!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_001 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 -2.298797658590185e-01 1.85089e-11 1.50581e-10 2 -2.360154395759346e-01 -2.360154395750875e-01 8.47045e-13 4.44311e-11 3 -4.471073740907341e-01 -4.471073740939241e-01 3.19000e-12 3.00114e-11 ----------------------------------------------------------------------------------------------------- 2 Al 1 -6.007954771900771e-01 -6.007954771996515e-01 9.57445e-12 1.23471e-09 * 2 1.996940143241504e+00 1.996940143230092e+00 1.14120e-11 2.91026e-10 3 -6.268567437261081e-01 -6.268567437205648e-01 5.54334e-12 1.12064e-11 ----------------------------------------------------------------------------------------------------- 3 Al 1 2.180451488222929e-01 2.180451488156690e-01 6.62392e-12 2.83326e-11 2 -7.232203837845719e-01 -7.232203837412748e-01 4.32970e-11 3.57095e-11 3 1.430525223296038e+00 1.430525223315704e+00 1.96658e-11 5.43050e-11 ----------------------------------------------------------------------------------------------------- 4 Al 1 -4.467443653153644e-01 -4.467443653181026e-01 2.73814e-12 1.95199e-11 2 7.244909105904427e-01 7.244909106082149e-01 1.77722e-11 1.35863e-09 * 3 5.514254835201837e-01 5.514254835082915e-01 1.18923e-11 1.68195e-11 ----------------------------------------------------------------------------------------------------- 5 Al 1 1.469065184834632e+00 1.469065184828456e+00 6.17617e-12 1.91684e-10 2 -1.137551050770265e+00 -1.137551050797967e+00 2.77021e-11 2.97800e-11 3 -4.375892720650685e-01 -4.375892720787418e-01 1.36733e-11 9.66071e-11 ----------------------------------------------------------------------------------------------------- 6 Al 1 1.615500622966042e-01 1.615500622930161e-01 3.58802e-12 7.84229e-11 2 6.922862630194445e-01 6.922862630403094e-01 2.08649e-11 4.77770e-11 3 -7.036497281909714e-01 -7.036497281874540e-01 3.51741e-12 1.08293e-10 ----------------------------------------------------------------------------------------------------- 7 Al 1 3.908864284582756e-01 3.908864284832896e-01 2.50140e-11 2.45692e-10 2 -2.222222235458320e+00 -2.222222235475541e+00 1.72209e-11 1.40281e-09 * 3 -1.517503430028148e+00 -1.517503430046605e+00 1.84566e-11 6.12384e-10 ----------------------------------------------------------------------------------------------------- 8 Al 1 -1.725961675176002e+00 -1.725961675165464e+00 1.05380e-11 2.40414e-11 2 -6.274432885855454e-01 -6.274432886081927e-01 2.26472e-11 1.95102e-10 3 -4.120850372408892e-02 -4.120850378804200e-02 6.39531e-11 1.62941e-10 ----------------------------------------------------------------------------------------------------- 9 Al 1 -2.635357654608567e-01 -2.635357654677849e-01 6.92818e-12 7.16987e-11 2 -1.009092215387007e+00 -1.009092215383147e+00 3.86002e-12 3.36502e-11 3 -6.010174492156901e-01 -6.010174492120609e-01 3.62921e-12 1.41649e-10 ----------------------------------------------------------------------------------------------------- 10 Al 1 -2.564842180122620e-01 -2.564842180004505e-01 1.18115e-11 1.55165e-11 2 1.004736932854355e+00 1.004736932835657e+00 1.86977e-11 4.53946e-11 3 -1.077871824441654e+00 -1.077871824441670e+00 1.64313e-14 1.11144e-11 ----------------------------------------------------------------------------------------------------- 11 Al 1 -3.125712608255014e-02 -3.125712605824590e-02 2.43042e-11 2.91169e-10 2 -1.192964367759541e+00 -1.192964367734087e+00 2.54536e-11 7.16815e-11 3 1.884730030912147e-01 1.884730030871677e-01 4.04701e-12 2.58007e-10 ----------------------------------------------------------------------------------------------------- 12 Al 1 -2.664555222053115e-01 -2.664555222026725e-01 2.63900e-12 9.18100e-11 2 9.481905823174493e-01 9.481905822957121e-01 2.17373e-11 6.53040e-11 3 4.090463277038338e-01 4.090463276989959e-01 4.83785e-12 8.65955e-11 ----------------------------------------------------------------------------------------------------- 13 Al 1 -6.688219450715254e-01 -6.688219450864489e-01 1.49235e-11 1.15847e-10 2 -1.451810082836168e+00 -1.451810082822621e+00 1.35478e-11 2.44258e-11 3 -2.930286522876107e+00 -2.930286522867318e+00 8.78808e-12 1.98046e-11 ----------------------------------------------------------------------------------------------------- 14 Al 1 -3.505572314107945e-01 -3.505572314147993e-01 4.00474e-12 6.27776e-11 2 -3.808309281965148e-02 -3.808309281870836e-02 9.43121e-13 2.01771e-10 3 4.381472808448724e-01 4.381472808561911e-01 1.13188e-11 1.39112e-11 ----------------------------------------------------------------------------------------------------- 15 Al 1 3.003558344320628e+00 3.003558344362252e+00 4.16231e-11 2.08928e-10 2 -7.641675774940795e-01 -7.641675774874312e-01 6.64824e-12 2.49852e-10 3 4.074106062041141e-01 4.074106061777862e-01 2.63278e-11 1.92187e-10 ----------------------------------------------------------------------------------------------------- 16 Al 1 4.699348465691718e-01 4.699348465609497e-01 8.22215e-12 2.25558e-11 2 2.483750035959828e+00 2.483750035941387e+00 1.84408e-11 1.39385e-10 3 7.159196628078611e-01 7.159196627715517e-01 3.63094e-11 2.20525e-09 * ----------------------------------------------------------------------------------------------------- 17 Al 1 -5.712459716599796e-01 -5.712459716601012e-01 1.21569e-13 2.35851e-10 2 -5.730602598884629e-01 -5.730602598877167e-01 7.46181e-13 7.38367e-11 3 -9.846786696145983e-01 -9.846786696184175e-01 3.81928e-12 3.95219e-10 ----------------------------------------------------------------------------------------------------- 18 Al 1 6.228262120052215e-01 6.228262120066189e-01 1.39744e-12 6.72121e-11 2 1.016842828670281e+00 1.016842828670341e+00 6.08402e-14 7.56090e-10 3 -7.903314360779723e-01 -7.903314360684432e-01 9.52904e-12 3.43877e-10 ----------------------------------------------------------------------------------------------------- 19 Al 1 1.025289594990458e+00 1.025289594993586e+00 3.12861e-12 5.02707e-11 2 -1.058583787967304e+00 -1.058583787938559e+00 2.87450e-11 1.24635e-10 3 5.468298658306566e-01 5.468298658416624e-01 1.10058e-11 6.57263e-10 ----------------------------------------------------------------------------------------------------- 20 Al 1 -7.214249768279752e-01 -7.214249768356994e-01 7.72415e-12 1.52142e-10 2 1.508991698520429e+00 1.508991698528573e+00 8.14349e-12 1.51711e-10 3 5.878438266443503e-01 5.878438266663756e-01 2.20253e-11 2.06597e-10 ----------------------------------------------------------------------------------------------------- 21 Al 1 -1.664433776015346e+00 -1.664433776012307e+00 3.03868e-12 1.76383e-11 2 -5.529557482797368e-01 -5.529557482950560e-01 1.53192e-11 7.14252e-11 3 1.486257054885563e-01 1.486257054986151e-01 1.00588e-11 8.37455e-11 ----------------------------------------------------------------------------------------------------- 22 Al 1 8.916590504358728e-01 8.916590504349037e-01 9.69114e-13 1.20806e-10 2 2.488458631203380e+00 2.488458631202914e+00 4.65850e-13 7.42202e-11 3 1.693897532061769e+00 1.693897532068643e+00 6.87383e-12 1.74933e-09 * ----------------------------------------------------------------------------------------------------- 23 Al 1 1.783783035336514e-01 1.783783035291026e-01 4.54889e-12 1.46040e-10 2 -7.791340999216645e-02 -7.791340999652363e-02 4.35718e-12 3.59019e-10 3 3.551790697205159e-01 3.551790697237848e-01 3.26883e-12 2.65576e-09 * ----------------------------------------------------------------------------------------------------- 24 Al 1 3.301881931915344e-01 3.301881932388911e-01 4.73567e-11 2.41885e-10 2 7.384829615360625e-01 7.384829615651363e-01 2.90737e-11 1.52198e-10 3 9.829313334020316e-02 9.829313333841597e-02 1.78720e-12 2.25768e-11 ----------------------------------------------------------------------------------------------------- 25 Al 1 -9.364316386656809e-01 -9.364316386630702e-01 2.61069e-12 9.90421e-11 2 -1.193355474534846e+00 -1.193355474554375e+00 1.95286e-11 4.18194e-11 3 6.832318646748557e-01 6.832318646683122e-01 6.54354e-12 3.98054e-11 ----------------------------------------------------------------------------------------------------- 26 Al 1 -6.446936359541227e-01 -6.446936359160440e-01 3.80787e-11 1.07222e-10 2 1.364784885541596e+00 1.364784885564026e+00 2.24294e-11 4.12163e-10 3 -9.412920707165238e-01 -9.412920707108922e-01 5.63161e-12 7.31357e-10 ----------------------------------------------------------------------------------------------------- 27 Al 1 4.809141032284361e-01 4.809141032060692e-01 2.23669e-11 8.96321e-11 2 -2.716775048249263e+00 -2.716775048200133e+00 4.91296e-11 5.04845e-10 3 6.642620564475352e-01 6.642620564584663e-01 1.09310e-11 3.70769e-11 ----------------------------------------------------------------------------------------------------- 28 Al 1 -9.366261673293801e-01 -9.366261673362494e-01 6.86928e-12 2.25133e-09 * 2 1.004165889401181e+00 1.004165889416775e+00 1.55940e-11 2.24832e-09 * 3 -6.654864531761645e-03 -6.654864515364932e-03 1.63967e-11 7.36722e-11 ----------------------------------------------------------------------------------------------------- 29 Al 1 -8.568925381441794e-01 -8.568925381265234e-01 1.76560e-11 2.99471e-10 2 -1.629691787776623e+00 -1.629691787767101e+00 9.52283e-12 2.33339e-09 * 3 7.610983964672700e-01 7.610983964104469e-01 5.68231e-11 2.49394e-10 ----------------------------------------------------------------------------------------------------- 30 Al 1 6.838923777822806e-01 6.838923777901998e-01 7.91922e-12 1.35847e-09 * 2 1.273528087524977e+00 1.273528087542073e+00 1.70961e-11 8.84221e-10 3 7.240892284156689e-02 7.240892285178410e-02 1.02172e-11 4.74355e-11 ----------------------------------------------------------------------------------------------------- 31 Al 1 7.501973032069158e-01 7.501973031987089e-01 8.20688e-12 2.47861e-10 2 -1.194656562069671e+00 -1.194656562069689e+00 1.84297e-14 3.07520e-10 3 5.435666526724782e-01 5.435666526267614e-01 4.57168e-11 9.66189e-10 ----------------------------------------------------------------------------------------------------- 32 Al 1 4.958566426859424e-01 4.958566426884798e-01 2.53741e-12 2.42729e-10 2 1.153911962848226e+00 1.153911962867970e+00 1.97440e-11 1.53034e-10 3 8.098632756415514e-01 8.098632756441285e-01 2.57716e-12 6.35014e-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 -1.897292238473028e-01 4.17924e-12 1.21459e-10 2 -7.453042916149067e-01 -7.453042916149389e-01 3.21965e-14 3.28833e-11 3 -5.892364470155395e-01 -5.892364469991411e-01 1.63983e-11 1.57831e-10 ----------------------------------------------------------------------------------------------------- 2 Ti 1 1.382220585595004e+00 1.382220585599218e+00 4.21330e-12 2.64331e-11 2 -1.242255390247175e+00 -1.242255390245657e+00 1.51790e-12 1.31601e-09 3 -1.586798838944697e+00 -1.586798838926436e+00 1.82614e-11 1.97375e-10 ----------------------------------------------------------------------------------------------------- 3 Ti 1 1.054042764274815e+00 1.054042764282419e+00 7.60347e-12 4.92411e-11 2 -8.169269739998096e-01 -8.169269740042534e-01 4.44378e-12 1.25972e-10 3 -4.357984869205593e-01 -4.357984869266015e-01 6.04217e-12 2.90955e-11 ----------------------------------------------------------------------------------------------------- 4 Ti 1 -1.084078188947323e+00 -1.084078188951680e+00 4.35652e-12 1.05567e-08 * 2 5.357057572846946e-01 5.357057572643756e-01 2.03190e-11 1.72434e-10 3 1.480212280410832e+00 1.480212280414788e+00 3.95595e-12 1.14548e-10 ----------------------------------------------------------------------------------------------------- 5 Ti 1 -2.553729734504588e+00 -2.553729734506704e+00 2.11653e-12 3.85267e-10 2 -4.153647796398620e-01 -4.153647796152456e-01 2.46164e-11 5.27377e-11 3 -1.362261760115741e+00 -1.362261760130942e+00 1.52014e-11 5.70279e-11 ----------------------------------------------------------------------------------------------------- 6 Ti 1 7.087215427902104e-01 7.087215427875300e-01 2.68041e-12 4.92182e-11 2 9.388298265220744e-01 9.388298264753541e-01 4.67203e-11 1.05983e-10 3 -3.781700589371810e-01 -3.781700589464217e-01 9.24072e-12 4.26260e-10 ----------------------------------------------------------------------------------------------------- 7 Ti 1 1.492884140732426e+00 1.492884140754516e+00 2.20901e-11 8.84515e-10 2 -1.374046062430479e-01 -1.374046062492375e-01 6.18960e-12 3.21920e-10 3 2.456223701515151e+00 2.456223701515868e+00 7.16316e-13 5.83076e-11 ----------------------------------------------------------------------------------------------------- 8 Ti 1 1.119354273513682e-01 1.119354273646947e-01 1.33264e-11 4.14661e-10 2 -1.295617019433302e+00 -1.295617019423320e+00 9.98224e-12 2.30258e-10 3 -6.364559130429924e-01 -6.364559130029005e-01 4.00919e-11 5.01288e-10 ----------------------------------------------------------------------------------------------------- 9 Ti 1 -7.445477549721005e-01 -7.445477547640451e-01 2.08055e-10 8.00110e-10 2 6.704834406032943e-01 6.704834406230085e-01 1.97141e-11 2.23324e-10 3 -5.009777304297304e-01 -5.009777303003699e-01 1.29361e-10 8.61501e-10 ----------------------------------------------------------------------------------------------------- 10 Ti 1 -2.966996781337451e-01 -2.966996781306897e-01 3.05544e-12 8.72715e-11 2 1.121246411934718e+00 1.121246411957530e+00 2.28124e-11 1.22717e-11 3 -5.733301779349959e-01 -5.733301779577219e-01 2.27260e-11 9.34736e-11 ----------------------------------------------------------------------------------------------------- 11 Ti 1 -7.208856327556270e-01 -7.208856326319171e-01 1.23710e-10 9.29995e-10 2 1.020961982683386e+00 1.020961982648739e+00 3.46476e-11 1.53592e-10 3 2.234850557986082e+00 2.234850558009946e+00 2.38645e-11 6.13781e-08 * ----------------------------------------------------------------------------------------------------- 12 Ti 1 1.989891773652651e-01 1.989891773663022e-01 1.03706e-12 1.06589e-10 2 2.293453909452040e-01 2.293453909328683e-01 1.23357e-11 5.88218e-11 3 3.669893266501560e-03 3.669893250194145e-03 1.63074e-11 2.00884e-11 ----------------------------------------------------------------------------------------------------- 13 Ti 1 6.335151682363090e-01 6.335151682617909e-01 2.54818e-11 3.76870e-11 2 -1.276066634149825e-01 -1.276066634137471e-01 1.23543e-12 6.08472e-10 3 -9.586723260677775e-01 -9.586723260846506e-01 1.68731e-11 4.19240e-11 ----------------------------------------------------------------------------------------------------- 14 Ti 1 3.500643257084756e-02 3.500643256883310e-02 2.01446e-12 1.05130e-10 2 6.218390129849584e-01 6.218390129813167e-01 3.64164e-12 2.22461e-11 3 -9.792389922271976e-01 -9.792389922309975e-01 3.79996e-12 3.21675e-11 ----------------------------------------------------------------------------------------------------- 15 Ti 1 1.505558454052619e+00 1.505558454064021e+00 1.14020e-11 2.87241e-09 * 2 -2.232198304318750e+00 -2.232198304342811e+00 2.40608e-11 1.00215e-10 3 2.934767025856169e-01 2.934767025804074e-01 5.20956e-12 1.97487e-10 ----------------------------------------------------------------------------------------------------- 16 Ti 1 -1.723744925752176e+00 -1.723744925647891e+00 1.04286e-10 3.50000e-10 2 1.933191161108453e+00 1.933191161126432e+00 1.79785e-11 8.85227e-11 3 -1.324664930510338e+00 -1.324664930551166e+00 4.08276e-11 7.55705e-10 ----------------------------------------------------------------------------------------------------- 17 Ti 1 -2.252851480342531e+00 -2.252851480341052e+00 1.47926e-12 7.46666e-10 2 -3.411851076373805e+00 -3.411851076447570e+00 7.37650e-11 2.35065e-10 3 -1.750208617639077e+00 -1.750208617639254e+00 1.76970e-13 9.52851e-11 ----------------------------------------------------------------------------------------------------- 18 Ti 1 2.494847411895384e+00 2.494847411954705e+00 5.93214e-11 1.04218e-09 2 3.273362013829456e+00 3.273362013797590e+00 3.18656e-11 6.35341e-11 3 -2.053795350578304e+00 -2.053795350553752e+00 2.45515e-11 2.05769e-09 * ----------------------------------------------------------------------------------------------------- 19 Ti 1 -1.955739700696419e+00 -1.955739700615291e+00 8.11284e-11 1.00547e-10 2 -1.241043768056757e+00 -1.241043768085572e+00 2.88154e-11 1.95322e-10 3 3.488762097187661e+00 3.488762097128096e+00 5.95657e-11 1.64929e-10 ----------------------------------------------------------------------------------------------------- 20 Ti 1 -1.777731362905508e+00 -1.777731362880770e+00 2.47382e-11 1.69520e-10 2 2.107157949912156e+00 2.107157949876990e+00 3.51665e-11 1.06124e-10 3 3.676126984403598e+00 3.676126984522489e+00 1.18891e-10 2.36783e-10 ----------------------------------------------------------------------------------------------------- 21 Ti 1 2.950787732667906e+00 2.950787732562715e+00 1.05190e-10 3.31520e-10 2 -8.694839296992667e-01 -8.694839296992283e-01 3.84137e-14 9.16345e-11 3 -3.113049936182730e+00 -3.113049936165138e+00 1.75921e-11 6.29745e-09 * ----------------------------------------------------------------------------------------------------- 22 Ti 1 1.191705276810932e+00 1.191705276820344e+00 9.41136e-12 3.26704e-10 2 -1.346851282367823e+00 -1.346851282389438e+00 2.16147e-11 4.50251e-10 3 -1.408519470422033e+00 -1.408519470434678e+00 1.26448e-11 3.11296e-10 ----------------------------------------------------------------------------------------------------- 23 Ti 1 -4.702069658915501e-01 -4.702069658847765e-01 6.77364e-12 9.49249e-11 2 3.585825246127650e-01 3.585825246037816e-01 8.98343e-12 1.16354e-10 3 -5.773333082419225e-01 -5.773333082432239e-01 1.30140e-12 2.23148e-10 ----------------------------------------------------------------------------------------------------- 24 Ti 1 -4.514772477458646e-01 -4.514772477672517e-01 2.13871e-11 8.23299e-11 2 1.171094807988668e+00 1.171094807989719e+00 1.05049e-12 2.35705e-10 3 1.148069220106420e+00 1.148069220061805e+00 4.46150e-11 8.75916e-09 * ----------------------------------------------------------------------------------------------------- 25 Ti 1 5.098116310921931e-02 5.098116305561862e-02 5.36007e-11 5.01960e-11 2 -9.277562619849832e-01 -9.277562620572001e-01 7.22169e-11 2.00243e-10 3 -6.213043305964211e-01 -6.213043307401172e-01 1.43696e-10 2.20309e-10 ----------------------------------------------------------------------------------------------------- 26 Ti 1 -7.911454267382002e-01 -7.911454267865549e-01 4.83547e-11 2.79674e-06 * 2 6.979572880195877e-01 6.979572880055004e-01 1.40873e-11 3.75422e-10 3 -7.220924234871193e-01 -7.220924234713105e-01 1.58088e-11 1.55954e-10 ----------------------------------------------------------------------------------------------------- 27 Ti 1 6.950699642354183e-01 6.950699642690488e-01 3.36304e-11 1.04851e-10 2 -8.562023311252634e-01 -8.562023310141106e-01 1.11153e-10 7.28550e-10 3 2.325074820210189e-01 2.325074819285397e-01 9.24792e-11 6.93222e-10 ----------------------------------------------------------------------------------------------------- 28 Ti 1 -3.798696707502696e-01 -3.798696707292742e-01 2.09954e-11 6.08904e-11 2 7.361340166568487e-01 7.361340166348965e-01 2.19522e-11 1.47352e-09 * 3 5.870997542544729e-01 5.870997543119557e-01 5.74828e-11 2.88372e-10 ----------------------------------------------------------------------------------------------------- 29 Ti 1 -5.082736395402088e-01 -5.082736396039569e-01 6.37481e-11 1.82084e-10 2 -1.368955054655010e+00 -1.368955054662158e+00 7.14762e-12 2.74084e-10 3 1.797899526904521e+00 1.797899526908231e+00 3.71059e-12 1.40139e-10 ----------------------------------------------------------------------------------------------------- 30 Ti 1 9.005431850888498e-01 9.005431850846793e-01 4.17044e-12 3.77826e-06 * 2 7.023061235622812e-01 7.023061235790381e-01 1.67569e-11 1.36793e-10 3 1.091965745454408e+00 1.091965745442276e+00 1.21327e-11 1.52709e-10 ----------------------------------------------------------------------------------------------------- 31 Ti 1 3.115109678412377e-02 3.115109677326477e-02 1.08590e-11 1.33941e-10 2 1.015103906668053e+00 1.015103906632864e+00 3.51887e-11 2.14279e-10 3 9.078077938211188e-01 9.078077938263286e-01 5.20983e-12 1.80914e-10 ----------------------------------------------------------------------------------------------------- 32 Ti 1 4.627511099585380e-01 4.627511099552069e-01 3.33117e-12 2.52411e-11 2 -9.847988214185363e-02 -9.847988214402563e-02 2.17200e-12 2.61789e-09 * 3 1.732373593769539e-01 1.732373593694919e-01 7.46206e-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 5.388437177482300e-02 2.09964e-13 4.72369e-11 2 9.836383905656207e-02 9.836383905696477e-02 4.02706e-13 2.03256e-11 3 3.144139988018715e-01 3.144139987901590e-01 1.17126e-11 1.53319e-10 ----------------------------------------------------------------------------------------------------- 2 Ti 1 3.116948298677521e+00 3.116948298685089e+00 7.56817e-12 9.09819e-11 2 -4.364704263280743e-01 -4.364704263104136e-01 1.76608e-11 8.96095e-11 3 -1.481242605759819e+00 -1.481242605746055e+00 1.37645e-11 8.11555e-11 ----------------------------------------------------------------------------------------------------- 3 Al 1 1.848572396363926e+00 1.848572396379586e+00 1.56608e-11 1.73352e-10 2 -3.327342085370153e-01 -3.327342084990506e-01 3.79647e-11 1.15720e-10 3 -6.912750752109119e-01 -6.912750752286555e-01 1.77436e-11 9.53807e-10 ----------------------------------------------------------------------------------------------------- 4 Ti 1 -1.880239694489075e+00 -1.880239694500281e+00 1.12064e-11 9.90958e-11 2 -7.265479050140264e-01 -7.265479050251610e-01 1.11345e-11 3.12818e-10 3 2.366500801101048e+00 2.366500801117023e+00 1.59757e-11 1.22603e-10 ----------------------------------------------------------------------------------------------------- 5 Ti 1 -4.936394580627724e+00 -4.936394580615847e+00 1.18767e-11 2.16268e-10 2 -4.657990644227412e-01 -4.657990644289587e-01 6.21758e-12 4.00123e-10 3 -3.844652810301612e+00 -3.844652810300603e+00 1.00853e-12 9.55018e-11 ----------------------------------------------------------------------------------------------------- 6 Al 1 1.145694086034167e+00 1.145694086035940e+00 1.77369e-12 9.79856e-11 2 9.449483882754952e-01 9.449483882795238e-01 4.02856e-12 8.76420e-11 3 -1.130706326932830e+00 -1.130706326946605e+00 1.37750e-11 2.63762e-10 ----------------------------------------------------------------------------------------------------- 7 Ti 1 4.288563961655659e+00 4.288563961659865e+00 4.20552e-12 4.40947e-10 2 -9.561451683663751e-01 -9.561451683507927e-01 1.55824e-11 2.33062e-11 3 5.071955537206166e+00 5.071955537216128e+00 9.96181e-12 8.90088e-11 ----------------------------------------------------------------------------------------------------- 8 Ti 1 -3.182629138649818e+00 -3.182629138766275e+00 1.16457e-10 1.78295e-09 * 2 -2.524558345869783e+00 -2.524558345834246e+00 3.55369e-11 3.47614e-10 3 -8.085780825419903e-01 -8.085787002647358e-01 6.17723e-07 4.72531e-08 * ----------------------------------------------------------------------------------------------------- 9 Al 1 -1.224083329855858e-01 -1.224083329861560e-01 5.70141e-13 1.02853e-11 2 1.286713374832247e+00 1.286713374839291e+00 7.04370e-12 1.85645e-11 3 -1.176291173404021e+00 -1.176291173359521e+00 4.45000e-11 8.92719e-11 ----------------------------------------------------------------------------------------------------- 10 Ti 1 1.088598291376440e+00 1.088598291375655e+00 7.84706e-13 1.70003e-09 * 2 -1.255524543518499e+00 -1.255524543521910e+00 3.41149e-12 7.45353e-11 3 -4.535135610090011e-01 -4.535135610176770e-01 8.67584e-12 2.48046e-09 * ----------------------------------------------------------------------------------------------------- 11 Al 1 7.907841934920238e-01 7.907841934800373e-01 1.19865e-11 1.39191e-10 2 -1.238629427465105e+00 -1.238629427416758e+00 4.83467e-11 1.16895e-10 3 -2.017184533615313e+00 -2.017184533609969e+00 5.34417e-12 1.36218e-10 ----------------------------------------------------------------------------------------------------- 12 Al 1 -1.048299233808627e+00 -1.048299233811157e+00 2.52975e-12 8.96166e-10 2 3.646416088391781e-01 3.646416088567807e-01 1.76026e-11 2.93547e-10 3 1.479221754442489e+00 1.479221754423233e+00 1.92566e-11 6.09290e-11 ----------------------------------------------------------------------------------------------------- 13 Ti 1 -2.584407396000136e+00 -2.584407396006069e+00 5.93259e-12 4.07150e-11 2 4.843360522196492e-01 4.843360522134559e-01 6.19327e-12 4.69707e-11 3 -2.323775598633194e+00 -2.323775598661749e+00 2.85545e-11 1.40615e-10 ----------------------------------------------------------------------------------------------------- 14 Al 1 7.028384307853823e-01 7.028384307848693e-01 5.13034e-13 3.15403e-12 2 7.135684246119106e-01 7.135684246090817e-01 2.82896e-12 4.95973e-11 3 -1.005325609519579e+00 -1.005325609520796e+00 1.21725e-12 1.37617e-09 * ----------------------------------------------------------------------------------------------------- 15 Ti 1 2.801098203021943e+00 2.801098203021680e+00 2.62901e-13 8.48358e-10 2 1.036445522166944e+00 1.036445522159473e+00 7.47091e-12 1.92330e-10 3 2.895896484784326e+00 2.895896484775497e+00 8.82938e-12 4.58021e-10 ----------------------------------------------------------------------------------------------------- 16 Al 1 -9.154398370059170e-01 -9.154398369796449e-01 2.62721e-11 2.10580e-10 2 1.004682601783308e+00 1.004682601759685e+00 2.36229e-11 1.02049e-10 3 1.031658493995137e+00 1.031658494003266e+00 8.12972e-12 1.97702e-10 ----------------------------------------------------------------------------------------------------- 17 Ti 1 -9.209764345683580e-01 -9.209764345554493e-01 1.29087e-11 5.21334e-11 2 3.594331263672627e-01 3.594331263653058e-01 1.95688e-12 1.79011e-10 3 9.503164374124367e-01 9.503164374146524e-01 2.21578e-12 1.51736e-10 ----------------------------------------------------------------------------------------------------- 18 Ti 1 -7.832763181151617e-01 -7.832763181449479e-01 2.97862e-11 3.33619e-10 2 -1.809002133928217e+00 -1.809002134053842e+00 1.25625e-10 2.76785e-10 3 -2.652268508416606e+00 -2.652268508509291e+00 9.26850e-11 5.74967e-10 ----------------------------------------------------------------------------------------------------- 19 Al 1 2.382985948571259e-01 2.382984235847455e-01 1.71272e-07 1.33523e-10 2 -1.288505723569025e+00 -1.288505001109413e+00 7.22460e-07 1.50209e-09 * 3 6.901888095717140e-01 6.901888095750202e-01 3.30613e-12 1.41357e-10 ----------------------------------------------------------------------------------------------------- 20 Al 1 -2.852357483627062e-01 -2.852357483861918e-01 2.34855e-11 1.23508e-10 2 1.954747582127177e-01 1.954747582236331e-01 1.09154e-11 7.00225e-11 3 -2.727952595270801e-01 -2.727952595269250e-01 1.55098e-13 5.43776e-11 ----------------------------------------------------------------------------------------------------- 21 Al 1 -1.470458901715735e+00 -1.470458901697932e+00 1.78031e-11 7.59201e-10 2 -7.043034012879079e-01 -7.043034012621665e-01 2.57414e-11 2.00373e-11 3 -1.353351197169138e+00 -1.353351197189377e+00 2.02389e-11 3.37359e-11 ----------------------------------------------------------------------------------------------------- 22 Ti 1 1.602703462702913e+00 1.602703462540291e+00 1.62622e-10 3.56970e-10 2 9.485476634486442e-01 9.485476634956519e-01 4.70077e-11 3.30209e-09 * 3 -6.132319224690457e-01 -6.132319225518891e-01 8.28434e-11 1.59720e-10 ----------------------------------------------------------------------------------------------------- 23 Al 1 9.953431052602916e-01 9.953431052677902e-01 7.49867e-12 1.07711e-10 2 -5.546405710216682e-01 -5.546405710187972e-01 2.87104e-12 4.51053e-11 3 8.017330240715185e-01 8.017330240706252e-01 8.93285e-13 3.23270e-10 ----------------------------------------------------------------------------------------------------- 24 Ti 1 1.712851722391189e-01 1.712851722255740e-01 1.35449e-11 5.19790e-10 2 7.867737749752226e-01 7.867737749877799e-01 1.25573e-11 1.80730e-09 * 3 1.884470500452507e+00 1.884470500447025e+00 5.48250e-12 3.69355e-10 ----------------------------------------------------------------------------------------------------- 25 Ti 1 -3.029363144120494e+00 -3.029363144106070e+00 1.44240e-11 2.41102e-10 2 1.159947352578034e+00 1.159947352575691e+00 2.34368e-12 2.15475e-10 3 5.863138968452628e-01 5.863138968331697e-01 1.20931e-11 3.81773e-10 ----------------------------------------------------------------------------------------------------- 26 Ti 1 9.184796396149281e-01 9.184796396756568e-01 6.07288e-11 3.11353e-10 2 1.989668609432630e+00 1.989668609415397e+00 1.72333e-11 1.41016e-09 * 3 -6.944330518561804e-01 -6.944330518776017e-01 2.14213e-11 3.98113e-11 ----------------------------------------------------------------------------------------------------- 27 Al 1 3.873184106811269e-01 3.873184107011329e-01 2.00059e-11 1.26192e-09 2 3.611203400612110e-01 3.611203400796650e-01 1.84540e-11 1.62902e-10 3 1.493206375977301e+00 1.493206376010479e+00 3.31779e-11 3.71218e-10 ----------------------------------------------------------------------------------------------------- 28 Al 1 4.564481489603648e-01 4.564481489422570e-01 1.81078e-11 1.06963e-09 2 -6.531920535738929e-01 -6.531920535717141e-01 2.17881e-12 5.42786e-11 3 -6.644170762394850e-01 -6.644170762435680e-01 4.08307e-12 3.97595e-11 ----------------------------------------------------------------------------------------------------- 29 Al 1 5.802207855476562e-01 5.802207855541678e-01 6.51157e-12 3.19855e-10 2 2.620075637517008e+00 2.620075637507923e+00 9.08518e-12 4.07095e-10 3 2.336057924817162e+00 2.336057924807544e+00 9.61853e-12 2.12586e-09 * ----------------------------------------------------------------------------------------------------- 30 Al 1 -8.319140739608264e-04 -8.319140748716067e-04 9.10780e-13 8.65838e-11 2 -4.550274062146407e-01 -4.550274062126708e-01 1.96987e-12 3.66039e-11 3 -7.104074615635030e-01 -7.104074615788402e-01 1.53372e-11 9.13662e-10 ----------------------------------------------------------------------------------------------------- 31 Ti 1 2.988029628256410e+00 2.988029628230285e+00 2.61249e-11 1.27753e-10 2 -3.777030690719853e+00 -3.777030690732996e+00 1.31428e-11 3.60123e-10 3 5.197176927323769e-02 5.197176927529915e-02 2.06146e-12 3.47483e-11 ----------------------------------------------------------------------------------------------------- 32 Ti 1 -3.015148506778313e+00 -3.015148506838127e+00 5.98135e-11 4.57505e-10 2 2.823369995458799e+00 2.823369995446143e+00 1.26557e-11 1.41085e-09 * 3 -6.045595458286687e-02 -6.045595457179247e-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.