!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_LeeLee_2014_ZrH__MO_946208788356_002 Supported species : H Zr 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 = H | a0 = 8.375 | (Configuration in file "config-H.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 H 1 -9.169844971544955e-02 -9.169844971597030e-02 5.20750e-13 1.23391e-11 2 -5.643407670946027e-02 -5.643407670633235e-02 3.12793e-12 1.71630e-11 3 -1.347176083842212e-01 -1.347176083795026e-01 4.71853e-12 3.88719e-11 ----------------------------------------------------------------------------------------------------- 2 H 1 1.506905206686426e-02 1.506905206726321e-02 3.98948e-13 1.81538e-10 * 2 -6.145209671357112e-02 -6.145209671834126e-02 4.77014e-12 1.53314e-11 3 -4.786896810062226e-01 -4.786896810068412e-01 6.18616e-13 9.58139e-12 ----------------------------------------------------------------------------------------------------- 3 H 1 -4.445062639171845e-02 -4.445062639532648e-02 3.60803e-12 2.50178e-11 2 -4.694264104004394e-01 -4.694264103972988e-01 3.14054e-12 3.12416e-11 3 4.159086888372108e-03 4.159086886262793e-03 2.10931e-12 9.42721e-11 ----------------------------------------------------------------------------------------------------- 4 H 1 -3.885227760789592e-01 -3.885227760780650e-01 8.94229e-13 1.72316e-11 2 -8.971893849189556e-02 -8.971893849054176e-02 1.35381e-12 3.42380e-11 3 -2.483393758744910e-02 -2.483393758943732e-02 1.98822e-12 1.93051e-11 ----------------------------------------------------------------------------------------------------- 5 H 1 -6.151610679147498e-02 -6.151610678954822e-02 1.92676e-12 7.40256e-11 2 -2.849275523409572e-01 -2.849275523409023e-01 5.49005e-14 2.19502e-12 3 -1.650450162515865e-01 -1.650450162518378e-01 2.51243e-13 5.66534e-11 ----------------------------------------------------------------------------------------------------- 6 H 1 2.644337269154138e-01 2.644337269141526e-01 1.26121e-12 6.00703e-12 2 -9.874327313243575e-02 -9.874327313192192e-02 5.13825e-13 8.16522e-12 3 -2.791070060072079e-01 -2.791070060078050e-01 5.97078e-13 2.20990e-12 ----------------------------------------------------------------------------------------------------- 7 H 1 -1.256976300202170e-01 -1.256976300222926e-01 2.07562e-12 2.65623e-11 2 7.167721536336735e-02 7.167721536466537e-02 1.29802e-12 2.35368e-11 3 1.585109212470241e-01 1.585109212458753e-01 1.14878e-12 9.88937e-12 ----------------------------------------------------------------------------------------------------- 8 H 1 5.554961403511913e-01 5.554961403481080e-01 3.08331e-12 3.00802e-11 2 1.971565411671027e-01 1.971565411721371e-01 5.03442e-12 2.13844e-11 3 2.788583978137942e-01 2.788583978106453e-01 3.14893e-12 4.06051e-11 ----------------------------------------------------------------------------------------------------- 9 H 1 -2.346652872522043e-01 -2.346652872532962e-01 1.09199e-12 1.35850e-11 2 1.553226178594343e-02 1.553226178586337e-02 8.00558e-14 2.73364e-11 3 -2.438788748275540e-01 -2.438788748288534e-01 1.29943e-12 3.84950e-12 ----------------------------------------------------------------------------------------------------- 10 H 1 -1.272892647950054e-02 -1.272892648303476e-02 3.53422e-12 5.37627e-12 2 4.109960617027422e-01 4.109960617058429e-01 3.10063e-12 3.90976e-12 3 -3.222600019142687e-01 -3.222600019134572e-01 8.11573e-13 1.09962e-11 ----------------------------------------------------------------------------------------------------- 11 H 1 -3.115959447656531e-02 -3.115959447844340e-02 1.87809e-12 1.32697e-11 2 -3.062506998984750e-01 -3.062506998978000e-01 6.75071e-13 2.06373e-10 * 3 2.275501491767205e-02 2.275501492006304e-02 2.39099e-12 1.05190e-11 ----------------------------------------------------------------------------------------------------- 12 H 1 -4.110445223547453e-01 -4.110445223549898e-01 2.44471e-13 6.67601e-11 2 1.546226116092307e-01 1.546226116092740e-01 4.32709e-14 4.09942e-11 3 -5.369793592138369e-02 -5.369793592032342e-02 1.06028e-12 1.02356e-11 ----------------------------------------------------------------------------------------------------- 13 H 1 1.679887383872832e-01 1.679887383883512e-01 1.06792e-12 8.57880e-12 2 1.802695731258278e-01 1.802695731235299e-01 2.29791e-12 8.01978e-12 3 -2.697097055785703e-01 -2.697097055783390e-01 2.31315e-13 1.31185e-10 ----------------------------------------------------------------------------------------------------- 14 H 1 2.277665308020522e-01 2.277665307997821e-01 2.27010e-12 7.46914e-12 2 1.475352076854806e-01 1.475352076810718e-01 4.40881e-12 9.33348e-12 3 -2.193468167472791e-01 -2.193468167474097e-01 1.30534e-13 2.48662e-12 ----------------------------------------------------------------------------------------------------- 15 H 1 2.040198471825766e-01 2.040198471827908e-01 2.14245e-13 1.40402e-11 2 4.558194413514390e-02 4.558194413449358e-02 6.50313e-13 7.60579e-12 3 -2.042456054218099e-01 -2.042456054216570e-01 1.52822e-13 1.02321e-11 ----------------------------------------------------------------------------------------------------- 16 H 1 -2.858180393340597e-01 -2.858180393340894e-01 2.96985e-14 2.87837e-10 * 2 2.669093438652731e-01 2.669093438584371e-01 6.83598e-12 6.83537e-12 3 -1.109185940562414e-01 -1.109185940608086e-01 4.56715e-12 4.51304e-12 ----------------------------------------------------------------------------------------------------- 17 H 1 -2.772358159374604e-01 -2.772358159354562e-01 2.00417e-12 5.22055e-12 2 -2.432261159061073e-01 -2.432261159062656e-01 1.58373e-13 1.54580e-11 3 2.136298978893605e-02 2.136298979101597e-02 2.07991e-12 4.74469e-11 ----------------------------------------------------------------------------------------------------- 18 H 1 -3.569133406324693e-01 -3.569133406325315e-01 6.22280e-14 1.47085e-10 * 2 -3.208671138889721e-02 -3.208671139242936e-02 3.53215e-12 1.42196e-11 3 -8.916879777228684e-02 -8.916879777333386e-02 1.04702e-12 7.86968e-12 ----------------------------------------------------------------------------------------------------- 19 H 1 1.536266945278383e-02 1.536266945785593e-02 5.07209e-12 1.44643e-11 2 -2.271840245610471e-01 -2.271840245608146e-01 2.32508e-13 6.55334e-12 3 2.043180967322878e-01 2.043180967351080e-01 2.82016e-12 4.87996e-11 ----------------------------------------------------------------------------------------------------- 20 H 1 -1.415382576101859e-01 -1.415382576090549e-01 1.13098e-12 1.22891e-11 2 -1.218424649831278e-01 -1.218424649810851e-01 2.04274e-12 1.49758e-10 * 3 2.880833877948590e-01 2.880833877955131e-01 6.54088e-13 9.88033e-11 ----------------------------------------------------------------------------------------------------- 21 H 1 9.260143322795603e-02 9.260143322679537e-02 1.16065e-12 1.96882e-11 2 -5.416792739171539e-01 -5.416792739193662e-01 2.21234e-12 2.18873e-10 * 3 5.062253573203958e-02 5.062253573330380e-02 1.26422e-12 8.85262e-11 ----------------------------------------------------------------------------------------------------- 22 H 1 5.805258527289143e-01 5.805258527287689e-01 1.45439e-13 1.36851e-10 2 -3.502585100756308e-01 -3.502585100753065e-01 3.24352e-13 9.80455e-12 3 -1.756601407580907e-01 -1.756601407592760e-01 1.18530e-12 1.54083e-11 ----------------------------------------------------------------------------------------------------- 23 H 1 1.364581948661837e-01 1.364581948648211e-01 1.36266e-12 1.37312e-11 2 -1.198634307502940e-01 -1.198634307507779e-01 4.83877e-13 1.27822e-10 3 1.540398444323721e-01 1.540398444356288e-01 3.25678e-12 1.22868e-11 ----------------------------------------------------------------------------------------------------- 24 H 1 -8.253431940386624e-02 -8.253431940099593e-02 2.87032e-12 1.49810e-10 * 2 -5.819537193123200e-02 -5.819537192780581e-02 3.42619e-12 6.51251e-12 3 4.524082471246172e-01 4.524082471247530e-01 1.35780e-13 5.45524e-11 ----------------------------------------------------------------------------------------------------- 25 H 1 1.284628257047571e-01 1.284628257058338e-01 1.07667e-12 1.77948e-11 2 2.740505569647699e-01 2.740505569659862e-01 1.21636e-12 2.82323e-11 3 -1.808434114307133e-01 -1.808434114261227e-01 4.59061e-12 1.15793e-11 ----------------------------------------------------------------------------------------------------- 26 H 1 1.383783632800407e-01 1.383783632804091e-01 3.68455e-13 1.00379e-11 2 1.367664641577579e-01 1.367664641583443e-01 5.86475e-13 2.78522e-12 3 3.470493228676275e-01 3.470493228698644e-01 2.23688e-12 1.31523e-10 ----------------------------------------------------------------------------------------------------- 27 H 1 -3.297355736504336e-01 -3.297355736496143e-01 8.19289e-13 4.24702e-11 2 3.475339637814058e-01 3.475339637817385e-01 3.32678e-13 7.24462e-11 3 3.741401329043518e-01 3.741401329032795e-01 1.07231e-12 6.08302e-12 ----------------------------------------------------------------------------------------------------- 28 H 1 -2.267717617013903e-01 -2.267717617011690e-01 2.21240e-13 1.09135e-11 2 1.155861471757763e-01 1.155861471772618e-01 1.48548e-12 8.39107e-11 3 2.998125463121348e-01 2.998125463092814e-01 2.85338e-12 1.73258e-11 ----------------------------------------------------------------------------------------------------- 29 H 1 5.464133189145268e-02 5.464133189415753e-02 2.70485e-12 2.92112e-11 2 3.554354518117634e-01 3.554354518134392e-01 1.67572e-12 1.44312e-11 3 -1.852020765860403e-01 -1.852020765696707e-01 1.63695e-11 1.87569e-11 ----------------------------------------------------------------------------------------------------- 30 H 1 4.229823803602925e-01 4.229823803630711e-01 2.77867e-12 1.49937e-11 2 1.334032932516421e-01 1.334032932520219e-01 3.79807e-13 3.80107e-12 3 8.349354905173773e-03 8.349354906679585e-03 1.50581e-12 1.54151e-10 * ----------------------------------------------------------------------------------------------------- 31 H 1 1.622800738462871e-01 1.622800738545903e-01 8.30319e-12 9.81060e-11 2 1.223950593289356e-01 1.223950593293325e-01 3.96919e-13 1.89391e-11 3 1.444606896742180e-01 1.444606896739969e-01 2.21018e-13 3.08551e-11 ----------------------------------------------------------------------------------------------------- 32 H 1 -6.443613323334960e-02 -6.443613323044145e-02 2.90815e-12 2.57073e-11 2 8.583725428856179e-02 8.583725428899013e-02 4.28338e-13 7.26776e-12 3 3.283946411154452e-01 3.283946411138781e-01 1.56708e-12 5.24741e-12 ----------------------------------------------------------------------------------------------------- * 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 = 3, direction = 3: |F_model - F_numer| error = ----------------------- = 5.07158e-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 = Zr | a0 = 4.532810211181641 | (Configuration in file "config-Zr.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Zr 1 2.231807160176716e-01 2.231807160365093e-01 1.88377e-11 1.54442e-10 2 6.799781590565785e-01 6.799781590421966e-01 1.43819e-11 1.01245e-10 3 3.669587200202556e-01 3.669587200223131e-01 2.05741e-12 1.02566e-10 ----------------------------------------------------------------------------------------------------- 2 Zr 1 -5.756891997780238e-01 -5.756891997978110e-01 1.97872e-11 3.33892e-10 2 -1.046255477358721e+00 -1.046255477366402e+00 7.68097e-12 1.22137e-10 3 4.671090450728181e-01 4.671090450479878e-01 2.48303e-11 1.12596e-10 ----------------------------------------------------------------------------------------------------- 3 Zr 1 -9.574874563386739e-01 -9.574874563717362e-01 3.30622e-11 3.17429e-09 * 2 -1.524470864312813e+00 -1.524470864285620e+00 2.71931e-11 2.84504e-11 3 -2.966823314021396e-01 -2.966823313919930e-01 1.01466e-11 2.36779e-11 ----------------------------------------------------------------------------------------------------- 4 Zr 1 6.949611342420665e-01 6.949611342575295e-01 1.54630e-11 4.11162e-11 2 -2.435949180142752e-01 -2.435949180281764e-01 1.39012e-11 2.83910e-09 * 3 -7.934015434522892e-01 -7.934015434549304e-01 2.64122e-12 2.51777e-09 * ----------------------------------------------------------------------------------------------------- 5 Zr 1 -2.363831754369207e-01 -2.363831754415451e-01 4.62438e-12 9.77046e-11 2 -3.076726725365578e-01 -3.076726725360959e-01 4.61964e-13 1.01567e-10 3 -1.099875321824740e+00 -1.099875321818554e+00 6.18594e-12 8.81657e-11 ----------------------------------------------------------------------------------------------------- 6 Zr 1 -4.469500275701786e-01 -4.469500275671189e-01 3.05966e-12 2.87759e-10 2 -1.018529992101574e-01 -1.018529992185234e-01 8.36595e-12 1.04093e-09 3 2.360946350524448e-01 2.360946350791392e-01 2.66943e-11 5.86447e-10 ----------------------------------------------------------------------------------------------------- 7 Zr 1 2.152881114961185e-01 2.152881114964252e-01 3.06671e-13 6.55477e-11 2 2.872442611277018e-01 2.872442611058230e-01 2.18788e-11 1.70109e-10 3 6.064498527833049e-01 6.064498527766492e-01 6.65568e-12 1.73949e-10 ----------------------------------------------------------------------------------------------------- 8 Zr 1 1.084569226447813e+00 1.084569226449950e+00 2.13696e-12 2.89340e-11 2 1.644192152408081e+00 1.644192152371309e+00 3.67724e-11 2.50444e-10 3 9.743539464358093e-01 9.743539464321308e-01 3.67850e-12 1.56868e-10 ----------------------------------------------------------------------------------------------------- 9 Zr 1 -1.272508815200626e-01 -1.272508815261548e-01 6.09221e-12 1.77353e-09 * 2 2.355231369860493e-01 2.355231369988660e-01 1.28167e-11 1.28822e-10 3 3.142088773874245e-01 3.142088773916379e-01 4.21346e-12 1.58990e-10 ----------------------------------------------------------------------------------------------------- 10 Zr 1 -8.678530190419385e-01 -8.678530190646179e-01 2.26794e-11 3.23092e-10 2 5.153367768520740e-01 5.153367768102172e-01 4.18569e-11 1.07984e-10 3 1.369908803824521e-01 1.369908803681290e-01 1.43231e-11 1.41776e-10 ----------------------------------------------------------------------------------------------------- 11 Zr 1 -2.385452858927509e-01 -2.385452859171132e-01 2.43622e-11 1.05980e-09 2 1.203035770857305e+00 1.203035770794253e+00 6.30516e-11 1.86097e-09 * 3 -6.812933539645696e-01 -6.812933539460124e-01 1.85572e-11 1.26965e-10 ----------------------------------------------------------------------------------------------------- 12 Zr 1 -3.984993405386081e-01 -3.984993405334665e-01 5.14155e-12 7.49552e-10 2 6.923283942571202e-01 6.923283942264563e-01 3.06639e-11 1.71809e-10 3 1.457267502519526e-01 1.457267503127075e-01 6.07550e-11 9.76488e-10 ----------------------------------------------------------------------------------------------------- 13 Zr 1 1.530241745555615e+00 1.530241745566364e+00 1.07485e-11 1.70991e-10 2 -4.057320324435408e-01 -4.057320324288773e-01 1.46634e-11 1.25674e-10 3 7.834847032302794e-01 7.834847032490099e-01 1.87305e-11 1.87588e-11 ----------------------------------------------------------------------------------------------------- 14 Zr 1 -5.522300510556006e-01 -5.522300510913271e-01 3.57264e-11 5.00117e-11 2 -4.507817104222960e-01 -4.507817104213206e-01 9.75386e-13 2.78957e-10 3 5.024207932424903e-01 5.024207932417457e-01 7.44627e-13 5.86408e-11 ----------------------------------------------------------------------------------------------------- 15 Zr 1 -6.837978428469251e-01 -6.837978428457084e-01 1.21669e-12 2.73298e-10 2 8.507733964378321e-01 8.507733964160359e-01 2.17962e-11 7.29032e-11 3 -4.027457133759269e-01 -4.027457133462125e-01 2.97144e-11 1.88531e-10 ----------------------------------------------------------------------------------------------------- 16 Zr 1 1.161320607067373e+00 1.161320607102845e+00 3.54718e-11 4.54284e-10 2 -5.698884748442853e-01 -5.698884748346078e-01 9.67748e-12 1.47176e-10 3 -1.392264963576887e+00 -1.392264963546610e+00 3.02773e-11 3.47332e-10 ----------------------------------------------------------------------------------------------------- 17 Zr 1 -6.277452411562257e-02 -6.277452411180202e-02 3.82054e-12 1.53812e-10 2 1.079758795906362e-01 1.079758795979041e-01 7.26784e-12 1.44839e-10 3 5.162133592738718e-01 5.162133592707355e-01 3.13627e-12 1.66896e-09 * ----------------------------------------------------------------------------------------------------- 18 Zr 1 1.329247851847861e+00 1.329247851854191e+00 6.32983e-12 2.55099e-10 2 -1.630381699995757e+00 -1.630381699959349e+00 3.64080e-11 1.82944e-09 * 3 3.034244229990528e-01 3.034244229657991e-01 3.32537e-11 3.25066e-10 ----------------------------------------------------------------------------------------------------- 19 Zr 1 -6.554967495550162e-01 -6.554967495736315e-01 1.86152e-11 2.41546e-10 2 2.192468951010279e-01 2.192468951155523e-01 1.45244e-11 2.29088e-09 * 3 7.123056045124917e-01 7.123056045251849e-01 1.26932e-11 1.41465e-10 ----------------------------------------------------------------------------------------------------- 20 Zr 1 6.284908332402753e-01 6.284908332383502e-01 1.92513e-12 9.74281e-10 2 -1.875185038635818e-01 -1.875185038622944e-01 1.28741e-12 4.20343e-11 3 -3.160241408865347e-01 -3.160241408409282e-01 4.56065e-11 2.37225e-10 ----------------------------------------------------------------------------------------------------- 21 Zr 1 6.341551794648941e-01 6.341551794402931e-01 2.46010e-11 6.99247e-11 2 -6.005883138390165e-01 -6.005883138436832e-01 4.66671e-12 2.65655e-10 3 -3.712256664920006e-01 -3.712256664997918e-01 7.79127e-12 2.81682e-10 ----------------------------------------------------------------------------------------------------- 22 Zr 1 -7.357147923585249e-01 -7.357147923653720e-01 6.84708e-12 2.51309e-09 * 2 -6.821050624075672e-01 -6.821050624420679e-01 3.45007e-11 1.76040e-10 3 6.301942893697055e-01 6.301942893610417e-01 8.66374e-12 9.33633e-11 ----------------------------------------------------------------------------------------------------- 23 Zr 1 -1.021755931140780e+00 -1.021755931147271e+00 6.49125e-12 2.61372e-10 2 5.176275871510675e-01 5.176275871398950e-01 1.11725e-11 4.87401e-10 3 -6.160749850828169e-01 -6.160749851048332e-01 2.20163e-11 1.32850e-10 ----------------------------------------------------------------------------------------------------- 24 Zr 1 3.877667952316736e-01 3.877667952286060e-01 3.06760e-12 1.08644e-10 2 -7.189050746474468e-01 -7.189050746594814e-01 1.20346e-11 2.55111e-09 * 3 -6.742185774233236e-01 -6.742185774272262e-01 3.90266e-12 7.50050e-11 ----------------------------------------------------------------------------------------------------- 25 Zr 1 2.613711282897162e-01 2.613711282846250e-01 5.09121e-12 1.22717e-10 2 -6.307319540931844e-01 -6.307319540840205e-01 9.16389e-12 1.10546e-10 3 -2.766163938595131e-01 -2.766163938239788e-01 3.55343e-11 2.46257e-10 ----------------------------------------------------------------------------------------------------- 26 Zr 1 -1.204366728166697e+00 -1.204366728162709e+00 3.98837e-12 2.91870e-09 * 2 2.904524950831224e-01 2.904524950730736e-01 1.00487e-11 1.76814e-10 3 1.594851572512648e+00 1.594851572555421e+00 4.27729e-11 3.48108e-10 ----------------------------------------------------------------------------------------------------- 27 Zr 1 8.727333441713128e-02 8.727333441737564e-02 2.44360e-13 2.76270e-10 2 2.659607172803136e-01 2.659607172797747e-01 5.38958e-13 2.58708e-10 3 -2.379915960040992e-01 -2.379915960556145e-01 5.15152e-11 3.04481e-10 ----------------------------------------------------------------------------------------------------- 28 Zr 1 5.404191509496516e-01 5.404191509460925e-01 3.55915e-12 1.75880e-10 2 5.471819489508772e-02 5.471819489135202e-02 3.73570e-12 3.91950e-11 3 -8.316114793829852e-01 -8.316114793961104e-01 1.31252e-11 2.63214e-11 ----------------------------------------------------------------------------------------------------- 29 Zr 1 1.027673759280758e+00 1.027673759331063e+00 5.03053e-11 1.44224e-08 * 2 2.597729274076974e+00 2.597729274102321e+00 2.53473e-11 1.82685e-09 * 3 7.928978309691633e-01 7.928978308499272e-01 1.19236e-10 1.62813e-10 ----------------------------------------------------------------------------------------------------- 30 Zr 1 -3.492697226942115e-01 -3.492697226855277e-01 8.68383e-12 3.40659e-10 2 -1.921485872794708e-01 -1.921485872755141e-01 3.95667e-12 2.29336e-10 3 -7.215921117553709e-01 -7.215921117964381e-01 4.10673e-11 1.84988e-10 ----------------------------------------------------------------------------------------------------- 31 Zr 1 -4.277474415590308e-01 -4.277474415763396e-01 1.73088e-11 1.81381e-10 2 -8.515132020888210e-01 -8.515132021159141e-01 2.70931e-11 8.73914e-10 3 1.866578202022214e-02 1.866578199488057e-02 2.53416e-11 9.37706e-10 ----------------------------------------------------------------------------------------------------- 32 Zr 1 -2.641474039390519e-01 -2.641474039738323e-01 3.47804e-11 8.76362e-11 2 -1.798154380348139e-02 -1.798154388779541e-02 8.43140e-11 3.25590e-10 3 -3.907328870331896e-01 -3.907328870410847e-01 7.89513e-12 4.10256e-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 = 32, direction = 2: |F_model - F_numer| error = ----------------------- = 4.68892e-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 = H Zr | a0 = 4.5555026467227435 | (Configuration in file "config-HZr.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Zr 1 2.752944306338252e+00 2.752944306347028e+00 8.77520e-12 6.74971e-12 2 2.262617936164028e+00 2.262617936165014e+00 9.86322e-13 4.55285e-11 3 2.257003556157315e+00 2.257003556148301e+00 9.01323e-12 6.71032e-11 ----------------------------------------------------------------------------------------------------- 2 H 1 -2.996174501468426e+00 -2.996174501468107e+00 3.18856e-13 2.51883e-11 2 -1.451073676694604e+00 -1.451073676691884e+00 2.72027e-12 2.31222e-11 3 -2.416032222953398e+00 -2.416032222954900e+00 1.50147e-12 4.33089e-11 ----------------------------------------------------------------------------------------------------- 3 H 1 -3.302128095713004e+00 -3.302128095729922e+00 1.69176e-11 1.95835e-10 2 -5.964503447669162e-02 -5.964503445558514e-02 2.11065e-11 1.32747e-11 3 2.780240803234309e+00 2.780240803232851e+00 1.45839e-12 6.90976e-11 ----------------------------------------------------------------------------------------------------- 4 Zr 1 4.495211531991099e+00 4.495211531984016e+00 7.08322e-12 2.22213e-10 2 1.339530225824056e+00 1.339530225822749e+00 1.30740e-12 8.88920e-11 3 -2.147860651683258e+00 -2.147860651686463e+00 3.20499e-12 2.47542e-10 ----------------------------------------------------------------------------------------------------- 5 H 1 2.975890232546003e+00 2.975890232517114e+00 2.88889e-11 3.63931e-11 2 1.134937658190440e+00 1.134937658185712e+00 4.72866e-12 6.40989e-11 3 -1.528504570628471e+00 -1.528504570572784e+00 5.56875e-11 4.46960e-11 ----------------------------------------------------------------------------------------------------- 6 Zr 1 -9.770395593677665e-01 -9.770395593512345e-01 1.65320e-11 5.37791e-11 2 -9.956343586339945e-02 -9.956343585548547e-02 7.91399e-12 1.13198e-11 3 1.483453573520802e+00 1.483453573523714e+00 2.91189e-12 1.05475e-09 * ----------------------------------------------------------------------------------------------------- 7 H 1 1.394224999646699e+00 1.394224999624843e+00 2.18561e-11 7.50286e-11 2 6.589676082147407e-01 6.589676082106047e-01 4.13591e-12 7.07143e-11 3 2.457498374360981e-01 2.457498374093323e-01 2.67658e-11 1.11734e-10 ----------------------------------------------------------------------------------------------------- 8 Zr 1 -1.737713488045623e+00 -1.737713488030574e+00 1.50486e-11 3.41398e-11 2 -2.420130684425634e+00 -2.420130684433246e+00 7.61169e-12 2.15662e-10 3 -1.798185260303532e+00 -1.798185260346483e+00 4.29508e-11 3.26382e-09 * ----------------------------------------------------------------------------------------------------- 9 H 1 -8.873752462583837e-01 -8.873752462580883e-01 2.95430e-13 8.55455e-11 2 8.077511803685016e-01 8.077511803664889e-01 2.01272e-12 8.82198e-11 3 1.076972734101383e-01 1.076972734030221e-01 7.11615e-12 2.26464e-11 ----------------------------------------------------------------------------------------------------- 10 Zr 1 -4.916584625506150e-01 -4.916584625507140e-01 9.89764e-14 1.08351e-10 2 -5.182884371955168e-01 -5.182884371860244e-01 9.49241e-12 1.79636e-10 3 1.733480177045693e+00 1.733480177050142e+00 4.44844e-12 4.76894e-11 ----------------------------------------------------------------------------------------------------- 11 H 1 -2.179177572085040e+00 -2.179177572098064e+00 1.30238e-11 8.53927e-10 * 2 2.385432940445538e+00 2.385432940435175e+00 1.03624e-11 9.41833e-11 3 -5.358065550957461e+00 -5.358065550982871e+00 2.54099e-11 7.01474e-11 ----------------------------------------------------------------------------------------------------- 12 Zr 1 3.221125780327090e+00 3.221125780312340e+00 1.47504e-11 7.80855e-11 2 -5.371713942434728e+00 -5.371713942443717e+00 8.98925e-12 3.06253e-11 3 3.067716143826854e+00 3.067716143843642e+00 1.67883e-11 2.37794e-10 ----------------------------------------------------------------------------------------------------- 13 Zr 1 5.632748773496457e-01 5.632748773526673e-01 3.02169e-12 3.44144e-10 2 -1.624799205753557e-01 -1.624799206068400e-01 3.14843e-11 2.15769e-09 * 3 1.791628510148874e+00 1.791628510156602e+00 7.72848e-12 4.28952e-11 ----------------------------------------------------------------------------------------------------- 14 H 1 7.201138437751436e-02 7.201138439310557e-02 1.55912e-11 3.40797e-11 2 1.584966274590259e-01 1.584966274647349e-01 5.70904e-12 1.71899e-11 3 -1.032141895704117e+00 -1.032141895704348e+00 2.31815e-13 2.82991e-11 ----------------------------------------------------------------------------------------------------- 15 H 1 1.169773686563184e+00 1.169773686572412e+00 9.22751e-12 2.65077e-11 2 -2.615654909969123e+00 -2.615654909970175e+00 1.05205e-12 2.50804e-11 3 -1.125057770446660e+00 -1.125057770433919e+00 1.27411e-11 3.88525e-11 ----------------------------------------------------------------------------------------------------- 16 H 1 -1.806712587841698e+00 -1.806712587841058e+00 6.39488e-13 5.38796e-11 2 -7.877375121650417e-01 -7.877375121614026e-01 3.63909e-12 7.19039e-11 3 -2.616470449337045e+00 -2.616470449336251e+00 7.94476e-13 1.79906e-10 ----------------------------------------------------------------------------------------------------- 17 Zr 1 1.732007985272210e-01 1.732007985148694e-01 1.23516e-11 8.34931e-11 2 9.235905194350633e-01 9.235905194390420e-01 3.97871e-12 4.48458e-11 3 -9.181633158146982e-01 -9.181633157896419e-01 2.50563e-11 8.96485e-11 ----------------------------------------------------------------------------------------------------- 18 Zr 1 1.162504854743828e+00 1.162504854754961e+00 1.11331e-11 1.78039e-06 * 2 2.047403985770280e-01 2.047403985598461e-01 1.71819e-11 3.15354e-10 3 9.512418054923694e-01 9.512418055148688e-01 2.24994e-11 1.47067e-05 * ----------------------------------------------------------------------------------------------------- 19 Zr 1 8.829705509814244e-01 8.829705509911377e-01 9.71334e-12 2.07085e-11 2 7.137400297593465e-01 7.137400297543801e-01 4.96636e-12 8.24255e-10 * 3 -2.004534135719023e-01 -2.004534135897834e-01 1.78811e-11 1.44174e-10 ----------------------------------------------------------------------------------------------------- 20 Zr 1 5.285369956640056e-01 5.285369956487711e-01 1.52345e-11 3.03694e-11 2 8.514634391023581e-01 8.514634391066138e-01 4.25571e-12 1.61587e-10 3 -6.471051042944047e-01 -6.471051042967034e-01 2.29872e-12 7.22430e-11 ----------------------------------------------------------------------------------------------------- 21 H 1 7.663930846253331e-02 7.663930845409926e-02 8.43405e-12 1.87983e-11 2 4.424908528221771e-01 4.424908528264718e-01 4.29473e-12 3.12129e-11 3 1.734649134373800e+00 1.734649134368014e+00 5.78648e-12 1.55185e-11 ----------------------------------------------------------------------------------------------------- 22 Zr 1 -1.945063479218128e+00 -1.945063479225928e+00 7.79998e-12 5.48745e-11 2 1.752788068294354e-01 1.752788068315225e-01 2.08711e-12 4.33163e-11 3 -3.043817063870669e-02 -3.043817064457752e-02 5.87083e-12 9.05716e-10 * ----------------------------------------------------------------------------------------------------- 23 Zr 1 -9.886834483261394e-01 -9.886834483176071e-01 8.53229e-12 5.50561e-11 2 8.915089713286046e-01 8.915089713410393e-01 1.24347e-11 1.51416e-09 * 3 -7.113140248591771e-01 -7.113140248593136e-01 1.36557e-13 1.68180e-10 ----------------------------------------------------------------------------------------------------- 24 Zr 1 4.555470870002087e-01 4.555470870103208e-01 1.01121e-11 1.79746e-09 * 2 9.367618209089477e-01 9.367618209001415e-01 8.80618e-12 3.29656e-10 3 -1.476356252416178e+00 -1.476356252418074e+00 1.89604e-12 1.25173e-10 ----------------------------------------------------------------------------------------------------- 25 H 1 -3.257205691884319e+00 -3.257205691873885e+00 1.04339e-11 1.12240e-10 2 1.923623385128387e+00 1.923623385134769e+00 6.38201e-12 4.92892e-06 * 3 -4.344042259185859e-01 -4.344042259284454e-01 9.85956e-12 9.76508e-11 ----------------------------------------------------------------------------------------------------- 26 H 1 -6.728150760315260e-01 -6.728150760376592e-01 6.13321e-12 2.83081e-11 2 2.713995728984080e+00 2.713995728981612e+00 2.46780e-12 1.85311e-10 3 3.912021239768738e+00 3.912021239734808e+00 3.39306e-11 7.30762e-11 ----------------------------------------------------------------------------------------------------- 27 H 1 -1.950488558580374e+00 -1.950488558564710e+00 1.56637e-11 5.93494e-11 2 -2.139599019236777e+00 -2.139599019237156e+00 3.79696e-13 4.49374e-11 3 3.241136924603174e+00 3.241136924600403e+00 2.77112e-12 4.20006e-11 ----------------------------------------------------------------------------------------------------- 28 Zr 1 1.161444907493556e+00 1.161444907496376e+00 2.81974e-12 1.69653e-11 2 -1.145122904453116e+00 -1.145122904455814e+00 2.69829e-12 2.82818e-11 3 -1.581997977150396e+00 -1.581997977151445e+00 1.04805e-12 3.40741e-11 ----------------------------------------------------------------------------------------------------- 29 H 1 1.967224282554916e+00 1.967224282565402e+00 1.04865e-11 1.07748e-10 2 -1.101567014680235e+00 -1.101567014680423e+00 1.88294e-13 5.41545e-12 3 -4.673819381164435e-01 -4.673819381200836e-01 3.64009e-12 2.13597e-10 ----------------------------------------------------------------------------------------------------- 30 H 1 6.212217454511528e-01 6.212217454580204e-01 6.86762e-12 5.25957e-11 2 1.736461328970934e+00 1.736461328983214e+00 1.22795e-11 5.78091e-11 3 1.911388950985904e+00 1.911388950989040e+00 3.13527e-12 3.49303e-11 ----------------------------------------------------------------------------------------------------- 31 H 1 -2.809157032909520e-01 -2.809157032849401e-01 6.01191e-12 3.08343e-11 2 -7.090627931714258e-01 -7.090627931848651e-01 1.34392e-11 2.55258e-11 3 6.642254380632134e-01 6.642254380595889e-01 3.62455e-12 1.08843e-10 ----------------------------------------------------------------------------------------------------- 32 Zr 1 -2.005958593563399e-01 -2.005958593507537e-01 5.58623e-12 5.02474e-11 2 -1.679750173171046e+00 -1.679750173166658e+00 4.38760e-12 2.51512e-11 3 -1.391700573272847e+00 -1.391700573262946e+00 9.90141e-12 9.03952e-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 = 3, direction = 2: |F_model - F_numer| error = ----------------------- = 3.53868e-10 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 4.68892e-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 4.68892e-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.