!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 = 2.9145584106445312 | (Configuration in file "config-O.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 O 1 -1.003031888600181e+01 -1.003031888598767e+01 1.41398e-11 3.05658e-10 2 -8.415602069865853e+00 -8.415602069785388e+00 8.04654e-11 2.88786e-09 3 -7.060777720498967e+00 -7.060777720481919e+00 1.70477e-11 3.77640e-10 ----------------------------------------------------------------------------------------------------- 2 O 1 3.270883819526257e+00 3.270883819504614e+00 2.16427e-11 7.50231e-11 2 1.797162830169120e+01 1.797162830168811e+01 3.09086e-12 1.00969e-09 3 -8.460831261002937e+00 -8.460831260997756e+00 5.18163e-12 5.61693e-10 ----------------------------------------------------------------------------------------------------- 3 O 1 3.186695964545477e+00 3.186695964593121e+00 4.76441e-11 2.99466e-10 2 -8.907299213738547e+00 -8.907299213796612e+00 5.80656e-11 5.35886e-10 3 8.250623802129714e-01 8.250623802294881e-01 1.65167e-11 1.05943e-10 ----------------------------------------------------------------------------------------------------- 4 O 1 -4.337772776883430e+00 -4.337772776904228e+00 2.07985e-11 2.76235e-10 2 1.234907823999709e+01 1.234907823994121e+01 5.58842e-11 2.37431e-10 3 2.232793800939542e+01 2.232793800932943e+01 6.59952e-11 3.49208e-09 ----------------------------------------------------------------------------------------------------- 5 O 1 1.186115339608094e+00 1.186115339607374e+00 7.19647e-13 9.74318e-10 2 -1.775681197539230e+01 -1.775681197541158e+01 1.92806e-11 2.59160e-10 3 -7.127557904684469e-01 -7.127557904552835e-01 1.31635e-11 7.74782e-11 ----------------------------------------------------------------------------------------------------- 6 O 1 6.991928701011311e+00 6.991928701012379e+00 1.06848e-12 1.18480e-07 * 2 9.745574313432467e-01 9.745574313320767e-01 1.11700e-11 3.32870e-11 3 -5.513227959254688e+00 -5.513227959262563e+00 7.87548e-12 7.83205e-11 ----------------------------------------------------------------------------------------------------- 7 O 1 9.299237665471896e+00 9.299237665474017e+00 2.12097e-12 2.43089e-09 2 -1.552921151579913e+01 -1.552921151577561e+01 2.35172e-11 6.13056e-10 3 -1.630433128970318e+01 -1.630433128975290e+01 4.97202e-11 1.24945e-10 ----------------------------------------------------------------------------------------------------- 8 O 1 -2.233195221085504e+01 -2.233195220939593e+01 1.45911e-09 3.37986e-09 2 -3.444457743316952e+00 -3.444457743235224e+00 8.17284e-11 3.71140e-10 3 1.571716868514294e+01 1.571716868492681e+01 2.16136e-10 1.08207e-08 * ----------------------------------------------------------------------------------------------------- 9 O 1 -2.672552289994514e+00 -2.672552289997323e+00 2.80886e-12 9.43610e-11 2 -7.596663324096549e+00 -7.596663323999922e+00 9.66276e-11 1.91622e-09 3 -1.206329254282973e+01 -1.206329254282534e+01 4.38938e-12 1.20894e-10 ----------------------------------------------------------------------------------------------------- 10 O 1 -1.013249064282106e+01 -1.013249064247946e+01 3.41601e-10 6.67603e-10 2 1.110933965561162e+01 1.110933965551330e+01 9.83196e-11 3.03612e-09 3 -1.780637647079894e+01 -1.780637647077545e+01 2.34941e-11 2.09855e-09 ----------------------------------------------------------------------------------------------------- 11 O 1 1.211152643884794e+01 1.211152643883505e+01 1.28875e-11 2.62498e-08 * 2 -2.293515006038984e+01 -2.293515006036611e+01 2.37286e-11 1.34428e-09 3 1.549249157607739e+01 1.549249157622122e+01 1.43825e-10 2.93998e-09 ----------------------------------------------------------------------------------------------------- 12 O 1 -3.940140939551267e+00 -3.940140939566662e+00 1.53952e-11 1.60969e-07 * 2 6.150571366017696e+00 6.150571366068904e+00 5.12079e-11 1.96923e-10 3 5.791433498197653e+00 5.791433498165116e+00 3.25375e-11 6.62033e-10 ----------------------------------------------------------------------------------------------------- 13 O 1 -1.177291852937333e+01 -1.177291852935401e+01 1.93197e-11 8.53978e-10 2 -6.076990520088357e+00 -6.076990519987572e+00 1.00785e-10 2.61781e-09 3 -3.614789617792353e+01 -3.614789617830507e+01 3.81540e-10 5.87998e-07 * ----------------------------------------------------------------------------------------------------- 14 O 1 3.485484967548165e+00 3.485484967559069e+00 1.09037e-11 6.77611e-09 2 6.480357120759739e+00 6.480357120808006e+00 4.82672e-11 1.44017e-10 3 -1.865200529484542e+00 -1.865200529500752e+00 1.62106e-11 9.23417e-12 ----------------------------------------------------------------------------------------------------- 15 O 1 3.760177703468777e+01 3.760177703498065e+01 2.92879e-10 6.96403e-10 2 -1.999435630336029e+00 -1.999435630320802e+00 1.52276e-11 2.60492e-11 3 1.334976903934053e+01 1.334976903936238e+01 2.18527e-11 4.17687e-10 ----------------------------------------------------------------------------------------------------- 16 O 1 8.251315043450544e+00 8.251315043392355e+00 5.81899e-11 9.81013e-10 2 2.739410253400365e+01 2.739410253442067e+01 4.17025e-10 4.64369e-09 3 1.615598369215873e+01 1.615598369221300e+01 5.42677e-11 2.22960e-09 ----------------------------------------------------------------------------------------------------- 17 O 1 -4.753179506751474e+00 -4.753179506740540e+00 1.09335e-11 6.42757e-11 2 -8.055904422982080e+00 -8.055904423005314e+00 2.32347e-11 1.10614e-11 3 -8.869983682950263e+00 -8.869983682876274e+00 7.39888e-11 1.69399e-10 ----------------------------------------------------------------------------------------------------- 18 O 1 9.978917986544703e+00 9.978917986574055e+00 2.93525e-11 3.40205e-09 2 1.951960611100340e+01 1.951960611099951e+01 3.89022e-12 1.22824e-10 3 -1.626414799507265e+01 -1.626414799504908e+01 2.35758e-11 4.91315e-10 ----------------------------------------------------------------------------------------------------- 19 O 1 5.534951019795943e+00 5.534951019811127e+00 1.51843e-11 7.58797e-11 2 -3.218159534426203e+00 -3.218159534424783e+00 1.42020e-12 1.25391e-10 3 1.378426377291846e+00 1.378426377295655e+00 3.80918e-12 4.87628e-11 ----------------------------------------------------------------------------------------------------- 20 O 1 -7.321884503875979e+00 -7.321884503992663e+00 1.16684e-10 1.83036e-09 2 9.219430018876468e+00 9.219430018883820e+00 7.35234e-12 1.89441e-10 3 1.214798489425494e+01 1.214798489435922e+01 1.04281e-10 5.86783e-09 ----------------------------------------------------------------------------------------------------- 21 O 1 -8.829654352419061e+00 -8.829654352425697e+00 6.63647e-12 1.01242e-09 2 -1.001355723511482e+01 -1.001355723533740e+01 2.22586e-10 1.15377e-09 3 3.901242999655705e+00 3.901242999693079e+00 3.73745e-11 2.19294e-10 ----------------------------------------------------------------------------------------------------- 22 O 1 7.319315580602079e+00 7.319315580619949e+00 1.78701e-11 4.97832e-10 2 1.321992909687844e+01 1.321992909695664e+01 7.81935e-11 3.58887e-08 * 3 3.023211445927407e+00 3.023211445886078e+00 4.13296e-11 2.73534e-10 ----------------------------------------------------------------------------------------------------- 23 O 1 8.352339768501972e+00 8.352339768507242e+00 5.27045e-12 1.16412e-08 * 2 -2.663014015552264e+00 -2.663014015552346e+00 8.12683e-14 3.98459e-10 3 4.459655610266452e+00 4.459655610290056e+00 2.36042e-11 9.84191e-11 ----------------------------------------------------------------------------------------------------- 24 O 1 -9.099768902010911e+00 -9.099768901948110e+00 6.28013e-11 1.62441e-09 2 6.507957592868076e+00 6.507957592825902e+00 4.21734e-11 2.84778e-10 3 4.172370772519968e+00 4.172370772480996e+00 3.89715e-11 3.29432e-10 ----------------------------------------------------------------------------------------------------- 25 O 1 -1.569543877366814e+01 -1.569543877321070e+01 4.57435e-10 5.52980e-09 2 -2.184583173747991e+01 -2.184583173740812e+01 7.17861e-11 9.82009e-10 3 -2.280796169965312e+01 -2.280796169998193e+01 3.28811e-10 5.58421e-09 ----------------------------------------------------------------------------------------------------- 26 O 1 -4.984891618205355e+00 -4.984891618148016e+00 5.73390e-11 7.99530e-10 2 1.727732095592332e+01 1.727732095597192e+01 4.86011e-11 1.13319e-09 3 -9.766875099461629e+00 -9.766875099431696e+00 2.99334e-11 7.28340e-10 ----------------------------------------------------------------------------------------------------- 27 O 1 5.540124865874034e+00 5.540124865682965e+00 1.91069e-10 8.90815e-10 2 -1.660820049284208e+01 -1.660820049290770e+01 6.56222e-11 5.20313e-10 3 2.213582611380437e+01 2.213582611499427e+01 1.18990e-09 2.85020e-09 ----------------------------------------------------------------------------------------------------- 28 O 1 -1.540521630393620e+01 -1.540521630373171e+01 2.04491e-10 1.82060e-09 2 1.922567652664831e+01 1.922567652732103e+01 6.72721e-10 1.11182e-08 * 3 7.372456272173327e+00 7.372456271561124e+00 6.12203e-10 2.26366e-09 ----------------------------------------------------------------------------------------------------- 29 O 1 -1.854415711264268e+01 -1.854415711293751e+01 2.94833e-10 1.04257e-09 2 -1.798952319083449e+01 -1.798952319120163e+01 3.67145e-10 9.23734e-10 3 -6.046216260424387e+00 -6.046216260364252e+00 6.01350e-11 5.14120e-10 ----------------------------------------------------------------------------------------------------- 30 O 1 6.518128896783424e+00 6.518128896780940e+00 2.48424e-12 7.52403e-11 2 1.356558146906470e+01 1.356558146918789e+01 1.23194e-10 1.02698e-10 3 -1.197148118394191e+01 -1.197148118398641e+01 4.45013e-11 6.55339e-10 ----------------------------------------------------------------------------------------------------- 31 O 1 1.696101945983943e+01 1.696101945975565e+01 8.37836e-11 1.28684e-07 * 2 -1.716409288315865e+01 -1.716409288299280e+01 1.65851e-10 4.28435e-08 * 3 1.985554477675143e+01 1.985554477671077e+01 4.06679e-11 5.21155e-10 ----------------------------------------------------------------------------------------------------- 32 O 1 4.262574796351180e+00 4.262574796342012e+00 9.16778e-12 8.34458e-10 2 9.254769144727090e+00 9.254769144805017e+00 7.79270e-11 5.83055e-10 3 1.355478952029788e+01 1.355478952024009e+01 5.77867e-11 1.08882e-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 = 28, direction = 3: |F_model - F_numer| error = ----------------------- = 8.30392e-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 = 3.4325170516967773 | (Configuration in file "config-Ti.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ti 1 2.165753737803242e-01 2.165753737799814e-01 3.42809e-13 2.63667e-12 2 3.477258898420652e-01 3.477258898421339e-01 6.87228e-14 1.25286e-11 3 3.301495408020739e-01 3.301495408004834e-01 1.59045e-12 1.98169e-12 ----------------------------------------------------------------------------------------------------- 2 Ti 1 -1.598495051592178e-01 -1.598495051593002e-01 8.24063e-14 4.29781e-12 2 -9.554597535917654e-01 -9.554597535917512e-01 1.42109e-14 5.52947e-12 3 1.047027962142874e+00 1.047027962143548e+00 6.74794e-13 3.05889e-12 ----------------------------------------------------------------------------------------------------- 3 Ti 1 -5.824976285599859e-01 -5.824976285603498e-01 3.63931e-13 1.08498e-11 2 8.360724886051440e-01 8.360724886023432e-01 2.80087e-12 1.53522e-12 3 -1.041159475295406e+00 -1.041159475294406e+00 1.00053e-12 9.48863e-12 ----------------------------------------------------------------------------------------------------- 4 Ti 1 9.935084049565919e-01 9.935084049563220e-01 2.69895e-13 1.60315e-11 2 -4.151568178825244e-01 -4.151568178802631e-01 2.26130e-12 5.09336e-11 * 3 -3.340259139322067e-01 -3.340259139321622e-01 4.44644e-14 2.76629e-12 ----------------------------------------------------------------------------------------------------- 5 Ti 1 4.313464580426079e-01 4.313464580423271e-01 2.80775e-13 1.74577e-12 2 7.333708310751270e-01 7.333708310752997e-01 1.72640e-13 9.16878e-12 3 6.729826758183048e-01 6.729826758186626e-01 3.57714e-13 7.80842e-12 ----------------------------------------------------------------------------------------------------- 6 Ti 1 -7.144167312899277e-01 -7.144167312893576e-01 5.70100e-13 1.95456e-11 2 -2.081447587182549e-01 -2.081447587189482e-01 6.93307e-13 4.46548e-12 3 6.922229322740086e-01 6.922229322733799e-01 6.28608e-13 8.25273e-12 ----------------------------------------------------------------------------------------------------- 7 Ti 1 -3.785562833015423e-01 -3.785562833007698e-01 7.72549e-13 1.30623e-12 2 5.950122471910618e-01 5.950122471907904e-01 2.71450e-13 2.78774e-11 3 -4.830186853261879e-01 -4.830186853264786e-01 2.90656e-13 7.59653e-12 ----------------------------------------------------------------------------------------------------- 8 Ti 1 4.876635323398058e-01 4.876635323382932e-01 1.51257e-12 2.95314e-12 2 -9.581861083314356e-01 -9.581861083291758e-01 2.25975e-12 2.05198e-11 3 -1.005226818947712e+00 -1.005226818950097e+00 2.38454e-12 4.88387e-12 ----------------------------------------------------------------------------------------------------- 9 Ti 1 3.816519273106503e-01 3.816519273105253e-01 1.25067e-13 2.37871e-12 2 5.804721088496894e-01 5.804721088488042e-01 8.85181e-13 3.72025e-12 3 3.399868981036088e-01 3.399868981037167e-01 1.07914e-13 6.52325e-11 * ----------------------------------------------------------------------------------------------------- 10 Ti 1 -3.357194312713095e-01 -3.357194312722012e-01 8.91620e-13 5.45425e-12 2 -4.069532305954557e-01 -4.069532305953120e-01 1.43718e-13 2.65982e-12 3 3.238110208669507e-01 3.238110208691961e-01 2.24537e-12 3.38929e-12 ----------------------------------------------------------------------------------------------------- 11 Ti 1 -3.376327991330139e-01 -3.376327991354807e-01 2.46680e-12 7.20957e-12 2 2.768447614128796e-01 2.768447614130466e-01 1.67033e-13 7.37405e-12 3 -5.680761629392295e-01 -5.680761629380722e-01 1.15730e-12 1.51164e-11 ----------------------------------------------------------------------------------------------------- 12 Ti 1 -9.597592976869318e-02 -9.597592976507942e-02 3.61376e-12 4.82146e-12 2 -4.231270209519614e-01 -4.231270209515993e-01 3.62044e-13 5.77804e-12 3 -2.222852127529413e-01 -2.222852127532655e-01 3.24185e-13 5.42055e-12 ----------------------------------------------------------------------------------------------------- 13 Ti 1 1.222667500299402e-01 1.222667500302628e-01 3.22659e-13 8.42297e-12 2 3.011619067284351e-01 3.011619067284280e-01 7.16094e-15 8.62532e-13 3 6.088854370165028e-01 6.088854370169332e-01 4.30433e-13 1.01169e-11 ----------------------------------------------------------------------------------------------------- 14 Ti 1 2.517902380082694e-01 2.517902380082601e-01 9.32587e-15 1.83259e-12 2 -4.735220476168972e-01 -4.735220476171925e-01 2.95264e-13 1.26815e-12 3 7.093507727965542e-02 7.093507728003862e-02 3.83193e-13 6.92085e-13 ----------------------------------------------------------------------------------------------------- 15 Ti 1 -4.692946914574835e-01 -4.692946914534737e-01 4.00974e-12 4.61752e-11 2 2.591198759648933e-01 2.591198759644017e-01 4.91662e-13 9.21319e-13 3 -8.311812225713742e-01 -8.311812225713742e-01 0.00000e+00 9.25582e-12 ----------------------------------------------------------------------------------------------------- 16 Ti 1 2.232888456466436e-01 2.232888456474182e-01 7.74547e-13 1.50868e-12 2 -2.747397883748009e-01 -2.747397883741321e-01 6.68798e-13 5.76367e-12 3 -1.151606214658285e-02 -1.151606214605468e-02 5.28171e-13 1.41916e-12 ----------------------------------------------------------------------------------------------------- 17 Ti 1 3.243884152296880e-01 3.243884152289946e-01 6.93390e-13 3.18456e-12 2 3.808197565111168e-01 3.808197565112372e-01 1.20404e-13 7.18992e-12 3 5.381043524255764e-01 5.381043524259230e-01 3.46612e-13 2.40813e-11 ----------------------------------------------------------------------------------------------------- 18 Ti 1 -6.491297845126356e-01 -6.491297845148680e-01 2.23244e-12 1.41304e-11 2 -4.908750717827726e-01 -4.908750717796860e-01 3.08664e-12 3.88963e-11 3 5.041371599032971e-01 5.041371599034532e-01 1.56097e-13 1.71465e-11 ----------------------------------------------------------------------------------------------------- 19 Ti 1 -4.588682258800588e-01 -4.588682258810090e-01 9.50184e-13 2.83836e-11 2 4.052623402337285e-01 4.052623402323507e-01 1.37779e-12 1.44942e-11 3 -5.374895093037058e-01 -5.374895093023497e-01 1.35603e-12 3.91965e-11 ----------------------------------------------------------------------------------------------------- 20 Ti 1 3.118380894918623e-01 3.118380894918413e-01 2.09832e-14 6.06887e-12 2 -7.406982135176762e-01 -7.406982135169198e-01 7.56395e-13 1.91402e-12 3 -5.346141967882101e-01 -5.346141967870071e-01 1.20304e-12 1.98900e-11 ----------------------------------------------------------------------------------------------------- 21 Ti 1 9.919372182653559e-01 9.919372182655170e-01 1.61093e-13 6.58329e-12 2 7.389831197674800e-01 7.389831197673744e-01 1.05582e-13 8.02469e-13 3 5.956427560682700e-01 5.956427560693865e-01 1.11655e-12 6.91036e-12 ----------------------------------------------------------------------------------------------------- 22 Ti 1 -8.542084465978524e-01 -8.542084465937458e-01 4.10660e-12 3.93430e-12 2 -1.015341741955812e+00 -1.015341741956034e+00 2.22267e-13 2.01861e-12 3 3.944451934774396e-01 3.944451934775371e-01 9.75331e-14 8.43081e-12 ----------------------------------------------------------------------------------------------------- 23 Ti 1 -1.546734327048231e-01 -1.546734327044348e-01 3.88301e-13 9.90724e-12 2 1.994402335863470e-01 1.994402335850512e-01 1.29580e-12 2.79879e-12 3 -4.253049021722170e-01 -4.253049021724754e-01 2.58349e-13 4.59394e-12 ----------------------------------------------------------------------------------------------------- 24 Ti 1 4.487305503936434e-01 4.487305503919466e-01 1.69675e-12 1.77358e-12 2 -4.039379881276987e-01 -4.039379881319231e-01 4.22440e-12 2.09915e-12 3 -2.704214745884289e-01 -2.704214745874127e-01 1.01619e-12 7.71827e-12 ----------------------------------------------------------------------------------------------------- 25 Ti 1 4.374315538741699e-01 4.374315538495270e-01 2.46430e-11 1.50188e-10 * 2 -1.434733897069533e-01 -1.434733897089654e-01 2.01208e-12 6.90758e-08 * 3 -3.262573344246859e-01 -3.262573344272491e-01 2.56323e-12 5.58271e-11 * ----------------------------------------------------------------------------------------------------- 26 Ti 1 3.041642619615073e-01 3.041642619612908e-01 2.16493e-13 6.11028e-12 2 -1.577760667432141e-01 -1.577760667493119e-01 6.09776e-12 5.73586e-12 3 5.172472931470997e-01 5.172472931480826e-01 9.82880e-13 4.45666e-12 ----------------------------------------------------------------------------------------------------- 27 Ti 1 6.461454240007658e-02 6.461454240393780e-02 3.86122e-12 1.04468e-11 2 4.576089963606711e-01 4.576089963610583e-01 3.87190e-13 3.87845e-12 3 -6.754454735810246e-01 -6.754454735813238e-01 2.99205e-13 7.63201e-12 ----------------------------------------------------------------------------------------------------- 28 Ti 1 2.020525870346216e-01 2.020525870388073e-01 4.18568e-12 1.03231e-12 2 2.164522464041344e-01 2.164522464053321e-01 1.19771e-12 2.43217e-11 3 3.543482666077621e-01 3.543482665986575e-01 9.10455e-12 2.83490e-11 ----------------------------------------------------------------------------------------------------- 29 Ti 1 6.069630475175206e-02 6.069630475208349e-02 3.31436e-13 2.26238e-12 2 1.543504365595458e+00 1.543504365595660e+00 2.01617e-13 2.68252e-12 3 1.323430019019582e+00 1.323430019019422e+00 1.60316e-13 5.01688e-12 ----------------------------------------------------------------------------------------------------- 30 Ti 1 -6.637469444659536e-01 -6.637469444723362e-01 6.38256e-12 1.82451e-10 * 2 -3.843189067534258e-01 -3.843189067513815e-01 2.04436e-12 5.99966e-11 * 3 5.452570551451497e-01 5.452570551467198e-01 1.57019e-12 1.66823e-11 ----------------------------------------------------------------------------------------------------- 31 Ti 1 -8.747671200376310e-01 -8.747671200358078e-01 1.82321e-12 6.37801e-12 2 5.853481594358336e-01 5.853481594358191e-01 1.45439e-14 1.66697e-11 3 -7.481517846756294e-01 -7.481517846776120e-01 1.98264e-12 5.94902e-12 ----------------------------------------------------------------------------------------------------- 32 Ti 1 4.753919006226182e-01 4.753919006222717e-01 3.46501e-13 5.98072e-12 2 -1.005488422913418e+00 -1.005488422913626e+00 2.08500e-13 1.75195e-11 3 -8.444394106526125e-01 -8.444394106549961e-01 2.38354e-12 4.47276e-12 ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as discontinuities. Maximum error obtained for particle = 27, direction = 1: |F_model - F_numer| error = ----------------------- = 5.97577e-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 = 2.687645454079392 | (Configuration in file "config-OTi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 O 1 -1.029365457488571e+01 -1.029365457495409e+01 6.83755e-11 2.49999e-10 2 -5.014313145032073e+00 -5.014313145027555e+00 4.51816e-12 4.68990e-10 3 -1.643772046661262e+01 -1.643772046634847e+01 2.64144e-10 4.86537e-10 ----------------------------------------------------------------------------------------------------- 2 Ti 1 -1.475791194409098e+00 -1.475791194442931e+00 3.38334e-11 1.88469e-10 2 -1.183550291890744e+00 -1.183550291918254e+00 2.75100e-11 4.67002e-10 3 -1.838566697889698e+00 -1.838566697843388e+00 4.63096e-11 5.88680e-10 ----------------------------------------------------------------------------------------------------- 3 O 1 2.357677976106975e+01 2.357677976111329e+01 4.35350e-11 1.33991e-10 2 -9.007605907654698e+00 -9.007605907384169e+00 2.70528e-10 2.39668e-08 * 3 -4.870849727614153e+00 -4.870849727585600e+00 2.85523e-11 4.98437e-11 ----------------------------------------------------------------------------------------------------- 4 O 1 -1.102111771326043e+01 -1.102111771324709e+01 1.33387e-11 1.26098e-10 2 5.028370391314363e+00 5.028370391318140e+00 3.77742e-12 3.49694e-11 3 -5.191345981281159e+00 -5.191345981313924e+00 3.27658e-11 2.07476e-10 ----------------------------------------------------------------------------------------------------- 5 Ti 1 2.520638610083107e-01 2.520638609947922e-01 1.35185e-11 1.05496e-10 2 4.880298703929306e-01 4.880298704013727e-01 8.44214e-12 8.77169e-11 3 -6.782937361247054e-01 -6.782937361225128e-01 2.19269e-12 2.50787e-11 ----------------------------------------------------------------------------------------------------- 6 Ti 1 -7.739476748264321e-01 -7.739476748438624e-01 1.74303e-11 3.21288e-10 2 -2.455530797539852e+00 -2.455530797567760e+00 2.79079e-11 1.43403e-10 3 6.516407568532619e-01 6.516407568565834e-01 3.32145e-12 2.60924e-10 ----------------------------------------------------------------------------------------------------- 7 Ti 1 1.341226928562888e+00 1.341226928580670e+00 1.77816e-11 1.11932e-10 2 -6.185129370988953e-02 -6.185129371169047e-02 1.80093e-12 1.51023e-10 3 -7.397949907880352e-01 -7.397949907955317e-01 7.49645e-12 3.28115e-11 ----------------------------------------------------------------------------------------------------- 8 O 1 9.241569889081111e+00 9.241569888974828e+00 1.06283e-10 6.91331e-10 2 -1.889229738508463e+01 -1.889229738508343e+01 1.19726e-12 7.29226e-10 3 -2.918438516250816e+01 -2.918438516251422e+01 6.06803e-12 5.77760e-10 ----------------------------------------------------------------------------------------------------- 9 Ti 1 -1.903770676462804e+00 -1.903770676453840e+00 8.96350e-12 5.81009e-11 2 1.098922070379891e+00 1.098922070378148e+00 1.74305e-12 5.75759e-11 3 -5.096176779835045e+00 -5.096176779843200e+00 8.15437e-12 1.99236e-11 ----------------------------------------------------------------------------------------------------- 10 Ti 1 -3.330981224323316e+00 -3.330981224325286e+00 1.97042e-12 1.47367e-10 2 -3.928818950938426e-01 -3.928818950927381e-01 1.10451e-12 1.73764e-11 3 -2.397825646756328e+00 -2.397825646750773e+00 5.55467e-12 1.50812e-10 ----------------------------------------------------------------------------------------------------- 11 O 1 -3.040915623643242e+01 -3.040915623661716e+01 1.84741e-10 1.11679e-09 2 -3.606964534495913e+00 -3.606964534487829e+00 8.08464e-12 3.03503e-10 3 -2.357696614792007e+01 -2.357696614792057e+01 4.97380e-13 1.32630e-09 ----------------------------------------------------------------------------------------------------- 12 Ti 1 -1.556212011265135e+00 -1.556212011226109e+00 3.90266e-11 1.80301e-10 2 2.232816869226831e+00 2.232816869186546e+00 4.02851e-11 6.34603e-11 3 -4.054484577330495e+00 -4.054484577330713e+00 2.17604e-13 7.55467e-11 ----------------------------------------------------------------------------------------------------- 13 Ti 1 5.060545817647666e-01 5.060545817829408e-01 1.81742e-11 3.51709e-10 2 -1.312609420721504e+00 -1.312609420743549e+00 2.20450e-11 1.59535e-10 3 -1.492164365457576e+00 -1.492164365484655e+00 2.70788e-11 8.65095e-11 ----------------------------------------------------------------------------------------------------- 14 O 1 6.940484813485496e+00 6.940484813414439e+00 7.10569e-11 5.47672e-10 2 1.292005115119131e+01 1.292005115115352e+01 3.77920e-11 4.19998e-10 3 -2.039830128849422e+01 -2.039830128848894e+01 5.28644e-12 1.89218e-10 ----------------------------------------------------------------------------------------------------- 15 O 1 1.496314708924345e+01 1.496314708924059e+01 2.86526e-12 7.71328e-10 2 -1.208882058471039e+01 -1.208882058474325e+01 3.28590e-11 2.12557e-10 3 1.189321681009549e+01 1.189321680995014e+01 1.45345e-10 3.38597e-10 ----------------------------------------------------------------------------------------------------- 16 O 1 7.446025882829762e+00 7.446025882835749e+00 5.98721e-12 1.67789e-10 2 2.897114119436835e+01 2.897114119449462e+01 1.26263e-10 1.37726e-09 3 -7.717332826184263e+00 -7.717332826191389e+00 7.12586e-12 2.10347e-11 ----------------------------------------------------------------------------------------------------- 17 O 1 -2.736032501263867e+01 -2.736032501256042e+01 7.82556e-11 8.30390e-10 2 -1.150692609355252e+01 -1.150692609359432e+01 4.18083e-11 2.64993e-08 * 3 -4.943799020591616e+00 -4.943799020585943e+00 5.67280e-12 5.47821e-10 ----------------------------------------------------------------------------------------------------- 18 Ti 1 4.235043551242134e-01 4.235043551239652e-01 2.48190e-13 1.24041e-10 2 -2.283519443164615e+00 -2.283519443167172e+00 2.55662e-12 1.28789e-10 3 -3.728765105211153e+00 -3.728765105225332e+00 1.41789e-11 2.60191e-10 ----------------------------------------------------------------------------------------------------- 19 O 1 -3.326244065044861e+00 -3.326244065056694e+00 1.18328e-11 3.65910e-05 * 2 -1.560158328798211e+01 -1.560158328802869e+01 4.65832e-11 1.75436e-04 * 3 1.344431945460723e+01 1.344431945467865e+01 7.14220e-11 1.26541e-09 ----------------------------------------------------------------------------------------------------- 20 O 1 -7.195095336640318e+00 -7.195095336643948e+00 3.62999e-12 3.24393e-10 2 8.000564326402719e+00 8.000564326418237e+00 1.55183e-11 2.03585e-09 * 3 1.756807513801216e+01 1.756807513800347e+01 8.68994e-12 1.66299e-10 ----------------------------------------------------------------------------------------------------- 21 O 1 1.129080064723896e+01 1.129080064737092e+01 1.31960e-10 1.42624e-09 2 -1.394685064718867e+01 -1.394685064717991e+01 8.75389e-12 2.98799e-10 3 1.426076360366428e-01 1.426076360473142e-01 1.06714e-11 7.86338e-11 ----------------------------------------------------------------------------------------------------- 22 Ti 1 7.047494003280272e+00 7.047494003289182e+00 8.91021e-12 4.13962e-11 2 -4.084883804186620e-01 -4.084883804144183e-01 4.24366e-12 7.32010e-11 3 -7.141007303876710e-01 -7.141007303852805e-01 2.39042e-12 5.74593e-11 ----------------------------------------------------------------------------------------------------- 23 Ti 1 3.267643223539393e+00 3.267643223536525e+00 2.86748e-12 5.23896e-11 2 -3.346777694561798e+00 -3.346777694561035e+00 7.62945e-13 1.67854e-10 3 1.578076630602105e+00 1.578076630584753e+00 1.73521e-11 8.62790e-11 ----------------------------------------------------------------------------------------------------- 24 O 1 1.140456939805843e+01 1.140456939806047e+01 2.03393e-12 1.47383e-10 2 2.056066127045724e+01 2.056066127046497e+01 7.72360e-12 3.46343e-10 3 1.068336254433589e+01 1.068336254424869e+01 8.71978e-11 7.44445e-10 ----------------------------------------------------------------------------------------------------- 25 O 1 -1.325541520565317e+01 -1.325541520563179e+01 2.13838e-11 2.80098e-10 2 -8.761567785531751e+00 -8.761567785537750e+00 5.99876e-12 4.07599e-09 * 3 9.882129845966673e-01 9.882129845444723e-01 5.21950e-11 2.34497e-10 ----------------------------------------------------------------------------------------------------- 26 O 1 -2.054216018689514e-01 -2.054216018790242e-01 1.00728e-11 7.86707e-11 2 1.887384386768315e+01 1.887384386769812e+01 1.49747e-11 8.59725e-10 3 9.459376046680768e+00 9.459376046739788e+00 5.90195e-11 1.15286e-11 ----------------------------------------------------------------------------------------------------- 27 Ti 1 3.075568778464458e+00 3.075568778459937e+00 4.52127e-12 9.23333e-11 2 8.941533840699664e+00 8.941533840689821e+00 9.84279e-12 4.84734e-10 3 5.982231767279272e+00 5.982231767314460e+00 3.51887e-11 3.55711e-10 ----------------------------------------------------------------------------------------------------- 28 Ti 1 -2.019915261699118e-02 -2.019915260355071e-02 1.34405e-11 7.03908e-11 2 4.984417592149503e+00 4.984417592148091e+00 1.41220e-12 5.05542e-11 3 7.889990153809157e+00 7.889990153800346e+00 8.81073e-12 6.02807e-11 ----------------------------------------------------------------------------------------------------- 29 O 1 1.294006838278760e+01 1.294006838259541e+01 1.92195e-10 2.23718e-10 2 1.544577960087106e+00 1.544577959898950e+00 1.88155e-10 2.71315e-10 3 4.582203003778957e+01 4.582203003765876e+01 1.30811e-10 1.74786e-10 ----------------------------------------------------------------------------------------------------- 30 Ti 1 -9.870816129927312e-01 -9.870816129776975e-01 1.50338e-11 8.42205e-11 2 -2.668823944591987e+00 -2.668823944584104e+00 7.88214e-12 6.72999e-11 3 3.929073902961772e+00 3.929073902970526e+00 8.75344e-12 8.42260e-12 ----------------------------------------------------------------------------------------------------- 31 Ti 1 1.914774754261974e+00 1.914774754253232e+00 8.74212e-12 4.53726e-11 2 3.048631594997674e+00 3.048631594994638e+00 3.03624e-12 7.04192e-11 3 1.139888665739818e+00 1.139888665743301e+00 3.48388e-12 1.97313e-10 ----------------------------------------------------------------------------------------------------- 32 Ti 1 -2.517363056479796e+00 -2.517363056479049e+00 7.46958e-13 3.06972e-09 * 2 -4.152599466425096e+00 -4.152599466457811e+00 3.27143e-11 3.72415e-10 3 1.888770721587167e+00 1.888770721599339e+00 1.21723e-11 6.63990e-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 = 28, direction = 1: |F_model - F_numer| error = ----------------------- = 6.65398e-10 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 6.65398e-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 6.65398e-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.