!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 : Tersoff_LAMMPS_ErhartAlbe_2005SiII_SiC__MO_408791041969_004 Supported species : C 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 = C | a0 = 2.7390480041503906 | (Configuration in file "config-C.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 C 1 4.656004944765240e+00 4.656004944769281e+00 4.04121e-12 7.27773e-12 2 2.245485921321180e+00 2.245485921318213e+00 2.96652e-12 7.55089e-11 3 4.843987397185602e+00 4.843987397181822e+00 3.78009e-12 5.45155e-11 ----------------------------------------------------------------------------------------------------- 2 C 1 -3.240984812291678e+00 -3.240984812290050e+00 1.62803e-12 1.24817e-10 2 1.868060167107370e+00 1.868060167107693e+00 3.23075e-13 7.72487e-11 3 -4.898658544179180e-02 -4.898658543806751e-02 3.72428e-12 5.71139e-11 ----------------------------------------------------------------------------------------------------- 3 C 1 6.849838494466502e+00 6.849838494481614e+00 1.51124e-11 1.25411e-11 2 -6.267667714674847e+00 -6.267667714663820e+00 1.10267e-11 5.74882e-11 3 -7.231110654083937e+00 -7.231110654073159e+00 1.07780e-11 1.04349e-10 ----------------------------------------------------------------------------------------------------- 4 C 1 -3.683460472083469e+00 -3.683460472083439e+00 3.01981e-14 1.25810e-11 2 1.210404907304017e+01 1.210404907305509e+01 1.49196e-11 4.28138e-11 3 -6.047482337619417e+00 -6.047482337626853e+00 7.43583e-12 3.20322e-11 ----------------------------------------------------------------------------------------------------- 5 C 1 -1.925286484887362e+00 -1.925286484888309e+00 9.47020e-13 1.90181e-11 2 1.834328138772020e+00 1.834328138763194e+00 8.82538e-12 2.85731e-11 3 2.293878323168900e+00 2.293878323169285e+00 3.85025e-13 9.09086e-11 ----------------------------------------------------------------------------------------------------- 6 C 1 -1.355828222078296e+00 -1.355828222072183e+00 6.11289e-12 2.08931e-11 2 -4.001382588039456e+00 -4.001382588035520e+00 3.93552e-12 1.36252e-10 3 1.306964931018395e+00 1.306964931023476e+00 5.08127e-12 2.06692e-11 ----------------------------------------------------------------------------------------------------- 7 C 1 -1.667098069537438e+00 -1.667098069532509e+00 4.92806e-12 2.47156e-11 2 -6.181506392895504e+00 -6.181506392897365e+00 1.86073e-12 4.21529e-11 3 -1.257192100141984e+01 -1.257192100141981e+01 3.37508e-14 1.04063e-10 ----------------------------------------------------------------------------------------------------- 8 C 1 -2.637829128386334e+00 -2.637829128380742e+00 5.59197e-12 5.26250e-11 2 2.631332197163546e+00 2.631332197173335e+00 9.78861e-12 4.17306e-11 3 6.333157814682888e+00 6.333157814664311e+00 1.85771e-11 4.22915e-11 ----------------------------------------------------------------------------------------------------- 9 C 1 -1.079354480439354e+00 -1.079354480444499e+00 5.14477e-12 4.94624e-11 2 -3.745731390933351e+00 -3.745731390939128e+00 5.77716e-12 2.10427e-11 3 3.046883312422037e+00 3.046883312419948e+00 2.08944e-12 2.16289e-11 ----------------------------------------------------------------------------------------------------- 10 C 1 -4.029410761140541e+00 -4.029410761143166e+00 2.62457e-12 2.13420e-11 2 8.804346810007485e-01 8.804346810004358e-01 3.12750e-13 2.92045e-11 3 -2.429547835823505e+00 -2.429547835822364e+00 1.14131e-12 1.36868e-12 ----------------------------------------------------------------------------------------------------- 11 C 1 -6.608884377862368e-01 -6.608884377935058e-01 7.26896e-12 7.74180e-11 2 -1.377065127701544e+01 -1.377065127699890e+01 1.65308e-11 1.21045e-10 3 -6.283995277341192e+00 -6.283995277341498e+00 3.06422e-13 1.86722e-11 ----------------------------------------------------------------------------------------------------- 12 C 1 -1.540049442890726e+00 -1.540049442887634e+00 3.09130e-12 5.07892e-11 2 1.772488490264889e+00 1.772488490266477e+00 1.58851e-12 8.87690e-12 3 -5.216682297190571e-01 -5.216682297182345e-01 8.22675e-13 3.60629e-11 ----------------------------------------------------------------------------------------------------- 13 C 1 -4.240427330196902e+00 -4.240427330197388e+00 4.85834e-13 4.41513e-12 2 -3.118823716369162e+00 -3.118823716365577e+00 3.58513e-12 4.08109e-11 3 -1.153084437032401e+01 -1.153084437032367e+01 3.48166e-13 1.02528e-10 ----------------------------------------------------------------------------------------------------- 14 C 1 2.708129400578022e+00 2.708129400573955e+00 4.06697e-12 3.85425e-11 2 2.873778376681213e-01 2.873778376650020e-01 3.11928e-12 4.51811e-12 3 -2.292413285601288e+00 -2.292413285606266e+00 4.97824e-12 4.40837e-10 * ----------------------------------------------------------------------------------------------------- 15 C 1 1.053410691836794e+01 1.053410691837083e+01 2.89369e-12 5.12390e-11 2 2.167899291248047e+00 2.167899291245075e+00 2.97184e-12 6.80402e-11 3 4.940953642373795e+00 4.940953642368641e+00 5.15410e-12 6.01742e-10 * ----------------------------------------------------------------------------------------------------- 16 C 1 -5.824188705066555e-01 -5.824188705027276e-01 3.92797e-12 6.45259e-11 2 7.358126409712392e+00 7.358126409713064e+00 6.72351e-13 3.98899e-11 3 4.216431050372625e+00 4.216431050369283e+00 3.34222e-12 1.47664e-10 ----------------------------------------------------------------------------------------------------- 17 C 1 -6.300009134354861e+00 -6.300009134357020e+00 2.15916e-12 1.57776e-11 2 -2.916541767976895e+00 -2.916541767978125e+00 1.22924e-12 9.93361e-11 3 -1.840539143841298e+00 -1.840539143845199e+00 3.90177e-12 1.14382e-11 ----------------------------------------------------------------------------------------------------- 18 C 1 2.499477896161983e+00 2.499477896166263e+00 4.27969e-12 1.28080e-10 2 7.084495241498399e+00 7.084495241493033e+00 5.36549e-12 1.36196e-10 3 -4.095641831394444e+00 -4.095641831391300e+00 3.14415e-12 4.45022e-11 ----------------------------------------------------------------------------------------------------- 19 C 1 1.014959298188866e+01 1.014959298189118e+01 2.51532e-12 8.65299e-11 2 -2.867380337243889e+00 -2.867380337241447e+00 2.44249e-12 1.36066e-10 3 3.205197049214308e+00 3.205197049211707e+00 2.60103e-12 3.04334e-12 ----------------------------------------------------------------------------------------------------- 20 C 1 -7.208306142101959e-01 -7.208306142104636e-01 2.67675e-13 7.45615e-12 2 9.032337972215777e-01 9.032337972188654e-01 2.71227e-12 7.15084e-12 3 1.138470390045089e+00 1.138470390044685e+00 4.04343e-13 9.83857e-12 ----------------------------------------------------------------------------------------------------- 21 C 1 -6.326196079661614e+00 -6.326196079660575e+00 1.03917e-12 2.09782e-10 2 -3.571465349841400e+00 -3.571465349845812e+00 4.41203e-12 1.18264e-10 3 6.759809582273682e+00 6.759809582269679e+00 4.00302e-12 4.38147e-11 ----------------------------------------------------------------------------------------------------- 22 C 1 3.419649484270082e+00 3.419649484267862e+00 2.22000e-12 2.39515e-11 2 4.422919124861607e+00 4.422919124860243e+00 1.36335e-12 1.75397e-11 3 9.307033357149416e+00 9.307033357150733e+00 1.31628e-12 2.41531e-11 ----------------------------------------------------------------------------------------------------- 23 C 1 -2.822378860357675e+00 -2.822378860355236e+00 2.43938e-12 1.34457e-11 2 2.547541596473742e+00 2.547541596470994e+00 2.74802e-12 1.01474e-11 3 -2.454115222441623e+00 -2.454115222451252e+00 9.62963e-12 4.95084e-11 ----------------------------------------------------------------------------------------------------- 24 C 1 6.927772877420286e+00 6.927772877414387e+00 5.89928e-12 2.58549e-11 2 5.095731465728432e+00 5.095731465738555e+00 1.01226e-11 5.78826e-11 3 -1.530458008713244e+00 -1.530458008717825e+00 4.58145e-12 1.75937e-10 ----------------------------------------------------------------------------------------------------- 25 C 1 -2.445581566713753e-01 -2.445581566646602e-01 6.71510e-12 2.29314e-11 2 -4.068959095094341e+00 -4.068959095093467e+00 8.73968e-13 7.51061e-10 * 3 -2.110905217132642e+00 -2.110905217140184e+00 7.54197e-12 1.53344e-11 ----------------------------------------------------------------------------------------------------- 26 C 1 -1.025267977761871e+00 -1.025267977766958e+00 5.08682e-12 1.50231e-10 2 4.717767568281057e+00 4.717767568267683e+00 1.33742e-11 8.36318e-11 3 2.231962628533409e+00 2.231962628535886e+00 2.47713e-12 2.59943e-11 ----------------------------------------------------------------------------------------------------- 27 C 1 5.836290926580494e+00 5.836290926574226e+00 6.26788e-12 2.62466e-11 2 -4.810953074594679e+00 -4.810953074596124e+00 1.44507e-12 1.72573e-11 3 2.803414093307831e+00 2.803414093310248e+00 2.41762e-12 1.90732e-11 ----------------------------------------------------------------------------------------------------- 28 C 1 -7.394668445151881e+00 -7.394668445155993e+00 4.11227e-12 3.69003e-11 2 5.593176192284607e+00 5.593176192285113e+00 5.06262e-13 9.72111e-12 3 3.012358348702978e-01 3.012358348725194e-01 2.22156e-12 3.23424e-11 ----------------------------------------------------------------------------------------------------- 29 C 1 7.590992499428431e-01 7.590992499542555e-01 1.14124e-11 9.53981e-12 2 -4.767615593042213e+00 -4.767615593040072e+00 2.14051e-12 5.03864e-11 3 -1.215616171167677e+00 -1.215616171166633e+00 1.04450e-12 2.93052e-11 ----------------------------------------------------------------------------------------------------- 30 C 1 1.996115213028594e+00 1.996115213047481e+00 1.88869e-11 3.22775e-11 2 2.719438101722911e-01 2.719438101775432e-01 5.25208e-12 2.38370e-11 3 -1.247642294790105e+00 -1.247642294790552e+00 4.46976e-13 8.37537e-11 ----------------------------------------------------------------------------------------------------- 31 C 1 -5.610523981277984e+00 -5.610523981276341e+00 1.64313e-12 2.36737e-10 2 -5.323819855392053e+00 -5.323819855391005e+00 1.04894e-12 5.20650e-11 3 5.451881928453909e+00 5.451881928460355e+00 6.44640e-12 6.15952e-12 ----------------------------------------------------------------------------------------------------- 32 C 1 7.513913742018117e-01 7.513913741928098e-01 9.00191e-12 7.74014e-12 2 1.626107149293011e+00 1.626107149294536e+00 1.52500e-12 2.31344e-11 3 5.271626131782883e+00 5.271626131783038e+00 1.55431e-13 4.81188e-11 ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as discontinuities. Maximum error obtained for particle = 2, direction = 3: |F_model - F_numer| error = ----------------------- = 7.60266e-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 = 3.9438276290893555 | (Configuration in file "config-Si.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Si 1 8.332300306712927e+00 8.332300306722706e+00 9.77884e-12 2.48246e-11 2 3.383027402234659e+00 3.383027402234084e+00 5.75096e-13 4.72555e-12 3 4.268961983424775e+00 4.268961983418349e+00 6.42686e-12 5.63354e-11 ----------------------------------------------------------------------------------------------------- 2 Si 1 -4.859563744433877e+00 -4.859563744432211e+00 1.66622e-12 2.20890e-11 2 1.711920267860776e+00 1.711920267857812e+00 2.96385e-12 8.70681e-12 3 7.165110293628001e-01 7.165110293639179e-01 1.11777e-12 1.18894e-12 ----------------------------------------------------------------------------------------------------- 3 Si 1 -2.603897859518862e+00 -2.603897859520984e+00 2.12186e-12 5.69100e-12 2 1.501808785799837e+00 1.501808785801392e+00 1.55498e-12 5.43898e-12 3 -3.318876231294785e+00 -3.318876231281277e+00 1.35083e-11 5.61085e-11 ----------------------------------------------------------------------------------------------------- 4 Si 1 5.688976198710249e+00 5.688976198705911e+00 4.33786e-12 1.28401e-10 2 -3.591635640294791e-01 -3.591635640190314e-01 1.04477e-11 3.13263e-11 3 5.774999889952598e+00 5.774999889949314e+00 3.28448e-12 1.05012e-10 ----------------------------------------------------------------------------------------------------- 5 Si 1 4.508812711072093e+00 4.508812711072856e+00 7.62057e-13 4.07381e-11 2 4.425713676194033e+00 4.425713676188973e+00 5.05995e-12 2.57963e-11 3 6.662441711660076e+00 6.662441711657041e+00 3.03491e-12 8.10108e-12 ----------------------------------------------------------------------------------------------------- 6 Si 1 -4.659476567807821e+00 -4.659476567793693e+00 1.41283e-11 2.11360e-11 2 -2.197002697837219e+00 -2.197002697833210e+00 4.00924e-12 2.44089e-11 3 4.077733294260606e+00 4.077733294261851e+00 1.24434e-12 1.79430e-11 ----------------------------------------------------------------------------------------------------- 7 Si 1 -3.548690069388225e+00 -3.548690069376331e+00 1.18936e-11 9.27365e-11 2 4.273105132918889e+00 4.273105132911213e+00 7.67653e-12 1.84883e-11 3 -1.275923148417801e+00 -1.275923148419774e+00 1.97309e-12 6.23590e-11 ----------------------------------------------------------------------------------------------------- 8 Si 1 -4.114499023652469e-01 -4.114499023714947e-01 6.24784e-12 3.03956e-11 2 8.022072225396549e-01 8.022072225336297e-01 6.02518e-12 6.14575e-12 3 -3.101788186626904e+00 -3.101788186625349e+00 1.55431e-12 2.21189e-10 ----------------------------------------------------------------------------------------------------- 9 Si 1 4.907131047026953e+00 4.907131047021667e+00 5.28555e-12 3.07550e-11 2 -4.203469729587179e+00 -4.203469729590021e+00 2.84217e-12 1.34664e-10 3 1.924365497192305e+00 1.924365497190934e+00 1.37135e-12 4.61704e-11 ----------------------------------------------------------------------------------------------------- 10 Si 1 1.312718947870841e+00 1.312718947871195e+00 3.54161e-13 8.11067e-11 2 -2.751730884771951e+00 -2.751730884779174e+00 7.22311e-12 3.31215e-11 3 6.493609975377391e+00 6.493609975364194e+00 1.31966e-11 4.82760e-11 ----------------------------------------------------------------------------------------------------- 11 Si 1 -5.809176330664155e+00 -5.809176330684186e+00 2.00311e-11 1.08174e-10 2 2.334405695934445e+00 2.334405695929107e+00 5.33840e-12 3.74256e-11 3 -9.404754769535317e-01 -9.404754769509912e-01 2.54052e-12 4.65864e-11 ----------------------------------------------------------------------------------------------------- 12 Si 1 5.298250560744279e+00 5.298250560747504e+00 3.22498e-12 2.68523e-11 2 -4.286291928624354e+00 -4.286291928616163e+00 8.19078e-12 3.78693e-11 3 -1.542271117918188e+00 -1.542271117913001e+00 5.18718e-12 2.11242e-11 ----------------------------------------------------------------------------------------------------- 13 Si 1 -6.899219558039226e+00 -6.899219558042735e+00 3.50919e-12 3.30838e-11 2 -7.614018467409636e-01 -7.614018467414913e-01 5.27689e-13 3.97845e-11 3 -9.409867612504731e-01 -9.409867612467275e-01 3.74556e-12 5.63927e-12 ----------------------------------------------------------------------------------------------------- 14 Si 1 -1.629295922681664e+00 -1.629295922680079e+00 1.58473e-12 2.46145e-11 2 -9.236120287482475e-01 -9.236120287469823e-01 1.26521e-12 9.41780e-12 3 1.632260081187722e+00 1.632260081187151e+00 5.71321e-13 2.10636e-11 ----------------------------------------------------------------------------------------------------- 15 Si 1 1.445007564902917e+00 1.445007564903857e+00 9.40137e-13 4.90712e-11 2 -7.872693715169287e-01 -7.872693715313811e-01 1.44524e-11 3.12936e-11 3 4.097208949199816e+00 4.097208949193322e+00 6.49347e-12 2.46079e-11 ----------------------------------------------------------------------------------------------------- 16 Si 1 -1.222648495232910e+00 -1.222648495223790e+00 9.11982e-12 1.82212e-11 2 -2.192840453344850e+00 -2.192840453336782e+00 8.06866e-12 1.67235e-11 3 -2.509578380616066e+00 -2.509578380619658e+00 3.59268e-12 8.95550e-11 ----------------------------------------------------------------------------------------------------- 17 Si 1 4.131198686670278e+00 4.131198686669253e+00 1.02496e-12 7.29372e-12 2 4.776763793867574e+00 4.776763793863285e+00 4.28901e-12 3.77769e-11 3 -2.247582344055551e+00 -2.247582344068164e+00 1.26130e-11 9.44178e-12 ----------------------------------------------------------------------------------------------------- 18 Si 1 -5.247159064242591e+00 -5.247159064234875e+00 7.71561e-12 1.04468e-10 2 1.621672206562845e-01 1.621672206485461e-01 7.73842e-12 1.46484e-10 3 3.271672788115326e-01 3.271672787779007e-01 3.36319e-11 5.60939e-11 ----------------------------------------------------------------------------------------------------- 19 Si 1 -3.843791488085052e+00 -3.843791488087612e+00 2.55929e-12 1.44391e-11 2 -1.418068036050430e+00 -1.418068036048393e+00 2.03682e-12 2.32963e-11 3 -3.239175764190457e+00 -3.239175764190133e+00 3.24629e-13 4.45044e-11 ----------------------------------------------------------------------------------------------------- 20 Si 1 3.844032753390175e+00 3.844032753390183e+00 7.54952e-15 7.05582e-11 2 3.900201874017800e+00 3.900201874016669e+00 1.13065e-12 1.68243e-11 3 -3.866423621181493e+00 -3.866423621185784e+00 4.29123e-12 1.82028e-11 ----------------------------------------------------------------------------------------------------- 21 Si 1 1.520061737018511e+00 1.520061737019115e+00 6.03961e-13 1.86240e-09 * 2 3.079775866231838e+00 3.079775866235454e+00 3.61533e-12 3.45559e-11 3 2.331320421913315e+00 2.331320421909040e+00 4.27480e-12 1.92841e-11 ----------------------------------------------------------------------------------------------------- 22 Si 1 1.146742061534605e-02 1.146742061853708e-02 3.19104e-12 3.81298e-11 2 -5.522011362165532e+00 -5.522011362164488e+00 1.04450e-12 2.20467e-10 3 2.269521902545376e+00 2.269521902531541e+00 1.38347e-11 5.67457e-11 ----------------------------------------------------------------------------------------------------- 23 Si 1 -3.335011293229776e+00 -3.335011293217179e+00 1.25975e-11 9.01674e-11 2 4.679529398241589e+00 4.679529398249938e+00 8.34977e-12 2.08171e-11 3 -6.410848899190126e+00 -6.410848899190089e+00 3.64153e-14 1.96376e-10 ----------------------------------------------------------------------------------------------------- 24 Si 1 1.448975466180410e+00 1.448975466179492e+00 9.17266e-13 3.76386e-11 2 5.203431514806827e+00 5.203431514813276e+00 6.44906e-12 2.85567e-11 3 -2.644819569608897e+00 -2.644819569610711e+00 1.81410e-12 1.58213e-10 ----------------------------------------------------------------------------------------------------- 25 Si 1 4.690243963006174e+00 4.690243963015496e+00 9.32232e-12 1.67848e-11 2 -1.804887401481651e+00 -1.804887401483024e+00 1.37290e-12 7.31504e-11 3 -4.644115881373992e-01 -4.644115881389264e-01 1.52717e-12 2.06286e-11 ----------------------------------------------------------------------------------------------------- 26 Si 1 -2.471699668676087e+00 -2.471699668674936e+00 1.15108e-12 4.62421e-11 2 -8.571631134033321e-01 -8.571631134162144e-01 1.28824e-11 2.82866e-11 3 3.202953813426837e+00 3.202953813439351e+00 1.25144e-11 2.57057e-10 * ----------------------------------------------------------------------------------------------------- 27 Si 1 -3.450045472300137e+00 -3.450045472296243e+00 3.89377e-12 5.19229e-11 2 -1.060010067048288e+00 -1.060010067053563e+00 5.27467e-12 3.78757e-11 3 -4.702352952800631e+00 -4.702352952810846e+00 1.02149e-11 7.52971e-11 ----------------------------------------------------------------------------------------------------- 28 Si 1 5.959567932296056e+00 5.959567932294788e+00 1.26832e-12 3.32987e-11 2 -3.936568216525588e+00 -3.936568216516728e+00 8.86002e-12 7.71361e-11 3 -2.275336049133381e+00 -2.275336049128078e+00 5.30287e-12 6.79932e-11 ----------------------------------------------------------------------------------------------------- 29 Si 1 3.497743601012606e+00 3.497743601007620e+00 4.98535e-12 1.26038e-10 2 1.314167644235530e+00 1.314167644231790e+00 3.74012e-12 1.20328e-11 3 6.520168962770651e-01 6.520168962777075e-01 6.42486e-13 2.79242e-11 ----------------------------------------------------------------------------------------------------- 30 Si 1 -3.143197119565202e+00 -3.143197119564890e+00 3.11307e-13 3.84439e-11 2 -3.941839890247358e+00 -3.941839890235328e+00 1.20295e-11 2.73886e-10 * 3 -1.974662749677961e+00 -1.974662749664804e+00 1.31573e-11 7.59079e-11 ----------------------------------------------------------------------------------------------------- 31 Si 1 -3.893306510549376e+00 -3.893306510558174e+00 8.79830e-12 4.44258e-11 2 -1.820523847972688e+00 -1.820523847971435e+00 1.25322e-12 1.43145e-10 3 -1.480889010728055e+00 -1.480889010728113e+00 5.75096e-14 2.47482e-11 ----------------------------------------------------------------------------------------------------- 32 Si 1 4.311401695504052e-01 4.311401695509229e-01 5.17753e-13 5.49531e-11 2 -2.724371055443700e+00 -2.724371055434458e+00 9.24283e-12 4.00127e-10 * 3 -1.494670872810516e+00 -1.494670872806239e+00 4.27702e-12 4.90914e-11 ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as discontinuities. Maximum error obtained for particle = 22, direction = 1: |F_model - F_numer| error = ----------------------- = 2.78270e-10 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 = C Si | a0 = 3.5119729515257863 | (Configuration in file "config-CSi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Si 1 8.785590609371358e+00 8.785590609866444e+00 4.95087e-10 5.95969e-09 2 3.617360969597433e+00 3.617360969272606e+00 3.24827e-10 3.95489e-09 3 3.370030282133196e+00 3.370030282322930e+00 1.89734e-10 6.92845e-10 ----------------------------------------------------------------------------------------------------- 2 C 1 -2.932054075066371e+00 -2.932054075108231e+00 4.18594e-11 9.25870e-10 2 -4.548504203048817e+00 -4.548504202760530e+00 2.88288e-10 1.91376e-09 3 -8.951321712900037e-01 -8.951321708701131e-01 4.19891e-10 3.34177e-09 ----------------------------------------------------------------------------------------------------- 3 C 1 1.426377401994492e+00 1.426377401169752e+00 8.24740e-10 2.73717e-09 2 1.860273991841373e+00 1.860273991600641e+00 2.40733e-10 9.44612e-10 3 -4.166438097606321e+00 -4.166438098295308e+00 6.88988e-10 6.44506e-09 ----------------------------------------------------------------------------------------------------- 4 Si 1 -3.084028509797223e+00 -3.084028509181134e+00 6.16089e-10 2.29331e-09 2 2.208744657629440e+00 2.208744658089754e+00 4.60314e-10 1.17842e-08 3 -1.616782282856964e+00 -1.616782281073664e+00 1.78330e-09 3.62553e-09 ----------------------------------------------------------------------------------------------------- 5 C 1 4.883977002939079e-01 4.883977001761639e-01 1.17744e-10 1.50949e-09 2 4.883676538104640e+00 4.883676538315009e+00 2.10369e-10 3.17473e-09 3 4.026481619968212e+00 4.026481619907946e+00 6.02665e-11 1.41467e-09 ----------------------------------------------------------------------------------------------------- 6 Si 1 3.734553262698704e-01 3.734553260981122e-01 1.71758e-10 1.19144e-09 2 -6.788902312113915e-01 -6.788902309596385e-01 2.51753e-10 5.23684e-09 3 1.968072342248275e+00 1.968072342529200e+00 2.80925e-10 9.23615e-10 ----------------------------------------------------------------------------------------------------- 7 C 1 -4.174310802276945e-01 -4.174310802381449e-01 1.04504e-11 9.72833e-12 2 3.879727083168908e-01 3.879727083159608e-01 9.30034e-13 3.21406e-10 3 2.479749357470080e-02 2.479749357273794e-02 1.96286e-12 1.10255e-11 ----------------------------------------------------------------------------------------------------- 8 Si 1 6.329808732717837e-01 6.329808729030993e-01 3.68684e-10 3.65633e-09 2 -8.264729121481199e+00 -8.264729122677720e+00 1.19652e-09 8.08780e-09 3 -5.970218042817096e+00 -5.970218042433472e+00 3.83624e-10 2.78125e-09 ----------------------------------------------------------------------------------------------------- 9 C 1 1.201737251758472e-01 1.201737253334248e-01 1.57578e-10 7.74524e-10 2 -3.386340643890780e+00 -3.386340643509996e+00 3.80784e-10 1.64341e-09 3 5.251834550537274e+00 5.251834550437013e+00 1.00261e-10 7.59380e-10 ----------------------------------------------------------------------------------------------------- 10 Si 1 -5.247255069781035e+00 -5.247255069976509e+00 1.95474e-10 4.91731e-09 2 5.853162343010541e+00 5.853162342630659e+00 3.79882e-10 1.15144e-09 3 -4.828065400548181e+00 -4.828065401167152e+00 6.18971e-10 1.91411e-09 ----------------------------------------------------------------------------------------------------- 11 C 1 -2.707207236481362e+00 -2.707207233218856e+00 3.26251e-09 2.22691e-08 * 2 -5.732722448283177e-01 -5.732722442640984e-01 5.64219e-10 9.70629e-09 3 2.097076317231925e+00 2.097076316387972e+00 8.43952e-10 4.82380e-08 * ----------------------------------------------------------------------------------------------------- 12 Si 1 1.866925789341964e+00 1.866925789807681e+00 4.65718e-10 2.76090e-09 2 -3.415876942359249e+00 -3.415876942040754e+00 3.18495e-10 1.37106e-09 3 2.422803050544198e+00 2.422803051028903e+00 4.84706e-10 3.95563e-09 ----------------------------------------------------------------------------------------------------- 13 Si 1 4.619012375171338e+00 4.619012375547344e+00 3.76006e-10 1.11212e-07 * 2 1.795412870676140e+00 1.795412870045557e+00 6.30583e-10 1.78566e-09 3 2.621473884487896e+00 2.621473884254846e+00 2.33050e-10 3.36837e-09 ----------------------------------------------------------------------------------------------------- 14 C 1 -1.917113475403107e+00 -1.917113475406740e+00 3.63287e-12 3.18079e-10 2 -1.880654286068119e+00 -1.880654286007446e+00 6.06728e-11 3.68930e-10 3 1.607327058905905e-01 1.607327059321298e-01 4.15393e-11 5.48908e-11 ----------------------------------------------------------------------------------------------------- 15 C 1 4.408686755887742e-01 4.408686745308676e-01 1.05791e-09 1.15571e-09 2 -4.364378834331803e+00 -4.364378834772263e+00 4.40460e-10 3.61928e-10 3 6.395462982722818e-01 6.395462982886437e-01 1.63619e-11 1.09360e-09 ----------------------------------------------------------------------------------------------------- 16 C 1 1.973608182073294e+00 1.973608182174792e+00 1.01499e-10 4.14355e-09 2 -1.344325838880095e+00 -1.344325839075410e+00 1.95315e-10 4.36743e-09 3 1.415393973962140e-01 1.415393977469587e-01 3.50745e-10 4.80393e-09 ----------------------------------------------------------------------------------------------------- 17 Si 1 -1.109750681900485e+00 -1.109750681847456e+00 5.30289e-11 7.64657e-10 2 3.071556549751958e+00 3.071556550046002e+00 2.94044e-10 3.21004e-09 3 -4.511466942464757e+00 -4.511466942661263e+00 1.96506e-10 6.71435e-10 ----------------------------------------------------------------------------------------------------- 18 Si 1 2.380746343455885e+00 2.380746343905531e+00 4.49646e-10 4.25027e-09 2 2.714903141359335e+00 2.714903141095624e+00 2.63711e-10 5.57347e-09 3 -3.655399960080284e+00 -3.655399960191943e+00 1.11659e-10 2.51348e-08 * ----------------------------------------------------------------------------------------------------- 19 Si 1 3.646110529231780e-01 3.646110523207536e-01 6.02424e-10 3.23084e-09 2 -3.907285324166763e+00 -3.907285324306250e+00 1.39487e-10 1.17663e-09 3 6.800683722945598e+00 6.800683723443803e+00 4.98205e-10 3.21874e-09 ----------------------------------------------------------------------------------------------------- 20 Si 1 -2.587066853821339e+00 -2.587066853775920e+00 4.54192e-11 1.11387e-09 2 5.578173724953115e+00 5.578173724913015e+00 4.01004e-11 6.97739e-09 3 -1.563609742193997e+00 -1.563609741509883e+00 6.84114e-10 6.44972e-09 ----------------------------------------------------------------------------------------------------- 21 C 1 2.320049854348780e+00 2.320049854305158e+00 4.36224e-11 6.19672e-09 2 2.020644473473879e+00 2.020644473726739e+00 2.52860e-10 2.45156e-09 3 1.682112883390858e+00 1.682112881943263e+00 1.44759e-09 4.54862e-09 ----------------------------------------------------------------------------------------------------- 22 Si 1 -5.842379831465641e+00 -5.842379831625003e+00 1.59362e-10 2.07182e-09 2 7.424962708462129e+00 7.424962709934503e+00 1.47237e-09 2.44513e-08 * 3 -4.550106127354840e+00 -4.550106127872239e+00 5.17399e-10 2.73844e-08 * ----------------------------------------------------------------------------------------------------- 23 Si 1 -1.774376729954760e+00 -1.774376729953938e+00 8.22231e-13 1.89538e-09 2 -3.718725198013602e+00 -3.718725197987287e+00 2.63150e-11 2.52816e-10 3 -1.965988260418510e+00 -1.965988260129601e+00 2.88909e-10 1.29418e-09 ----------------------------------------------------------------------------------------------------- 24 Si 1 2.846181337101067e+00 2.846181337378909e+00 2.77842e-10 3.07553e-09 2 1.383663280910174e+00 1.383663281626752e+00 7.16578e-10 6.51702e-08 * 3 3.320433316619960e+00 3.320433318988756e+00 2.36880e-09 5.37276e-08 * ----------------------------------------------------------------------------------------------------- 25 C 1 -1.364711109711567e+00 -1.364711109707915e+00 3.65197e-12 3.25728e-08 * 2 4.653811610679327e+00 4.653811611441506e+00 7.62179e-10 4.56212e-08 * 3 6.535410550693698e+00 6.535410550537540e+00 1.56159e-10 3.15725e-09 ----------------------------------------------------------------------------------------------------- 26 C 1 -3.664894938582842e+00 -3.664894938629641e+00 4.67990e-11 1.69326e-08 2 1.546898203958868e+00 1.546898203894967e+00 6.39009e-11 3.42824e-10 3 6.141414657377895e+00 6.141414656941170e+00 4.36725e-10 2.50208e-09 ----------------------------------------------------------------------------------------------------- 27 C 1 -1.545007116373676e+00 -1.545007117282350e+00 9.08674e-10 3.30496e-09 2 -1.020174954758552e+00 -1.020174954511377e+00 2.47175e-10 7.23403e-09 3 -1.499575802919869e+00 -1.499575802945480e+00 2.56111e-11 2.04349e-09 ----------------------------------------------------------------------------------------------------- 28 Si 1 5.700764007440004e+00 5.700764007001629e+00 4.38375e-10 3.50939e-09 2 -6.291657849663430e+00 -6.291657850281240e+00 6.17810e-10 3.59904e-09 3 -8.623919022126342e+00 -8.623919022068110e+00 5.82325e-11 1.52883e-09 ----------------------------------------------------------------------------------------------------- 29 C 1 2.707359261079116e+00 2.707359260722146e+00 3.56970e-10 8.24460e-10 2 -2.950401838908046e+00 -2.950401841014028e+00 2.10598e-09 2.20749e-08 * 3 4.839386348593494e-01 4.839386353005341e-01 4.41185e-10 3.70903e-09 ----------------------------------------------------------------------------------------------------- 30 C 1 -1.713151538055215e+00 -1.713151538139387e+00 8.41720e-11 3.96035e-10 2 -5.124919022930077e-02 -5.124919025717978e-02 2.78790e-11 5.58048e-11 3 1.658493849016825e+00 1.658493849003922e+00 1.29026e-11 1.68005e-10 ----------------------------------------------------------------------------------------------------- 31 C 1 -1.252401420645508e+00 -1.252401420703525e+00 5.80167e-11 1.84305e-09 2 -2.020862995852113e+00 -2.020862996278016e+00 4.25903e-10 5.54953e-10 3 -1.585637464976328e+00 -1.585637463945577e+00 1.03075e-09 5.88332e-09 ----------------------------------------------------------------------------------------------------- 32 Si 1 1.117271523671625e-01 1.117271519630341e-01 4.04128e-10 3.99927e-09 2 -5.838880750336756e-01 -5.838880739851001e-01 1.04858e-09 8.45067e-09 3 -3.914536239535474e+00 -3.914536239480178e+00 5.52958e-11 8.20555e-09 ----------------------------------------------------------------------------------------------------- * 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 = 32, direction = 1: |F_model - F_numer| error = ----------------------- = 3.61710e-09 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 3.61710e-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 3.61710e-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.