!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_003 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 4.656004944769278e+00 4.03855e-12 7.28129e-12 2 2.245485921321180e+00 2.245485921318215e+00 2.96518e-12 7.55089e-11 3 4.843987397185602e+00 4.843987397181820e+00 3.78186e-12 5.45226e-11 ----------------------------------------------------------------------------------------------------- 2 C 1 -3.240984812291678e+00 -3.240984812290047e+00 1.63070e-12 1.24815e-10 2 1.868060167107370e+00 1.868060167107692e+00 3.21965e-13 7.72480e-11 3 -4.898658544179180e-02 -4.898658543806747e-02 3.72433e-12 5.71139e-11 ----------------------------------------------------------------------------------------------------- 3 C 1 6.849838494466502e+00 6.849838494481609e+00 1.51070e-11 1.25437e-11 2 -6.267667714674847e+00 -6.267667714663816e+00 1.10303e-11 5.74927e-11 3 -7.231110654083937e+00 -7.231110654073159e+00 1.07780e-11 1.04353e-10 ----------------------------------------------------------------------------------------------------- 4 C 1 -3.683460472083469e+00 -3.683460472083437e+00 3.24185e-14 1.25806e-11 2 1.210404907304017e+01 1.210404907305508e+01 1.49125e-11 4.28191e-11 3 -6.047482337619417e+00 -6.047482337626850e+00 7.43228e-12 3.20330e-11 ----------------------------------------------------------------------------------------------------- 5 C 1 -1.925286484887362e+00 -1.925286484888310e+00 9.48130e-13 1.90181e-11 2 1.834328138772020e+00 1.834328138763193e+00 8.82650e-12 2.85740e-11 3 2.293878323168900e+00 2.293878323169286e+00 3.86358e-13 9.09099e-11 ----------------------------------------------------------------------------------------------------- 6 C 1 -1.355828222078296e+00 -1.355828222072182e+00 6.11378e-12 2.08926e-11 2 -4.001382588039456e+00 -4.001382588035518e+00 3.93818e-12 1.36252e-10 3 1.306964931018395e+00 1.306964931023475e+00 5.08016e-12 2.06681e-11 ----------------------------------------------------------------------------------------------------- 7 C 1 -1.667098069537438e+00 -1.667098069532510e+00 4.92717e-12 2.47160e-11 2 -6.181506392895504e+00 -6.181506392897368e+00 1.86340e-12 4.21529e-11 3 -1.257192100141984e+01 -1.257192100141980e+01 4.26326e-14 1.04063e-10 ----------------------------------------------------------------------------------------------------- 8 C 1 -2.637829128386334e+00 -2.637829128380739e+00 5.59419e-12 5.26228e-11 2 2.631332197163546e+00 2.631332197173335e+00 9.78950e-12 4.17306e-11 3 6.333157814682888e+00 6.333157814664305e+00 1.85834e-11 4.22897e-11 ----------------------------------------------------------------------------------------------------- 9 C 1 -1.079354480439354e+00 -1.079354480444498e+00 5.14411e-12 4.94633e-11 2 -3.745731390933351e+00 -3.745731390939131e+00 5.77938e-12 2.10423e-11 3 3.046883312422037e+00 3.046883312419949e+00 2.08811e-12 2.16294e-11 ----------------------------------------------------------------------------------------------------- 10 C 1 -4.029410761140541e+00 -4.029410761143163e+00 2.62190e-12 2.13420e-11 2 8.804346810007485e-01 8.804346810004352e-01 3.13305e-13 2.92045e-11 3 -2.429547835823505e+00 -2.429547835822365e+00 1.13998e-12 1.36957e-12 ----------------------------------------------------------------------------------------------------- 11 C 1 -6.608884377862368e-01 -6.608884377935054e-01 7.26852e-12 7.74180e-11 2 -1.377065127701544e+01 -1.377065127699891e+01 1.65254e-11 1.21036e-10 3 -6.283995277341192e+00 -6.283995277341494e+00 3.01981e-13 1.86740e-11 ----------------------------------------------------------------------------------------------------- 12 C 1 -1.540049442890726e+00 -1.540049442887635e+00 3.09042e-12 5.07892e-11 2 1.772488490264889e+00 1.772488490266476e+00 1.58740e-12 8.87690e-12 3 -5.216682297190571e-01 -5.216682297182347e-01 8.22453e-13 3.60632e-11 ----------------------------------------------------------------------------------------------------- 13 C 1 -4.240427330196902e+00 -4.240427330197385e+00 4.83169e-13 4.42046e-12 2 -3.118823716369162e+00 -3.118823716365578e+00 3.58424e-12 4.08087e-11 3 -1.153084437032401e+01 -1.153084437032365e+01 3.58824e-13 1.02521e-10 ----------------------------------------------------------------------------------------------------- 14 C 1 2.708129400578022e+00 2.708129400573955e+00 4.06652e-12 3.85443e-11 2 2.873778376681213e-01 2.873778376650018e-01 3.11950e-12 4.51827e-12 3 -2.292413285601288e+00 -2.292413285606266e+00 4.97735e-12 4.40835e-10 * ----------------------------------------------------------------------------------------------------- 15 C 1 1.053410691836794e+01 1.053410691837083e+01 2.88658e-12 5.12532e-11 2 2.167899291248047e+00 2.167899291245074e+00 2.97318e-12 6.80385e-11 3 4.940953642373795e+00 4.940953642368638e+00 5.15765e-12 6.01747e-10 * ----------------------------------------------------------------------------------------------------- 16 C 1 -5.824188705066555e-01 -5.824188705027274e-01 3.92808e-12 6.45255e-11 2 7.358126409712392e+00 7.358126409713058e+00 6.66134e-13 3.98908e-11 3 4.216431050372625e+00 4.216431050369280e+00 3.34488e-12 1.47664e-10 ----------------------------------------------------------------------------------------------------- 17 C 1 -6.300009134354861e+00 -6.300009134357015e+00 2.15472e-12 1.57776e-11 2 -2.916541767976895e+00 -2.916541767978126e+00 1.23057e-12 9.93361e-11 3 -1.840539143841298e+00 -1.840539143845198e+00 3.90066e-12 1.14382e-11 ----------------------------------------------------------------------------------------------------- 18 C 1 2.499477896161983e+00 2.499477896166264e+00 4.28146e-12 1.28079e-10 2 7.084495241498399e+00 7.084495241493037e+00 5.36193e-12 1.36196e-10 3 -4.095641831394444e+00 -4.095641831391302e+00 3.14238e-12 4.45022e-11 ----------------------------------------------------------------------------------------------------- 19 C 1 1.014959298188866e+01 1.014959298189119e+01 2.52065e-12 8.65299e-11 2 -2.867380337243889e+00 -2.867380337241444e+00 2.44471e-12 1.36064e-10 3 3.205197049214308e+00 3.205197049211705e+00 2.60325e-12 3.04246e-12 ----------------------------------------------------------------------------------------------------- 20 C 1 -7.208306142101959e-01 -7.208306142104629e-01 2.67009e-13 7.45681e-12 2 9.032337972215777e-01 9.032337972188652e-01 2.71250e-12 7.15150e-12 3 1.138470390045089e+00 1.138470390044686e+00 4.03677e-13 9.83924e-12 ----------------------------------------------------------------------------------------------------- 21 C 1 -6.326196079661614e+00 -6.326196079660578e+00 1.03562e-12 2.09784e-10 2 -3.571465349841400e+00 -3.571465349845814e+00 4.41380e-12 1.18264e-10 3 6.759809582273682e+00 6.759809582269683e+00 3.99947e-12 4.38147e-11 ----------------------------------------------------------------------------------------------------- 22 C 1 3.419649484270082e+00 3.419649484267860e+00 2.22222e-12 2.39515e-11 2 4.422919124861607e+00 4.422919124860241e+00 1.36602e-12 1.75397e-11 3 9.307033357149416e+00 9.307033357150727e+00 1.31095e-12 2.41425e-11 ----------------------------------------------------------------------------------------------------- 23 C 1 -2.822378860357675e+00 -2.822378860355233e+00 2.44205e-12 1.34461e-11 2 2.547541596473742e+00 2.547541596470993e+00 2.74891e-12 1.01492e-11 3 -2.454115222441623e+00 -2.454115222451254e+00 9.63096e-12 4.95097e-11 ----------------------------------------------------------------------------------------------------- 24 C 1 6.927772877420286e+00 6.927772877414382e+00 5.90372e-12 2.58584e-11 2 5.095731465728432e+00 5.095731465738552e+00 1.01190e-11 5.78826e-11 3 -1.530458008713244e+00 -1.530458008717825e+00 4.58100e-12 1.75937e-10 ----------------------------------------------------------------------------------------------------- 25 C 1 -2.445581566713753e-01 -2.445581566646600e-01 6.71527e-12 2.29314e-11 2 -4.068959095094341e+00 -4.068959095093464e+00 8.76632e-13 7.51061e-10 * 3 -2.110905217132642e+00 -2.110905217140183e+00 7.54063e-12 1.53344e-11 ----------------------------------------------------------------------------------------------------- 26 C 1 -1.025267977761871e+00 -1.025267977766957e+00 5.08593e-12 1.50231e-10 2 4.717767568281057e+00 4.717767568267685e+00 1.33724e-11 8.36344e-11 3 2.231962628533409e+00 2.231962628535885e+00 2.47580e-12 2.59934e-11 ----------------------------------------------------------------------------------------------------- 27 C 1 5.836290926580494e+00 5.836290926574222e+00 6.27232e-12 2.62466e-11 2 -4.810953074594679e+00 -4.810953074596123e+00 1.44329e-12 1.72538e-11 3 2.803414093307831e+00 2.803414093310245e+00 2.41451e-12 1.90750e-11 ----------------------------------------------------------------------------------------------------- 28 C 1 -7.394668445151881e+00 -7.394668445155989e+00 4.10783e-12 3.68994e-11 2 5.593176192284607e+00 5.593176192285116e+00 5.08926e-13 9.72111e-12 3 3.012358348702978e-01 3.012358348725192e-01 2.22139e-12 3.23420e-11 ----------------------------------------------------------------------------------------------------- 29 C 1 7.590992499428431e-01 7.590992499542549e-01 1.14119e-11 9.53959e-12 2 -4.767615593042213e+00 -4.767615593040075e+00 2.13785e-12 5.03864e-11 3 -1.215616171167677e+00 -1.215616171166632e+00 1.04516e-12 2.93046e-11 ----------------------------------------------------------------------------------------------------- 30 C 1 1.996115213028594e+00 1.996115213047479e+00 1.88847e-11 3.22766e-11 2 2.719438101722911e-01 2.719438101775430e-01 5.25191e-12 2.38372e-11 3 -1.247642294790105e+00 -1.247642294790553e+00 4.47642e-13 8.37537e-11 ----------------------------------------------------------------------------------------------------- 31 C 1 -5.610523981277984e+00 -5.610523981276336e+00 1.64757e-12 2.36734e-10 2 -5.323819855392053e+00 -5.323819855391001e+00 1.05249e-12 5.20650e-11 3 5.451881928453909e+00 5.451881928460353e+00 6.44462e-12 6.15419e-12 ----------------------------------------------------------------------------------------------------- 32 C 1 7.513913742018117e-01 7.513913741928092e-01 9.00247e-12 7.74036e-12 2 1.626107149293011e+00 1.626107149294535e+00 1.52389e-12 2.31344e-11 3 5.271626131782883e+00 5.271626131783035e+00 1.51879e-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 = ----------------------- = 7.60275e-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 8.332300306722711e+00 9.78417e-12 2.48210e-11 2 3.383027402234659e+00 3.383027402234083e+00 5.75984e-13 4.72777e-12 3 4.268961983424775e+00 4.268961983418350e+00 6.42508e-12 5.63372e-11 ----------------------------------------------------------------------------------------------------- 2 Si 1 -4.859563744433877e+00 -4.859563744432213e+00 1.66356e-12 2.20908e-11 2 1.711920267860776e+00 1.711920267857811e+00 2.96496e-12 8.70659e-12 3 7.165110293628001e-01 7.165110293639174e-01 1.11733e-12 1.18971e-12 ----------------------------------------------------------------------------------------------------- 3 Si 1 -2.603897859518862e+00 -2.603897859520984e+00 2.12186e-12 5.69367e-12 2 1.501808785799837e+00 1.501808785801391e+00 1.55453e-12 5.43987e-12 3 -3.318876231294785e+00 -3.318876231281279e+00 1.35070e-11 5.61071e-11 ----------------------------------------------------------------------------------------------------- 4 Si 1 5.688976198710249e+00 5.688976198705907e+00 4.34142e-12 1.28396e-10 2 -3.591635640294791e-01 -3.591635640190310e-01 1.04480e-11 3.13266e-11 3 5.774999889952598e+00 5.774999889949310e+00 3.28804e-12 1.05015e-10 ----------------------------------------------------------------------------------------------------- 5 Si 1 4.508812711072093e+00 4.508812711072857e+00 7.63833e-13 4.07372e-11 2 4.425713676194033e+00 4.425713676188971e+00 5.06262e-12 2.57971e-11 3 6.662441711660076e+00 6.662441711657045e+00 3.03135e-12 8.10285e-12 ----------------------------------------------------------------------------------------------------- 6 Si 1 -4.659476567807821e+00 -4.659476567793687e+00 1.41336e-11 2.11360e-11 2 -2.197002697837219e+00 -2.197002697833210e+00 4.00879e-12 2.44129e-11 3 4.077733294260606e+00 4.077733294261853e+00 1.24700e-12 1.79412e-11 ----------------------------------------------------------------------------------------------------- 7 Si 1 -3.548690069388225e+00 -3.548690069376329e+00 1.18958e-11 9.27374e-11 2 4.273105132918889e+00 4.273105132911208e+00 7.68097e-12 1.84919e-11 3 -1.275923148417801e+00 -1.275923148419775e+00 1.97375e-12 6.23592e-11 ----------------------------------------------------------------------------------------------------- 8 Si 1 -4.114499023652469e-01 -4.114499023714944e-01 6.24756e-12 3.03955e-11 2 8.022072225396549e-01 8.022072225336291e-01 6.02585e-12 6.14564e-12 3 -3.101788186626904e+00 -3.101788186625351e+00 1.55254e-12 2.21190e-10 ----------------------------------------------------------------------------------------------------- 9 Si 1 4.907131047026953e+00 4.907131047021669e+00 5.28377e-12 3.07594e-11 2 -4.203469729587179e+00 -4.203469729590018e+00 2.83862e-12 1.34663e-10 3 1.924365497192305e+00 1.924365497190933e+00 1.37268e-12 4.61704e-11 ----------------------------------------------------------------------------------------------------- 10 Si 1 1.312718947870841e+00 1.312718947871193e+00 3.52607e-13 8.11047e-11 2 -2.751730884771951e+00 -2.751730884779175e+00 7.22444e-12 3.31215e-11 3 6.493609975377391e+00 6.493609975364198e+00 1.31930e-11 4.82760e-11 ----------------------------------------------------------------------------------------------------- 11 Si 1 -5.809176330664155e+00 -5.809176330684188e+00 2.00338e-11 1.08174e-10 2 2.334405695934445e+00 2.334405695929108e+00 5.33706e-12 3.74256e-11 3 -9.404754769535317e-01 -9.404754769509905e-01 2.54119e-12 4.65866e-11 ----------------------------------------------------------------------------------------------------- 12 Si 1 5.298250560744279e+00 5.298250560747506e+00 3.22675e-12 2.68541e-11 2 -4.286291928624354e+00 -4.286291928616151e+00 8.20233e-12 3.78835e-11 3 -1.542271117918188e+00 -1.542271117913002e+00 5.18630e-12 2.11240e-11 ----------------------------------------------------------------------------------------------------- 13 Si 1 -6.899219558039226e+00 -6.899219558042731e+00 3.50475e-12 3.30838e-11 2 -7.614018467409636e-01 -7.614018467414915e-01 5.27911e-13 3.97838e-11 3 -9.409867612504731e-01 -9.409867612467272e-01 3.74589e-12 5.63904e-12 ----------------------------------------------------------------------------------------------------- 14 Si 1 -1.629295922681664e+00 -1.629295922680078e+00 1.58562e-12 2.46148e-11 2 -9.236120287482475e-01 -9.236120287469817e-01 1.26588e-12 9.41769e-12 3 1.632260081187722e+00 1.632260081187150e+00 5.72431e-13 2.10640e-11 ----------------------------------------------------------------------------------------------------- 15 Si 1 1.445007564902917e+00 1.445007564903855e+00 9.38361e-13 4.90705e-11 2 -7.872693715169287e-01 -7.872693715313805e-01 1.44519e-11 3.12945e-11 3 4.097208949199816e+00 4.097208949193320e+00 6.49614e-12 2.46079e-11 ----------------------------------------------------------------------------------------------------- 16 Si 1 -1.222648495232910e+00 -1.222648495223791e+00 9.11937e-12 1.82214e-11 2 -2.192840453344850e+00 -2.192840453336783e+00 8.06777e-12 1.67240e-11 3 -2.509578380616066e+00 -2.509578380619660e+00 3.59401e-12 8.95541e-11 ----------------------------------------------------------------------------------------------------- 17 Si 1 4.131198686670278e+00 4.131198686669251e+00 1.02762e-12 7.29372e-12 2 4.776763793867574e+00 4.776763793863283e+00 4.29079e-12 3.77840e-11 3 -2.247582344055551e+00 -2.247582344068164e+00 1.26130e-11 9.44445e-12 ----------------------------------------------------------------------------------------------------- 18 Si 1 -5.247159064242591e+00 -5.247159064234871e+00 7.72005e-12 1.04466e-10 2 1.621672206562845e-01 1.621672206485462e-01 7.73837e-12 1.46484e-10 3 3.271672788115326e-01 3.271672787779005e-01 3.36321e-11 5.60940e-11 ----------------------------------------------------------------------------------------------------- 19 Si 1 -3.843791488085052e+00 -3.843791488087609e+00 2.55662e-12 1.44391e-11 2 -1.418068036050430e+00 -1.418068036048394e+00 2.03593e-12 2.32963e-11 3 -3.239175764190457e+00 -3.239175764190134e+00 3.23297e-13 4.45031e-11 ----------------------------------------------------------------------------------------------------- 20 Si 1 3.844032753390175e+00 3.844032753390185e+00 9.76996e-15 7.05578e-11 2 3.900201874017800e+00 3.900201874016667e+00 1.13332e-12 1.68243e-11 3 -3.866423621181493e+00 -3.866423621185783e+00 4.28946e-12 1.82037e-11 ----------------------------------------------------------------------------------------------------- 21 Si 1 1.520061737018511e+00 1.520061737019114e+00 6.02851e-13 1.86240e-09 * 2 3.079775866231838e+00 3.079775866235452e+00 3.61355e-12 3.45546e-11 3 2.331320421913315e+00 2.331320421909040e+00 4.27436e-12 1.92846e-11 ----------------------------------------------------------------------------------------------------- 22 Si 1 1.146742061534605e-02 1.146742061853709e-02 3.19104e-12 3.81298e-11 2 -5.522011362165532e+00 -5.522011362164482e+00 1.04983e-12 2.20473e-10 3 2.269521902545376e+00 2.269521902531543e+00 1.38329e-11 5.67453e-11 ----------------------------------------------------------------------------------------------------- 23 Si 1 -3.335011293229776e+00 -3.335011293217177e+00 1.25993e-11 9.01661e-11 2 4.679529398241589e+00 4.679529398249937e+00 8.34799e-12 2.08216e-11 3 -6.410848899190126e+00 -6.410848899190085e+00 4.08562e-14 1.96373e-10 ----------------------------------------------------------------------------------------------------- 24 Si 1 1.448975466180410e+00 1.448975466179493e+00 9.16378e-13 3.76388e-11 2 5.203431514806827e+00 5.203431514813274e+00 6.44729e-12 2.85585e-11 3 -2.644819569608897e+00 -2.644819569610708e+00 1.81188e-12 1.58212e-10 ----------------------------------------------------------------------------------------------------- 25 Si 1 4.690243963006174e+00 4.690243963015491e+00 9.31699e-12 1.67839e-11 2 -1.804887401481651e+00 -1.804887401483025e+00 1.37379e-12 7.31499e-11 3 -4.644115881373992e-01 -4.644115881389260e-01 1.52683e-12 2.06284e-11 ----------------------------------------------------------------------------------------------------- 26 Si 1 -2.471699668676087e+00 -2.471699668674935e+00 1.15197e-12 4.62426e-11 2 -8.571631134033321e-01 -8.571631134162139e-01 1.28818e-11 2.82868e-11 3 3.202953813426837e+00 3.202953813439352e+00 1.25153e-11 2.57056e-10 * ----------------------------------------------------------------------------------------------------- 27 Si 1 -3.450045472300137e+00 -3.450045472296245e+00 3.89200e-12 5.19229e-11 2 -1.060010067048288e+00 -1.060010067053562e+00 5.27445e-12 3.78748e-11 3 -4.702352952800631e+00 -4.702352952810840e+00 1.02096e-11 7.52962e-11 ----------------------------------------------------------------------------------------------------- 28 Si 1 5.959567932296056e+00 5.959567932294784e+00 1.27187e-12 3.32969e-11 2 -3.936568216525588e+00 -3.936568216516729e+00 8.85869e-12 7.71374e-11 3 -2.275336049133381e+00 -2.275336049128080e+00 5.30154e-12 6.79918e-11 ----------------------------------------------------------------------------------------------------- 29 Si 1 3.497743601012606e+00 3.497743601007618e+00 4.98757e-12 1.26036e-10 2 1.314167644235530e+00 1.314167644231789e+00 3.74145e-12 1.20333e-11 3 6.520168962770651e-01 6.520168962777070e-01 6.41931e-13 2.79243e-11 ----------------------------------------------------------------------------------------------------- 30 Si 1 -3.143197119565202e+00 -3.143197119564892e+00 3.09974e-13 3.84444e-11 2 -3.941839890247358e+00 -3.941839890235326e+00 1.20317e-11 2.73888e-10 * 3 -1.974662749677961e+00 -1.974662749664804e+00 1.31566e-11 7.59086e-11 ----------------------------------------------------------------------------------------------------- 31 Si 1 -3.893306510549376e+00 -3.893306510558176e+00 8.80052e-12 4.44258e-11 2 -1.820523847972688e+00 -1.820523847971434e+00 1.25477e-12 1.43145e-10 3 -1.480889010728055e+00 -1.480889010728111e+00 5.57332e-14 2.47504e-11 ----------------------------------------------------------------------------------------------------- 32 Si 1 4.311401695504052e-01 4.311401695509231e-01 5.17919e-13 5.49529e-11 2 -2.724371055443700e+00 -2.724371055434456e+00 9.24416e-12 4.00125e-10 * 3 -1.494670872810516e+00 -1.494670872806238e+00 4.27769e-12 4.90912e-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 8.785590609866439e+00 4.95081e-10 5.95970e-09 2 3.617360969597433e+00 3.617360969272608e+00 3.24825e-10 3.95489e-09 3 3.370030282133196e+00 3.370030282322932e+00 1.89736e-10 6.92845e-10 ----------------------------------------------------------------------------------------------------- 2 C 1 -2.932054075066371e+00 -2.932054075108229e+00 4.18576e-11 9.25869e-10 2 -4.548504203048817e+00 -4.548504202760531e+00 2.88286e-10 1.91376e-09 3 -8.951321712900037e-01 -8.951321708701137e-01 4.19890e-10 3.34177e-09 ----------------------------------------------------------------------------------------------------- 3 C 1 1.426377401994492e+00 1.426377401169751e+00 8.24741e-10 2.73717e-09 2 1.860273991841373e+00 1.860273991600639e+00 2.40734e-10 9.44612e-10 3 -4.166438097606321e+00 -4.166438098295311e+00 6.88990e-10 6.44506e-09 ----------------------------------------------------------------------------------------------------- 4 Si 1 -3.084028509797223e+00 -3.084028509181132e+00 6.16091e-10 2.29331e-09 2 2.208744657629440e+00 2.208744658089755e+00 4.60315e-10 1.17842e-08 3 -1.616782282856964e+00 -1.616782281073663e+00 1.78330e-09 3.62553e-09 ----------------------------------------------------------------------------------------------------- 5 C 1 4.883977002939079e-01 4.883977001761635e-01 1.17744e-10 1.50949e-09 2 4.883676538104640e+00 4.883676538315012e+00 2.10371e-10 3.17473e-09 3 4.026481619968212e+00 4.026481619907943e+00 6.02691e-11 1.41467e-09 ----------------------------------------------------------------------------------------------------- 6 Si 1 3.734553262698704e-01 3.734553260981119e-01 1.71758e-10 1.19144e-09 2 -6.788902312113915e-01 -6.788902309596389e-01 2.51753e-10 5.23684e-09 3 1.968072342248275e+00 1.968072342529199e+00 2.80924e-10 9.23615e-10 ----------------------------------------------------------------------------------------------------- 7 C 1 -4.174310802276945e-01 -4.174310802381446e-01 1.04501e-11 9.72833e-12 2 3.879727083168908e-01 3.879727083159605e-01 9.30367e-13 3.21406e-10 3 2.479749357470080e-02 2.479749357273792e-02 1.96288e-12 1.10255e-11 ----------------------------------------------------------------------------------------------------- 8 Si 1 6.329808732717837e-01 6.329808729030988e-01 3.68685e-10 3.65633e-09 2 -8.264729121481199e+00 -8.264729122677721e+00 1.19652e-09 8.08780e-09 3 -5.970218042817096e+00 -5.970218042433475e+00 3.83621e-10 2.78124e-09 ----------------------------------------------------------------------------------------------------- 9 C 1 1.201737251758472e-01 1.201737253334247e-01 1.57577e-10 7.74524e-10 2 -3.386340643890780e+00 -3.386340643509994e+00 3.80787e-10 1.64341e-09 3 5.251834550537274e+00 5.251834550437008e+00 1.00266e-10 7.59377e-10 ----------------------------------------------------------------------------------------------------- 10 Si 1 -5.247255069781035e+00 -5.247255069976504e+00 1.95469e-10 4.91731e-09 2 5.853162343010541e+00 5.853162342630664e+00 3.79877e-10 1.15143e-09 3 -4.828065400548181e+00 -4.828065401167154e+00 6.18973e-10 1.91412e-09 ----------------------------------------------------------------------------------------------------- 11 C 1 -2.707207236481362e+00 -2.707207233218854e+00 3.26251e-09 2.22691e-08 * 2 -5.732722448283177e-01 -5.732722442640986e-01 5.64219e-10 9.70629e-09 3 2.097076317231925e+00 2.097076316387971e+00 8.43953e-10 4.82380e-08 * ----------------------------------------------------------------------------------------------------- 12 Si 1 1.866925789341964e+00 1.866925789807680e+00 4.65717e-10 2.76090e-09 2 -3.415876942359249e+00 -3.415876942040752e+00 3.18497e-10 1.37106e-09 3 2.422803050544198e+00 2.422803051028902e+00 4.84704e-10 3.95563e-09 ----------------------------------------------------------------------------------------------------- 13 Si 1 4.619012375171338e+00 4.619012375547340e+00 3.76002e-10 1.11212e-07 * 2 1.795412870676140e+00 1.795412870045555e+00 6.30585e-10 1.78566e-09 3 2.621473884487896e+00 2.621473884254844e+00 2.33051e-10 3.36837e-09 ----------------------------------------------------------------------------------------------------- 14 C 1 -1.917113475403107e+00 -1.917113475406738e+00 3.63154e-12 3.18079e-10 2 -1.880654286068119e+00 -1.880654286007444e+00 6.06741e-11 3.68931e-10 3 1.607327058905905e-01 1.607327059321297e-01 4.15392e-11 5.48907e-11 ----------------------------------------------------------------------------------------------------- 15 C 1 4.408686755887742e-01 4.408686745308678e-01 1.05791e-09 1.15571e-09 2 -4.364378834331803e+00 -4.364378834772265e+00 4.40462e-10 3.61928e-10 3 6.395462982722818e-01 6.395462982886440e-01 1.63621e-11 1.09360e-09 ----------------------------------------------------------------------------------------------------- 16 C 1 1.973608182073294e+00 1.973608182174791e+00 1.01497e-10 4.14355e-09 2 -1.344325838880095e+00 -1.344325839075410e+00 1.95315e-10 4.36743e-09 3 1.415393973962140e-01 1.415393977469588e-01 3.50745e-10 4.80393e-09 ----------------------------------------------------------------------------------------------------- 17 Si 1 -1.109750681900485e+00 -1.109750681847455e+00 5.30298e-11 7.64657e-10 2 3.071556549751958e+00 3.071556550046000e+00 2.94043e-10 3.21004e-09 3 -4.511466942464757e+00 -4.511466942661261e+00 1.96503e-10 6.71434e-10 ----------------------------------------------------------------------------------------------------- 18 Si 1 2.380746343455885e+00 2.380746343905533e+00 4.49647e-10 4.25027e-09 2 2.714903141359335e+00 2.714903141095625e+00 2.63709e-10 5.57347e-09 3 -3.655399960080284e+00 -3.655399960191945e+00 1.11661e-10 2.51348e-08 * ----------------------------------------------------------------------------------------------------- 19 Si 1 3.646110529231780e-01 3.646110523207539e-01 6.02424e-10 3.23084e-09 2 -3.907285324166763e+00 -3.907285324306247e+00 1.39484e-10 1.17664e-09 3 6.800683722945598e+00 6.800683723443806e+00 4.98208e-10 3.21874e-09 ----------------------------------------------------------------------------------------------------- 20 Si 1 -2.587066853821339e+00 -2.587066853775918e+00 4.54210e-11 1.11386e-09 2 5.578173724953115e+00 5.578173724913010e+00 4.01048e-11 6.97740e-09 3 -1.563609742193997e+00 -1.563609741509884e+00 6.84113e-10 6.44972e-09 ----------------------------------------------------------------------------------------------------- 21 C 1 2.320049854348780e+00 2.320049854305159e+00 4.36216e-11 6.19672e-09 2 2.020644473473879e+00 2.020644473726738e+00 2.52859e-10 2.45156e-09 3 1.682112883390858e+00 1.682112881943262e+00 1.44760e-09 4.54862e-09 ----------------------------------------------------------------------------------------------------- 22 Si 1 -5.842379831465641e+00 -5.842379831624998e+00 1.59357e-10 2.07182e-09 2 7.424962708462129e+00 7.424962709934498e+00 1.47237e-09 2.44513e-08 * 3 -4.550106127354840e+00 -4.550106127872236e+00 5.17396e-10 2.73844e-08 * ----------------------------------------------------------------------------------------------------- 23 Si 1 -1.774376729954760e+00 -1.774376729953937e+00 8.23341e-13 1.89538e-09 2 -3.718725198013602e+00 -3.718725197987284e+00 2.63176e-11 2.52815e-10 3 -1.965988260418510e+00 -1.965988260129600e+00 2.88910e-10 1.29418e-09 ----------------------------------------------------------------------------------------------------- 24 Si 1 2.846181337101067e+00 2.846181337378909e+00 2.77842e-10 3.07553e-09 2 1.383663280910174e+00 1.383663281626751e+00 7.16577e-10 6.51702e-08 * 3 3.320433316619960e+00 3.320433318988754e+00 2.36879e-09 5.37276e-08 * ----------------------------------------------------------------------------------------------------- 25 C 1 -1.364711109711567e+00 -1.364711109707914e+00 3.65286e-12 3.25728e-08 * 2 4.653811610679327e+00 4.653811611441504e+00 7.62177e-10 4.56212e-08 * 3 6.535410550693698e+00 6.535410550537543e+00 1.56155e-10 3.15725e-09 ----------------------------------------------------------------------------------------------------- 26 C 1 -3.664894938582842e+00 -3.664894938629639e+00 4.67968e-11 1.69326e-08 2 1.546898203958868e+00 1.546898203894966e+00 6.39022e-11 3.42824e-10 3 6.141414657377895e+00 6.141414656941174e+00 4.36722e-10 2.50208e-09 ----------------------------------------------------------------------------------------------------- 27 C 1 -1.545007116373676e+00 -1.545007117282349e+00 9.08673e-10 3.30496e-09 2 -1.020174954758552e+00 -1.020174954511377e+00 2.47175e-10 7.23403e-09 3 -1.499575802919869e+00 -1.499575802945479e+00 2.56100e-11 2.04349e-09 ----------------------------------------------------------------------------------------------------- 28 Si 1 5.700764007440004e+00 5.700764007001627e+00 4.38376e-10 3.50939e-09 2 -6.291657849663430e+00 -6.291657850281235e+00 6.17805e-10 3.59904e-09 3 -8.623919022126342e+00 -8.623919022068099e+00 5.82432e-11 1.52883e-09 ----------------------------------------------------------------------------------------------------- 29 C 1 2.707359261079116e+00 2.707359260722144e+00 3.56972e-10 8.24462e-10 2 -2.950401838908046e+00 -2.950401841014026e+00 2.10598e-09 2.20749e-08 * 3 4.839386348593494e-01 4.839386353005339e-01 4.41184e-10 3.70903e-09 ----------------------------------------------------------------------------------------------------- 30 C 1 -1.713151538055215e+00 -1.713151538139388e+00 8.41729e-11 3.96034e-10 2 -5.124919022930077e-02 -5.124919025717975e-02 2.78790e-11 5.58049e-11 3 1.658493849016825e+00 1.658493849003921e+00 1.29037e-11 1.68005e-10 ----------------------------------------------------------------------------------------------------- 31 C 1 -1.252401420645508e+00 -1.252401420703525e+00 5.80174e-11 1.84305e-09 2 -2.020862995852113e+00 -2.020862996278014e+00 4.25902e-10 5.54953e-10 3 -1.585637464976328e+00 -1.585637463945575e+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 -5.838880739851000e-01 1.04858e-09 8.45068e-09 3 -3.914536239535474e+00 -3.914536239480180e+00 5.52935e-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.