!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! VERIFICATION CHECK: vc-forces-numerical-derivative !!!!! !!!!! !!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Description: Comparison of the analytical forces obtained from the model with forces computed by numerical differentiation using Richardson extrapolation for a randomly distorted non-periodic structure based off the equilibrium face-centered cubic (fcc) structure. Separate configurations are tested for each species supported by the model, as well as one containing a random distribution of all species. Configurations used for testing are provided as auxiliary files. Author: Ellad Tadmor ----------------------------------------------------------------------------------------------------- Results for KIM Model : EAM_Mendelev_2019_CuZr__MO_945018740343_000 Supported species : Cu Zr 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 = Cu | a0 = 3.6406450271606445 | (Configuration in file "config-Cu.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Cu 1 2.836172623072608e-01 2.836172624450140e-01 1.37753e-10 1.07129e-09 2 7.736474892253720e-02 7.736474848337382e-02 4.39163e-10 7.02291e-10 3 -1.545069045800876e-01 -1.545069046969465e-01 1.16859e-10 5.55250e-10 ----------------------------------------------------------------------------------------------------- 2 Cu 1 -4.440734253536964e-01 -4.440734255644085e-01 2.10712e-10 1.86345e-09 2 8.949587815560771e-01 8.949587813857187e-01 1.70358e-10 1.05265e-09 3 9.839772077872021e-01 9.839772078096932e-01 2.24911e-11 1.15611e-09 ----------------------------------------------------------------------------------------------------- 3 Cu 1 4.147344082976602e-01 4.147344079495292e-01 3.48131e-10 2.19315e-09 2 6.588383927004241e-01 6.588383925239433e-01 1.76481e-10 3.30112e-09 3 4.408591335931607e-01 4.408591334579373e-01 1.35223e-10 1.29944e-09 ----------------------------------------------------------------------------------------------------- 4 Cu 1 9.507656686189818e-01 9.507656677567039e-01 8.62278e-10 4.10684e-09 2 5.297719836040682e-01 5.297719842564449e-01 6.52377e-10 4.61800e-10 3 2.563702331782377e-01 2.563702332138595e-01 3.56218e-11 1.69767e-09 ----------------------------------------------------------------------------------------------------- 5 Cu 1 4.042506252121071e-01 4.042506256434092e-01 4.31302e-10 2.60102e-10 2 2.340903276810453e-01 2.340903275005136e-01 1.80532e-10 4.23561e-09 3 3.560252982447342e-01 3.560252985274719e-01 2.82738e-10 1.68242e-09 ----------------------------------------------------------------------------------------------------- 6 Cu 1 -9.111225451957308e-01 -9.111225452388607e-01 4.31299e-11 1.95774e-08 * 2 6.554196655256900e-01 6.554196655922437e-01 6.65538e-11 1.07325e-10 3 9.075642062989129e-01 9.075642062002796e-01 9.86333e-11 9.23505e-10 ----------------------------------------------------------------------------------------------------- 7 Cu 1 3.186598492161783e-01 3.186598493655739e-01 1.49396e-10 5.41120e-10 2 -8.188296563484875e-01 -8.188296539438679e-01 2.40462e-09 8.55864e-09 3 -1.021854779957576e+00 -1.021854781637102e+00 1.67953e-09 9.39744e-10 ----------------------------------------------------------------------------------------------------- 8 Cu 1 -1.261718374955839e+00 -1.261718375416229e+00 4.60391e-10 3.79082e-09 2 -1.308948699876809e+00 -1.308948700051637e+00 1.74828e-10 1.14021e-08 3 -6.428642847297401e-01 -6.428642850511420e-01 3.21402e-10 6.22529e-09 ----------------------------------------------------------------------------------------------------- 9 Cu 1 2.174947855179587e-01 2.174947859649724e-01 4.47014e-10 9.88557e-10 2 -1.096584573332108e+00 -1.096584573652316e+00 3.20207e-10 3.46244e-09 3 -1.002747226898302e-01 -1.002747228303045e-01 1.40474e-10 1.07130e-09 ----------------------------------------------------------------------------------------------------- 10 Cu 1 -3.430119263442643e-01 -3.430119265827962e-01 2.38532e-10 1.46934e-09 2 3.867597305376756e-01 3.867597309645440e-01 4.26868e-10 1.94883e-09 3 -4.956232706843994e-01 -4.956232703051210e-01 3.79278e-10 1.34168e-09 ----------------------------------------------------------------------------------------------------- 11 Cu 1 -2.055607231831814e-01 -2.055607229408685e-01 2.42313e-10 1.79872e-08 * 2 -9.847775217848461e-01 -9.847775212603781e-01 5.24468e-10 2.10411e-09 3 2.131261484101886e-01 2.131261486394754e-01 2.29287e-10 2.27942e-09 ----------------------------------------------------------------------------------------------------- 12 Cu 1 3.074953310920680e-01 3.074953312412760e-01 1.49208e-10 4.12302e-10 2 4.405221245051935e-01 4.405221246431975e-01 1.38004e-10 4.99403e-10 3 3.876334960454280e-01 3.876334959654348e-01 7.99932e-11 2.00325e-09 ----------------------------------------------------------------------------------------------------- 13 Cu 1 -6.619214155705870e-01 -6.619214154354557e-01 1.35131e-10 5.71059e-10 2 -1.429010458886056e+00 -1.429010458274391e+00 6.11665e-10 1.46666e-09 3 -1.302664765089679e+00 -1.302664764868356e+00 2.21323e-10 3.55639e-09 ----------------------------------------------------------------------------------------------------- 14 Cu 1 -3.339515748068032e-02 -3.339515745974981e-02 2.09305e-11 3.44283e-09 2 4.894942127767209e-01 4.894942126940071e-01 8.27139e-11 4.72863e-10 3 6.082177611148627e-02 6.082177595008879e-02 1.61397e-10 7.14841e-10 ----------------------------------------------------------------------------------------------------- 15 Cu 1 1.358567209243458e+00 1.358567210113850e+00 8.70393e-10 2.19730e-09 2 -1.169251350408604e+00 -1.169251349870875e+00 5.37729e-10 1.01455e-09 3 3.530261507893655e-01 3.530261509630659e-01 1.73700e-10 3.69142e-09 ----------------------------------------------------------------------------------------------------- 16 Cu 1 8.280431525799975e-01 8.280431536394709e-01 1.05947e-09 1.16977e-09 2 1.003318208964043e+00 1.003318208891966e+00 7.20770e-11 8.80989e-09 3 6.684302204610979e-01 6.684302201688831e-01 2.92215e-10 1.51548e-09 ----------------------------------------------------------------------------------------------------- 17 Cu 1 -7.685087344990542e-01 -7.685087344660911e-01 3.29631e-11 1.72227e-09 2 -1.611159617917725e-01 -1.611159614187395e-01 3.73033e-10 4.15005e-10 3 -7.424056305239549e-01 -7.424056305105285e-01 1.34264e-11 3.30076e-09 ----------------------------------------------------------------------------------------------------- 18 Cu 1 1.333015216574745e+00 1.333015218141203e+00 1.56646e-09 2.20632e-09 2 1.088983544580810e+00 1.088983544455943e+00 1.24866e-10 4.20421e-09 3 2.325193582385436e-01 2.325193584830842e-01 2.44541e-10 9.10424e-10 ----------------------------------------------------------------------------------------------------- 19 Cu 1 6.644208994377669e-01 6.644208993399919e-01 9.77750e-11 1.18727e-09 2 1.728764119081427e-01 1.728764119171572e-01 9.01451e-12 3.40667e-09 3 5.633050549761116e-02 5.633050587589906e-02 3.78288e-10 8.06221e-10 ----------------------------------------------------------------------------------------------------- 20 Cu 1 7.272824529520935e-01 7.272824537695122e-01 8.17419e-10 1.30605e-09 2 7.019126198437958e-01 7.019126198752120e-01 3.14162e-11 1.57890e-09 3 -4.869407590393485e-01 -4.869407593805108e-01 3.41162e-10 3.61043e-10 ----------------------------------------------------------------------------------------------------- 21 Cu 1 -1.247039896890695e+00 -1.247039897368874e+00 4.78179e-10 1.81671e-09 2 5.891303637025738e-01 5.891303639504784e-01 2.47905e-10 1.10203e-09 3 2.689884855978878e-01 2.689884859523882e-01 3.54500e-10 7.99720e-09 ----------------------------------------------------------------------------------------------------- 22 Cu 1 -2.216068107396286e-01 -2.216068105833355e-01 1.56293e-10 4.11747e-09 2 1.571439242130015e+00 1.571439241769883e+00 3.60133e-10 3.99491e-09 3 1.038154625350035e+00 1.038154625407525e+00 5.74907e-11 1.71865e-09 ----------------------------------------------------------------------------------------------------- 23 Cu 1 -5.700624947321855e-01 -5.700624946123624e-01 1.19823e-10 8.78051e-10 2 5.072043390964799e-01 5.072043395462699e-01 4.49790e-10 2.21878e-09 3 -3.907186647596617e-01 -3.907186647160053e-01 4.36564e-11 5.01374e-10 ----------------------------------------------------------------------------------------------------- 24 Cu 1 3.235610676814051e-01 3.235610678917160e-01 2.10311e-10 3.41659e-10 2 3.379764909944857e-01 3.379764910266003e-01 3.21146e-11 8.70706e-09 3 -1.210417389031002e+00 -1.210417389008519e+00 2.24825e-11 1.45992e-09 ----------------------------------------------------------------------------------------------------- 25 Cu 1 -3.350356481948881e-01 -3.350356483348231e-01 1.39935e-10 6.48823e-09 2 -8.882796903818638e-01 -8.882796902643987e-01 1.17465e-10 5.84595e-10 3 5.086233030287099e-01 5.086233030767621e-01 4.80521e-11 4.87671e-10 ----------------------------------------------------------------------------------------------------- 26 Cu 1 -1.062561991714014e+00 -1.062561991594527e+00 1.19487e-10 7.35825e-10 2 4.375425343808017e-01 4.375425342030465e-01 1.77755e-10 1.33290e-09 3 -1.074492467492860e+00 -1.074492467980942e+00 4.88081e-10 2.23181e-09 ----------------------------------------------------------------------------------------------------- 27 Cu 1 5.600819404703363e-01 5.600819405497747e-01 7.94383e-11 1.09204e-08 2 -1.995301856264609e+00 -1.995301856020371e+00 2.44238e-10 3.55007e-09 3 -1.781822198413235e-01 -1.781822200027966e-01 1.61473e-10 5.76212e-10 ----------------------------------------------------------------------------------------------------- 28 Cu 1 -2.679678906626148e-01 -2.679678903714380e-01 2.91177e-10 1.15339e-09 2 4.348053398153584e-01 4.348053390503305e-01 7.65028e-10 5.13009e-10 3 -2.685884362879069e-01 -2.685884365517364e-01 2.63829e-10 2.94074e-09 ----------------------------------------------------------------------------------------------------- 29 Cu 1 -9.825077621304658e-01 -9.825077628034653e-01 6.73000e-10 1.01926e-09 2 -1.400190489060105e+00 -1.400190488392339e+00 6.67766e-10 1.34418e-10 3 4.570248252099912e-01 4.570248284495117e-01 3.23952e-09 7.68965e-09 ----------------------------------------------------------------------------------------------------- 30 Cu 1 -2.729903163189018e-01 -2.729903163280298e-01 9.12803e-12 8.37374e-10 2 8.336304253438875e-01 8.336304252763281e-01 6.75594e-11 4.55642e-09 3 -1.988436384347825e-01 -1.988436383481534e-01 8.66291e-11 7.31440e-10 ----------------------------------------------------------------------------------------------------- 31 Cu 1 2.701212155306156e-01 2.701212166084928e-01 1.07788e-09 5.32419e-09 2 -1.332158716171961e+00 -1.332158715287731e+00 8.84231e-10 2.77363e-09 3 4.920189637351892e-01 4.920189638442165e-01 1.09027e-10 1.21879e-08 * ----------------------------------------------------------------------------------------------------- 32 Cu 1 6.269740292337951e-01 6.269740281782229e-01 1.05557e-09 2.65223e-09 2 5.384094857373980e-01 5.384094856685944e-01 6.88036e-11 4.10122e-09 3 5.868839955643711e-01 5.868839957420809e-01 1.77710e-10 3.44114e-08 * ----------------------------------------------------------------------------------------------------- * 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 = 29, direction = 3: |F_model - F_numer| error = ----------------------- = 7.08828e-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. MONOATOMIC STRUCTURE -- Species = Zr | a0 = 4.544677734375 | (Configuration in file "config-Zr.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Zr 1 5.644066452040279e-01 5.644066453957496e-01 1.91722e-10 6.34207e-10 2 6.216803423016446e-01 6.216803423262465e-01 2.46019e-11 8.05404e-10 3 4.283339516465872e-01 4.283339517196845e-01 7.30973e-11 7.09360e-10 ----------------------------------------------------------------------------------------------------- 2 Zr 1 -2.877218715180325e-01 -2.877218715481784e-01 3.01458e-11 1.63971e-09 2 -1.814289913886356e-01 -1.814289914201718e-01 3.15362e-11 1.16945e-09 3 -9.242726964943788e-01 -9.242726966396051e-01 1.45226e-10 6.28629e-10 ----------------------------------------------------------------------------------------------------- 3 Zr 1 4.740782191773671e-01 4.740782191728525e-01 4.51467e-12 8.50416e-10 2 7.228907645583003e-01 7.228907645195473e-01 3.87530e-11 1.23839e-09 3 3.427192792750571e-01 3.427192792800018e-01 4.94466e-12 8.74833e-10 ----------------------------------------------------------------------------------------------------- 4 Zr 1 -9.745708477334352e-01 -9.745708477351193e-01 1.68410e-12 1.08537e-09 2 -8.651044363702037e-01 -8.651044363754852e-01 5.28144e-12 3.12534e-10 3 5.677665246794201e-01 5.677665249342776e-01 2.54857e-10 2.97940e-10 ----------------------------------------------------------------------------------------------------- 5 Zr 1 -3.473438656941654e-01 -3.473438656075891e-01 8.65762e-11 5.33366e-10 2 -4.283498827693097e-01 -4.283498828509089e-01 8.15992e-11 1.06197e-09 3 2.191788507855419e-01 2.191788507298465e-01 5.56954e-11 1.75302e-09 ----------------------------------------------------------------------------------------------------- 6 Zr 1 -7.633324988991761e-01 -7.633324989796718e-01 8.04957e-11 1.49894e-10 2 7.544066967022577e-01 7.544066966268402e-01 7.54175e-11 2.05242e-10 3 9.897768769046092e-01 9.897768768769799e-01 2.76293e-11 6.73520e-10 ----------------------------------------------------------------------------------------------------- 7 Zr 1 -8.904392247449751e-01 -8.904392247588874e-01 1.39123e-11 2.93506e-10 2 1.229127223180712e+00 1.229127223192103e+00 1.13911e-11 8.06116e-10 3 3.717652819985754e-01 3.717652817301496e-01 2.68426e-10 4.07067e-09 * ----------------------------------------------------------------------------------------------------- 8 Zr 1 1.291649075459371e+00 1.291649075515036e+00 5.56653e-11 1.73457e-09 2 -2.517978216065737e-01 -2.517978216550637e-01 4.84900e-11 4.21757e-09 * 3 1.400851772558355e+00 1.400851772299971e+00 2.58384e-10 3.10113e-09 ----------------------------------------------------------------------------------------------------- 9 Zr 1 5.181989405440858e-01 5.181989404658595e-01 7.82263e-11 2.92197e-10 2 3.314990565612332e-01 3.314990565416868e-01 1.95464e-11 4.81236e-10 3 9.079816545364993e-01 9.079816544864650e-01 5.00343e-11 1.47567e-09 ----------------------------------------------------------------------------------------------------- 10 Zr 1 -7.053357613282173e-01 -7.053357611538346e-01 1.74383e-10 7.92592e-10 2 1.062106197903770e-01 1.062106198112077e-01 2.08307e-11 5.95723e-10 3 6.433181163578885e-01 6.433181164691801e-01 1.11292e-10 1.00263e-09 ----------------------------------------------------------------------------------------------------- 11 Zr 1 8.160163445690273e-01 8.160163444095980e-01 1.59429e-10 2.11900e-09 2 1.420327958153572e+00 1.420327957936736e+00 2.16836e-10 1.04215e-09 3 -1.896636687022854e+00 -1.896636687125687e+00 1.02833e-10 9.24731e-11 ----------------------------------------------------------------------------------------------------- 12 Zr 1 3.545815801732753e-01 3.545815802401683e-01 6.68930e-11 1.23244e-09 2 2.153085152315624e-01 2.153085154689877e-01 2.37425e-10 7.31681e-10 3 -1.188714887112102e+00 -1.188714887359422e+00 2.47320e-10 4.95783e-10 ----------------------------------------------------------------------------------------------------- 13 Zr 1 9.942334638094172e-01 9.942334637082093e-01 1.01208e-10 1.01720e-09 2 -1.048212849020968e+00 -1.048212849123050e+00 1.02083e-10 1.01407e-09 3 4.337691534847865e-01 4.337691531971636e-01 2.87623e-10 3.58660e-10 ----------------------------------------------------------------------------------------------------- 14 Zr 1 -7.188497799083167e-01 -7.188497801025168e-01 1.94200e-10 4.99319e-10 2 -8.889529276360619e-01 -8.889529275463145e-01 8.97474e-11 1.90412e-10 3 6.947829468027017e-01 6.947829468875403e-01 8.48386e-11 9.97512e-10 ----------------------------------------------------------------------------------------------------- 15 Zr 1 3.195966993802622e-01 3.195966994782255e-01 9.79633e-11 9.24258e-10 2 4.480483102774078e-01 4.480483099019112e-01 3.75497e-10 9.14352e-10 3 -7.168734520690155e-01 -7.168734521671524e-01 9.81368e-11 2.28125e-09 ----------------------------------------------------------------------------------------------------- 16 Zr 1 -3.108403721484068e-01 -3.108403724873623e-01 3.38956e-10 4.52151e-10 2 -6.512076265540698e-01 -6.512076265066878e-01 4.73820e-11 2.71579e-10 3 8.392110672243008e-01 8.392110674047867e-01 1.80486e-10 6.23700e-10 ----------------------------------------------------------------------------------------------------- 17 Zr 1 3.959649188332884e-01 3.959649188615597e-01 2.82713e-11 4.66694e-10 2 8.585750857635986e-01 8.585750857509220e-01 1.26766e-11 1.37614e-09 3 -9.247931298750717e-01 -9.247931297679749e-01 1.07097e-10 4.31022e-10 ----------------------------------------------------------------------------------------------------- 18 Zr 1 1.201087981413836e-01 1.201087980928528e-01 4.85308e-11 1.45794e-09 2 -1.898745596121673e+00 -1.898745596307571e+00 1.85899e-10 3.74728e-10 3 6.780549803354200e-01 6.780549804293612e-01 9.39412e-11 2.98128e-09 ----------------------------------------------------------------------------------------------------- 19 Zr 1 4.640090647465033e-01 4.640090648104319e-01 6.39286e-11 1.09746e-10 2 9.638628622786951e-01 9.638628624178220e-01 1.39127e-10 1.29140e-09 3 -3.184380067642076e-01 -3.184380070010524e-01 2.36845e-10 7.27220e-10 ----------------------------------------------------------------------------------------------------- 20 Zr 1 7.322652060810589e-01 7.322652061670568e-01 8.59979e-11 1.92632e-10 2 4.524365309272828e-01 4.524365310309940e-01 1.03711e-10 1.30879e-09 3 -7.324986592918273e-01 -7.324986593234466e-01 3.16193e-11 2.77986e-10 ----------------------------------------------------------------------------------------------------- 21 Zr 1 2.682488205006481e-01 2.682488204352786e-01 6.53695e-11 7.81292e-10 2 7.413918585722992e-01 7.413918582151620e-01 3.57137e-10 4.18464e-09 * 3 -2.007157159657066e-01 -2.007157161189541e-01 1.53248e-10 6.08908e-09 * ----------------------------------------------------------------------------------------------------- 22 Zr 1 -5.576749500479994e-01 -5.576749499884806e-01 5.95188e-11 1.80019e-09 2 -6.789523895634910e-01 -6.789523897931814e-01 2.29690e-10 3.69837e-09 3 8.028398589717452e-02 8.028398601071902e-02 1.13545e-10 4.93261e-09 * ----------------------------------------------------------------------------------------------------- 23 Zr 1 -1.415654827672297e+00 -1.415654827529846e+00 1.42451e-10 4.87940e-10 2 1.291688488375719e+00 1.291688488438497e+00 6.27780e-11 2.93695e-10 3 -1.280933181229852e+00 -1.280933181316961e+00 8.71092e-11 7.16417e-10 ----------------------------------------------------------------------------------------------------- 24 Zr 1 9.946560810853003e-01 9.946560811739158e-01 8.86154e-11 1.35917e-09 2 -3.233234033578066e-01 -3.233234033615002e-01 3.69360e-12 8.92940e-09 * 3 -3.892179413780337e-01 -3.892179413348587e-01 4.31750e-11 9.48789e-10 ----------------------------------------------------------------------------------------------------- 25 Zr 1 -1.255639766763102e+00 -1.255639766895256e+00 1.32153e-10 1.75834e-08 * 2 -1.839592286197537e+00 -1.839592286005975e+00 1.91562e-10 8.82650e-10 3 1.098761397753249e+00 1.098761398025244e+00 2.71995e-10 5.49302e-10 ----------------------------------------------------------------------------------------------------- 26 Zr 1 1.773878119998198e+00 1.773878120430845e+00 4.32647e-10 3.44662e-10 2 5.692766281394944e-01 5.692766283106975e-01 1.71203e-10 5.42313e-10 3 -6.620897327353452e-01 -6.620897327325150e-01 2.83018e-12 2.46768e-10 ----------------------------------------------------------------------------------------------------- 27 Zr 1 3.259582102255222e-01 3.259582102935415e-01 6.80193e-11 1.72243e-10 2 3.615151830234464e-01 3.615151828244264e-01 1.99020e-10 2.25547e-09 3 -6.370510801898281e-01 -6.370510799662313e-01 2.23597e-10 6.35185e-10 ----------------------------------------------------------------------------------------------------- 28 Zr 1 -4.717185963346861e-01 -4.717185958533719e-01 4.81314e-10 1.26883e-08 * 2 1.144038248934850e-01 1.144038246523896e-01 2.41095e-10 1.33250e-09 3 7.394931546181130e-01 7.394931545349078e-01 8.32052e-11 8.72640e-10 ----------------------------------------------------------------------------------------------------- 29 Zr 1 1.092548261046366e+00 1.092548261243116e+00 1.96750e-10 1.28458e-09 2 3.656409167932932e-01 3.656409167368607e-01 5.64325e-11 2.86456e-10 3 1.579303277261868e+00 1.579303277200015e+00 6.18525e-11 1.14279e-09 ----------------------------------------------------------------------------------------------------- 30 Zr 1 -8.794849034701164e-01 -8.794849035553377e-01 8.52213e-11 1.75576e-09 2 -1.181442625823563e+00 -1.181442625821232e+00 2.33125e-12 3.40917e-09 3 -7.941330214998553e-01 -7.941330214592470e-01 4.06083e-11 1.14649e-10 ----------------------------------------------------------------------------------------------------- 31 Zr 1 -1.252666673760371e+00 -1.252666673720475e+00 3.98961e-11 1.70447e-10 2 -3.921433131344348e-01 -3.921433131103978e-01 2.40370e-11 8.30176e-10 3 -1.017106537653788e+00 -1.017106537554290e+00 9.94973e-11 6.41708e-10 ----------------------------------------------------------------------------------------------------- 32 Zr 1 -6.691245089518043e-01 -6.691245089483837e-01 3.42060e-12 6.00878e-10 2 -9.390367159800541e-01 -9.390367160635662e-01 8.35121e-11 1.01524e-10 3 -3.318775428382794e-01 -3.318775424683124e-01 3.69967e-10 7.82122e-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 = 28, direction = 2: |F_model - F_numer| error = ----------------------- = 2.10741e-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 = Cu Zr | a0 = 4.076190442059669 | (Configuration in file "config-CuZr.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Zr 1 1.096468574251886e+00 1.096468573509040e+00 7.42846e-10 1.26990e-08 2 7.728055914474518e-01 7.728055920349641e-01 5.87512e-10 5.21818e-09 3 1.205037184983614e+00 1.205037182375680e+00 2.60793e-09 6.28568e-09 ----------------------------------------------------------------------------------------------------- 2 Zr 1 -3.761071446961390e-01 -3.761071469412213e-01 2.24508e-09 5.34378e-10 2 -1.205823964681645e+00 -1.205823963552358e+00 1.12929e-09 1.89001e-08 3 -3.410701233868777e-02 -3.410701266707357e-02 3.28386e-10 1.05296e-07 * ----------------------------------------------------------------------------------------------------- 3 Cu 1 6.718284768276774e-01 6.718284771550739e-01 3.27396e-10 8.36413e-09 2 7.900861451550204e-01 7.900861455153952e-01 3.60375e-10 1.88637e-08 3 -5.562122523176556e-01 -5.562122524108278e-01 9.31722e-11 2.83357e-09 ----------------------------------------------------------------------------------------------------- 4 Cu 1 -2.077412746798358e-01 -2.077412738825511e-01 7.97285e-10 1.85296e-07 * 2 -5.660509535481023e-01 -5.660509529028676e-01 6.45235e-10 1.27258e-08 3 -1.153324834430611e-01 -1.153324836745536e-01 2.31492e-10 9.27462e-09 ----------------------------------------------------------------------------------------------------- 5 Zr 1 -8.145516203862143e-01 -8.145516207383082e-01 3.52094e-10 1.60165e-09 2 4.617353653462780e-01 4.617353660138315e-01 6.67554e-10 4.32043e-09 3 4.007758604971070e-01 4.007758605065607e-01 9.45372e-12 5.22737e-09 ----------------------------------------------------------------------------------------------------- 6 Cu 1 -6.347316302554137e-01 -6.347316306344156e-01 3.79002e-10 4.18423e-09 2 2.417632656911658e-01 2.417632670467629e-01 1.35560e-09 1.99362e-09 3 1.016226276522818e+00 1.016226277198071e+00 6.75254e-10 3.80994e-07 * ----------------------------------------------------------------------------------------------------- 7 Zr 1 -6.377345084335549e-02 -6.377345082562337e-02 1.77321e-11 3.35815e-09 2 6.965348515922041e-01 6.965348530099975e-01 1.41779e-09 2.41472e-09 3 8.388642993342345e-01 8.388643000711959e-01 7.36961e-10 2.23085e-08 ----------------------------------------------------------------------------------------------------- 8 Cu 1 -1.010199012567893e+00 -1.010199012617938e+00 5.00449e-11 1.21236e-08 2 -1.391987178881087e+00 -1.391987177918852e+00 9.62236e-10 4.98387e-09 3 -5.973175889544734e-01 -5.973175890697868e-01 1.15313e-10 2.06522e-09 ----------------------------------------------------------------------------------------------------- 9 Cu 1 -9.701426363347269e-02 -9.701426410950030e-02 4.76028e-10 2.60689e-09 2 4.094366564850280e-03 4.094366035537575e-03 5.29313e-10 2.92171e-09 3 3.263978369142632e-01 3.263978368631429e-01 5.11203e-11 1.07067e-09 ----------------------------------------------------------------------------------------------------- 10 Cu 1 -4.293077090818840e-01 -4.293077087648648e-01 3.17019e-10 3.85931e-09 2 -7.227939816874688e-01 -7.227939798581808e-01 1.82929e-09 1.16395e-08 3 -1.846352854129968e-02 -1.846352821014458e-02 3.31155e-10 4.78527e-10 ----------------------------------------------------------------------------------------------------- 11 Zr 1 1.410706030106955e+00 1.410706027226550e+00 2.88041e-09 1.36503e-08 2 1.352263422166621e+00 1.352263415002732e+00 7.16389e-09 1.14157e-08 3 1.087558029895926e+00 1.087558028780567e+00 1.11536e-09 7.01345e-09 ----------------------------------------------------------------------------------------------------- 12 Cu 1 6.676538101190392e-01 6.676538104011562e-01 2.82117e-10 1.29735e-08 2 -6.405276016752891e-01 -6.405276012495212e-01 4.25768e-10 5.61311e-09 3 1.156580937577753e-01 1.156580919505721e-01 1.80720e-09 2.96066e-09 ----------------------------------------------------------------------------------------------------- 13 Cu 1 7.838674425402055e-01 7.838674367038738e-01 5.83633e-09 1.10622e-08 2 5.685977414204078e-01 5.685977392302896e-01 2.19012e-09 3.53428e-09 3 6.700832764790179e-01 6.700832772829711e-01 8.03953e-10 1.53808e-08 ----------------------------------------------------------------------------------------------------- 14 Zr 1 -1.574098361222425e-01 -1.574098358455911e-01 2.76651e-10 2.80449e-10 2 -6.244738393639734e-01 -6.244738390823280e-01 2.81645e-10 1.02152e-09 3 2.060774104774183e-01 2.060774112699106e-01 7.92492e-10 2.29371e-09 ----------------------------------------------------------------------------------------------------- 15 Zr 1 6.403842081103186e-01 6.403842072755701e-01 8.34748e-10 5.56193e-09 2 5.519332908060524e-01 5.519332910215725e-01 2.15520e-10 5.13297e-09 3 -2.580554902913842e+00 -2.580554903567176e+00 6.53334e-10 1.92837e-09 ----------------------------------------------------------------------------------------------------- 16 Zr 1 -1.297792648473647e+00 -1.297792647979356e+00 4.94291e-10 1.14116e-08 2 -4.255648442739709e-01 -4.255648441527708e-01 1.21200e-10 1.02626e-09 3 2.597554377344802e-01 2.597554376852690e-01 4.92111e-11 7.80982e-09 ----------------------------------------------------------------------------------------------------- 17 Cu 1 6.955127370331167e-01 6.955127372090237e-01 1.75907e-10 3.38823e-09 2 1.038943935213551e+00 1.038943935440938e+00 2.27387e-10 3.43400e-09 3 2.753035899568949e-01 2.753035902835404e-01 3.26645e-10 1.34555e-09 ----------------------------------------------------------------------------------------------------- 18 Cu 1 -5.479452340415409e-01 -5.479452367059485e-01 2.66441e-09 2.22732e-09 2 -1.108415524957787e+00 -1.108415524193746e+00 7.64041e-10 8.80925e-09 3 2.017078717008527e-01 2.017078736842195e-01 1.98337e-09 6.13033e-08 * ----------------------------------------------------------------------------------------------------- 19 Cu 1 3.512340330344643e-01 3.512340318264344e-01 1.20803e-09 1.30849e-08 2 8.597434678376183e-01 8.597434672496371e-01 5.87981e-10 3.99418e-09 3 -1.181301340001448e+00 -1.181301339494307e+00 5.07141e-10 5.88275e-08 * ----------------------------------------------------------------------------------------------------- 20 Zr 1 5.630827054465978e-01 5.630827056594047e-01 2.12807e-10 1.14832e-09 2 -5.656447520228409e-01 -5.656447508318879e-01 1.19095e-09 2.39922e-09 3 -5.351964694477710e-01 -5.351964689217148e-01 5.26056e-10 6.94930e-09 ----------------------------------------------------------------------------------------------------- 21 Cu 1 3.141835455003237e-01 3.141835463648439e-01 8.64520e-10 7.02552e-09 2 1.252515637225936e+00 1.252515637586552e+00 3.60616e-10 4.89444e-08 * 3 1.260685234474188e-01 1.260685231222373e-01 3.25181e-10 1.55760e-09 ----------------------------------------------------------------------------------------------------- 22 Zr 1 8.636015128239574e-02 8.636015153942193e-02 2.57026e-10 1.98859e-09 2 -2.793605571840473e+00 -2.793605572147429e+00 3.06956e-10 7.97255e-09 3 9.572549835336694e-01 9.572549828309392e-01 7.02730e-10 5.52358e-09 ----------------------------------------------------------------------------------------------------- 23 Zr 1 -1.103926399538327e+00 -1.103926399453693e+00 8.46341e-11 1.50451e-08 2 1.565817964420011e+00 1.565817964493392e+00 7.33813e-11 1.68202e-09 3 -1.525108159261624e+00 -1.525108159106542e+00 1.55082e-10 3.07238e-09 ----------------------------------------------------------------------------------------------------- 24 Cu 1 1.334573898254377e-01 1.334573894598888e-01 3.65549e-10 8.24999e-09 2 -5.253116036543194e-01 -5.253116068424506e-01 3.18813e-09 4.31938e-09 3 -1.053001025201296e+00 -1.053001027882709e+00 2.68141e-09 2.18322e-09 ----------------------------------------------------------------------------------------------------- 25 Zr 1 2.465139763058045e-01 2.465139770152593e-01 7.09455e-10 4.35178e-09 2 1.019091140039044e+00 1.019091140082601e+00 4.35574e-11 6.99803e-09 3 3.771373509821290e-01 3.771373512482015e-01 2.66073e-10 5.38231e-09 ----------------------------------------------------------------------------------------------------- 26 Cu 1 -5.631050294621398e-02 -5.631050351775268e-02 5.71539e-10 1.21987e-08 2 -1.062954553941037e+00 -1.062954553100239e+00 8.40799e-10 4.35231e-09 3 -8.492033114494707e-02 -8.492033053577312e-02 6.09174e-10 1.17600e-08 ----------------------------------------------------------------------------------------------------- 27 Zr 1 -1.119054901647732e+00 -1.119054901424411e+00 2.23320e-10 1.35515e-08 2 4.223665694380980e-01 4.223665707686448e-01 1.33055e-09 7.09576e-09 3 5.478878839293441e-01 5.478878830418052e-01 8.87539e-10 4.29292e-09 ----------------------------------------------------------------------------------------------------- 28 Cu 1 9.936935004612925e-01 9.936935005114762e-01 5.01837e-11 4.31826e-09 2 -1.008168468355403e+00 -1.008168467742796e+00 6.12607e-10 1.24766e-09 3 -9.252403191998128e-01 -9.252403196414046e-01 4.41592e-10 4.11715e-09 ----------------------------------------------------------------------------------------------------- 29 Zr 1 -2.821085737623862e+00 -2.821085737197947e+00 4.25914e-10 3.36064e-09 2 1.835878582178508e-01 1.835878600546942e-01 1.83684e-09 4.96417e-09 3 -1.582633040619935e+00 -1.582633039694837e+00 9.25098e-10 1.96714e-08 ----------------------------------------------------------------------------------------------------- 30 Zr 1 7.984327928323989e-01 7.984327927133223e-01 1.19077e-10 1.27368e-09 2 9.464149923913483e-01 9.464149924848916e-01 9.35433e-11 1.13009e-09 3 8.483020851480154e-01 8.483020852027756e-01 5.47602e-11 9.41342e-10 ----------------------------------------------------------------------------------------------------- 31 Zr 1 8.051193729863837e-01 8.051193750036075e-01 2.01722e-09 4.73777e-09 2 1.567603719544333e-01 1.567603719253063e-01 2.91270e-11 1.01507e-07 * 3 1.965292389018142e+00 1.965292388163413e+00 8.54729e-10 5.34062e-09 ----------------------------------------------------------------------------------------------------- 32 Cu 1 4.784526198734760e-01 4.784526211522619e-01 1.27879e-09 2.38577e-08 2 -2.437331380445429e-01 -2.437331371036977e-01 9.40845e-10 1.81613e-08 3 -6.359999309272665e-01 -6.359999303662801e-01 5.60986e-10 5.89470e-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 = 9, direction = 2: |F_model - F_numer| error = ----------------------- = 1.29278e-07 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 1.29278e-07 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: B Comment: The letter grade B was assigned because the normalized error in the computation was 1.29278e-07 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.