!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_Vashishta_BroughtonMeliVashishta_1997_SiO__SM_422553794879_000 Supported species : O Si 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 = 8.375 | (Configuration in file "config-O.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 O 1 -5.710258811565033e-01 -5.710258811564030e-01 1.00364e-13 2.55906e-13 2 -5.768893240718410e-01 -5.768893240723798e-01 5.38791e-13 2.92200e-12 3 -6.869394371453241e-01 -6.869394371442686e-01 1.05549e-12 1.09779e-12 ----------------------------------------------------------------------------------------------------- 2 O 1 -2.781137375284255e-01 -2.781137375280979e-01 3.27627e-13 3.50675e-12 2 2.365502227360254e-01 2.365502227363685e-01 3.43142e-13 4.36645e-12 3 -8.981641467547409e-01 -8.981641467541490e-01 5.91860e-13 1.06448e-12 ----------------------------------------------------------------------------------------------------- 3 O 1 -7.599744517651666e-02 -7.599744517676893e-02 2.52270e-13 1.86193e-11 * 2 -7.610296700356642e-01 -7.610296700356003e-01 6.39488e-14 1.48170e-12 3 3.190900650945303e-01 3.190900650937651e-01 7.65166e-13 6.02890e-12 ----------------------------------------------------------------------------------------------------- 4 O 1 -7.475616068584777e-01 -7.475616068587400e-01 2.62235e-13 5.29621e-12 2 2.605054068693969e-01 2.605054068703138e-01 9.16878e-13 1.20568e-10 * 3 1.572702323554371e-01 1.572702323560758e-01 6.38684e-13 3.13685e-12 ----------------------------------------------------------------------------------------------------- 5 O 1 4.218878946905025e-01 4.218878946907738e-01 2.71339e-13 2.41740e-12 2 -9.250968170451074e-01 -9.250968170451839e-01 7.64944e-14 1.74305e-12 3 -6.918437811164974e-01 -6.918437811171737e-01 6.76348e-13 1.61082e-12 ----------------------------------------------------------------------------------------------------- 6 O 1 5.932503769973595e-01 5.932503769972396e-01 1.19904e-13 7.60836e-13 2 7.810632897515760e-02 7.810632897472364e-02 4.33958e-13 1.24754e-12 3 -7.498909061752511e-01 -7.498909061758996e-01 6.48481e-13 1.20948e-12 ----------------------------------------------------------------------------------------------------- 7 O 1 7.580445845087058e-01 7.580445845086220e-01 8.38218e-14 6.39255e-12 2 -1.231476415163608e+00 -1.231476415163805e+00 1.97398e-13 9.71889e-13 3 -5.587273168008607e-01 -5.587273168019411e-01 1.08036e-12 2.83196e-12 ----------------------------------------------------------------------------------------------------- 8 O 1 -3.132459126341870e-01 -3.132459126338344e-01 3.52607e-13 8.92897e-13 2 -3.255543752617723e-01 -3.255543752620446e-01 2.72227e-13 1.50446e-12 3 -1.037377283587675e-01 -1.037377283593630e-01 5.95524e-13 3.71828e-12 ----------------------------------------------------------------------------------------------------- 9 O 1 -8.117688285509806e-01 -8.117688285508509e-01 1.29785e-13 1.30164e-11 2 -4.566382507055327e-01 -4.566382507063351e-01 8.02414e-13 2.24021e-12 3 -1.142971296382372e+00 -1.142971296382403e+00 3.15303e-14 1.25833e-12 ----------------------------------------------------------------------------------------------------- 10 O 1 -3.499059158386419e-02 -3.499059158462365e-02 7.59455e-13 2.39603e-12 2 1.153777707065436e+00 1.153777707065484e+00 4.81837e-14 5.85265e-12 3 -9.978750892479552e-01 -9.978750892473941e-01 5.61107e-13 2.41906e-12 ----------------------------------------------------------------------------------------------------- 11 O 1 -4.383522201942051e-01 -4.383522201949966e-01 7.91534e-13 7.55046e-12 2 -3.834956840252486e-01 -3.834956840251181e-01 1.30507e-13 5.25913e-13 3 4.368007525528584e-01 4.368007525538463e-01 9.87876e-13 1.08050e-11 ----------------------------------------------------------------------------------------------------- 12 O 1 -7.976812897629633e-01 -7.976812897630451e-01 8.18234e-14 1.34348e-12 2 9.039185049019625e-01 9.039185049020387e-01 7.62723e-14 5.51836e-12 3 4.650468020753009e-01 4.650468020790787e-01 3.77787e-12 4.57229e-12 ----------------------------------------------------------------------------------------------------- 13 O 1 3.370790849338391e-02 3.370790849535295e-02 1.96904e-12 1.09309e-11 2 -3.412546468071537e-01 -3.412546468100831e-01 2.92938e-12 2.32026e-12 3 -1.689397024653265e+00 -1.689397024653670e+00 4.05231e-13 2.72382e-12 ----------------------------------------------------------------------------------------------------- 14 O 1 5.659744738374033e-01 5.659744738380411e-01 6.37823e-13 4.11471e-12 2 7.101740280000564e-01 7.101740280000874e-01 3.10862e-14 3.57492e-13 3 -6.437033670038135e-01 -6.437033670056783e-01 1.86484e-12 6.80556e-12 ----------------------------------------------------------------------------------------------------- 15 O 1 1.514658149620649e+00 1.514658149620524e+00 1.24567e-13 3.02558e-12 2 -2.814430461617933e-01 -2.814430461608687e-01 9.24538e-13 4.94765e-12 3 2.320240382135404e-01 2.320240382123478e-01 1.19257e-12 1.56794e-12 ----------------------------------------------------------------------------------------------------- 16 O 1 2.064314645051924e-01 2.064314645044181e-01 7.74270e-13 4.10549e-12 2 1.405834392856025e+00 1.405834392856196e+00 1.70308e-13 7.87281e-12 3 2.689957027829060e-01 2.689957027831689e-01 2.62845e-13 3.49093e-12 ----------------------------------------------------------------------------------------------------- 17 O 1 -8.902715855607671e-01 -8.902715855605420e-01 2.25153e-13 5.98965e-13 2 -6.568816790340314e-01 -6.568816790339863e-01 4.50751e-14 4.04354e-12 3 -2.900664400227340e-01 -2.900664400236672e-01 9.33253e-13 8.65918e-13 ----------------------------------------------------------------------------------------------------- 18 O 1 9.612164930148133e-02 9.612164930149636e-02 1.50296e-14 1.85155e-11 * 2 1.855394014000034e-01 1.855394014020660e-01 2.06266e-12 1.10051e-11 3 -2.938439246693112e-01 -2.938439246771636e-01 7.85239e-12 7.21080e-11 * ----------------------------------------------------------------------------------------------------- 19 O 1 3.473703055928343e-01 3.473703055937792e-01 9.44911e-13 1.20398e-12 2 -9.742959057248398e-01 -9.742959057245947e-01 2.45137e-13 4.65405e-12 3 8.267132037672699e-01 8.267132037691662e-01 1.89637e-12 2.97162e-12 ----------------------------------------------------------------------------------------------------- 20 O 1 -7.968041528144091e-01 -7.968041528148729e-01 4.63851e-13 1.39353e-11 2 2.640649608325380e-01 2.640649608331388e-01 6.00797e-13 5.73608e-12 3 7.337546408905682e-01 7.337546408895619e-01 1.00631e-12 9.45621e-12 ----------------------------------------------------------------------------------------------------- 21 O 1 -3.358238171798821e-01 -3.358238171804029e-01 5.20806e-13 7.40352e-12 2 -8.743730316405790e-01 -8.743730316407581e-01 1.79079e-13 1.69356e-11 3 2.529057197634219e-01 2.529057197635033e-01 8.14349e-14 6.96343e-12 ----------------------------------------------------------------------------------------------------- 22 O 1 1.031027038142879e+00 1.031027038142342e+00 5.36682e-13 6.54787e-12 2 5.290052057384885e-01 5.290052057366801e-01 1.80844e-12 3.30214e-12 3 5.419082081164935e-01 5.419082081168410e-01 3.47500e-13 6.09179e-12 ----------------------------------------------------------------------------------------------------- 23 O 1 4.595991556985733e-01 4.595991556987381e-01 1.64757e-13 5.52258e-12 2 -3.792146451747841e-01 -3.792146451746610e-01 1.23124e-13 4.13747e-12 3 5.897125876721402e-01 5.897125876720313e-01 1.08913e-13 2.19902e-12 ----------------------------------------------------------------------------------------------------- 24 O 1 1.423624076764870e-01 1.423624076767832e-01 2.96152e-13 4.81026e-12 2 -4.835014715032729e-02 -4.835014714962302e-02 7.04270e-13 8.22431e-12 3 8.056780397500226e-01 8.056780397498964e-01 1.26232e-13 2.89491e-12 ----------------------------------------------------------------------------------------------------- 25 O 1 -1.006238399449840e+00 -1.006238399449480e+00 3.59712e-13 6.25211e-12 2 -1.956107045006677e-01 -1.956107045000200e-01 6.47649e-13 1.72251e-12 3 -3.518784864821758e-01 -3.518784864803277e-01 1.84808e-12 9.16556e-12 ----------------------------------------------------------------------------------------------------- 26 O 1 -2.389993455285898e-01 -2.389993455281085e-01 4.81254e-13 2.68488e-12 2 1.109039304269395e+00 1.109039304269408e+00 1.31006e-14 1.16560e-11 3 -2.380664494024388e-01 -2.380664494019568e-01 4.81976e-13 8.62080e-12 ----------------------------------------------------------------------------------------------------- 27 O 1 2.863089526263946e-01 2.863089526265143e-01 1.19738e-13 4.95815e-12 2 -6.624444684861186e-01 -6.624444684859633e-01 1.55320e-13 4.43034e-12 3 1.046343581180061e+00 1.046343581180396e+00 3.35953e-13 2.74647e-12 ----------------------------------------------------------------------------------------------------- 28 O 1 -9.369977596137268e-01 -9.369977596150985e-01 1.37168e-12 7.36089e-12 2 9.587914424648121e-01 9.587914424669167e-01 2.10465e-12 4.42613e-12 3 5.984933133536879e-01 5.984933133535668e-01 1.21125e-13 2.24842e-12 ----------------------------------------------------------------------------------------------------- 29 O 1 -1.503455893727776e-01 -1.503455893721698e-01 6.07875e-13 4.54919e-12 2 -2.400726431396906e-01 -2.400726431387656e-01 9.25010e-13 3.56185e-12 3 2.347018368838729e-01 2.347018368844349e-01 5.62050e-13 4.59682e-12 ----------------------------------------------------------------------------------------------------- 30 O 1 7.421214952823907e-01 7.421214952829830e-01 5.92304e-13 3.54727e-12 2 8.124379447365293e-01 8.124379447374555e-01 9.26148e-13 1.09857e-12 3 1.489036204610377e-01 1.489036204616936e-01 6.55975e-13 2.46272e-12 ----------------------------------------------------------------------------------------------------- 31 O 1 9.046026320469642e-01 9.046026320475428e-01 5.78537e-13 3.60167e-12 2 -1.603071012410093e-01 -1.603071012421840e-01 1.17475e-12 9.68781e-13 3 8.180148974860173e-01 8.180148974859147e-01 1.02585e-13 2.47424e-12 ----------------------------------------------------------------------------------------------------- 32 O 1 3.207496739449149e-01 3.207496739452126e-01 2.97706e-13 3.51824e-12 2 8.666837045239415e-01 8.666837045246892e-01 7.47735e-13 6.23479e-12 3 8.607481518163411e-01 8.607481518167480e-01 4.06897e-13 5.79781e-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 dicontinuities. Maximum error obtained for particle = 13, direction = 1: |F_model - F_numer| error = ----------------------- = 5.84149e-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 = Si | a0 = 8.375 | (Configuration in file "config-Si.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Si 1 -1.250654328512916e+00 -1.250654328512944e+00 2.79776e-14 2.35949e-11 2 -1.619666111375157e+00 -1.619666111376991e+00 1.83453e-12 4.39360e-12 3 -1.418214798626262e+00 -1.418214798624423e+00 1.83897e-12 5.37259e-12 ----------------------------------------------------------------------------------------------------- 2 Si 1 -4.594218728514100e-01 -4.594218728501093e-01 1.30068e-12 1.01198e-11 2 -2.879533737455499e-01 -2.879533737453452e-01 2.04670e-13 8.07926e-12 3 -2.501454392919850e+00 -2.501454392921235e+00 1.38467e-12 4.24967e-11 * ----------------------------------------------------------------------------------------------------- 3 Si 1 -3.737410493152997e-01 -3.737410493150073e-01 2.92377e-13 5.25496e-12 2 -2.485267295165518e+00 -2.485267295164812e+00 7.06102e-13 1.11808e-11 3 1.171161191636422e-03 1.171161190384023e-03 1.25240e-12 1.04450e-12 ----------------------------------------------------------------------------------------------------- 4 Si 1 -2.089206795639925e+00 -2.089206795641200e+00 1.27498e-12 2.72182e-12 2 9.607320974780409e-02 9.607320974689383e-02 9.10258e-13 3.54698e-12 3 4.140790504000891e-01 4.140790504007395e-01 6.50424e-13 1.06511e-11 ----------------------------------------------------------------------------------------------------- 5 Si 1 4.008130079668101e-01 4.008130079661437e-01 6.66411e-13 5.39685e-12 2 -1.710747754916558e+00 -1.710747754916258e+00 3.00648e-13 1.66978e-12 3 -1.743671928147846e+00 -1.743671928147105e+00 7.40741e-13 8.05733e-12 ----------------------------------------------------------------------------------------------------- 6 Si 1 1.844707336143382e+00 1.844707336143732e+00 3.49276e-13 4.92539e-12 2 -1.680573879453048e-01 -1.680573879401010e-01 5.20387e-12 9.31058e-12 3 -1.468438037334743e+00 -1.468438037334088e+00 6.54143e-13 9.39471e-13 ----------------------------------------------------------------------------------------------------- 7 Si 1 1.484441771778436e+00 1.484441771778976e+00 5.40235e-13 4.20775e-13 2 -1.458513004816325e+00 -1.458513004817514e+00 1.18883e-12 5.16365e-12 3 -2.084074771718688e-01 -2.084074771734600e-01 1.59125e-12 5.52286e-12 ----------------------------------------------------------------------------------------------------- 8 Si 1 8.732148324497994e-01 8.732148324482666e-01 1.53277e-12 5.67135e-12 2 -4.851947725394443e-01 -4.851947725412575e-01 1.81327e-12 3.73956e-12 3 3.963234313113968e-02 3.963234313196216e-02 8.22474e-13 9.28571e-12 ----------------------------------------------------------------------------------------------------- 9 Si 1 -1.584372232911738e+00 -1.584372232911847e+00 1.09690e-13 8.68194e-12 2 2.951526197423666e-01 2.951526197394806e-01 2.88602e-12 3.42282e-12 3 -1.762647495746535e+00 -1.762647495747207e+00 6.72573e-13 6.66378e-12 ----------------------------------------------------------------------------------------------------- 10 Si 1 -1.939143308355867e-01 -1.939143308361545e-01 5.67879e-13 1.98952e-12 2 1.556930092780108e+00 1.556930092782155e+00 2.04681e-12 2.31415e-12 3 -1.524115392353730e+00 -1.524115392353958e+00 2.28262e-13 7.88924e-13 ----------------------------------------------------------------------------------------------------- 11 Si 1 -7.383416055902506e-01 -7.383416055913572e-01 1.10656e-12 1.13152e-11 2 5.889517002369328e-01 5.889517002416341e-01 4.70135e-12 1.53932e-11 3 -4.778925765479450e-02 -4.778925765483780e-02 4.32987e-14 4.53784e-12 ----------------------------------------------------------------------------------------------------- 12 Si 1 -1.726455456787961e+00 -1.726455456787125e+00 8.35776e-13 8.50187e-12 2 1.654074384178676e+00 1.654074384175232e+00 3.44391e-12 6.02074e-12 3 -3.659193590661130e-01 -3.659193590684471e-01 2.33413e-12 2.88586e-12 ----------------------------------------------------------------------------------------------------- 13 Si 1 5.332982408855665e-01 5.332982408878657e-01 2.29916e-12 5.78759e-12 2 4.176745494277206e-01 4.176745494302394e-01 2.51876e-12 9.56901e-12 3 -2.553873801200208e+00 -2.553873801200915e+00 7.06546e-13 6.18172e-12 ----------------------------------------------------------------------------------------------------- 14 Si 1 1.294244607797650e+00 1.294244607796269e+00 1.38090e-12 4.42379e-12 2 1.073075923981574e+00 1.073075923979816e+00 1.75726e-12 3.21121e-12 3 -1.396991925664883e+00 -1.396991925667670e+00 2.78710e-12 3.44769e-12 ----------------------------------------------------------------------------------------------------- 15 Si 1 2.296183605240200e+00 2.296183605240725e+00 5.24913e-13 6.04539e-12 2 -2.695905262238513e-01 -2.695905262268543e-01 3.00304e-12 6.08502e-12 3 -2.620191588535045e-01 -2.620191588542667e-01 7.62168e-13 1.74996e-11 ----------------------------------------------------------------------------------------------------- 16 Si 1 -1.229655619387751e-01 -1.229655619384273e-01 3.47805e-13 2.99462e-12 2 2.614781914657131e+00 2.614781914656367e+00 7.63833e-13 7.26086e-13 3 -1.919191354065690e-01 -1.919191354092133e-01 2.64430e-12 1.03762e-11 ----------------------------------------------------------------------------------------------------- 17 Si 1 -1.669676795503271e+00 -1.669676795501045e+00 2.22533e-12 4.97979e-12 2 -1.435148575015417e+00 -1.435148575012706e+00 2.71161e-12 1.83187e-11 3 5.075209693882216e-03 5.075209693922745e-03 4.05292e-14 4.43452e-12 ----------------------------------------------------------------------------------------------------- 18 Si 1 -5.892339021044113e-01 -5.892339021034031e-01 1.00819e-12 4.68906e-11 * 2 -2.256524728185329e-01 -2.256524728175537e-01 9.79217e-13 8.68247e-11 * 3 1.204888069276758e-01 1.204888069255508e-01 2.12493e-12 2.01041e-11 ----------------------------------------------------------------------------------------------------- 19 Si 1 1.653038242367768e-01 1.653038242371413e-01 3.64486e-13 9.22379e-12 2 -1.898426885575537e+00 -1.898426885575871e+00 3.34177e-13 2.62612e-12 3 1.713792248741958e+00 1.713792248742958e+00 1.00009e-12 8.59579e-12 ----------------------------------------------------------------------------------------------------- 20 Si 1 -1.787337295425258e+00 -1.787337295425852e+00 5.93969e-13 3.38618e-12 2 4.643337703946865e-02 4.643337703797075e-02 1.49790e-12 8.98354e-12 3 1.662403250215186e+00 1.662403250214001e+00 1.18439e-12 6.61693e-12 ----------------------------------------------------------------------------------------------------- 21 Si 1 3.547241235550770e-01 3.547241235546488e-01 4.28158e-13 1.53483e-12 2 -2.046440222150319e+00 -2.046440222148448e+00 1.87095e-12 4.71903e-11 * 3 4.785545186504683e-01 4.785545186509679e-01 4.99656e-13 1.44195e-11 ----------------------------------------------------------------------------------------------------- 22 Si 1 2.331154132852844e+00 2.331154132852576e+00 2.67786e-13 4.32943e-12 2 -4.419047463550567e-01 -4.419047463497666e-01 5.29005e-12 2.20868e-12 3 -1.380215441567236e-01 -1.380215441548302e-01 1.89343e-12 6.46877e-12 ----------------------------------------------------------------------------------------------------- 23 Si 1 9.915896006697726e-01 9.915896006674669e-01 2.30571e-12 5.17875e-12 2 -1.119331366194189e+00 -1.119331366193266e+00 9.22151e-13 8.08109e-12 3 1.001097856077048e+00 1.001097856075703e+00 1.34515e-12 2.70206e-12 ----------------------------------------------------------------------------------------------------- 24 Si 1 2.639802360954671e-01 2.639802360956662e-01 1.99118e-13 1.37401e-11 2 -9.680802464272119e-01 -9.680802464277217e-01 5.09814e-13 3.00193e-12 3 2.215573486522714e+00 2.215573486522276e+00 4.37872e-13 2.05658e-12 ----------------------------------------------------------------------------------------------------- 25 Si 1 -2.296399601293647e+00 -2.296399601293831e+00 1.83853e-13 1.17883e-11 2 -3.185824960714741e-02 -3.185824960904899e-02 1.90158e-12 4.83080e-12 3 3.755260739763773e-01 3.755260739791380e-01 2.76063e-12 9.85229e-12 ----------------------------------------------------------------------------------------------------- 26 Si 1 -1.430714226612964e-01 -1.430714226617919e-01 4.95520e-13 4.88676e-12 2 2.175572907663228e+00 2.175572907662028e+00 1.20037e-12 1.03291e-11 3 3.116791555101913e-01 3.116791555106497e-01 4.58411e-13 4.93727e-12 ----------------------------------------------------------------------------------------------------- 27 Si 1 -6.890957027564063e-01 -6.890957027546183e-01 1.78801e-12 4.60931e-12 2 4.882432433293772e-01 4.882432433316471e-01 2.26991e-12 9.96747e-12 3 2.086907259498706e+00 2.086907259500284e+00 1.57785e-12 2.13518e-12 ----------------------------------------------------------------------------------------------------- 28 Si 1 -9.434921253087771e-01 -9.434921253115430e-01 2.76590e-12 9.13136e-12 2 1.079885598777006e+00 1.079885598776996e+00 1.06581e-14 3.13420e-11 * 3 1.043529917924208e+00 1.043529917924076e+00 1.31894e-13 9.17177e-12 ----------------------------------------------------------------------------------------------------- 29 Si 1 1.085846396060785e-01 1.085846396075305e-01 1.45206e-12 3.79066e-12 2 4.057306903671407e-01 4.057306903709739e-01 3.83316e-12 7.90334e-12 3 2.471799371089989e-02 2.471799371085243e-02 4.74586e-14 1.27931e-11 ----------------------------------------------------------------------------------------------------- 30 Si 1 1.764779384315470e+00 1.764779384314820e+00 6.50591e-13 1.41163e-11 2 1.776950256345168e+00 1.776950256344068e+00 1.09979e-12 9.57812e-12 3 5.209375885674323e-01 5.209375885650862e-01 2.34612e-12 9.75398e-12 ----------------------------------------------------------------------------------------------------- 31 Si 1 1.823647458117835e+00 1.823647458118206e+00 3.71259e-13 9.02212e-12 2 4.064753567914794e-01 4.064753567925532e-01 1.07375e-12 4.52388e-12 3 1.983015343007600e+00 1.983015343007869e+00 2.68896e-13 8.91620e-12 ----------------------------------------------------------------------------------------------------- 32 Si 1 1.267132777257612e-01 1.267132777252012e-01 5.60024e-13 6.56966e-12 2 1.975827165805938e+00 1.975827165807367e+00 1.42975e-12 8.22165e-12 3 1.585302440556418e+00 1.585302440556479e+00 6.03961e-14 2.86726e-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 dicontinuities. Maximum error obtained for particle = 3, direction = 3: |F_model - F_numer| error = ----------------------- = 1.06937e-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 = O Si | a0 = 8.375 | (Configuration in file "config-OSi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 O 1 3.806449357420432e-01 3.806449357420916e-01 4.84057e-14 4.39870e-13 2 1.005585536046430e-01 1.005585536046794e-01 3.64292e-14 3.45390e-13 3 1.643244352591238e-01 1.643244352591737e-01 4.99045e-14 5.01654e-13 ----------------------------------------------------------------------------------------------------- 2 Si 1 -2.056533768759338e-01 -2.056533768757573e-01 1.76525e-13 6.66328e-13 2 -3.279680819900416e-02 -3.279680819854482e-02 4.59341e-13 2.22786e-12 3 -6.405827239192401e-01 -6.405827239192270e-01 1.31006e-14 8.79408e-13 ----------------------------------------------------------------------------------------------------- 3 Si 1 1.976123140606777e-01 1.976123140607818e-01 1.04111e-13 2.37524e-12 2 -2.145713276136398e-01 -2.145713276130591e-01 5.80702e-13 2.59973e-12 3 4.312412444311711e-01 4.312412444312654e-01 9.43134e-14 8.43214e-14 ----------------------------------------------------------------------------------------------------- 4 O 1 -6.914907535998056e-01 -6.914907535992559e-01 5.49671e-13 2.90749e-11 * 2 -2.561212001856528e-01 -2.561212001856458e-01 6.99441e-15 1.02018e-12 3 -9.456348373571996e-01 -9.456348373570990e-01 1.00586e-13 7.49178e-13 ----------------------------------------------------------------------------------------------------- 5 O 1 -7.097382716851096e-01 -7.097382716851534e-01 4.37428e-14 4.29989e-13 2 2.809023730735901e-01 2.809023730736476e-01 5.75651e-14 2.94559e-12 3 1.057617667798667e+00 1.057617667798741e+00 7.48290e-14 1.33915e-12 ----------------------------------------------------------------------------------------------------- 6 O 1 2.595852644397609e-01 2.595852644397310e-01 2.98650e-14 5.27300e-13 2 2.160281952099705e-02 2.160281952097089e-02 2.61562e-14 7.85063e-13 3 8.971100025150572e-01 8.971100025150545e-01 2.77556e-15 2.83373e-12 ----------------------------------------------------------------------------------------------------- 7 Si 1 2.858636739600632e-01 2.858636739600660e-01 2.83107e-15 3.83082e-13 2 -7.801770654471006e-01 -7.801770654470387e-01 6.19504e-14 7.75380e-13 3 -1.050505936061534e+00 -1.050505936061451e+00 8.37108e-14 1.13087e-12 ----------------------------------------------------------------------------------------------------- 8 Si 1 -8.099584250940761e-01 -8.099584250941888e-01 1.12688e-13 1.23743e-11 * 2 -1.014325575488451e-01 -1.014325575486308e-01 2.14329e-13 1.12549e-12 3 -7.894988586483851e-01 -7.894988586482857e-01 9.93650e-14 1.95510e-13 ----------------------------------------------------------------------------------------------------- 9 Si 1 -3.860256452605410e-01 -3.860256452605226e-01 1.83742e-14 1.37679e-12 2 -1.363969746347329e-01 -1.363969746346232e-01 1.09718e-13 5.01401e-11 * 3 7.902450956892489e-01 7.902450956890436e-01 2.05391e-13 1.86029e-12 ----------------------------------------------------------------------------------------------------- 10 Si 1 9.909364503861448e-01 9.909364503862143e-01 6.95000e-14 9.13158e-13 2 3.108517343578301e-02 3.108517343579017e-02 7.15747e-15 5.14217e-13 3 8.970339028942662e-01 8.970339028944309e-01 1.64646e-13 2.78033e-12 ----------------------------------------------------------------------------------------------------- 11 O 1 5.314392089502418e-01 5.314392089503462e-01 1.04472e-13 2.29960e-12 2 -6.540684726122683e-01 -6.540684726122664e-01 1.88738e-15 6.71130e-13 3 -9.423927261474258e-02 -9.423927261445754e-02 2.85036e-13 1.43192e-12 ----------------------------------------------------------------------------------------------------- 12 O 1 -3.548642555538452e-01 -3.548642555538395e-01 5.60663e-15 3.62099e-13 2 2.557754400684240e-01 2.557754400683975e-01 2.64788e-14 1.19627e-13 3 -9.351474473495709e-02 -9.351474473513222e-02 1.75124e-13 1.94471e-12 ----------------------------------------------------------------------------------------------------- 13 O 1 -7.019519326087472e-01 -7.019519326089320e-01 1.84741e-13 5.62772e-13 2 -6.754835178332228e-01 -6.754835178331782e-01 4.46310e-14 2.23210e-12 3 3.248615763551524e-01 3.248615763552337e-01 8.12683e-14 6.55087e-13 ----------------------------------------------------------------------------------------------------- 14 O 1 4.486320066474200e-01 4.486320066474879e-01 6.79456e-14 8.93396e-13 2 2.974607121205732e-01 2.974607121206029e-01 2.96985e-14 2.41640e-13 3 2.059614378651536e-01 2.059614378648931e-01 2.60514e-13 2.89796e-13 ----------------------------------------------------------------------------------------------------- 15 Si 1 5.906480576675674e-01 5.906480576679898e-01 4.22329e-13 1.55742e-12 2 5.590986929956487e-01 5.590986929952786e-01 3.70148e-13 1.40876e-12 3 -2.378169757367760e+00 -2.378169757368273e+00 5.12479e-13 6.83897e-13 ----------------------------------------------------------------------------------------------------- 16 O 1 2.061059279461382e-01 2.061059279463762e-01 2.37976e-13 1.84416e-12 2 -2.585703178478327e-02 -2.585703178491674e-02 1.33473e-13 1.68924e-12 3 1.065214437308832e+00 1.065214437308920e+00 8.85958e-14 1.20881e-12 ----------------------------------------------------------------------------------------------------- 17 Si 1 3.584269808877804e-01 3.584269808876944e-01 8.59868e-14 9.35640e-13 2 3.328788751752148e-01 3.328788751752615e-01 4.67404e-14 7.44238e-13 3 1.560771697043427e-01 1.560771697044173e-01 7.46347e-14 4.92217e-13 ----------------------------------------------------------------------------------------------------- 18 O 1 7.137291500295402e-01 7.137291500296711e-01 1.30895e-13 3.33622e-13 2 -3.939164062390842e-01 -3.939164062389550e-01 1.29230e-13 1.82315e-12 3 5.592911434317855e-01 5.592911434321044e-01 3.18856e-13 4.28879e-13 ----------------------------------------------------------------------------------------------------- 19 O 1 -1.156348513264852e+00 -1.156348513264876e+00 2.37588e-14 5.90639e-13 2 -3.631363857001609e-01 -3.631363857001025e-01 5.83977e-14 2.00306e-12 3 6.380873853655286e-02 6.380873853660964e-02 5.67740e-14 6.68923e-13 ----------------------------------------------------------------------------------------------------- 20 Si 1 7.097790724245676e-01 7.097790724244238e-01 1.43774e-13 1.17173e-12 2 2.200631226133706e-01 2.200631226134911e-01 1.20515e-13 5.26135e-13 3 4.121453550679574e-01 4.121453550681285e-01 1.71085e-13 1.15202e-12 ----------------------------------------------------------------------------------------------------- 21 O 1 3.099036005197930e-02 3.099036005202092e-02 4.16230e-14 7.73246e-13 2 2.998064292250432e-01 2.998064292250056e-01 3.75810e-14 8.37497e-13 3 -1.719393472728088e+00 -1.719393472728206e+00 1.17906e-13 1.71574e-12 ----------------------------------------------------------------------------------------------------- 22 Si 1 1.748134463773876e-01 1.748134463774477e-01 6.00908e-14 1.26044e-12 2 -1.694294565715231e+00 -1.694294565715251e+00 2.04281e-14 4.25437e-13 3 1.788509731744120e+00 1.788509731743892e+00 2.27818e-13 2.56994e-12 ----------------------------------------------------------------------------------------------------- 23 O 1 4.477857388953130e-01 4.477857388952718e-01 4.12448e-14 8.73801e-13 2 2.100706505726342e-01 2.100706505726221e-01 1.21292e-14 4.55580e-13 3 -2.725862265633422e-01 -2.725862265634074e-01 6.51701e-14 1.17517e-13 ----------------------------------------------------------------------------------------------------- 24 O 1 8.403557197214847e-01 8.403557197211924e-01 2.92322e-13 1.31917e-12 2 9.934446497940523e-01 9.934446497940300e-01 2.23155e-14 1.01130e-12 3 -3.489251123038182e-01 -3.489251123035691e-01 2.49079e-13 8.43547e-13 ----------------------------------------------------------------------------------------------------- 25 Si 1 4.082503603369368e-02 4.082503603372867e-02 3.49928e-14 4.62415e-13 2 -2.933403643641808e-02 -2.933403643658099e-02 1.62915e-13 1.84061e-11 * 3 -3.964167176424850e-01 -3.964167176425121e-01 2.70894e-14 8.74079e-13 ----------------------------------------------------------------------------------------------------- 26 Si 1 -1.306828224674087e+00 -1.306828224674097e+00 9.99201e-15 1.36913e-12 2 4.671811091351846e-01 4.671811091353014e-01 1.16795e-13 1.11999e-12 3 -9.190701635334243e-01 -9.190701635331509e-01 2.73448e-13 2.15283e-12 ----------------------------------------------------------------------------------------------------- 27 O 1 -7.748736931050915e-02 -7.748736931041882e-02 9.03305e-14 7.25045e-13 2 5.752788155939744e-01 5.752788155939915e-01 1.70974e-14 1.76792e-12 3 -6.379949424197833e-01 -6.379949424199635e-01 1.80189e-13 5.82090e-13 ----------------------------------------------------------------------------------------------------- 28 O 1 2.149265305098995e-01 2.149265305099695e-01 6.99718e-14 4.47947e-13 2 -1.729107093265321e-01 -1.729107093265027e-01 2.94209e-14 5.97078e-13 3 -6.335144495109266e-01 -6.335144495107951e-01 1.31561e-13 5.57332e-13 ----------------------------------------------------------------------------------------------------- 29 Si 1 -1.996559037393510e+00 -1.996559037393635e+00 1.25011e-13 1.40399e-12 2 -8.260297458957000e-01 -8.260297458957848e-01 8.48210e-14 1.22802e-12 3 -3.240637273485117e-01 -3.240637273485459e-01 3.41949e-14 1.72229e-12 ----------------------------------------------------------------------------------------------------- 30 Si 1 8.701268055975020e-01 8.701268055974103e-01 9.17044e-14 1.25535e-11 * 2 1.745697462733635e+00 1.745697462733804e+00 1.69198e-13 5.47340e-13 3 -5.920725853731524e-01 -5.920725853732564e-01 1.03917e-13 1.66533e-12 ----------------------------------------------------------------------------------------------------- 31 Si 1 5.530488898146095e-01 5.530488898145817e-01 2.78666e-14 4.98268e-13 2 -7.656061047863906e-01 -7.656061047865166e-01 1.26010e-13 1.48770e-13 3 1.453871322432226e+00 1.453871322432278e+00 5.24025e-14 2.85771e-13 ----------------------------------------------------------------------------------------------------- 32 Si 1 -4.493697648227983e-01 -4.493697648227988e-01 5.55112e-16 8.17291e-13 2 7.312280302959981e-01 7.312280302960271e-01 2.89768e-14 9.50240e-13 3 1.568870267093695e+00 1.568870267094027e+00 3.31957e-13 8.59424e-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 dicontinuities. Maximum error obtained for particle = 2, direction = 2: |F_model - F_numer| error = ----------------------- = 1.40057e-11 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 1.06937e-09 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 1.06937e-09 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.