!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_000 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 1.767645297282364e-01 1.16035e-12 4.46725e-07 * 2 2.385926081008855e-01 2.385926081017048e-01 8.19261e-13 2.11584e-12 3 2.751641757415170e-01 2.751641757423129e-01 7.95919e-13 3.76366e-12 ----------------------------------------------------------------------------------------------------- 2 O 1 -6.505020876208873e-01 -6.505020876208637e-01 2.36478e-14 2.52298e-12 2 -7.558146252738979e-01 -7.558146252739777e-01 7.98250e-14 3.54683e-12 3 4.101539591221023e-01 4.101539591219250e-01 1.77247e-13 4.48402e-12 ----------------------------------------------------------------------------------------------------- 3 O 1 -1.005775450395860e+00 -1.005775450396468e+00 6.07736e-13 3.87681e-11 2 4.830188394637912e-01 4.830188394667871e-01 2.99588e-12 1.36408e-11 3 -5.359678132025841e-01 -5.359678132033374e-01 7.53286e-13 3.48244e-12 ----------------------------------------------------------------------------------------------------- 4 O 1 7.469670621344281e-01 7.469670621343554e-01 7.27196e-14 8.23563e-13 2 -6.912272053660796e-01 -6.912272053661084e-01 2.87548e-14 1.30009e-11 3 -4.933827006328435e-01 -4.933827006327615e-01 8.19345e-14 3.80379e-12 ----------------------------------------------------------------------------------------------------- 5 O 1 4.751285786872130e-01 4.751285786873254e-01 1.12410e-13 2.78300e-12 2 5.801898691809048e-01 5.801898691829311e-01 2.02638e-12 2.68684e-09 * 3 1.626372542067204e-01 1.626372542009540e-01 5.76639e-12 7.30717e-10 * ----------------------------------------------------------------------------------------------------- 6 O 1 -4.608335656065853e-01 -4.608335656040504e-01 2.53492e-12 1.22949e-11 2 -6.725806243860267e-01 -6.725806243848393e-01 1.18738e-12 1.30602e-11 3 4.868838347887531e-01 4.868838347886814e-01 7.17204e-14 3.98402e-11 ----------------------------------------------------------------------------------------------------- 7 O 1 -2.610308939078376e-01 -2.610308939076270e-01 2.10554e-13 2.38329e-11 2 4.181877275636612e-01 4.181877275637870e-01 1.25844e-13 6.07864e-12 3 -2.612498208004533e-01 -2.612498208014217e-01 9.68392e-13 6.04794e-12 ----------------------------------------------------------------------------------------------------- 8 O 1 1.046976954740026e+00 1.046976954740613e+00 5.86864e-13 3.96083e-12 2 -2.878853907357656e-01 -2.878853907356851e-01 8.04912e-14 4.19209e-12 3 -7.284994223929757e-01 -7.284994223922806e-01 6.95111e-13 3.79052e-12 ----------------------------------------------------------------------------------------------------- 9 O 1 3.106218611942297e-01 3.106218611912669e-01 2.96280e-12 3.89553e-09 * 2 6.875872322800739e-01 6.875872322795824e-01 4.91496e-13 2.33003e-12 3 6.940910690393597e-01 6.940910690420543e-01 2.69462e-12 3.91005e-09 * ----------------------------------------------------------------------------------------------------- 10 O 1 -7.261246824049136e-01 -7.261246824049329e-01 1.93179e-14 2.86549e-12 2 -6.467237629918428e-01 -6.467237629922037e-01 3.60934e-13 8.55771e-12 3 3.856018721448581e-01 3.856018721449754e-01 1.17295e-13 2.51787e-12 ----------------------------------------------------------------------------------------------------- 11 O 1 -2.164321577015100e-02 -2.164321577008794e-02 6.30607e-14 8.46391e-12 2 1.204237563616396e+00 1.204237563616974e+00 5.77982e-13 2.40119e-12 3 -5.374361659814390e-01 -5.374361659820084e-01 5.69433e-13 8.11462e-13 ----------------------------------------------------------------------------------------------------- 12 O 1 5.142217163735631e-01 5.142217163743081e-01 7.45071e-13 1.05614e-11 2 -6.859458813466575e-01 -6.859458813512941e-01 4.63662e-12 2.97199e-11 3 -7.213546091409866e-01 -7.213546091395502e-01 1.43641e-12 1.80134e-12 ----------------------------------------------------------------------------------------------------- 13 O 1 3.489535145510055e-01 3.489535145515021e-01 4.96603e-13 4.42102e-12 2 9.110523685200844e-01 9.110523685221934e-01 2.10898e-12 2.87148e-12 3 1.303037228540986e+00 1.303037228541451e+00 4.64517e-13 2.03726e-12 ----------------------------------------------------------------------------------------------------- 14 O 1 -2.754396632027297e-01 -2.754396632028438e-01 1.14075e-13 2.23271e-12 2 -4.225100908949244e-01 -4.225100908954532e-01 5.28744e-13 5.76603e-11 3 1.722061028858167e-01 1.722061028862305e-01 4.13836e-13 3.66915e-12 ----------------------------------------------------------------------------------------------------- 15 O 1 -9.519865131647087e-01 -9.519865131646004e-01 1.08358e-13 1.01501e-11 2 8.752290990149563e-01 8.752290990155381e-01 5.81868e-13 3.76854e-12 3 -3.209132741354782e-01 -3.209132741359618e-01 4.83613e-13 7.06935e-13 ----------------------------------------------------------------------------------------------------- 16 O 1 8.093193920031820e-01 8.093193920031224e-01 5.96190e-14 2.98328e-12 2 -1.197881274640576e+00 -1.197881274640724e+00 1.47882e-13 3.91776e-12 3 -7.817565528696421e-01 -7.817565528696908e-01 4.87388e-14 6.42131e-12 ----------------------------------------------------------------------------------------------------- 17 O 1 1.047957531497518e+00 1.047957531497690e+00 1.72307e-13 8.11573e-12 2 5.569738162992908e-01 5.569738162973392e-01 1.95155e-12 1.59821e-11 3 6.810741028875620e-01 6.810741028880650e-01 5.03042e-13 1.89537e-12 ----------------------------------------------------------------------------------------------------- 18 O 1 -9.211393244474628e-01 -9.211393244492631e-01 1.80023e-12 1.92083e-11 2 -1.128096310021620e+00 -1.128096310020853e+00 7.66942e-13 1.50384e-11 3 7.379580311906274e-01 7.379580311881303e-01 2.49711e-12 2.56928e-12 ----------------------------------------------------------------------------------------------------- 19 O 1 -5.667280757963920e-01 -5.667280757964409e-01 4.89608e-14 1.10806e-11 2 9.798451156879030e-01 9.798451156881308e-01 2.27818e-13 7.94576e-12 3 -6.142216469041153e-01 -6.142216469016168e-01 2.49845e-12 5.65015e-12 ----------------------------------------------------------------------------------------------------- 20 O 1 4.208744890933218e-01 4.208744890924068e-01 9.14935e-13 7.87159e-12 2 -1.164460660972227e+00 -1.164460660972142e+00 8.54872e-14 1.06137e-11 3 -4.538169686002920e-01 -4.538169686006537e-01 3.61655e-13 2.62923e-12 ----------------------------------------------------------------------------------------------------- 21 O 1 7.912590206747698e-01 7.912590206739951e-01 7.74714e-13 4.19114e-11 2 8.301620250413110e-01 8.301620250398821e-01 1.42886e-12 5.36369e-11 3 4.998157084588142e-01 4.998157084585583e-01 2.55906e-13 2.19584e-11 ----------------------------------------------------------------------------------------------------- 22 O 1 -7.594141464056990e-01 -7.594141464072752e-01 1.57618e-12 1.40957e-11 2 -1.092937134760936e+00 -1.092937134761107e+00 1.70308e-13 2.04925e-12 3 9.780175160236811e-02 9.780175159963832e-02 2.72979e-12 6.44226e-12 ----------------------------------------------------------------------------------------------------- 23 O 1 -3.155541602538668e-01 -3.155541602539970e-01 1.30118e-13 9.59838e-12 2 6.380734881538026e-02 6.380734881503576e-02 3.44502e-13 4.29132e-12 3 -3.779306061451967e-01 -3.779306061477439e-01 2.54718e-12 2.78136e-11 ----------------------------------------------------------------------------------------------------- 24 O 1 2.898151019175695e-01 2.898151019176822e-01 1.12632e-13 5.01771e-11 2 -9.405579694963746e-01 -9.405579694949813e-01 1.39333e-12 2.81036e-11 3 -9.671129814940842e-02 -9.671129814990856e-02 5.00142e-13 2.10540e-12 ----------------------------------------------------------------------------------------------------- 25 O 1 3.857870553899221e-01 3.857870553900997e-01 1.77636e-13 2.32958e-12 2 8.526043997681740e-01 8.526043997682269e-01 5.28466e-14 1.38203e-11 3 4.584760852199582e-01 4.584760852202831e-01 3.24907e-13 1.76326e-12 ----------------------------------------------------------------------------------------------------- 26 O 1 -7.031542549213695e-01 -7.031542549218426e-01 4.73066e-13 1.18138e-11 2 -9.144810872547839e-01 -9.144810872508240e-01 3.95994e-12 5.63480e-11 3 9.771384221034445e-01 9.771384221042153e-01 7.70828e-13 1.60955e-11 ----------------------------------------------------------------------------------------------------- 27 O 1 -6.957527643484124e-01 -6.957527643490342e-01 6.21836e-13 9.59210e-12 2 1.247778303846541e+00 1.247778303850536e+00 3.99525e-12 5.82305e-11 * 3 -4.852488396140467e-01 -4.852488396097460e-01 4.30073e-12 8.49212e-11 * ----------------------------------------------------------------------------------------------------- 28 O 1 6.002905087791576e-01 6.002905087794554e-01 2.97873e-13 1.55652e-11 2 -3.581290767628806e-01 -3.581290767616973e-01 1.18339e-12 1.52369e-11 3 -4.158382507217816e-01 -4.158382507223832e-01 6.01630e-13 7.69057e-12 ----------------------------------------------------------------------------------------------------- 29 O 1 7.462756252375524e-01 7.462756252392245e-01 1.67211e-12 4.46544e-11 2 1.294193076576651e+00 1.294193076580643e+00 3.99258e-12 7.54221e-11 * 3 -4.101229710933571e-01 -4.101229710922281e-01 1.12904e-12 1.90383e-10 * ----------------------------------------------------------------------------------------------------- 30 O 1 -4.034245700846663e-01 -4.034245700848332e-01 1.66922e-13 1.44355e-11 2 -6.507358065492502e-01 -6.507358065489455e-01 3.04756e-13 1.30689e-11 3 4.630506375929035e-01 4.630506375915100e-01 1.39355e-12 1.28601e-11 ----------------------------------------------------------------------------------------------------- 31 O 1 -1.758438831038673e-01 -1.758438831039306e-01 6.33105e-14 3.29034e-12 2 8.784034558294405e-01 8.784034558297532e-01 3.12750e-13 4.26326e-12 3 -1.145674817080354e-01 -1.145674817065517e-01 1.48366e-12 2.25439e-12 ----------------------------------------------------------------------------------------------------- 32 O 1 1.831343094325556e-01 1.831343094324641e-01 9.14824e-14 5.70367e-11 2 -4.918959481516008e-01 -4.918959481525641e-01 9.63341e-13 4.36085e-12 3 -4.560718134331568e-01 -4.560718134338006e-01 6.43818e-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 = ----------------------- = 2.79114e-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 -1.387968513515549e+00 8.32934e-12 1.30560e-10 2 -9.037725426022496e+00 -9.037725426040968e+00 1.84723e-11 3.43036e-10 3 -1.009214661521177e+01 -1.009214661520218e+01 9.59055e-12 1.41309e-11 ----------------------------------------------------------------------------------------------------- 2 Ti 1 1.643015811995841e+01 1.643015811989477e+01 6.36362e-11 2.16183e-10 2 -1.253187534866812e+01 -1.253187534869102e+01 2.29008e-11 4.10857e-10 3 -1.928211573307655e+01 -1.928211573320372e+01 1.27166e-10 1.21058e-09 ----------------------------------------------------------------------------------------------------- 3 Ti 1 9.755565263731262e+00 9.755565263727510e+00 3.75167e-12 1.95772e-11 2 -8.266776760300688e-01 -8.266776760379154e-01 7.84661e-12 8.68462e-11 3 9.854709831049801e+00 9.854709831053942e+00 4.14069e-12 2.43181e-10 ----------------------------------------------------------------------------------------------------- 4 Ti 1 -1.259298216185305e+01 -1.259298216203913e+01 1.86086e-10 1.55998e-09 2 2.280967793607957e+01 2.280967793627978e+01 2.00213e-10 8.32515e-10 3 2.452850623988343e+00 2.452850623987345e+00 9.97868e-13 1.54577e-09 ----------------------------------------------------------------------------------------------------- 5 Ti 1 -1.883589292070800e+00 -1.883589291917908e+00 1.52892e-10 1.02817e-09 2 -4.040932205800835e+00 -4.040932205742274e+00 5.85612e-11 9.07673e-10 3 -3.764272466105202e+00 -3.764272466120396e+00 1.51932e-11 3.33217e-10 ----------------------------------------------------------------------------------------------------- 6 Ti 1 5.667059993539637e+00 5.667059993565399e+00 2.57616e-11 1.87801e-10 2 2.404266223216668e+00 2.404266223225808e+00 9.14024e-12 1.09975e-10 3 -6.933534045748672e+00 -6.933534045749006e+00 3.33955e-13 5.81880e-09 * ----------------------------------------------------------------------------------------------------- 7 Ti 1 4.591378146210580e+00 4.591378146207974e+00 2.60592e-12 5.13500e-11 2 -7.010120522276013e+00 -7.010120522290387e+00 1.43734e-11 2.09420e-10 3 2.703704673121417e+00 2.703704673093291e+00 2.81268e-11 4.01285e-10 ----------------------------------------------------------------------------------------------------- 8 Ti 1 8.134785222861820e+00 8.134785222919831e+00 5.80105e-11 1.09440e-09 2 -2.165429985907528e+01 -2.165429985855406e+01 5.21222e-10 1.07461e-09 3 -1.869231501475779e+01 -1.869231501509160e+01 3.33806e-10 1.55931e-09 ----------------------------------------------------------------------------------------------------- 9 Ti 1 -2.786050956849105e+01 -2.786050956832768e+01 1.63379e-10 2.16702e-09 2 8.579969362403885e+00 8.579969362330504e+00 7.33813e-11 1.44707e-10 3 -1.471259509715859e+01 -1.471259509694547e+01 2.13120e-10 1.19688e-09 ----------------------------------------------------------------------------------------------------- 10 Ti 1 -1.506503237581937e+01 -1.506503237585874e+01 3.93694e-11 4.27605e-11 2 2.329730031993360e+01 2.329730031985109e+01 8.25082e-11 6.17678e-10 3 -1.448213439563357e+01 -1.448213439568756e+01 5.39888e-11 3.59901e-10 ----------------------------------------------------------------------------------------------------- 11 Ti 1 -7.990393770903302e-01 -7.990393770462166e-01 4.41136e-11 2.58797e-09 2 5.566544604593512e+00 5.566544604571440e+00 2.20721e-11 2.06905e-10 3 1.871978289973024e+01 1.871978289970051e+01 2.97291e-11 9.02808e-10 ----------------------------------------------------------------------------------------------------- 12 Ti 1 -5.305596888009935e+00 -5.305596888015738e+00 5.80247e-12 2.96479e-10 2 7.646885064421348e+00 7.646885064429785e+00 8.43769e-12 2.43459e-10 3 2.699581566038672e+00 2.699581566053673e+00 1.50009e-11 1.02710e-10 ----------------------------------------------------------------------------------------------------- 13 Ti 1 -6.288243078889231e-01 -6.288243079496564e-01 6.07333e-11 7.51037e-07 * 2 -1.718463682211265e+01 -1.718463682216416e+01 5.15072e-11 2.76653e-10 3 -1.699319588095417e+01 -1.699319588094293e+01 1.12372e-11 2.27395e-10 ----------------------------------------------------------------------------------------------------- 14 Ti 1 3.884271993028942e+00 3.884271993031502e+00 2.56062e-12 2.57192e-10 2 8.175911249298343e+00 8.175911249256560e+00 4.17835e-11 3.46182e-10 3 -7.219158617397791e+00 -7.219158617396129e+00 1.66178e-12 3.71792e-08 * ----------------------------------------------------------------------------------------------------- 15 Ti 1 2.119070507590342e+01 2.119070507601236e+01 1.08940e-10 4.32799e-10 2 -1.075989841097622e+01 -1.075989841101357e+01 3.73568e-11 3.43537e-10 3 5.897444485334728e+00 5.897444485296671e+00 3.80576e-11 6.54384e-10 ----------------------------------------------------------------------------------------------------- 16 Ti 1 -2.738761880373689e+00 -2.738761880275215e+00 9.84741e-11 8.46095e-10 2 2.428392545160918e+01 2.428392545161477e+01 5.58842e-12 6.01506e-10 3 1.215323856099765e+01 1.215323856102146e+01 2.38121e-11 1.35032e-09 ----------------------------------------------------------------------------------------------------- 17 Ti 1 -2.988269828198304e+00 -2.988269828185008e+00 1.32960e-11 1.66449e-11 2 -1.522530950327490e+01 -1.522530950325728e+01 1.76232e-11 1.60616e-10 3 1.335235430246749e+01 1.335235430246520e+01 2.29683e-12 1.22453e-10 ----------------------------------------------------------------------------------------------------- 18 Ti 1 -1.220844931312505e+01 -1.220844931362644e+01 5.01389e-10 2.80158e-09 2 -4.816494747498573e+00 -4.816494747062249e+00 4.36324e-10 3.70116e-09 3 6.030510687074999e+00 6.030510687045576e+00 2.94236e-11 1.23911e-10 ----------------------------------------------------------------------------------------------------- 19 Ti 1 3.010925540992953e+00 3.010925540986630e+00 6.32294e-12 2.15241e-11 2 -5.994144678509643e+00 -5.994144678522748e+00 1.31051e-11 5.69562e-11 3 -1.155940964233239e+00 -1.155940964208209e+00 2.50298e-11 5.75697e-11 ----------------------------------------------------------------------------------------------------- 20 Ti 1 -1.225264133370069e+01 -1.225264133375108e+01 5.03881e-11 4.41096e-10 2 5.443066490472584e+00 5.443066490517118e+00 4.45342e-11 9.53132e-10 3 8.313193561019435e+00 8.313193560948353e+00 7.10827e-11 2.68949e-10 ----------------------------------------------------------------------------------------------------- 21 Ti 1 -2.163020781209194e+00 -2.163020781209576e+00 3.81917e-13 1.08970e-10 2 -1.673628380077804e+01 -1.673628380078310e+01 5.05906e-12 1.02421e-10 3 -1.447408389231136e+01 -1.447408389225527e+01 5.60885e-11 1.17728e-09 ----------------------------------------------------------------------------------------------------- 22 Ti 1 2.313654489021783e+01 2.313654489025095e+01 3.31148e-11 2.36746e-10 2 -1.869176065346242e+01 -1.869176065351377e+01 5.13509e-11 1.09971e-10 3 5.081198379868922e+00 5.081198379891493e+00 2.25713e-11 2.14866e-09 ----------------------------------------------------------------------------------------------------- 23 Ti 1 1.205628036037506e+01 1.205628036035938e+01 1.56781e-11 4.48063e-10 2 3.187760577220136e+00 3.187760577222037e+00 1.90159e-12 8.34026e-11 3 1.123320416705951e+01 1.123320416707510e+01 1.55893e-11 4.90932e-11 ----------------------------------------------------------------------------------------------------- 24 Ti 1 -1.744654468658234e+00 -1.744654468691116e+00 3.28819e-11 1.10399e-06 * 2 -1.970968715112140e+00 -1.970968715121030e+00 8.88978e-12 6.96297e-10 3 9.252310458161565e+00 9.252310458174394e+00 1.28288e-11 5.99426e-10 ----------------------------------------------------------------------------------------------------- 25 Ti 1 -6.381165088634758e+00 -6.381165088143056e+00 4.91702e-10 1.77863e-09 2 -5.072993053717503e+00 -5.072993054261492e+00 5.43990e-10 8.22586e-10 3 -9.072212347555343e+00 -9.072212347560558e+00 5.21538e-12 3.48729e-07 * ----------------------------------------------------------------------------------------------------- 26 Ti 1 8.428772155094375e+00 8.428772154998889e+00 9.54863e-11 6.09219e-11 2 6.232851486786503e+00 6.232851486861924e+00 7.54214e-11 5.38854e-10 3 -4.947489367689723e+00 -4.947489367768810e+00 7.90870e-11 6.25100e-10 ----------------------------------------------------------------------------------------------------- 27 Ti 1 -4.761670665449780e-01 -4.761670665677039e-01 2.27259e-11 3.08741e-10 2 4.790449222521599e+00 4.790449222430988e+00 9.06111e-11 3.57382e-10 3 1.134696447813924e+01 1.134696447820866e+01 6.94236e-11 1.28201e-10 ----------------------------------------------------------------------------------------------------- 28 Ti 1 -3.040824047610202e+00 -3.040824047604476e+00 5.72564e-12 1.10671e-08 * 2 3.945509329109094e+00 3.945509329103103e+00 5.99076e-12 9.24955e-10 3 5.779621526102662e+00 5.779621526147963e+00 4.53015e-11 3.98490e-11 ----------------------------------------------------------------------------------------------------- 29 Ti 1 -1.418117462867325e+01 -1.418117462765220e+01 1.02105e-09 4.87504e-09 * 2 1.128398964720117e+01 1.128398964725518e+01 5.40084e-11 8.27605e-10 3 5.812716128618481e+00 5.812716128700148e+00 8.16671e-11 1.86396e-10 ----------------------------------------------------------------------------------------------------- 30 Ti 1 8.167524845932673e+00 8.167524845942729e+00 1.00560e-11 2.16772e-10 2 1.315114333581046e+01 1.315114333583164e+01 2.11742e-11 1.18330e-10 3 1.855960915205980e+00 1.855960915191949e+00 1.40314e-11 3.46775e-10 ----------------------------------------------------------------------------------------------------- 31 Ti 1 7.884493446357727e+00 7.884493446420165e+00 6.24381e-11 9.32987e-11 2 -5.276985967414198e+00 -5.276985967413625e+00 5.73763e-13 8.11820e-09 * 3 6.708696515567744e+00 6.708696515547095e+00 2.06493e-11 7.27356e-11 ----------------------------------------------------------------------------------------------------- 32 Ti 1 -8.639794132745658e+00 -8.639794132739278e+00 6.38067e-12 1.91098e-08 * 2 6.031857090051431e+00 6.031857090076795e+00 2.53646e-11 5.88774e-10 3 2.573150678286892e+00 2.573150678437883e+00 1.50990e-10 9.51554e-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 -1.800328583341243e+00 4.86566e-12 1.26937e-10 2 -1.053718756297158e+00 -1.053718756309880e+00 1.27216e-11 3.75540e-11 3 5.576221556670287e-01 5.576221556774976e-01 1.04690e-11 4.44953e-10 ----------------------------------------------------------------------------------------------------- 2 Ti 1 -2.133019984297350e+01 -2.133019984293454e+01 3.89626e-11 1.00599e-10 2 1.245496602279340e+01 1.245496602281995e+01 2.65423e-11 2.34623e-10 3 -2.493664709860291e+01 -2.493664709809294e+01 5.09971e-10 1.19354e-09 ----------------------------------------------------------------------------------------------------- 3 Ti 1 -8.759668643875761e+00 -8.759668643889187e+00 1.34257e-11 4.54925e-12 2 -3.575395038213804e+01 -3.575395038212539e+01 1.26548e-11 2.51433e-10 3 1.405786448306104e+01 1.405786448305216e+01 8.88356e-12 1.59323e-10 ----------------------------------------------------------------------------------------------------- 4 Ti 1 -2.089613501457363e+01 -2.089613501451425e+01 5.93801e-11 2.34266e-10 2 8.637238429468109e+00 8.637238429425418e+00 4.26912e-11 7.78062e-11 3 8.933539244497219e+00 8.933539244490623e+00 6.59561e-12 3.17019e-10 ----------------------------------------------------------------------------------------------------- 5 Ti 1 5.710711578402579e+00 5.710711578397977e+00 4.60165e-12 2.48057e-10 2 -3.952834716475246e+01 -3.952834716466328e+01 8.91802e-11 2.19188e-10 3 -3.644625858026345e+01 -3.644625858014424e+01 1.19208e-10 3.53756e-09 * ----------------------------------------------------------------------------------------------------- 6 Ti 1 3.198731683072709e+01 3.198731683071167e+01 1.54152e-11 2.44949e-10 2 1.884275950032329e+01 1.884275950029165e+01 3.16476e-11 2.48797e-10 3 -2.064274683692373e+01 -2.064274683687520e+01 4.85301e-11 8.21391e-10 ----------------------------------------------------------------------------------------------------- 7 Ti 1 8.862935534065384e+00 8.862935534068084e+00 2.70006e-12 5.06338e-10 2 -1.831726673104584e+01 -1.831726673104112e+01 4.72511e-12 5.19414e-10 3 1.189488600096150e+01 1.189488600091958e+01 4.19256e-11 6.33946e-11 ----------------------------------------------------------------------------------------------------- 8 Ti 1 8.666648443043043e+00 8.666648443032567e+00 1.04752e-11 7.24305e-09 * 2 3.561364375022774e+01 3.561364374951579e+01 7.11957e-10 3.73871e-09 * 3 3.909047838567156e+01 3.909047838519012e+01 4.81435e-10 2.99008e-09 * ----------------------------------------------------------------------------------------------------- 9 Ti 1 -6.902956598912946e+00 -6.902956598889439e+00 2.35065e-11 1.51650e-10 2 8.187361806292593e+00 8.187361806288544e+00 4.04832e-12 9.49729e-11 3 -2.421469966448315e+00 -2.421469966443913e+00 4.40226e-12 1.76952e-10 ----------------------------------------------------------------------------------------------------- 10 O 1 -2.289122621762569e-01 -2.289122621763335e-01 7.65499e-14 7.05859e-11 2 1.907981242062009e+00 1.907981242068957e+00 6.94778e-12 4.38907e-11 3 -3.862526502624608e+00 -3.862526502621558e+00 3.04956e-12 1.49658e-11 ----------------------------------------------------------------------------------------------------- 11 O 1 -1.370988510969255e+00 -1.370988510975628e+00 6.37312e-12 5.88629e-08 * 2 -7.277207978095011e-02 -7.277207977853857e-02 2.41154e-12 9.17461e-11 3 -5.042874760495038e+00 -5.042874760529493e+00 3.44551e-11 2.41307e-10 ----------------------------------------------------------------------------------------------------- 12 O 1 -4.800350162742452e+00 -4.800350162741213e+00 1.23901e-12 1.64766e-11 2 1.374056508879889e+00 1.374056508881668e+00 1.77969e-12 4.42631e-10 3 -3.180585813781995e+00 -3.180585813780824e+00 1.17062e-12 4.38724e-09 * ----------------------------------------------------------------------------------------------------- 13 O 1 -3.077119461102360e-02 -3.077119460787563e-02 3.14796e-12 5.41572e-11 2 3.788695347741505e+00 3.788695347743957e+00 2.45226e-12 9.67693e-11 3 3.526042908784122e+00 3.526042908797226e+00 1.31042e-11 2.14166e-10 ----------------------------------------------------------------------------------------------------- 14 Ti 1 4.464059517196186e-01 4.464059517170603e-01 2.55823e-12 7.93920e-11 2 9.965530627990972e-01 9.965530628085481e-01 9.45088e-12 5.01778e-11 3 -3.441538045467281e+00 -3.441538045468840e+00 1.55920e-12 9.49751e-11 ----------------------------------------------------------------------------------------------------- 15 O 1 -2.265659691120359e+00 -2.265659691135019e+00 1.46594e-11 2.68184e-10 2 4.459252223946900e+00 4.459252223936613e+00 1.02878e-11 7.17613e-11 3 2.022586475632166e+00 2.022586475634370e+00 2.20401e-12 1.06607e-10 ----------------------------------------------------------------------------------------------------- 16 O 1 5.781125445960858e+00 5.781125445897344e+00 6.35136e-11 2.93135e-10 2 4.200812196479960e-02 4.200812197762565e-02 1.28261e-11 3.31250e-10 3 -4.252785918927507e+00 -4.252785919010901e+00 8.33937e-11 2.14089e-10 ----------------------------------------------------------------------------------------------------- 17 O 1 -1.780839265564391e+00 -1.780839265580706e+00 1.63145e-11 1.08732e-09 2 -9.092076947660940e-01 -9.092076948232777e-01 5.71837e-11 2.08706e-10 3 7.130194826981582e-01 7.130194826990881e-01 9.29923e-13 2.72269e-11 ----------------------------------------------------------------------------------------------------- 18 O 1 -3.236304783758014e-01 -3.236304783921920e-01 1.63906e-11 4.17654e-10 2 -2.664897533434571e+00 -2.664897533503096e+00 6.85247e-11 2.84892e-10 3 4.229098539574739e+00 4.229098539568474e+00 6.26521e-12 6.14255e-11 ----------------------------------------------------------------------------------------------------- 19 Ti 1 1.052765603820874e+01 1.052765603819315e+01 1.55911e-11 2.54774e-10 2 -2.011382461051295e+01 -2.011382461051567e+01 2.72138e-12 1.46887e-10 3 7.773032824410224e-01 7.773032824483125e-01 7.29006e-12 8.02675e-10 ----------------------------------------------------------------------------------------------------- 20 Ti 1 -2.701880487597109e+01 -2.701880487602389e+01 5.28075e-11 1.79955e-08 * 2 -1.464362309482451e+00 -1.464362309475954e+00 6.49680e-12 1.72087e-10 3 -5.756037731773715e-01 -5.756037731780320e-01 6.60472e-13 4.28118e-11 ----------------------------------------------------------------------------------------------------- 21 O 1 1.805369265412172e+00 1.805369265328731e+00 8.34415e-11 2.55167e-10 2 -6.589030695427320e-01 -6.589030697640748e-01 2.21343e-10 5.46339e-10 3 1.651457618782916e+00 1.651457618817071e+00 3.41551e-11 1.04775e-09 ----------------------------------------------------------------------------------------------------- 22 O 1 -5.363045100753627e-01 -5.363045101129270e-01 3.75643e-11 7.39565e-10 2 2.515454302044381e+00 2.515454302040083e+00 4.29790e-12 5.82459e-11 3 1.092255822681982e+00 1.092255822682036e+00 5.39568e-14 1.35145e-10 ----------------------------------------------------------------------------------------------------- 23 Ti 1 8.965254807452904e+00 8.965254807447460e+00 5.44453e-12 1.69358e-11 2 -1.078405225145755e+01 -1.078405225146519e+01 7.64366e-12 1.31507e-06 * 3 2.635312135493792e+00 2.635312135500013e+00 6.22080e-12 1.65888e-05 * ----------------------------------------------------------------------------------------------------- 24 Ti 1 -5.759067901532163e-01 -5.759067901435756e-01 9.64073e-12 8.07233e-10 2 1.075420596896061e+01 1.075420596886226e+01 9.83498e-11 5.92594e-10 3 -3.489607307960469e+00 -3.489607308067992e+00 1.07523e-10 2.89434e-10 ----------------------------------------------------------------------------------------------------- 25 O 1 -3.008655412331065e+00 -3.008655412329693e+00 1.37179e-12 2.19902e-10 2 -2.558825155121613e+00 -2.558825155119445e+00 2.16849e-12 5.42295e-09 * 3 1.853530406626297e+00 1.853530406631500e+00 5.20339e-12 8.52529e-11 ----------------------------------------------------------------------------------------------------- 26 Ti 1 1.003571000347391e+01 1.003571000348319e+01 9.27436e-12 1.70417e-10 2 8.010104275477586e+00 8.010104275494975e+00 1.73888e-11 1.12086e-09 3 -6.972540337736040e+00 -6.972540337732689e+00 3.35021e-12 1.90805e-10 ----------------------------------------------------------------------------------------------------- 27 Ti 1 6.375513355484549e+00 6.375513355504167e+00 1.96181e-11 1.28958e-10 2 1.410547604401621e+01 1.410547604389069e+01 1.25519e-10 2.51665e-10 3 1.220268729549413e+01 1.220268729549315e+01 9.80549e-13 6.10655e-10 ----------------------------------------------------------------------------------------------------- 28 O 1 -4.720987853750997e+00 -4.720987853746400e+00 4.59721e-12 1.09524e-10 2 8.028357439113677e-01 8.028357439104771e-01 8.90621e-13 4.81742e-10 3 3.215473762107181e+00 3.215473762115592e+00 8.41061e-12 4.93547e-11 ----------------------------------------------------------------------------------------------------- 29 O 1 8.009907542426888e+00 8.009907542441088e+00 1.42002e-11 2.01410e-10 2 2.115515849394549e+00 2.115515849385777e+00 8.77165e-12 1.74673e-10 3 3.369080189086708e+00 3.369080189103991e+00 1.72826e-11 1.97947e-09 * ----------------------------------------------------------------------------------------------------- 30 Ti 1 -3.631399598171031e+00 -3.631399598323644e+00 1.52613e-10 2.56371e-10 2 -7.293086568945290e-01 -7.293086568798607e-01 1.46683e-11 9.13924e-11 3 5.706233787306473e+00 5.706233787265448e+00 4.10250e-11 1.72441e-10 ----------------------------------------------------------------------------------------------------- 31 O 1 -2.316758832018812e+00 -2.316758832013687e+00 5.12435e-12 1.67307e-10 2 2.348824055707193e+00 2.348824055716358e+00 9.16467e-12 5.86606e-11 3 -3.580955006976026e+00 -3.580955007114188e+00 1.38162e-10 4.09028e-10 ----------------------------------------------------------------------------------------------------- 32 O 1 5.124703325325590e+00 5.124703325312401e+00 1.31886e-11 7.34195e-11 2 -2.347495860784354e+00 -2.347495860773766e+00 1.05884e-11 8.56670e-11 3 1.317667972816710e+00 1.317667972815640e+00 1.07048e-12 3.03373e-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 = ----------------------- = 3.35926e-10 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 3.35926e-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 3.35926e-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.