!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_SunRamachandranWick_2018_TiAl__MO_022920256108_000 Supported species : Al 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 = Al | a0 = 4.049985885620117 | (Configuration in file "config-Al.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Al 1 -2.298797658405096e-01 -2.298797658590184e-01 1.85088e-11 1.50581e-10 2 -2.360154395759346e-01 -2.360154395750874e-01 8.47211e-13 4.44312e-11 3 -4.471073740907341e-01 -4.471073740939236e-01 3.18950e-12 3.00112e-11 ----------------------------------------------------------------------------------------------------- 2 Al 1 -6.007954771900771e-01 -6.007954771996519e-01 9.57479e-12 1.23471e-09 * 2 1.996940143241504e+00 1.996940143230093e+00 1.14109e-11 2.91026e-10 3 -6.268567437261081e-01 -6.268567437205642e-01 5.54390e-12 1.12067e-11 ----------------------------------------------------------------------------------------------------- 3 Al 1 2.180451488222929e-01 2.180451488156688e-01 6.62412e-12 2.83326e-11 2 -7.232203837845719e-01 -7.232203837412742e-01 4.32977e-11 3.57094e-11 3 1.430525223296038e+00 1.430525223315702e+00 1.96645e-11 5.43048e-11 ----------------------------------------------------------------------------------------------------- 4 Al 1 -4.467443653153644e-01 -4.467443653181015e-01 2.73709e-12 1.95207e-11 2 7.244909105904427e-01 7.244909106082152e-01 1.77726e-11 1.35863e-09 * 3 5.514254835201837e-01 5.514254835082907e-01 1.18930e-11 1.68191e-11 ----------------------------------------------------------------------------------------------------- 5 Al 1 1.469065184834632e+00 1.469065184828455e+00 6.17750e-12 1.91684e-10 2 -1.137551050770265e+00 -1.137551050797966e+00 2.77005e-11 2.97813e-11 3 -4.375892720650685e-01 -4.375892720787415e-01 1.36730e-11 9.66071e-11 ----------------------------------------------------------------------------------------------------- 6 Al 1 1.615500622966042e-01 1.615500622930161e-01 3.58807e-12 7.84229e-11 2 6.922862630194445e-01 6.922862630403089e-01 2.08644e-11 4.77774e-11 3 -7.036497281909714e-01 -7.036497281874536e-01 3.51774e-12 1.08292e-10 ----------------------------------------------------------------------------------------------------- 7 Al 1 3.908864284582756e-01 3.908864284832894e-01 2.50137e-11 2.45692e-10 2 -2.222222235458320e+00 -2.222222235475542e+00 1.72222e-11 1.40281e-09 * 3 -1.517503430028148e+00 -1.517503430046604e+00 1.84557e-11 6.12384e-10 ----------------------------------------------------------------------------------------------------- 8 Al 1 -1.725961675176002e+00 -1.725961675165462e+00 1.05393e-11 2.40408e-11 2 -6.274432885855454e-01 -6.274432886081922e-01 2.26468e-11 1.95102e-10 3 -4.120850372408892e-02 -4.120850378804193e-02 6.39530e-11 1.62941e-10 ----------------------------------------------------------------------------------------------------- 9 Al 1 -2.635357654608567e-01 -2.635357654677847e-01 6.92796e-12 7.16985e-11 2 -1.009092215387007e+00 -1.009092215383146e+00 3.86113e-12 3.36506e-11 3 -6.010174492156901e-01 -6.010174492120607e-01 3.62943e-12 1.41649e-10 ----------------------------------------------------------------------------------------------------- 10 Al 1 -2.564842180122620e-01 -2.564842180004503e-01 1.18117e-11 1.55165e-11 2 1.004736932854355e+00 1.004736932835657e+00 1.86984e-11 4.53946e-11 3 -1.077871824441654e+00 -1.077871824441670e+00 1.62093e-14 1.11122e-11 ----------------------------------------------------------------------------------------------------- 11 Al 1 -3.125712608255014e-02 -3.125712605824588e-02 2.43043e-11 2.91169e-10 2 -1.192964367759541e+00 -1.192964367734086e+00 2.54543e-11 7.16815e-11 3 1.884730030912147e-01 1.884730030871676e-01 4.04715e-12 2.58007e-10 ----------------------------------------------------------------------------------------------------- 12 Al 1 -2.664555222053115e-01 -2.664555222026723e-01 2.63917e-12 9.18100e-11 2 9.481905823174493e-01 9.481905822957115e-01 2.17378e-11 6.53035e-11 3 4.090463277038338e-01 4.090463276989956e-01 4.83813e-12 8.65955e-11 ----------------------------------------------------------------------------------------------------- 13 Al 1 -6.688219450715254e-01 -6.688219450864493e-01 1.49240e-11 1.15847e-10 2 -1.451810082836168e+00 -1.451810082822619e+00 1.35492e-11 2.44276e-11 3 -2.930286522876107e+00 -2.930286522867316e+00 8.79030e-12 1.98046e-11 ----------------------------------------------------------------------------------------------------- 14 Al 1 -3.505572314107945e-01 -3.505572314147994e-01 4.00491e-12 6.27779e-11 2 -3.808309281965148e-02 -3.808309281870838e-02 9.43100e-13 2.01771e-10 3 4.381472808448724e-01 4.381472808561909e-01 1.13185e-11 1.39112e-11 ----------------------------------------------------------------------------------------------------- 15 Al 1 3.003558344320628e+00 3.003558344362250e+00 4.16218e-11 2.08927e-10 2 -7.641675774940795e-01 -7.641675774874317e-01 6.64779e-12 2.49852e-10 3 4.074106062041141e-01 4.074106061777859e-01 2.63282e-11 1.92187e-10 ----------------------------------------------------------------------------------------------------- 16 Al 1 4.699348465691718e-01 4.699348465609494e-01 8.22248e-12 2.25558e-11 2 2.483750035959828e+00 2.483750035941385e+00 1.84430e-11 1.39387e-10 3 7.159196628078611e-01 7.159196627715522e-01 3.63090e-11 2.20525e-09 * ----------------------------------------------------------------------------------------------------- 17 Al 1 -5.712459716599796e-01 -5.712459716601007e-01 1.21125e-13 2.35852e-10 2 -5.730602598884629e-01 -5.730602598877166e-01 7.46292e-13 7.38365e-11 3 -9.846786696145983e-01 -9.846786696184169e-01 3.81861e-12 3.95219e-10 ----------------------------------------------------------------------------------------------------- 18 Al 1 6.228262120052215e-01 6.228262120066188e-01 1.39733e-12 6.72125e-11 2 1.016842828670281e+00 1.016842828670342e+00 6.12843e-14 7.56090e-10 3 -7.903314360779723e-01 -7.903314360684427e-01 9.52960e-12 3.43877e-10 ----------------------------------------------------------------------------------------------------- 19 Al 1 1.025289594990458e+00 1.025289594993586e+00 3.12794e-12 5.02707e-11 2 -1.058583787967304e+00 -1.058583787938558e+00 2.87463e-11 1.24636e-10 3 5.468298658306566e-01 5.468298658416625e-01 1.10059e-11 6.57263e-10 ----------------------------------------------------------------------------------------------------- 20 Al 1 -7.214249768279752e-01 -7.214249768356987e-01 7.72349e-12 1.52143e-10 2 1.508991698520429e+00 1.508991698528573e+00 8.14393e-12 1.51710e-10 3 5.878438266443503e-01 5.878438266663752e-01 2.20249e-11 2.06598e-10 ----------------------------------------------------------------------------------------------------- 21 Al 1 -1.664433776015346e+00 -1.664433776012306e+00 3.03979e-12 1.76383e-11 2 -5.529557482797368e-01 -5.529557482950554e-01 1.53186e-11 7.14245e-11 3 1.486257054885563e-01 1.486257054986150e-01 1.00586e-11 8.37454e-11 ----------------------------------------------------------------------------------------------------- 22 Al 1 8.916590504358728e-01 8.916590504349029e-01 9.69891e-13 1.20806e-10 2 2.488458631203380e+00 2.488458631202914e+00 4.66294e-13 7.42197e-11 3 1.693897532061769e+00 1.693897532068644e+00 6.87450e-12 1.74932e-09 * ----------------------------------------------------------------------------------------------------- 23 Al 1 1.783783035336514e-01 1.783783035291024e-01 4.54906e-12 1.46040e-10 2 -7.791340999216645e-02 -7.791340999652366e-02 4.35721e-12 3.59019e-10 3 3.551790697205159e-01 3.551790697237850e-01 3.26905e-12 2.65576e-09 * ----------------------------------------------------------------------------------------------------- 24 Al 1 3.301881931915344e-01 3.301881932388909e-01 4.73566e-11 2.41885e-10 2 7.384829615360625e-01 7.384829615651357e-01 2.90732e-11 1.52198e-10 3 9.829313334020316e-02 9.829313333841588e-02 1.78728e-12 2.25768e-11 ----------------------------------------------------------------------------------------------------- 25 Al 1 -9.364316386656809e-01 -9.364316386630696e-01 2.61136e-12 9.90420e-11 2 -1.193355474534846e+00 -1.193355474554374e+00 1.95277e-11 4.18190e-11 3 6.832318646748557e-01 6.832318646683119e-01 6.54388e-12 3.98050e-11 ----------------------------------------------------------------------------------------------------- 26 Al 1 -6.446936359541227e-01 -6.446936359160436e-01 3.80791e-11 1.07223e-10 2 1.364784885541596e+00 1.364784885564025e+00 2.24289e-11 4.12163e-10 3 -9.412920707165238e-01 -9.412920707108926e-01 5.63116e-12 7.31357e-10 ----------------------------------------------------------------------------------------------------- 27 Al 1 4.809141032284361e-01 4.809141032060689e-01 2.23672e-11 8.96319e-11 2 -2.716775048249263e+00 -2.716775048200132e+00 4.91314e-11 5.04845e-10 3 6.642620564475352e-01 6.642620564584627e-01 1.09275e-11 3.70740e-11 ----------------------------------------------------------------------------------------------------- 28 Al 1 -9.366261673293801e-01 -9.366261673362498e-01 6.86973e-12 2.25133e-09 * 2 1.004165889401181e+00 1.004165889416775e+00 1.55944e-11 2.24832e-09 * 3 -6.654864531761645e-03 -6.654864515364928e-03 1.63967e-11 7.36722e-11 ----------------------------------------------------------------------------------------------------- 29 Al 1 -8.568925381441794e-01 -8.568925381265228e-01 1.76567e-11 2.99471e-10 2 -1.629691787776623e+00 -1.629691787767101e+00 9.52216e-12 2.33339e-09 * 3 7.610983964672700e-01 7.610983964104463e-01 5.68237e-11 2.49394e-10 ----------------------------------------------------------------------------------------------------- 30 Al 1 6.838923777822806e-01 6.838923777902002e-01 7.91955e-12 1.35846e-09 * 2 1.273528087524977e+00 1.273528087542074e+00 1.70965e-11 8.84221e-10 3 7.240892284156689e-02 7.240892285178405e-02 1.02172e-11 4.74355e-11 ----------------------------------------------------------------------------------------------------- 31 Al 1 7.501973032069158e-01 7.501973031987084e-01 8.20743e-12 2.47861e-10 2 -1.194656562069671e+00 -1.194656562069688e+00 1.70974e-14 3.07520e-10 3 5.435666526724782e-01 5.435666526267616e-01 4.57165e-11 9.66189e-10 ----------------------------------------------------------------------------------------------------- 32 Al 1 4.958566426859424e-01 4.958566426884795e-01 2.53703e-12 2.42730e-10 2 1.153911962848226e+00 1.153911962867969e+00 1.97433e-11 1.53036e-10 3 8.098632756415514e-01 8.098632756441279e-01 2.57649e-12 6.35015e-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 = 28, direction = 3: |F_model - F_numer| error = ----------------------- = 2.46387e-09 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 = 4.181670188903809 | (Configuration in file "config-Ti.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ti 1 -1.897292238431236e-01 -1.897292238473068e-01 4.18326e-12 1.21479e-10 2 -7.453042916149067e-01 -7.453042916149385e-01 3.17524e-14 3.28833e-11 3 -5.892364470155395e-01 -5.892364469991407e-01 1.63988e-11 1.57831e-10 ----------------------------------------------------------------------------------------------------- 2 Ti 1 1.382220585595004e+00 1.382220585599218e+00 4.21330e-12 2.64313e-11 2 -1.242255390247175e+00 -1.242255390245658e+00 1.51745e-12 1.31601e-09 3 -1.586798838944697e+00 -1.586798838926435e+00 1.82625e-11 1.97375e-10 ----------------------------------------------------------------------------------------------------- 3 Ti 1 1.054042764274815e+00 1.054042764282418e+00 7.60303e-12 4.92413e-11 2 -8.169269739998096e-01 -8.169269740042530e-01 4.44333e-12 1.25971e-10 3 -4.357984869205593e-01 -4.357984869266012e-01 6.04183e-12 2.90957e-11 ----------------------------------------------------------------------------------------------------- 4 Ti 1 -1.084078188947323e+00 -1.084078188951680e+00 4.35696e-12 1.05567e-08 * 2 5.357057572846946e-01 5.357057572643754e-01 2.03192e-11 1.72433e-10 3 1.480212280410832e+00 1.480212280414787e+00 3.95484e-12 1.14550e-10 ----------------------------------------------------------------------------------------------------- 5 Ti 1 -2.553729734504588e+00 -2.553729734506703e+00 2.11475e-12 3.85267e-10 2 -4.153647796398620e-01 -4.153647796152453e-01 2.46168e-11 5.27379e-11 3 -1.362261760115741e+00 -1.362261760130941e+00 1.52005e-11 5.70279e-11 ----------------------------------------------------------------------------------------------------- 6 Ti 1 7.087215427902104e-01 7.087215427875295e-01 2.68086e-12 4.92186e-11 2 9.388298265220744e-01 9.388298264753535e-01 4.67208e-11 1.05983e-10 3 -3.781700589371810e-01 -3.781700589464212e-01 9.24022e-12 4.26260e-10 ----------------------------------------------------------------------------------------------------- 7 Ti 1 1.492884140732426e+00 1.492884140754517e+00 2.20910e-11 8.84515e-10 2 -1.374046062430479e-01 -1.374046062492375e-01 6.18963e-12 3.21920e-10 3 2.456223701515151e+00 2.456223701515866e+00 7.14984e-13 5.83085e-11 ----------------------------------------------------------------------------------------------------- 8 Ti 1 1.119354273513682e-01 1.119354273646946e-01 1.33264e-11 4.14661e-10 2 -1.295617019433302e+00 -1.295617019423319e+00 9.98290e-12 2.30257e-10 3 -6.364559130429924e-01 -6.364559130029002e-01 4.00923e-11 5.01287e-10 ----------------------------------------------------------------------------------------------------- 9 Ti 1 -7.445477549721005e-01 -7.445477547640446e-01 2.08056e-10 8.00110e-10 2 6.704834406032943e-01 6.704834406230080e-01 1.97137e-11 2.23323e-10 3 -5.009777304297304e-01 -5.009777303003695e-01 1.29361e-10 8.61501e-10 ----------------------------------------------------------------------------------------------------- 10 Ti 1 -2.966996781337451e-01 -2.966996781306895e-01 3.05567e-12 8.72717e-11 2 1.121246411934718e+00 1.121246411957538e+00 2.28206e-11 1.22804e-11 3 -5.733301779349959e-01 -5.733301779577212e-01 2.27254e-11 9.34735e-11 ----------------------------------------------------------------------------------------------------- 11 Ti 1 -7.208856327556270e-01 -7.208856326319166e-01 1.23710e-10 9.29995e-10 2 1.020961982683386e+00 1.020961982648738e+00 3.46483e-11 1.53592e-10 3 2.234850557986082e+00 2.234850558009948e+00 2.38658e-11 6.13781e-08 * ----------------------------------------------------------------------------------------------------- 12 Ti 1 1.989891773652651e-01 1.989891773663021e-01 1.03695e-12 1.06589e-10 2 2.293453909452040e-01 2.293453909328681e-01 1.23358e-11 5.88221e-11 3 3.669893266501560e-03 3.669893250194142e-03 1.63074e-11 2.00884e-11 ----------------------------------------------------------------------------------------------------- 13 Ti 1 6.335151682363090e-01 6.335151682617907e-01 2.54816e-11 3.76876e-11 2 -1.276066634149825e-01 -1.276066634137470e-01 1.23551e-12 6.08472e-10 3 -9.586723260677775e-01 -9.586723260846501e-01 1.68726e-11 4.19238e-11 ----------------------------------------------------------------------------------------------------- 14 Ti 1 3.500643257084756e-02 3.500643256883308e-02 2.01448e-12 1.05130e-10 2 6.218390129849584e-01 6.218390129813164e-01 3.64198e-12 2.22462e-11 3 -9.792389922271976e-01 -9.792389922309969e-01 3.79929e-12 3.21675e-11 ----------------------------------------------------------------------------------------------------- 15 Ti 1 1.505558454052619e+00 1.505558454064022e+00 1.14029e-11 2.87241e-09 * 2 -2.232198304318750e+00 -2.232198304342810e+00 2.40594e-11 1.00216e-10 3 2.934767025856169e-01 2.934767025804071e-01 5.20983e-12 1.97488e-10 ----------------------------------------------------------------------------------------------------- 16 Ti 1 -1.723744925752176e+00 -1.723744925647889e+00 1.04287e-10 3.50001e-10 2 1.933191161108453e+00 1.933191161126431e+00 1.79772e-11 8.85227e-11 3 -1.324664930510338e+00 -1.324664930551165e+00 4.08265e-11 7.55706e-10 ----------------------------------------------------------------------------------------------------- 17 Ti 1 -2.252851480342531e+00 -2.252851480341051e+00 1.48015e-12 7.46665e-10 2 -3.411851076373805e+00 -3.411851076447567e+00 7.37623e-11 2.35068e-10 3 -1.750208617639077e+00 -1.750208617639252e+00 1.75415e-13 9.52858e-11 ----------------------------------------------------------------------------------------------------- 18 Ti 1 2.494847411895384e+00 2.494847411954703e+00 5.93192e-11 1.04218e-09 2 3.273362013829456e+00 3.273362013797588e+00 3.18678e-11 6.35323e-11 3 -2.053795350578304e+00 -2.053795350553751e+00 2.45532e-11 2.05769e-09 * ----------------------------------------------------------------------------------------------------- 19 Ti 1 -1.955739700696419e+00 -1.955739700615290e+00 8.11298e-11 1.00547e-10 2 -1.241043768056757e+00 -1.241043768085572e+00 2.88147e-11 1.95324e-10 3 3.488762097187661e+00 3.488762097128093e+00 5.95684e-11 1.64930e-10 ----------------------------------------------------------------------------------------------------- 20 Ti 1 -1.777731362905508e+00 -1.777731362880769e+00 2.47393e-11 1.69520e-10 2 2.107157949912156e+00 2.107157949876989e+00 3.51674e-11 1.06121e-10 3 3.676126984403598e+00 3.676126984522487e+00 1.18888e-10 2.36786e-10 ----------------------------------------------------------------------------------------------------- 21 Ti 1 2.950787732667906e+00 2.950787732562714e+00 1.05192e-10 3.31516e-10 2 -8.694839296992667e-01 -8.694839296992277e-01 3.89688e-14 9.16345e-11 3 -3.113049936182730e+00 -3.113049936165139e+00 1.75908e-11 6.29745e-09 * ----------------------------------------------------------------------------------------------------- 22 Ti 1 1.191705276810932e+00 1.191705276820343e+00 9.41069e-12 3.26705e-10 2 -1.346851282367823e+00 -1.346851282389437e+00 2.16138e-11 4.50251e-10 3 -1.408519470422033e+00 -1.408519470434677e+00 1.26439e-11 3.11296e-10 ----------------------------------------------------------------------------------------------------- 23 Ti 1 -4.702069658915501e-01 -4.702069658847762e-01 6.77391e-12 9.49250e-11 2 3.585825246127650e-01 3.585825246037814e-01 8.98359e-12 1.16354e-10 3 -5.773333082419225e-01 -5.773333082432235e-01 1.30096e-12 2.23148e-10 ----------------------------------------------------------------------------------------------------- 24 Ti 1 -4.514772477458646e-01 -4.514772477672514e-01 2.13868e-11 8.23299e-11 2 1.171094807988668e+00 1.171094807989718e+00 1.04983e-12 2.35707e-10 3 1.148069220106420e+00 1.148069220061805e+00 4.46145e-11 8.75916e-09 * ----------------------------------------------------------------------------------------------------- 25 Ti 1 5.098116310921931e-02 5.098116305561860e-02 5.36007e-11 5.01960e-11 2 -9.277562619849832e-01 -9.277562620571994e-01 7.22162e-11 2.00243e-10 3 -6.213043305964211e-01 -6.213043307401167e-01 1.43696e-10 2.20309e-10 ----------------------------------------------------------------------------------------------------- 26 Ti 1 -7.911454267382002e-01 -7.911454267865552e-01 4.83550e-11 2.79674e-06 * 2 6.979572880195877e-01 6.979572880054998e-01 1.40878e-11 3.75422e-10 3 -7.220924234871193e-01 -7.220924234713101e-01 1.58092e-11 1.55955e-10 ----------------------------------------------------------------------------------------------------- 27 Ti 1 6.950699642354183e-01 6.950699642690484e-01 3.36301e-11 1.04851e-10 2 -8.562023311252634e-01 -8.562023310141100e-01 1.11153e-10 7.28549e-10 3 2.325074820210189e-01 2.325074819285395e-01 9.24793e-11 6.93223e-10 ----------------------------------------------------------------------------------------------------- 28 Ti 1 -3.798696707502696e-01 -3.798696707292745e-01 2.09952e-11 6.08901e-11 2 7.361340166568487e-01 7.361340166348960e-01 2.19528e-11 1.47353e-09 * 3 5.870997542544729e-01 5.870997543119552e-01 5.74822e-11 2.88373e-10 ----------------------------------------------------------------------------------------------------- 29 Ti 1 -5.082736395402088e-01 -5.082736396039566e-01 6.37478e-11 1.82084e-10 2 -1.368955054655010e+00 -1.368955054662157e+00 7.14651e-12 2.74083e-10 3 1.797899526904521e+00 1.797899526908229e+00 3.70770e-12 1.40140e-10 ----------------------------------------------------------------------------------------------------- 30 Ti 1 9.005431850888498e-01 9.005431850846798e-01 4.17000e-12 3.77826e-06 * 2 7.023061235622812e-01 7.023061235790374e-01 1.67563e-11 1.36792e-10 3 1.091965745454408e+00 1.091965745442275e+00 1.21336e-11 1.52709e-10 ----------------------------------------------------------------------------------------------------- 31 Ti 1 3.115109678412377e-02 3.115109677326475e-02 1.08590e-11 1.33941e-10 2 1.015103906668053e+00 1.015103906632864e+00 3.51894e-11 2.14279e-10 3 9.078077938211188e-01 9.078077938263280e-01 5.20928e-12 1.80914e-10 ----------------------------------------------------------------------------------------------------- 32 Ti 1 4.627511099585380e-01 4.627511099552067e-01 3.33134e-12 2.52410e-11 2 -9.847988214185363e-02 -9.847988214402568e-02 2.17205e-12 2.61789e-09 * 3 1.732373593769539e-01 1.732373593694917e-01 7.46220e-12 2.89465e-10 ----------------------------------------------------------------------------------------------------- * 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 = 12, direction = 3: |F_model - F_numer| error = ----------------------- = 4.44357e-09 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 = Al Ti | a0 = 4.032374436315694 | (Configuration in file "config-AlTi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Al 1 5.388437177461304e-02 5.388437177482303e-02 2.09992e-13 4.72369e-11 2 9.836383905656207e-02 9.836383905696469e-02 4.02622e-13 2.03256e-11 3 3.144139988018715e-01 3.144139987901591e-01 1.17124e-11 1.53319e-10 ----------------------------------------------------------------------------------------------------- 2 Ti 1 3.116948298677521e+00 3.116948298685087e+00 7.56595e-12 9.09814e-11 2 -4.364704263280743e-01 -4.364704263104132e-01 1.76611e-11 8.96091e-11 3 -1.481242605759819e+00 -1.481242605746053e+00 1.37663e-11 8.11564e-11 ----------------------------------------------------------------------------------------------------- 3 Al 1 1.848572396363926e+00 1.848572396379585e+00 1.56595e-11 1.73353e-10 2 -3.327342085370153e-01 -3.327342084990501e-01 3.79652e-11 1.15720e-10 3 -6.912750752109119e-01 -6.912750752286552e-01 1.77433e-11 9.53806e-10 ----------------------------------------------------------------------------------------------------- 4 Ti 1 -1.880239694489075e+00 -1.880239694500280e+00 1.12053e-11 9.90976e-11 2 -7.265479050140264e-01 -7.265479050251604e-01 1.11340e-11 3.12817e-10 3 2.366500801101048e+00 2.366500801117022e+00 1.59748e-11 1.22602e-10 ----------------------------------------------------------------------------------------------------- 5 Ti 1 -4.936394580627724e+00 -4.936394580615844e+00 1.18794e-11 2.16271e-10 2 -4.657990644227412e-01 -4.657990644289585e-01 6.21730e-12 4.00124e-10 3 -3.844652810301612e+00 -3.844652810300601e+00 1.01075e-12 9.55040e-11 ----------------------------------------------------------------------------------------------------- 6 Al 1 1.145694086034167e+00 1.145694086035939e+00 1.77280e-12 9.79863e-11 2 9.449483882754952e-01 9.449483882795230e-01 4.02778e-12 8.76420e-11 3 -1.130706326932830e+00 -1.130706326946605e+00 1.37752e-11 2.63762e-10 ----------------------------------------------------------------------------------------------------- 7 Ti 1 4.288563961655659e+00 4.288563961659862e+00 4.20286e-12 4.40947e-10 2 -9.561451683663751e-01 -9.561451683507920e-01 1.55831e-11 2.33060e-11 3 5.071955537206166e+00 5.071955537216128e+00 9.96181e-12 8.90124e-11 ----------------------------------------------------------------------------------------------------- 8 Ti 1 -3.182629138649818e+00 -3.182629138766273e+00 1.16455e-10 1.78295e-09 * 2 -2.524558345869783e+00 -2.524558345834245e+00 3.55387e-11 3.47616e-10 3 -8.085780825419903e-01 -8.085787002647356e-01 6.17723e-07 4.72531e-08 * ----------------------------------------------------------------------------------------------------- 9 Al 1 -1.224083329855858e-01 -1.224083329861559e-01 5.70058e-13 1.02853e-11 2 1.286713374832247e+00 1.286713374839290e+00 7.04281e-12 1.85645e-11 3 -1.176291173404021e+00 -1.176291173359520e+00 4.45006e-11 8.92717e-11 ----------------------------------------------------------------------------------------------------- 10 Ti 1 1.088598291376440e+00 1.088598291375655e+00 7.84262e-13 1.70003e-09 * 2 -1.255524543518499e+00 -1.255524543521910e+00 3.41083e-12 7.45362e-11 3 -4.535135610090011e-01 -4.535135610176772e-01 8.67606e-12 2.48046e-09 * ----------------------------------------------------------------------------------------------------- 11 Al 1 7.907841934920238e-01 7.907841934800366e-01 1.19872e-11 1.39191e-10 2 -1.238629427465105e+00 -1.238629427416757e+00 4.83480e-11 1.16894e-10 3 -2.017184533615313e+00 -2.017184533609968e+00 5.34550e-12 1.36218e-10 ----------------------------------------------------------------------------------------------------- 12 Al 1 -1.048299233808627e+00 -1.048299233811157e+00 2.53020e-12 8.96166e-10 2 3.646416088391781e-01 3.646416088567809e-01 1.76028e-11 2.93547e-10 3 1.479221754442489e+00 1.479221754423232e+00 1.92575e-11 6.09284e-11 ----------------------------------------------------------------------------------------------------- 13 Ti 1 -2.584407396000136e+00 -2.584407396006065e+00 5.92948e-12 4.07137e-11 2 4.843360522196492e-01 4.843360522134555e-01 6.19366e-12 4.69705e-11 3 -2.323775598633194e+00 -2.323775598661747e+00 2.85527e-11 1.40610e-10 ----------------------------------------------------------------------------------------------------- 14 Al 1 7.028384307853823e-01 7.028384307848689e-01 5.13478e-13 3.15425e-12 2 7.135684246119106e-01 7.135684246090812e-01 2.82940e-12 4.95977e-11 3 -1.005325609519579e+00 -1.005325609520796e+00 1.21769e-12 1.37617e-09 * ----------------------------------------------------------------------------------------------------- 15 Ti 1 2.801098203021943e+00 2.801098203021679e+00 2.64233e-13 8.48356e-10 2 1.036445522166944e+00 1.036445522159472e+00 7.47180e-12 1.92330e-10 3 2.895896484784326e+00 2.895896484775498e+00 8.82805e-12 4.58021e-10 ----------------------------------------------------------------------------------------------------- 16 Al 1 -9.154398370059170e-01 -9.154398369796444e-01 2.62727e-11 2.10580e-10 2 1.004682601783308e+00 1.004682601759684e+00 2.36238e-11 1.02048e-10 3 1.031658493995137e+00 1.031658494003267e+00 8.13016e-12 1.97702e-10 ----------------------------------------------------------------------------------------------------- 17 Ti 1 -9.209764345683580e-01 -9.209764345554488e-01 1.29092e-11 5.21331e-11 2 3.594331263672627e-01 3.594331263653074e-01 1.95532e-12 1.79009e-10 3 9.503164374124367e-01 9.503164374146518e-01 2.21512e-12 1.51736e-10 ----------------------------------------------------------------------------------------------------- 18 Ti 1 -7.832763181151617e-01 -7.832763181449474e-01 2.97856e-11 3.33618e-10 2 -1.809002133928217e+00 -1.809002134053841e+00 1.25624e-10 2.76786e-10 3 -2.652268508416606e+00 -2.652268508509290e+00 9.26832e-11 5.74969e-10 ----------------------------------------------------------------------------------------------------- 19 Al 1 2.382985948571259e-01 2.382984235847453e-01 1.71272e-07 1.33523e-10 2 -1.288505723569025e+00 -1.288505001109411e+00 7.22460e-07 1.50209e-09 * 3 6.901888095717140e-01 6.901888095750198e-01 3.30580e-12 1.41356e-10 ----------------------------------------------------------------------------------------------------- 20 Al 1 -2.852357483627062e-01 -2.852357483861916e-01 2.34854e-11 1.23508e-10 2 1.954747582127177e-01 1.954747582236330e-01 1.09153e-11 7.00225e-11 3 -2.727952595270801e-01 -2.727952595269247e-01 1.55320e-13 5.43780e-11 ----------------------------------------------------------------------------------------------------- 21 Al 1 -1.470458901715735e+00 -1.470458901697932e+00 1.78024e-11 7.59201e-10 2 -7.043034012879079e-01 -7.043034012621660e-01 2.57420e-11 2.00379e-11 3 -1.353351197169138e+00 -1.353351197189376e+00 2.02380e-11 3.37337e-11 ----------------------------------------------------------------------------------------------------- 22 Ti 1 1.602703462702913e+00 1.602703462540290e+00 1.62622e-10 3.56970e-10 2 9.485476634486442e-01 9.485476634956523e-01 4.70082e-11 3.30209e-09 * 3 -6.132319224690457e-01 -6.132319225518901e-01 8.28444e-11 1.59722e-10 ----------------------------------------------------------------------------------------------------- 23 Al 1 9.953431052602916e-01 9.953431052677896e-01 7.49800e-12 1.07711e-10 2 -5.546405710216682e-01 -5.546405710187966e-01 2.87159e-12 4.51053e-11 3 8.017330240715185e-01 8.017330240706256e-01 8.92841e-13 3.23270e-10 ----------------------------------------------------------------------------------------------------- 24 Ti 1 1.712851722391189e-01 1.712851722255739e-01 1.35451e-11 5.19790e-10 2 7.867737749752226e-01 7.867737749877803e-01 1.25577e-11 1.80730e-09 * 3 1.884470500452507e+00 1.884470500447024e+00 5.48361e-12 3.69355e-10 ----------------------------------------------------------------------------------------------------- 25 Ti 1 -3.029363144120494e+00 -3.029363144106068e+00 1.44258e-11 2.41103e-10 2 1.159947352578034e+00 1.159947352575690e+00 2.34435e-12 2.15473e-10 3 5.863138968452628e-01 5.863138968331693e-01 1.20935e-11 3.81772e-10 ----------------------------------------------------------------------------------------------------- 26 Ti 1 9.184796396149281e-01 9.184796396756563e-01 6.07282e-11 3.11353e-10 2 1.989668609432630e+00 1.989668609415398e+00 1.72322e-11 1.41016e-09 * 3 -6.944330518561804e-01 -6.944330518776013e-01 2.14209e-11 3.98110e-11 ----------------------------------------------------------------------------------------------------- 27 Al 1 3.873184106811269e-01 3.873184107011331e-01 2.00062e-11 1.26192e-09 2 3.611203400612110e-01 3.611203400796650e-01 1.84540e-11 1.62902e-10 3 1.493206375977301e+00 1.493206376010478e+00 3.31770e-11 3.71220e-10 ----------------------------------------------------------------------------------------------------- 28 Al 1 4.564481489603648e-01 4.564481489422573e-01 1.81076e-11 1.06963e-09 2 -6.531920535738929e-01 -6.531920535717141e-01 2.17881e-12 5.42779e-11 3 -6.644170762394850e-01 -6.644170762435676e-01 4.08262e-12 3.97606e-11 ----------------------------------------------------------------------------------------------------- 29 Al 1 5.802207855476562e-01 5.802207855541675e-01 6.51124e-12 3.19855e-10 2 2.620075637517008e+00 2.620075637507921e+00 9.08740e-12 4.07092e-10 3 2.336057924817162e+00 2.336057924807543e+00 9.61942e-12 2.12586e-09 * ----------------------------------------------------------------------------------------------------- 30 Al 1 -8.319140739608264e-04 -8.319140748716062e-04 9.10780e-13 8.65838e-11 2 -4.550274062146407e-01 -4.550274062126706e-01 1.97015e-12 3.66039e-11 3 -7.104074615635030e-01 -7.104074615788405e-01 1.53375e-11 9.13662e-10 ----------------------------------------------------------------------------------------------------- 31 Ti 1 2.988029628256410e+00 2.988029628230283e+00 2.61271e-11 1.27753e-10 2 -3.777030690719853e+00 -3.777030690732993e+00 1.31402e-11 3.60122e-10 3 5.197176927323769e-02 5.197176927529910e-02 2.06141e-12 3.47483e-11 ----------------------------------------------------------------------------------------------------- 32 Ti 1 -3.015148506778313e+00 -3.015148506838125e+00 5.98113e-11 4.57505e-10 2 2.823369995458799e+00 2.823369995446145e+00 1.26543e-11 1.41085e-09 * 3 -6.045595458286687e-02 -6.045595457179243e-02 1.10744e-11 1.81670e-10 ----------------------------------------------------------------------------------------------------- * 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 = 19, direction = 1: |F_model - F_numer| error = ----------------------- = 7.18731e-07 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 7.18731e-07 Machine precision = 2.22045e-16 Note: Lower grades can reflect errors in the analytical forces, a lack of smoothness in the potential, or loss of precision in the numerical derivative computation. Grade: B Comment: The letter grade B was assigned because the normalized error in the computation was 7.18731e-07 compared with a machine precision of 2.22045e-16. The letter grade was based on 'score=log10(error/eps)', with ranges A=[0, 7.5], B=(7.5, 10.0], C=(10.0, 12.5], D=(12.5, 15.0), F>15.0. 'A' is the best grade, and 'F' indicates failure.