!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_002 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 2.385926081017050e-01 8.19483e-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 -7.558146252739785e-01 8.06022e-14 3.54639e-12 3 4.101539591221023e-01 4.101539591219254e-01 1.76859e-13 4.48402e-12 ----------------------------------------------------------------------------------------------------- 3 O 1 -1.005775450395860e+00 -1.005775450396469e+00 6.08624e-13 3.87679e-11 2 4.830188394637912e-01 4.830188394667875e-01 2.99627e-12 1.36410e-11 3 -5.359678132025841e-01 -5.359678132033378e-01 7.53619e-13 3.48244e-12 ----------------------------------------------------------------------------------------------------- 4 O 1 7.469670621344281e-01 7.469670621343557e-01 7.23865e-14 8.23008e-13 2 -6.912272053660796e-01 -6.912272053661093e-01 2.96430e-14 1.30006e-11 3 -4.933827006328435e-01 -4.933827006327619e-01 8.16014e-14 3.80379e-12 ----------------------------------------------------------------------------------------------------- 5 O 1 4.751285786872130e-01 4.751285786873259e-01 1.12854e-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 -4.608335656040508e-01 2.53453e-12 1.22946e-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 2.10221e-13 2.38332e-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 -2.878853907356854e-01 8.02136e-14 4.19231e-12 3 -7.284994223929757e-01 -7.284994223922812e-01 6.94556e-13 3.79063e-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 2.33091e-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 -6.467237629922044e-01 3.61600e-13 8.55771e-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 -5.374361659820088e-01 5.69877e-13 8.11795e-13 ----------------------------------------------------------------------------------------------------- 12 O 1 5.142217163735631e-01 5.142217163743085e-01 7.45404e-13 1.05614e-11 2 -6.859458813466575e-01 -6.859458813512948e-01 4.63729e-12 2.97197e-11 3 -7.213546091409866e-01 -7.213546091395507e-01 1.43585e-12 1.80167e-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 4.66072e-13 2.03926e-12 ----------------------------------------------------------------------------------------------------- 14 O 1 -2.754396632027297e-01 -2.754396632028441e-01 1.14408e-13 2.23255e-12 2 -4.225100908949244e-01 -4.225100908954535e-01 5.29132e-13 5.76604e-11 3 1.722061028858167e-01 1.722061028862306e-01 4.13947e-13 3.66909e-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 -3.209132741359622e-01 4.83946e-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 3.91820e-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 8.11595e-12 2 5.569738162992908e-01 5.569738162973398e-01 1.95099e-12 1.59824e-11 3 6.810741028875620e-01 6.810741028880647e-01 5.02709e-13 1.89537e-12 ----------------------------------------------------------------------------------------------------- 18 O 1 -9.211393244474628e-01 -9.211393244492639e-01 1.80111e-12 1.92081e-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 9.798451156881316e-01 2.28595e-13 7.94653e-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 -4.538169686006541e-01 3.62044e-13 2.62912e-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 5.36374e-11 3 4.998157084588142e-01 4.998157084585581e-01 2.56128e-13 2.19585e-11 ----------------------------------------------------------------------------------------------------- 22 O 1 -7.594141464056990e-01 -7.594141464072757e-01 1.57663e-12 1.40957e-11 2 -1.092937134760936e+00 -1.092937134761106e+00 1.69420e-13 2.04903e-12 3 9.780175160236811e-02 9.780175159963840e-02 2.72971e-12 6.44233e-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 -9.405579694949822e-01 1.39244e-12 2.81039e-11 3 -9.671129814940842e-02 -9.671129814990853e-02 5.00114e-13 2.10532e-12 ----------------------------------------------------------------------------------------------------- 25 O 1 3.857870553899221e-01 3.857870553901002e-01 1.78080e-13 2.32980e-12 2 8.526043997681740e-01 8.526043997682264e-01 5.24025e-14 1.38203e-11 3 4.584760852199582e-01 4.584760852202834e-01 3.25240e-13 1.76353e-12 ----------------------------------------------------------------------------------------------------- 26 O 1 -7.031542549213695e-01 -7.031542549218432e-01 4.73732e-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 9.59188e-12 2 1.247778303846541e+00 1.247778303850537e+00 3.99636e-12 5.82294e-11 * 3 -4.852488396140467e-01 -4.852488396097464e-01 4.30034e-12 8.49212e-11 * ----------------------------------------------------------------------------------------------------- 28 O 1 6.002905087791576e-01 6.002905087794561e-01 2.98539e-13 1.55645e-11 2 -3.581290767628806e-01 -3.581290767616971e-01 1.18355e-12 1.52367e-11 3 -4.158382507217816e-01 -4.158382507223836e-01 6.01963e-13 7.69029e-12 ----------------------------------------------------------------------------------------------------- 29 O 1 7.462756252375524e-01 7.462756252392251e-01 1.67266e-12 4.46537e-11 2 1.294193076576651e+00 1.294193076580644e+00 3.99347e-12 7.54221e-11 * 3 -4.101229710933571e-01 -4.101229710922284e-01 1.12865e-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 8.784034558297538e-01 3.13305e-13 4.26315e-12 3 -1.145674817080354e-01 -1.145674817065518e-01 1.48356e-12 2.25439e-12 ----------------------------------------------------------------------------------------------------- 32 O 1 1.831343094325556e-01 1.831343094324643e-01 9.13158e-14 5.70367e-11 2 -4.918959481516008e-01 -4.918959481525646e-01 9.63840e-13 4.36101e-12 3 -4.560718134331568e-01 -4.560718134338009e-01 6.44151e-13 1.27204e-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 = ----------------------- = 2.79106e-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 8.33045e-12 1.30561e-10 2 -9.037725426022496e+00 -9.037725426040963e+00 1.84670e-11 3.43039e-10 3 -1.009214661521177e+01 -1.009214661520219e+01 9.58167e-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 4.10854e-10 3 -1.928211573307655e+01 -1.928211573320374e+01 1.27184e-10 1.21060e-09 ----------------------------------------------------------------------------------------------------- 3 Ti 1 9.755565263731262e+00 9.755565263727517e+00 3.74456e-12 1.95772e-11 2 -8.266776760300688e-01 -8.266776760379160e-01 7.84717e-12 8.68455e-11 3 9.854709831049801e+00 9.854709831053952e+00 4.15135e-12 2.43181e-10 ----------------------------------------------------------------------------------------------------- 4 Ti 1 -1.259298216185305e+01 -1.259298216203914e+01 1.86098e-10 1.55998e-09 2 2.280967793607957e+01 2.280967793627980e+01 2.00231e-10 8.32518e-10 3 2.452850623988343e+00 2.452850623987348e+00 9.94760e-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 9.07677e-10 3 -3.764272466105202e+00 -3.764272466120398e+00 1.51958e-11 3.33217e-10 ----------------------------------------------------------------------------------------------------- 6 Ti 1 5.667059993539637e+00 5.667059993565404e+00 2.57669e-11 1.87806e-10 2 2.404266223216668e+00 2.404266223225810e+00 9.14202e-12 1.09975e-10 3 -6.933534045748672e+00 -6.933534045749003e+00 3.30402e-13 5.81880e-09 * ----------------------------------------------------------------------------------------------------- 7 Ti 1 4.591378146210580e+00 4.591378146207977e+00 2.60325e-12 5.13500e-11 2 -7.010120522276013e+00 -7.010120522290392e+00 1.43787e-11 2.09423e-10 3 2.703704673121417e+00 2.703704673093293e+00 2.81246e-11 4.01285e-10 ----------------------------------------------------------------------------------------------------- 8 Ti 1 8.134785222861820e+00 8.134785222919840e+00 5.80194e-11 1.09439e-09 2 -2.165429985907528e+01 -2.165429985855408e+01 5.21208e-10 1.07460e-09 3 -1.869231501475779e+01 -1.869231501509161e+01 3.33820e-10 1.55931e-09 ----------------------------------------------------------------------------------------------------- 9 Ti 1 -2.786050956849105e+01 -2.786050956832770e+01 1.63354e-10 2.16702e-09 2 8.579969362403885e+00 8.579969362330509e+00 7.33760e-11 1.44707e-10 3 -1.471259509715859e+01 -1.471259509694548e+01 2.13110e-10 1.19688e-09 ----------------------------------------------------------------------------------------------------- 10 Ti 1 -1.506503237581937e+01 -1.506503237585875e+01 3.93801e-11 4.27605e-11 2 2.329730031993360e+01 2.329730031985111e+01 8.24869e-11 6.17678e-10 3 -1.448213439563357e+01 -1.448213439568758e+01 5.40012e-11 3.59904e-10 ----------------------------------------------------------------------------------------------------- 11 Ti 1 -7.990393770903302e-01 -7.990393770462171e-01 4.41132e-11 2.58797e-09 2 5.566544604593512e+00 5.566544604571443e+00 2.20686e-11 2.06905e-10 3 1.871978289973024e+01 1.871978289970052e+01 2.97149e-11 9.02805e-10 ----------------------------------------------------------------------------------------------------- 12 Ti 1 -5.305596888009935e+00 -5.305596888015742e+00 5.80691e-12 2.96475e-10 2 7.646885064421348e+00 7.646885064429791e+00 8.44391e-12 2.43456e-10 3 2.699581566038672e+00 2.699581566053675e+00 1.50036e-11 1.02713e-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 2.76650e-10 3 -1.699319588095417e+01 -1.699319588094295e+01 1.12266e-11 2.27395e-10 ----------------------------------------------------------------------------------------------------- 14 Ti 1 3.884271993028942e+00 3.884271993031505e+00 2.56373e-12 2.57194e-10 2 8.175911249298343e+00 8.175911249256565e+00 4.17781e-11 3.46175e-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 3.73621e-11 3.43535e-10 3 5.897444485334728e+00 5.897444485296676e+00 3.80522e-11 6.54382e-10 ----------------------------------------------------------------------------------------------------- 16 Ti 1 -2.738761880373689e+00 -2.738761880275217e+00 9.84715e-11 8.46095e-10 2 2.428392545160918e+01 2.428392545161479e+01 5.60618e-12 6.01510e-10 3 1.215323856099765e+01 1.215323856102147e+01 2.38245e-11 1.35031e-09 ----------------------------------------------------------------------------------------------------- 17 Ti 1 -2.988269828198304e+00 -2.988269828185010e+00 1.32938e-11 1.66440e-11 2 -1.522530950327490e+01 -1.522530950325729e+01 1.76090e-11 1.60624e-10 3 1.335235430246749e+01 1.335235430246521e+01 2.28617e-12 1.22448e-10 ----------------------------------------------------------------------------------------------------- 18 Ti 1 -1.220844931312505e+01 -1.220844931362645e+01 5.01400e-10 2.80158e-09 2 -4.816494747498573e+00 -4.816494747062253e+00 4.36320e-10 3.70116e-09 3 6.030510687074999e+00 6.030510687045579e+00 2.94200e-11 1.23913e-10 ----------------------------------------------------------------------------------------------------- 19 Ti 1 3.010925540992953e+00 3.010925540986632e+00 6.32028e-12 2.15219e-11 2 -5.994144678509643e+00 -5.994144678522752e+00 1.31095e-11 5.69580e-11 3 -1.155940964233239e+00 -1.155940964208211e+00 2.50286e-11 5.75697e-11 ----------------------------------------------------------------------------------------------------- 20 Ti 1 -1.225264133370069e+01 -1.225264133375109e+01 5.04006e-11 4.41096e-10 2 5.443066490472584e+00 5.443066490517122e+00 4.45377e-11 9.53135e-10 3 8.313193561019435e+00 8.313193560948360e+00 7.10756e-11 2.68944e-10 ----------------------------------------------------------------------------------------------------- 21 Ti 1 -2.163020781209194e+00 -2.163020781209577e+00 3.83693e-13 1.08971e-10 2 -1.673628380077804e+01 -1.673628380078311e+01 5.07328e-12 1.02411e-10 3 -1.447408389231136e+01 -1.447408389225528e+01 5.60743e-11 1.17727e-09 ----------------------------------------------------------------------------------------------------- 22 Ti 1 2.313654489021783e+01 2.313654489025097e+01 3.31362e-11 2.36763e-10 2 -1.869176065346242e+01 -1.869176065351377e+01 5.13509e-11 1.09985e-10 3 5.081198379868922e+00 5.081198379891498e+00 2.25766e-11 2.14866e-09 ----------------------------------------------------------------------------------------------------- 23 Ti 1 1.205628036037506e+01 1.205628036035938e+01 1.56710e-11 4.48063e-10 2 3.187760577220136e+00 3.187760577222039e+00 1.90381e-12 8.34035e-11 3 1.123320416705951e+01 1.123320416707510e+01 1.55964e-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 -6.381165088143062e+00 4.91696e-10 1.77863e-09 2 -5.072993053717503e+00 -5.072993054261497e+00 5.43994e-10 8.22589e-10 3 -9.072212347555343e+00 -9.072212347560553e+00 5.21005e-12 3.48729e-07 * ----------------------------------------------------------------------------------------------------- 26 Ti 1 8.428772155094375e+00 8.428772154998896e+00 9.54792e-11 6.09255e-11 2 6.232851486786503e+00 6.232851486861928e+00 7.54250e-11 5.38856e-10 3 -4.947489367689723e+00 -4.947489367768815e+00 7.90923e-11 6.25098e-10 ----------------------------------------------------------------------------------------------------- 27 Ti 1 -4.761670665449780e-01 -4.761670665677042e-01 2.27263e-11 3.08741e-10 2 4.790449222521599e+00 4.790449222430990e+00 9.06093e-11 3.57383e-10 3 1.134696447813924e+01 1.134696447820867e+01 6.94325e-11 1.28200e-10 ----------------------------------------------------------------------------------------------------- 28 Ti 1 -3.040824047610202e+00 -3.040824047604475e+00 5.72697e-12 1.10671e-08 * 2 3.945509329109094e+00 3.945509329103107e+00 5.98632e-12 9.24958e-10 3 5.779621526102662e+00 5.779621526147968e+00 4.53069e-11 3.98472e-11 ----------------------------------------------------------------------------------------------------- 29 Ti 1 -1.418117462867325e+01 -1.418117462765222e+01 1.02103e-09 4.87503e-09 * 2 1.128398964720117e+01 1.128398964725519e+01 5.40172e-11 8.27599e-10 3 5.812716128618481e+00 5.812716128700154e+00 8.16724e-11 1.86394e-10 ----------------------------------------------------------------------------------------------------- 30 Ti 1 8.167524845932673e+00 8.167524845942737e+00 1.00631e-11 2.16767e-10 2 1.315114333581046e+01 1.315114333583165e+01 2.11831e-11 1.18334e-10 3 1.855960915205980e+00 1.855960915191950e+00 1.40297e-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 6.708696515547101e+00 2.06430e-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 = ----------------------- = 1.07233e-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 -1.800328583341245e+00 4.86722e-12 1.26937e-10 2 -1.053718756297158e+00 -1.053718756309881e+00 1.27227e-11 3.75540e-11 3 5.576221556670287e-01 5.576221556774982e-01 1.04695e-11 4.44952e-10 ----------------------------------------------------------------------------------------------------- 2 Ti 1 -2.133019984297350e+01 -2.133019984293456e+01 3.89448e-11 1.00588e-10 2 1.245496602279340e+01 1.245496602281996e+01 2.65530e-11 2.34632e-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 4.55280e-12 2 -3.575395038213804e+01 -3.575395038212542e+01 1.26263e-11 2.51397e-10 3 1.405786448306104e+01 1.405786448305217e+01 8.87113e-12 1.59323e-10 ----------------------------------------------------------------------------------------------------- 4 Ti 1 -2.089613501457363e+01 -2.089613501451427e+01 5.93587e-11 2.34273e-10 2 8.637238429468109e+00 8.637238429425425e+00 4.26841e-11 7.78044e-11 3 8.933539244497219e+00 8.933539244490628e+00 6.59028e-12 3.17019e-10 ----------------------------------------------------------------------------------------------------- 5 Ti 1 5.710711578402579e+00 5.710711578397981e+00 4.59810e-12 2.48058e-10 2 -3.952834716475246e+01 -3.952834716466332e+01 8.91447e-11 2.19181e-10 3 -3.644625858026345e+01 -3.644625858014422e+01 1.19229e-10 3.53756e-09 * ----------------------------------------------------------------------------------------------------- 6 Ti 1 3.198731683072709e+01 3.198731683071171e+01 1.53797e-11 2.44963e-10 2 1.884275950032329e+01 1.884275950029166e+01 3.16298e-11 2.48775e-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 1.189488600091959e+01 4.19149e-11 6.33964e-11 ----------------------------------------------------------------------------------------------------- 8 Ti 1 8.666648443043043e+00 8.666648443032562e+00 1.04805e-11 7.24305e-09 * 2 3.561364375022774e+01 3.561364374951581e+01 7.11935e-10 3.73871e-09 * 3 3.909047838567156e+01 3.909047838519015e+01 4.81407e-10 2.99005e-09 * ----------------------------------------------------------------------------------------------------- 9 Ti 1 -6.902956598912946e+00 -6.902956598889445e+00 2.35003e-11 1.51650e-10 2 8.187361806292593e+00 8.187361806288552e+00 4.04121e-12 9.49676e-11 3 -2.421469966448315e+00 -2.421469966443915e+00 4.40048e-12 1.76952e-10 ----------------------------------------------------------------------------------------------------- 10 O 1 -2.289122621762569e-01 -2.289122621763337e-01 7.67719e-14 7.05860e-11 2 1.907981242062009e+00 1.907981242068959e+00 6.94955e-12 4.38911e-11 3 -3.862526502624608e+00 -3.862526502621562e+00 3.04645e-12 1.49663e-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 9.17462e-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 1.64766e-11 2 1.374056508879889e+00 1.374056508881669e+00 1.78058e-12 4.42631e-10 3 -3.180585813781995e+00 -3.180585813780823e+00 1.17195e-12 4.38724e-09 * ----------------------------------------------------------------------------------------------------- 13 O 1 -3.077119461102360e-02 -3.077119460787577e-02 3.14783e-12 5.41571e-11 2 3.788695347741505e+00 3.788695347743960e+00 2.45493e-12 9.67684e-11 3 3.526042908784122e+00 3.526042908797225e+00 1.31029e-11 2.14166e-10 ----------------------------------------------------------------------------------------------------- 14 Ti 1 4.464059517196186e-01 4.464059517170607e-01 2.55790e-12 7.93919e-11 2 9.965530627990972e-01 9.965530628085488e-01 9.45166e-12 5.01770e-11 3 -3.441538045467281e+00 -3.441538045468843e+00 1.56231e-12 9.49769e-11 ----------------------------------------------------------------------------------------------------- 15 O 1 -2.265659691120359e+00 -2.265659691135021e+00 1.46612e-11 2.68185e-10 2 4.459252223946900e+00 4.459252223936610e+00 1.02904e-11 7.17630e-11 3 2.022586475632166e+00 2.022586475634372e+00 2.20624e-12 1.06607e-10 ----------------------------------------------------------------------------------------------------- 16 O 1 5.781125445960858e+00 5.781125445897349e+00 6.35092e-11 2.93134e-10 2 4.200812196479960e-02 4.200812197762568e-02 1.28261e-11 3.31250e-10 3 -4.252785918927507e+00 -4.252785919010898e+00 8.33911e-11 2.14080e-10 ----------------------------------------------------------------------------------------------------- 17 O 1 -1.780839265564391e+00 -1.780839265580705e+00 1.63136e-11 1.08732e-09 2 -9.092076947660940e-01 -9.092076948232818e-01 5.71878e-11 2.08710e-10 3 7.130194826981582e-01 7.130194826990890e-01 9.30811e-13 2.72271e-11 ----------------------------------------------------------------------------------------------------- 18 O 1 -3.236304783758014e-01 -3.236304783921923e-01 1.63909e-11 4.17653e-10 2 -2.664897533434571e+00 -2.664897533503098e+00 6.85265e-11 2.84892e-10 3 4.229098539574739e+00 4.229098539568476e+00 6.26343e-12 6.14282e-11 ----------------------------------------------------------------------------------------------------- 19 Ti 1 1.052765603820874e+01 1.052765603819315e+01 1.55946e-11 2.54770e-10 2 -2.011382461051295e+01 -2.011382461051569e+01 2.74269e-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 6.49547e-12 1.72087e-10 3 -5.756037731773715e-01 -5.756037731780325e-01 6.60916e-13 4.28111e-11 ----------------------------------------------------------------------------------------------------- 21 O 1 1.805369265412172e+00 1.805369265328732e+00 8.34399e-11 2.55167e-10 2 -6.589030695427320e-01 -6.589030697640752e-01 2.21343e-10 5.46339e-10 3 1.651457618782916e+00 1.651457618817072e+00 3.41567e-11 1.04775e-09 ----------------------------------------------------------------------------------------------------- 22 O 1 -5.363045100753627e-01 -5.363045101129275e-01 3.75647e-11 7.39565e-10 2 2.515454302044381e+00 2.515454302040085e+00 4.29612e-12 5.82459e-11 3 1.092255822681982e+00 1.092255822682037e+00 5.48450e-14 1.35146e-10 ----------------------------------------------------------------------------------------------------- 23 Ti 1 8.965254807452904e+00 8.965254807447481e+00 5.42322e-12 1.69251e-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 9.83373e-11 5.92600e-10 3 -3.489607307960469e+00 -3.489607308067995e+00 1.07526e-10 2.89434e-10 ----------------------------------------------------------------------------------------------------- 25 O 1 -3.008655412331065e+00 -3.008655412329695e+00 1.36957e-12 2.19901e-10 2 -2.558825155121613e+00 -2.558825155119443e+00 2.16982e-12 5.42295e-09 * 3 1.853530406626297e+00 1.853530406631502e+00 5.20517e-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 6.375513355504172e+00 1.96225e-11 1.28958e-10 2 1.410547604401621e+01 1.410547604389070e+01 1.25508e-10 2.51665e-10 3 1.220268729549413e+01 1.220268729549316e+01 9.69891e-13 6.10649e-10 ----------------------------------------------------------------------------------------------------- 28 O 1 -4.720987853750997e+00 -4.720987853746404e+00 4.59277e-12 1.09534e-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 3.369080189103994e+00 1.72853e-11 1.97947e-09 * ----------------------------------------------------------------------------------------------------- 30 Ti 1 -3.631399598171031e+00 -3.631399598323646e+00 1.52615e-10 2.56373e-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 -2.316758832013689e+00 5.12301e-12 1.67307e-10 2 2.348824055707193e+00 2.348824055716360e+00 9.16689e-12 5.86620e-11 3 -3.580955006976026e+00 -3.580955007114191e+00 1.38165e-10 4.09027e-10 ----------------------------------------------------------------------------------------------------- 32 O 1 5.124703325325590e+00 5.124703325312405e+00 1.31850e-11 7.34159e-11 2 -2.347495860784354e+00 -2.347495860773769e+00 1.05853e-11 8.56675e-11 3 1.317667972816710e+00 1.317667972815641e+00 1.06937e-12 3.03375e-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.