!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_Dynamo_LandaWynblattSiegel_2000_AlPb__MO_699137396381_005 Supported species : Al Pb 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 = Al | a0 = 4.031036376953125 | (Configuration in file "config-Al.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Al 1 1.599866776178732e-01 1.599866776249548e-01 7.08164e-12 2.41022e-09 2 -8.876071716314185e-02 -8.876071717638814e-02 1.32463e-11 3.00059e-10 3 -3.888217056248279e-01 -3.888217056443955e-01 1.95676e-11 8.97828e-09 * ----------------------------------------------------------------------------------------------------- 2 Al 1 -3.988240747470994e-01 -3.988240748121992e-01 6.50998e-11 3.16612e-10 2 8.454171049675216e-01 8.454171049937709e-01 2.62492e-11 1.65280e-09 3 6.318095309131225e-01 6.318095308920839e-01 2.10386e-11 1.36874e-10 ----------------------------------------------------------------------------------------------------- 3 Al 1 4.677623094058946e-01 4.677623082382189e-01 1.16768e-09 1.82848e-09 2 6.128897738007452e-01 6.128897737256009e-01 7.51442e-11 1.32386e-09 3 9.447265438152463e-01 9.447265439680912e-01 1.52845e-10 9.39429e-10 ----------------------------------------------------------------------------------------------------- 4 Al 1 6.745119471409337e-01 6.745119468694230e-01 2.71511e-10 1.71206e-09 2 4.106489063686919e-01 4.106489062231555e-01 1.45536e-10 1.19640e-09 3 9.466520925216145e-01 9.466520925325930e-01 1.09784e-11 6.33473e-10 ----------------------------------------------------------------------------------------------------- 5 Al 1 3.084813391441203e-01 3.084813391705790e-01 2.64587e-11 1.98200e-09 2 4.187037687992067e-02 4.187037708197911e-02 2.02058e-10 1.80473e-10 3 1.879818460779047e-02 1.879818476031942e-02 1.52529e-10 7.10690e-10 ----------------------------------------------------------------------------------------------------- 6 Al 1 -7.254138915042543e-01 -7.254138914979184e-01 6.33593e-12 2.01012e-09 2 4.467129265191091e-01 4.467129265272987e-01 8.18962e-12 1.83951e-10 3 6.341390949695787e-01 6.341390949652105e-01 4.36817e-12 3.70343e-10 ----------------------------------------------------------------------------------------------------- 7 Al 1 1.222492549770046e+00 1.222492549776917e+00 6.87073e-12 3.50913e-08 * 2 -2.072748476830046e+00 -2.072748476900092e+00 7.00453e-11 4.74475e-10 3 -2.376642895083067e+00 -2.376642895072840e+00 1.02269e-11 5.12335e-10 ----------------------------------------------------------------------------------------------------- 8 Al 1 -2.190170476696896e+00 -2.190170476653631e+00 4.32645e-11 7.80192e-09 * 2 -1.700767178504967e-01 -1.700767178417782e-01 8.71853e-12 6.02127e-10 3 -6.032300440929446e-01 -6.032300440861110e-01 6.83353e-12 6.11685e-10 ----------------------------------------------------------------------------------------------------- 9 Al 1 -1.167434426970921e-01 -1.167434427177780e-01 2.06860e-11 6.71386e-10 2 -1.687672001889381e+00 -1.687672001927433e+00 3.80525e-11 5.71681e-10 3 -1.936323473382547e+00 -1.936323473137714e+00 2.44833e-10 1.62757e-09 ----------------------------------------------------------------------------------------------------- 10 Al 1 -6.298938150866912e-01 -6.298938151925288e-01 1.05838e-10 5.23485e-10 2 1.465829629557806e-01 1.465829629512750e-01 4.50562e-12 2.82125e-10 3 -6.764358458437537e-01 -6.764358458751386e-01 3.13849e-11 1.03186e-09 ----------------------------------------------------------------------------------------------------- 11 Al 1 1.122017090110831e+00 1.122017090101846e+00 8.98503e-12 1.37773e-09 2 -1.127989071727034e+00 -1.127989071743501e+00 1.64675e-11 3.97239e-10 3 1.170516754088760e+00 1.170516754054405e+00 3.43550e-11 3.76146e-10 ----------------------------------------------------------------------------------------------------- 12 Al 1 6.608743672933781e-02 6.608743669138863e-02 3.79492e-11 3.35639e-10 2 1.609118960466649e+00 1.609118960473475e+00 6.82543e-12 1.23765e-10 3 1.847641134169584e+00 1.847641134121913e+00 4.76710e-11 2.23727e-10 ----------------------------------------------------------------------------------------------------- 13 Al 1 -1.422035350925680e+00 -1.422035351099392e+00 1.73712e-10 1.76758e-09 2 -1.616079113901057e+00 -1.616079114008723e+00 1.07666e-10 1.40674e-09 3 -2.109858103942613e+00 -2.109858103924731e+00 1.78813e-11 8.29047e-10 ----------------------------------------------------------------------------------------------------- 14 Al 1 6.606015802576022e-02 6.606015795499152e-02 7.07687e-11 2.32744e-10 2 6.131667532414972e-01 6.131667532479864e-01 6.48925e-12 9.03060e-10 3 -1.018841378091024e-01 -1.018841377966272e-01 1.24752e-11 2.68203e-10 ----------------------------------------------------------------------------------------------------- 15 Al 1 2.194244582953135e+00 2.194244582988322e+00 3.51874e-11 7.71532e-09 * 2 -6.041680197197429e-01 -6.041680197807434e-01 6.10005e-11 8.37823e-09 * 3 1.621752042705629e+00 1.621752042662117e+00 4.35116e-11 6.11834e-10 ----------------------------------------------------------------------------------------------------- 16 Al 1 5.798436718382444e-01 5.798436718311515e-01 7.09288e-12 8.65018e-09 * 2 1.286854471571993e+00 1.286854471584489e+00 1.24962e-11 2.43079e-10 3 1.149955849525606e+00 1.149955849526404e+00 7.98250e-13 3.26514e-09 ----------------------------------------------------------------------------------------------------- 17 Al 1 -4.910772102142713e-01 -4.910772101996278e-01 1.46435e-11 4.52620e-10 2 2.333763523834685e-01 2.333763524668031e-01 8.33346e-11 3.60302e-10 3 -9.913079837394306e-01 -9.913079837358204e-01 3.61022e-12 5.50802e-10 ----------------------------------------------------------------------------------------------------- 18 Al 1 3.557184404797287e-01 3.557184405085395e-01 2.88108e-11 2.13429e-10 2 1.363269687895046e+00 1.363269687894370e+00 6.76792e-13 2.68990e-10 3 -1.468126963309230e+00 -1.468126963432870e+00 1.23640e-10 2.75967e-09 ----------------------------------------------------------------------------------------------------- 19 Al 1 9.321343647433270e-01 9.321343648722260e-01 1.28899e-10 5.05292e-10 2 -4.879810830509868e-01 -4.879810830630144e-01 1.20275e-11 2.31275e-10 3 7.169263909750406e-01 7.169263909614151e-01 1.36255e-11 5.32818e-12 ----------------------------------------------------------------------------------------------------- 20 Al 1 2.918257005257585e-01 2.918257005322951e-01 6.53660e-12 5.69325e-08 * 2 6.707595070976569e-01 6.707595069529450e-01 1.44712e-10 3.48025e-10 3 -2.344385969594107e-01 -2.344385969006789e-01 5.87317e-11 2.45083e-10 ----------------------------------------------------------------------------------------------------- 21 Al 1 -2.354469605301627e+00 -2.354469605284681e+00 1.69464e-11 7.18208e-10 2 -2.998425680021786e-01 -2.998425680205879e-01 1.84093e-11 4.13346e-10 3 8.048262259494872e-01 8.048262259418750e-01 7.61213e-12 7.69427e-11 ----------------------------------------------------------------------------------------------------- 22 Al 1 8.045897693518784e-01 8.045897708282701e-01 1.47639e-09 3.00569e-09 2 2.724851593259774e+00 2.724851593114270e+00 1.45504e-10 2.37270e-10 3 1.281795009239071e+00 1.281795009329790e+00 9.07190e-11 6.93269e-10 ----------------------------------------------------------------------------------------------------- 23 Al 1 3.782249218766463e-02 3.782249222109687e-02 3.34322e-11 8.21039e-11 2 8.467998566638153e-02 8.467998565883077e-02 7.55077e-12 4.35261e-11 3 5.962623765945192e-01 5.962623765851109e-01 9.40825e-12 1.46693e-09 ----------------------------------------------------------------------------------------------------- 24 Al 1 1.750685949681869e-01 1.750685949814815e-01 1.32946e-11 3.37945e-09 2 4.030473785747876e-01 4.030473785984623e-01 2.36748e-11 3.11992e-08 * 3 -5.131389690383551e-01 -5.131389690203135e-01 1.80416e-11 8.28998e-09 * ----------------------------------------------------------------------------------------------------- 25 Al 1 -2.645697339169750e-01 -2.645697338898194e-01 2.71557e-11 1.44320e-09 2 -1.333470767046529e+00 -1.333470766967212e+00 7.93177e-11 1.92659e-10 3 -9.387667903936640e-01 -9.387667904380210e-01 4.43571e-11 3.85607e-10 ----------------------------------------------------------------------------------------------------- 26 Al 1 -4.543784676493481e-01 -4.543784676227057e-01 2.66425e-11 3.37170e-10 2 4.112223751903568e-01 4.112223751806778e-01 9.67904e-12 7.94255e-10 3 -7.853805346866483e-01 -7.853805346733672e-01 1.32810e-11 3.34408e-10 ----------------------------------------------------------------------------------------------------- 27 Al 1 1.324819537894587e+00 1.324819538047536e+00 1.52949e-10 3.87001e-09 2 -2.615012870093182e+00 -2.615012870018343e+00 7.48384e-11 1.44972e-09 3 1.928312410064705e-01 1.928312412181545e-01 2.11684e-10 1.19484e-09 ----------------------------------------------------------------------------------------------------- 28 Al 1 -1.180904947282354e+00 -1.180904947283184e+00 8.29781e-13 2.01798e-09 2 1.649598354804301e+00 1.649598354802568e+00 1.73284e-12 9.84876e-10 3 2.267350908298272e-01 2.267350908970939e-01 6.72667e-11 1.93614e-10 ----------------------------------------------------------------------------------------------------- 29 Al 1 -1.076488646873588e+00 -1.076488646776007e+00 9.75806e-11 1.63953e-10 2 -7.003640271724453e-01 -7.003640274861467e-01 3.13701e-10 5.69481e-09 3 2.967636377174587e-01 2.967636381244486e-01 4.06990e-10 2.56625e-09 ----------------------------------------------------------------------------------------------------- 30 Al 1 -6.094317713545976e-01 -6.094317713758811e-01 2.12835e-11 1.30997e-09 2 3.406115119222446e-01 3.406115119259883e-01 3.74367e-12 1.09914e-10 3 -8.179080599137570e-01 -8.179080601859888e-01 2.72232e-10 4.06999e-10 ----------------------------------------------------------------------------------------------------- 31 Al 1 6.134963118119855e-01 6.134963118798870e-01 6.79015e-11 3.58638e-10 2 -1.515725804072185e+00 -1.515725804082658e+00 1.04730e-11 1.58229e-10 3 8.235438967967804e-01 8.235438967904750e-01 6.30540e-12 2.59652e-10 ----------------------------------------------------------------------------------------------------- 32 Al 1 5.174384595511827e-01 5.174384600526573e-01 5.01475e-10 6.13873e-10 2 4.252122549524803e-01 4.252122549320755e-01 2.04048e-11 5.48833e-09 3 3.658900739376758e-02 3.658900741710719e-02 2.33396e-11 3.55918e-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 = 5, direction = 3: |F_model - F_numer| error = ----------------------- = 8.11403e-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 = Pb | a0 = 4.9091223716735835 | (Configuration in file "config-Pb.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Pb 1 3.565197336473972e-01 3.565197336479641e-01 5.66880e-13 1.00831e-10 2 3.553656944128217e-01 3.553656944128181e-01 3.55271e-15 5.53846e-12 3 3.193535740371709e-01 3.193535740351883e-01 1.98264e-12 3.46252e-11 ----------------------------------------------------------------------------------------------------- 2 Pb 1 3.066522099740622e-01 3.066522100094115e-01 3.53493e-11 5.76684e-11 2 1.173455927492374e-01 1.173455927307296e-01 1.85077e-11 1.36917e-10 3 4.419267680837324e-01 4.419267680676194e-01 1.61131e-11 8.03805e-11 ----------------------------------------------------------------------------------------------------- 3 Pb 1 2.401918503547116e-01 2.401918503524095e-01 2.30202e-12 7.65993e-10 2 5.260710620352773e-01 5.260710620350945e-01 1.82854e-13 1.59766e-07 * 3 1.446359667430365e-01 1.446359667451538e-01 2.11731e-12 5.07838e-10 ----------------------------------------------------------------------------------------------------- 4 Pb 1 4.028110581311516e-01 4.028110581332264e-01 2.07473e-12 3.22750e-11 2 2.085317219876038e-01 2.085317219732887e-01 1.43150e-11 2.02611e-10 3 8.828596688733448e-02 8.828596690219109e-02 1.48566e-11 3.13660e-11 ----------------------------------------------------------------------------------------------------- 5 Pb 1 -1.764098317184491e-01 -1.764098317362364e-01 1.77873e-11 9.43605e-11 2 3.458845109112106e-01 3.458845109194870e-01 8.27632e-12 3.27313e-10 3 3.297759896203810e-01 3.297759896290485e-01 8.66746e-12 5.77529e-11 ----------------------------------------------------------------------------------------------------- 6 Pb 1 -3.092927198419088e-01 -3.092927198422982e-01 3.89355e-13 7.24579e-11 2 3.812800485583041e-01 3.812800485520276e-01 6.27648e-12 3.98348e-11 3 1.423618108194072e-01 1.423618108182782e-01 1.12901e-12 2.87077e-10 ----------------------------------------------------------------------------------------------------- 7 Pb 1 -1.582214769367982e-01 -1.582214768876092e-01 4.91890e-11 2.89984e-10 2 -7.218288778485143e-02 -7.218288778377549e-02 1.07594e-12 8.00946e-11 3 4.131998990959417e-01 4.131998990973610e-01 1.41931e-12 1.39613e-10 ----------------------------------------------------------------------------------------------------- 8 Pb 1 -5.793791316947872e-01 -5.793791316735287e-01 2.12584e-11 1.27104e-11 2 3.735125473585780e-01 3.735125474312179e-01 7.26399e-11 1.98151e-09 * 3 2.330140756897355e-01 2.330140756997300e-01 9.99453e-12 2.67069e-10 ----------------------------------------------------------------------------------------------------- 9 Pb 1 3.558850757972318e-01 3.558850758010249e-01 3.79302e-12 4.65791e-11 2 -8.616478077491589e-02 -8.616478073894826e-02 3.59676e-11 2.98944e-10 3 4.060452031882597e-01 4.060452031746331e-01 1.36266e-11 1.49534e-10 ----------------------------------------------------------------------------------------------------- 10 Pb 1 1.018756038642731e-01 1.018756038685738e-01 4.30067e-12 1.51039e-09 * 2 -4.053457586453129e-01 -4.053457586389563e-01 6.35658e-12 2.61581e-11 3 2.541668556489434e-01 2.541668556515465e-01 2.60314e-12 1.41866e-10 ----------------------------------------------------------------------------------------------------- 11 Pb 1 -9.680920415569326e-02 -9.680920419807502e-02 4.23818e-11 3.34221e-10 2 5.900150656897313e-02 5.900150653888817e-02 3.00850e-11 1.36704e-10 3 3.834744483181161e-02 3.834744484780025e-02 1.59886e-11 3.33315e-10 ----------------------------------------------------------------------------------------------------- 12 Pb 1 4.637812096088245e-01 4.637812096064229e-01 2.40163e-12 3.66675e-10 2 -3.915167782224847e-01 -3.915167782469429e-01 2.44582e-11 1.27491e-10 3 1.889339502507662e-01 1.889339502649903e-01 1.42241e-11 3.49154e-11 ----------------------------------------------------------------------------------------------------- 13 Pb 1 -5.218159452888410e-01 -5.218159452795363e-01 9.30467e-12 2.44970e-09 * 2 -4.940834034560908e-01 -4.940834034674325e-01 1.13416e-11 1.28364e-10 3 3.438981447482772e-01 3.438981447488128e-01 5.35627e-13 2.49671e-11 ----------------------------------------------------------------------------------------------------- 14 Pb 1 6.075480024599621e-02 6.075480025135577e-02 5.35956e-12 2.52956e-11 2 -2.859657256241690e-02 -2.859657258852130e-02 2.61044e-11 1.66910e-11 3 1.550291859430724e-01 1.550291859647201e-01 2.16477e-11 1.49061e-10 ----------------------------------------------------------------------------------------------------- 15 Pb 1 -2.957849751338492e-01 -2.957849750092026e-01 1.24647e-10 7.15035e-10 2 -2.587352207623860e-01 -2.587352207658585e-01 3.47250e-12 3.31415e-10 3 5.835992360116879e-02 5.835992361775711e-02 1.65883e-11 4.61324e-11 ----------------------------------------------------------------------------------------------------- 16 Pb 1 -1.810106118307511e-01 -1.810106117934306e-01 3.73205e-11 3.43614e-10 2 -4.568826915108694e-01 -4.568826916472729e-01 1.36403e-10 4.27958e-10 3 3.772547805340146e-01 3.772547805269311e-01 7.08344e-12 1.42657e-10 ----------------------------------------------------------------------------------------------------- 17 Pb 1 3.492731513312506e-01 3.492731513250407e-01 6.20992e-12 6.18572e-11 2 -4.633643830799200e-03 -4.633643816391359e-03 1.44078e-11 3.28506e-10 3 -5.002514919950364e-01 -5.002514920017698e-01 6.73339e-12 2.60567e-11 ----------------------------------------------------------------------------------------------------- 18 Pb 1 2.528366460617837e-01 2.528366460595784e-01 2.20529e-12 4.65822e-09 * 2 -2.545792403637360e-01 -2.545792403657397e-01 2.00368e-12 1.13838e-10 3 -3.814219714486770e-01 -3.814219714631449e-01 1.44680e-11 9.16461e-09 * ----------------------------------------------------------------------------------------------------- 19 Pb 1 2.801113040880845e-01 2.801113040907593e-01 2.67480e-12 3.77886e-11 2 1.944544086756590e-01 1.944544086689197e-01 6.73930e-12 1.21803e-10 3 -3.970085389333714e-01 -3.970085389285941e-01 4.77735e-12 4.88974e-10 ----------------------------------------------------------------------------------------------------- 20 Pb 1 8.694168315065191e-03 8.694168315205534e-03 1.40343e-13 1.48336e-11 2 6.774036384373585e-01 6.774036384352873e-01 2.07123e-12 1.57580e-08 * 3 2.670416736835408e-01 2.670416737001481e-01 1.66074e-11 3.18073e-09 * ----------------------------------------------------------------------------------------------------- 21 Pb 1 -3.309089445057919e-01 -3.309089444956225e-01 1.01695e-11 2.06922e-10 2 3.077002821317750e-01 3.077002821258063e-01 5.96873e-12 1.48013e-10 3 -3.590283366395376e-01 -3.590283366373677e-01 2.16993e-12 1.88337e-10 ----------------------------------------------------------------------------------------------------- 22 Pb 1 -2.095946308672486e-01 -2.095946309669142e-01 9.96656e-11 4.19562e-10 2 -1.719024916371421e-01 -1.719024915902526e-01 4.68895e-11 2.34016e-10 3 -7.027502575596853e-02 -7.027502576481899e-02 8.85046e-12 3.52533e-10 ----------------------------------------------------------------------------------------------------- 23 Pb 1 -9.357765636495699e-02 -9.357765636291748e-02 2.03951e-12 7.71670e-11 2 3.372866352577891e-01 3.372866352508317e-01 6.95738e-12 2.10429e-10 3 -1.747108171128264e-01 -1.747108171150866e-01 2.26016e-12 4.58087e-10 ----------------------------------------------------------------------------------------------------- 24 Pb 1 -2.252598519249924e-01 -2.252598519208892e-01 4.10316e-12 8.87690e-11 2 2.614062732707455e-01 2.614062732875534e-01 1.68079e-11 3.47529e-11 3 -3.971054056099890e-01 -3.971054056083761e-01 1.61288e-12 5.74043e-11 ----------------------------------------------------------------------------------------------------- 25 Pb 1 1.917879509411171e-01 1.917879509277946e-01 1.33225e-11 1.40824e-09 * 2 -4.137999634989294e-01 -4.137999635084827e-01 9.55330e-12 2.40230e-10 3 -1.857584003003164e-01 -1.857584003274089e-01 2.70925e-11 2.49058e-10 ----------------------------------------------------------------------------------------------------- 26 Pb 1 3.041793202806060e-01 3.041793202712003e-01 9.40564e-12 9.67874e-11 2 -2.984061112252370e-01 -2.984061112321637e-01 6.92674e-12 2.08155e-11 3 -2.467755196937151e-01 -2.467755196709318e-01 2.27834e-11 8.70320e-11 ----------------------------------------------------------------------------------------------------- 27 Pb 1 1.024602307470459e-01 1.024602307504564e-01 3.41051e-12 5.13813e-11 2 -2.266304000990060e-02 -2.266304001836937e-02 8.46877e-12 2.94180e-10 3 -3.039195512385451e-01 -3.039195512286840e-01 9.86117e-12 8.95200e-11 ----------------------------------------------------------------------------------------------------- 28 Pb 1 4.198400337132779e-01 4.198400337176371e-01 4.35918e-12 1.01918e-10 2 -3.113977582910655e-01 -3.113977582971713e-01 6.10578e-12 2.99283e-10 3 -3.134265188297021e-01 -3.134265188206364e-01 9.06569e-12 2.08115e-10 ----------------------------------------------------------------------------------------------------- 29 Pb 1 -7.516023219095438e-02 -7.516023203335506e-02 1.57599e-10 4.99330e-10 2 2.260640954207275e-01 2.260640953675646e-01 5.31628e-11 3.60475e-10 3 -1.207944209216668e-01 -1.207944209500988e-01 2.84320e-11 1.74609e-09 * ----------------------------------------------------------------------------------------------------- 30 Pb 1 -4.212535257089619e-01 -4.212535256556652e-01 5.32967e-11 2.53750e-10 2 -1.148535742227959e-01 -1.148535742018689e-01 2.09270e-11 1.27245e-10 3 6.351492950545030e-02 6.351492948960662e-02 1.58437e-11 6.99763e-10 ----------------------------------------------------------------------------------------------------- 31 Pb 1 -3.341276480892393e-01 -3.341276480954455e-01 6.20615e-12 3.63619e-09 * 2 -1.951808162774203e-01 -1.951808162684163e-01 9.00394e-12 1.05078e-10 3 -4.249845464409727e-01 -4.249845464171084e-01 2.38643e-11 2.04398e-10 ----------------------------------------------------------------------------------------------------- 32 Pb 1 -1.890479608486554e-01 -1.890479608358890e-01 1.27663e-11 2.37992e-08 * 2 -3.903832846997064e-01 -3.903832847118530e-01 1.21466e-11 7.63835e-11 3 -3.896855979917201e-01 -3.896855980117724e-01 2.00523e-11 3.56494e-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 = 17, direction = 2: |F_model - F_numer| error = ----------------------- = 3.10940e-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 = Al Pb | a0 = 4.575947566220828 | (Configuration in file "config-AlPb.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Pb 1 -4.517961697656994e-01 -4.517961697776534e-01 1.19540e-11 3.44383e-11 2 -2.751800947517720e-01 -2.751800947515951e-01 1.76859e-13 2.31963e-10 3 2.278228861278499e-01 2.278228861367902e-01 8.94035e-12 1.62195e-10 ----------------------------------------------------------------------------------------------------- 2 Pb 1 9.286716998839925e-01 9.286716998536350e-01 3.03575e-11 1.20261e-10 2 9.370026037146271e-01 9.370026037207075e-01 6.08047e-12 1.49718e-10 3 3.109519228328189e-01 3.109519228464767e-01 1.36578e-11 4.52345e-11 ----------------------------------------------------------------------------------------------------- 3 Pb 1 -1.639936083404353e-01 -1.639936083745264e-01 3.40911e-11 2.17938e-10 2 3.362241534924326e-01 3.362241534935534e-01 1.12083e-12 3.74872e-11 3 4.788702156850665e-02 4.788702157240479e-02 3.89814e-12 2.44405e-10 ----------------------------------------------------------------------------------------------------- 4 Al 1 2.706376539503044e-01 2.706376540005642e-01 5.02599e-11 1.27374e-10 2 -1.445271681596465e-01 -1.445271681411323e-01 1.85142e-11 3.96487e-10 3 2.893272167790125e-01 2.893272167681412e-01 1.08714e-11 4.57858e-10 ----------------------------------------------------------------------------------------------------- 5 Al 1 -2.320038784293184e-01 -2.320038784355012e-01 6.18280e-12 4.27365e-11 2 3.407197430128022e-01 3.407197430488770e-01 3.60748e-11 3.24813e-10 3 5.119794354386618e-02 5.119794361416436e-02 7.02982e-11 1.30956e-10 ----------------------------------------------------------------------------------------------------- 6 Al 1 -7.824641848525005e-01 -7.824641848425489e-01 9.95160e-12 6.80553e-11 2 1.893593242642104e-01 1.893593242584861e-01 5.72434e-12 1.15930e-10 3 6.072852962402628e-01 6.072852962706545e-01 3.03917e-11 4.69513e-10 ----------------------------------------------------------------------------------------------------- 7 Pb 1 -1.932256474841201e-01 -1.932256474759346e-01 8.18556e-12 4.04727e-11 2 3.698399253336279e-01 3.698399253334973e-01 1.30618e-13 4.03172e-10 3 1.731490923273369e-01 1.731490923583010e-01 3.09641e-11 3.19773e-10 ----------------------------------------------------------------------------------------------------- 8 Al 1 1.278838938742116e-01 1.278838938729769e-01 1.23468e-12 4.99367e-09 * 2 4.492111855768313e-01 4.492111855761685e-01 6.62859e-13 4.98308e-10 3 5.830112029416831e-02 5.830112028771770e-02 6.45060e-12 7.78982e-11 ----------------------------------------------------------------------------------------------------- 9 Pb 1 2.090771851888495e-01 2.090771851924474e-01 3.59787e-12 7.35622e-11 2 -3.147461255405171e-01 -3.147461255473279e-01 6.81083e-12 2.98821e-11 3 -1.607858534478811e-01 -1.607858534207722e-01 2.71089e-11 3.90783e-10 ----------------------------------------------------------------------------------------------------- 10 Al 1 2.181043811755615e-01 2.181043811684722e-01 7.08930e-12 2.35066e-10 2 -3.597525431682868e-01 -3.597525431707377e-01 2.45087e-12 4.55845e-10 3 4.023416159244865e-01 4.023416159439530e-01 1.94665e-11 1.90523e-10 ----------------------------------------------------------------------------------------------------- 11 Pb 1 1.050488244322278e+00 1.050488244271374e+00 5.09042e-11 1.23427e-09 2 -8.241266631418573e-01 -8.241266631498017e-01 7.94431e-12 2.47763e-11 3 3.480883522421169e-01 3.480883522668836e-01 2.47667e-11 3.05757e-10 ----------------------------------------------------------------------------------------------------- 12 Pb 1 -1.489563813864873e-01 -1.489563813758974e-01 1.05899e-11 2.33469e-09 * 2 7.305496112471276e-01 7.305496112154869e-01 3.16407e-11 3.92980e-10 3 3.705629170670768e-01 3.705629170520771e-01 1.49997e-11 4.30468e-11 ----------------------------------------------------------------------------------------------------- 13 Al 1 7.444473718120695e-02 7.444473716529287e-02 1.59141e-11 6.96909e-10 2 -2.586986164541168e-01 -2.586986164568817e-01 2.76495e-12 6.51111e-08 * 3 3.301636016777839e-01 3.301636016689111e-01 8.87274e-12 3.01049e-10 ----------------------------------------------------------------------------------------------------- 14 Pb 1 -4.629102109937111e-01 -4.629102110013299e-01 7.61879e-12 1.15881e-10 2 -4.128398413334001e-01 -4.128398414071306e-01 7.37305e-11 4.41558e-10 3 4.070799896834003e-01 4.070799896924265e-01 9.02617e-12 1.30594e-10 ----------------------------------------------------------------------------------------------------- 15 Pb 1 -5.158026245213839e-01 -5.158026244924735e-01 2.89104e-11 8.86355e-10 2 -1.034753170113256e-01 -1.034753169653453e-01 4.59803e-11 8.26505e-11 3 -1.251188239199900e-01 -1.251188239254701e-01 5.48012e-12 1.79510e-10 ----------------------------------------------------------------------------------------------------- 16 Al 1 2.139040212363638e-02 2.139040208843917e-02 3.51972e-11 1.42748e-10 2 -3.479506445297636e-01 -3.479506445240482e-01 5.71543e-12 1.65263e-10 3 3.231244975488602e-01 3.231244974547601e-01 9.41001e-11 5.67896e-09 * ----------------------------------------------------------------------------------------------------- 17 Pb 1 2.238713798942444e-01 2.238713798789767e-01 1.52677e-11 4.44501e-10 2 1.105669079275816e-02 1.105669079527329e-02 2.51513e-12 9.16189e-10 3 -4.905960354588343e-01 -4.905960354538669e-01 4.96742e-12 1.84093e-10 ----------------------------------------------------------------------------------------------------- 18 Pb 1 4.965551040628334e-01 4.965551040582215e-01 4.61198e-12 5.09435e-10 2 -2.125889047685434e-01 -2.125889048569185e-01 8.83751e-11 5.12321e-10 3 -1.173007720364614e+00 -1.173007720341937e+00 2.26767e-11 3.08122e-10 ----------------------------------------------------------------------------------------------------- 19 Al 1 3.414808268390305e-01 3.414808268709969e-01 3.19664e-11 1.45637e-10 2 4.125751582373854e-01 4.125751582444277e-01 7.04226e-12 3.03657e-10 3 -2.931492769100569e-01 -2.931492769008767e-01 9.18021e-12 6.82667e-10 ----------------------------------------------------------------------------------------------------- 20 Pb 1 -4.423019139116575e-01 -4.423019138989758e-01 1.26817e-11 5.19393e-11 2 -8.986317973130764e-02 -8.986317974875065e-02 1.74430e-11 2.76649e-10 3 2.269623425147677e-01 2.269623425195280e-01 4.76033e-12 5.83185e-11 ----------------------------------------------------------------------------------------------------- 21 Pb 1 5.670625893696518e-01 5.670625893204576e-01 4.91942e-11 8.73047e-10 2 2.824783760593159e-02 2.824783764055701e-02 3.46254e-11 1.42239e-10 3 4.367861932753281e-01 4.367861932350903e-01 4.02379e-11 1.04882e-07 * ----------------------------------------------------------------------------------------------------- 22 Al 1 -8.376915650882848e-01 -8.376915650873743e-01 9.10494e-13 1.38682e-10 2 -1.570577988153460e-02 -1.570577988474415e-02 3.20955e-12 1.22650e-10 3 4.160152389388295e-01 4.160152388281315e-01 1.10698e-10 2.80868e-10 ----------------------------------------------------------------------------------------------------- 23 Al 1 -4.940344211532973e-01 -4.940344211507514e-01 2.54596e-12 1.57133e-10 2 5.353949361199295e-01 5.353949361195258e-01 4.03677e-13 5.61974e-11 3 -4.903954893287890e-01 -4.903954893321882e-01 3.39917e-12 3.01965e-10 ----------------------------------------------------------------------------------------------------- 24 Al 1 5.011841364879539e-02 5.011841363840469e-02 1.03907e-11 1.34399e-09 2 9.439901566798203e-02 9.439901565890302e-02 9.07902e-12 2.07482e-11 3 -5.630308781043190e-01 -5.630308781059704e-01 1.65146e-12 2.03642e-11 ----------------------------------------------------------------------------------------------------- 25 Al 1 1.865746686955203e-01 1.865746687106488e-01 1.51285e-11 5.13568e-10 2 -5.918479958868188e-02 -5.918479960248847e-02 1.38066e-11 1.40626e-10 3 -3.398555737010842e-01 -3.398555736294795e-01 7.16046e-11 3.51387e-10 ----------------------------------------------------------------------------------------------------- 26 Al 1 -1.736669690524337e-01 -1.736669690541267e-01 1.69303e-12 3.82074e-10 2 -5.007016832252811e-01 -5.007016832004964e-01 2.47847e-11 2.32914e-10 3 -6.586100291165483e-01 -6.586100291198070e-01 3.25873e-12 6.17378e-08 * ----------------------------------------------------------------------------------------------------- 27 Pb 1 7.448743821716977e-01 7.448743821032603e-01 6.84374e-11 1.29030e-10 2 8.652106390007329e-01 8.652106389934638e-01 7.26907e-12 6.13194e-11 3 5.028241865156072e-01 5.028241864589437e-01 5.66636e-11 7.51512e-09 * ----------------------------------------------------------------------------------------------------- 28 Pb 1 2.106050239872062e-01 2.106050239921197e-01 4.91354e-12 4.86536e-08 * 2 -2.776810170412393e-01 -2.776810170489465e-01 7.70722e-12 2.28952e-09 * 3 -1.697470651403053e-01 -1.697470651383921e-01 1.91319e-12 3.01196e-11 ----------------------------------------------------------------------------------------------------- 29 Al 1 2.747823363777688e-01 2.747823363604880e-01 1.72808e-11 2.26332e-10 2 -4.011383801234357e-02 -4.011383799029771e-02 2.20459e-11 4.16419e-08 * 3 1.057102981981586e-01 1.057102982054008e-01 7.24223e-12 2.87291e-10 ----------------------------------------------------------------------------------------------------- 30 Al 1 -6.028784689322521e-01 -6.028784689320809e-01 1.71196e-13 5.45256e-11 2 -5.132701043668383e-01 -5.132701043737162e-01 6.87794e-12 1.53132e-10 3 -1.765937363748047e-01 -1.765937363853464e-01 1.05417e-11 1.10432e-10 ----------------------------------------------------------------------------------------------------- 31 Al 1 -6.934606453663816e-01 -6.934606453781662e-01 1.17846e-11 9.66655e-11 2 -4.864121176052635e-02 -4.864121175829070e-02 2.23566e-12 6.33895e-11 3 -8.364556503999681e-01 -8.364556504195013e-01 1.95333e-11 6.67913e-09 * ----------------------------------------------------------------------------------------------------- 32 Pb 1 1.985637665311742e-01 1.985637665252545e-01 5.91968e-12 3.99737e-11 2 -5.007432915993968e-01 -5.007432916137051e-01 1.43083e-11 1.54163e-10 3 -1.582356010330430e-01 -1.582356010310290e-01 2.01406e-12 4.22097e-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 = 16, direction = 1: |F_model - F_numer| error = ----------------------- = 1.64547e-09 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 8.11403e-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: B Comment: The letter grade B was assigned because the normalized error in the computation was 8.11403e-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.