!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 : Sim_LAMMPS_Polymorphic_NordAlbeErhart_2003_GaN__SM_333071728528_000 Supported species : Ga N 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 = Ga | a0 = 3.9710893631 | (Configuration in file "config-Ga.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ga 1 6.089489822605355e+00 6.089489825136777e+00 2.53142e-09 1.10349e-08 2 2.691966557080955e+00 2.691966556719292e+00 3.61664e-10 2.34795e-09 3 2.510912405100294e+00 2.510912404287650e+00 8.12644e-10 4.71834e-07 * ----------------------------------------------------------------------------------------------------- 2 Ga 1 -2.587402039222194e+00 -2.587402038508694e+00 7.13500e-10 3.70435e-09 2 -1.477608161493278e+00 -1.477608159993500e+00 1.49978e-09 2.74195e-08 3 3.221314607914113e+00 3.221314607472905e+00 4.41208e-10 3.04651e-08 ----------------------------------------------------------------------------------------------------- 3 Ga 1 -2.025547888268771e+00 -2.025547888066346e+00 2.02425e-10 3.69336e-08 2 2.728744963675637e+00 2.728744962676148e+00 9.99489e-10 5.13224e-09 3 -5.025871573645738e+00 -5.025871575036299e+00 1.39056e-09 1.70226e-07 * ----------------------------------------------------------------------------------------------------- 4 Ga 1 3.874854350219693e+00 3.874854345215412e+00 5.00428e-09 1.63652e-08 2 6.956545584180384e-01 6.956545584298589e-01 1.18205e-11 4.58962e-09 3 1.104107910378898e+00 1.104107910298346e+00 8.05525e-11 1.88168e-08 ----------------------------------------------------------------------------------------------------- 5 Ga 1 3.937121588201127e-01 3.937117626066636e-01 3.96213e-07 4.49622e-07 * 2 2.349777136908381e+00 2.349777373035157e+00 2.36127e-07 3.14282e-07 * 3 3.564498470654780e+00 3.564498290358679e+00 1.80296e-07 6.35839e-07 * ----------------------------------------------------------------------------------------------------- 6 Ga 1 -3.293255886654685e+00 -3.293255886632152e+00 2.25335e-11 3.56447e-09 2 -1.002289004248644e+00 -1.002289003464246e+00 7.84399e-10 2.41459e-09 3 1.466882264477159e+00 1.466882264554737e+00 7.75788e-11 7.19058e-09 ----------------------------------------------------------------------------------------------------- 7 Ga 1 -7.682086748023839e-01 -7.682086769600349e-01 2.15765e-09 1.13765e-08 2 -7.011913027719980e-01 -7.011913027648147e-01 7.18337e-12 2.18061e-09 3 -2.566279332301194e+00 -2.566279333325344e+00 1.02415e-09 2.35673e-08 ----------------------------------------------------------------------------------------------------- 8 Ga 1 -1.267229851516802e+00 -1.267229604113910e+00 2.47403e-07 2.67702e-07 * 2 -1.592268302250512e+00 -1.592268688577143e+00 3.86327e-07 3.01742e-06 * 3 -5.977970370590087e-01 -5.977970311406827e-01 5.91833e-09 1.36015e-07 * ----------------------------------------------------------------------------------------------------- 9 Ga 1 -2.569500944262511e-01 -2.569500927956991e-01 1.63055e-09 5.76115e-09 2 -1.807463176613974e+00 -1.807463177507203e+00 8.93229e-10 3.02193e-09 3 2.000602075101326e+00 2.000602081348986e+00 6.24766e-09 2.50377e-08 ----------------------------------------------------------------------------------------------------- 10 Ga 1 -1.637194823483823e+00 -1.637194826541594e+00 3.05777e-09 3.61353e-08 2 -5.756150823154726e-01 -5.756150719927355e-01 1.03227e-08 2.76819e-08 3 2.073845663838230e+00 2.073845664164315e+00 3.26085e-10 3.67892e-08 ----------------------------------------------------------------------------------------------------- 11 Ga 1 -1.264722596910893e+00 -1.264722630867299e+00 3.39564e-08 1.20405e-07 * 2 -2.185076007697982e+00 -2.185076008279021e+00 5.81039e-10 1.17841e-07 * 3 -1.193524702254353e+00 -1.193524700599372e+00 1.65498e-09 1.01777e-08 ----------------------------------------------------------------------------------------------------- 12 Ga 1 2.857731852070267e+00 2.857731853382625e+00 1.31236e-09 4.87489e-09 2 -8.933237597111956e-01 -8.933237588904623e-01 8.20733e-10 5.21243e-09 3 -2.155094911559605e+00 -2.155094912358761e+00 7.99156e-10 1.07285e-08 ----------------------------------------------------------------------------------------------------- 13 Ga 1 -1.054009626013477e+00 -1.054009624774659e+00 1.23882e-09 1.27014e-08 2 2.116623756103553e-01 2.116623767587390e-01 1.14838e-09 2.95531e-08 3 -2.385936456043952e+00 -2.385936454174869e+00 1.86908e-09 1.72284e-08 ----------------------------------------------------------------------------------------------------- 14 Ga 1 -9.861786547927732e-01 -9.861786548878696e-01 9.50964e-11 1.67292e-08 2 -3.275241193976289e-01 -3.275241210690707e-01 1.67144e-09 2.70803e-08 3 9.034720081215880e-01 9.034720032141333e-01 4.90745e-09 7.57125e-09 ----------------------------------------------------------------------------------------------------- 15 Ga 1 2.352676674358547e+00 2.352676674981259e+00 6.22713e-10 1.52023e-08 2 4.824627337934725e-01 4.824627326221632e-01 1.17131e-09 2.05368e-08 3 2.621102526648233e+00 2.621102527783095e+00 1.13486e-09 2.99094e-08 ----------------------------------------------------------------------------------------------------- 16 Ga 1 2.308551580443072e+00 2.308551578612839e+00 1.83023e-09 3.44178e-08 2 5.997430650690682e-01 5.997430553768582e-01 9.69221e-09 7.75248e-08 3 1.213715611966711e-01 1.213715569528725e-01 4.24380e-09 1.30543e-07 * ----------------------------------------------------------------------------------------------------- 17 Ga 1 1.241973273181931e+00 1.241973272450796e+00 7.31135e-10 3.51200e-09 2 2.046118944737014e+00 2.046118944421869e+00 3.15145e-10 8.36545e-09 3 -1.810736302673594e+00 -1.810736303954235e+00 1.28064e-09 8.51152e-09 ----------------------------------------------------------------------------------------------------- 18 Ga 1 -1.789855776550240e+00 -1.789855775725965e+00 8.24275e-10 1.54942e-08 2 -9.091414244514354e-01 -9.091414232371503e-01 1.21429e-09 2.96768e-08 3 2.092417181291088e+00 2.092417182247151e+00 9.56063e-10 1.46504e-09 ----------------------------------------------------------------------------------------------------- 19 Ga 1 3.061567585822127e+00 3.061567585829213e+00 7.08589e-12 1.74511e-09 2 1.323778576113244e+00 1.323778576101018e+00 1.22258e-11 5.80904e-10 3 -1.773827901136755e+00 -1.773827901450562e+00 3.13807e-10 2.86374e-09 ----------------------------------------------------------------------------------------------------- 20 Ga 1 2.118269165567220e+00 2.118269165414083e+00 1.53138e-10 3.02414e-09 2 1.005772795623077e-01 1.005772794262163e-01 1.36091e-10 4.20816e-10 3 -2.129871787347672e+00 -2.129871787447942e+00 1.00270e-10 2.42497e-09 ----------------------------------------------------------------------------------------------------- 21 Ga 1 -3.925340805021712e+00 -3.925340804664116e+00 3.57596e-10 6.64810e-10 2 4.217452755048742e+00 4.217452759557269e+00 4.50853e-09 8.69955e-09 3 5.158699434951682e+00 5.158699432909697e+00 2.04199e-09 2.40236e-08 ----------------------------------------------------------------------------------------------------- 22 Ga 1 -7.411479726243883e-01 -7.411479794600989e-01 6.83571e-09 2.88729e-07 * 2 1.689130383164299e+00 1.689130379145060e+00 4.01924e-09 8.73347e-07 * 3 -3.891997968840281e-01 -3.891998201337208e-01 2.32497e-08 9.09675e-07 * ----------------------------------------------------------------------------------------------------- 23 Ga 1 -3.300850836399342e+00 -3.300850834499435e+00 1.89991e-09 6.84366e-09 2 2.202166360756902e+00 2.202166362634160e+00 1.87726e-09 1.63303e-09 3 -8.906469286206360e-01 -8.906469308722307e-01 2.25159e-09 2.62631e-09 ----------------------------------------------------------------------------------------------------- 24 Ga 1 3.502140776951119e+00 3.502140780252541e+00 3.30142e-09 4.76532e-09 2 -2.605977648446211e+00 -2.605977647913911e+00 5.32300e-10 2.64380e-08 3 -4.337843008037927e+00 -4.337843015252153e+00 7.21423e-09 4.87826e-08 ----------------------------------------------------------------------------------------------------- 25 Ga 1 2.227324901003231e+00 2.227324902238122e+00 1.23489e-09 2.61862e-09 2 -2.009078667249483e+00 -2.009078666166317e+00 1.08317e-09 1.98655e-08 3 1.719874962087583e+00 1.719874962644380e+00 5.56796e-10 6.75109e-09 ----------------------------------------------------------------------------------------------------- 26 Ga 1 -1.669525523848870e+00 -1.669525524451862e+00 6.02992e-10 8.59270e-06 * 2 2.683905868636954e-01 2.683905866084041e-01 2.55291e-10 1.56297e-08 3 6.826571983998772e-01 6.826571975615606e-01 8.38317e-10 2.94353e-08 ----------------------------------------------------------------------------------------------------- 27 Ga 1 -1.048582374492825e+00 -1.048582380830362e+00 6.33754e-09 1.54415e-08 2 -1.793227139418746e+00 -1.793227113414801e+00 2.60039e-08 1.51374e-07 * 3 -5.488602801666187e-01 -5.488602712536074e-01 8.91301e-09 1.82470e-08 ----------------------------------------------------------------------------------------------------- 28 Ga 1 6.280701509049099e-01 6.280701514183702e-01 5.13460e-10 7.29338e-09 2 -7.565250699772605e-02 -7.565250721706694e-02 2.19341e-10 1.37130e-09 3 -2.481681986812065e+00 -2.481681986463027e+00 3.49038e-10 2.33966e-09 ----------------------------------------------------------------------------------------------------- 29 Ga 1 1.110006417112319e+00 1.110006416697077e+00 4.15241e-10 6.65643e-09 2 1.741615001454204e-01 1.741615012313397e-01 1.08592e-09 1.65015e-08 3 9.037345869546812e-03 9.037330151252364e-03 1.57183e-08 9.38258e-08 ----------------------------------------------------------------------------------------------------- 30 Ga 1 -2.429974850292309e+00 -2.429974850687279e+00 3.94970e-10 1.01362e-08 2 -1.776097926129495e+00 -1.776097925577523e+00 5.51972e-10 8.58909e-09 3 -1.485096127510128e+00 -1.485096128927964e+00 1.41784e-09 1.32798e-08 ----------------------------------------------------------------------------------------------------- 31 Ga 1 -2.742293350147257e+00 -2.742293368333608e+00 1.81864e-08 2.30004e-08 2 -2.716008090445065e+00 -2.716008090651288e+00 2.06223e-10 2.44328e-08 3 1.375204571117919e-01 1.375204567442102e-01 3.67582e-10 7.89942e-09 ----------------------------------------------------------------------------------------------------- 32 Ga 1 1.021902916409054e+00 1.021902916630290e+00 2.21236e-10 1.71101e-08 2 6.657545426913527e-01 6.657545044716155e-01 3.82197e-08 1.99766e-07 * 3 3.839520589104031e-01 3.839520587127223e-01 1.97681e-10 4.92209e-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 dicontinuities. Maximum error obtained for particle = 29, direction = 3: |F_model - F_numer| error = ----------------------- = 1.73926e-06 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 = N | a0 = 3.10151481628 | (Configuration in file "config-N.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 N 1 2.139094046534260e+00 2.139094046349167e+00 1.85092e-10 3.40195e-09 2 2.318573558890740e+00 2.318573558852003e+00 3.87370e-11 7.10175e-10 3 3.460236164054905e+00 3.460236163729230e+00 3.25675e-10 2.04927e-09 ----------------------------------------------------------------------------------------------------- 2 N 1 -1.891784051561597e+00 -1.891784051573892e+00 1.22955e-11 4.32369e-10 2 8.423062397490202e-01 8.423062294953947e-01 1.02536e-08 2.32723e-08 3 -4.782864474180456e-01 -4.782864457690018e-01 1.64904e-09 5.51009e-08 ----------------------------------------------------------------------------------------------------- 3 N 1 2.274460587060885e+00 2.274460574512682e+00 1.25482e-08 4.44822e-06 * 2 1.119135086496480e+00 1.119135065128056e+00 2.13684e-08 2.39356e-07 * 3 -3.718115327281769e+00 -3.718115226396768e+00 1.00885e-07 3.63300e-06 * ----------------------------------------------------------------------------------------------------- 4 N 1 -8.619963477606972e-01 -8.619963365648560e-01 1.11958e-08 6.50193e-08 2 2.055617855362883e+00 2.055617858752888e+00 3.39000e-09 5.65658e-08 3 -5.595964366099822e-01 -5.595964340613725e-01 2.54861e-09 5.47310e-08 ----------------------------------------------------------------------------------------------------- 5 N 1 -1.991427039678726e+00 -1.991427036379071e+00 3.29965e-09 1.24704e-08 2 -1.197390090769476e-01 -1.197390071057343e-01 1.97121e-09 4.25493e-09 3 4.081386251051323e+00 4.081386251305702e+00 2.54379e-10 8.28594e-10 ----------------------------------------------------------------------------------------------------- 6 N 1 -3.794996400784305e+00 -3.794996400605770e+00 1.78535e-10 1.23938e-07 2 -6.638752793320282e-01 -6.638752805306227e-01 1.19859e-09 6.75777e-09 3 3.722627651944705e+00 3.722627654026671e+00 2.08197e-09 8.83591e-09 ----------------------------------------------------------------------------------------------------- 7 N 1 -1.626617169785432e+00 -1.626617169670940e+00 1.14493e-10 8.83282e-10 2 2.763749020954014e+00 2.763749020495538e+00 4.58476e-10 2.80754e-09 3 6.625808995623986e-02 6.625808996375668e-02 7.51682e-12 3.66082e-10 ----------------------------------------------------------------------------------------------------- 8 N 1 3.952747676013634e+00 3.952747677151858e+00 1.13822e-09 7.19788e-08 2 -4.063082518314391e+00 -4.063082523067580e+00 4.75319e-09 7.17867e-08 3 -1.630758807888416e+00 -1.630758790025892e+00 1.78625e-08 2.97299e-08 ----------------------------------------------------------------------------------------------------- 9 N 1 9.919591352727746e-01 9.919591354247890e-01 1.52014e-10 2.58778e-09 2 -1.256771115742948e+00 -1.256771115166692e+00 5.76257e-10 4.20139e-10 3 1.153046926341134e+00 1.153046925869384e+00 4.71750e-10 4.32634e-09 ----------------------------------------------------------------------------------------------------- 10 N 1 -1.490737417758682e+00 -1.490737417314546e+00 4.44136e-10 1.07483e-09 2 -2.045808123221541e+00 -2.045808105205997e+00 1.80155e-08 4.38106e-08 3 3.439478980840341e+00 3.439478973105222e+00 7.73512e-09 1.72030e-08 ----------------------------------------------------------------------------------------------------- 11 N 1 -1.882545643119818e+00 -1.882545652061046e+00 8.94123e-09 2.78340e-08 2 2.016205177745178e+00 2.016205156151041e+00 2.15941e-08 2.18566e-08 3 -1.360245575023716e+00 -1.360245575742182e+00 7.18466e-10 8.44445e-08 ----------------------------------------------------------------------------------------------------- 12 N 1 3.532868651940195e+00 3.532868647347503e+00 4.59269e-09 7.00305e-09 2 -1.756763514826530e+00 -1.756763517244170e+00 2.41764e-09 1.57301e-08 3 -4.655018153713551e-01 -4.655018154578336e-01 8.64785e-11 1.21928e-08 ----------------------------------------------------------------------------------------------------- 13 N 1 2.538884400675796e+00 2.538884407180347e+00 6.50455e-09 1.89202e-08 2 9.706485450694465e-01 9.706485446583093e-01 4.11137e-10 1.04056e-08 3 9.062527926326627e-03 9.062526066219255e-03 1.86011e-09 1.53875e-08 ----------------------------------------------------------------------------------------------------- 14 N 1 5.915093163653742e-01 5.915093152694466e-01 1.09593e-09 1.06424e-08 2 -1.126426380535202e+00 -1.126426381006861e+00 4.71658e-10 6.90813e-09 3 -1.232330408057217e+00 -1.232330408131496e+00 7.42792e-11 1.40213e-09 ----------------------------------------------------------------------------------------------------- 15 N 1 -2.323508575626793e-01 -2.323508575541677e-01 8.51158e-12 2.68713e-09 2 -3.876631157747887e-02 -3.876631179181449e-02 2.14336e-10 6.51758e-09 3 -7.796155592460423e-01 -7.796155591728591e-01 7.31832e-11 5.16357e-09 ----------------------------------------------------------------------------------------------------- 16 N 1 -2.633933187322364e+00 -2.633933187857633e+00 5.35269e-10 9.73038e-09 2 -3.936934548034675e-01 -3.936934438658403e-01 1.09376e-08 4.64815e-08 3 1.712870238286754e+00 1.712870238016272e+00 2.70482e-10 6.69996e-09 ----------------------------------------------------------------------------------------------------- 17 N 1 3.412933686392318e+00 3.412933686693417e+00 3.01099e-10 2.61046e-09 2 1.795802290378325e+00 1.795802290647013e+00 2.68688e-10 4.52493e-09 3 8.453049953256252e-01 8.453049945286266e-01 7.96999e-10 3.69392e-09 ----------------------------------------------------------------------------------------------------- 18 N 1 -2.372489554004805e+00 -2.372489555315020e+00 1.31022e-09 1.78215e-09 2 -2.797146545448341e+00 -2.797146545019852e+00 4.28489e-10 3.16767e-09 3 1.424290245778628e+00 1.424290245426139e+00 3.52489e-10 5.37355e-09 ----------------------------------------------------------------------------------------------------- 19 N 1 -1.186726762320072e+00 -1.186726762212185e+00 1.07887e-10 1.23655e-08 2 2.897832783189712e+00 2.897832782951709e+00 2.38004e-10 1.85207e-09 3 -2.275956593361695e+00 -2.275956593523330e+00 1.61635e-10 1.91146e-09 ----------------------------------------------------------------------------------------------------- 20 N 1 2.234959211548151e+00 2.234959210731971e+00 8.16180e-10 2.20387e-09 2 -1.516220837041995e+00 -1.516220836998210e+00 4.37856e-11 1.24442e-09 3 -1.484388760950881e+00 -1.484388760760870e+00 1.90012e-10 4.42834e-10 ----------------------------------------------------------------------------------------------------- 21 N 1 6.638975914003157e-01 6.638963583760951e-01 1.23302e-06 1.82264e-06 * 2 2.634025288510353e+00 2.634025291055112e+00 2.54476e-09 4.41662e-07 * 3 4.964432623998186e-01 4.964433886395196e-01 1.26240e-07 7.67290e-06 * ----------------------------------------------------------------------------------------------------- 22 N 1 -1.947329073278994e+00 -1.947329073245581e+00 3.34126e-11 4.44604e-09 2 1.732145835499953e+00 1.732145835692035e+00 1.92081e-10 1.67448e-09 3 1.633979926431599e+00 1.633979926526464e+00 9.48654e-11 2.50363e-09 ----------------------------------------------------------------------------------------------------- 23 N 1 -3.793874487645478e+00 -3.793874487586342e+00 5.91363e-11 5.37260e-10 2 2.202240043072184e+00 2.202240043948942e+00 8.76758e-10 3.00011e-09 3 -1.731614380308742e+00 -1.731614380981729e+00 6.72988e-10 3.99604e-09 ----------------------------------------------------------------------------------------------------- 24 N 1 1.728069640250735e+00 1.728069640357981e+00 1.07247e-10 1.03866e-08 2 -4.200259474828815e+00 -4.200259473752483e+00 1.07633e-09 9.86396e-09 3 -1.467221313750367e-01 -1.467221315938706e-01 2.18834e-10 1.80970e-08 ----------------------------------------------------------------------------------------------------- 25 N 1 4.673616240978077e-01 4.673616258517722e-01 1.75396e-09 1.65828e-08 2 -1.749110084285975e+00 -1.749110083256229e+00 1.02975e-09 9.77631e-09 3 -1.958228138638450e+00 -1.958228137655982e+00 9.82469e-10 3.38693e-08 ----------------------------------------------------------------------------------------------------- 26 N 1 -1.531281997620013e-01 -1.531281995097044e-01 2.52297e-10 3.06397e-09 2 -1.971007663951988e-01 -1.971007714392829e-01 5.04408e-09 4.58282e-09 3 -1.955103115100466e+00 -1.955103115500185e+00 3.99719e-10 1.62411e-08 ----------------------------------------------------------------------------------------------------- 27 N 1 -1.855114972501944e+00 -1.855114971468489e+00 1.03345e-09 4.90706e-08 2 4.774199760843693e+00 4.774199762795454e+00 1.95176e-09 3.37449e-08 3 -8.212600639906035e-01 -8.212600651138438e-01 1.12324e-09 5.22356e-09 ----------------------------------------------------------------------------------------------------- 28 N 1 3.491236446906753e+00 3.491236446996573e+00 8.98197e-11 1.37656e-10 2 -2.819122815917706e+00 -2.819122815831794e+00 8.59122e-11 3.37734e-10 3 5.328674407794225e-01 5.328674408085093e-01 2.90868e-11 3.04577e-09 ----------------------------------------------------------------------------------------------------- 29 N 1 2.026298668692021e+00 2.026298619379573e+00 4.93124e-08 2.95077e-07 * 2 2.215322191016729e-01 2.215321989506335e-01 2.01510e-08 3.40227e-08 3 4.025744083096773e-01 4.025743475259587e-01 6.07837e-08 4.83939e-07 * ----------------------------------------------------------------------------------------------------- 30 N 1 -7.991100020033256e-01 -7.991099566755370e-01 4.53278e-08 8.01168e-08 2 -4.851659939021175e-01 -4.851659682105580e-01 2.56916e-08 5.88671e-08 3 2.619427821508275e+00 2.619427817170406e+00 4.33787e-09 1.68815e-07 * ----------------------------------------------------------------------------------------------------- 31 N 1 -9.310590143987927e-01 -9.310589989719579e-01 1.54268e-08 7.75240e-09 2 4.961235544546868e-02 4.961236141657286e-02 5.97110e-09 3.20374e-08 3 -4.206447493731402e+00 -4.206447514372082e+00 2.06407e-08 3.27381e-08 ----------------------------------------------------------------------------------------------------- 32 N 1 -6.010605019013068e-01 -6.010604926958315e-01 9.20548e-09 4.53078e-08 2 -3.164573835058446e+00 -3.164573798766979e+00 3.62915e-08 6.14111e-08 3 -7.956838765809595e-01 -7.956838769773730e-01 3.96413e-10 5.49519e-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 dicontinuities. Maximum error obtained for particle = 13, direction = 3: |F_model - F_numer| error = ----------------------- = 2.05253e-07 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 = Ga N | a0 = 3.43157038294 | (Configuration in file "config-GaN.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ga 1 8.229261451627388e-02 8.229261447163565e-02 4.46382e-11 7.99772e-10 2 2.232890376663607e-01 2.232890377586612e-01 9.23004e-11 7.45520e-10 3 -1.155408808609629e+00 -1.155408808675734e+00 6.61058e-11 7.49107e-10 ----------------------------------------------------------------------------------------------------- 2 N 1 -6.060597207124578e-01 -6.060597209843493e-01 2.71892e-10 3.75514e-08 2 -1.232367918529891e+01 -1.232367918422526e+01 1.07365e-09 3.14165e-09 3 -1.527455164673333e+01 -1.527455164587510e+01 8.58236e-10 2.89059e-09 ----------------------------------------------------------------------------------------------------- 3 Ga 1 2.754893556953411e+00 2.754893558866496e+00 1.91309e-09 4.48908e-09 2 -1.027948921762463e+01 -1.027948921784798e+01 2.23350e-10 1.99145e-09 3 -6.873947697689141e+00 -6.873947697786791e+00 9.76499e-11 5.51686e-09 ----------------------------------------------------------------------------------------------------- 4 N 1 -1.748297202075784e+01 -1.748297201930178e+01 1.45605e-09 8.00626e-09 2 4.700579699658767e+00 4.700579697679195e+00 1.97957e-09 1.55049e-08 3 -1.504615381338953e+01 -1.504615381355779e+01 1.68258e-10 8.49200e-10 ----------------------------------------------------------------------------------------------------- 5 N 1 -1.012448639187726e-01 -1.012448637082164e-01 2.10556e-10 8.09171e-10 2 1.526159073234574e-01 1.526159070417920e-01 2.81665e-10 2.62182e-09 3 4.338130273301300e-01 4.338130273644967e-01 3.43667e-11 6.71269e-10 ----------------------------------------------------------------------------------------------------- 6 Ga 1 4.979056535831480e+00 4.979056528122864e+00 7.70862e-09 5.93553e-08 2 -1.816809170594332e+00 -1.816809175343802e+00 4.74947e-09 4.06440e-08 3 -5.899842157971730e+00 -5.899842165681299e+00 7.70957e-09 4.11083e-08 ----------------------------------------------------------------------------------------------------- 7 Ga 1 4.068184540490317e+00 4.068184539783764e+00 7.06553e-10 2.10857e-09 2 -3.880453377097925e+00 -3.880453376261224e+00 8.36701e-10 6.79072e-10 3 -1.968657199931947e+00 -1.968657201115393e+00 1.18345e-09 3.05522e-09 ----------------------------------------------------------------------------------------------------- 8 Ga 1 -4.834404309070290e+00 -4.834404298775870e+00 1.02944e-08 6.30300e-08 2 -1.139793324089167e+00 -1.139793306828443e+00 1.72607e-08 8.25700e-08 3 -1.042327054485886e+00 -1.042327036220254e+00 1.82656e-08 2.76238e-08 ----------------------------------------------------------------------------------------------------- 9 N 1 1.193068897976432e+00 1.193068897058531e+00 9.17900e-10 1.39128e-08 2 1.179011834530713e+00 1.179011835176510e+00 6.45797e-10 1.50057e-09 3 -8.795485842952426e-02 -8.795485754540866e-02 8.84116e-10 3.84013e-09 ----------------------------------------------------------------------------------------------------- 10 Ga 1 -2.812816998084300e+00 -2.812816997435941e+00 6.48360e-10 2.16678e-08 2 -8.041167917749883e-01 -8.041167927309255e-01 9.55937e-10 6.43321e-09 3 6.634121518392896e-01 6.634121473351000e-01 4.50419e-09 1.01155e-08 ----------------------------------------------------------------------------------------------------- 11 N 1 1.424131176775949e+00 1.424131171466402e+00 5.30955e-09 1.97158e-08 2 2.628318114192883e+01 2.628318113832334e+01 3.60549e-09 1.83400e-08 3 5.051388804047182e+00 5.051388802728688e+00 1.31849e-09 1.37505e-08 ----------------------------------------------------------------------------------------------------- 12 N 1 2.162456715736427e+00 2.162456715530362e+00 2.06065e-10 1.07590e-09 2 3.221488140225067e-01 3.221488134286062e-01 5.93900e-10 1.39162e-07 3 -6.969688617536635e-03 -6.969688726159350e-03 1.08623e-10 6.96520e-09 ----------------------------------------------------------------------------------------------------- 13 Ga 1 -2.156849143547896e+00 -2.156849136567913e+00 6.97998e-09 2.86818e-08 2 4.665699828612383e+00 4.665699838793363e+00 1.01810e-08 6.90099e-08 3 -6.705011880715982e+00 -6.705011885260618e+00 4.54464e-09 4.78771e-08 ----------------------------------------------------------------------------------------------------- 14 N 1 -7.254101090421867e-01 -7.254101091020148e-01 5.98280e-11 1.26780e-09 2 -1.591582972241464e+00 -1.591582972198373e+00 4.30909e-11 5.87619e-09 3 7.801193022152230e-01 7.801193022302877e-01 1.50647e-11 1.10793e-09 ----------------------------------------------------------------------------------------------------- 15 Ga 1 4.426821439412588e+00 4.426821438695066e+00 7.17522e-10 6.41750e-09 2 3.707390236381634e+00 3.707390237694602e+00 1.31297e-09 3.28748e-08 3 -1.226380984240321e-01 -1.226380981480388e-01 2.75993e-10 1.51386e-08 ----------------------------------------------------------------------------------------------------- 16 N 1 -7.120349603956909e+00 -7.120349600643356e+00 3.31355e-09 5.61835e-09 2 1.004056861406774e+00 1.004056865359138e+00 3.95236e-09 4.91463e-08 3 -1.139726459039555e+01 -1.139726459406117e+01 3.66563e-09 3.09833e-07 * ----------------------------------------------------------------------------------------------------- 17 N 1 -2.462594976425196e+00 -2.462594976453102e+00 2.79057e-11 5.85645e-09 2 -7.921008822196808e+00 -7.921008822899471e+00 7.02663e-10 4.31211e-09 3 7.079383753288058e+00 7.079383753413319e+00 1.25262e-10 1.80317e-09 ----------------------------------------------------------------------------------------------------- 18 N 1 -9.355672824347765e+00 -9.355672321110859e+00 5.03237e-07 1.35774e-06 * 2 1.822238609755520e+01 1.822238496615320e+01 1.13140e-06 1.36346e-05 * 3 1.606049982058830e+01 1.606049980554372e+01 1.50446e-08 2.70473e-07 * ----------------------------------------------------------------------------------------------------- 19 Ga 1 -5.089521461168639e+00 -5.089521462404019e+00 1.23538e-09 4.70172e-08 2 -6.301269983942751e-01 -6.301270000244960e-01 1.63022e-09 1.43170e-08 3 5.449082882057989e+00 5.449082839842868e+00 4.22151e-08 1.55921e-07 * ----------------------------------------------------------------------------------------------------- 20 N 1 1.067124055758202e+00 1.067124055907135e+00 1.48933e-10 4.61160e-10 2 -1.632388792806630e+00 -1.632388792777598e+00 2.90319e-11 5.76698e-09 3 5.348786922645125e-01 5.348786930703260e-01 8.05814e-10 2.75498e-09 ----------------------------------------------------------------------------------------------------- 21 N 1 1.766490298015006e+01 1.766490298023733e+01 8.72618e-11 3.18904e-06 * 2 -5.555802808500691e+01 -5.555802614831324e+01 1.93669e-06 2.89516e-06 * 3 -2.335927893958301e+01 -2.335927907650676e+01 1.36924e-07 2.09090e-06 * ----------------------------------------------------------------------------------------------------- 22 Ga 1 4.574123363680277e+00 4.574123364211438e+00 5.31161e-10 2.55341e-08 2 1.830217170344525e+00 1.830217168319602e+00 2.02492e-09 5.13925e-07 * 3 -3.088048369814345e-01 -3.088048369480005e-01 3.34340e-11 1.08089e-08 ----------------------------------------------------------------------------------------------------- 23 Ga 1 4.549365065941084e+00 4.549365060337072e+00 5.60401e-09 3.04160e-08 2 -2.960899797843548e+00 -2.960899797283285e+00 5.60263e-10 6.16544e-10 3 5.155918938439809e+00 5.155918938622501e+00 1.82692e-10 6.81834e-08 ----------------------------------------------------------------------------------------------------- 24 N 1 -7.474180292286809e-01 -7.474180316469275e-01 2.41825e-09 4.19060e-09 2 3.144727627177139e+01 3.144727627122432e+01 5.47068e-10 4.50174e-09 3 2.954999056009890e+01 2.954999055835658e+01 1.74232e-09 4.26480e-09 ----------------------------------------------------------------------------------------------------- 25 N 1 -9.936091000085477e-01 -9.936090998723812e-01 1.36167e-10 1.46660e-09 2 5.141669908211608e+00 5.141669909279546e+00 1.06794e-09 2.76008e-07 * 3 4.816487617585421e+00 4.816487641915494e+00 2.43301e-08 2.61290e-08 ----------------------------------------------------------------------------------------------------- 26 Ga 1 -5.058674405202485e+00 -5.058674409706080e+00 4.50359e-09 1.12954e-08 2 3.392552950380999e+00 3.392552946740787e+00 3.64021e-09 7.88708e-08 3 -2.820759819737579e+00 -2.820759824495458e+00 4.75788e-09 9.67832e-08 ----------------------------------------------------------------------------------------------------- 27 N 1 1.277826911042848e+01 1.277826910923056e+01 1.19792e-09 2.34410e-09 2 -5.622982262858621e+00 -5.622982262019131e+00 8.39490e-10 1.15851e-08 3 2.147988037139666e+00 2.147988036975005e+00 1.64661e-10 5.24067e-09 ----------------------------------------------------------------------------------------------------- 28 N 1 -1.312289940092659e+01 -1.312289939727970e+01 3.64689e-09 5.48678e-09 2 2.512211797725429e+00 2.512211782770431e+00 1.49550e-08 2.40548e-08 3 -5.991292762076665e+00 -5.991292763615260e+00 1.53860e-09 2.10544e-08 ----------------------------------------------------------------------------------------------------- 29 Ga 1 -6.023360659681273e+00 -6.023360642435813e+00 1.72455e-08 2.72600e-08 2 -4.627521235963319e+00 -4.627521250220819e+00 1.42575e-08 6.78199e-08 3 -2.401444578332368e+00 -2.401444582478002e+00 4.14563e-09 1.32764e-08 ----------------------------------------------------------------------------------------------------- 30 Ga 1 1.279798389007715e+01 1.279798388861973e+01 1.45742e-09 4.85251e-07 * 2 4.628583529097291e+00 4.628583529595628e+00 4.98336e-10 1.94528e-08 3 6.593085420639460e+00 6.593085421166252e+00 5.26793e-10 5.63279e-09 ----------------------------------------------------------------------------------------------------- 31 Ga 1 5.381534467250714e+00 5.381534467085740e+00 1.64974e-10 2.82015e-09 2 -1.973803807820030e+00 -1.973803808155211e+00 3.35182e-10 2.96666e-09 3 3.951444105923653e+00 3.951444106098945e+00 1.75292e-10 6.38421e-10 ----------------------------------------------------------------------------------------------------- 32 Ga 1 -1.210350784899067e+00 -1.210350784916509e+00 1.74418e-11 6.67502e-10 2 3.349812754993731e+00 3.349812756460609e+00 1.46688e-09 3.49249e-09 3 1.219481531864729e+01 1.219481531864508e+01 2.20446e-12 2.73497e-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 dicontinuities. Maximum error obtained for particle = 8, direction = 3: |F_model - F_numer| error = ----------------------- = 1.75239e-08 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 1.73926e-06 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: B Comment: The letter grade B was assigned because the normalized error in the computation was 1.73926e-06 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.