855445539e+00 2.96740e-12 7.09819e-11 2 -4.882068425714876e-01 -4.882068425673751e-01 4.11249e-12 2.04549e-10 3 1.776884279525594e+00 1.776884279529597e+00 4.00302e-12 1.92300e-10 ----------------------------------------------------------------------------------------------------- 7 Nb 1 -1.461246744497956e+00 -1.461246744496349e+00 1.60694e-12 1.22909e-10 2 1.374620457711140e+00 1.374620457740759e+00 2.96185e-11 3.19524e-10 3 -3.096122878175267e-01 -3.096122877656844e-01 5.18423e-11 2.58106e-09 ----------------------------------------------------------------------------------------------------- 8 Nb 1 8.369681306574528e-01 8.369681306602146e-01 2.76179e-12 1.99532e-10 2 -1.055246986107518e+00 -1.055246986107692e+00 1.74749e-13 4.09634e-09 * 3 -6.783977861059791e-01 -6.783977861200213e-01 1.40422e-11 2.88866e-10 ----------------------------------------------------------------------------------------------------- 9 Nb 1 1.790444947496148e+00 1.790444947502462e+00 6.31362e-12 2.18811e-10 2 3.668249378363103e-01 3.668249377861032e-01 5.02071e-11 2.18249e-10 3 1.638691423661875e+00 1.638691423663421e+00 1.54565e-12 9.80382e-11 ----------------------------------------------------------------------------------------------------- 10 Nb 1 -5.936923118848586e-01 -5.936923118748503e-01 1.00083e-11 2.21414e-10 2 -1.688250424685476e+00 -1.688250424647829e+00 3.76466e-11 1.13749e-10 3 1.242036289200644e+00 1.242036289146713e+00 5.39315e-11 1.29455e-09 ----------------------------------------------------------------------------------------------------- 11 Nb 1 -9.112234326177492e-01 -9.112234325951900e-01 2.25592e-11 3.02110e-10 2 2.087260192573432e-01 2.087260192171549e-01 4.01882e-11 4.50936e-11 3 -2.372478802576970e-01 -2.372478802626289e-01 4.93189e-12 4.27965e-09 * ----------------------------------------------------------------------------------------------------- 12 Nb 1 1.216563917431161e+00 1.216563917555701e+00 1.24540e-10 5.38414e-12 2 -1.322937955401183e+00 -1.322937955418199e+00 1.70157e-11 9.31222e-11 3 -4.312696638986420e-01 -4.312696639142378e-01 1.55957e-11 3.90828e-09 * ----------------------------------------------------------------------------------------------------- 13 Nb 1 9.548494271076221e-01 9.548494270694167e-01 3.82054e-11 1.64598e-10 2 7.233211079086960e-01 7.233211078998322e-01 8.86380e-12 3.14052e-10 3 6.117428631705961e-01 6.117428632007310e-01 3.01349e-11 1.54702e-09 ----------------------------------------------------------------------------------------------------- 14 Nb 1 -1.430676235295308e+00 -1.430676235290405e+00 4.90297e-12 5.39782e-11 2 -1.419818099692517e+00 -1.419818099704049e+00 1.15319e-11 1.09655e-10 3 1.259451239216052e+00 1.259451239223813e+00 7.76024e-12 3.20745e-10 ----------------------------------------------------------------------------------------------------- 15 Nb 1 -1.345419342866834e+00 -1.345419342867997e+00 1.16351e-12 4.32013e-10 2 4.810943440098325e-01 4.810943439997074e-01 1.01251e-11 9.35532e-11 3 -4.884398999840189e-01 -4.884398999747411e-01 9.27780e-12 6.99170e-10 ----------------------------------------------------------------------------------------------------- 16 Nb 1 7.809866542024169e-01 7.809866541239688e-01 7.84480e-11 3.72056e-10 2 -5.035548654793179e-01 -5.035548655238387e-01 4.45207e-11 7.87947e-11 3 -5.519855949689458e-01 -5.519855949515502e-01 1.73956e-11 7.65291e-11 ----------------------------------------------------------------------------------------------------- 17 Nb 1 1.572715402738380e+00 1.572715402739837e+00 1.45639e-12 4.45957e-10 2 1.394992544987569e+00 1.394992545008831e+00 2.12621e-11 1.04886e-10 3 3.997509536633500e-01 3.997509535817945e-01 8.15555e-11 5.86836e-11 ----------------------------------------------------------------------------------------------------- 18 Nb 1 -1.241150152275541e+00 -1.241150152416493e+00 1.40952e-10 2.32456e-10 2 -5.202732452872043e-01 -5.202732452462728e-01 4.09315e-11 1.01227e-09 3 -7.834528220037691e-01 -7.834528220346670e-01 3.08980e-11 3.98722e-10 ----------------------------------------------------------------------------------------------------- 19 Nb 1 -3.488258410770902e-01 -3.488258410737904e-01 3.29986e-12 2.99818e-10 2 1.088452556857416e+00 1.088452556750862e+00 1.06554e-10 1.38547e-09 3 -1.590854605193682e+00 -1.590854605183339e+00 1.03433e-11 3.16187e-09 ----------------------------------------------------------------------------------------------------- 20 Nb 1 8.409360816467845e-01 8.409360816424017e-01 4.38272e-12 1.50992e-10 2 -5.355698618053822e-01 -5.355698618067567e-01 1.37446e-12 1.96769e-09 3 -1.071818244642609e+00 -1.071818244620851e+00 2.17584e-11 6.21383e-11 ----------------------------------------------------------------------------------------------------- 21 Nb 1 6.330909830137220e-01 6.330909830532259e-01 3.95038e-11 2.63799e-10 2 4.959663839582463e-01 4.959663841181888e-01 1.59943e-10 4.04913e-10 3 4.629296485132410e-01 4.629296485158975e-01 2.65643e-12 1.52935e-10 ----------------------------------------------------------------------------------------------------- 22 Nb 1 -9.142420488825743e-01 -9.142420489009483e-01 1.83740e-11 1.16160e-10 2 -4.480351257138292e-01 -4.480351257576100e-01 4.37808e-11 5.96057e-11 3 7.773571328785936e-02 7.773571328604105e-02 1.81831e-12 1.92122e-10 ----------------------------------------------------------------------------------------------------- 23 Nb 1 -9.765525580809759e-01 -9.765525580747825e-01 6.19338e-12 2.12038e-09 2 1.202728217702955e+00 1.202728217692926e+00 1.00289e-11 1.26720e-09 3 -1.695192429113197e+00 -1.695192429114849e+00 1.65223e-12 1.41594e-10 ----------------------------------------------------------------------------------------------------- 24 Nb 1 8.631248837322721e-01 8.631248837947540e-01 6.24819e-11 7.88228e-10 2 -8.535362261350883e-01 -8.535362261295507e-01 5.53757e-12 1.24632e-09 3 6.885793901662987e-01 6.885793900658613e-01 1.00437e-10 5.28220e-10 ----------------------------------------------------------------------------------------------------- 25 Nb 1 5.706831119827525e-01 5.706831120060222e-01 2.32697e-11 1.03463e-10 2 8.165802658528892e-01 8.165802659361255e-01 8.32363e-11 2.84319e-09 3 7.053285530435439e-01 7.053285530353814e-01 8.16247e-12 3.13307e-10 ----------------------------------------------------------------------------------------------------- 26 Nb 1 -3.535810483863259e-01 -3.535810484068817e-01 2.05558e-11 8.63958e-11 2 -7.006739358046272e-01 -7.006739357637710e-01 4.08562e-11 6.98320e-10 3 4.270427673894720e-01 4.270427673967367e-01 7.26469e-12 1.40637e-09 ----------------------------------------------------------------------------------------------------- 27 Nb 1 -3.391378959114812e-01 -3.391378958723560e-01 3.91253e-11 4.93611e-09 * 2 1.121678127144729e+00 1.121678127181215e+00 3.64859e-11 2.04899e-10 3 -1.007565151821562e-01 -1.007565151030515e-01 7.91048e-11 1.14939e-09 ----------------------------------------------------------------------------------------------------- 28 Nb 1 8.829751811203789e-01 8.829751811119309e-01 8.44802e-12 2.82315e-09 2 -1.527689895024449e+00 -1.527689894955100e+00 6.93487e-11 6.18602e-10 3 -1.679571948807752e+00 -1.679571948816483e+00 8.73146e-12 4.35954e-10 ----------------------------------------------------------------------------------------------------- 29 Nb 1 6.738629444570953e-01 6.738629444778430e-01 2.07477e-11 3.13807e-10 2 9.024421381464082e-01 9.024421381712543e-01 2.48461e-11 4.87195e-10 3 1.853899249494755e-01 1.853899250100205e-01 6.05450e-11 6.48214e-09 * ----------------------------------------------------------------------------------------------------- 30 Nb 1 -1.395504854880864e+00 -1.395504854887160e+00 6.29630e-12 1.18679e-10 2 -1.587675983672167e+00 -1.587675983680050e+00 7.88347e-12 1.29687e-10 3 9.081798560865360e-02 9.081798558922173e-02 1.94319e-11 1.44084e-10 ----------------------------------------------------------------------------------------------------- 31 Nb 1 -1.095183968859378e+00 -1.095183968863786e+00 4.40803e-12 3.26075e-09 2 8.810150775008030e-01 8.810150774974461e-01 3.35687e-12 7.73637e-10 3 -1.137961964951466e+00 -1.137961965035433e+00 8.39668e-11 3.01498e-10 ----------------------------------------------------------------------------------------------------- 32 Nb 1 3.752961891192524e-01 3.752961891223209e-01 3.06849e-12 2.81840e-10 2 -1.869729265197341e+00 -1.869729265263938e+00 6.65978e-11 2.78166e-10 3 -1.534053186467258e+00 -1.534053186460007e+00 7.25064e-12 2.15242e-10 ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as discontinuities. Maximum error obtained for particle = 27, direction = 3: |F_model - F_numer| error = ----------------------- = 7.85108e-10 max{|F_numer|, eps} Comparison of analytical forces obtained from the model, the force computed as a numerical derivative of the energy, the difference between them, and the uncertainty in the numerical estimate of the force. The computed equilibrium lattice constant for the crystal (a0) is given in the heading. MIXED STRUCTURE -- Species = Fe Nb | a0 = 3.8908368364967836 | (Configuration in file "config-FeNb.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Nb 1 1.799545190510361e+00 1.799545190537103e+00 2.67419e-11 1.84741e-10 2 1.759687723562144e+00 1.759687723606049e+00 4.39042e-11 2.16098e-10 3 6.903479797190735e-01 6.903479797095859e-01 9.48752e-12 1.61186e-10 ----------------------------------------------------------------------------------------------------- 2 Nb 1 -8.346099532304497e-01 -8.346099532627377e-01 3.22880e-11 4.82619e-11 2 -3.584833610422612e-01 -3.584833610237851e-01 1.84761e-11 1.39959e-09 3 1.057560529740129e+00 1.057560529790097e+00 4.99680e-11 1.05817e-10 ----------------------------------------------------------------------------------------------------- 3 Nb 1 -9.477358125563574e-01 -9.477358125648976e-01 8.54017e-12 3.80807e-10 2 -3.931197479761800e-01 -3.931197479463391e-01 2.98409e-11 1.51901e-10 3 -4.115781108003610e-01 -4.115781108073174e-01 6.95644e-12 7.41088e-11 ----------------------------------------------------------------------------------------------------- 4 Fe 1 -1.168755786129819e+00 -1.168755786164900e+00 3.50806e-11 4.59446e-09 * 2 -1.138001588536367e+00 -1.138001588576025e+00 3.96581e-11 1.51192e-10 3 2.881717540872627e-01 2.881717540801667e-01 7.09599e-12 3.36695e-10 ----------------------------------------------------------------------------------------------------- 5 Fe 1 1.577936588660794e-01 1.577936588593642e-01 6.71516e-12 2.14450e-10 2 -9.524348715500536e-02 -9.524348714524201e-02 9.76334e-12 1.40881e-09 3 -1.939179177851746e-01 -1.939179177639183e-01 2.12562e-11 4.58417e-11 ----------------------------------------------------------------------------------------------------- 6 Fe 1 -6.124673018302286e-01 -6.124673018126492e-01 1.75794e-11 3.08445e-10 2 1.162934271813037e-01 1.162934272396259e-01 5.83222e-11 2.25324e-10 3 1.338068964689521e+00 1.338068964736574e+00 4.70524e-11 7.59750e-11 ----------------------------------------------------------------------------------------------------- 7 Nb 1 -1.236302586822342e+00 -1.236302586813277e+00 9.06497e-12 1.98186e-09 2 1.320829088847507e+00 1.320829088844816e+00 2.69162e-12 1.84103e-09 3 8.239004599468573e-01 8.239004599310489e-01 1.58085e-11 2.47756e-10 ----------------------------------------------------------------------------------------------------- 8 Fe 1 9.897186412106405e-01 9.897186412145217e-01 3.88123e-12 7.04660e-11 2 9.660334188142597e-01 9.660334188054467e-01 8.81306e-12 3.87175e-10 3 3.180052155393462e-01 3.180052154761327e-01 6.32135e-11 1.53698e-10 ----------------------------------------------------------------------------------------------------- 9 Nb 1 1.582934871595581e+00 1.582934871611935e+00 1.63536e-11 1.12846e-09 2 1.379333642139920e-01 1.379333641976555e-01 1.63365e-11 3.98314e-10 3 1.326245493380828e+00 1.326245493390850e+00 1.00220e-11 2.79990e-10 ----------------------------------------------------------------------------------------------------- 10 Fe 1 -4.430213126293325e-01 -4.430213126365934e-01 7.26097e-12 6.32515e-10 2 -6.284633019971974e-01 -6.284633019694047e-01 2.77927e-11 1.50568e-10 3 7.403047073115087e-01 7.403047072997503e-01 1.17584e-11 1.18017e-09 ----------------------------------------------------------------------------------------------------- 11 Nb 1 7.017086498882931e-01 7.017086499291191e-01 4.08260e-11 5.44870e-09 * 2 1.598753144381993e+00 1.598753144427443e+00 4.54496e-11 3.76647e-10 3 -8.985091196705729e-01 -8.985091196587093e-01 1.18636e-11 2.13019e-10 ----------------------------------------------------------------------------------------------------- 12 Nb 1 1.522052014845128e+00 1.522052014875074e+00 2.99458e-11 3.13253e-10 2 -1.325760616853864e+00 -1.325760616875986e+00 2.21216e-11 1.21382e-10 3 -9.574181221802377e-01 -9.574181221725662e-01 7.67153e-12 1.45948e-10 ----------------------------------------------------------------------------------------------------- 13 Fe 1 5.459846335291588e-01 5.459846335849735e-01 5.58147e-11 8.00876e-10 2 -3.955975555693064e-01 -3.955975555461351e-01 2.31713e-11 1.81082e-10 3 3.121660202383121e-01 3.121660202335972e-01 4.71490e-12 6.65162e-11 ----------------------------------------------------------------------------------------------------- 14 Nb 1 -1.200744975921132e+00 -1.200744975992950e+00 7.18179e-11 2.18112e-09 2 -1.703820460012857e+00 -1.703820460011163e+00 1.69442e-12 6.19560e-11 3 2.533187934069723e+00 2.533187934069468e+00 2.55351e-13 8.44569e-11 ----------------------------------------------------------------------------------------------------- 15 Nb 1 -1.687186420980763e+00 -1.687186420888081e+00 9.26828e-11 4.01399e-10 2 6.255301587957174e-01 6.255301587029293e-01 9.27881e-11 2.69124e-09 3 -7.089859736490444e-01 -7.089859736452226e-01 3.82172e-12 2.02415e-10 ----------------------------------------------------------------------------------------------------- 16 Fe 1 6.980631266926479e-01 6.980631266691114e-01 2.35365e-11 1.25548e-10 2 -3.375992098880030e-01 -3.375992098351119e-01 5.28911e-11 2.20840e-09 3 4.533090438069221e-01 4.533090437705640e-01 3.63581e-11 6.14506e-05 * ----------------------------------------------------------------------------------------------------- 17 Nb 1 -1.474261656582159e-01 -1.474261655984950e-01 5.97209e-11 1.59773e-10 2 1.805334629729695e+00 1.805334629727668e+00 2.02727e-12 1.53883e-09 3 -5.402804896083313e-01 -5.402804895216238e-01 8.67075e-11 1.41239e-10 ----------------------------------------------------------------------------------------------------- 18 Nb 1 -8.297155457489099e-01 -8.297155457672714e-01 1.83614e-11 5.78728e-09 * 2 4.957658070449979e-01 4.957658070593001e-01 1.43022e-11 3.04803e-10 3 -1.103012106440731e+00 -1.103012106393197e+00 4.75335e-11 9.05258e-11 ----------------------------------------------------------------------------------------------------- 19 Fe 1 1.015500206589501e+00 1.015500206582524e+00 6.97753e-12 6.74962e-10 2 -9.967590117147551e-02 -9.967590112004335e-02 5.14322e-11 1.09082e-09 3 1.033805251553152e+00 1.033805251496707e+00 5.64453e-11 3.26598e-10 ----------------------------------------------------------------------------------------------------- 20 Nb 1 9.081358275985199e-01 9.081358273556209e-01 2.42899e-10 6.41163e-10 2 -9.560316944640062e-01 -9.560316944912907e-01 2.72845e-11 7.08983e-11 3 -1.124301205933717e+00 -1.124301205962718e+00 2.90008e-11 2.27961e-10 ----------------------------------------------------------------------------------------------------- 21 Nb 1 7.942919084572631e-01 7.942919084719494e-01 1.46864e-11 1.38876e-09 2 1.351579186579887e+00 1.351579186568978e+00 1.09091e-11 1.57897e-10 3 -4.194597187485850e-01 -4.194597187253611e-01 2.32238e-11 3.71330e-10 ----------------------------------------------------------------------------------------------------- 22 Fe 1 -1.252402816140350e+00 -1.252402816137333e+00 3.01670e-12 1.46586e-09 2 -1.772312603544007e-01 -1.772312603228559e-01 3.15449e-11 1.56496e-10 3 -2.939352745705636e-01 -2.939352746142072e-01 4.36436e-11 5.07720e-10 ----------------------------------------------------------------------------------------------------- 23 Fe 1 -5.835415055770763e-01 -5.835415054927937e-01 8.42826e-11 1.59173e-10 2 6.080720095311574e-01 6.080720095156508e-01 1.55066e-11 1.96888e-10 3 -8.678401399503082e-01 -8.678401399943027e-01 4.39945e-11 3.95440e-10 ----------------------------------------------------------------------------------------------------- 24 Fe 1 6.894376008538632e-01 6.894376006899089e-01 1.63954e-10 2.18143e-09 2 -3.318377007777261e-01 -3.318377008536342e-01 7.59081e-11 7.04912e-10 3 -5.281008255796600e-01 -5.281008255717460e-01 7.91400e-12 3.06506e-10 ----------------------------------------------------------------------------------------------------- 25 Fe 1 -8.581107803509106e-01 -8.581107803558062e-01 4.89564e-12 1.16799e-09 2 -4.749729180186651e-01 -4.749729180715230e-01 5.28579e-11 4.69811e-10 3 -8.878046163655146e-02 -8.878046162630042e-02 1.02510e-11 4.69747e-10 ----------------------------------------------------------------------------------------------------- 26 Fe 1 -2.568791142550591e-01 -2.568791143019746e-01 4.69155e-11 6.44946e-10 2 2.199789851100227e+00 2.199789851077359e+00 2.28679e-11 1.12602e-10 3 -2.499428129571004e+00 -2.499428129535023e+00 3.59810e-11 1.72318e-09 ----------------------------------------------------------------------------------------------------- 27 Nb 1 4.727272976863700e-01 4.727272976860870e-01 2.82996e-13 2.18870e-09 2 -1.395357220732422e+00 -1.395357220716755e+00 1.56668e-11 5.09365e-10 3 2.435223153109361e+00 2.435223153140670e+00 3.13087e-11 2.51950e-10 ----------------------------------------------------------------------------------------------------- 28 Nb 1 7.979676178961894e-01 7.979676179459625e-01 4.97731e-11 3.43306e-10 2 -1.013559720240798e+00 -1.013559720246353e+00 5.55511e-12 6.16452e-09 * 3 -6.448837047786647e-01 -6.448837047266109e-01 5.20538e-11 3.65441e-10 ----------------------------------------------------------------------------------------------------- 29 Fe 1 4.506062806153547e-01 4.506062806341724e-01 1.88176e-11 5.11586e-10 2 3.508235519439437e-01 3.508235518957916e-01 4.81521e-11 2.06770e-10 3 6.414957885325240e-01 6.414957885220613e-01 1.04626e-11 8.38275e-11 ----------------------------------------------------------------------------------------------------- 30 Fe 1 -8.825874145405155e-01 -8.825874144841818e-01 5.63337e-11 4.71126e-10 2 -1.021763390470665e+00 -1.021763390449545e+00 2.11200e-11 9.65584e-10 3 -9.711075463507264e-01 -9.711075464041768e-01 5.34505e-11 2.25101e-10 ----------------------------------------------------------------------------------------------------- 31 Fe 1 -7.667058151992726e-01 -7.667058150796308e-01 1.19642e-10 1.82238e-09 2 3.028737290067275e-01 3.028737289690956e-01 3.76319e-11 7.12923e-10 3 -1.031941265794050e+00 -1.031941265634549e+00 1.59501e-10 4.33617e-10 ----------------------------------------------------------------------------------------------------- 32 Nb 1 5.817257807357845e-01 5.817257806458845e-01 8.99000e-11 2.75416e-10 2 -1.792779955472354e+00 -1.792779955534669e+00 6.23146e-11 1.72504e-10 3 -7.083121826762380e-01 -7.083121826552103e-01 2.10276e-11 2.01518e-10 ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as discontinuities. Maximum error obtained for particle = 19, direction = 2: |F_model - F_numer| error = ----------------------- = 5.15994e-10 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 2.17652e-09 Machine precision = 2.22045e-16 Note: Lower grades can reflect errors in the analytical forces, a lack of smoothness in the potential, or loss of precision in the numerical derivative computation. Grade: A Comment: The letter grade A was assigned because the normalized error in the computation was 2.17652e-09 compared with a machine precision of 2.22045e-16. The letter grade was based on 'score=log10(error/eps)', with ranges A=[0, 7.5], B=(7.5, 10.0], C=(10.0, 12.5], D=(12.5, 15.0), F>15.0. 'A' is the best grade, and 'F' indicates failure.