!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 : MEAM_LAMMPS_JeongLee_2020_PdC__MO_068985622065_001 Supported species : C Pd 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 = 3.379122734069824 | (Configuration in file "config-C.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 C 1 1.092309830761578e+00 1.092309830772645e+00 1.10671e-11 1.10298e-10 2 1.319831826400909e+00 1.319831826394857e+00 6.05183e-12 2.10776e-10 3 1.328900853730179e+00 1.328900853719571e+00 1.06082e-11 1.02236e-10 ----------------------------------------------------------------------------------------------------- 2 C 1 1.492183345020174e-01 1.492183345100956e-01 8.07823e-12 1.67503e-10 2 1.026998445884790e-01 1.026998446215088e-01 3.30297e-11 8.04284e-11 3 -2.288644397149875e+00 -2.288644397166733e+00 1.68581e-11 1.57717e-10 ----------------------------------------------------------------------------------------------------- 3 C 1 -1.448196704790096e+00 -1.448196704773935e+00 1.61606e-11 9.36127e-11 2 -8.832314050943950e-01 -8.832314050510576e-01 4.33374e-11 2.80576e-10 3 1.658458342149162e-01 1.658458342282808e-01 1.33646e-11 1.64759e-10 ----------------------------------------------------------------------------------------------------- 4 C 1 -3.628311870237289e+00 -3.628311870186167e+00 5.11227e-11 1.41839e-10 2 -4.591922352379775e-01 -4.591922352594068e-01 2.14293e-11 3.03924e-10 3 -1.207589798044527e+00 -1.207589798060598e+00 1.60705e-11 3.75180e-10 ----------------------------------------------------------------------------------------------------- 5 C 1 6.858700793924168e-01 6.858700794102297e-01 1.78129e-11 5.88967e-10 2 -5.153106640680629e-01 -5.153106641331036e-01 6.50406e-11 5.62349e-10 3 -2.258894168046437e+00 -2.258894168016279e+00 3.01585e-11 2.56419e-10 ----------------------------------------------------------------------------------------------------- 6 C 1 2.110833937237838e-01 2.110833936347595e-01 8.90243e-11 4.30190e-10 2 -1.117054757952925e+00 -1.117054758023488e+00 7.05633e-11 2.96431e-10 3 -4.880986686415933e-01 -4.880986686293266e-01 1.22667e-11 3.30557e-10 ----------------------------------------------------------------------------------------------------- 7 C 1 3.431911963438815e-01 3.431911963110958e-01 3.27857e-11 1.02238e-10 2 -2.569399848199392e+00 -2.569399848166438e+00 3.29541e-11 1.53027e-09 3 -7.952248793086802e-01 -7.952248792880607e-01 2.06195e-11 5.75071e-10 ----------------------------------------------------------------------------------------------------- 8 C 1 5.473813321422672e-02 5.473813327558651e-02 6.13598e-11 7.50021e-09 * 2 1.563464211448300e+00 1.563464211549310e+00 1.01010e-10 3.08455e-10 3 7.934802631890240e-01 7.934802630930695e-01 9.59545e-11 4.30942e-10 ----------------------------------------------------------------------------------------------------- 9 C 1 -3.464296227710182e+00 -3.464296227698080e+00 1.21019e-11 2.41703e-10 2 -3.424179763805477e+00 -3.424179763811198e+00 5.72120e-12 1.19033e-10 3 5.112569275362000e-02 5.112569271763271e-02 3.59873e-11 3.66258e-10 ----------------------------------------------------------------------------------------------------- 10 C 1 -1.408664868571794e+00 -1.408664868549291e+00 2.25036e-11 7.12359e-11 2 7.681547630367758e+00 7.681547630379659e+00 1.19007e-11 1.52427e-10 3 -4.728738609288344e+00 -4.728738609310578e+00 2.22338e-11 1.50411e-09 ----------------------------------------------------------------------------------------------------- 11 C 1 -3.218321639478736e+00 -3.218321639504405e+00 2.56692e-11 2.67615e-10 2 -4.704251417317991e+00 -4.704251417299543e+00 1.84484e-11 4.89378e-10 3 -1.919712300068316e+00 -1.919712300006247e+00 6.20688e-11 5.26689e-10 ----------------------------------------------------------------------------------------------------- 12 C 1 -2.993055346980078e+00 -2.993055346976662e+00 3.41549e-12 3.56977e-11 2 1.325975401226325e+00 1.325975401249105e+00 2.27791e-11 6.88170e-11 3 9.093391701767757e-01 9.093391701663580e-01 1.04177e-11 4.49003e-10 ----------------------------------------------------------------------------------------------------- 13 C 1 4.590136086008497e+00 4.590136085976855e+00 3.16422e-11 5.44446e-10 2 -1.663281241978062e+00 -1.663281242013247e+00 3.51847e-11 5.20265e-09 * 3 -7.883992620333652e+00 -7.883992620280933e+00 5.27187e-11 4.94028e-10 ----------------------------------------------------------------------------------------------------- 14 C 1 1.546639148260378e+00 1.546639148284782e+00 2.44045e-11 6.16645e-11 2 1.382080238482530e-01 1.382080238557419e-01 7.48890e-12 1.17310e-10 3 -1.453227625699374e+00 -1.453227625704398e+00 5.02376e-12 2.83336e-11 ----------------------------------------------------------------------------------------------------- 15 C 1 8.683784953615403e+00 8.683784953656184e+00 4.07816e-11 4.97238e-10 2 -5.423129967584334e+00 -5.423129967568960e+00 1.53735e-11 4.54247e-10 3 -3.414020365718696e-01 -3.414020366355233e-01 6.36536e-11 4.01655e-10 ----------------------------------------------------------------------------------------------------- 16 C 1 -5.498095065224441e+00 -5.498095065213999e+00 1.04423e-11 1.79689e-10 2 1.051576874221785e+01 1.051576874230447e+01 8.66169e-11 8.10934e-10 3 6.363586992346232e+00 6.363586992311066e+00 3.51656e-11 1.09054e-10 ----------------------------------------------------------------------------------------------------- 17 C 1 -2.888011844567568e+00 -2.888011844566789e+00 7.78932e-13 3.13340e-11 2 -3.584056113560441e+00 -3.584056113557613e+00 2.82885e-12 9.98177e-10 3 -1.094685389439817e+00 -1.094685389385390e+00 5.44269e-11 1.61106e-08 * ----------------------------------------------------------------------------------------------------- 18 C 1 1.281709217754617e+00 1.281709217688285e+00 6.63318e-11 3.76281e-10 2 2.089589244584773e+00 2.089589244501123e+00 8.36495e-11 4.74874e-10 3 -1.760938972461792e+00 -1.760938972509566e+00 4.77736e-11 3.39456e-10 ----------------------------------------------------------------------------------------------------- 19 C 1 7.049561701727833e-01 7.049561700077321e-01 1.65051e-10 1.26718e-10 2 -2.849817364308621e+00 -2.849817364263389e+00 4.52327e-11 4.84579e-10 3 2.486429246392488e+00 2.486429246387602e+00 4.88631e-12 1.53013e-10 ----------------------------------------------------------------------------------------------------- 20 C 1 -2.087024485161280e+00 -2.087024485156935e+00 4.34452e-12 2.96098e-10 2 1.905507099197575e+00 1.905507099318834e+00 1.21259e-10 5.06043e-10 3 2.882481472440060e+00 2.882481472366222e+00 7.38383e-11 2.13775e-10 ----------------------------------------------------------------------------------------------------- 21 C 1 8.950419265577767e-01 8.950419265744979e-01 1.67212e-11 1.80104e-10 2 -4.380691683427155e+00 -4.380691683407482e+00 1.96723e-11 5.17538e-10 3 2.298247779319476e+00 2.298247779363214e+00 4.37388e-11 2.31991e-10 ----------------------------------------------------------------------------------------------------- 22 C 1 6.172679963637309e+00 6.172679963608412e+00 2.88969e-11 1.52662e-10 2 2.886466150278788e+00 2.886466150275025e+00 3.76277e-12 6.87407e-10 3 3.606962580263052e+00 3.606962580247948e+00 1.51039e-11 2.20433e-10 ----------------------------------------------------------------------------------------------------- 23 C 1 -1.080359095471988e+00 -1.080359095529962e+00 5.79738e-11 3.85983e-10 2 4.007065522212708e-01 4.007065522097683e-01 1.15025e-11 1.07530e-10 3 -1.587128474382808e+00 -1.587128474291059e+00 9.17488e-11 5.32274e-11 ----------------------------------------------------------------------------------------------------- 24 C 1 2.741909983231208e-01 2.741909982937534e-01 2.93674e-11 1.31372e-10 2 5.072927910943383e-01 5.072927911782834e-01 8.39451e-11 3.13842e-10 3 6.379951459816882e-01 6.379951459935250e-01 1.18369e-11 2.18723e-10 ----------------------------------------------------------------------------------------------------- 25 C 1 1.450094253463424e-01 1.450094253456682e-01 6.74155e-13 6.60135e-11 2 -1.320626123330087e+00 -1.320626123329088e+00 9.98535e-13 2.09910e-10 3 -1.732980176939414e+00 -1.732980176938620e+00 7.93365e-13 5.46104e-10 ----------------------------------------------------------------------------------------------------- 26 C 1 1.970944217322042e+00 1.970944217281858e+00 4.01847e-11 1.21971e-09 2 2.387488411099212e+00 2.387488411103014e+00 3.80140e-12 2.64180e-11 3 -2.776032599080335e+00 -2.776032599064033e+00 1.63025e-11 2.45414e-10 ----------------------------------------------------------------------------------------------------- 27 C 1 -4.445179751047403e+00 -4.445179751067006e+00 1.96030e-11 1.56406e-09 * 2 7.159566356237588e-01 7.159566356464282e-01 2.26694e-11 9.51292e-10 3 2.367241190755745e+00 2.367241190760276e+00 4.53015e-12 3.32430e-10 ----------------------------------------------------------------------------------------------------- 28 C 1 -2.436705572942337e+00 -2.436705573030499e+00 8.81624e-11 1.26393e-10 2 2.496988806146537e-01 2.496988806094667e-01 5.18702e-12 2.10273e-10 3 4.099964366343430e+00 4.099964366290187e+00 5.32427e-11 3.70686e-10 ----------------------------------------------------------------------------------------------------- 29 C 1 9.263003963243019e-02 9.263003968184505e-02 4.94149e-11 1.17569e-09 2 -3.175489440176560e+00 -3.175489440171847e+00 4.71356e-12 2.00833e-09 * 3 3.241923769180135e-01 3.241923769098065e-01 8.20699e-12 3.45514e-10 ----------------------------------------------------------------------------------------------------- 30 C 1 3.282266697808694e+00 3.282266697752147e+00 5.65472e-11 1.12901e-10 2 -5.810755344810068e-01 -5.810755344923734e-01 1.13666e-11 5.22742e-11 3 -2.973366236360493e-01 -2.973366236352746e-01 7.74658e-13 1.82283e-10 ----------------------------------------------------------------------------------------------------- 31 C 1 2.882510236076805e-01 2.882510236022719e-01 5.40856e-12 6.55556e-10 2 9.345825319623818e-01 9.345825319613036e-01 1.07825e-12 4.48782e-09 * 3 -5.600674464499613e-01 -5.600674464603419e-01 1.03806e-11 3.90944e-10 ----------------------------------------------------------------------------------------------------- 32 C 1 2.131571636198211e+00 2.131571636210841e+00 1.26308e-11 3.88594e-10 2 1.926003583747859e+00 1.926003583730776e+00 1.70830e-11 9.28619e-11 3 4.858901820718145e+00 4.858901820720084e+00 1.93889e-12 4.82893e-10 ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as discontinuities. Maximum error obtained for particle = 9, direction = 3: |F_model - F_numer| error = ----------------------- = 7.03898e-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. MONOATOMIC STRUCTURE -- Species = Pd | a0 = 3.889087677001953 | (Configuration in file "config-Pd.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Pd 1 1.020375888998226e+00 1.020375888991899e+00 6.32694e-12 1.08361e-10 2 7.112934708439705e-01 7.112934708455539e-01 1.58340e-12 5.37952e-11 3 9.536810698091642e-01 9.536810698181067e-01 8.94251e-12 7.83814e-11 ----------------------------------------------------------------------------------------------------- 2 Pd 1 -5.967062843059638e-01 -5.967062842806413e-01 2.53225e-11 4.95276e-11 2 -3.488388354551437e-01 -3.488388354688121e-01 1.36684e-11 1.46655e-11 3 8.224918960537896e-01 8.224918960251330e-01 2.86566e-11 1.43127e-10 ----------------------------------------------------------------------------------------------------- 3 Pd 1 -1.205742646838988e-01 -1.205742646659828e-01 1.79160e-11 1.59709e-10 2 9.852512107081168e-01 9.852512106815839e-01 2.65329e-11 2.48266e-10 3 7.443142490103483e-02 7.443142490219212e-02 1.15730e-12 9.85952e-11 ----------------------------------------------------------------------------------------------------- 4 Pd 1 7.630213788353342e-01 7.630213788247684e-01 1.05658e-11 8.67815e-11 2 -7.249470567748914e-01 -7.249470568330804e-01 5.81890e-11 1.84286e-10 3 8.900213743050112e-03 8.900213786946968e-03 4.38969e-11 1.60317e-10 ----------------------------------------------------------------------------------------------------- 5 Pd 1 -4.986705323313650e+00 -4.986705323326200e+00 1.25500e-11 1.25298e-10 2 2.788432954946788e-01 2.788432955151215e-01 2.04428e-11 3.63151e-11 3 -3.968656465444207e+00 -3.968656465448228e+00 4.02034e-12 1.30793e-10 ----------------------------------------------------------------------------------------------------- 6 Pd 1 2.085534726059986e+00 2.085534726081771e+00 2.17852e-11 3.38315e-10 2 -3.300088560581102e+00 -3.300088560624028e+00 4.29257e-11 2.05171e-10 3 2.351933619211747e-01 2.351933619181411e-01 3.03360e-12 1.32219e-09 * ----------------------------------------------------------------------------------------------------- 7 Pd 1 4.551985321063414e+00 4.551985321035839e+00 2.75753e-11 5.10453e-09 * 2 1.093070092615015e+00 1.093070092599573e+00 1.54419e-11 5.79286e-11 3 5.139192883320702e+00 5.139192883287097e+00 3.36051e-11 8.22303e-09 * ----------------------------------------------------------------------------------------------------- 8 Pd 1 1.576359332709979e+00 1.576359332709232e+00 7.47402e-13 4.67288e-11 2 -3.156533513842416e+00 -3.156533513833471e+00 8.94440e-12 7.01399e-10 3 -3.810153271313307e+00 -3.810153271337053e+00 2.37468e-11 1.27061e-10 ----------------------------------------------------------------------------------------------------- 9 Pd 1 1.227891356680826e+00 1.227891356687320e+00 6.49347e-12 1.15126e-10 2 3.099199124091758e-01 3.099199124046010e-01 4.57478e-12 1.66449e-11 3 8.279607753745756e-01 8.279607753952236e-01 2.06480e-11 5.71369e-11 ----------------------------------------------------------------------------------------------------- 10 Pd 1 3.117320995277617e-03 3.117320996038510e-03 7.60893e-13 6.31709e-10 2 -1.601727605995171e+00 -1.601727606001272e+00 6.10134e-12 1.09205e-10 3 8.104665674079830e-01 8.104665674090383e-01 1.05538e-12 8.58487e-11 ----------------------------------------------------------------------------------------------------- 11 Pd 1 -2.852101169312235e+00 -2.852101169233038e+00 7.91971e-11 4.55243e-10 2 3.719052197847839e-03 3.719052181860555e-03 1.59873e-11 5.31242e-11 3 -7.657681639836671e-01 -7.657681639604259e-01 2.32412e-11 8.63875e-10 ----------------------------------------------------------------------------------------------------- 12 Pd 1 5.854186361200180e-01 5.854186361289266e-01 8.90865e-12 1.50658e-10 2 -7.765792660932744e-01 -7.765792660882822e-01 4.99223e-12 1.45697e-10 3 -2.693482580794651e-01 -2.693482580460266e-01 3.34385e-11 7.11575e-11 ----------------------------------------------------------------------------------------------------- 13 Pd 1 -3.576517063605802e+00 -3.576517063646967e+00 4.11644e-11 9.78950e-11 2 2.968238693104468e+00 2.968238693144087e+00 3.96190e-11 2.43385e-10 3 -5.729614795120550e-01 -5.729614795215583e-01 9.50329e-12 1.47431e-08 * ----------------------------------------------------------------------------------------------------- 14 Pd 1 -1.292596914632911e+00 -1.292596914653400e+00 2.04885e-11 1.43557e-10 2 -3.653973171125955e-01 -3.653973170856095e-01 2.69860e-11 6.61065e-11 3 1.226524280207688e+00 1.226524280217862e+00 1.01739e-11 8.02247e-11 ----------------------------------------------------------------------------------------------------- 15 Pd 1 4.047688359958697e-01 4.047688360187323e-01 2.28625e-11 1.05544e-10 2 2.000624542206621e-01 2.000624542021236e-01 1.85385e-11 7.34319e-11 3 -1.137052142877192e+00 -1.137052142951906e+00 7.47142e-11 9.41091e-10 ----------------------------------------------------------------------------------------------------- 16 Pd 1 2.020698149688233e+00 2.020698149725879e+00 3.76459e-11 1.77519e-10 2 1.340036918528615e+00 1.340036918522234e+00 6.38112e-12 1.36408e-10 3 8.906140858712349e-01 8.906140858816680e-01 1.04331e-11 2.29635e-10 ----------------------------------------------------------------------------------------------------- 17 Pd 1 8.393182430972187e-01 8.393182430695353e-01 2.76834e-11 5.93728e-10 2 8.554380449356911e-01 8.554380449187133e-01 1.69778e-11 1.25900e-10 3 -1.297953729110115e-01 -1.297953729832957e-01 7.22842e-11 2.20367e-10 ----------------------------------------------------------------------------------------------------- 18 Pd 1 -3.036910649786084e+00 -3.036910649796324e+00 1.02403e-11 1.73953e-10 2 1.512388518414359e+00 1.512388518411281e+00 3.07776e-12 1.24886e-10 3 -1.271986798097760e+00 -1.271986798102942e+00 5.18208e-12 2.34914e-10 ----------------------------------------------------------------------------------------------------- 19 Pd 1 -2.975109405225704e+00 -2.975109405252351e+00 2.66471e-11 1.93424e-10 2 -3.176007761117679e+00 -3.176007761124517e+00 6.83853e-12 9.08122e-11 3 7.230009060618823e-01 7.230009060490397e-01 1.28426e-11 8.33621e-11 ----------------------------------------------------------------------------------------------------- 20 Pd 1 8.044262372945704e-01 8.044262372770166e-01 1.75538e-11 7.84280e-11 2 1.227558673947698e-01 1.227558673744776e-01 2.02921e-11 1.89401e-09 * 3 -4.801710727102744e-01 -4.801710727290657e-01 1.87912e-11 3.09955e-10 ----------------------------------------------------------------------------------------------------- 21 Pd 1 -1.799067170031781e+00 -1.799067170054890e+00 2.31088e-11 1.23379e-10 2 -3.297478764886163e+00 -3.297478764866103e+00 2.00604e-11 1.41733e-10 3 -1.871451644672190e+00 -1.871451644669791e+00 2.39875e-12 4.82431e-09 * ----------------------------------------------------------------------------------------------------- 22 Pd 1 4.398199673796460e+00 4.398199673844708e+00 4.82476e-11 4.88225e-10 2 2.331330809156130e+00 2.331330809148561e+00 7.56817e-12 2.74633e-10 3 -4.079592746247881e+00 -4.079592746231833e+00 1.60485e-11 2.20616e-10 ----------------------------------------------------------------------------------------------------- 23 Pd 1 -5.924567314750206e-01 -5.924567314845751e-01 9.55447e-12 1.69238e-10 2 -5.886046814148593e-01 -5.886046814063935e-01 8.46578e-12 1.05941e-10 3 1.076394893212113e+00 1.076394893222762e+00 1.06493e-11 5.31773e-10 ----------------------------------------------------------------------------------------------------- 24 Pd 1 1.580810885422407e+00 1.580810885425338e+00 2.93121e-12 1.99275e-10 2 4.607183160817904e+00 4.607183160815952e+00 1.95222e-12 2.49298e-10 3 5.116558059448624e+00 5.116558059461082e+00 1.24576e-11 3.16938e-09 * ----------------------------------------------------------------------------------------------------- 25 Pd 1 -2.671328477500001e-01 -2.671328477459799e-01 4.02023e-12 6.96151e-10 2 -6.389564301336171e-01 -6.389564300709671e-01 6.26500e-11 3.59532e-10 3 -1.536514020618650e+00 -1.536514020667336e+00 4.86862e-11 1.05012e-10 ----------------------------------------------------------------------------------------------------- 26 Pd 1 1.960300761346650e-01 1.960300761298220e-01 4.84301e-12 4.60023e-10 2 -1.871133766474777e-02 -1.871133764386649e-02 2.08813e-11 4.96552e-09 * 3 -5.456546601067552e-01 -5.456546600601336e-01 4.66216e-11 2.10764e-09 * ----------------------------------------------------------------------------------------------------- 27 Pd 1 -8.859478118988120e-01 -8.859478118689219e-01 2.98901e-11 5.84116e-10 2 -2.300757489732926e+00 -2.300757489737484e+00 4.55769e-12 1.20435e-08 * 3 3.959044757276017e-01 3.959044757111649e-01 1.64367e-11 1.21102e-09 * ----------------------------------------------------------------------------------------------------- 28 Pd 1 2.600790808636931e-01 2.600790808704067e-01 6.71363e-12 1.65075e-10 2 2.107409862023993e-01 2.107409862074432e-01 5.04397e-12 1.20844e-10 3 2.153066520328286e-01 2.153066520174277e-01 1.54008e-11 3.77781e-10 ----------------------------------------------------------------------------------------------------- 29 Pd 1 1.258936762733916e-01 1.258936762249190e-01 4.84726e-11 2.38286e-10 2 1.981434849532913e+00 1.981434849505329e+00 2.75839e-11 4.45626e-10 3 2.463135962604272e+00 2.463135962700907e+00 9.66351e-11 2.39422e-10 ----------------------------------------------------------------------------------------------------- 30 Pd 1 -6.652132146670524e-01 -6.652132146712905e-01 4.23805e-12 4.64416e-11 2 -2.210643215027425e-01 -2.210643215094553e-01 6.71282e-12 1.94780e-10 3 4.084401445975934e-01 4.084401446124191e-01 1.48256e-11 2.30885e-10 ----------------------------------------------------------------------------------------------------- 31 Pd 1 -7.828214404739937e-01 -7.828214404926950e-01 1.87013e-11 6.39876e-11 2 6.145848406469978e-03 6.145848399460732e-03 7.00925e-12 1.49870e-10 3 -4.062259965274502e-01 -4.062259965467357e-01 1.92855e-11 1.54127e-10 ----------------------------------------------------------------------------------------------------- 32 Pd 1 1.985931471133340e+00 1.985931471136229e+00 2.88924e-12 9.44209e-11 2 9.978397573241471e-01 9.978397572855344e-01 3.86127e-11 1.19061e-10 3 -5.428655591934440e-01 -5.428655592065843e-01 1.31403e-11 6.61088e-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 = 4, direction = 3: |F_model - F_numer| error = ----------------------- = 4.93211e-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 = C Pd | a0 = 3.669341514229472 | (Configuration in file "config-CPd.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 C 1 9.373187428342671e-01 9.373187428487819e-01 1.45148e-11 1.37165e-11 2 7.678307499248533e-01 7.678307499246219e-01 2.31482e-13 2.64781e-10 3 8.785146910647738e-01 8.785146910594369e-01 5.33684e-12 4.24626e-11 ----------------------------------------------------------------------------------------------------- 2 Pd 1 -6.375085343155209e-01 -6.375085343384475e-01 2.29265e-11 6.57786e-11 2 -2.895603105122999e+00 -2.895603105078491e+00 4.45080e-11 4.35096e-11 3 -2.896306280373283e-01 -2.896306280282462e-01 9.08201e-12 3.03437e-10 ----------------------------------------------------------------------------------------------------- 3 Pd 1 -3.580467719559798e+00 -3.580467719613283e+00 5.34857e-11 1.75620e-10 2 4.575463112956828e-01 4.575463112815156e-01 1.41672e-11 4.70481e-10 3 -6.224329093750716e-01 -6.224329093132769e-01 6.17947e-11 1.41589e-10 ----------------------------------------------------------------------------------------------------- 4 C 1 1.749030410910865e-01 1.749030411098377e-01 1.87512e-11 8.86177e-11 2 5.391824545475310e-01 5.391824545430810e-01 4.45000e-12 1.51588e-10 3 -2.625806212491734e+00 -2.625806212471279e+00 2.04552e-11 6.19136e-11 ----------------------------------------------------------------------------------------------------- 5 C 1 -2.320648499034568e+00 -2.320648499021470e+00 1.30975e-11 9.99925e-11 2 8.734846393300478e-01 8.734846393521095e-01 2.20617e-11 4.70566e-11 3 -7.474205486023479e-01 -7.474205485992563e-01 3.09153e-12 4.73075e-11 ----------------------------------------------------------------------------------------------------- 6 C 1 -2.654748052279718e-01 -2.654748052464408e-01 1.84690e-11 8.03163e-11 2 9.880340205752943e-01 9.880340205789558e-01 3.66152e-12 1.56192e-10 3 -4.787733617944536e-01 -4.787733617899939e-01 4.45965e-12 4.21553e-10 ----------------------------------------------------------------------------------------------------- 7 C 1 -1.037225566505761e+00 -1.037225566508327e+00 2.56573e-12 5.89730e-10 2 -8.431848378685197e-02 -8.431848378497643e-02 1.87554e-12 1.44465e-10 3 2.534194055215570e+00 2.534194055183594e+00 3.19753e-11 1.20353e-10 ----------------------------------------------------------------------------------------------------- 8 Pd 1 -7.232883252383856e+00 -7.232883252438785e+00 5.49285e-11 1.04265e-10 2 -1.012073556716679e+00 -1.012073556753644e+00 3.69647e-11 7.61172e-10 3 -7.523259712574864e+00 -7.523259712506518e+00 6.83462e-11 8.66257e-10 ----------------------------------------------------------------------------------------------------- 9 Pd 1 -3.435926402559185e+00 -3.435926402570412e+00 1.12275e-11 1.01000e-10 2 -7.882671555930212e+00 -7.882671555977962e+00 4.77494e-11 1.83072e-10 3 -4.364972286672235e+00 -4.364972286687319e+00 1.50839e-11 3.73956e-10 ----------------------------------------------------------------------------------------------------- 10 C 1 3.294353923618555e+00 3.294353923568953e+00 4.96025e-11 1.90163e-10 2 1.231116824492396e+00 1.231116824452368e+00 4.00284e-11 2.96167e-10 3 -6.681065486960731e-01 -6.681065486683530e-01 2.77202e-11 2.42303e-10 ----------------------------------------------------------------------------------------------------- 11 Pd 1 1.639269495944487e+00 1.639269495980462e+00 3.59750e-11 1.87720e-09 * 2 -2.550394377028975e+00 -2.550394376906710e+00 1.22265e-10 1.47574e-09 * 3 7.384938029567458e-01 7.384938030399316e-01 8.31858e-11 9.55000e-10 ----------------------------------------------------------------------------------------------------- 12 Pd 1 -3.309088295114469e+00 -3.309088295152221e+00 3.77516e-11 2.89052e-10 2 5.020968803484729e+00 5.020968803405003e+00 7.97264e-11 4.10089e-10 3 2.569239178026231e+00 2.569239178063305e+00 3.70743e-11 3.24035e-10 ----------------------------------------------------------------------------------------------------- 13 Pd 1 8.554311857465475e-01 8.554311857896543e-01 4.31067e-11 4.53860e-10 2 3.410764293914401e+00 3.410764293912545e+00 1.85540e-12 2.93696e-10 3 -2.173584662417472e+00 -2.173584662436208e+00 1.87361e-11 1.77240e-09 * ----------------------------------------------------------------------------------------------------- 14 Pd 1 -2.539564590955766e+00 -2.539564590860127e+00 9.56386e-11 1.44771e-10 2 -1.534723340914010e+00 -1.534723340847305e+00 6.67049e-11 3.13545e-10 3 -4.863336377365126e-01 -4.863336377070023e-01 2.95103e-11 6.32913e-11 ----------------------------------------------------------------------------------------------------- 15 C 1 3.428163337839647e+00 3.428163337893613e+00 5.39662e-11 1.26050e-10 2 -1.611850490740814e+00 -1.611850490705287e+00 3.55265e-11 1.83362e-10 3 4.589269303054151e-01 4.589269302895589e-01 1.58562e-11 1.34082e-10 ----------------------------------------------------------------------------------------------------- 16 C 1 -9.629302413539728e-01 -9.629302413498730e-01 4.09972e-12 6.34709e-10 2 1.604833774905992e+00 1.604833774903242e+00 2.74958e-12 1.15639e-10 3 1.927772754270588e+00 1.927772754330095e+00 5.95066e-11 1.23213e-09 ----------------------------------------------------------------------------------------------------- 17 C 1 1.608202329278602e+00 1.608202329310748e+00 3.21467e-11 1.99235e-10 2 -8.351622749978774e-01 -8.351622749638277e-01 3.40498e-11 8.36182e-11 3 1.525513476187226e+00 1.525513476155621e+00 3.16052e-11 3.16431e-11 ----------------------------------------------------------------------------------------------------- 18 C 1 5.087555228112421e-01 5.087555226645283e-01 1.46714e-10 5.18606e-10 2 7.211434322425329e-01 7.211434322376548e-01 4.87810e-12 9.10222e-11 3 -2.670392337615584e+00 -2.670392337520656e+00 9.49276e-11 8.14354e-10 ----------------------------------------------------------------------------------------------------- 19 Pd 1 -9.271080996701976e-01 -9.271080996619375e-01 8.26006e-12 1.21231e-10 2 1.688476800691088e-01 1.688476800226844e-01 4.64244e-11 3.47558e-10 3 -6.836061580708508e-01 -6.836061580380980e-01 3.27528e-11 9.44801e-10 ----------------------------------------------------------------------------------------------------- 20 Pd 1 9.982213259693088e-01 9.982213259738721e-01 4.56335e-12 3.99821e-10 2 -3.283489336150041e-01 -3.283489336391338e-01 2.41296e-11 2.32257e-10 3 -7.617325606642976e-01 -7.617325606467386e-01 1.75591e-11 2.86019e-10 ----------------------------------------------------------------------------------------------------- 21 Pd 1 3.859284303287591e+00 3.859284303237167e+00 5.04237e-11 4.01321e-10 2 3.758574149019930e-01 3.758574148903923e-01 1.16007e-11 1.26784e-10 3 9.604259518445475e-01 9.604259518288528e-01 1.56947e-11 2.49549e-09 * ----------------------------------------------------------------------------------------------------- 22 Pd 1 1.111277267125739e+01 1.111277267130869e+01 5.12976e-11 2.97461e-09 * 2 -3.379864704005255e+00 -3.379864704077491e+00 7.22364e-11 2.68347e-10 3 9.932666187314096e+00 9.932666187467458e+00 1.53362e-10 1.99916e-09 * ----------------------------------------------------------------------------------------------------- 23 C 1 -9.384786908139160e-01 -9.384786908073297e-01 6.58629e-12 6.65323e-11 2 3.669198591723847e-01 3.669198591729235e-01 5.38736e-13 3.03918e-10 3 -1.202003989106739e+00 -1.202003989105140e+00 1.59983e-12 2.65452e-11 ----------------------------------------------------------------------------------------------------- 24 C 1 1.422201775815447e-01 1.422201776221793e-01 4.06346e-11 3.17749e-11 2 -1.149653602157974e+00 -1.149653602285114e+00 1.27140e-10 3.04417e-10 3 -5.539009762271248e-01 -5.539009764336342e-01 2.06509e-10 7.77520e-10 ----------------------------------------------------------------------------------------------------- 25 C 1 -1.393029328080309e-01 -1.393029327235247e-01 8.45062e-11 3.43628e-10 2 1.514243218384046e+00 1.514243218350977e+00 3.30693e-11 9.45328e-10 3 -3.594362718328666e-01 -3.594362718017062e-01 3.11604e-11 2.93462e-10 ----------------------------------------------------------------------------------------------------- 26 Pd 1 -3.826309068205853e-01 -3.826309068046830e-01 1.59023e-11 5.68062e-11 2 1.689536617635533e+00 1.689536617712351e+00 7.68177e-11 7.48883e-11 3 4.670974431623135e+00 4.670974431781033e+00 1.57899e-10 1.28161e-09 ----------------------------------------------------------------------------------------------------- 27 C 1 -1.450604129993883e+00 -1.450604130073618e+00 7.97349e-11 2.94972e-10 2 1.476281872121258e+00 1.476281871993485e+00 1.27773e-10 3.67908e-10 3 7.572911123584021e-01 7.572911124356494e-01 7.72473e-11 3.79009e-10 ----------------------------------------------------------------------------------------------------- 28 Pd 1 2.047777649955543e+00 2.047777649970731e+00 1.51883e-11 2.16479e-10 2 -9.445638879952154e-01 -9.445638879971272e-01 1.91180e-12 1.74373e-10 3 -1.809877848267891e+00 -1.809877848266878e+00 1.01341e-12 1.30977e-10 ----------------------------------------------------------------------------------------------------- 29 Pd 1 -3.359001721596019e+00 -3.359001721619998e+00 2.39786e-11 1.67843e-09 * 2 -2.625101544800884e-01 -2.625101544860774e-01 5.98899e-12 2.14616e-10 3 -2.119597580845679e+00 -2.119597580932890e+00 8.72116e-11 1.09386e-10 ----------------------------------------------------------------------------------------------------- 30 Pd 1 -7.548615059604187e-02 -7.548615059637605e-02 3.34177e-13 2.05204e-09 * 2 4.595759823121642e-01 4.595759823234594e-01 1.12952e-11 3.04627e-10 3 2.544696670606569e-01 2.544696670997310e-01 3.90741e-11 3.67956e-10 ----------------------------------------------------------------------------------------------------- 31 C 1 3.896119327991126e+00 3.896119327965208e+00 2.59175e-11 6.27018e-11 2 -1.524023451171871e+00 -1.524023451143248e+00 2.86224e-11 5.22076e-11 3 2.741377942269195e-01 2.741377942273067e-01 3.87190e-13 5.56321e-11 ----------------------------------------------------------------------------------------------------- 32 C 1 -1.908462495897393e+00 -1.908462495910646e+00 1.32527e-11 5.74362e-10 2 4.329593969353871e+00 4.329593969370733e+00 1.68621e-11 1.02634e-10 3 2.658248198574818e+00 2.658248198578328e+00 3.51008e-12 3.64779e-10 ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as discontinuities. Maximum error obtained for particle = 25, direction = 1: |F_model - F_numer| error = ----------------------- = 6.06636e-10 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 4.93211e-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 4.93211e-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.