!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_ZhangTrinkle_2016_TiO__MO_612732924171_001 Supported species : O Ti random seed = 13 perturbation amplitude = 0.250 number unit cells per side = 2 ----------------------------------------------------------------------------------------------------- Comparison of analytical forces obtained from the model, the force computed as a numerical derivative of the energy, the difference between them, and the uncertainty in the numerical estimate of the force. The computed equilibrium lattice constant for the crystal (a0) is given in the heading. MONOATOMIC STRUCTURE -- Species = O | a0 = 3.4325170516967773 | (Configuration in file "config-O.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 O 1 1.767645297293968e-01 1.767645297282363e-01 1.16043e-12 4.46725e-07 * 2 2.385926081008855e-01 2.385926081017049e-01 8.19428e-13 2.11584e-12 3 2.751641757415170e-01 2.751641757423127e-01 7.95752e-13 3.76360e-12 ----------------------------------------------------------------------------------------------------- 2 O 1 -6.505020876208873e-01 -6.505020876208634e-01 2.39808e-14 2.52309e-12 2 -7.558146252738979e-01 -7.558146252739784e-01 8.04912e-14 3.54672e-12 3 4.101539591221023e-01 4.101539591219253e-01 1.76970e-13 4.48402e-12 ----------------------------------------------------------------------------------------------------- 3 O 1 -1.005775450395860e+00 -1.005775450396469e+00 6.08402e-13 3.87681e-11 2 4.830188394637912e-01 4.830188394667874e-01 2.99621e-12 1.36407e-11 3 -5.359678132025841e-01 -5.359678132033378e-01 7.53619e-13 3.48266e-12 ----------------------------------------------------------------------------------------------------- 4 O 1 7.469670621344281e-01 7.469670621343562e-01 7.19425e-14 8.24119e-13 2 -6.912272053660796e-01 -6.912272053661090e-01 2.94209e-14 1.30008e-11 3 -4.933827006328435e-01 -4.933827006327619e-01 8.16014e-14 3.80379e-12 ----------------------------------------------------------------------------------------------------- 5 O 1 4.751285786872130e-01 4.751285786873258e-01 1.12743e-13 2.78300e-12 2 5.801898691809048e-01 5.801898691829310e-01 2.02627e-12 2.68684e-09 * 3 1.626372542067204e-01 1.626372542009540e-01 5.76647e-12 7.30717e-10 * ----------------------------------------------------------------------------------------------------- 6 O 1 -4.608335656065853e-01 -4.608335656040507e-01 2.53458e-12 1.22949e-11 2 -6.725806243860267e-01 -6.725806243848390e-01 1.18772e-12 1.30604e-11 3 4.868838347887531e-01 4.868838347886812e-01 7.19425e-14 3.98403e-11 ----------------------------------------------------------------------------------------------------- 7 O 1 -2.610308939078376e-01 -2.610308939076273e-01 2.10276e-13 2.38330e-11 2 4.181877275636612e-01 4.181877275637869e-01 1.25677e-13 6.07842e-12 3 -2.612498208004533e-01 -2.612498208014216e-01 9.68281e-13 6.04811e-12 ----------------------------------------------------------------------------------------------------- 8 O 1 1.046976954740026e+00 1.046976954740612e+00 5.86420e-13 3.96128e-12 2 -2.878853907357656e-01 -2.878853907356853e-01 8.02691e-14 4.19226e-12 3 -7.284994223929757e-01 -7.284994223922810e-01 6.94667e-13 3.79075e-12 ----------------------------------------------------------------------------------------------------- 9 O 1 3.106218611942297e-01 3.106218611912668e-01 2.96291e-12 3.89553e-09 * 2 6.875872322800739e-01 6.875872322795828e-01 4.91052e-13 2.33047e-12 3 6.940910690393597e-01 6.940910690420540e-01 2.69429e-12 3.91005e-09 * ----------------------------------------------------------------------------------------------------- 10 O 1 -7.261246824049136e-01 -7.261246824049326e-01 1.89848e-14 2.86549e-12 2 -6.467237629918428e-01 -6.467237629922046e-01 3.61822e-13 8.55838e-12 3 3.856018721448581e-01 3.856018721449752e-01 1.17129e-13 2.51799e-12 ----------------------------------------------------------------------------------------------------- 11 O 1 -2.164321577015100e-02 -2.164321577008792e-02 6.30745e-14 8.46392e-12 2 1.204237563616396e+00 1.204237563616974e+00 5.77316e-13 2.40186e-12 3 -5.374361659814390e-01 -5.374361659820087e-01 5.69766e-13 8.12794e-13 ----------------------------------------------------------------------------------------------------- 12 O 1 5.142217163735631e-01 5.142217163743085e-01 7.45404e-13 1.05614e-11 2 -6.859458813466575e-01 -6.859458813512945e-01 4.63707e-12 2.97197e-11 3 -7.213546091409866e-01 -7.213546091395506e-01 1.43596e-12 1.80134e-12 ----------------------------------------------------------------------------------------------------- 13 O 1 3.489535145510055e-01 3.489535145515019e-01 4.96436e-13 4.42102e-12 2 9.110523685200844e-01 9.110523685221934e-01 2.10898e-12 2.87192e-12 3 1.303037228540986e+00 1.303037228541452e+00 4.65628e-13 2.03926e-12 ----------------------------------------------------------------------------------------------------- 14 O 1 -2.754396632027297e-01 -2.754396632028440e-01 1.14297e-13 2.23255e-12 2 -4.225100908949244e-01 -4.225100908954534e-01 5.29021e-13 5.76602e-11 3 1.722061028858167e-01 1.722061028862306e-01 4.13919e-13 3.66912e-12 ----------------------------------------------------------------------------------------------------- 15 O 1 -9.519865131647087e-01 -9.519865131645999e-01 1.08802e-13 1.01501e-11 2 8.752290990149563e-01 8.752290990155377e-01 5.81424e-13 3.76854e-12 3 -3.209132741354782e-01 -3.209132741359620e-01 4.83835e-13 7.06379e-13 ----------------------------------------------------------------------------------------------------- 16 O 1 8.093193920031820e-01 8.093193920031221e-01 5.99520e-14 2.98350e-12 2 -1.197881274640576e+00 -1.197881274640725e+00 1.48992e-13 3.91864e-12 3 -7.817565528696421e-01 -7.817565528696906e-01 4.85167e-14 6.42086e-12 ----------------------------------------------------------------------------------------------------- 17 O 1 1.047957531497518e+00 1.047957531497691e+00 1.73195e-13 8.11373e-12 2 5.569738162992908e-01 5.569738162973396e-01 1.95122e-12 1.59824e-11 3 6.810741028875620e-01 6.810741028880647e-01 5.02709e-13 1.89537e-12 ----------------------------------------------------------------------------------------------------- 18 O 1 -9.211393244474628e-01 -9.211393244492638e-01 1.80100e-12 1.92082e-11 2 -1.128096310021620e+00 -1.128096310020852e+00 7.67608e-13 1.50389e-11 3 7.379580311906274e-01 7.379580311881299e-01 2.49756e-12 2.56939e-12 ----------------------------------------------------------------------------------------------------- 19 O 1 -5.667280757963920e-01 -5.667280757964407e-01 4.87388e-14 1.10810e-11 2 9.798451156879030e-01 9.798451156881315e-01 2.28484e-13 7.94576e-12 3 -6.142216469041153e-01 -6.142216469016165e-01 2.49878e-12 5.64981e-12 ----------------------------------------------------------------------------------------------------- 20 O 1 4.208744890933218e-01 4.208744890924067e-01 9.15046e-13 7.87137e-12 2 -1.164460660972227e+00 -1.164460660972142e+00 8.59313e-14 1.06128e-11 3 -4.538169686002920e-01 -4.538169686006540e-01 3.61988e-13 2.62940e-12 ----------------------------------------------------------------------------------------------------- 21 O 1 7.912590206747698e-01 7.912590206739947e-01 7.75158e-13 4.19115e-11 2 8.301620250413110e-01 8.301620250398828e-01 1.42819e-12 5.36370e-11 3 4.998157084588142e-01 4.998157084585581e-01 2.56128e-13 2.19585e-11 ----------------------------------------------------------------------------------------------------- 22 O 1 -7.594141464056990e-01 -7.594141464072754e-01 1.57641e-12 1.40953e-11 2 -1.092937134760936e+00 -1.092937134761106e+00 1.69420e-13 2.04903e-12 3 9.780175160236811e-02 9.780175159963839e-02 2.72972e-12 6.44226e-12 ----------------------------------------------------------------------------------------------------- 23 O 1 -3.155541602538668e-01 -3.155541602539968e-01 1.29952e-13 9.59838e-12 2 6.380734881538026e-02 6.380734881503573e-02 3.44530e-13 4.29132e-12 3 -3.779306061451967e-01 -3.779306061477438e-01 2.54702e-12 2.78138e-11 ----------------------------------------------------------------------------------------------------- 24 O 1 2.898151019175695e-01 2.898151019176821e-01 1.12521e-13 5.01771e-11 2 -9.405579694963746e-01 -9.405579694949819e-01 1.39266e-12 2.81039e-11 3 -9.671129814940842e-02 -9.671129814990853e-02 5.00114e-13 2.10532e-12 ----------------------------------------------------------------------------------------------------- 25 O 1 3.857870553899221e-01 3.857870553901001e-01 1.77969e-13 2.32980e-12 2 8.526043997681740e-01 8.526043997682264e-01 5.24025e-14 1.38203e-11 3 4.584760852199582e-01 4.584760852202833e-01 3.25129e-13 1.76353e-12 ----------------------------------------------------------------------------------------------------- 26 O 1 -7.031542549213695e-01 -7.031542549218430e-01 4.73510e-13 1.18143e-11 2 -9.144810872547839e-01 -9.144810872508236e-01 3.96039e-12 5.63480e-11 3 9.771384221034445e-01 9.771384221042149e-01 7.70384e-13 1.60955e-11 ----------------------------------------------------------------------------------------------------- 27 O 1 -6.957527643484124e-01 -6.957527643490347e-01 6.22280e-13 9.59166e-12 2 1.247778303846541e+00 1.247778303850537e+00 3.99614e-12 5.82305e-11 * 3 -4.852488396140467e-01 -4.852488396097462e-01 4.30045e-12 8.49212e-11 * ----------------------------------------------------------------------------------------------------- 28 O 1 6.002905087791576e-01 6.002905087794559e-01 2.98317e-13 1.55645e-11 2 -3.581290767628806e-01 -3.581290767616971e-01 1.18355e-12 1.52367e-11 3 -4.158382507217816e-01 -4.158382507223835e-01 6.01907e-13 7.69057e-12 ----------------------------------------------------------------------------------------------------- 29 O 1 7.462756252375524e-01 7.462756252392250e-01 1.67255e-12 4.46534e-11 2 1.294193076576651e+00 1.294193076580644e+00 3.99347e-12 7.54221e-11 * 3 -4.101229710933571e-01 -4.101229710922283e-01 1.12876e-12 1.90383e-10 * ----------------------------------------------------------------------------------------------------- 30 O 1 -4.034245700846663e-01 -4.034245700848332e-01 1.66922e-13 1.44351e-11 2 -6.507358065492502e-01 -6.507358065489453e-01 3.04978e-13 1.30689e-11 3 4.630506375929035e-01 4.630506375915098e-01 1.39377e-12 1.28601e-11 ----------------------------------------------------------------------------------------------------- 31 O 1 -1.758438831038673e-01 -1.758438831039305e-01 6.31994e-14 3.29040e-12 2 8.784034558294405e-01 8.784034558297537e-01 3.13194e-13 4.26370e-12 3 -1.145674817080354e-01 -1.145674817065518e-01 1.48359e-12 2.25439e-12 ----------------------------------------------------------------------------------------------------- 32 O 1 1.831343094325556e-01 1.831343094324642e-01 9.13714e-14 5.70367e-11 2 -4.918959481516008e-01 -4.918959481525644e-01 9.63618e-13 4.36057e-12 3 -4.560718134331568e-01 -4.560718134338009e-01 6.44096e-13 1.27232e-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 = 22, direction = 3: |F_model - F_numer| error = ----------------------- = 2.79107e-11 max{|F_numer|, eps} Comparison of analytical forces obtained from the model, the force computed as a numerical derivative of the energy, the difference between them, and the uncertainty in the numerical estimate of the force. The computed equilibrium lattice constant for the crystal (a0) is given in the heading. MONOATOMIC STRUCTURE -- Species = Ti | a0 = 2.9145584106445312 | (Configuration in file "config-Ti.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ti 1 -1.387968513507220e+00 -1.387968513515550e+00 8.33067e-12 1.30562e-10 2 -9.037725426022496e+00 -9.037725426040963e+00 1.84670e-11 3.43039e-10 3 -1.009214661521177e+01 -1.009214661520219e+01 9.58522e-12 1.41274e-11 ----------------------------------------------------------------------------------------------------- 2 Ti 1 1.643015811995841e+01 1.643015811989478e+01 6.36255e-11 2.16183e-10 2 -1.253187534866812e+01 -1.253187534869103e+01 2.29132e-11 4.10861e-10 3 -1.928211573307655e+01 -1.928211573320373e+01 1.27176e-10 1.21062e-09 ----------------------------------------------------------------------------------------------------- 3 Ti 1 9.755565263731262e+00 9.755565263727515e+00 3.74634e-12 1.95719e-11 2 -8.266776760300688e-01 -8.266776760379159e-01 7.84706e-12 8.68450e-11 3 9.854709831049801e+00 9.854709831053951e+00 4.14957e-12 2.43180e-10 ----------------------------------------------------------------------------------------------------- 4 Ti 1 -1.259298216185305e+01 -1.259298216203914e+01 1.86095e-10 1.55998e-09 2 2.280967793607957e+01 2.280967793627980e+01 2.00231e-10 8.32497e-10 3 2.452850623988343e+00 2.452850623987347e+00 9.95648e-13 1.54577e-09 ----------------------------------------------------------------------------------------------------- 5 Ti 1 -1.883589292070800e+00 -1.883589291917909e+00 1.52891e-10 1.02817e-09 2 -4.040932205800835e+00 -4.040932205742276e+00 5.85585e-11 9.07673e-10 3 -3.764272466105202e+00 -3.764272466120398e+00 1.51954e-11 3.33216e-10 ----------------------------------------------------------------------------------------------------- 6 Ti 1 5.667059993539637e+00 5.667059993565402e+00 2.57652e-11 1.87803e-10 2 2.404266223216668e+00 2.404266223225809e+00 9.14158e-12 1.09976e-10 3 -6.933534045748672e+00 -6.933534045749003e+00 3.30402e-13 5.81880e-09 * ----------------------------------------------------------------------------------------------------- 7 Ti 1 4.591378146210580e+00 4.591378146207975e+00 2.60503e-12 5.13518e-11 2 -7.010120522276013e+00 -7.010120522290391e+00 1.43778e-11 2.09420e-10 3 2.703704673121417e+00 2.703704673093292e+00 2.81251e-11 4.01286e-10 ----------------------------------------------------------------------------------------------------- 8 Ti 1 8.134785222861820e+00 8.134785222919838e+00 5.80176e-11 1.09440e-09 2 -2.165429985907528e+01 -2.165429985855408e+01 5.21208e-10 1.07459e-09 3 -1.869231501475779e+01 -1.869231501509161e+01 3.33817e-10 1.55931e-09 ----------------------------------------------------------------------------------------------------- 9 Ti 1 -2.786050956849105e+01 -2.786050956832769e+01 1.63361e-10 2.16702e-09 2 8.579969362403885e+00 8.579969362330507e+00 7.33777e-11 1.44698e-10 3 -1.471259509715859e+01 -1.471259509694548e+01 2.13110e-10 1.19689e-09 ----------------------------------------------------------------------------------------------------- 10 Ti 1 -1.506503237581937e+01 -1.506503237585873e+01 3.93623e-11 4.27498e-11 2 2.329730031993360e+01 2.329730031985111e+01 8.24940e-11 6.17678e-10 3 -1.448213439563357e+01 -1.448213439568757e+01 5.39977e-11 3.59904e-10 ----------------------------------------------------------------------------------------------------- 11 Ti 1 -7.990393770903302e-01 -7.990393770462171e-01 4.41132e-11 2.58797e-09 2 5.566544604593512e+00 5.566544604571441e+00 2.20703e-11 2.06906e-10 3 1.871978289973024e+01 1.871978289970052e+01 2.97220e-11 9.02805e-10 ----------------------------------------------------------------------------------------------------- 12 Ti 1 -5.305596888009935e+00 -5.305596888015741e+00 5.80602e-12 2.96478e-10 2 7.646885064421348e+00 7.646885064429791e+00 8.44302e-12 2.43459e-10 3 2.699581566038672e+00 2.699581566053675e+00 1.50031e-11 1.02714e-10 ----------------------------------------------------------------------------------------------------- 13 Ti 1 -6.288243078889231e-01 -6.288243079496562e-01 6.07331e-11 7.51037e-07 * 2 -1.718463682211265e+01 -1.718463682216418e+01 5.15215e-11 2.76657e-10 3 -1.699319588095417e+01 -1.699319588094295e+01 1.12195e-11 2.27409e-10 ----------------------------------------------------------------------------------------------------- 14 Ti 1 3.884271993028942e+00 3.884271993031505e+00 2.56328e-12 2.57192e-10 2 8.175911249298343e+00 8.175911249256565e+00 4.17781e-11 3.46182e-10 3 -7.219158617397791e+00 -7.219158617396126e+00 1.66533e-12 3.71792e-08 * ----------------------------------------------------------------------------------------------------- 15 Ti 1 2.119070507590342e+01 2.119070507601238e+01 1.08955e-10 4.32799e-10 2 -1.075989841097622e+01 -1.075989841101358e+01 3.73586e-11 3.43528e-10 3 5.897444485334728e+00 5.897444485296674e+00 3.80540e-11 6.54386e-10 ----------------------------------------------------------------------------------------------------- 16 Ti 1 -2.738761880373689e+00 -2.738761880275217e+00 9.84719e-11 8.46093e-10 2 2.428392545160918e+01 2.428392545161478e+01 5.60263e-12 6.01492e-10 3 1.215323856099765e+01 1.215323856102147e+01 2.38227e-11 1.35030e-09 ----------------------------------------------------------------------------------------------------- 17 Ti 1 -2.988269828198304e+00 -2.988269828185009e+00 1.32947e-11 1.66422e-11 2 -1.522530950327490e+01 -1.522530950325729e+01 1.76126e-11 1.60624e-10 3 1.335235430246749e+01 1.335235430246521e+01 2.28795e-12 1.22453e-10 ----------------------------------------------------------------------------------------------------- 18 Ti 1 -1.220844931312505e+01 -1.220844931362645e+01 5.01396e-10 2.80158e-09 2 -4.816494747498573e+00 -4.816494747062253e+00 4.36319e-10 3.70116e-09 3 6.030510687074999e+00 6.030510687045577e+00 2.94218e-11 1.23915e-10 ----------------------------------------------------------------------------------------------------- 19 Ti 1 3.010925540992953e+00 3.010925540986632e+00 6.32028e-12 2.15219e-11 2 -5.994144678509643e+00 -5.994144678522751e+00 1.31086e-11 5.69553e-11 3 -1.155940964233239e+00 -1.155940964208210e+00 2.50291e-11 5.75697e-11 ----------------------------------------------------------------------------------------------------- 20 Ti 1 -1.225264133370069e+01 -1.225264133375109e+01 5.04059e-11 4.41108e-10 2 5.443066490472584e+00 5.443066490517120e+00 4.45359e-11 9.53135e-10 3 8.313193561019435e+00 8.313193560948358e+00 7.10774e-11 2.68949e-10 ----------------------------------------------------------------------------------------------------- 21 Ti 1 -2.163020781209194e+00 -2.163020781209577e+00 3.82805e-13 1.08971e-10 2 -1.673628380077804e+01 -1.673628380078311e+01 5.06972e-12 1.02421e-10 3 -1.447408389231136e+01 -1.447408389225528e+01 5.60743e-11 1.17727e-09 ----------------------------------------------------------------------------------------------------- 22 Ti 1 2.313654489021783e+01 2.313654489025096e+01 3.31326e-11 2.36753e-10 2 -1.869176065346242e+01 -1.869176065351380e+01 5.13829e-11 1.09953e-10 3 5.081198379868922e+00 5.081198379891497e+00 2.25757e-11 2.14866e-09 ----------------------------------------------------------------------------------------------------- 23 Ti 1 1.205628036037506e+01 1.205628036035938e+01 1.56746e-11 4.48063e-10 2 3.187760577220136e+00 3.187760577222039e+00 1.90292e-12 8.34035e-11 3 1.123320416705951e+01 1.123320416707510e+01 1.55929e-11 4.90967e-11 ----------------------------------------------------------------------------------------------------- 24 Ti 1 -1.744654468658234e+00 -1.744654468691115e+00 3.28810e-11 1.10399e-06 * 2 -1.970968715112140e+00 -1.970968715121031e+00 8.89111e-12 6.96297e-10 3 9.252310458161565e+00 9.252310458174401e+00 1.28360e-11 5.99437e-10 ----------------------------------------------------------------------------------------------------- 25 Ti 1 -6.381165088634758e+00 -6.381165088143060e+00 4.91697e-10 1.77863e-09 2 -5.072993053717503e+00 -5.072993054261498e+00 5.43995e-10 8.22588e-10 3 -9.072212347555343e+00 -9.072212347560553e+00 5.21005e-12 3.48729e-07 * ----------------------------------------------------------------------------------------------------- 26 Ti 1 8.428772155094375e+00 8.428772154998892e+00 9.54827e-11 6.09219e-11 2 6.232851486786503e+00 6.232851486861927e+00 7.54241e-11 5.38861e-10 3 -4.947489367689723e+00 -4.947489367768815e+00 7.90923e-11 6.25102e-10 ----------------------------------------------------------------------------------------------------- 27 Ti 1 -4.761670665449780e-01 -4.761670665677042e-01 2.27262e-11 3.08741e-10 2 4.790449222521599e+00 4.790449222430989e+00 9.06102e-11 3.57384e-10 3 1.134696447813924e+01 1.134696447820867e+01 6.94307e-11 1.28205e-10 ----------------------------------------------------------------------------------------------------- 28 Ti 1 -3.040824047610202e+00 -3.040824047604475e+00 5.72697e-12 1.10671e-08 * 2 3.945509329109094e+00 3.945509329103106e+00 5.98810e-12 9.24955e-10 3 5.779621526102662e+00 5.779621526147967e+00 4.53051e-11 3.98490e-11 ----------------------------------------------------------------------------------------------------- 29 Ti 1 -1.418117462867325e+01 -1.418117462765222e+01 1.02104e-09 4.87503e-09 * 2 1.128398964720117e+01 1.128398964725519e+01 5.40172e-11 8.27603e-10 3 5.812716128618481e+00 5.812716128700154e+00 8.16724e-11 1.86394e-10 ----------------------------------------------------------------------------------------------------- 30 Ti 1 8.167524845932673e+00 8.167524845942735e+00 1.00613e-11 2.16772e-10 2 1.315114333581046e+01 1.315114333583164e+01 2.11813e-11 1.18339e-10 3 1.855960915205980e+00 1.855960915191950e+00 1.40301e-11 3.46776e-10 ----------------------------------------------------------------------------------------------------- 31 Ti 1 7.884493446357727e+00 7.884493446420170e+00 6.24434e-11 9.32987e-11 2 -5.276985967414198e+00 -5.276985967413622e+00 5.76428e-13 8.11821e-09 * 3 6.708696515567744e+00 6.708696515547099e+00 2.06448e-11 7.27320e-11 ----------------------------------------------------------------------------------------------------- 32 Ti 1 -8.639794132745658e+00 -8.639794132739274e+00 6.38423e-12 1.91098e-08 * 2 6.031857090051431e+00 6.031857090076793e+00 2.53619e-11 5.88776e-10 3 2.573150678286892e+00 2.573150678437885e+00 1.50993e-10 9.51546e-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 = 25, direction = 2: |F_model - F_numer| error = ----------------------- = 1.07234e-10 max{|F_numer|, eps} Comparison of analytical forces obtained from the model, the force computed as a numerical derivative of the energy, the difference between them, and the uncertainty in the numerical estimate of the force. The computed equilibrium lattice constant for the crystal (a0) is given in the heading. MIXED STRUCTURE -- Species = O Ti | a0 = 2.679803131759399 | (Configuration in file "config-OTi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 O 1 -1.800328583336377e+00 -1.800328583341244e+00 4.86677e-12 1.26937e-10 2 -1.053718756297158e+00 -1.053718756309881e+00 1.27223e-11 3.75535e-11 3 5.576221556670287e-01 5.576221556774981e-01 1.04694e-11 4.44952e-10 ----------------------------------------------------------------------------------------------------- 2 Ti 1 -2.133019984297350e+01 -2.133019984293455e+01 3.89520e-11 1.00588e-10 2 1.245496602279340e+01 1.245496602281995e+01 2.65512e-11 2.34616e-10 3 -2.493664709860291e+01 -2.493664709809296e+01 5.09953e-10 1.19354e-09 ----------------------------------------------------------------------------------------------------- 3 Ti 1 -8.759668643875761e+00 -8.759668643889196e+00 1.34346e-11 4.55636e-12 2 -3.575395038213804e+01 -3.575395038212541e+01 1.26334e-11 2.51433e-10 3 1.405786448306104e+01 1.405786448305217e+01 8.87468e-12 1.59320e-10 ----------------------------------------------------------------------------------------------------- 4 Ti 1 -2.089613501457363e+01 -2.089613501451427e+01 5.93587e-11 2.34266e-10 2 8.637238429468109e+00 8.637238429425425e+00 4.26841e-11 7.78009e-11 3 8.933539244497219e+00 8.933539244490630e+00 6.58851e-12 3.17018e-10 ----------------------------------------------------------------------------------------------------- 5 Ti 1 5.710711578402579e+00 5.710711578397981e+00 4.59810e-12 2.48057e-10 2 -3.952834716475246e+01 -3.952834716466331e+01 8.91518e-11 2.19146e-10 3 -3.644625858026345e+01 -3.644625858014422e+01 1.19229e-10 3.53756e-09 * ----------------------------------------------------------------------------------------------------- 6 Ti 1 3.198731683072709e+01 3.198731683071170e+01 1.53904e-11 2.44981e-10 2 1.884275950032329e+01 1.884275950029166e+01 3.16369e-11 2.48789e-10 3 -2.064274683692373e+01 -2.064274683687519e+01 4.85443e-11 8.21391e-10 ----------------------------------------------------------------------------------------------------- 7 Ti 1 8.862935534065384e+00 8.862935534068082e+00 2.69829e-12 5.06335e-10 2 -1.831726673104584e+01 -1.831726673104113e+01 4.71090e-12 5.19428e-10 3 1.189488600096150e+01 1.189488600091958e+01 4.19185e-11 6.33928e-11 ----------------------------------------------------------------------------------------------------- 8 Ti 1 8.666648443043043e+00 8.666648443032562e+00 1.04805e-11 7.24305e-09 * 2 3.561364375022774e+01 3.561364374951579e+01 7.11950e-10 3.73874e-09 * 3 3.909047838567156e+01 3.909047838519015e+01 4.81407e-10 2.99008e-09 * ----------------------------------------------------------------------------------------------------- 9 Ti 1 -6.902956598912946e+00 -6.902956598889443e+00 2.35021e-11 1.51654e-10 2 8.187361806292593e+00 8.187361806288550e+00 4.04299e-12 9.49729e-11 3 -2.421469966448315e+00 -2.421469966443914e+00 4.40092e-12 1.76951e-10 ----------------------------------------------------------------------------------------------------- 10 O 1 -2.289122621762569e-01 -2.289122621763337e-01 7.67442e-14 7.05861e-11 2 1.907981242062009e+00 1.907981242068958e+00 6.94911e-12 4.38907e-11 3 -3.862526502624608e+00 -3.862526502621561e+00 3.04690e-12 1.49658e-11 ----------------------------------------------------------------------------------------------------- 11 O 1 -1.370988510969255e+00 -1.370988510975627e+00 6.37268e-12 5.88629e-08 * 2 -7.277207978095011e-02 -7.277207977853863e-02 2.41149e-12 9.17461e-11 3 -5.042874760495038e+00 -5.042874760529490e+00 3.44524e-11 2.41303e-10 ----------------------------------------------------------------------------------------------------- 12 O 1 -4.800350162742452e+00 -4.800350162741217e+00 1.23546e-12 1.64748e-11 2 1.374056508879889e+00 1.374056508881669e+00 1.78035e-12 4.42631e-10 3 -3.180585813781995e+00 -3.180585813780823e+00 1.17195e-12 4.38724e-09 * ----------------------------------------------------------------------------------------------------- 13 O 1 -3.077119461102360e-02 -3.077119460787565e-02 3.14794e-12 5.41572e-11 2 3.788695347741505e+00 3.788695347743959e+00 2.45448e-12 9.67679e-11 3 3.526042908784122e+00 3.526042908797225e+00 1.31029e-11 2.14166e-10 ----------------------------------------------------------------------------------------------------- 14 Ti 1 4.464059517196186e-01 4.464059517170606e-01 2.55795e-12 7.93921e-11 2 9.965530627990972e-01 9.965530628085487e-01 9.45155e-12 5.01778e-11 3 -3.441538045467281e+00 -3.441538045468843e+00 1.56186e-12 9.49774e-11 ----------------------------------------------------------------------------------------------------- 15 O 1 -2.265659691120359e+00 -2.265659691135020e+00 1.46607e-11 2.68184e-10 2 4.459252223946900e+00 4.459252223936610e+00 1.02904e-11 7.17630e-11 3 2.022586475632166e+00 2.022586475634371e+00 2.20579e-12 1.06609e-10 ----------------------------------------------------------------------------------------------------- 16 O 1 5.781125445960858e+00 5.781125445897349e+00 6.35092e-11 2.93140e-10 2 4.200812196479960e-02 4.200812197762566e-02 1.28261e-11 3.31250e-10 3 -4.252785918927507e+00 -4.252785919010897e+00 8.33902e-11 2.14078e-10 ----------------------------------------------------------------------------------------------------- 17 O 1 -1.780839265564391e+00 -1.780839265580705e+00 1.63136e-11 1.08732e-09 2 -9.092076947660940e-01 -9.092076948232799e-01 5.71859e-11 2.08708e-10 3 7.130194826981582e-01 7.130194826990888e-01 9.30589e-13 2.72271e-11 ----------------------------------------------------------------------------------------------------- 18 O 1 -3.236304783758014e-01 -3.236304783921923e-01 1.63909e-11 4.17654e-10 2 -2.664897533434571e+00 -2.664897533503098e+00 6.85270e-11 2.84895e-10 3 4.229098539574739e+00 4.229098539568472e+00 6.26699e-12 6.14317e-11 ----------------------------------------------------------------------------------------------------- 19 Ti 1 1.052765603820874e+01 1.052765603819315e+01 1.55946e-11 2.54770e-10 2 -2.011382461051295e+01 -2.011382461051568e+01 2.73559e-12 1.46915e-10 3 7.773032824410224e-01 7.773032824483120e-01 7.28961e-12 8.02675e-10 ----------------------------------------------------------------------------------------------------- 20 Ti 1 -2.701880487597109e+01 -2.701880487602388e+01 5.27969e-11 1.79955e-08 * 2 -1.464362309482451e+00 -1.464362309475955e+00 6.49569e-12 1.72087e-10 3 -5.756037731773715e-01 -5.756037731780325e-01 6.60916e-13 4.28115e-11 ----------------------------------------------------------------------------------------------------- 21 O 1 1.805369265412172e+00 1.805369265328732e+00 8.34404e-11 2.55167e-10 2 -6.589030695427320e-01 -6.589030697640751e-01 2.21343e-10 5.46340e-10 3 1.651457618782916e+00 1.651457618817072e+00 3.41565e-11 1.04775e-09 ----------------------------------------------------------------------------------------------------- 22 O 1 -5.363045100753627e-01 -5.363045101129273e-01 3.75646e-11 7.39565e-10 2 2.515454302044381e+00 2.515454302040085e+00 4.29656e-12 5.82481e-11 3 1.092255822681982e+00 1.092255822682036e+00 5.44009e-14 1.35146e-10 ----------------------------------------------------------------------------------------------------- 23 Ti 1 8.965254807452904e+00 8.965254807447504e+00 5.40012e-12 1.68985e-11 2 -1.078405225145755e+01 -1.078405225146518e+01 7.63656e-12 1.31507e-06 * 3 2.635312135493792e+00 2.635312135500012e+00 6.21991e-12 1.65888e-05 * ----------------------------------------------------------------------------------------------------- 24 Ti 1 -5.759067901532163e-01 -5.759067901435753e-01 9.64107e-12 8.07233e-10 2 1.075420596896061e+01 1.075420596886227e+01 9.83409e-11 5.92600e-10 3 -3.489607307960469e+00 -3.489607308067995e+00 1.07526e-10 2.89434e-10 ----------------------------------------------------------------------------------------------------- 25 O 1 -3.008655412331065e+00 -3.008655412329694e+00 1.37046e-12 2.19901e-10 2 -2.558825155121613e+00 -2.558825155119443e+00 2.16982e-12 5.42295e-09 * 3 1.853530406626297e+00 1.853530406631502e+00 5.20473e-12 8.52529e-11 ----------------------------------------------------------------------------------------------------- 26 Ti 1 1.003571000347391e+01 1.003571000348319e+01 9.28146e-12 1.70404e-10 2 8.010104275477586e+00 8.010104275494980e+00 1.73941e-11 1.12086e-09 3 -6.972540337736040e+00 -6.972540337732686e+00 3.35376e-12 1.90805e-10 ----------------------------------------------------------------------------------------------------- 27 Ti 1 6.375513355484549e+00 6.375513355504171e+00 1.96216e-11 1.28963e-10 2 1.410547604401621e+01 1.410547604389070e+01 1.25510e-10 2.51671e-10 3 1.220268729549413e+01 1.220268729549316e+01 9.71667e-13 6.10640e-10 ----------------------------------------------------------------------------------------------------- 28 O 1 -4.720987853750997e+00 -4.720987853746404e+00 4.59277e-12 1.09530e-10 2 8.028357439113677e-01 8.028357439104766e-01 8.91065e-13 4.81742e-10 3 3.215473762107181e+00 3.215473762115590e+00 8.40927e-12 4.93552e-11 ----------------------------------------------------------------------------------------------------- 29 O 1 8.009907542426888e+00 8.009907542441093e+00 1.42055e-11 2.01410e-10 2 2.115515849394549e+00 2.115515849385779e+00 8.76943e-12 1.74673e-10 3 3.369080189086708e+00 3.369080189103993e+00 1.72844e-11 1.97946e-09 * ----------------------------------------------------------------------------------------------------- 30 Ti 1 -3.631399598171031e+00 -3.631399598323646e+00 1.52615e-10 2.56375e-10 2 -7.293086568945290e-01 -7.293086568798611e-01 1.46678e-11 9.13927e-11 3 5.706233787306473e+00 5.706233787265451e+00 4.10214e-11 1.72444e-10 ----------------------------------------------------------------------------------------------------- 31 O 1 -2.316758832018812e+00 -2.316758832013688e+00 5.12346e-12 1.67311e-10 2 2.348824055707193e+00 2.348824055716360e+00 9.16645e-12 5.86597e-11 3 -3.580955006976026e+00 -3.580955007114190e+00 1.38164e-10 4.09027e-10 ----------------------------------------------------------------------------------------------------- 32 O 1 5.124703325325590e+00 5.124703325312403e+00 1.31868e-11 7.34159e-11 2 -2.347495860784354e+00 -2.347495860773769e+00 1.05858e-11 8.56661e-11 3 1.317667972816710e+00 1.317667972815641e+00 1.06937e-12 3.03384e-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 = 21, direction = 2: |F_model - F_numer| error = ----------------------- = 3.35927e-10 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 3.35927e-10 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 3.35927e-10 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.