!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_CaiYe_1996_AlCu__MO_942551040047_005 Supported species : Al Cu 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 = 4.0497636795 | (Configuration in file "config-Al.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Al 1 1.821723049998889e-01 1.821723050139187e-01 1.40297e-11 2.72774e-10 2 -5.131290190063593e-01 -5.131290189805234e-01 2.58359e-11 5.88846e-10 3 -5.401038915076132e-01 -5.401038914836891e-01 2.39241e-11 4.79692e-10 ----------------------------------------------------------------------------------------------------- 2 Al 1 -1.371143241785678e-01 -1.371143241944652e-01 1.58974e-11 2.47465e-10 2 2.244744914456360e-01 2.244744914325849e-01 1.30512e-11 9.33575e-10 3 5.479308579805842e-01 5.479308579579336e-01 2.26505e-11 1.10961e-09 ----------------------------------------------------------------------------------------------------- 3 Al 1 1.885875378260023e-01 1.885875378995733e-01 7.35710e-11 9.70311e-11 2 5.171456481840753e-01 5.171456481737354e-01 1.03398e-11 7.65289e-10 3 7.014004890828605e-02 7.014004890462180e-02 3.66425e-12 9.03977e-10 ----------------------------------------------------------------------------------------------------- 4 Al 1 5.171447651631794e-01 5.171447651236624e-01 3.95171e-11 3.35847e-10 2 7.592343290942437e-01 7.592343291769943e-01 8.27506e-11 3.54387e-10 3 8.037051492778299e-01 8.037051493211654e-01 4.33356e-11 9.69275e-11 ----------------------------------------------------------------------------------------------------- 5 Al 1 -4.842868803784873e-02 -4.842868805265111e-02 1.48024e-11 1.18899e-10 2 1.166791619420475e-01 1.166791620429223e-01 1.00875e-10 2.55614e-10 3 3.623971490070830e-01 3.623971490045345e-01 2.54852e-12 1.16356e-10 ----------------------------------------------------------------------------------------------------- 6 Al 1 -1.569252091335669e-01 -1.569252091708298e-01 3.72629e-11 8.11597e-11 2 3.039842617760394e-01 3.039842617406796e-01 3.53598e-11 3.09383e-11 3 -4.022099171498634e-02 -4.022099158187156e-02 1.33115e-10 2.82819e-10 ----------------------------------------------------------------------------------------------------- 7 Al 1 1.406917972172262e-01 1.406917971064335e-01 1.10793e-10 2.13250e-09 * 2 -1.245308000414926e+00 -1.245308000423933e+00 9.00746e-12 3.44820e-10 3 -1.040499491666133e+00 -1.040499491663023e+00 3.10929e-12 6.57305e-10 ----------------------------------------------------------------------------------------------------- 8 Al 1 -1.452492547671443e+00 -1.452492547657859e+00 1.35834e-11 1.19300e-09 2 -1.216482565761554e+00 -1.216482565827511e+00 6.59572e-11 3.13006e-09 * 3 -2.513513201804498e-01 -2.513513201976618e-01 1.72121e-11 3.21389e-10 ----------------------------------------------------------------------------------------------------- 9 Al 1 -5.092187715145615e-01 -5.092187715287921e-01 1.42306e-11 6.68614e-10 2 -1.038731007263545e+00 -1.038731007281345e+00 1.78004e-11 2.44693e-10 3 -8.850220113794153e-01 -8.850220113797167e-01 3.01426e-13 5.95809e-10 ----------------------------------------------------------------------------------------------------- 10 Al 1 -2.878314010708692e-01 -2.878314009827884e-01 8.80808e-11 4.42313e-10 2 8.453136702716503e-01 8.453136702996432e-01 2.79929e-11 2.38341e-10 3 -7.848978305226502e-01 -7.848978305277409e-01 5.09071e-12 3.08433e-10 ----------------------------------------------------------------------------------------------------- 11 Al 1 7.551396606153019e-02 7.551396594172650e-02 1.19804e-10 4.64590e-10 2 -1.069007637285617e+00 -1.069007637398898e+00 1.13281e-10 3.25071e-10 3 9.601820995662305e-01 9.601820995616935e-01 4.53693e-12 2.76613e-10 ----------------------------------------------------------------------------------------------------- 12 Al 1 -1.892578452392191e-02 -1.892578451139200e-02 1.25299e-11 2.07655e-10 2 1.123976419582322e+00 1.123976419583094e+00 7.71827e-13 3.21571e-10 3 1.412391947944243e-01 1.412391947896450e-01 4.77929e-12 3.03239e-10 ----------------------------------------------------------------------------------------------------- 13 Al 1 2.353125879576852e-01 2.353125879185786e-01 3.91066e-11 3.61713e-10 2 -3.253147443068182e-01 -3.253147442850819e-01 2.17363e-11 1.22808e-10 3 -1.626717566147697e+00 -1.626717566199718e+00 5.20213e-11 3.82899e-10 ----------------------------------------------------------------------------------------------------- 14 Al 1 -9.690452140289115e-01 -9.690452140416550e-01 1.27435e-11 3.47786e-11 2 -9.233292238119005e-01 -9.233292238513090e-01 3.94085e-11 9.72269e-11 3 8.098566028756595e-01 8.098566028832463e-01 7.58682e-12 8.11385e-10 ----------------------------------------------------------------------------------------------------- 15 Al 1 1.866047630025326e+00 1.866047629973861e+00 5.14648e-11 2.47365e-10 2 9.995846078643413e-01 9.995846078933163e-01 2.89749e-11 2.80794e-10 3 1.817707645506156e-01 1.817707645271170e-01 2.34985e-11 3.85047e-10 ----------------------------------------------------------------------------------------------------- 16 Al 1 9.942079555085388e-01 9.942079555698790e-01 6.13402e-11 1.16444e-10 2 1.076791593908506e+00 1.076791593855524e+00 5.29818e-11 2.22975e-10 3 4.890198700350699e-01 4.890198700014445e-01 3.36254e-11 2.15151e-10 ----------------------------------------------------------------------------------------------------- 17 Al 1 2.508147762455906e-01 2.508147762119845e-01 3.36061e-11 1.30540e-09 * 2 2.356180634371101e-01 2.356180634405861e-01 3.47600e-12 3.67063e-10 3 -1.338149905187083e-01 -1.338149904725065e-01 4.62018e-11 2.12232e-10 ----------------------------------------------------------------------------------------------------- 18 Al 1 2.863282703471228e-01 2.863282702761042e-01 7.10185e-11 7.66628e-10 2 3.666578473329385e-01 3.666578473603821e-01 2.74436e-11 4.21222e-10 3 -5.983671348875357e-01 -5.983671348648254e-01 2.27103e-11 1.78302e-10 ----------------------------------------------------------------------------------------------------- 19 Al 1 2.348404795661742e-01 2.348404795883619e-01 2.21878e-11 2.04393e-10 2 2.669533127875059e-02 2.669533124408429e-02 3.46663e-11 4.01734e-10 3 -1.374115814764449e-01 -1.374115814722331e-01 4.21177e-12 1.62090e-10 ----------------------------------------------------------------------------------------------------- 20 Al 1 6.359041719731021e-03 6.359041765798401e-03 4.60674e-11 1.50685e-10 2 1.741228747661806e-01 1.741228748175624e-01 5.13818e-11 3.49720e-09 * 3 -6.996356568205342e-02 -6.996356566561594e-02 1.64375e-11 2.54439e-10 ----------------------------------------------------------------------------------------------------- 21 Al 1 -2.387072897800628e-01 -2.387072897813088e-01 1.24600e-12 1.24805e-10 2 2.524416504412040e-01 2.524416504359920e-01 5.21200e-12 9.74156e-11 3 7.755283293839572e-01 7.755283293910737e-01 7.11653e-12 1.85277e-10 ----------------------------------------------------------------------------------------------------- 22 Al 1 2.101520044371338e-01 2.101520044689032e-01 3.17693e-11 4.27982e-10 2 7.972972268365354e-01 7.972972268314638e-01 5.07161e-12 5.45677e-10 3 1.766231321453365e+00 1.766231321444422e+00 8.94262e-12 4.10102e-10 ----------------------------------------------------------------------------------------------------- 23 Al 1 -9.549365515092419e-01 -9.549365514723398e-01 3.69021e-11 4.00106e-10 2 7.581930630875200e-01 7.581930631206643e-01 3.31443e-11 1.02464e-10 3 -1.130330709504459e+00 -1.130330709430190e+00 7.42693e-11 1.85982e-10 ----------------------------------------------------------------------------------------------------- 24 Al 1 3.353769803200209e-01 3.353769802892714e-01 3.07496e-11 2.94684e-10 2 -2.082034035097646e-01 -2.082034034954786e-01 1.42860e-11 3.25048e-10 3 -4.210013777370574e-01 -4.210013777295860e-01 7.47141e-12 1.86578e-10 ----------------------------------------------------------------------------------------------------- 25 Al 1 5.264062226553008e-02 5.264062226801770e-02 2.48762e-12 1.99790e-10 2 -8.014999155670772e-01 -8.014999155538456e-01 1.32316e-11 1.89046e-10 3 8.125041749650616e-01 8.125041749803654e-01 1.53039e-11 1.45670e-10 ----------------------------------------------------------------------------------------------------- 26 Al 1 -4.534727483662568e-01 -4.534727483805767e-01 1.43198e-11 1.58162e-10 2 2.667516776657005e-01 2.667516776760849e-01 1.03844e-11 5.52642e-10 3 -4.322488335699582e-01 -4.322488335767097e-01 6.75149e-12 4.48305e-10 ----------------------------------------------------------------------------------------------------- 27 Al 1 9.275804816361793e-01 9.275804815891631e-01 4.70163e-11 1.14748e-09 2 -1.586996978034241e+00 -1.586996978023621e+00 1.06199e-11 1.76614e-10 3 -1.073181253174713e-01 -1.073181253396016e-01 2.21303e-11 4.82803e-10 ----------------------------------------------------------------------------------------------------- 28 Al 1 -9.512615217797110e-01 -9.512615218171474e-01 3.74364e-11 1.23790e-10 2 8.865157761157880e-01 8.865157761124592e-01 3.32878e-12 2.82153e-10 3 -3.742335263630023e-02 -3.742335260324058e-02 3.30597e-11 1.45883e-10 ----------------------------------------------------------------------------------------------------- 29 Al 1 -2.729004526380540e-01 -2.729004526561408e-01 1.80868e-11 1.63357e-10 2 -3.582224082803168e-01 -3.582224082259732e-01 5.43436e-11 5.15809e-11 3 7.214743243945867e-01 7.214743244138256e-01 1.92389e-11 1.73570e-10 ----------------------------------------------------------------------------------------------------- 30 Al 1 -3.230339614967271e-01 -3.230339614274142e-01 6.93129e-11 7.40182e-11 2 1.634818018970875e-01 1.634818018219666e-01 7.51209e-11 3.86816e-10 3 -3.635665855019868e-01 -3.635665855129083e-01 1.09215e-11 3.61236e-10 ----------------------------------------------------------------------------------------------------- 31 Al 1 -2.458717508380273e-01 -2.458717508539731e-01 1.59458e-11 1.81493e-10 2 -4.831175319560584e-01 -4.831175319239708e-01 3.20876e-11 6.92309e-11 3 1.914054335610489e-01 1.914054335389559e-01 2.20931e-11 3.61729e-10 ----------------------------------------------------------------------------------------------------- 32 Al 1 5.163950152709100e-01 5.163950152922848e-01 2.13748e-11 1.46996e-10 2 -1.256170617294985e-01 -1.256170616415500e-01 8.79485e-11 1.40459e-10 3 -3.312596080288219e-02 -3.312596081740679e-02 1.45246e-11 2.40252e-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 dicontinuities. Maximum error obtained for particle = 20, direction = 1: |F_model - F_numer| error = ----------------------- = 7.24439e-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 = Cu | a0 = 3.61472797394 | (Configuration in file "config-Cu.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Cu 1 1.604716788931273e+00 1.604716788909391e+00 2.18821e-11 1.14498e-10 2 1.769244198847294e+00 1.769244198862542e+00 1.52476e-11 1.85989e-10 3 1.716300599198801e+00 1.716300599212858e+00 1.40568e-11 1.23236e-10 ----------------------------------------------------------------------------------------------------- 2 Cu 1 -4.654908896081262e-01 -4.654908895976444e-01 1.04818e-11 2.26277e-10 2 -1.054505224781017e+00 -1.054505224734022e+00 4.69957e-11 2.56254e-10 3 -1.140245898056477e+00 -1.140245898041589e+00 1.48881e-11 2.82623e-10 ----------------------------------------------------------------------------------------------------- 3 Cu 1 4.770792851789719e-01 4.770792851662127e-01 1.27592e-11 2.75827e-10 2 -7.107130381333202e-01 -7.107130380955091e-01 3.78111e-11 1.85722e-10 3 -1.548506817999893e+00 -1.548506817934785e+00 6.51084e-11 1.34801e-10 ----------------------------------------------------------------------------------------------------- 4 Cu 1 -8.632853770692845e-01 -8.632853770471403e-01 2.21443e-11 7.13657e-11 2 -1.800230203279474e+00 -1.800230203338798e+00 5.93239e-11 1.04896e-10 3 9.740048981294512e-01 9.740048981311746e-01 1.72340e-12 2.22648e-10 ----------------------------------------------------------------------------------------------------- 5 Cu 1 -2.206769147759216e-01 -2.206769148152114e-01 3.92898e-11 2.12863e-10 2 1.560451712232473e-01 1.560451712231458e-01 1.01558e-13 1.64575e-10 3 3.248447416207811e-01 3.248447416083908e-01 1.23903e-11 1.26976e-10 ----------------------------------------------------------------------------------------------------- 6 Cu 1 -7.442417121221295e-02 -7.442417118438593e-02 2.78270e-11 1.37021e-10 2 7.607519153605238e-02 7.607519153599183e-02 6.05488e-14 7.11878e-11 3 6.786033221972037e-01 6.786033221831629e-01 1.40408e-11 3.22896e-10 ----------------------------------------------------------------------------------------------------- 7 Cu 1 7.483250649173395e-02 7.483250649636657e-02 4.63261e-12 5.93345e-11 2 -4.765394731415177e-01 -4.765394731512509e-01 9.73316e-12 1.64767e-10 3 -1.311890613455305e+00 -1.311890613536055e+00 8.07499e-11 5.01574e-10 ----------------------------------------------------------------------------------------------------- 8 Cu 1 9.681708222175361e-01 9.681708222095573e-01 7.97884e-12 2.48693e-10 2 1.023607988181390e+00 1.023607988132646e+00 4.87441e-11 7.89258e-11 3 -4.495862795986544e-01 -4.495862796374679e-01 3.88136e-11 2.06545e-10 ----------------------------------------------------------------------------------------------------- 9 Cu 1 -1.752368498845158e-01 -1.752368498766058e-01 7.91003e-12 2.47969e-10 2 1.300608994535050e+00 1.300608994529510e+00 5.54068e-12 1.92942e-10 3 -1.327512421111785e+00 -1.327512421112995e+00 1.21059e-12 9.75313e-11 ----------------------------------------------------------------------------------------------------- 10 Cu 1 3.409942924120464e-01 3.409942924032922e-01 8.75422e-12 1.75983e-10 2 -2.161091153166288e-01 -2.161091152733861e-01 4.32427e-11 4.62060e-10 3 -2.542876970698348e-03 -2.542876975458644e-03 4.76030e-12 6.80810e-10 ----------------------------------------------------------------------------------------------------- 11 Cu 1 2.583956709651667e+00 2.583956709618183e+00 3.34843e-11 2.79979e-10 2 -4.138886277432929e-01 -4.138886277480897e-01 4.79677e-12 3.67966e-10 3 5.380527368362293e-02 5.380527363972323e-02 4.38997e-11 1.62303e-10 ----------------------------------------------------------------------------------------------------- 12 Cu 1 -1.457754986789543e+00 -1.457754986742239e+00 4.73039e-11 3.81576e-10 2 1.687583499314053e+00 1.687583499307110e+00 6.94267e-12 5.20376e-10 3 -1.557211114262234e+00 -1.557211114291534e+00 2.92999e-11 9.30761e-10 ----------------------------------------------------------------------------------------------------- 13 Cu 1 6.204877448166137e-01 6.204877448073516e-01 9.26215e-12 3.27994e-10 2 1.187211166230518e+00 1.187211166398694e+00 1.68176e-10 5.87099e-10 3 7.001757304818663e-01 7.001757304393621e-01 4.25042e-11 4.52038e-11 ----------------------------------------------------------------------------------------------------- 14 Cu 1 -1.705517490617284e+00 -1.705517490586607e+00 3.06775e-11 1.82556e-10 2 -1.956217298678596e+00 -1.956217298783614e+00 1.05018e-10 2.70109e-10 3 2.093614857307308e+00 2.093614857342654e+00 3.53459e-11 8.57371e-10 ----------------------------------------------------------------------------------------------------- 15 Cu 1 -7.470820994976145e-01 -7.470820995593314e-01 6.17169e-11 1.70406e-10 2 5.378619604264440e-02 5.378619604201858e-02 6.25812e-13 1.88383e-10 3 -8.480812976375639e-01 -8.480812976157303e-01 2.18336e-11 9.10464e-11 ----------------------------------------------------------------------------------------------------- 16 Cu 1 -1.083186697599727e+00 -1.083186697627927e+00 2.81999e-11 6.35862e-11 2 1.264810968909035e+00 1.264810968878665e+00 3.03708e-11 1.36876e-09 3 -4.497653600040289e+00 -4.497653599963035e+00 7.72538e-11 2.99547e-10 ----------------------------------------------------------------------------------------------------- 17 Cu 1 -6.117603603021203e-01 -6.117603603118097e-01 9.68936e-12 1.11103e-10 2 -1.270809402183509e+00 -1.270809402149348e+00 3.41609e-11 6.87530e-10 3 -2.237397436479464e-01 -2.237397436522164e-01 4.27003e-12 1.96233e-09 * ----------------------------------------------------------------------------------------------------- 18 Cu 1 -1.571028896421602e+00 -1.571028896389996e+00 3.16058e-11 3.63948e-10 2 3.521098068457887e-02 3.521098066607402e-02 1.85049e-11 6.25262e-11 3 -1.298384518352411e+00 -1.298384518276523e+00 7.58882e-11 1.00064e-09 ----------------------------------------------------------------------------------------------------- 19 Cu 1 1.827663775969949e-02 1.827663774984451e-02 9.85498e-12 3.98269e-10 2 -5.560052135979396e-01 -5.560052135107135e-01 8.72261e-11 1.10949e-10 3 -1.775638617582955e-01 -1.775638618301945e-01 7.18990e-11 4.32884e-10 ----------------------------------------------------------------------------------------------------- 20 Cu 1 -9.225225200077411e-03 -9.225225184087985e-03 1.59894e-11 2.75380e-10 2 1.556889528466448e+00 1.556889528429545e+00 3.69031e-11 1.54783e-10 3 1.220051583077644e+00 1.220051583055765e+00 2.18785e-11 2.59967e-09 * ----------------------------------------------------------------------------------------------------- 21 Cu 1 -3.306907156620907e-01 -3.306907155633864e-01 9.87043e-11 8.13160e-07 * 2 -1.099557241231015e+00 -1.099557241253084e+00 2.20692e-11 9.71381e-10 3 2.316421247503055e+00 2.316421247493918e+00 9.13625e-12 1.96840e-10 ----------------------------------------------------------------------------------------------------- 22 Cu 1 1.229935502084373e-02 1.229935500326619e-02 1.75775e-11 2.61046e-10 2 1.304478221279195e+00 1.304478221171738e+00 1.07457e-10 8.39848e-10 3 1.265862953163016e+00 1.265862953178178e+00 1.51619e-11 1.62095e-06 * ----------------------------------------------------------------------------------------------------- 23 Cu 1 -1.391924943662552e+00 -1.391924943667761e+00 5.20894e-12 1.86258e-10 2 1.502183058430460e+00 1.502183058447330e+00 1.68701e-11 3.03868e-10 3 -2.121868254788160e+00 -2.121868254784109e+00 4.05098e-12 3.43228e-11 ----------------------------------------------------------------------------------------------------- 24 Cu 1 1.945144883702463e+00 1.945144883686071e+00 1.63916e-11 2.75093e-10 2 -3.086659876204574e-02 -3.086659881685752e-02 5.48118e-11 2.17672e-10 3 8.380238839207270e-01 8.380238837978264e-01 1.22901e-10 2.72796e-10 ----------------------------------------------------------------------------------------------------- 25 Cu 1 -2.125745944761875e+00 -2.125745944770047e+00 8.17213e-12 3.38215e-10 2 -2.252828290668062e+00 -2.252828290654210e+00 1.38520e-11 1.30122e-09 3 4.317090633061531e-01 4.317090632825994e-01 2.35537e-11 3.89946e-10 ----------------------------------------------------------------------------------------------------- 26 Cu 1 1.876495076579658e+00 1.876495076591477e+00 1.18190e-11 1.12571e-08 * 2 1.874737622342621e+00 1.874737622279335e+00 6.32860e-11 6.23797e-10 3 -7.844931099078342e-01 -7.844931099068707e-01 9.63452e-13 1.44668e-10 ----------------------------------------------------------------------------------------------------- 27 Cu 1 1.226714605465502e+00 1.226714605459307e+00 6.19438e-12 1.08252e-10 2 -1.185925440441161e+00 -1.185925440433012e+00 8.14926e-12 2.41183e-10 3 2.344937749068373e+00 2.344937749042680e+00 2.56932e-11 1.69526e-09 * ----------------------------------------------------------------------------------------------------- 28 Cu 1 -3.801875935346921e-01 -3.801875935274351e-01 7.25697e-12 1.68886e-10 2 6.605902558684654e-02 6.605902549983583e-02 8.70107e-11 2.61097e-10 3 1.350278010602162e-01 1.350278010509615e-01 9.25476e-12 1.71008e-10 ----------------------------------------------------------------------------------------------------- 29 Cu 1 -9.602977695183689e-01 -9.602977693995068e-01 1.18862e-10 1.64180e-10 2 -2.286928130552493e+00 -2.286928130534008e+00 1.84857e-11 1.55013e-09 * 3 8.331820815486450e-01 8.331820814134822e-01 1.35163e-10 7.89991e-10 ----------------------------------------------------------------------------------------------------- 30 Cu 1 3.429555855964645e+00 3.429555856008181e+00 4.35358e-11 4.55689e-09 * 2 1.510860991569568e+00 1.510860991579598e+00 1.00304e-11 7.35641e-10 3 4.780511949985402e-01 4.780511950270044e-01 2.84642e-11 3.62095e-10 ----------------------------------------------------------------------------------------------------- 31 Cu 1 -3.092342904101589e-02 -3.092342900431141e-02 3.67045e-11 2.24273e-10 2 -1.107856528562996e+00 -1.107856528485646e+00 7.73506e-11 2.85539e-10 3 4.699194046864492e-01 4.699194047284118e-01 4.19625e-11 1.72171e-10 ----------------------------------------------------------------------------------------------------- 32 Cu 1 -9.742842090340273e-01 -9.742842090561891e-01 2.21617e-11 5.69773e-11 2 4.958702389406777e-02 4.958702389016366e-02 3.90411e-12 6.26968e-10 3 4.147440226356933e-01 4.147440226829214e-01 4.72282e-11 5.18302e-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 dicontinuities. Maximum error obtained for particle = 10, direction = 3: |F_model - F_numer| error = ----------------------- = 1.87201e-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 Cu | a0 = 3.73177918923 | (Configuration in file "config-AlCu.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Cu 1 1.302673140973146e+00 1.302673140958142e+00 1.50047e-11 2.08297e-10 2 1.502954991142756e+00 1.502954991133210e+00 9.54636e-12 9.41989e-11 3 1.801912784073367e+00 1.801912784084022e+00 1.06546e-11 1.04594e-10 ----------------------------------------------------------------------------------------------------- 2 Al 1 -4.611877012132052e+00 -4.611877012136571e+00 4.51816e-12 5.58146e-10 2 -1.678492484576203e+00 -1.678492484617872e+00 4.16693e-11 4.17796e-10 3 -5.216878294019305e+00 -5.216878294134044e+00 1.14738e-10 1.29894e-10 ----------------------------------------------------------------------------------------------------- 3 Al 1 1.221838337799998e+00 1.221838337782763e+00 1.72351e-11 3.90778e-10 2 -2.919779054114609e+00 -2.919779054092876e+00 2.17328e-11 1.00960e-10 3 -3.482631335062518e+00 -3.482631335041669e+00 2.08491e-11 2.39975e-10 ----------------------------------------------------------------------------------------------------- 4 Cu 1 -1.391975419035786e+00 -1.391975419028334e+00 7.45159e-12 2.31690e-10 2 -4.870216379086002e-01 -4.870216379393508e-01 3.07506e-11 1.35665e-10 3 -5.495053521088649e-01 -5.495053521417612e-01 3.28964e-11 1.81830e-10 ----------------------------------------------------------------------------------------------------- 5 Cu 1 4.411238072793446e-02 4.411238076798602e-02 4.00516e-11 2.17797e-10 2 2.136049094288257e-01 2.136049094784596e-01 4.96338e-11 3.44643e-10 3 2.871337632587658e-01 2.871337632645365e-01 5.77077e-12 2.73789e-10 ----------------------------------------------------------------------------------------------------- 6 Al 1 4.758582790944280e-01 4.758582790697168e-01 2.47111e-11 1.44610e-09 * 2 -9.851332915737046e-01 -9.851332915939538e-01 2.02492e-11 2.70190e-10 3 -2.968267891757692e-01 -2.968267891780910e-01 2.32175e-12 2.92500e-10 ----------------------------------------------------------------------------------------------------- 7 Cu 1 2.725766893660784e-01 2.725766893658512e-01 2.27207e-13 2.84102e-10 2 -4.143062482917111e-01 -4.143062482052523e-01 8.64588e-11 3.27174e-10 3 -2.985824318669254e-01 -2.985824318244369e-01 4.24885e-11 3.14179e-10 ----------------------------------------------------------------------------------------------------- 8 Al 1 4.097951611224163e+00 4.097951611201095e+00 2.30678e-11 4.41890e-10 2 1.587877493233057e-01 1.587877493671580e-01 4.38523e-11 3.04522e-10 3 3.895106718538369e+00 3.895106718604407e+00 6.60374e-11 5.92982e-10 ----------------------------------------------------------------------------------------------------- 9 Cu 1 -9.186536529839120e-01 -9.186536529804481e-01 3.46390e-12 2.01837e-10 2 -1.311052240734261e-01 -1.311052240819840e-01 8.55782e-12 1.01128e-09 3 -1.818431036955208e+00 -1.818431036958381e+00 3.17346e-12 7.28184e-10 ----------------------------------------------------------------------------------------------------- 10 Cu 1 2.077752941607264e-01 2.077752941954667e-01 3.47402e-11 1.14115e-10 2 -2.885145565267068e-01 -2.885145565235915e-01 3.11529e-12 2.37949e-10 3 1.355731400704674e-01 1.355731400584883e-01 1.19791e-11 1.95379e-10 ----------------------------------------------------------------------------------------------------- 11 Al 1 1.903398212926936e+00 1.903398212984099e+00 5.71634e-11 5.24204e-10 2 2.444963311937371e-01 2.444963311861775e-01 7.55959e-12 2.03776e-10 3 1.324514012826904e+00 1.324514012823065e+00 3.83915e-12 7.24696e-10 ----------------------------------------------------------------------------------------------------- 12 Al 1 -9.604738518769049e-01 -9.604738519013813e-01 2.44764e-11 4.62840e-10 2 2.413467365524130e+00 2.413467365508307e+00 1.58233e-11 3.60100e-10 3 -4.071241135453623e-01 -4.071241136294677e-01 8.41053e-11 4.33098e-10 ----------------------------------------------------------------------------------------------------- 13 Cu 1 7.978547971636885e-01 7.978547971326517e-01 3.10367e-11 5.64366e-10 2 2.474943487902437e+00 2.474943487878713e+00 2.37246e-11 2.81136e-10 3 -5.363998925285250e-01 -5.363998925260082e-01 2.51688e-12 2.81426e-10 ----------------------------------------------------------------------------------------------------- 14 Cu 1 -5.790393771868250e-01 -5.790393771567717e-01 3.00533e-11 1.49863e-10 2 -7.626367809736389e-01 -7.626367809558469e-01 1.77920e-11 9.49836e-11 3 7.893443175672558e-01 7.893443175602715e-01 6.98430e-12 3.26400e-10 ----------------------------------------------------------------------------------------------------- 15 Al 1 1.286424607914997e+00 1.286424607892594e+00 2.24030e-11 1.41588e-09 2 -5.759379513233054e-01 -5.759379513034141e-01 1.98913e-11 3.29799e-10 3 -3.879323868619596e+00 -3.879323868587004e+00 3.25922e-11 8.67634e-10 ----------------------------------------------------------------------------------------------------- 16 Al 1 -7.576535370273300e-01 -7.576535370371581e-01 9.82814e-12 2.00013e-09 * 2 1.090182540243616e+00 1.090182540280064e+00 3.64471e-11 1.79695e-10 3 -1.120357277479189e+00 -1.120357277501771e+00 2.25824e-11 7.34229e-09 * ----------------------------------------------------------------------------------------------------- 17 Al 1 -4.043572659461143e+00 -4.043572659486479e+00 2.53362e-11 2.28239e-10 2 -1.973869361770043e+00 -1.973869361784619e+00 1.45768e-11 1.75890e-10 3 1.652511123800782e+00 1.652511123780973e+00 1.98097e-11 5.27303e-11 ----------------------------------------------------------------------------------------------------- 18 Al 1 2.379405593777195e+00 2.379405593805593e+00 2.83986e-11 7.31278e-10 2 3.131385576780260e+00 3.131385576715402e+00 6.48579e-11 1.48393e-10 3 7.637885496659593e-01 7.637885497212875e-01 5.53282e-11 2.05070e-10 ----------------------------------------------------------------------------------------------------- 19 Al 1 6.390275329028292e-01 6.390275328512338e-01 5.15954e-11 2.55494e-10 2 -6.472779416432350e-01 -6.472779415163765e-01 1.26859e-10 6.67617e-10 3 1.320637905655150e+00 1.320637905630061e+00 2.50897e-11 3.23441e-10 ----------------------------------------------------------------------------------------------------- 20 Cu 1 -5.720191379023981e-01 -5.720191379074315e-01 5.03342e-12 2.36107e-10 2 7.063661113217430e-01 7.063661114421365e-01 1.20393e-10 7.50228e-10 3 5.164122987288229e-01 5.164122986901124e-01 3.87105e-11 7.18778e-10 ----------------------------------------------------------------------------------------------------- 21 Cu 1 1.800333419362562e+00 1.800333419168647e+00 1.93914e-10 4.59844e-10 2 3.120521983006785e-01 3.120521983320216e-01 3.13431e-11 3.73733e-10 3 9.660550402082905e-01 9.660550401858985e-01 2.23920e-11 2.47376e-10 ----------------------------------------------------------------------------------------------------- 22 Al 1 2.048371510575160e-01 2.048371509872548e-01 7.02612e-11 2.07221e-10 2 -2.356387449147619e+00 -2.356387449198344e+00 5.07252e-11 3.04964e-10 3 2.861085567680175e+00 2.861085567809351e+00 1.29176e-10 3.34350e-10 ----------------------------------------------------------------------------------------------------- 23 Al 1 -2.029778555963950e+00 -2.029778555977678e+00 1.37277e-11 2.91880e-10 2 1.774031474379839e+00 1.774031474392602e+00 1.27629e-11 1.82201e-10 3 -2.136517460363538e+00 -2.136517460338316e+00 2.52216e-11 3.13123e-11 ----------------------------------------------------------------------------------------------------- 24 Cu 1 5.013166546396305e-01 5.013166546553859e-01 1.57554e-11 8.83216e-10 2 -1.415197588171535e-01 -1.415197588056039e-01 1.15496e-11 1.97375e-10 3 -9.474504308989991e-01 -9.474504309099168e-01 1.09177e-11 1.02622e-10 ----------------------------------------------------------------------------------------------------- 25 Al 1 -9.746270537346665e-01 -9.746270536205804e-01 1.14086e-10 1.01508e-09 2 -1.528210913463816e+00 -1.528210913459133e+00 4.68270e-12 3.83272e-10 3 1.310934783822640e+00 1.310934783816465e+00 6.17484e-12 1.34794e-10 ----------------------------------------------------------------------------------------------------- 26 Cu 1 1.503259980978865e-01 1.503259980686628e-01 2.92237e-11 1.79970e-10 2 7.506999429967031e-01 7.506999429547496e-01 4.19534e-11 1.98371e-09 * 3 -6.468727170654754e-01 -6.468727171045876e-01 3.91122e-11 2.06097e-10 ----------------------------------------------------------------------------------------------------- 27 Cu 1 1.077296288139228e-01 1.077296288628971e-01 4.89743e-11 1.77299e-10 2 -5.792873822596842e-01 -5.792873821769905e-01 8.26937e-11 6.67613e-10 3 -2.483723259794535e-01 -2.483723259066816e-01 7.27719e-11 3.30323e-10 ----------------------------------------------------------------------------------------------------- 28 Cu 1 3.656174642330087e-02 3.656174641661254e-02 6.68833e-12 4.55694e-10 2 -1.259616659603388e-01 -1.259616659737977e-01 1.34589e-11 4.95257e-10 3 -2.343245946950295e-02 -2.343245940330007e-02 6.62029e-11 2.68400e-10 ----------------------------------------------------------------------------------------------------- 29 Cu 1 -1.665070388657767e+00 -1.665070388659702e+00 1.93490e-12 4.35797e-10 2 -1.249941694720139e+00 -1.249941694721961e+00 1.82232e-12 9.94017e-10 3 1.262863430691137e+00 1.262863430647712e+00 4.34250e-11 1.42412e-10 ----------------------------------------------------------------------------------------------------- 30 Al 1 1.087844575856283e+00 1.087844575831465e+00 2.48186e-11 5.77931e-10 2 2.051044934487689e+00 2.051044934504206e+00 1.65166e-11 1.93465e-09 * 3 2.039092246799980e+00 2.039092246801779e+00 1.79901e-12 3.72245e-10 ----------------------------------------------------------------------------------------------------- 31 Cu 1 -3.708275092038777e-01 -3.708275092009786e-01 2.89907e-12 1.72359e-10 2 -4.992181684433037e-01 -4.992181684381327e-01 5.17109e-12 1.47593e-10 3 -3.949435615344283e-01 -3.949435615672973e-01 3.28690e-11 2.58135e-10 ----------------------------------------------------------------------------------------------------- 32 Al 1 3.577225028833890e-01 3.577225028424937e-01 4.08952e-11 2.52698e-11 2 5.205839525615173e-01 5.205839525742197e-01 1.27024e-11 8.32711e-10 3 1.076683663284589e+00 1.076683663104360e+00 1.80229e-10 2.76964e-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 dicontinuities. Maximum error obtained for particle = 28, direction = 3: |F_model - F_numer| error = ----------------------- = 2.82526e-09 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 7.24439e-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 7.24439e-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.