!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 = 3.9710893630981445 | (Configuration in file "config-Ga.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ga 1 6.089489822605490e+00 6.089489824963823e+00 2.35833e-09 3.71182e-08 2 2.691966557080980e+00 2.691966557310514e+00 2.29533e-10 3.30833e-09 3 2.510912405100396e+00 2.510912405453617e+00 3.53221e-10 1.52974e-08 ----------------------------------------------------------------------------------------------------- 2 Ga 1 -2.587402039222297e+00 -2.587402039058909e+00 1.63388e-10 4.09893e-09 2 -1.477608161493133e+00 -1.477608155468860e+00 6.02427e-09 3.29369e-08 3 3.221314607914150e+00 3.221314608077753e+00 1.63603e-10 7.60642e-09 ----------------------------------------------------------------------------------------------------- 3 Ga 1 -2.025547888268817e+00 -2.025547883112029e+00 5.15679e-09 5.09757e-08 2 2.728744963675511e+00 2.728744962634902e+00 1.04061e-09 1.26794e-08 3 -5.025871573645759e+00 -5.025871561932925e+00 1.17128e-08 1.72420e-08 ----------------------------------------------------------------------------------------------------- 4 Ga 1 3.874854350219461e+00 3.874854346068942e+00 4.15052e-09 5.84878e-08 2 6.956545584179293e-01 6.956545594187297e-01 1.00080e-09 4.38820e-09 3 1.104107910378667e+00 1.104107910547509e+00 1.68842e-10 2.38667e-08 ----------------------------------------------------------------------------------------------------- 5 Ga 1 3.937121588201443e-01 3.937123871227126e-01 2.28303e-07 5.41251e-06 * 2 2.349777136908282e+00 2.349777168924624e+00 3.20163e-08 1.66899e-06 * 3 3.564498470654687e+00 3.564498247256514e+00 2.23398e-07 7.84448e-07 * ----------------------------------------------------------------------------------------------------- 6 Ga 1 -3.293255886654554e+00 -3.293255886839920e+00 1.85366e-10 2.07730e-09 2 -1.002289004248641e+00 -1.002289003200504e+00 1.04814e-09 1.25461e-08 3 1.466882264477027e+00 1.466882273887619e+00 9.41059e-09 1.41905e-08 ----------------------------------------------------------------------------------------------------- 7 Ga 1 -7.682086748024063e-01 -7.682086734952986e-01 1.30711e-09 1.74131e-08 2 -7.011913027720837e-01 -7.011912847188063e-01 1.80533e-08 2.87101e-08 3 -2.566279332301106e+00 -2.566279327467930e+00 4.83318e-09 1.51479e-08 ----------------------------------------------------------------------------------------------------- 8 Ga 1 -1.267229851516751e+00 -1.267229659521628e+00 1.91995e-07 1.95660e-07 * 2 -1.592268302250495e+00 -1.592268684410132e+00 3.82160e-07 6.81037e-07 * 3 -5.977970370589332e-01 -5.977970313583937e-01 5.70054e-09 1.25359e-07 ----------------------------------------------------------------------------------------------------- 9 Ga 1 -2.569500944262417e-01 -2.569500952274633e-01 8.01222e-10 1.81461e-09 2 -1.807463176614044e+00 -1.807463177165487e+00 5.51442e-10 2.95552e-08 3 2.000602075101326e+00 2.000602078765810e+00 3.66448e-09 1.73027e-08 ----------------------------------------------------------------------------------------------------- 10 Ga 1 -1.637194823483724e+00 -1.637194812688004e+00 1.07957e-08 2.62550e-08 2 -5.756150823154582e-01 -5.756150953794108e-01 1.30640e-08 7.24321e-08 3 2.073845663838215e+00 2.073845657318375e+00 6.51984e-09 2.25442e-08 ----------------------------------------------------------------------------------------------------- 11 Ga 1 -1.264722596910943e+00 -1.264722615310130e+00 1.83992e-08 3.09404e-08 2 -2.185076007698066e+00 -2.185076008513324e+00 8.15259e-10 3.82234e-08 3 -1.193524702254414e+00 -1.193524699923535e+00 2.33088e-09 1.38382e-08 ----------------------------------------------------------------------------------------------------- 12 Ga 1 2.857731852070282e+00 2.857731847889911e+00 4.18037e-09 5.76979e-08 2 -8.933237597112368e-01 -8.933237602775017e-01 5.66265e-10 3.73465e-09 3 -2.155094911559592e+00 -2.155094908457014e+00 3.10258e-09 5.52620e-09 ----------------------------------------------------------------------------------------------------- 13 Ga 1 -1.054009626013576e+00 -1.054009623160610e+00 2.85297e-09 9.41761e-09 2 2.116623756105181e-01 2.116623494046053e-01 2.62059e-08 2.63097e-08 3 -2.385936456043979e+00 -2.385936449090929e+00 6.95305e-09 2.58983e-08 ----------------------------------------------------------------------------------------------------- 14 Ga 1 -9.861786547926683e-01 -9.861786514886459e-01 3.30402e-09 4.15173e-09 2 -3.275241193976311e-01 -3.275241197113011e-01 3.13670e-10 2.15890e-08 3 9.034720081215050e-01 9.034720055193594e-01 2.60215e-09 4.29667e-09 ----------------------------------------------------------------------------------------------------- 15 Ga 1 2.352676674358531e+00 2.352676681398448e+00 7.03992e-09 1.97762e-08 2 4.824627337934669e-01 4.824627353845122e-01 1.59105e-09 4.01049e-08 3 2.621102526648262e+00 2.621102533449662e+00 6.80140e-09 7.26816e-09 ----------------------------------------------------------------------------------------------------- 16 Ga 1 2.308551580443049e+00 2.308551586901647e+00 6.45860e-09 1.63196e-08 2 5.997430650690601e-01 5.997430593345127e-01 5.73455e-09 3.27335e-08 3 1.213715611967910e-01 1.213715706856746e-01 9.48888e-09 2.46651e-08 ----------------------------------------------------------------------------------------------------- 17 Ga 1 1.241973273181957e+00 1.241973270509708e+00 2.67225e-09 1.93006e-08 2 2.046118944737054e+00 2.046118945677793e+00 9.40739e-10 3.00324e-09 3 -1.810736302673618e+00 -1.810736291519302e+00 1.11543e-08 6.57318e-07 * ----------------------------------------------------------------------------------------------------- 18 Ga 1 -1.789855776550227e+00 -1.789855771277052e+00 5.27317e-09 5.61359e-09 2 -9.091414244513868e-01 -9.091414267401774e-01 2.28879e-09 2.48167e-08 3 2.092417181291214e+00 2.092417181615368e+00 3.24154e-10 4.31116e-09 ----------------------------------------------------------------------------------------------------- 19 Ga 1 3.061567585822097e+00 3.061567585777185e+00 4.49121e-11 1.39274e-08 2 1.323778576113170e+00 1.323778576515665e+00 4.02495e-10 2.98821e-09 3 -1.773827901136755e+00 -1.773827902698959e+00 1.56220e-09 1.22937e-09 ----------------------------------------------------------------------------------------------------- 20 Ga 1 2.118269165567220e+00 2.118269165922806e+00 3.55587e-10 3.75621e-09 2 1.005772795623331e-01 1.005772794833827e-01 7.89504e-11 4.44708e-10 3 -2.129871787347670e+00 -2.129871787552952e+00 2.05282e-10 3.39032e-09 ----------------------------------------------------------------------------------------------------- 21 Ga 1 -3.925340805021548e+00 -3.925340799572390e+00 5.44916e-09 7.05694e-09 2 4.217452755048739e+00 4.217452765789312e+00 1.07406e-08 9.70958e-09 3 5.158699434951775e+00 5.158699435180746e+00 2.28972e-10 1.31746e-08 ----------------------------------------------------------------------------------------------------- 22 Ga 1 -7.411479726243688e-01 -7.411479533139359e-01 1.93104e-08 2.74381e-07 * 2 1.689130383164311e+00 1.689130356368188e+00 2.67961e-08 1.02547e-06 * 3 -3.891997968839900e-01 -3.891997790759808e-01 1.78080e-08 9.87623e-07 * ----------------------------------------------------------------------------------------------------- 23 Ga 1 -3.300850836399275e+00 -3.300850836488929e+00 8.96541e-11 2.51974e-09 2 2.202166360756747e+00 2.202166359620289e+00 1.13646e-09 6.95146e-09 3 -8.906469286207704e-01 -8.906469290041368e-01 3.83366e-10 6.54826e-09 ----------------------------------------------------------------------------------------------------- 24 Ga 1 3.502140776950920e+00 3.502140784253208e+00 7.30229e-09 1.37112e-08 2 -2.605977648445984e+00 -2.605977631778197e+00 1.66678e-08 2.28850e-08 3 -4.337843008037971e+00 -4.337842966397801e+00 4.16402e-08 4.16209e-08 ----------------------------------------------------------------------------------------------------- 25 Ga 1 2.227324901003282e+00 2.227324900794531e+00 2.08750e-10 1.11946e-08 2 -2.009078667249333e+00 -2.009078652081604e+00 1.51677e-08 2.45919e-08 3 1.719874962087760e+00 1.719874963378802e+00 1.29104e-09 1.85272e-08 ----------------------------------------------------------------------------------------------------- 26 Ga 1 -1.669525523848917e+00 -1.669525523835462e+00 1.34543e-11 3.05918e-09 2 2.683905868637037e-01 2.683905762903313e-01 1.05734e-08 5.82044e-09 3 6.826571983998767e-01 6.826571964519037e-01 1.94797e-09 2.55923e-08 ----------------------------------------------------------------------------------------------------- 27 Ga 1 -1.048582374492779e+00 -1.048582370205849e+00 4.28693e-09 3.66284e-08 2 -1.793227139418751e+00 -1.793227156558121e+00 1.71394e-08 2.65010e-08 3 -5.488602801665433e-01 -5.488602775089571e-01 2.65759e-09 2.39001e-08 ----------------------------------------------------------------------------------------------------- 28 Ga 1 6.280701509049075e-01 6.280701507839509e-01 1.20957e-10 1.48349e-08 2 -7.565250699776832e-02 -7.565250677244802e-02 2.25320e-10 3.28855e-09 3 -2.481681986812140e+00 -2.481681987056158e+00 2.44018e-10 2.30270e-09 ----------------------------------------------------------------------------------------------------- 29 Ga 1 1.110006417112405e+00 1.110006416935300e+00 1.77105e-10 4.89030e-09 2 1.741615001454542e-01 1.741614995827254e-01 5.62729e-10 1.82368e-09 3 9.037345869556887e-03 9.037349800423766e-03 3.93087e-09 4.50126e-07 * ----------------------------------------------------------------------------------------------------- 30 Ga 1 -2.429974850292421e+00 -2.429974846768828e+00 3.52359e-09 1.08664e-07 2 -1.776097926129550e+00 -1.776097925300429e+00 8.29121e-10 4.11611e-08 3 -1.485096127510172e+00 -1.485096127788726e+00 2.78553e-10 1.47965e-08 ----------------------------------------------------------------------------------------------------- 31 Ga 1 -2.742293350147268e+00 -2.742293355016053e+00 4.86879e-09 3.66835e-08 2 -2.716008090445075e+00 -2.716008087976702e+00 2.46837e-09 4.54606e-07 * 3 1.375204571117961e-01 1.375204563383092e-01 7.73487e-10 3.75168e-09 ----------------------------------------------------------------------------------------------------- 32 Ga 1 1.021902916409087e+00 1.021902915204683e+00 1.20440e-09 4.13620e-07 * 2 6.657545426913529e-01 6.657544615895268e-01 8.11018e-08 5.22884e-07 * 3 3.839520589104006e-01 3.839520576953507e-01 1.21505e-09 1.78073e-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 = 13, direction = 2: |F_model - F_numer| error = ----------------------- = 1.23810e-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. MONOATOMIC STRUCTURE -- Species = N | a0 = 3.1015148162841797 | (Configuration in file "config-N.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 N 1 2.139094046534299e+00 2.139094046002979e+00 5.31320e-10 2.20757e-09 2 2.318573558890761e+00 2.318573558771409e+00 1.19351e-10 2.31218e-09 3 3.460236164054923e+00 3.460236164147211e+00 9.22884e-11 1.80531e-09 ----------------------------------------------------------------------------------------------------- 2 N 1 -1.891784051561634e+00 -1.891784050717201e+00 8.44432e-10 5.48173e-08 2 8.423062397489860e-01 8.423062304506308e-01 9.29836e-09 5.36264e-07 3 -4.782864474180328e-01 -4.782864447562709e-01 2.66176e-09 5.47259e-07 ----------------------------------------------------------------------------------------------------- 3 N 1 2.274460587060825e+00 2.274462138921565e+00 1.55186e-06 5.47204e-06 * 2 1.119135086496488e+00 1.119135903896411e+00 8.17400e-07 9.57962e-07 * 3 -3.718115327281725e+00 -3.718117022861694e+00 1.69558e-06 9.81473e-06 * ----------------------------------------------------------------------------------------------------- 4 N 1 -8.619963477607523e-01 -8.619962012453679e-01 1.46515e-07 4.11402e-07 2 2.055617855362890e+00 2.055617525801518e+00 3.29561e-07 8.43752e-07 * 3 -5.595964366100120e-01 -5.595964421242805e-01 5.51427e-09 1.26390e-08 ----------------------------------------------------------------------------------------------------- 5 N 1 -1.991427039678733e+00 -1.991427042459560e+00 2.78083e-09 3.79581e-07 2 -1.197390090769513e-01 -1.197390070130915e-01 2.06386e-09 2.23030e-08 3 4.081386251051317e+00 4.081386251103795e+00 5.24780e-11 1.69140e-09 ----------------------------------------------------------------------------------------------------- 6 N 1 -3.794996400784355e+00 -3.794996382542699e+00 1.82417e-08 2.32162e-08 2 -6.638752793320186e-01 -6.638752801190062e-01 7.86988e-10 7.13744e-08 3 3.722627651944739e+00 3.722627652378944e+00 4.34205e-10 7.06009e-09 ----------------------------------------------------------------------------------------------------- 7 N 1 -1.626617169785373e+00 -1.626617169723684e+00 6.16889e-11 8.96793e-10 2 2.763749020953927e+00 2.763749020880136e+00 7.37916e-11 7.83599e-10 3 6.625808995624730e-02 6.625808997600144e-02 1.97541e-11 5.48081e-10 ----------------------------------------------------------------------------------------------------- 8 N 1 3.952747676013665e+00 3.952747654364934e+00 2.16487e-08 1.22160e-06 * 2 -4.063082518314320e+00 -4.063082985183023e+00 4.66869e-07 6.43429e-07 3 -1.630758807888452e+00 -1.630758796337568e+00 1.15509e-08 5.32550e-08 ----------------------------------------------------------------------------------------------------- 9 N 1 9.919591352727923e-01 9.919591351741616e-01 9.86308e-11 2.75971e-08 2 -1.256771115743005e+00 -1.256771116569272e+00 8.26267e-10 4.40657e-09 3 1.153046926341152e+00 1.153046926206127e+00 1.35025e-10 4.43276e-09 ----------------------------------------------------------------------------------------------------- 10 N 1 -1.490737417758722e+00 -1.490737417939673e+00 1.80951e-10 1.70927e-09 2 -2.045808123221488e+00 -2.045808109174201e+00 1.40473e-08 3.42054e-08 3 3.439478980840406e+00 3.439478979837518e+00 1.00289e-09 1.97927e-08 ----------------------------------------------------------------------------------------------------- 11 N 1 -1.882545643119840e+00 -1.882545642007151e+00 1.11269e-09 3.00360e-08 2 2.016205177745105e+00 2.016205170350690e+00 7.39441e-09 1.46325e-07 3 -1.360245575023759e+00 -1.360245584948597e+00 9.92484e-09 1.86802e-08 ----------------------------------------------------------------------------------------------------- 12 N 1 3.532868651940323e+00 3.532868673666719e+00 2.17264e-08 2.30321e-08 2 -1.756763514826502e+00 -1.756763509387082e+00 5.43942e-09 1.67253e-08 3 -4.655018153714378e-01 -4.655018169399877e-01 1.56855e-09 1.01591e-08 ----------------------------------------------------------------------------------------------------- 13 N 1 2.538884400675803e+00 2.538884402369342e+00 1.69354e-09 1.76545e-08 2 9.706485450695241e-01 9.706485440175275e-01 1.05200e-09 4.05581e-09 3 9.062527926367895e-03 9.062527219651888e-03 7.06716e-10 5.14825e-09 ----------------------------------------------------------------------------------------------------- 14 N 1 5.915093163653762e-01 5.915093169976960e-01 6.32320e-10 1.27438e-07 2 -1.126426380535267e+00 -1.126426380270122e+00 2.65145e-10 8.79136e-08 3 -1.232330408057216e+00 -1.232330407251087e+00 8.06129e-10 9.32412e-08 ----------------------------------------------------------------------------------------------------- 15 N 1 -2.323508575627217e-01 -2.323508578007878e-01 2.38066e-10 9.67954e-10 2 -3.876631157746108e-02 -3.876631258941474e-02 1.01195e-09 4.91735e-07 3 -7.796155592460117e-01 -7.796155648438116e-01 5.59780e-09 3.36437e-09 ----------------------------------------------------------------------------------------------------- 16 N 1 -2.633933187322438e+00 -2.633933185831652e+00 1.49079e-09 3.93245e-07 2 -3.936934548035116e-01 -3.936934524566541e-01 2.34686e-09 2.11552e-08 3 1.712870238286833e+00 1.712870238627937e+00 3.41104e-10 8.96235e-09 ----------------------------------------------------------------------------------------------------- 17 N 1 3.412933686392351e+00 3.412933685095202e+00 1.29715e-09 1.68394e-08 2 1.795802290378354e+00 1.795802290490636e+00 1.12282e-10 3.39337e-09 3 8.453049953255970e-01 8.453049923341455e-01 2.99145e-09 3.52059e-08 ----------------------------------------------------------------------------------------------------- 18 N 1 -2.372489554004788e+00 -2.372489553459074e+00 5.45715e-10 3.23039e-07 2 -2.797146545448402e+00 -2.797146545653788e+00 2.05385e-10 4.78035e-09 3 1.424290245778712e+00 1.424290239873566e+00 5.90515e-09 5.26918e-09 ----------------------------------------------------------------------------------------------------- 19 N 1 -1.186726762320103e+00 -1.186726761729192e+00 5.90912e-10 6.39614e-09 2 2.897832783189760e+00 2.897832783006933e+00 1.82827e-10 1.49375e-09 3 -2.275956593361737e+00 -2.275956593850298e+00 4.88561e-10 7.76711e-09 ----------------------------------------------------------------------------------------------------- 20 N 1 2.234959211548191e+00 2.234959212258649e+00 7.10458e-10 2.80444e-09 2 -1.516220837041992e+00 -1.516220837086581e+00 4.45894e-11 1.48095e-09 3 -1.484388760950905e+00 -1.484388761018149e+00 6.72449e-11 2.34363e-09 ----------------------------------------------------------------------------------------------------- 21 N 1 6.638975914002514e-01 6.638993512629807e-01 1.75986e-06 2.31728e-06 * 2 2.634025288510386e+00 2.634025283880554e+00 4.62983e-09 2.48308e-09 3 4.964432623997423e-01 4.964447441925119e-01 1.48179e-06 1.15020e-06 * ----------------------------------------------------------------------------------------------------- 22 N 1 -1.947329073278996e+00 -1.947329073422781e+00 1.43785e-10 7.28320e-09 2 1.732145835500031e+00 1.732145836563352e+00 1.06332e-09 1.35579e-08 3 1.633979926431600e+00 1.633979926440801e+00 9.20086e-12 5.62521e-09 ----------------------------------------------------------------------------------------------------- 23 N 1 -3.793874487645488e+00 -3.793874487422108e+00 2.23380e-10 1.69506e-09 2 2.202240043072212e+00 2.202240044101400e+00 1.02919e-09 2.28161e-09 3 -1.731614380308718e+00 -1.731614380464152e+00 1.55435e-10 1.30640e-09 ----------------------------------------------------------------------------------------------------- 24 N 1 1.728069640250776e+00 1.728069641296636e+00 1.04586e-09 1.89313e-07 2 -4.200259474828819e+00 -4.200259477060016e+00 2.23120e-09 3.01953e-07 3 -1.467221313750124e-01 -1.467221317691377e-01 3.94125e-10 2.98008e-07 ----------------------------------------------------------------------------------------------------- 25 N 1 4.673616240978672e-01 4.673616254827020e-01 1.38483e-09 1.62145e-08 2 -1.749110084286021e+00 -1.749110084668886e+00 3.82865e-10 6.26498e-09 3 -1.958228138638456e+00 -1.958228126486643e+00 1.21518e-08 1.85640e-08 ----------------------------------------------------------------------------------------------------- 26 N 1 -1.531281997619269e-01 -1.531281998822172e-01 1.20290e-10 1.30967e-09 2 -1.971007663951818e-01 -1.971007661563748e-01 2.38807e-10 1.12801e-08 3 -1.955103115100557e+00 -1.955103106967169e+00 8.13339e-09 6.52045e-08 ----------------------------------------------------------------------------------------------------- 27 N 1 -1.855114972502127e+00 -1.855114965744893e+00 6.75723e-09 5.24903e-08 2 4.774199760843833e+00 4.774199743372558e+00 1.74713e-08 1.61073e-07 3 -8.212600639906230e-01 -8.212600629262951e-01 1.06433e-09 7.23736e-09 ----------------------------------------------------------------------------------------------------- 28 N 1 3.491236446906859e+00 3.491236446903500e+00 3.35909e-12 1.15818e-07 2 -2.819122815917864e+00 -2.819122815871813e+00 4.60512e-11 8.68715e-08 3 5.328674407795146e-01 5.328674406863869e-01 9.31277e-11 4.80532e-10 ----------------------------------------------------------------------------------------------------- 29 N 1 2.026298668692048e+00 2.026298627446710e+00 4.12453e-08 3.72883e-07 2 2.215322191017275e-01 2.215322181090321e-01 9.92695e-10 5.29098e-09 3 4.025744083096971e-01 4.025744777982371e-01 6.94885e-08 3.57782e-07 ----------------------------------------------------------------------------------------------------- 30 N 1 -7.991100020033578e-01 -7.991099845897442e-01 1.74136e-08 1.32939e-07 2 -4.851659939021614e-01 -4.851660056811408e-01 1.17790e-08 1.65520e-07 3 2.619427821508268e+00 2.619427859607979e+00 3.80997e-08 7.80780e-07 * ----------------------------------------------------------------------------------------------------- 31 N 1 -9.310590143987919e-01 -9.310590331968217e-01 1.87980e-08 8.75295e-07 * 2 4.961235544547771e-02 4.961236234039425e-02 6.89492e-09 9.16577e-07 * 3 -4.206447493731448e+00 -4.206447499570927e+00 5.83948e-09 2.66792e-08 ----------------------------------------------------------------------------------------------------- 32 N 1 -6.010605019012859e-01 -6.010604944557876e-01 7.44550e-09 1.71690e-08 2 -3.164573835058505e+00 -3.164577081517045e+00 3.24646e-06 8.73917e-06 * 3 -7.956838765810093e-01 -7.956838776967852e-01 1.11578e-09 1.08681e-08 ----------------------------------------------------------------------------------------------------- * 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 = 29, direction = 3: |F_model - F_numer| error = ----------------------- = 1.72610e-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 = 3.700531771527949 | (Configuration in file "config-GaN.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 N 1 -9.340935045488179e-01 -9.340935045007037e-01 4.81142e-11 6.31900e-10 2 -1.204966604475293e+00 -1.204966604564042e+00 8.87492e-11 6.58398e-10 3 1.549279497781957e-01 1.549279497626286e-01 1.55672e-11 2.99983e-11 ----------------------------------------------------------------------------------------------------- 2 N 1 1.483733762472068e+00 1.483733763487537e+00 1.01547e-09 5.21338e-08 2 1.705240438640540e+00 1.705240440897846e+00 2.25731e-09 4.04779e-09 3 2.918449727268645e-01 2.918449716174035e-01 1.10946e-09 9.77113e-09 ----------------------------------------------------------------------------------------------------- 3 N 1 1.267525482585730e+00 1.267525482219896e+00 3.65834e-10 7.33579e-10 2 6.136050043311743e-01 6.136050042743708e-01 5.68035e-11 1.53888e-10 3 -5.412273472700705e-01 -5.412273473280684e-01 5.79979e-11 1.24709e-10 ----------------------------------------------------------------------------------------------------- 4 N 1 -2.817467978073493e-01 -2.817467963323688e-01 1.47498e-09 2.49026e-09 2 9.850008347398187e-01 9.850008247644482e-01 9.97537e-09 1.07458e-09 3 8.404276713211668e-01 8.404276720829505e-01 7.61784e-10 6.12403e-09 ----------------------------------------------------------------------------------------------------- 5 Ga 1 -3.509832178010005e+00 -3.509832177614274e+00 3.95731e-10 1.15507e-08 2 1.086501432542397e+00 1.086501432909087e+00 3.66690e-10 5.45457e-09 3 8.280145971687678e-01 8.280145975517600e-01 3.82992e-10 1.80336e-09 ----------------------------------------------------------------------------------------------------- 6 Ga 1 5.497147227326892e-01 5.497120414385999e-01 2.68129e-06 1.05255e-06 * 2 -5.877728730531523e-01 -5.877743373385046e-01 1.46429e-06 1.73423e-06 * 3 2.922745799253924e+00 2.922744481645163e+00 1.31761e-06 2.24943e-06 * ----------------------------------------------------------------------------------------------------- 7 Ga 1 -9.849304374981355e-01 -9.849304371978932e-01 3.00242e-10 4.11111e-09 2 3.878684980146449e+00 3.878684979579843e+00 5.66605e-10 6.23460e-10 3 2.183119763017458e+00 2.183119765068923e+00 2.05147e-09 4.13177e-08 ----------------------------------------------------------------------------------------------------- 8 N 1 1.840276768409413e+00 1.840276776430203e+00 8.02079e-09 4.74167e-08 2 -5.007257982780338e-01 -5.007257969637573e-01 1.31428e-09 4.10573e-09 3 -8.899085455920070e-01 -8.899085482845729e-01 2.69257e-09 2.29090e-08 ----------------------------------------------------------------------------------------------------- 9 Ga 1 -4.140370239023728e-01 -4.140370234066347e-01 4.95738e-10 3.20679e-09 2 -1.945489756543121e+00 -1.945489755511189e+00 1.03193e-09 3.58380e-08 3 -1.353593957870313e+00 -1.353593957874340e+00 4.02700e-12 1.85510e-09 ----------------------------------------------------------------------------------------------------- 10 Ga 1 -1.412220314990743e+00 -1.412220314561963e+00 4.28780e-10 2.93138e-09 2 9.207501930376950e-01 9.207501933816906e-01 3.43996e-10 2.31890e-09 3 -8.111489670316525e-01 -8.111489664292582e-01 6.02394e-10 5.61498e-09 ----------------------------------------------------------------------------------------------------- 11 Ga 1 3.288971763477063e+00 3.288971751684297e+00 1.17928e-08 2.91695e-08 2 -1.474332391409988e+00 -1.474332384647840e+00 6.76215e-09 3.50026e-08 3 1.408613801428961e+00 1.408613789974681e+00 1.14543e-08 1.54577e-08 ----------------------------------------------------------------------------------------------------- 12 Ga 1 -1.597310666159665e+00 -1.597310666667306e+00 5.07641e-10 1.38811e-08 2 3.230785707454849e+00 3.230785706838030e+00 6.16819e-10 6.66962e-06 * 3 4.693030363682021e-01 4.693030373034032e-01 9.35201e-10 9.64829e-09 ----------------------------------------------------------------------------------------------------- 13 Ga 1 1.638284815035774e+00 1.638284767635087e+00 4.74007e-08 4.75744e-07 * 2 -1.867910779981736e+00 -1.867913590962146e+00 2.81098e-06 7.51046e-07 * 3 -7.929178185790419e-01 -7.929170141221077e-01 8.04457e-07 1.98145e-06 * ----------------------------------------------------------------------------------------------------- 14 Ga 1 -1.455642778128879e+00 -1.455642778087066e+00 4.18130e-11 2.46064e-09 2 -1.493253122041617e+00 -1.493253121779689e+00 2.61928e-10 3.39599e-10 3 1.817687115453503e+00 1.817687115088207e+00 3.65296e-10 1.29662e-09 ----------------------------------------------------------------------------------------------------- 15 N 1 -1.810732597139971e+00 -1.810733606497199e+00 1.00936e-06 1.34910e-06 * 2 -5.565937154451540e-01 -5.565927049142605e-01 1.01053e-06 2.70039e-06 * 3 -1.033659221941795e+00 -1.033656378169342e+00 2.84377e-06 9.73305e-06 * ----------------------------------------------------------------------------------------------------- 16 Ga 1 1.591693309901457e+00 1.591693312677064e+00 2.77561e-09 2.27923e-08 2 2.589534066911101e+00 2.589534066323566e+00 5.87535e-10 1.39838e-08 3 1.747287126134027e+00 1.747287127864209e+00 1.73018e-09 3.52855e-08 ----------------------------------------------------------------------------------------------------- 17 N 1 -1.899170309967781e+00 -1.899170309234771e+00 7.33010e-10 3.39127e-09 2 1.423106603020162e+00 1.423106603420981e+00 4.00819e-10 2.84436e-09 3 -1.392467346182257e+00 -1.392467346238344e+00 5.60871e-11 8.49277e-10 ----------------------------------------------------------------------------------------------------- 18 Ga 1 1.014463622919006e+00 1.014463625562890e+00 2.64388e-09 9.31593e-08 2 -4.508290882901978e+00 -4.508290876764167e+00 6.13781e-09 2.86409e-08 3 -2.908616749355721e+00 -2.908616747445385e+00 1.91034e-09 2.30321e-08 ----------------------------------------------------------------------------------------------------- 19 N 1 1.408982498291029e+00 1.408982495278873e+00 3.01216e-09 1.08667e-08 2 1.601939443136582e+00 1.601939442679248e+00 4.57334e-10 9.97610e-10 3 1.856574372278027e+00 1.856574371792024e+00 4.86003e-10 7.88611e-09 ----------------------------------------------------------------------------------------------------- 20 Ga 1 -7.569150375762121e-01 -7.569150362443497e-01 1.33186e-09 8.12245e-09 2 -2.374593287199904e+00 -2.374593288213208e+00 1.01330e-09 9.04477e-09 3 1.870303316358499e+00 1.870303311025897e+00 5.33260e-09 8.71558e-09 ----------------------------------------------------------------------------------------------------- 21 N 1 1.342349323870973e-01 1.342349331839140e-01 7.96817e-10 8.19839e-09 2 8.217906999099175e-01 8.217907000975834e-01 1.87666e-10 6.57562e-09 3 -1.246854483080476e+00 -1.246854482461887e+00 6.18589e-10 9.08337e-10 ----------------------------------------------------------------------------------------------------- 22 Ga 1 8.664013473810934e-01 8.664013493360556e-01 1.95496e-09 3.37021e-09 2 -3.151649573382373e+00 -3.151649570977413e+00 2.40496e-09 1.19913e-08 3 -5.159142695777171e-01 -5.159142697047598e-01 1.27043e-10 1.94705e-09 ----------------------------------------------------------------------------------------------------- 23 N 1 7.261946957418408e-01 7.261946955169225e-01 2.24918e-10 3.92456e-09 2 1.168702287076820e+00 1.168702287056268e+00 2.05524e-11 5.86149e-09 3 -6.961909010879755e-01 -6.961909009258951e-01 1.62080e-10 2.92613e-09 ----------------------------------------------------------------------------------------------------- 24 N 1 -5.301544987299814e+00 -5.301544985740609e+00 1.55921e-09 3.41401e-09 2 -5.148033518507964e+00 -5.148033518520826e+00 1.28617e-11 1.40651e-09 3 -8.869294511540604e-01 -8.869294511545959e-01 5.35461e-13 2.46640e-10 ----------------------------------------------------------------------------------------------------- 25 Ga 1 -2.379885356305577e+00 -2.379885356060622e+00 2.44955e-10 2.11714e-09 2 2.019145695660612e-01 2.019145661604996e-01 3.40556e-09 1.77020e-08 3 1.189951935204985e+00 1.189951917211737e+00 1.79932e-08 3.01518e-08 ----------------------------------------------------------------------------------------------------- 26 Ga 1 1.580033833010654e+00 1.580033811647661e+00 2.13630e-08 8.40375e-08 2 1.188297449416061e+00 1.188297427254563e+00 2.21615e-08 4.21224e-08 3 1.019696645138553e+00 1.019696634478791e+00 1.06598e-08 3.86929e-08 ----------------------------------------------------------------------------------------------------- 27 N 1 -1.961173773067235e+00 -1.961173759555060e+00 1.35122e-08 7.43272e-08 2 -2.557149549698805e-01 -2.557149411101171e-01 1.38598e-08 3.15405e-08 3 -1.661674749100175e+00 -1.661674749419757e+00 3.19582e-10 7.73764e-08 ----------------------------------------------------------------------------------------------------- 28 N 1 1.131859339292524e+00 1.131859339255997e+00 3.65266e-11 6.54296e-10 2 -1.083236305268255e+00 -1.083236304694825e+00 5.73430e-10 3.35027e-09 3 -2.079271064526659e+00 -2.079271063724177e+00 8.02482e-10 1.97610e-08 ----------------------------------------------------------------------------------------------------- 29 Ga 1 2.690375456313668e+00 2.690375455768264e+00 5.45404e-10 7.97786e-07 * 2 1.033338008212799e+00 1.033338006717998e+00 1.49480e-09 1.81178e-08 3 1.602240551627379e-01 1.602240529058177e-01 2.25692e-09 3.93785e-08 ----------------------------------------------------------------------------------------------------- 30 N 1 -1.625516518249756e+00 -1.625516519135416e+00 8.85660e-10 5.24590e-09 2 -7.403227964617314e-01 -7.403227952298325e-01 1.23190e-09 2.06728e-09 3 -9.051391056684874e-01 -9.051391056246573e-01 4.38302e-11 2.03844e-09 ----------------------------------------------------------------------------------------------------- 31 N 1 6.505832952998885e+00 6.505832952525391e+00 4.73494e-10 2.11288e-09 2 5.138026565944722e+00 5.138026566143430e+00 1.98708e-10 6.93727e-10 3 5.638461247370393e-01 5.638461250291557e-01 2.92116e-10 1.12645e-09 ----------------------------------------------------------------------------------------------------- 32 N 1 -1.393827022297658e+00 -1.393827021266122e+00 1.03154e-09 2.77164e-08 2 -6.943319241669688e-01 -6.943319415471817e-01 1.73802e-08 2.49203e-07 * 3 -1.609054303512521e+00 -1.609054309989771e+00 6.47725e-09 2.62117e-08 ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as discontinuities. Maximum error obtained for particle = 27, direction = 2: |F_model - F_numer| error = ----------------------- = 5.42001e-08 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 1.72610e-07 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 1.72610e-07 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.