!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! VERIFICATION CHECK: vc-forces-numerical-derivative !!!!! !!!!! !!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Description: Comparison of the analytical forces obtained from the model with forces computed by numerical differentiation using Richardson extrapolation for a randomly distorted non-periodic structure based off the equilibrium face-centered cubic (fcc) structure. Separate configurations are tested for each species supported by the model, as well as one containing a random distribution of all species. Configurations used for testing are provided as auxiliary files. Author: Ellad Tadmor ----------------------------------------------------------------------------------------------------- Results for KIM Model : Sim_LAMMPS_Polymorphic_BereSerra_2006_GaN__SM_518345582208_000 Supported species : Ga N 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 = Ga | a0 = 3.7290544509887695 | (Configuration in file "config-Ga.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ga 1 1.040551060165641e+00 1.040551056324318e+00 3.84132e-09 2.12740e-07 * 2 -6.050291778565735e-02 -6.050292186740555e-02 4.08175e-09 2.32897e-07 * 3 -2.398921796819437e-01 -2.398921781502460e-01 1.53170e-09 3.77757e-09 ----------------------------------------------------------------------------------------------------- 2 Ga 1 -5.492510504262473e-01 -5.492510523803329e-01 1.95409e-09 5.12024e-09 2 3.715488899093379e-01 3.715488898387760e-01 7.05619e-11 1.12591e-08 3 1.522924878851550e+00 1.522924874067308e+00 4.78424e-09 2.11121e-07 * ----------------------------------------------------------------------------------------------------- 3 Ga 1 6.268981167792483e-02 6.268981183774743e-02 1.59823e-10 1.16317e-09 2 1.162767997826218e+00 1.162767997867783e+00 4.15648e-11 2.13715e-10 3 -1.284082561354487e-01 -1.284082560395590e-01 9.58897e-11 1.74708e-09 ----------------------------------------------------------------------------------------------------- 4 Ga 1 1.134612478499557e+00 1.134612510212577e+00 3.17130e-08 2.88127e-08 2 9.538912322921798e-01 9.538912302663265e-01 2.02585e-09 2.29129e-08 3 8.397311483438960e-01 8.397311456019666e-01 2.74193e-09 4.66693e-08 ----------------------------------------------------------------------------------------------------- 5 Ga 1 2.697926131883166e-01 2.697926130952564e-01 9.30602e-11 1.03048e-10 2 6.687746927649088e-01 6.687746926990624e-01 6.58463e-11 1.18112e-07 * 3 8.468302451906630e-01 8.468302451079617e-01 8.27013e-11 8.35374e-10 ----------------------------------------------------------------------------------------------------- 6 Ga 1 -7.405160952035396e-01 -7.405160951701418e-01 3.33977e-11 4.66778e-09 2 -4.074894285885713e-01 -4.074894286119358e-01 2.33645e-11 1.21958e-10 3 5.181869007320093e-01 5.181869008020481e-01 7.00388e-11 1.09728e-10 ----------------------------------------------------------------------------------------------------- 7 Ga 1 8.058699276004382e-01 8.058699276732652e-01 7.28270e-11 1.00077e-09 2 -2.401414422158545e+00 -2.401414421984260e+00 1.74285e-10 1.72988e-09 3 -3.113225077003890e+00 -3.113225077001760e+00 2.12985e-12 4.32667e-10 ----------------------------------------------------------------------------------------------------- 8 Ga 1 -2.473821416589528e+00 -2.473821412596930e+00 3.99260e-09 4.29939e-09 2 -1.591089659057653e+00 -1.591089658046883e+00 1.01077e-09 1.17077e-09 3 -1.381452771995233e+00 -1.381452767589686e+00 4.40555e-09 6.39020e-09 ----------------------------------------------------------------------------------------------------- 9 Ga 1 1.087256324761785e+00 1.087256324400796e+00 3.60989e-10 1.15254e-09 2 -1.950513308291376e-01 -1.950513308108834e-01 1.82542e-11 7.89683e-10 3 1.063623482976346e+00 1.063623483067994e+00 9.16485e-11 8.70756e-10 ----------------------------------------------------------------------------------------------------- 10 Ga 1 -3.296872131515733e+00 -3.296872131268336e+00 2.47397e-10 1.14296e-09 2 9.137173317424715e-01 9.137173318084442e-01 6.59727e-11 1.75103e-09 3 -2.033957217397184e+00 -2.033957217193710e+00 2.03474e-10 7.83264e-10 ----------------------------------------------------------------------------------------------------- 11 Ga 1 -3.424204146776944e+00 -3.424204143165305e+00 3.61164e-09 4.22670e-09 2 -4.178271680419934e+00 -4.178271680337087e+00 8.28475e-11 1.78425e-09 3 -1.330834130819682e+00 -1.330834129338795e+00 1.48089e-09 1.87637e-09 ----------------------------------------------------------------------------------------------------- 12 Ga 1 4.485049288888952e-01 4.485049174297533e-01 1.14591e-08 6.26781e-07 * 2 -1.160597457935864e-01 -1.160597458211812e-01 2.75948e-11 1.40943e-09 3 -5.499491744522335e-01 -5.499491835256806e-01 9.07345e-09 6.01402e-07 * ----------------------------------------------------------------------------------------------------- 13 Ga 1 5.962801436637349e-01 5.962801432976136e-01 3.66121e-10 1.01821e-08 2 -2.684918631018741e+00 -2.684918635217944e+00 4.19920e-09 1.19312e-08 3 -4.034379119838277e+00 -4.034379105684222e+00 1.41541e-08 1.62981e-08 ----------------------------------------------------------------------------------------------------- 14 Ga 1 -1.401615765155024e-01 -1.401615767870402e-01 2.71538e-10 3.71847e-09 2 3.077236410556758e-01 3.077236412960194e-01 2.40344e-10 1.14136e-09 3 -2.106179759396632e-01 -2.106179762299766e-01 2.90313e-10 5.29706e-09 ----------------------------------------------------------------------------------------------------- 15 Ga 1 2.933838254483008e+00 2.933838256509317e+00 2.02631e-09 6.69529e-09 2 3.805106740525189e-01 3.805106745342648e-01 4.81746e-10 5.77480e-09 3 1.116359648854109e+00 1.116359647574282e+00 1.27983e-09 2.09049e-08 ----------------------------------------------------------------------------------------------------- 16 Ga 1 2.731718623388228e+00 2.731718622994002e+00 3.94225e-10 9.31593e-09 2 4.882914648357278e+00 4.882914648172833e+00 1.84444e-10 3.57026e-09 3 1.501841888718231e+00 1.501841888864197e+00 1.45966e-10 5.63540e-09 ----------------------------------------------------------------------------------------------------- 17 Ga 1 6.944860273790152e-02 6.944860255482886e-02 1.83073e-10 7.67688e-10 2 4.337633057360010e-01 4.337633058773797e-01 1.41379e-10 5.76734e-09 3 -9.257261206388588e-01 -9.257261206718520e-01 3.29932e-11 3.27099e-09 ----------------------------------------------------------------------------------------------------- 18 Ga 1 4.678417562866001e-01 4.678417558977975e-01 3.88803e-10 2.07162e-08 2 2.051482659679074e+00 2.051482659633715e+00 4.53588e-11 2.17322e-09 3 -2.070996482437506e+00 -2.070996481674064e+00 7.63442e-10 4.81021e-09 ----------------------------------------------------------------------------------------------------- 19 Ga 1 1.295241293427614e-01 1.295241293683359e-01 2.55745e-11 1.53947e-09 2 -1.166429532467949e+00 -1.166429532117311e+00 3.50638e-10 1.59251e-09 3 7.846481948619155e-01 7.846481947722634e-01 8.96521e-11 1.72435e-09 ----------------------------------------------------------------------------------------------------- 20 Ga 1 1.834750632576597e-01 1.834750619225257e-01 1.33513e-09 2.14704e-07 * 2 4.016905555491810e-01 4.016905557498163e-01 2.00635e-10 1.10930e-09 3 -1.593458245384443e-01 -1.593458245167517e-01 2.16926e-11 3.97720e-10 ----------------------------------------------------------------------------------------------------- 21 Ga 1 -2.075521416363246e+00 -2.075521416471735e+00 1.08490e-10 1.18396e-09 2 -7.231872129363581e-01 -7.231872128752542e-01 6.11039e-11 8.82980e-10 3 1.323685559063231e+00 1.323685559018425e+00 4.48062e-11 8.32467e-10 ----------------------------------------------------------------------------------------------------- 22 Ga 1 1.753780303198315e+00 1.753780303144663e+00 5.36520e-11 1.17928e-09 2 2.538162121340458e+00 2.538162121554397e+00 2.13939e-10 1.29453e-08 3 2.754069677075188e+00 2.754069677337172e+00 2.61983e-10 7.81929e-10 ----------------------------------------------------------------------------------------------------- 23 Ga 1 -9.628460759076091e-01 -9.628460759406832e-01 3.30741e-11 4.59555e-10 2 7.767963791102381e-01 7.767963792831974e-01 1.72959e-10 1.61476e-09 3 -7.240693556369755e-01 -7.240693556442852e-01 7.30971e-12 1.47263e-09 ----------------------------------------------------------------------------------------------------- 24 Ga 1 1.191263711189468e+00 1.191263711067929e+00 1.21539e-10 9.50090e-10 2 4.136014868449244e-01 4.136014868916095e-01 4.66851e-11 1.83206e-09 3 -1.270009652614910e-03 -1.270009351521949e-03 3.01093e-10 1.85017e-09 ----------------------------------------------------------------------------------------------------- 25 Ga 1 -1.089059955928851e+00 -1.089059955856198e+00 7.26521e-11 2.21232e-09 2 -8.182589653503627e-01 -8.182589652302628e-01 1.20100e-10 4.12461e-09 3 6.013542515088292e-01 6.013542528705532e-01 1.36172e-09 4.19887e-10 ----------------------------------------------------------------------------------------------------- 26 Ga 1 -1.172553930752312e+00 -1.172553868053134e+00 6.26992e-08 6.37771e-07 * 2 2.936099109048896e+00 2.936099108127868e+00 9.21029e-10 2.23215e-08 3 4.023635280062839e-01 4.023635261746766e-01 1.83161e-09 6.31614e-07 * ----------------------------------------------------------------------------------------------------- 27 Ga 1 6.724738970021207e-01 6.724739022824947e-01 5.28037e-09 2.37818e-08 2 -3.149516886967996e+00 -3.149516887981183e+00 1.01319e-09 1.36920e-08 3 6.718540928768416e-01 6.718540926238201e-01 2.53021e-10 1.83388e-09 ----------------------------------------------------------------------------------------------------- 28 Ga 1 -1.246098035806431e+00 -1.246098031949957e+00 3.85647e-09 3.20594e-09 2 8.596708513961308e-01 8.596708483757558e-01 3.02037e-09 3.77869e-09 3 -5.613191847230808e-02 -5.613191810531670e-02 3.66991e-10 5.46454e-10 ----------------------------------------------------------------------------------------------------- 29 Ga 1 4.718885510675617e-01 4.718886102337921e-01 5.91662e-08 2.74812e-07 * 2 -2.416099033686988e+00 -2.416099042787719e+00 9.10073e-09 8.19754e-08 * 3 1.756118552355437e+00 1.756118553158412e+00 8.02975e-10 1.06240e-09 ----------------------------------------------------------------------------------------------------- 30 Ga 1 -6.788496794493207e-02 -6.788496767699559e-02 2.67936e-10 2.11673e-08 2 -1.747525510114964e-01 -1.747525509439367e-01 6.75597e-11 1.34188e-09 3 -5.180319850596263e-01 -5.180319854089475e-01 3.49321e-10 1.42848e-09 ----------------------------------------------------------------------------------------------------- 31 Ga 1 7.663222737701223e-01 7.663222737083100e-01 6.18123e-11 6.09728e-08 * 2 -1.168491578360382e+00 -1.168491578384967e+00 2.45848e-11 8.93970e-10 3 5.059091811088938e-01 5.059091805963012e-01 5.12593e-10 3.29635e-09 ----------------------------------------------------------------------------------------------------- 32 Ga 1 4.216583455608339e-01 4.216583449932146e-01 5.67619e-10 5.26046e-08 * 2 1.198417999727863e+00 1.198417999172711e+00 5.55152e-10 5.02714e-08 * 3 1.268786369176465e+00 1.268786369934625e+00 7.58159e-10 2.07957e-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 = 24, direction = 3: |F_model - F_numer| error = ----------------------- = 2.37079e-07 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 = N | a0 = 2.635988235473633 | (Configuration in file "config-N.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 N 1 1.784689377225731e+00 1.784689377131249e+00 9.44815e-11 2.92258e-09 2 2.915347233372213e+00 2.915347233271719e+00 1.00494e-10 2.23928e-10 3 1.213323383026829e+00 1.213323383147413e+00 1.20584e-10 4.45264e-10 ----------------------------------------------------------------------------------------------------- 2 N 1 -2.134661043784618e+00 -2.134661044960322e+00 1.17570e-09 5.79291e-09 2 -6.922323802913860e-01 -6.922323802422184e-01 4.91676e-11 3.73809e-10 3 2.781717556688487e+00 2.781717555911702e+00 7.76785e-10 7.88551e-09 ----------------------------------------------------------------------------------------------------- 3 N 1 1.520169961562583e+00 1.520169961832254e+00 2.69671e-10 1.92218e-09 2 -5.588872422670442e-01 -5.588872423960191e-01 1.28975e-10 2.15446e-09 3 -4.574420998002207e-01 -4.574420983829214e-01 1.41730e-09 1.60139e-09 ----------------------------------------------------------------------------------------------------- 4 N 1 -2.892466818419545e-01 -2.892466824770168e-01 6.35062e-10 1.68551e-07 * 2 -9.116468548062857e-01 -9.116468551182432e-01 3.11957e-10 1.04679e-07 * 3 -3.951120067844669e+00 -3.951120069786516e+00 1.94185e-09 6.45309e-09 ----------------------------------------------------------------------------------------------------- 5 N 1 -4.102646817164917e+00 -4.102646815597780e+00 1.56714e-09 6.58097e-09 2 -8.023714231544614e-01 -8.023714231019631e-01 5.24983e-11 6.88799e-10 3 -2.009224487625432e+00 -2.009224487685072e+00 5.96407e-11 3.57393e-09 ----------------------------------------------------------------------------------------------------- 6 N 1 2.014003590696344e+00 2.014003590878961e+00 1.82617e-10 5.13834e-09 2 4.066064566920724e+00 4.066064567767796e+00 8.47073e-10 1.89083e-09 3 -4.552322800102937e+00 -4.552322799824438e+00 2.78499e-10 2.21963e-09 ----------------------------------------------------------------------------------------------------- 7 N 1 3.905830719281666e+00 3.905830726294134e+00 7.01247e-09 2.14476e-08 2 -5.277410424475800e+00 -5.277410431822054e+00 7.34625e-09 3.10765e-08 3 3.441926876436996e+00 3.441926879748201e+00 3.31120e-09 2.57432e-08 ----------------------------------------------------------------------------------------------------- 8 N 1 -5.736041010262404e+00 -5.736041007978515e+00 2.28389e-09 1.98935e-08 2 5.421609116257461e+00 5.421609115132077e+00 1.12538e-09 1.73506e-08 3 4.935680452300671e+00 4.935680454672306e+00 2.37163e-09 1.65294e-06 * ----------------------------------------------------------------------------------------------------- 9 N 1 3.058676714698974e+00 3.058676714694206e+00 4.76819e-12 3.40665e-09 2 1.702073661420989e-01 1.702073661808231e-01 3.87242e-11 1.96244e-09 3 9.505204953406602e-01 9.505204955508565e-01 2.10196e-10 6.36038e-08 * ----------------------------------------------------------------------------------------------------- 10 N 1 -1.494998509007308e+00 -1.494998509083898e+00 7.65905e-11 1.63383e-09 2 -2.650079721764183e+00 -2.650079722088233e+00 3.24050e-10 9.89525e-09 3 2.640605514054504e+00 2.640605514402063e+00 3.47558e-10 2.76110e-09 ----------------------------------------------------------------------------------------------------- 11 N 1 2.244592776764393e+00 2.244592775339494e+00 1.42490e-09 1.63989e-09 2 1.190455303337646e+00 1.190455303316536e+00 2.11100e-11 6.39543e-09 3 -5.060670779913743e+00 -5.060670779945572e+00 3.18288e-11 1.08943e-08 ----------------------------------------------------------------------------------------------------- 12 N 1 2.322288566493302e+00 2.322288566584254e+00 9.09517e-11 2.93418e-09 2 -1.177814760150317e+00 -1.177814760169778e+00 1.94607e-11 4.64742e-10 3 -1.026447662374186e+00 -1.026447662161704e+00 2.12482e-10 5.80188e-10 ----------------------------------------------------------------------------------------------------- 13 N 1 -2.522232265700720e+00 -2.522232265354964e+00 3.45756e-10 4.85983e-09 2 -3.520490254509456e+00 -3.520490252819897e+00 1.68956e-09 2.78715e-08 3 -2.095074221672300e+00 -2.095074230536737e+00 8.86444e-09 2.49294e-08 ----------------------------------------------------------------------------------------------------- 14 N 1 1.364664954523666e+00 1.364664954514034e+00 9.63141e-12 2.68848e-10 2 3.494156072983616e+00 3.494156073352829e+00 3.69213e-10 8.80180e-10 3 -3.227023937362367e+00 -3.227023936637738e+00 7.24630e-10 4.64041e-09 ----------------------------------------------------------------------------------------------------- 15 N 1 5.337702828029067e+00 5.337702828643420e+00 6.14353e-10 1.05051e-09 2 -4.719964836392990e+00 -4.719964838174490e+00 1.78150e-09 1.17448e-08 3 5.909856921073517e-01 5.909856856415588e-01 6.46579e-09 7.33483e-09 ----------------------------------------------------------------------------------------------------- 16 N 1 -5.005623770901567e+00 -5.005623771134956e+00 2.33389e-10 1.51054e-09 2 2.411815463892420e+00 2.411815466275450e+00 2.38303e-09 1.56597e-08 3 1.063003319639313e+00 1.063003325452551e+00 5.81324e-09 1.10318e-08 ----------------------------------------------------------------------------------------------------- 17 N 1 -4.680702079329197e+00 -4.680702077232203e+00 2.09699e-09 2.34459e-09 2 -6.818393724565485e+00 -6.818393726782400e+00 2.21691e-09 1.02502e-08 3 -3.066343313807208e+00 -3.066343313768316e+00 3.88920e-11 4.09275e-10 ----------------------------------------------------------------------------------------------------- 18 N 1 4.247645216357707e+00 4.247645197301568e+00 1.90561e-08 9.14789e-09 2 5.415040510331278e-01 5.415040530597461e-01 2.02662e-09 3.02372e-07 * 3 -2.408266802343307e+00 -2.408266800951248e+00 1.39206e-09 3.49239e-09 ----------------------------------------------------------------------------------------------------- 19 N 1 4.605690126597889e+00 4.605690127065744e+00 4.67855e-10 1.49227e-07 * 2 -8.029171539633453e-01 -8.029171540656108e-01 1.02266e-10 6.81024e-10 3 1.545851911478666e+00 1.545851911777414e+00 2.98748e-10 1.24764e-09 ----------------------------------------------------------------------------------------------------- 20 N 1 -1.860074696488849e+00 -1.860074696537301e+00 4.84512e-11 1.52440e-08 2 3.578788062820799e+00 3.578788062105321e+00 7.15478e-10 4.99121e-09 3 4.696513732099534e+00 4.696513732303760e+00 2.04226e-10 1.63963e-08 ----------------------------------------------------------------------------------------------------- 21 N 1 -3.877778165243922e+00 -3.877778171298118e+00 6.05420e-09 1.49075e-08 2 1.120485880499386e-01 1.120485738260568e-01 1.42239e-08 2.33725e-08 3 -5.430507079713591e+00 -5.430507079177564e+00 5.36027e-10 1.29184e-09 ----------------------------------------------------------------------------------------------------- 22 N 1 1.636256076076404e+00 1.636256076427596e+00 3.51192e-10 7.49084e-09 2 -3.753514153091548e+00 -3.753514153832637e+00 7.41089e-10 2.33398e-09 3 5.891492681016577e-01 5.891492681711376e-01 6.94799e-11 1.05280e-09 ----------------------------------------------------------------------------------------------------- 23 N 1 3.158428141562195e+00 3.158428140894896e+00 6.67300e-10 2.74448e-07 * 2 -2.969612512163923e-01 -2.969612512585976e-01 4.22052e-11 3.06789e-10 3 3.075522169692472e+00 3.075522169977829e+00 2.85357e-10 6.16327e-10 ----------------------------------------------------------------------------------------------------- 24 N 1 -6.635865823285347e-01 -6.635865722069532e-01 1.01216e-08 5.06462e-08 2 2.531869690553369e+00 2.531869691289922e+00 7.36553e-10 4.47266e-09 3 4.236930672350082e-01 4.236930650912434e-01 2.14376e-09 1.56515e-08 ----------------------------------------------------------------------------------------------------- 25 N 1 -4.292813927387030e+00 -4.292813928075550e+00 6.88520e-10 5.96226e-09 2 2.663408445225564e+00 2.663408445927923e+00 7.02359e-10 1.16269e-09 3 1.007672505469173e-01 1.007672506273563e-01 8.04390e-11 9.31951e-09 ----------------------------------------------------------------------------------------------------- 26 N 1 2.907229731250176e+00 2.907229729628548e+00 1.62163e-09 2.30038e-09 2 2.327785326513762e+00 2.327785326662745e+00 1.48983e-10 8.64202e-10 3 4.234976420453158e-01 4.234976414959253e-01 5.49391e-10 3.86163e-09 ----------------------------------------------------------------------------------------------------- 27 N 1 2.956408636469291e+00 2.956408636993148e+00 5.23857e-10 5.15603e-09 2 7.462448416630924e-01 7.462448420448655e-01 3.81773e-10 6.59214e-09 3 3.926979765282021e+00 3.926979765440529e+00 1.58508e-10 2.12786e-09 ----------------------------------------------------------------------------------------------------- 28 N 1 1.029616504540099e+00 1.029616504964153e+00 4.24054e-10 1.61653e-09 2 -9.302827895214952e-01 -9.302827899663715e-01 4.44876e-10 2.14736e-09 3 -1.494302825344755e+00 -1.494302825491667e+00 1.46911e-10 2.21570e-09 ----------------------------------------------------------------------------------------------------- 29 N 1 -3.744964122653810e+00 -3.744964111962829e+00 1.06910e-08 1.27965e-08 2 2.264190851675469e+00 2.264190851178327e+00 4.97142e-10 2.92128e-07 * 3 3.709464943199790e+00 3.709464941673652e+00 1.52614e-09 2.45855e-09 ----------------------------------------------------------------------------------------------------- 30 N 1 -2.175064071145494e-01 -2.175064071151259e-01 5.76483e-13 2.49400e-09 2 1.220841950558172e+00 1.220841949070829e+00 1.48734e-09 3.39835e-08 3 2.428909595797031e+00 2.428909595569090e+00 2.27940e-10 2.29726e-08 ----------------------------------------------------------------------------------------------------- 31 N 1 -2.813750565914729e+00 -2.813750566831061e+00 9.16331e-10 1.91329e-09 2 5.683611780023283e-01 5.683611773628842e-01 6.39444e-10 1.08506e-09 3 -1.841611896100896e+00 -1.841611897407293e+00 1.30640e-09 5.38467e-09 ----------------------------------------------------------------------------------------------------- 32 N 1 -6.572672770053865e-01 -6.572672758112109e-01 1.19418e-09 1.75035e-08 2 -3.311731138831609e+00 -3.311731139530906e+00 6.99297e-10 1.80014e-09 3 -1.917754661067608e+00 -1.917754660837283e+00 2.30325e-10 1.64743e-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 = 21, direction = 2: |F_model - F_numer| error = ----------------------- = 1.26944e-07 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 = Ga N | a0 = 3.4580715982566295 | (Configuration in file "config-GaN.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 N 1 1.041713945830975e+00 1.041713945882361e+00 5.13858e-11 5.25901e-10 2 1.057766404273333e+00 1.057766404270443e+00 2.88947e-12 3.96168e-11 3 1.757884009344975e-02 1.757884005516069e-02 3.82891e-11 2.59747e-10 ----------------------------------------------------------------------------------------------------- 2 Ga 1 -6.175202775156914e+00 -6.175202774837889e+00 3.19026e-10 5.51205e-09 2 8.138411388267232e-01 8.138411388411373e-01 1.44141e-11 3.00956e-09 3 -2.788450244471959e+00 -2.788450245417854e+00 9.45895e-10 4.59687e-09 ----------------------------------------------------------------------------------------------------- 3 N 1 -1.588374820588215e-01 -1.588374819780322e-01 8.07893e-11 1.42664e-09 2 -2.072328326969477e+00 -2.072328319524307e+00 7.44517e-09 1.19143e-08 3 -1.336283936457286e+00 -1.336283933731264e+00 2.72602e-09 2.58480e-08 ----------------------------------------------------------------------------------------------------- 4 N 1 9.490472009144436e-01 9.490472010428522e-01 1.28409e-10 3.61204e-10 2 1.898215790632180e+00 1.898215790694431e+00 6.22511e-11 2.45000e-10 3 1.570968344494375e+00 1.570968344464461e+00 2.99138e-11 8.47008e-10 ----------------------------------------------------------------------------------------------------- 5 Ga 1 1.164133613482667e+00 1.164133613442196e+00 4.04710e-11 3.90652e-10 2 -4.597834034316862e+00 -4.597834034282488e+00 3.43743e-11 1.12413e-08 3 -2.201814657369257e-01 -2.201814656916129e-01 4.53128e-11 2.00595e-08 ----------------------------------------------------------------------------------------------------- 6 Ga 1 2.166146665148711e+00 2.166146665186620e+00 3.79092e-11 7.58731e-10 2 -1.163728620120838e+00 -1.163728620335183e+00 2.14344e-10 2.55772e-09 3 -4.516428935236201e-01 -4.516428934951333e-01 2.84868e-11 1.19860e-09 ----------------------------------------------------------------------------------------------------- 7 N 1 -1.202222925456344e+00 -1.202222925810795e+00 3.54451e-10 1.83276e-07 * 2 1.471199021723113e+00 1.471199020259408e+00 1.46370e-09 2.81513e-06 * 3 -3.084107457424318e+00 -3.084107455798820e+00 1.62550e-09 7.35618e-09 ----------------------------------------------------------------------------------------------------- 8 Ga 1 4.540204436671801e+00 4.540204438545724e+00 1.87392e-09 1.28094e-08 2 -1.565072480935525e+00 -1.565072483632808e+00 2.69728e-09 2.75575e-07 * 3 2.926339509127550e+00 2.926339508262529e+00 8.65022e-10 3.15740e-09 ----------------------------------------------------------------------------------------------------- 9 Ga 1 2.862739689649237e-01 2.862739689711195e-01 6.19577e-12 6.96330e-10 2 2.617533112634121e+00 2.617533112617168e+00 1.69527e-11 4.14009e-07 * 3 2.851170804377224e+00 2.851170804380636e+00 3.41194e-12 1.39442e-09 ----------------------------------------------------------------------------------------------------- 10 N 1 7.863785193645541e-01 7.863785194865157e-01 1.21962e-10 2.30670e-10 2 -2.718972208977166e-02 -2.718972207514059e-02 1.46311e-11 5.05910e-10 3 1.054487366428374e+00 1.054487366417834e+00 1.05391e-11 6.78425e-10 ----------------------------------------------------------------------------------------------------- 11 N 1 -5.745512710350418e+00 -5.745512783894134e+00 7.35437e-08 3.40375e-05 * 2 -1.274106685864911e+00 -1.274106785132161e+00 9.92673e-08 3.28850e-05 * 3 -1.946032099236895e+00 -1.946032099068738e+00 1.68157e-10 5.66001e-09 ----------------------------------------------------------------------------------------------------- 12 N 1 -3.568277792684538e-01 -3.568277791553143e-01 1.13140e-10 5.21429e-10 2 -3.098822106467511e+00 -3.098822108810370e+00 2.34286e-09 4.54285e-08 3 -1.130785024149223e+00 -1.130785022539859e+00 1.60936e-09 1.79689e-08 ----------------------------------------------------------------------------------------------------- 13 N 1 7.234396764546772e-01 7.234396773203302e-01 8.65653e-10 4.32352e-09 2 4.925648815471738e-02 4.925648803994688e-02 1.14770e-10 6.24381e-10 3 -3.910123403576478e+00 -3.910123416126367e+00 1.25499e-08 2.17829e-08 ----------------------------------------------------------------------------------------------------- 14 Ga 1 9.721172599010476e-01 9.721172606900710e-01 7.89023e-10 8.98178e-10 2 2.641456885415993e+00 2.641456885419782e+00 3.78853e-12 1.29725e-09 3 -4.787148102772175e+00 -4.787148102972559e+00 2.00384e-10 2.18612e-09 ----------------------------------------------------------------------------------------------------- 15 Ga 1 3.827906778076132e+00 3.827906779499855e+00 1.42372e-09 5.01809e-08 2 -2.586877057985123e+00 -2.586877057307178e+00 6.77946e-10 9.96595e-09 3 5.278547891004168e+00 5.278547890338853e+00 6.65315e-10 1.35342e-08 ----------------------------------------------------------------------------------------------------- 16 Ga 1 -2.780852070712937e+00 -2.780852047840427e+00 2.28725e-08 3.00083e-05 * 2 6.159443648051453e+00 6.159443635846542e+00 1.22049e-08 2.94024e-05 * 3 -1.391635563342629e+00 -1.391635562472902e+00 8.69727e-10 5.47658e-10 ----------------------------------------------------------------------------------------------------- 17 N 1 1.385439633193748e+00 1.385439633247647e+00 5.38989e-11 2.69784e-10 2 1.082937750538817e+00 1.082937750534393e+00 4.42402e-12 2.56305e-10 3 2.065048055632119e-01 2.065048056096816e-01 4.64697e-11 5.37919e-10 ----------------------------------------------------------------------------------------------------- 18 Ga 1 -7.474138021302664e+00 -7.474138021870799e+00 5.68136e-10 6.25576e-08 2 -6.567412385866701e+00 -6.567412439658210e+00 5.37915e-08 2.46033e-07 * 3 4.202645861473187e+00 4.202645860216519e+00 1.25667e-09 7.14129e-09 ----------------------------------------------------------------------------------------------------- 19 N 1 1.650495088341997e+00 1.650495088786360e+00 4.44363e-10 1.61328e-09 2 3.030285925296104e+00 3.030285923040129e+00 2.25598e-09 1.56896e-09 3 -1.349054941736690e+00 -1.349054945640742e+00 3.90405e-09 4.74680e-09 ----------------------------------------------------------------------------------------------------- 20 N 1 9.214693754316012e-01 9.214693763183017e-01 8.86700e-10 1.58719e-09 2 1.633840073635478e+00 1.633840073624589e+00 1.08886e-11 6.02993e-10 3 -2.502052600091600e+00 -2.502052600162825e+00 7.12252e-11 1.17756e-09 ----------------------------------------------------------------------------------------------------- 21 N 1 5.167171005518072e-01 5.167171001391476e-01 4.12660e-10 1.54012e-09 2 2.031094545308370e+00 2.031094545794543e+00 4.86174e-10 1.61717e-09 3 5.920618693023916e-01 5.920618682863810e-01 1.01601e-09 5.82088e-08 ----------------------------------------------------------------------------------------------------- 22 Ga 1 -2.096480386717758e-01 -2.096480381179192e-01 5.53857e-10 5.53537e-09 2 -1.549814296011768e+00 -1.549814297834344e+00 1.82258e-09 1.10651e-09 3 3.767446966705439e+00 3.767446964933157e+00 1.77228e-09 1.78694e-08 ----------------------------------------------------------------------------------------------------- 23 N 1 -1.594867939955027e+00 -1.594867939774589e+00 1.80438e-10 1.99820e-09 2 3.177196822631759e+00 3.177196822373785e+00 2.57974e-10 1.95237e-09 3 -2.302331357985053e+00 -2.302331357939516e+00 4.55365e-11 8.39565e-08 * ----------------------------------------------------------------------------------------------------- 24 Ga 1 1.334694259280464e+00 1.334692989220505e+00 1.27006e-06 3.68205e-06 * 2 -5.255556302473332e+00 -5.255558063960271e+00 1.76149e-06 2.91640e-06 * 3 3.286261667443777e+00 3.286261667905315e+00 4.61538e-10 1.77147e-08 ----------------------------------------------------------------------------------------------------- 25 Ga 1 1.607158300985258e+00 1.607158304186572e+00 3.20131e-09 6.87085e-09 2 -2.216816031751179e-01 -2.216815927278052e-01 1.04473e-08 1.68251e-08 3 -1.058341774408790e+00 -1.058341773931646e+00 4.77144e-10 1.85954e-08 ----------------------------------------------------------------------------------------------------- 26 N 1 -3.802294863442389e-01 -3.802294854109102e-01 9.33329e-10 1.01203e-08 2 -1.443494873924889e+00 -1.443494877182206e+00 3.25732e-09 3.74929e-08 3 2.243303392404229e+00 2.243303395219563e+00 2.81533e-09 3.06612e-09 ----------------------------------------------------------------------------------------------------- 27 N 1 -1.155202576246420e+00 -1.155202518144509e+00 5.81019e-08 3.75357e-07 * 2 1.949151487587759e-01 1.949148641885605e-01 2.84570e-07 1.00364e-06 * 3 -2.931302284294107e-01 -2.931302279138968e-01 5.15514e-10 7.98860e-09 ----------------------------------------------------------------------------------------------------- 28 Ga 1 2.319000714322932e+00 2.319000712100203e+00 2.22273e-09 6.60117e-09 2 -6.250332685865569e-01 -6.250332658983248e-01 2.68823e-09 6.71939e-09 3 -1.871629823547672e+00 -1.871629820502468e+00 3.04520e-09 6.13256e-09 ----------------------------------------------------------------------------------------------------- 29 Ga 1 1.281157409373417e-01 1.281157426454515e-01 1.70811e-09 1.67407e-08 2 4.238463538502882e+00 4.238463537409978e+00 1.09290e-09 9.81009e-09 3 2.636561061067473e+00 2.636561046842514e+00 1.42250e-08 1.49355e-08 ----------------------------------------------------------------------------------------------------- 30 Ga 1 4.298365806776371e-01 4.298365826016525e-01 1.92402e-09 8.61407e-09 2 -9.069158978342812e-01 -9.069158965382472e-01 1.29603e-09 5.90908e-09 3 -5.618880578208946e-01 -5.618880584719973e-01 6.51103e-10 1.41265e-08 ----------------------------------------------------------------------------------------------------- 31 N 1 1.314487602302112e+00 1.314487600204975e+00 2.09714e-09 1.82930e-08 2 4.626118668169755e-01 4.626118749634426e-01 8.14647e-09 1.52662e-06 * 3 -3.735098287814139e-01 -3.735098271840684e-01 1.59735e-09 1.10531e-08 ----------------------------------------------------------------------------------------------------- 32 Ga 1 -8.312346553108083e-01 -8.312346555881033e-01 2.77295e-10 1.11207e-07 * 2 3.958095014218741e-01 3.958095015266928e-01 1.04819e-10 2.16531e-09 3 7.244504240081817e-01 7.244504245614337e-01 5.53252e-10 1.01195e-07 * ----------------------------------------------------------------------------------------------------- * 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 = 2: |F_model - F_numer| error = ----------------------- = 4.71276e-08 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 2.37079e-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 2.37079e-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.