!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_MurallesParkKim_NiTi__MO_182729415169_000 Supported species : Ni Ti 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 = Ni | a0 = 3.5213918685913086 | (Configuration in file "config-Ni.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ni 1 2.993129356938787e-02 2.993129355022612e-02 1.91617e-11 1.05545e-10 2 2.566013680155932e-01 2.566013680156207e-01 2.75335e-14 1.74914e-10 3 -6.644807028077782e-01 -6.644807028124342e-01 4.65605e-12 2.11494e-09 * ----------------------------------------------------------------------------------------------------- 2 Ni 1 -7.331144693900852e-01 -7.331144693949577e-01 4.87255e-12 1.92798e-10 2 1.210392183474773e+00 1.210392183468120e+00 6.65268e-12 5.12757e-11 3 6.778162172228126e-01 6.778162171726083e-01 5.02043e-11 1.46679e-10 ----------------------------------------------------------------------------------------------------- 3 Ni 1 1.155497146197981e+00 1.155497146164354e+00 3.36264e-11 4.76876e-11 2 1.370639690782891e+00 1.370639690883039e+00 1.00149e-10 1.32893e-10 3 2.504110595085407e-01 2.504110595213626e-01 1.28219e-11 8.32352e-10 ----------------------------------------------------------------------------------------------------- 4 Ni 1 1.002434666050504e+00 1.002434666049795e+00 7.08988e-13 4.79650e-09 * 2 8.630782306407908e-01 8.630782306130226e-01 2.77682e-11 4.60920e-10 3 2.195099691040965e+00 2.195099691083979e+00 4.30136e-11 7.83600e-11 ----------------------------------------------------------------------------------------------------- 5 Ni 1 7.812997147820825e-01 7.812997147664433e-01 1.56392e-11 8.70740e-11 2 -9.501891459552876e-01 -9.501891459574348e-01 2.14717e-12 1.01195e-09 3 5.652539321640839e-01 5.652539321862752e-01 2.21912e-11 9.95829e-10 ----------------------------------------------------------------------------------------------------- 6 Ni 1 -1.034099086137576e+00 -1.034099086125578e+00 1.19982e-11 1.69454e-10 2 8.980420358702248e-01 8.980420358217078e-01 4.85170e-11 9.25910e-11 3 5.016739562499376e-01 5.016739562495001e-01 4.37539e-13 2.87192e-10 ----------------------------------------------------------------------------------------------------- 7 Ni 1 6.835699945456409e-01 6.835699945507258e-01 5.08482e-12 5.01825e-10 2 -3.175649212634594e+00 -3.175649212627373e+00 7.22133e-12 4.74434e-11 3 -3.746349503155148e+00 -3.746349503193854e+00 3.87059e-11 5.66329e-11 ----------------------------------------------------------------------------------------------------- 8 Ni 1 -2.091924412690188e+00 -2.091924412776893e+00 8.67049e-11 1.76738e-10 2 -1.782918528291190e+00 -1.782918528203741e+00 8.74494e-11 6.30526e-10 3 -1.136012553331759e+00 -1.136012553320365e+00 1.13933e-11 1.39830e-10 ----------------------------------------------------------------------------------------------------- 9 Ni 1 -9.339140932235837e-02 -9.339140929803882e-02 2.43195e-11 4.23919e-11 2 -2.576536558769303e+00 -2.576536558768936e+00 3.66818e-13 2.42824e-10 3 -1.719624866414846e+00 -1.719624866482066e+00 6.72193e-11 2.87370e-10 ----------------------------------------------------------------------------------------------------- 10 Ni 1 2.010266717351228e+00 2.010266717366035e+00 1.48068e-11 7.98703e-11 2 9.156621155674247e-01 9.156621156161368e-01 4.87120e-11 3.98928e-09 * 3 -2.399484047600260e+00 -2.399484047578668e+00 2.15921e-11 8.02642e-11 ----------------------------------------------------------------------------------------------------- 11 Ni 1 1.121688295659815e-01 1.121688296202276e-01 5.42461e-11 4.62679e-10 2 -2.674939826616392e+00 -2.674939826612983e+00 3.40838e-12 9.89306e-10 3 -4.793361201477665e-02 -4.793361201207344e-02 2.70321e-12 9.81715e-11 ----------------------------------------------------------------------------------------------------- 12 Ni 1 -2.283876123813223e+00 -2.283876123868037e+00 5.48144e-11 3.07596e-10 2 2.162378650009821e+00 2.162378650021912e+00 1.20912e-11 3.29864e-09 * 3 2.516991812091658e+00 2.516991812012443e+00 7.92153e-11 3.29354e-10 ----------------------------------------------------------------------------------------------------- 13 Ni 1 -1.752504457036263e+00 -1.752504457047397e+00 1.11333e-11 7.88735e-10 2 -1.756160319325138e+00 -1.756160319328453e+00 3.31446e-12 1.71478e-11 3 -4.317495166063084e+00 -4.317495166215922e+00 1.52838e-10 8.51406e-10 ----------------------------------------------------------------------------------------------------- 14 Ni 1 -1.617096861603765e-01 -1.617096861498273e-01 1.05492e-11 8.33867e-11 2 1.760479960712706e-01 1.760479960319155e-01 3.93550e-11 2.76803e-10 3 6.851085205451664e-01 6.851085205768710e-01 3.17046e-11 1.05592e-10 ----------------------------------------------------------------------------------------------------- 15 Ni 1 4.170848923542075e+00 4.170848923573610e+00 3.15348e-11 1.38567e-09 2 -5.150641550666267e-01 -5.150641550574299e-01 9.19687e-12 1.34578e-10 3 1.090971508243117e+00 1.090971508241960e+00 1.15707e-12 4.18173e-10 ----------------------------------------------------------------------------------------------------- 16 Ni 1 6.922653254207429e-01 6.922653254174871e-01 3.25584e-12 8.63434e-11 2 3.012946369049796e+00 3.012946369069203e+00 1.94063e-11 2.65239e-10 3 6.669804419808381e-01 6.669804420336261e-01 5.27880e-11 3.86906e-10 ----------------------------------------------------------------------------------------------------- 17 Ni 1 -1.217551594929950e+00 -1.217551594939880e+00 9.92983e-12 1.72261e-10 2 2.204211675629019e-01 2.204211675459513e-01 1.69506e-11 8.80071e-11 3 -1.812789561759284e+00 -1.812789561792969e+00 3.36844e-11 4.17253e-10 ----------------------------------------------------------------------------------------------------- 18 Ni 1 -1.527779747047341e-01 -1.527779747177973e-01 1.30632e-11 2.90421e-10 2 2.559036841910625e+00 2.559036841966897e+00 5.62719e-11 4.04712e-10 3 -1.569369186039286e+00 -1.569369185922906e+00 1.16380e-10 6.81716e-10 ----------------------------------------------------------------------------------------------------- 19 Ni 1 1.637431227447316e+00 1.637431227480183e+00 3.28677e-11 8.51272e-11 2 -2.547974887782968e+00 -2.547974887887169e+00 1.04200e-10 1.55582e-10 3 2.171813870746838e+00 2.171813870835210e+00 8.83724e-11 2.47588e-10 ----------------------------------------------------------------------------------------------------- 20 Ni 1 1.942434818046766e-01 1.942434817821485e-01 2.25281e-11 3.45874e-10 2 1.379938573073417e+00 1.379938573027563e+00 4.58544e-11 1.40967e-10 3 -2.738255028817081e-01 -2.738255029199650e-01 3.82569e-11 1.86725e-10 ----------------------------------------------------------------------------------------------------- 21 Ni 1 -1.694579214689887e+00 -1.694579214695751e+00 5.86420e-12 7.85815e-10 2 1.403605595380940e-01 1.403605594482504e-01 8.98436e-11 7.20923e-10 3 8.323204513636990e-01 8.323204513363628e-01 2.73362e-11 1.78252e-10 ----------------------------------------------------------------------------------------------------- 22 Ni 1 5.597437224876650e-01 5.597437224688522e-01 1.88128e-11 8.53100e-09 * 2 3.510083101920550e+00 3.510083102075365e+00 1.54815e-10 4.18126e-10 3 3.281640250125504e+00 3.281640250102024e+00 2.34799e-11 5.53243e-09 * ----------------------------------------------------------------------------------------------------- 23 Ni 1 -1.944132734581616e-01 -1.944132734533681e-01 4.79355e-12 2.88215e-11 2 4.748939491232138e-01 4.748939491118325e-01 1.13813e-11 1.50366e-10 3 5.642885710268759e-02 5.642885711402523e-02 1.13376e-11 1.16793e-11 ----------------------------------------------------------------------------------------------------- 24 Ni 1 -9.083480505287314e-02 -9.083480503446067e-02 1.84125e-11 9.47987e-11 2 7.409046396225019e-01 7.409046396276560e-01 5.15410e-12 1.10757e-10 3 -1.133927051152733e+00 -1.133927051151190e+00 1.54299e-12 3.03991e-09 * ----------------------------------------------------------------------------------------------------- 25 Ni 1 -1.223678675053403e+00 -1.223678675074453e+00 2.10507e-11 3.67387e-05 * 2 -2.011873364450764e+00 -2.011873364341115e+00 1.09650e-10 1.17478e-10 3 3.842642808167909e-01 3.842642807407601e-01 7.60308e-11 2.86106e-10 ----------------------------------------------------------------------------------------------------- 26 Ni 1 -6.832762428007126e-01 -6.832762428130958e-01 1.23832e-11 2.77158e-10 2 1.378539748484422e+00 1.378539748444321e+00 4.01015e-11 1.07164e-10 3 -1.996933100978209e+00 -1.996933100997453e+00 1.92442e-11 3.64373e-10 ----------------------------------------------------------------------------------------------------- 27 Ni 1 1.804931691161967e+00 1.804931691161820e+00 1.46771e-13 6.51806e-10 2 -4.932085221526112e+00 -4.932085221504525e+00 2.15872e-11 1.51415e-10 3 1.381284320038828e+00 1.381284320040254e+00 1.42597e-12 1.75847e-10 ----------------------------------------------------------------------------------------------------- 28 Ni 1 -2.688763414540286e+00 -2.688763414583543e+00 4.32574e-11 1.09106e-10 2 2.762960698826976e+00 2.762960698819164e+00 7.81242e-12 3.38786e-10 3 6.436208825624302e-01 6.436208825394071e-01 2.30231e-11 1.24499e-10 ----------------------------------------------------------------------------------------------------- 29 Ni 1 -6.790326950441277e-01 -6.790326950091926e-01 3.49351e-11 9.52397e-10 2 -1.209000097037112e+00 -1.209000096991976e+00 4.51359e-11 1.38813e-10 3 1.640851343966684e+00 1.640851344049659e+00 8.29750e-11 1.33464e-09 ----------------------------------------------------------------------------------------------------- 30 Ni 1 -6.029359963956218e-01 -6.029359963959874e-01 3.65596e-13 1.48381e-10 2 8.975974152809130e-01 8.975974152666736e-01 1.42394e-11 1.49518e-10 3 -3.057123143108492e-01 -3.057123142915990e-01 1.92502e-11 3.47187e-10 ----------------------------------------------------------------------------------------------------- 31 Ni 1 1.226410573023821e+00 1.226410573008713e+00 1.51079e-11 3.64965e-10 2 -1.768245134410244e+00 -1.768245134374436e+00 3.58078e-11 3.94622e-10 3 8.015032067680780e-01 8.015032068159534e-01 4.78755e-11 1.79485e-10 ----------------------------------------------------------------------------------------------------- 32 Ni 1 1.317420224268759e+00 1.317420224223766e+00 4.49933e-11 6.17362e-11 2 9.701111170395300e-01 9.701111170922352e-01 5.27052e-11 2.08176e-10 3 7.799025659710616e-01 7.799025659892725e-01 1.82110e-11 1.15641e-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 = 1, direction = 1: |F_model - F_numer| error = ----------------------- = 6.40191e-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. MONOATOMIC STRUCTURE -- Species = Ti | a0 = 4.169121742248535 | (Configuration in file "config-Ti.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ti 1 7.049737871992912e-01 7.049737871837790e-01 1.55121e-11 2.26528e-11 2 3.049769333038938e-01 3.049769333055398e-01 1.64596e-12 1.93083e-11 3 -3.926147117297730e-01 -3.926147117295455e-01 2.27540e-13 2.27560e-09 * ----------------------------------------------------------------------------------------------------- 2 Ti 1 7.302874634731777e-01 7.302874634759998e-01 2.82208e-12 1.83827e-10 2 2.589243513716563e-01 2.589243513695839e-01 2.07245e-12 2.05072e-11 3 -3.372300946209257e-02 -3.372300946519310e-02 3.10053e-12 1.15984e-10 ----------------------------------------------------------------------------------------------------- 3 Ti 1 -1.555494317863631e-01 -1.555494317815025e-01 4.86064e-12 2.89511e-10 2 9.664975764038709e-01 9.664975764116492e-01 7.77833e-12 4.28617e-11 3 1.414505340059220e+00 1.414505340085918e+00 2.66986e-11 4.16415e-09 * ----------------------------------------------------------------------------------------------------- 4 Ti 1 5.249634786131436e-01 5.249634785955023e-01 1.76413e-11 1.62452e-11 2 -8.988990103574445e-01 -8.988990103706980e-01 1.32535e-11 3.17428e-11 3 1.114450984541762e+00 1.114450984536022e+00 5.74008e-12 1.11047e-10 ----------------------------------------------------------------------------------------------------- 5 Ti 1 8.450130814238110e-01 8.450130814553666e-01 3.15555e-11 3.54520e-11 2 8.181518249563464e-02 8.181518250304023e-02 7.40559e-12 1.36604e-11 3 -7.738863544433037e-01 -7.738863544266488e-01 1.66549e-11 1.34754e-11 ----------------------------------------------------------------------------------------------------- 6 Ti 1 -6.598101735492147e-01 -6.598101735538368e-01 4.62208e-12 2.81852e-11 2 5.023701663842857e-01 5.023701663822185e-01 2.06712e-12 3.52823e-11 3 1.208789095156638e+00 1.208789095169434e+00 1.27962e-11 3.10183e-10 ----------------------------------------------------------------------------------------------------- 7 Ti 1 -6.182028097704411e-01 -6.182028097616795e-01 8.76155e-12 1.51811e-10 2 3.344690222599097e-01 3.344690222433212e-01 1.65885e-11 5.13483e-11 3 5.361094719237833e-01 5.361094719236109e-01 1.72418e-13 2.77630e-11 ----------------------------------------------------------------------------------------------------- 8 Ti 1 -1.564806103531152e+00 -1.564806103537542e+00 6.38933e-12 1.55588e-10 2 1.243864699087964e+00 1.243864699064612e+00 2.33520e-11 4.99107e-11 3 -1.352712877537156e+00 -1.352712877584095e+00 4.69389e-11 2.10602e-10 ----------------------------------------------------------------------------------------------------- 9 Ti 1 -9.402273890485221e-01 -9.402273890393469e-01 9.17522e-12 9.59393e-10 * 2 3.732123010930903e-01 3.732123010343289e-01 5.87614e-11 2.80043e-10 3 -6.176168493682636e-01 -6.176168493627798e-01 5.48372e-12 4.47393e-11 ----------------------------------------------------------------------------------------------------- 10 Ti 1 3.779548713129861e-01 3.779548712944222e-01 1.85639e-11 1.30279e-10 2 -7.195313100346054e-01 -7.195313100398667e-01 5.26135e-12 5.60966e-10 3 7.623871382974565e-01 7.623871382852235e-01 1.22330e-11 1.97273e-10 ----------------------------------------------------------------------------------------------------- 11 Ti 1 1.241332535081388e+00 1.241332535075422e+00 5.96612e-12 2.28372e-09 * 2 -5.648286113749557e-01 -5.648286113753612e-01 4.05564e-13 3.63540e-11 3 1.484094163560720e+00 1.484094163530954e+00 2.97655e-11 1.70238e-10 ----------------------------------------------------------------------------------------------------- 12 Ti 1 -7.613804867133547e-01 -7.613804867021228e-01 1.12319e-11 7.82052e-10 2 -3.925318816251882e-01 -3.925318816013668e-01 2.38214e-11 1.41632e-10 3 -4.050270363253571e-01 -4.050270363295978e-01 4.24066e-12 1.95448e-10 ----------------------------------------------------------------------------------------------------- 13 Ti 1 -2.136974982136289e+00 -2.136974982145535e+00 9.24638e-12 1.51589e-10 2 -1.827227382962299e+00 -1.827227382986174e+00 2.38747e-11 7.80371e-11 3 -7.694755750223048e-02 -7.694755749399471e-02 8.23577e-12 3.77718e-09 * ----------------------------------------------------------------------------------------------------- 14 Ti 1 1.625956764518254e+00 1.625956764520393e+00 2.13962e-12 1.68840e-11 2 1.879967869767178e+00 1.879967869789386e+00 2.22082e-11 2.40481e-11 3 -2.637683191183230e-01 -2.637683191113075e-01 7.01544e-12 8.19709e-09 * ----------------------------------------------------------------------------------------------------- 15 Ti 1 3.673623720372894e-01 3.673623720410473e-01 3.75794e-12 3.61302e-11 2 -4.093061879219970e+00 -4.093061879222805e+00 2.83507e-12 1.34126e-10 3 -2.204021321117047e+00 -2.204021321130016e+00 1.29696e-11 1.05139e-10 ----------------------------------------------------------------------------------------------------- 16 Ti 1 -3.748436706823704e-01 -3.748436707221143e-01 3.97439e-11 3.66393e-10 2 7.580926468857672e-01 7.580926468898409e-01 4.07374e-12 3.45480e-10 3 3.946538992176455e-03 3.946538997814749e-03 5.63829e-12 4.44858e-10 ----------------------------------------------------------------------------------------------------- 17 Ti 1 -6.856926681581764e-01 -6.856926681754834e-01 1.73069e-11 5.63889e-11 2 -4.596462118030580e-02 -4.596462116995316e-02 1.03526e-11 2.22264e-10 3 -5.361524942057670e-01 -5.361524942046959e-01 1.07114e-12 3.46777e-11 ----------------------------------------------------------------------------------------------------- 18 Ti 1 1.499902659828456e+00 1.499902659865751e+00 3.72946e-11 5.27469e-10 2 1.476515659122381e+00 1.476515659105967e+00 1.64135e-11 9.30718e-11 3 -1.552299915761592e+00 -1.552299915766840e+00 5.24758e-12 2.69204e-10 ----------------------------------------------------------------------------------------------------- 19 Ti 1 1.604913804917284e+00 1.604913804887358e+00 2.99263e-11 3.00979e-11 2 -1.547970804627249e+00 -1.547970804551142e+00 7.61069e-11 1.49768e-10 3 9.383381398834285e-01 9.383381398840769e-01 6.48370e-13 1.39929e-10 ----------------------------------------------------------------------------------------------------- 20 Ti 1 -8.958828105297729e-01 -8.958828105308020e-01 1.02907e-12 1.41877e-10 2 1.347719934826287e+00 1.347719934825075e+00 1.21214e-12 2.33749e-10 3 2.298942362768168e-01 2.298942363018112e-01 2.49945e-11 4.58804e-11 ----------------------------------------------------------------------------------------------------- 21 Ti 1 -4.642115758465901e-01 -4.642115758496843e-01 3.09414e-12 8.26295e-11 2 8.426768752309317e-02 8.426768756838446e-02 4.52913e-11 1.18836e-10 3 -5.660639622536597e-01 -5.660639622506226e-01 3.03713e-12 6.40770e-10 ----------------------------------------------------------------------------------------------------- 22 Ti 1 1.650325511194871e-01 1.650325510934399e-01 2.60472e-11 3.24218e-10 2 -5.337865870410690e-01 -5.337865870556199e-01 1.45509e-11 5.76593e-11 3 9.229297960065999e-01 9.229297960606317e-01 5.40319e-11 1.09723e-09 * ----------------------------------------------------------------------------------------------------- 23 Ti 1 4.510929144381161e-01 4.510929144342590e-01 3.85708e-12 3.68104e-11 2 5.170911377544715e-02 5.170911377681339e-02 1.36623e-12 7.29024e-12 3 -5.719855656936047e-01 -5.719855656907253e-01 2.87936e-12 7.38130e-11 ----------------------------------------------------------------------------------------------------- 24 Ti 1 -8.364491190024851e-01 -8.364491190400913e-01 3.76063e-11 9.98933e-11 2 2.402208030956368e+00 2.402208030972107e+00 1.57385e-11 1.49201e-09 * 3 -9.273117018419158e-01 -9.273117018784067e-01 3.64909e-11 3.41525e-09 * ----------------------------------------------------------------------------------------------------- 25 Ti 1 3.708459983823948e-01 3.708459983409986e-01 4.13963e-11 8.19517e-11 2 8.483638178560188e-01 8.483638178655224e-01 9.50362e-12 1.35444e-10 3 2.543724990244758e-01 2.543724990371177e-01 1.26419e-11 3.42817e-11 ----------------------------------------------------------------------------------------------------- 26 Ti 1 1.451050168996032e+00 1.451050168977613e+00 1.84190e-11 2.08808e-10 2 -9.305992137837482e-01 -9.305992137471991e-01 3.65491e-11 5.46254e-11 3 1.025375517159687e+00 1.025375517109530e+00 5.01568e-11 7.23976e-11 ----------------------------------------------------------------------------------------------------- 27 Ti 1 6.217493980504394e-01 6.217493980657816e-01 1.53422e-11 4.33220e-11 2 -1.537497786483659e+00 -1.537497786494821e+00 1.11620e-11 2.92446e-10 3 -1.069574022089929e+00 -1.069574022090599e+00 6.69909e-13 1.75382e-10 ----------------------------------------------------------------------------------------------------- 28 Ti 1 -3.092999538645249e-01 -3.092999538740853e-01 9.56046e-12 4.62312e-11 2 -1.995408449104479e-01 -1.995408449423367e-01 3.18888e-11 1.69778e-09 * 3 -7.722404226880100e-01 -7.722404226033086e-01 8.47014e-11 1.45715e-10 ----------------------------------------------------------------------------------------------------- 29 Ti 1 -2.131671904739835e+00 -2.131671904715462e+00 2.43734e-11 1.93674e-09 * 2 -1.572297306240858e+00 -1.572297306226025e+00 1.48337e-11 3.74855e-10 3 1.454253772567791e+00 1.454253772576732e+00 8.94107e-12 1.39716e-10 ----------------------------------------------------------------------------------------------------- 30 Ti 1 6.034381399522025e-01 6.034381399451864e-01 7.01617e-12 2.15163e-10 2 2.184717292812631e+00 2.184717292819081e+00 6.45084e-12 1.69298e-10 3 1.576284464668423e+00 1.576284464666420e+00 2.00373e-12 6.01978e-11 ----------------------------------------------------------------------------------------------------- 31 Ti 1 -4.259876625245435e-01 -4.259876625267849e-01 2.24137e-12 3.09042e-11 2 -7.101837322465056e-01 -7.101837322438475e-01 2.65810e-12 1.30859e-10 3 -2.035676813088354e-01 -2.035676812907286e-01 1.81068e-11 2.20382e-10 ----------------------------------------------------------------------------------------------------- 32 Ti 1 -2.248792474601181e-01 -2.248792474765860e-01 1.64679e-11 1.28051e-11 2 4.742286861628304e-01 4.742286861650114e-01 2.18098e-12 3.41599e-11 3 -6.062173556721181e-01 -6.062173556659016e-01 6.21647e-12 6.07460e-11 ----------------------------------------------------------------------------------------------------- * 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 = 16, direction = 3: |F_model - F_numer| error = ----------------------- = 1.42867e-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. MIXED STRUCTURE -- Species = Ni Ti | a0 = 3.829681068653735 | (Configuration in file "config-NiTi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ti 1 4.114880952142024e-01 4.114880952294936e-01 1.52912e-11 7.18385e-11 2 -8.220320879695240e-01 -8.220320879771844e-01 7.66043e-12 5.94060e-11 3 -3.683602491360676e-01 -3.683602491383469e-01 2.27929e-12 1.30087e-10 ----------------------------------------------------------------------------------------------------- 2 Ni 1 -2.095021910016259e+00 -2.095021910113646e+00 9.73870e-11 7.96221e-11 2 -3.559082190153970e+00 -3.559082190030207e+00 1.23763e-10 1.34518e-10 3 -1.652488782390889e+00 -1.652488782396439e+00 5.55000e-12 1.99726e-10 ----------------------------------------------------------------------------------------------------- 3 Ti 1 -1.227891049780867e+00 -1.227891049763340e+00 1.75262e-11 6.35391e-10 2 -1.399702850706907e+00 -1.399702850687762e+00 1.91458e-11 3.77879e-10 3 -7.184459197391331e-01 -7.184459197542983e-01 1.51652e-11 1.14390e-10 ----------------------------------------------------------------------------------------------------- 4 Ni 1 -2.327723339350269e-01 -2.327723337767091e-01 1.58318e-10 3.09566e-10 2 2.745128257132786e+00 2.745128257218030e+00 8.52447e-11 1.59047e-10 3 1.007748891821754e-01 1.007748891642453e-01 1.79301e-11 1.12163e-10 ----------------------------------------------------------------------------------------------------- 5 Ti 1 -3.520123092895468e+00 -3.520123092842031e+00 5.34364e-11 8.38081e-11 2 -9.752587763219399e-01 -9.752587762318827e-01 9.00572e-11 9.16935e-10 3 -3.628636218867492e+00 -3.628636218870091e+00 2.59925e-12 1.75230e-10 ----------------------------------------------------------------------------------------------------- 6 Ti 1 1.695225717877734e+00 1.695225717868274e+00 9.46043e-12 3.53800e-10 2 2.472003242288780e+00 2.472003242279283e+00 9.49685e-12 1.07936e-10 3 -1.027065257359824e+00 -1.027065257363765e+00 3.94040e-12 9.77263e-11 ----------------------------------------------------------------------------------------------------- 7 Ti 1 1.038622145508188e+00 1.038622145485788e+00 2.23994e-11 5.55878e-11 2 -2.205617079798071e+00 -2.205617079798543e+00 4.71179e-13 2.54873e-10 3 2.282602878521054e+00 2.282602878544582e+00 2.35283e-11 1.27326e-10 ----------------------------------------------------------------------------------------------------- 8 Ti 1 1.223004906600275e+00 1.223004906603025e+00 2.75002e-12 5.66998e-11 2 4.647828920729224e+00 4.647828920759627e+00 3.04032e-11 1.35289e-08 * 3 3.228017836721511e+00 3.228017836764435e+00 4.29248e-11 2.64356e-10 ----------------------------------------------------------------------------------------------------- 9 Ni 1 8.254966356939190e-01 8.254966357264426e-01 3.25237e-11 2.09308e-09 * 2 -8.770347094703559e-01 -8.770347094189305e-01 5.14254e-11 3.32494e-10 3 7.668908570178169e-01 7.668908570224577e-01 4.64084e-12 4.90232e-11 ----------------------------------------------------------------------------------------------------- 10 Ti 1 -1.186066006818232e+00 -1.186066007282494e+00 4.64262e-10 3.90649e-10 2 1.255209603478871e+00 1.255209603484559e+00 5.68789e-12 8.44826e-10 3 -5.261840943751716e-01 -5.261840943906114e-01 1.54399e-11 3.37672e-09 * ----------------------------------------------------------------------------------------------------- 11 Ni 1 6.454863441647196e+00 6.454863441650437e+00 3.24096e-12 1.33883e-10 2 1.089277947908257e+00 1.089277947914717e+00 6.45972e-12 4.40010e-10 3 -5.577859752852749e+00 -5.577859752864524e+00 1.17746e-11 4.51563e-10 ----------------------------------------------------------------------------------------------------- 12 Ni 1 -2.206283422890939e+00 -2.206283422880124e+00 1.08149e-11 1.59222e-10 2 -7.151933258824658e-01 -7.151933258864781e-01 4.01235e-12 1.61179e-10 3 3.787946453195151e+00 3.787946453180029e+00 1.51212e-11 7.89653e-11 ----------------------------------------------------------------------------------------------------- 13 Ti 1 2.434354137011058e+00 2.434354137021619e+00 1.05609e-11 2.27439e-10 2 -1.779732505595036e+00 -1.779732505608672e+00 1.36358e-11 1.45693e-10 3 7.661834292670423e+00 7.661834292615506e+00 5.49170e-11 8.28990e-11 ----------------------------------------------------------------------------------------------------- 14 Ni 1 1.910429900446748e+00 1.910429900474136e+00 2.73888e-11 2.46982e-10 2 1.635767898540965e+00 1.635767898519075e+00 2.18903e-11 1.32151e-10 3 -1.354197070816618e+00 -1.354197070825320e+00 8.70171e-12 4.62954e-11 ----------------------------------------------------------------------------------------------------- 15 Ni 1 -2.029929676973318e+00 -2.029929676970198e+00 3.12061e-12 6.65308e-11 2 4.598305819929084e-01 4.598305820317554e-01 3.88469e-11 2.98482e-10 3 -8.709812632438632e-02 -8.709812633470626e-02 1.03199e-11 1.36259e-11 ----------------------------------------------------------------------------------------------------- 16 Ni 1 -6.650007925390569e+00 -6.650007925383720e+00 6.84874e-12 2.42935e-09 * 2 1.346126651477481e+00 1.346126651486837e+00 9.35585e-12 6.52656e-11 3 -8.917743815013123e-01 -8.917743815084227e-01 7.11042e-12 3.48998e-10 ----------------------------------------------------------------------------------------------------- 17 Ti 1 1.001057847848168e+00 1.001057847781604e+00 6.65648e-11 2.67852e-10 2 1.130243929987925e+00 1.130243929990509e+00 2.58460e-12 2.92725e-09 * 3 5.432682473813570e-01 5.432682474460829e-01 6.47259e-11 4.50838e-10 ----------------------------------------------------------------------------------------------------- 18 Ni 1 -4.868906776642935e+00 -4.868906776631857e+00 1.10782e-11 2.06610e-10 2 -3.309591663240206e+00 -3.309591663281343e+00 4.11364e-11 1.75305e-10 3 3.789347889075179e+00 3.789347889043885e+00 3.12941e-11 2.17781e-09 * ----------------------------------------------------------------------------------------------------- 19 Ni 1 4.695868297783712e-01 4.695868297613706e-01 1.70006e-11 1.66030e-10 2 1.044963605175029e+00 1.044963605183300e+00 8.27116e-12 2.64706e-10 3 -9.278951562232129e-01 -9.278951562567893e-01 3.35764e-11 2.63882e-10 ----------------------------------------------------------------------------------------------------- 20 Ti 1 -4.375537792860210e-01 -4.375537792695982e-01 1.64228e-11 1.28017e-10 2 -2.000818447140690e+00 -2.000818447165027e+00 2.43365e-11 4.38274e-10 3 -9.953339569549952e-01 -9.953339569638479e-01 8.85270e-12 6.84915e-11 ----------------------------------------------------------------------------------------------------- 21 Ni 1 1.344129922718415e+00 1.344129922725270e+00 6.85518e-12 8.27362e-10 2 6.501079740484133e-01 6.501079740193159e-01 2.90974e-11 3.23979e-10 3 2.722909696753051e+00 2.722909696725913e+00 2.71387e-11 8.13062e-10 ----------------------------------------------------------------------------------------------------- 22 Ni 1 2.914615592748338e+00 2.914615592735955e+00 1.23834e-11 7.15820e-10 2 -4.967900781605374e+00 -4.967900781571291e+00 3.40830e-11 5.51689e-10 3 -1.347159314664203e+00 -1.347159314642403e+00 2.17999e-11 9.22074e-10 ----------------------------------------------------------------------------------------------------- 23 Ni 1 -6.129141891091161e-01 -6.129141891124573e-01 3.34122e-12 1.53637e-11 2 5.418667310063725e-01 5.418667310081762e-01 1.80367e-12 9.85678e-12 3 -8.663910820882514e-01 -8.663910820982503e-01 9.99889e-12 2.63928e-10 ----------------------------------------------------------------------------------------------------- 24 Ni 1 -1.417100211889420e+00 -1.417100211940034e+00 5.06142e-11 1.63092e-10 2 1.867882782890812e+00 1.867882782972491e+00 8.16798e-11 2.98965e-10 3 6.687165407738249e-01 6.687165406624020e-01 1.11423e-10 2.79384e-10 ----------------------------------------------------------------------------------------------------- 25 Ti 1 -7.978526380883464e-01 -7.978526380813071e-01 7.03926e-12 1.49641e-10 2 2.143094022767668e-01 2.143094022205064e-01 5.62604e-11 1.95001e-10 3 -2.909101828661503e+00 -2.909101828595578e+00 6.59246e-11 7.18042e-10 ----------------------------------------------------------------------------------------------------- 26 Ni 1 1.712987524734588e-02 1.712987524882232e-02 1.47644e-12 2.26114e-10 2 -4.097606320734877e+00 -4.097606320773755e+00 3.88782e-11 4.74790e-09 * 3 9.944911572218857e-01 9.944911572265765e-01 4.69080e-12 2.24803e-09 * ----------------------------------------------------------------------------------------------------- 27 Ti 1 -2.269681255753729e+00 -2.269681255767015e+00 1.32858e-11 2.97250e-10 2 8.283802578777948e-01 8.283802579457422e-01 6.79474e-11 1.18164e-10 3 3.804997289866529e+00 3.804997289865322e+00 1.20748e-12 1.81291e-09 * ----------------------------------------------------------------------------------------------------- 28 Ti 1 3.900883307869277e-01 3.900883307804640e-01 6.46372e-12 2.93943e-09 * 2 -3.663658132814834e-01 -3.663658132986071e-01 1.71236e-11 6.35533e-11 3 7.582981074563508e-02 7.582981071545866e-02 3.01764e-11 1.17615e-10 ----------------------------------------------------------------------------------------------------- 29 Ti 1 4.745891240077975e+00 4.745891239978209e+00 9.97655e-11 2.83895e-10 2 9.058227518173435e+00 9.058227518098693e+00 7.47420e-11 5.29814e-10 3 -8.927851319225690e+00 -8.927851319316419e+00 9.07292e-11 1.26961e-09 ----------------------------------------------------------------------------------------------------- 30 Ti 1 1.405455814881390e+00 1.405455814897043e+00 1.56528e-11 5.46860e-11 2 -3.728143752300060e+00 -3.728143752201065e+00 9.89946e-11 1.09182e-09 3 -9.068833489763592e-02 -9.068833490126492e-02 3.62900e-12 1.93743e-10 ----------------------------------------------------------------------------------------------------- 31 Ti 1 -2.269553476932784e+00 -2.269553476888926e+00 4.38578e-11 5.26356e-10 2 9.347283992697293e-01 9.347283993131549e-01 4.34256e-11 1.81678e-10 3 2.893459472236499e+00 2.893459472281564e+00 4.50644e-11 2.53087e-10 ----------------------------------------------------------------------------------------------------- 32 Ni 1 3.540217312316778e+00 3.540217312300618e+00 1.61609e-11 1.00453e-10 2 -1.117803400054584e+00 -1.117803400066337e+00 1.17530e-11 8.22022e-10 3 -1.424556465282962e+00 -1.424556465277279e+00 5.68301e-12 1.78334e-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 = 4, direction = 1: |F_model - F_numer| error = ----------------------- = 6.80140e-10 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 1.42867e-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 1.42867e-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.