!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 : EAM_Dynamo_Foiles_1985_Ni__MO_010059867259_000 Supported species : Ni 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 = Ni | a0 = 3.52000007629 | (Configuration in file "config-Ni.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ni 1 -9.829783404965021e-01 -9.829783404411450e-01 5.53572e-11 4.01670e-09 * 2 -5.352894688048426e-01 -5.352894689434127e-01 1.38570e-10 3.47421e-10 3 -2.174729447547939e+00 -2.174729447709571e+00 1.61632e-10 1.12987e-09 ----------------------------------------------------------------------------------------------------- 2 Ni 1 -3.854522698984005e-01 -3.854522698900720e-01 8.32850e-12 5.00033e-10 2 1.029792193990158e+00 1.029792193937899e+00 5.22595e-11 4.78581e-10 3 3.767685093073244e-01 3.767685091163359e-01 1.90989e-10 9.12895e-10 ----------------------------------------------------------------------------------------------------- 3 Ni 1 3.163352420073636e+00 3.163352419973261e+00 1.00375e-10 1.22142e-09 2 -1.403181407057670e+00 -1.403181407103624e+00 4.59535e-11 1.20523e-09 3 8.480247607717065e-01 8.480247607910620e-01 1.93555e-11 2.32662e-09 ----------------------------------------------------------------------------------------------------- 4 Ni 1 -1.968811658283286e-01 -1.968811658620961e-01 3.37675e-11 3.55097e-10 2 2.064145808136814e+00 2.064145808424914e+00 2.88100e-10 2.98832e-09 * 3 9.463270090322065e-01 9.463270091374105e-01 1.05204e-10 5.22584e-10 ----------------------------------------------------------------------------------------------------- 5 Ni 1 5.354781553406821e-01 5.354781554252225e-01 8.45404e-11 5.02868e-10 2 3.375046745183012e-01 3.375046745061118e-01 1.21894e-11 9.02985e-10 3 9.124834930707150e-01 9.124834930253837e-01 4.53313e-11 2.01627e-10 ----------------------------------------------------------------------------------------------------- 6 Ni 1 -1.163638277137532e+00 -1.163638277118691e+00 1.88409e-11 2.91979e-10 2 5.033438429559199e-01 5.033438427781113e-01 1.77809e-10 1.67329e-09 3 9.434608671476390e-01 9.434608671254695e-01 2.21695e-11 2.78704e-10 ----------------------------------------------------------------------------------------------------- 7 Ni 1 7.557339605431902e-01 7.557339607264130e-01 1.83223e-10 1.72583e-09 2 -4.504498768701346e+00 -4.504498768856702e+00 1.55356e-10 9.21018e-10 3 -5.557830938845114e+00 -5.557830938811425e+00 3.36886e-11 3.55532e-10 ----------------------------------------------------------------------------------------------------- 8 Ni 1 -3.301888114686775e+00 -3.301888114567516e+00 1.19259e-10 2.61887e-08 * 2 -2.725575574681450e+00 -2.725575575233669e+00 5.52219e-10 1.19537e-09 3 -1.470410924767833e+00 -1.470410924869740e+00 1.01907e-10 9.58896e-10 ----------------------------------------------------------------------------------------------------- 9 Ni 1 -2.799270019096533e+00 -2.799270019139760e+00 4.32272e-11 2.57265e-10 2 -1.914041419488307e+00 -1.914041419876482e+00 3.88175e-10 4.70454e-10 3 -3.694700891643757e+00 -3.694700891806860e+00 1.63104e-10 1.24936e-09 ----------------------------------------------------------------------------------------------------- 10 Ni 1 -1.025732424652854e+00 -1.025732424483623e+00 1.69231e-10 1.17777e-09 2 2.324214650426982e+00 2.324214650387538e+00 3.94431e-11 1.99230e-10 3 -2.391708570113778e+00 -2.391708569964845e+00 1.48933e-10 7.27063e-11 ----------------------------------------------------------------------------------------------------- 11 Ni 1 9.351061181088030e-01 9.351061182089137e-01 1.00111e-10 1.24445e-09 2 -2.764726424105162e+00 -2.764726424076492e+00 2.86700e-11 2.68159e-10 3 4.868116257177340e+00 4.868116257238283e+00 6.09424e-11 1.00083e-09 ----------------------------------------------------------------------------------------------------- 12 Ni 1 2.084823864840905e-01 2.084823865080082e-01 2.39176e-11 4.05878e-10 2 1.691291140337090e+00 1.691291140326459e+00 1.06313e-11 5.99320e-10 3 8.330516222045430e-01 8.330516222291731e-01 2.46301e-11 1.05064e-09 ----------------------------------------------------------------------------------------------------- 13 Ni 1 -1.101449984809938e+00 -1.101449984720017e+00 8.99210e-11 2.08945e-10 2 -2.425778699886933e+00 -2.425778700062634e+00 1.75702e-10 3.00635e-11 3 -6.215448544348162e+00 -6.215448544249453e+00 9.87086e-11 1.40532e-09 ----------------------------------------------------------------------------------------------------- 14 Ni 1 -2.754549270086374e-01 -2.754549270303459e-01 2.17085e-11 3.53460e-10 2 2.074218799559499e-01 2.074218798733361e-01 8.26138e-11 6.56714e-10 3 4.642657233712139e-01 4.642657232250094e-01 1.46204e-10 2.96231e-10 ----------------------------------------------------------------------------------------------------- 15 Ni 1 5.896027580769391e+00 5.896027580942207e+00 1.72816e-10 6.75808e-10 2 -7.176111384600710e-01 -7.176111386625742e-01 2.02503e-10 2.42553e-10 3 1.029520304763955e+00 1.029520304776027e+00 1.20717e-11 3.91651e-10 ----------------------------------------------------------------------------------------------------- 16 Ni 1 1.016712731274847e+00 1.016712731427751e+00 1.52904e-10 4.82586e-10 2 3.577737693076340e+00 3.577737693185263e+00 1.08923e-10 2.09159e-10 3 1.931425669518139e+00 1.931425669448251e+00 6.98881e-11 7.14521e-10 ----------------------------------------------------------------------------------------------------- 17 Ni 1 -3.930795108484110e-01 -3.930795110605004e-01 2.12089e-10 6.16317e-10 2 -1.335495577960675e+00 -1.335495577917521e+00 4.31548e-11 8.31402e-10 3 -1.545449481323911e+00 -1.545449481344592e+00 2.06815e-11 1.50490e-10 ----------------------------------------------------------------------------------------------------- 18 Ni 1 -9.802498259731493e-02 -9.802498260549580e-02 8.18087e-12 7.63746e-10 2 1.742716974967709e+00 1.742716975128483e+00 1.60774e-10 9.03135e-10 3 9.328052428708052e-01 9.328052428611056e-01 9.69969e-12 6.68080e-10 ----------------------------------------------------------------------------------------------------- 19 Ni 1 2.071545295681511e-01 2.071545295467499e-01 2.14012e-11 2.09218e-10 2 -5.444234401282290e-01 -5.444234400276876e-01 1.00541e-10 2.60228e-09 3 -5.428603808939589e-01 -5.428603807734617e-01 1.20497e-10 2.60173e-10 ----------------------------------------------------------------------------------------------------- 20 Ni 1 5.513518032876175e-01 5.513518032463033e-01 4.13142e-11 6.18014e-10 2 2.411876335951806e+00 2.411876336026708e+00 7.49023e-11 2.01732e-10 3 1.015998156575399e+00 1.015998156607214e+00 3.18148e-11 1.04118e-09 ----------------------------------------------------------------------------------------------------- 21 Ni 1 -2.435993550727830e+00 -2.435993550800373e+00 7.25429e-11 2.07637e-10 2 -3.106191805924974e-01 -3.106191806091024e-01 1.66050e-11 1.12793e-09 3 1.397138420848544e+00 1.397138420714453e+00 1.34091e-10 3.47415e-10 ----------------------------------------------------------------------------------------------------- 22 Ni 1 1.470300807317798e+00 1.470300807315788e+00 2.00973e-12 2.54855e-10 2 4.948119856757850e+00 4.948119856734410e+00 2.34399e-11 8.29945e-10 3 4.424834126664599e+00 4.424834126592442e+00 7.21574e-11 6.79291e-10 ----------------------------------------------------------------------------------------------------- 23 Ni 1 -5.525458888191630e-01 -5.525458888150525e-01 4.11049e-12 3.82172e-10 2 4.738985892562412e-01 4.738985892892082e-01 3.29670e-11 4.58056e-10 3 -4.762101144328375e-02 -4.762101147609547e-02 3.28117e-11 3.75459e-10 ----------------------------------------------------------------------------------------------------- 24 Ni 1 9.752743012710717e-01 9.752743012538372e-01 1.72345e-11 5.33564e-10 2 1.158350465293462e+00 1.158350465240690e+00 5.27716e-11 1.26250e-09 3 -8.267719569172075e-01 -8.267719568530533e-01 6.41542e-11 5.55542e-11 ----------------------------------------------------------------------------------------------------- 25 Ni 1 -1.344093198161076e-01 -1.344093198317718e-01 1.56642e-11 2.42080e-10 2 -1.651893225768151e+00 -1.651893225805473e+00 3.73215e-11 2.14568e-10 3 1.125352720039755e+00 1.125352719977010e+00 6.27451e-11 2.89539e-10 ----------------------------------------------------------------------------------------------------- 26 Ni 1 -1.302047849019178e+00 -1.302047849063952e+00 4.47742e-11 9.22955e-11 2 1.605003773795316e+00 1.605003773821567e+00 2.62506e-11 4.43614e-10 3 -1.896365037555573e+00 -1.896365037483937e+00 7.16358e-11 1.10010e-09 ----------------------------------------------------------------------------------------------------- 27 Ni 1 2.330374652883984e+00 2.330374652855006e+00 2.89773e-11 2.45430e-10 2 -5.967359800815621e+00 -5.967359800825776e+00 1.01554e-11 4.37982e-10 3 5.690007857772326e-01 5.690007860311594e-01 2.53927e-10 3.07964e-10 ----------------------------------------------------------------------------------------------------- 28 Ni 1 -3.187472743809188e+00 -3.187472743807554e+00 1.63425e-12 2.48833e-10 2 2.970781129952927e+00 2.970781129910849e+00 4.20779e-11 2.91188e-10 3 -4.202819238070166e-01 -4.202819240107434e-01 2.03727e-10 4.14934e-10 ----------------------------------------------------------------------------------------------------- 29 Ni 1 -2.300196710689554e+00 -2.300196711026516e+00 3.36962e-10 4.96109e-10 2 -2.291624052257316e+00 -2.291624052640682e+00 3.83366e-10 4.81120e-10 3 1.502874008405511e+00 1.502874008365865e+00 3.96454e-11 6.67831e-10 ----------------------------------------------------------------------------------------------------- 30 Ni 1 1.188316871460285e+00 1.188316871461097e+00 8.12239e-13 8.55927e-10 2 2.127418993614005e+00 2.127418993633801e+00 1.97962e-11 5.83441e-09 * 3 1.393443666906678e+00 1.393443666874098e+00 3.25799e-11 6.05507e-10 ----------------------------------------------------------------------------------------------------- 31 Ni 1 1.048810764446384e+00 1.048810764439006e+00 7.37788e-12 3.72720e-10 2 -1.482349570232479e+00 -1.482349570119710e+00 1.12769e-10 3.25504e-10 3 3.634475075113167e-01 3.634475076003452e-01 8.90285e-11 5.28579e-10 ----------------------------------------------------------------------------------------------------- 32 Ni 1 1.354038997112317e+00 1.354038997164655e+00 5.23379e-11 2.83318e-10 2 1.400849745953880e+00 1.400849745903031e+00 5.08491e-11 1.33224e-09 3 9.058402572429126e-01 9.058402571423358e-01 1.00577e-10 8.73598e-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 = 23, direction = 3: |F_model - F_numer| error = ----------------------- = 6.89018e-10 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 6.89018e-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 6.89018e-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.