!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 : Sim_LAMMPS_MEAM_ZhangTrinkle_2016_TiO__SM_513612626462_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 = 2.91455841064 | (Configuration in file "config-O.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 O 1 -1.003031888600211e+01 -1.003031888602691e+01 2.47997e-11 1.21245e-10 2 -8.415602069865692e+00 -8.415602069667248e+00 1.98444e-10 6.34339e-10 3 -7.060777720499093e+00 -7.060777720492391e+00 6.70219e-12 5.40741e-11 ----------------------------------------------------------------------------------------------------- 2 O 1 3.270883819526565e+00 3.270883819526230e+00 3.35287e-13 4.86007e-10 2 1.797162830169128e+01 1.797162830170358e+01 1.22995e-11 3.88418e-11 3 -8.460831261003216e+00 -8.460831261147517e+00 1.44301e-10 2.49269e-09 ----------------------------------------------------------------------------------------------------- 3 O 1 3.186695964545883e+00 3.186695964573831e+00 2.79474e-11 1.70122e-10 2 -8.907299213738659e+00 -8.907299213719650e+00 1.90088e-11 2.06150e-10 3 8.250623802132573e-01 8.250623802129615e-01 2.95763e-13 1.79588e-10 ----------------------------------------------------------------------------------------------------- 4 O 1 -4.337772776883591e+00 -4.337772776854239e+00 2.93525e-11 9.32469e-06 * 2 1.234907823999683e+01 1.234907824004089e+01 4.40536e-11 6.59019e-05 * 3 2.232793800939543e+01 2.232793800938418e+01 1.12443e-11 1.35274e-09 ----------------------------------------------------------------------------------------------------- 5 O 1 1.186115339607964e+00 1.186115339607604e+00 3.60378e-13 4.94662e-11 2 -1.775681197539244e+01 -1.775681197540356e+01 1.11129e-11 2.16005e-11 3 -7.127557904685931e-01 -7.127557904690526e-01 4.59521e-13 2.56770e-09 ----------------------------------------------------------------------------------------------------- 6 O 1 6.991928701011332e+00 6.991928701006430e+00 4.90186e-12 1.28161e-10 2 9.745574313434249e-01 9.745574313396917e-01 3.73312e-12 4.43564e-11 3 -5.513227959254510e+00 -5.513227959268025e+00 1.35145e-11 3.12514e-11 ----------------------------------------------------------------------------------------------------- 7 O 1 9.299237665471447e+00 9.299237665469699e+00 1.74794e-12 6.11417e-10 2 -1.552921151579916e+01 -1.552921151579753e+01 1.62892e-12 8.02718e-11 3 -1.630433128970279e+01 -1.630433128969467e+01 8.11795e-12 1.49001e-11 ----------------------------------------------------------------------------------------------------- 8 O 1 -2.233195221085458e+01 -2.233195221083493e+01 1.96501e-11 3.90543e-09 2 -3.444457743316497e+00 -3.444457743256547e+00 5.99498e-11 1.73106e-10 3 1.571716868514305e+01 1.571716868512338e+01 1.96660e-11 7.33271e-10 ----------------------------------------------------------------------------------------------------- 9 O 1 -2.672552289994235e+00 -2.672552289995501e+00 1.26521e-12 4.60760e-11 2 -7.596663324096462e+00 -7.596663324064306e+00 3.21556e-11 5.08706e-10 3 -1.206329254282962e+01 -1.206329254282518e+01 4.43912e-12 9.02105e-11 ----------------------------------------------------------------------------------------------------- 10 O 1 -1.013249064282116e+01 -1.013249064280790e+01 1.32623e-11 6.53113e-11 2 1.110933965561119e+01 1.110933965574269e+01 1.31504e-10 1.29614e-09 3 -1.780637647079885e+01 -1.780637647082087e+01 2.20197e-11 4.13027e-08 * ----------------------------------------------------------------------------------------------------- 11 O 1 1.211152643884808e+01 1.211152643886343e+01 1.53424e-11 3.95838e-10 2 -2.293515006038959e+01 -2.293515006040044e+01 1.08464e-11 2.30035e-10 3 1.549249157607749e+01 1.549249157604776e+01 2.97273e-11 1.64865e-10 ----------------------------------------------------------------------------------------------------- 12 O 1 -3.940140939551251e+00 -3.940140939566093e+00 1.48423e-11 1.20791e-10 2 6.150571366017604e+00 6.150571366015061e+00 2.54285e-12 9.62164e-12 3 5.791433498197898e+00 5.791433498208924e+00 1.10267e-11 2.21625e-10 ----------------------------------------------------------------------------------------------------- 13 O 1 -1.177291852937328e+01 -1.177291852938710e+01 1.38201e-11 3.50198e-10 2 -6.076990520088531e+00 -6.076990520086552e+00 1.97886e-12 1.43366e-10 3 -3.614789617792345e+01 -3.614789617791524e+01 8.20677e-12 5.12173e-09 * ----------------------------------------------------------------------------------------------------- 14 O 1 3.485484967548079e+00 3.485484967561561e+00 1.34817e-11 1.63498e-10 2 6.480357120759623e+00 6.480357120753147e+00 6.47660e-12 8.25739e-11 3 -1.865200529484561e+00 -1.865200529480154e+00 4.40670e-12 4.96088e-11 ----------------------------------------------------------------------------------------------------- 15 O 1 3.760177703468744e+01 3.760177703468223e+01 5.20828e-12 4.40465e-11 2 -1.999435630336019e+00 -1.999435630307537e+00 2.84821e-11 2.25473e-10 3 1.334976903934026e+01 1.334976903933956e+01 7.06990e-13 3.84190e-11 ----------------------------------------------------------------------------------------------------- 16 O 1 8.251315043450216e+00 8.251315043448194e+00 2.02149e-12 2.80623e-09 2 2.739410253400351e+01 2.739410253421287e+01 2.09361e-10 1.95494e-08 * 3 1.615598369215892e+01 1.615598369211589e+01 4.30269e-11 1.19203e-09 ----------------------------------------------------------------------------------------------------- 17 O 1 -4.753179506751628e+00 -4.753179506757607e+00 5.97833e-12 4.40358e-10 2 -8.055904422981881e+00 -8.055904422988062e+00 6.18172e-12 9.24327e-11 3 -8.869983682949792e+00 -8.869983682952745e+00 2.95231e-12 1.36689e-10 ----------------------------------------------------------------------------------------------------- 18 O 1 9.978917986544891e+00 9.978917986555215e+00 1.03242e-11 6.90875e-10 2 1.951960611100353e+01 1.951960611101595e+01 1.24132e-11 1.15937e-07 * 3 -1.626414799507313e+01 -1.626414799507102e+01 2.10676e-12 5.84848e-11 ----------------------------------------------------------------------------------------------------- 19 O 1 5.534951019795725e+00 5.534951019796244e+00 5.18696e-13 1.39428e-10 2 -3.218159534426153e+00 -3.218159534426472e+00 3.18856e-13 8.20446e-11 3 1.378426377291904e+00 1.378426377285580e+00 6.32383e-12 6.58804e-11 ----------------------------------------------------------------------------------------------------- 20 O 1 -7.321884503876038e+00 -7.321884503539759e+00 3.36279e-10 1.36604e-09 2 9.219430018875993e+00 9.219430018869380e+00 6.61338e-12 2.93756e-11 3 1.214798489425482e+01 1.214798489410005e+01 1.54763e-10 5.46610e-09 * ----------------------------------------------------------------------------------------------------- 21 O 1 -8.829654352418851e+00 -8.829654352412820e+00 6.03073e-12 7.69948e-09 * 2 -1.001355723511421e+01 -1.001355723514404e+01 2.98321e-11 2.65320e-10 3 3.901242999655301e+00 3.901242999652371e+00 2.92966e-12 6.44378e-11 ----------------------------------------------------------------------------------------------------- 22 O 1 7.319315580602041e+00 7.319315580587741e+00 1.42997e-11 1.82524e-10 2 1.321992909687804e+01 1.321992909688901e+01 1.09726e-11 1.33342e-10 3 3.023211445927384e+00 3.023211445929697e+00 2.31282e-12 1.28319e-10 ----------------------------------------------------------------------------------------------------- 23 O 1 8.352339768501887e+00 8.352339768505940e+00 4.05365e-12 1.09180e-10 2 -2.663014015552293e+00 -2.663014015558306e+00 6.01297e-12 1.68304e-10 3 4.459655610266412e+00 4.459655610398508e+00 1.32096e-10 1.62130e-10 ----------------------------------------------------------------------------------------------------- 24 O 1 -9.099768902010961e+00 -9.099768901972194e+00 3.87672e-11 7.40044e-10 2 6.507957592867921e+00 6.507957592862788e+00 5.13278e-12 1.58693e-09 3 4.172370772520032e+00 4.172370772482738e+00 3.72937e-11 1.98669e-07 * ----------------------------------------------------------------------------------------------------- 25 O 1 -1.569543877366813e+01 -1.569543877367133e+01 3.19744e-12 3.01229e-10 2 -2.184583173747994e+01 -2.184583173745759e+01 2.23466e-11 2.38429e-09 3 -2.280796169965355e+01 -2.280796169962520e+01 2.83507e-11 1.44292e-09 ----------------------------------------------------------------------------------------------------- 26 O 1 -4.984891618204654e+00 -4.984891618259534e+00 5.48805e-11 1.46642e-09 2 1.727732095592318e+01 1.727732095593881e+01 1.56355e-11 9.56280e-08 * 3 -9.766875099461229e+00 -9.766875099460306e+00 9.23706e-13 9.48628e-11 ----------------------------------------------------------------------------------------------------- 27 O 1 5.540124865874636e+00 5.540124866047961e+00 1.73324e-10 5.94939e-10 2 -1.660820049284196e+01 -1.660820049307133e+01 2.29374e-10 1.96717e-10 3 2.213582611380453e+01 2.213582611379666e+01 7.87637e-12 4.48271e-10 ----------------------------------------------------------------------------------------------------- 28 O 1 -1.540521630393613e+01 -1.540521630393099e+01 5.13900e-12 5.71278e-10 2 1.922567652664835e+01 1.922567652681943e+01 1.71081e-10 1.26826e-09 3 7.372456272173223e+00 7.372456272248036e+00 7.48130e-11 9.89865e-10 ----------------------------------------------------------------------------------------------------- 29 O 1 -1.854415711264265e+01 -1.854415711267535e+01 3.27063e-11 6.09354e-10 2 -1.798952319083387e+01 -1.798952319082147e+01 1.24025e-11 2.00915e-09 3 -6.046216260423936e+00 -6.046216260417246e+00 6.68976e-12 8.12713e-09 * ----------------------------------------------------------------------------------------------------- 30 O 1 6.518128896783326e+00 6.518128896783885e+00 5.59552e-13 8.64286e-11 2 1.356558146906441e+01 1.356558146906345e+01 9.68114e-13 3.48503e-11 3 -1.197148118394168e+01 -1.197148118393834e+01 3.34133e-12 6.61924e-11 ----------------------------------------------------------------------------------------------------- 31 O 1 1.696101945983877e+01 1.696101945984558e+01 6.81766e-12 7.06716e-10 2 -1.716409288315799e+01 -1.716409288316290e+01 4.90985e-12 3.75667e-10 3 1.985554477675090e+01 1.985554477672657e+01 2.43325e-11 2.92534e-10 ----------------------------------------------------------------------------------------------------- 32 O 1 4.262574796350977e+00 4.262574796348217e+00 2.76046e-12 5.93947e-10 2 9.254769144726520e+00 9.254769144775453e+00 4.89333e-11 1.10404e-10 3 1.355478952029724e+01 1.355478952020116e+01 9.60885e-11 1.53589e-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 dicontinuities. Maximum error obtained for particle = 20, direction = 1: |F_model - F_numer| error = ----------------------- = 4.59279e-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 = 3.4325170517 | (Configuration in file "config-Ti.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ti 1 2.165753737803242e-01 2.165753737795930e-01 7.31221e-13 1.74699e-12 2 3.477258898420585e-01 3.477258898426456e-01 5.87141e-13 1.96121e-12 3 3.301495408020718e-01 3.301495408023861e-01 3.14360e-13 1.47821e-12 ----------------------------------------------------------------------------------------------------- 2 Ti 1 -1.598495051592134e-01 -1.598495051601285e-01 9.15074e-13 6.15896e-12 2 -9.554597535917639e-01 -9.554597535932982e-01 1.53422e-12 2.41707e-12 3 1.047027962142871e+00 1.047027962138365e+00 4.50595e-12 1.42515e-11 ----------------------------------------------------------------------------------------------------- 3 Ti 1 -5.824976285599806e-01 -5.824976285581006e-01 1.87994e-12 8.05900e-12 2 8.360724886051418e-01 8.360724886063954e-01 1.25355e-12 1.46172e-12 3 -1.041159475295402e+00 -1.041159475295583e+00 1.81632e-13 7.72937e-13 ----------------------------------------------------------------------------------------------------- 4 Ti 1 9.935084049565867e-01 9.935084049572505e-01 6.63802e-13 2.65854e-12 2 -4.151568178825258e-01 -4.151568178840591e-01 1.53327e-12 2.61156e-11 3 -3.340259139322048e-01 -3.340259139321148e-01 8.99836e-14 1.72838e-11 ----------------------------------------------------------------------------------------------------- 5 Ti 1 4.313464580426091e-01 4.313464580432889e-01 6.79790e-13 3.72880e-12 2 7.333708310751329e-01 7.333708310748931e-01 2.39808e-13 1.07315e-11 3 6.729826758183020e-01 6.729826758206144e-01 2.31248e-12 1.12873e-11 ----------------------------------------------------------------------------------------------------- 6 Ti 1 -7.144167312899289e-01 -7.144167312887731e-01 1.15574e-12 7.14118e-12 2 -2.081447587182598e-01 -2.081447587189462e-01 6.86368e-13 5.56299e-12 3 6.922229322740113e-01 6.922229322712696e-01 2.74170e-12 1.73832e-11 ----------------------------------------------------------------------------------------------------- 7 Ti 1 -3.785562833015439e-01 -3.785562833006860e-01 8.57869e-13 9.49663e-12 2 5.950122471910552e-01 5.950122471925489e-01 1.49369e-12 3.59146e-12 3 -4.830186853261889e-01 -4.830186853274163e-01 1.22741e-12 1.54032e-12 ----------------------------------------------------------------------------------------------------- 8 Ti 1 4.876635323398152e-01 4.876635323396911e-01 1.24178e-13 1.13676e-11 2 -9.581861083314334e-01 -9.581861083308668e-01 5.66547e-13 3.31394e-11 3 -1.005226818947714e+00 -1.005226818950096e+00 2.38165e-12 1.03282e-11 ----------------------------------------------------------------------------------------------------- 9 Ti 1 3.816519273106470e-01 3.816519273104832e-01 1.63758e-13 8.63060e-12 2 5.804721088496942e-01 5.804721088495172e-01 1.77081e-13 7.18436e-12 3 3.399868981036107e-01 3.399868981032358e-01 3.74811e-13 2.37649e-12 ----------------------------------------------------------------------------------------------------- 10 Ti 1 -3.357194312713088e-01 -3.357194312704699e-01 8.38885e-13 4.45372e-12 2 -4.069532305954563e-01 -4.069532305943661e-01 1.09018e-12 5.29754e-12 3 3.238110208669516e-01 3.238110208667701e-01 1.81521e-13 3.96494e-12 ----------------------------------------------------------------------------------------------------- 11 Ti 1 -3.376327991330128e-01 -3.376327991323974e-01 6.15397e-13 8.56274e-11 * 2 2.768447614128904e-01 2.768447614126091e-01 2.81331e-13 2.59233e-11 3 -5.680761629392270e-01 -5.680761629401924e-01 9.65339e-13 4.42958e-11 ----------------------------------------------------------------------------------------------------- 12 Ti 1 -9.597592976868549e-02 -9.597592976831554e-02 3.69954e-13 5.73802e-12 2 -4.231270209519647e-01 -4.231270209525999e-01 6.35159e-13 1.69052e-11 3 -2.222852127529449e-01 -2.222852127508232e-01 2.12164e-12 3.31968e-12 ----------------------------------------------------------------------------------------------------- 13 Ti 1 1.222667500299407e-01 1.222667500283823e-01 1.55845e-12 5.10149e-12 2 3.011619067284324e-01 3.011619067280566e-01 3.75755e-13 6.12582e-12 3 6.088854370164914e-01 6.088854370161283e-01 3.63154e-13 1.51037e-11 ----------------------------------------------------------------------------------------------------- 14 Ti 1 2.517902380082655e-01 2.517902380088557e-01 5.90195e-13 2.03049e-11 2 -4.735220476168949e-01 -4.735220476176326e-01 7.37688e-13 2.26952e-12 3 7.093507727964656e-02 7.093507727588076e-02 3.76579e-12 4.18572e-12 ----------------------------------------------------------------------------------------------------- 15 Ti 1 -4.692946914574821e-01 -4.692946914660976e-01 8.61555e-12 1.10012e-10 * 2 2.591198759648827e-01 2.591198759638162e-01 1.06648e-12 6.46910e-12 3 -8.311812225713592e-01 -8.311812225739497e-01 2.59048e-12 1.21978e-11 ----------------------------------------------------------------------------------------------------- 16 Ti 1 2.232888456466396e-01 2.232888456466340e-01 5.63438e-15 3.71186e-12 2 -2.747397883747920e-01 -2.747397883750267e-01 2.34757e-13 1.08892e-11 3 -1.151606214657405e-02 -1.151606214659799e-02 2.39409e-14 2.87727e-12 ----------------------------------------------------------------------------------------------------- 17 Ti 1 3.243884152296842e-01 3.243884152296138e-01 7.03881e-14 2.91530e-11 2 3.808197565111220e-01 3.808197565073480e-01 3.77409e-12 1.60325e-10 * 3 5.381043524255733e-01 5.381043524243833e-01 1.19005e-12 2.45937e-12 ----------------------------------------------------------------------------------------------------- 18 Ti 1 -6.491297845126396e-01 -6.491297845108076e-01 1.83198e-12 6.33693e-12 2 -4.908750717827719e-01 -4.908750717805851e-01 2.18675e-12 1.75693e-11 3 5.041371599033098e-01 5.041371599036069e-01 2.97096e-13 4.41747e-12 ----------------------------------------------------------------------------------------------------- 19 Ti 1 -4.588682258800619e-01 -4.588682258770682e-01 2.99366e-12 1.20773e-11 2 4.052623402337285e-01 4.052623402343169e-01 5.88363e-13 9.88792e-12 3 -5.374895093037084e-01 -5.374895093018528e-01 1.85563e-12 1.50054e-11 ----------------------------------------------------------------------------------------------------- 20 Ti 1 3.118380894918658e-01 3.118380894916486e-01 2.17160e-13 1.56803e-11 2 -7.406982135176780e-01 -7.406982135176379e-01 4.00791e-14 2.06513e-12 3 -5.346141967881995e-01 -5.346141967868554e-01 1.34415e-12 7.81486e-13 ----------------------------------------------------------------------------------------------------- 21 Ti 1 9.919372182653490e-01 9.919372182653947e-01 4.57412e-14 2.56462e-12 2 7.389831197674744e-01 7.389831197663228e-01 1.15163e-12 5.39802e-12 3 5.956427560682602e-01 5.956427560690591e-01 7.98916e-13 7.91145e-13 ----------------------------------------------------------------------------------------------------- 22 Ti 1 -8.542084465978407e-01 -8.542084465988691e-01 1.02840e-12 6.54654e-12 2 -1.015341741955801e+00 -1.015341741954869e+00 9.31921e-13 1.52833e-12 3 3.944451934774348e-01 3.944451934779584e-01 5.23581e-13 9.79272e-13 ----------------------------------------------------------------------------------------------------- 23 Ti 1 -1.546734327048185e-01 -1.546734327051829e-01 3.64431e-13 3.99120e-12 2 1.994402335863455e-01 1.994402335859587e-01 3.86802e-13 7.19208e-12 3 -4.253049021722139e-01 -4.253049021729211e-01 7.07157e-13 8.13627e-13 ----------------------------------------------------------------------------------------------------- 24 Ti 1 4.487305503936302e-01 4.487305503949879e-01 1.35775e-12 5.20517e-12 2 -4.039379881276856e-01 -4.039379881281841e-01 4.98546e-13 4.12109e-12 3 -2.704214745884259e-01 -2.704214745862838e-01 2.14201e-12 3.25651e-12 ----------------------------------------------------------------------------------------------------- 25 Ti 1 4.374315538741624e-01 4.374315538708912e-01 3.27116e-12 1.37683e-07 * 2 -1.434733897069577e-01 -1.434733897179505e-01 1.09928e-11 5.29414e-11 * 3 -3.262573344246850e-01 -3.262573344263984e-01 1.71341e-12 1.66743e-11 ----------------------------------------------------------------------------------------------------- 26 Ti 1 3.041642619615047e-01 3.041642619656016e-01 4.09689e-12 3.74306e-12 2 -1.577760667432129e-01 -1.577760667445798e-01 1.36691e-12 7.19397e-12 3 5.172472931470982e-01 5.172472931455585e-01 1.53966e-12 1.33203e-11 ----------------------------------------------------------------------------------------------------- 27 Ti 1 6.461454240008291e-02 6.461454239936236e-02 7.20549e-13 2.67884e-12 2 4.576089963606640e-01 4.576089963614748e-01 8.10851e-13 1.43918e-12 3 -6.754454735810302e-01 -6.754454735824784e-01 1.44817e-12 1.45789e-11 ----------------------------------------------------------------------------------------------------- 28 Ti 1 2.020525870346240e-01 2.020525870326277e-01 1.99626e-12 7.10471e-12 2 2.164522464041333e-01 2.164522464054676e-01 1.33435e-12 6.13551e-12 3 3.543482666077588e-01 3.543482666071074e-01 6.51423e-13 6.76903e-12 ----------------------------------------------------------------------------------------------------- 29 Ti 1 6.069630475175552e-02 6.069630475226016e-02 5.04638e-13 1.50754e-11 2 1.543504365595456e+00 1.543504365594099e+00 1.35691e-12 2.03333e-11 3 1.323430019019573e+00 1.323430019018481e+00 1.09224e-12 4.17977e-12 ----------------------------------------------------------------------------------------------------- 30 Ti 1 -6.637469444659587e-01 -6.637469445025829e-01 3.66241e-11 1.19469e-10 * 2 -3.843189067534240e-01 -3.843189067553680e-01 1.94400e-12 3.84510e-11 3 5.452570551451495e-01 5.452570551479471e-01 2.79754e-12 8.66363e-12 ----------------------------------------------------------------------------------------------------- 31 Ti 1 -8.747671200376308e-01 -8.747671200406624e-01 3.03157e-12 1.42434e-11 2 5.853481594358299e-01 5.853481594356520e-01 1.77858e-13 6.10689e-12 3 -7.481517846756232e-01 -7.481517846741995e-01 1.42364e-12 1.06705e-11 ----------------------------------------------------------------------------------------------------- 32 Ti 1 4.753919006226200e-01 4.753919006231552e-01 5.35183e-13 6.04555e-12 2 -1.005488422913420e+00 -1.005488422916323e+00 2.90301e-12 1.04690e-11 3 -8.444394106526134e-01 -8.444394106563035e-01 3.69005e-12 1.15460e-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 dicontinuities. Maximum error obtained for particle = 14, direction = 3: |F_model - F_numer| error = ----------------------- = 5.30879e-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. MIXED STRUCTURE -- Species = O Ti | a0 = 3.18436783544 | (Configuration in file "config-OTi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ti 1 -1.826709643596161e-01 -1.826709643503891e-01 9.22698e-12 4.25089e-11 2 -7.316392380729149e-01 -7.316392380856035e-01 1.26886e-11 5.24117e-11 3 -5.260216527440693e-01 -5.260216527412171e-01 2.85216e-12 2.04483e-11 ----------------------------------------------------------------------------------------------------- 2 O 1 2.555994521886832e+00 2.555994521935843e+00 4.90106e-11 2.83070e-10 2 -7.250163049117508e-03 -7.250162968089100e-03 8.10284e-11 3.48027e-09 * 3 -3.286411188296167e+00 -3.286411188365764e+00 6.95968e-11 1.10956e-10 ----------------------------------------------------------------------------------------------------- 3 O 1 1.303900982638823e+00 1.303900982635693e+00 3.12950e-12 1.52263e-10 2 -2.846433046990516e+00 -2.846433046920311e+00 7.02056e-11 2.27743e-10 3 -1.585524074250103e+00 -1.585524074227743e+00 2.23601e-11 8.42295e-11 ----------------------------------------------------------------------------------------------------- 4 O 1 -3.797433297819288e+00 -3.797433297825445e+00 6.15685e-12 2.97034e-11 2 6.254385134894176e-01 6.254385134912940e-01 1.87639e-12 1.99085e-10 3 -8.388282072863718e-01 -8.388282072827725e-01 3.59923e-12 2.01579e-10 ----------------------------------------------------------------------------------------------------- 5 Ti 1 8.226125596242784e-01 8.226125596284690e-01 4.19065e-12 4.26981e-11 2 1.195644065453105e+00 1.195644065450812e+00 2.29305e-12 6.35050e-11 3 -3.167868273991356e-02 -3.167868272733643e-02 1.25771e-11 6.12429e-11 ----------------------------------------------------------------------------------------------------- 6 O 1 -2.591893575033121e-01 -2.591893575095870e-01 6.27493e-12 7.99287e-11 2 -1.463271565548898e+00 -1.463271565574191e+00 2.52935e-11 1.24039e-10 3 5.729310518860651e-01 5.729310519061022e-01 2.00371e-11 1.11790e-10 ----------------------------------------------------------------------------------------------------- 7 Ti 1 -7.700541566340391e-01 -7.700541566415905e-01 7.55140e-12 1.51302e-10 2 6.679957116848587e-01 6.679957116836407e-01 1.21803e-12 1.02611e-10 3 -4.924080653736180e-01 -4.924080653777160e-01 4.09794e-12 1.92956e-11 ----------------------------------------------------------------------------------------------------- 8 Ti 1 1.277783351828685e+00 1.277783351824572e+00 4.11227e-12 1.63278e-11 2 -4.508337185890411e-01 -4.508337185956627e-01 6.62159e-12 2.74297e-10 3 -5.832034872988912e-01 -5.832034872798757e-01 1.90155e-11 2.13512e-10 ----------------------------------------------------------------------------------------------------- 9 O 1 -3.922690363293365e+00 -3.922690363292226e+00 1.13864e-12 4.80784e-11 2 1.008171679618977e+00 1.008171679608553e+00 1.04243e-11 9.98579e-12 3 -1.916284396770924e+00 -1.916284396769101e+00 1.82387e-12 1.63094e-10 ----------------------------------------------------------------------------------------------------- 10 O 1 2.826339684609539e+00 2.826339684613116e+00 3.57669e-12 1.47705e-10 2 4.837451073974687e-01 4.837451073984246e-01 9.55847e-13 5.14629e-10 3 -3.243743427367508e+00 -3.243743427368885e+00 1.37668e-12 3.22604e-11 ----------------------------------------------------------------------------------------------------- 11 Ti 1 1.121813696389245e+00 1.121813696389102e+00 1.42997e-13 1.62332e-10 2 2.797251748789519e+00 2.797251748786795e+00 2.72360e-12 1.05132e-10 3 -6.354387871619566e-01 -6.354387871619245e-01 3.20854e-14 1.12712e-11 ----------------------------------------------------------------------------------------------------- 12 O 1 -2.650069853960689e+00 -2.650069853943496e+00 1.71934e-11 3.27234e-10 2 1.623466028417550e+00 1.623466028443213e+00 2.56635e-11 1.47245e-10 3 2.328049744546984e+00 2.328049744540260e+00 6.72351e-12 6.36273e-11 ----------------------------------------------------------------------------------------------------- 13 Ti 1 -3.996567681695913e-01 -3.996567681962570e-01 2.66657e-11 7.71213e-11 2 4.187927936608283e-01 4.187927936594458e-01 1.38251e-12 6.99569e-11 3 5.521916693953328e-01 5.521916693929099e-01 2.42295e-12 2.17500e-10 ----------------------------------------------------------------------------------------------------- 14 O 1 4.912517036624341e-01 4.912517036579956e-01 4.43851e-12 6.64195e-11 2 1.144617606853615e-01 1.144617606814812e-01 3.88035e-12 8.00180e-11 3 -7.745069789637935e-01 -7.745069789724673e-01 8.67384e-12 2.32097e-11 ----------------------------------------------------------------------------------------------------- 15 Ti 1 -3.100242459542336e+00 -3.100242459527794e+00 1.45426e-11 2.86098e-10 2 -1.219255327825042e+00 -1.219255327832866e+00 7.82419e-12 3.51115e-10 3 1.378435617515134e-01 1.378435617352787e-01 1.62347e-11 1.96318e-10 ----------------------------------------------------------------------------------------------------- 16 Ti 1 -2.307497608721439e+00 -2.307497608710827e+00 1.06115e-11 2.75833e-10 2 -1.537981843332870e+00 -1.537981843336851e+00 3.98104e-12 4.38618e-11 3 1.094848039071650e+00 1.094848039070005e+00 1.64557e-12 1.76823e-10 ----------------------------------------------------------------------------------------------------- 17 O 1 -2.368302987988090e+00 -2.368302987982765e+00 5.32552e-12 9.50973e-12 2 -2.173156082778481e+00 -2.173156082789750e+00 1.12683e-11 3.37024e-11 3 1.355041992124557e+00 1.355041992132804e+00 8.24674e-12 5.22553e-11 ----------------------------------------------------------------------------------------------------- 18 Ti 1 3.543336279545573e-01 3.543336279095847e-01 4.49726e-11 4.06197e-10 2 2.926037857847795e-01 2.926037857824496e-01 2.32991e-12 6.99037e-11 3 1.653552850012932e+00 1.653552850003320e+00 9.61120e-12 4.07779e-10 ----------------------------------------------------------------------------------------------------- 19 O 1 8.666248964102816e-01 8.666248964285413e-01 1.82597e-11 4.21733e-11 2 1.797559644216361e+00 1.797559644229234e+00 1.28724e-11 2.00969e-10 3 1.234175586093930e+00 1.234175586064630e+00 2.92992e-11 2.95182e-10 ----------------------------------------------------------------------------------------------------- 20 Ti 1 -5.295566460043778e-01 -5.295566460045978e-01 2.20046e-13 3.99156e-11 2 -4.157138734568899e-02 -4.157138734609327e-02 4.04274e-13 2.15880e-11 3 3.746015727476791e-02 3.746015727194283e-02 2.82508e-12 6.82041e-11 ----------------------------------------------------------------------------------------------------- 21 O 1 1.489341152747879e+00 1.489341152746356e+00 1.52300e-12 2.36248e-09 * 2 -2.084476715569393e-01 -2.084476715627862e-01 5.84685e-12 3.14649e-10 3 6.278294514349385e-01 6.278294514283266e-01 6.61193e-12 1.54126e-11 ----------------------------------------------------------------------------------------------------- 22 O 1 2.169145650204782e+00 2.169145650204598e+00 1.83853e-13 7.64580e-11 2 -1.092532417745171e+00 -1.092532417757230e+00 1.20595e-11 2.33158e-10 3 1.903313072597347e+00 1.903313072590595e+00 6.75260e-12 3.35065e-11 ----------------------------------------------------------------------------------------------------- 23 Ti 1 1.184127788122399e-01 1.184127788103965e-01 1.84337e-12 6.45563e-12 2 9.979414322175112e-02 9.979414322936338e-02 7.61226e-12 1.33460e-11 3 -8.205843198630469e-02 -8.205843198356529e-02 2.73941e-12 3.82347e-11 ----------------------------------------------------------------------------------------------------- 24 Ti 1 1.472289196878901e+00 1.472289196874015e+00 4.88587e-12 1.77610e-10 2 5.080295689004769e-01 5.080295688941735e-01 6.30340e-12 1.49476e-10 3 -4.250348951742011e-01 -4.250348951948292e-01 2.06282e-11 1.49088e-10 ----------------------------------------------------------------------------------------------------- 25 O 1 -4.093878603062532e-01 -4.093878602559722e-01 5.02809e-11 1.28091e-09 * 2 -1.475810004882927e+00 -1.475810004867671e+00 1.52560e-11 2.32106e-10 3 -8.651419318412870e-01 -8.651419318813124e-01 4.00254e-11 3.64719e-10 ----------------------------------------------------------------------------------------------------- 26 Ti 1 1.241328427911744e+00 1.241328427888265e+00 2.34783e-11 1.00577e-10 2 -1.507249371486395e+00 -1.507249371478619e+00 7.77667e-12 1.16285e-10 3 -1.610446492208278e-02 -1.610446491965032e-02 2.43247e-12 5.79951e-11 ----------------------------------------------------------------------------------------------------- 27 O 1 1.728642736536434e+00 1.728642736621238e+00 8.48037e-11 4.87740e-10 2 -2.363808306280661e+00 -2.363808306247105e+00 3.35554e-11 4.83684e-11 3 2.706841803842306e+00 2.706841803909959e+00 6.76534e-11 4.42706e-10 ----------------------------------------------------------------------------------------------------- 28 O 1 -1.403711778562262e+00 -1.403711778582993e+00 2.07312e-11 1.67870e-10 2 3.314125198885600e+00 3.314125198892908e+00 7.30749e-12 2.98440e-10 3 5.329604630635790e-01 5.329604630619456e-01 1.63347e-12 1.25640e-10 ----------------------------------------------------------------------------------------------------- 29 Ti 1 6.238972109045604e-01 6.238972108213549e-01 8.32056e-11 1.14699e-09 * 2 1.819502224772890e+00 1.819502224770166e+00 2.72404e-12 1.54781e-10 3 9.159401920089353e-01 9.159401919745588e-01 3.43765e-11 3.46125e-10 ----------------------------------------------------------------------------------------------------- 30 O 1 2.022592065955339e+00 2.022592066154234e+00 1.98895e-10 7.43053e-09 * 2 9.325345487146356e-01 9.325345487425900e-01 2.79544e-11 4.67925e-10 3 2.012295024952168e+00 2.012295025034081e+00 8.19131e-11 6.86483e-10 ----------------------------------------------------------------------------------------------------- 31 Ti 1 -1.422110349575559e+00 -1.422110349577959e+00 2.39986e-12 1.51737e-10 2 1.926689404355264e-02 1.926689403787096e-02 5.68168e-12 4.35881e-11 3 -1.135835431230112e+00 -1.135835431214838e+00 1.52742e-11 2.62819e-11 ----------------------------------------------------------------------------------------------------- 32 Ti 1 1.036270207483665e+00 1.036270207490225e+00 6.55964e-12 2.47818e-10 2 -5.991432722524707e-01 -5.991432722468093e-01 5.66136e-12 3.29032e-11 3 -1.227050556649703e+00 -1.227050556649695e+00 7.77156e-15 6.13556e-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 dicontinuities. Maximum error obtained for particle = 5, direction = 3: |F_model - F_numer| error = ----------------------- = 3.97022e-10 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 3.97022e-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 3.97022e-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.