!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_BOP_ZhouWardFoster_2016_AlCu__SM_566399258279_000 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 = 4.0662689208984375 | (Configuration in file "config-Al.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Al 1 8.423585806124422e-01 8.423585809390900e-01 3.26648e-10 4.59262e-10 2 4.898430120453185e-01 4.898430127597801e-01 7.14462e-10 2.46367e-09 3 4.858018739623052e-01 4.858018742200164e-01 2.57711e-10 1.22329e-07 * ----------------------------------------------------------------------------------------------------- 2 Al 1 -6.706736485646031e-01 -6.706736489993289e-01 4.34726e-10 2.46527e-09 2 4.815648209356713e-01 4.815648209397980e-01 4.12664e-12 2.29005e-09 3 7.136862671010386e-01 7.136862669385872e-01 1.62451e-10 4.13999e-10 ----------------------------------------------------------------------------------------------------- 3 Al 1 4.234478082259434e-01 4.234478086631595e-01 4.37216e-10 3.39749e-09 2 3.842966456678272e-01 3.842966460617513e-01 3.93924e-10 5.42127e-09 3 -4.368072606332887e-01 -4.368072585617265e-01 2.07156e-09 2.73226e-09 ----------------------------------------------------------------------------------------------------- 4 Al 1 7.265478387395453e-01 7.265478389895190e-01 2.49974e-10 7.33903e-09 2 2.133081771210907e-01 2.133081787961959e-01 1.67511e-09 2.89188e-09 3 2.761270168779434e-01 2.761270174267682e-01 5.48825e-10 1.32348e-08 ----------------------------------------------------------------------------------------------------- 5 Al 1 -8.647182545383639e-02 -8.647182523386047e-02 2.19976e-10 7.10585e-10 2 4.880417737189724e-01 4.880417742352415e-01 5.16269e-10 8.48538e-09 3 4.072897631385599e-01 4.072897632393022e-01 1.00742e-10 1.97992e-09 ----------------------------------------------------------------------------------------------------- 6 Al 1 -9.712819558007849e-01 -9.712819557592204e-01 4.15645e-11 2.31494e-09 2 5.257639347738803e-01 5.257639345885959e-01 1.85284e-10 8.03737e-10 3 8.533296819966961e-01 8.533296818986730e-01 9.80231e-11 2.93907e-09 ----------------------------------------------------------------------------------------------------- 7 Al 1 5.372585869462754e-01 5.372585864377371e-01 5.08538e-10 8.07425e-10 2 -5.934590615883581e-01 -5.934590616254872e-01 3.71291e-11 1.60843e-09 3 -9.726726623712930e-01 -9.726726610053261e-01 1.36597e-09 9.70166e-10 ----------------------------------------------------------------------------------------------------- 8 Al 1 -5.190766112721626e-01 -5.190766109971218e-01 2.75041e-10 2.29272e-09 2 -4.671064850646441e-01 -4.671064826427395e-01 2.42190e-09 1.48415e-08 3 -7.332517623961070e-01 -7.332517622026867e-01 1.93420e-10 1.01072e-08 ----------------------------------------------------------------------------------------------------- 9 Al 1 4.059860940015368e-01 4.059860941312965e-01 1.29760e-10 4.63979e-09 2 -6.923756250637301e-01 -6.923756252760984e-01 2.12368e-10 2.54728e-09 3 5.338018276385804e-01 5.338018277065187e-01 6.79383e-11 1.97680e-09 ----------------------------------------------------------------------------------------------------- 10 Al 1 -5.812897729950844e-01 -5.812897742430805e-01 1.24800e-09 3.87558e-10 2 -4.532819722513825e-03 -4.532819436200049e-03 2.86314e-10 2.65849e-09 3 -1.377480917021061e-02 -1.377480843621301e-02 7.33998e-10 3.20272e-09 ----------------------------------------------------------------------------------------------------- 11 Al 1 -5.783128122503016e-01 -5.783128117891234e-01 4.61178e-10 9.91189e-09 2 -4.650327315977341e-01 -4.650327285331503e-01 3.06458e-09 7.47409e-09 3 4.859309252444731e-01 4.859309250840425e-01 1.60431e-10 4.39693e-10 ----------------------------------------------------------------------------------------------------- 12 Al 1 8.160121161871234e-01 8.160121163899817e-01 2.02858e-10 2.35718e-09 2 -2.417161084106476e-01 -2.417161082660566e-01 1.44591e-10 2.49786e-07 * 3 2.669821879945917e-01 2.669821887682869e-01 7.73695e-10 3.38562e-09 ----------------------------------------------------------------------------------------------------- 13 Al 1 4.420149454617571e-01 4.420149455346504e-01 7.28932e-11 3.17927e-09 2 -9.366058068705400e-01 -9.366058057418938e-01 1.12865e-09 9.37560e-09 3 -1.188033167397691e+00 -1.188033169377290e+00 1.97960e-09 9.57097e-09 ----------------------------------------------------------------------------------------------------- 14 Al 1 -7.281740221318611e-01 -7.281740221085767e-01 2.32844e-11 1.26533e-09 2 -2.623472003940693e-01 -2.623472005996024e-01 2.05533e-10 1.47069e-09 3 5.570426265312592e-01 5.570426254385970e-01 1.09266e-09 1.06005e-09 ----------------------------------------------------------------------------------------------------- 15 Al 1 1.071977125662699e+00 1.071977124831171e+00 8.31528e-10 6.98205e-10 2 -7.256127030127607e-01 -7.256127032737760e-01 2.61015e-10 6.51998e-09 3 5.189487776807079e-01 5.189487780202421e-01 3.39534e-10 7.21488e-09 ----------------------------------------------------------------------------------------------------- 16 Al 1 7.179579208802305e-01 7.179579225315579e-01 1.65133e-09 6.99381e-09 2 9.840760976049920e-01 9.840760973621417e-01 2.42850e-10 3.75712e-09 3 2.540841925211219e-01 2.540841925775534e-01 5.64316e-11 1.25717e-08 ----------------------------------------------------------------------------------------------------- 17 Al 1 3.923634530767389e-01 3.923634524078896e-01 6.68849e-10 2.79125e-09 2 6.384975019066408e-01 6.384975022063241e-01 2.99683e-10 1.21668e-09 3 -3.065614195204647e-01 -3.065614215016462e-01 1.98118e-09 2.70857e-09 ----------------------------------------------------------------------------------------------------- 18 Al 1 -8.555072845424565e-01 -8.555072852887792e-01 7.46323e-10 4.19777e-09 2 6.335565646270399e-01 6.335565643870176e-01 2.40022e-10 5.71847e-09 3 8.606030088346380e-01 8.606030071861157e-01 1.64852e-09 8.36738e-09 ----------------------------------------------------------------------------------------------------- 19 Al 1 3.158074057814773e-01 3.158074060201855e-01 2.38708e-10 2.80256e-09 2 7.263354706660394e-01 7.263354707381282e-01 7.20888e-11 1.22437e-09 3 -3.856094950871063e-01 -3.856094946980373e-01 3.89069e-10 6.34863e-10 ----------------------------------------------------------------------------------------------------- 20 Al 1 9.355252102209208e-01 9.355252105175560e-01 2.96635e-10 2.26833e-09 2 7.465679962986278e-01 7.465679961621757e-01 1.36452e-10 1.25187e-09 3 -1.138056326081442e+00 -1.138056326508309e+00 4.26867e-10 3.27593e-09 ----------------------------------------------------------------------------------------------------- 21 Al 1 -9.892062622951823e-01 -9.892062614477375e-01 8.47445e-10 4.79268e-09 2 6.661922788453632e-02 6.661922858796655e-02 7.03430e-10 2.10830e-09 3 6.445599122997822e-01 6.445599121917422e-01 1.08040e-10 1.47330e-09 ----------------------------------------------------------------------------------------------------- 22 Al 1 -2.918260855255013e-01 -2.918260858994819e-01 3.73981e-10 2.79085e-09 2 1.357797382379259e+00 1.357797381057061e+00 1.32220e-09 6.86894e-09 3 1.109370116350707e+00 1.109370116226462e+00 1.24246e-10 5.53595e-09 ----------------------------------------------------------------------------------------------------- 23 Al 1 -8.159447664856437e-01 -8.159447664598592e-01 2.57845e-11 1.91022e-09 2 6.665882940513008e-01 6.665882940084265e-01 4.28744e-11 2.68254e-09 3 -6.673944143305048e-01 -6.673944142570196e-01 7.34852e-11 5.07310e-10 ----------------------------------------------------------------------------------------------------- 24 Al 1 4.333656214761078e-01 4.333656208569774e-01 6.19130e-10 9.46362e-09 2 2.710666646358186e-01 2.710666649937254e-01 3.57907e-10 3.53329e-07 * 3 -8.986312382976190e-01 -8.986312387619801e-01 4.64361e-10 8.97798e-09 ----------------------------------------------------------------------------------------------------- 25 Al 1 -1.556645894178955e-01 -1.556645895359357e-01 1.18040e-10 4.30647e-09 2 -9.468994976010086e-01 -9.468994977366818e-01 1.35673e-10 6.15631e-09 3 2.141618920680792e-01 2.141618894517048e-01 2.61637e-09 7.59359e-09 ----------------------------------------------------------------------------------------------------- 26 Al 1 -7.924961102007991e-01 -7.924961088911761e-01 1.30962e-09 3.84163e-09 2 3.346175018882921e-01 3.346175007475624e-01 1.14073e-09 7.66432e-09 3 -4.879357774713637e-01 -4.879357777086776e-01 2.37314e-10 6.38848e-09 ----------------------------------------------------------------------------------------------------- 27 Al 1 2.829033986100926e-01 2.829034002936953e-01 1.68360e-09 5.50485e-10 2 -1.763302543843792e+00 -1.763302542636306e+00 1.20749e-09 2.71845e-09 3 1.808031996610457e-01 1.808032034813122e-01 3.82027e-09 9.22391e-09 ----------------------------------------------------------------------------------------------------- 28 Al 1 3.059718145592747e-01 3.059718143827052e-01 1.76569e-10 1.01485e-09 2 -1.586695069976652e-01 -1.586695069504156e-01 4.72497e-11 3.58108e-09 3 -6.241727145076430e-01 -6.241727148793144e-01 3.71671e-10 7.53340e-09 ----------------------------------------------------------------------------------------------------- 29 Al 1 1.037838275905006e-01 1.037838273486434e-01 2.41857e-10 1.67369e-09 2 -6.216006127392323e-01 -6.216006123369636e-01 4.02269e-10 6.81025e-09 3 5.680803195027405e-01 5.680803196109724e-01 1.08232e-10 7.34220e-09 ----------------------------------------------------------------------------------------------------- 30 Al 1 -8.404883727170674e-01 -8.404883715531513e-01 1.16392e-09 1.17094e-08 2 -4.998127166352200e-01 -4.998127177413559e-01 1.10614e-09 7.37595e-09 3 2.282407607684850e-01 2.282407606815713e-01 8.69137e-11 9.38532e-09 ----------------------------------------------------------------------------------------------------- 31 Al 1 -4.698037798642396e-01 -4.698037797026338e-01 1.61606e-10 1.11511e-09 2 -6.436331868508344e-01 -6.436331857407830e-01 1.11005e-09 7.43202e-09 3 -7.707005686563267e-01 -7.707005677196798e-01 9.36647e-10 2.45635e-09 ----------------------------------------------------------------------------------------------------- 32 Al 1 5.929361514847551e-01 5.929361518804309e-01 3.95676e-10 1.54750e-08 2 1.416554018744284e-02 1.416554080486275e-02 6.17420e-10 1.05030e-08 3 -5.352427342516912e-01 -5.352427337176972e-01 5.33994e-10 3.84697e-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 = 10, direction = 2: |F_model - F_numer| error = ----------------------- = 6.31646e-08 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 = 3.6195430755615234 | (Configuration in file "config-Cu.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Cu 1 5.773038422029809e-01 5.773038423979167e-01 1.94936e-10 4.04744e-10 2 3.020199269552583e-01 3.020199269654033e-01 1.01450e-11 2.42410e-09 3 7.723750779543779e-01 7.723750780642467e-01 1.09869e-10 2.70815e-09 ----------------------------------------------------------------------------------------------------- 2 Cu 1 -5.253980191866382e-01 -5.253980193460845e-01 1.59446e-10 4.14754e-10 2 -2.602108494823553e-01 -2.602108490734938e-01 4.08862e-10 1.59108e-09 3 -1.690124752912110e+00 -1.690124752689601e+00 2.22510e-10 1.41765e-09 ----------------------------------------------------------------------------------------------------- 3 Cu 1 8.448077444830521e-01 8.448077453124159e-01 8.29364e-10 4.09206e-09 2 -6.260439484674215e-01 -6.260439482115776e-01 2.55844e-10 7.06572e-10 3 -1.121365183356141e+00 -1.121365184309872e+00 9.53731e-10 2.95077e-08 * ----------------------------------------------------------------------------------------------------- 4 Cu 1 -2.340228134948818e-01 -2.340228138370329e-01 3.42151e-10 8.83096e-10 2 2.320121524436140e+00 2.320121524641845e+00 2.05705e-10 1.44158e-09 3 -9.226466890309428e-01 -9.226466881740403e-01 8.56903e-10 1.58431e-09 ----------------------------------------------------------------------------------------------------- 5 Cu 1 -5.458122489734868e-01 -5.458122488829721e-01 9.05147e-11 2.34358e-09 2 4.105002470782123e-01 4.105002469668333e-01 1.11379e-10 8.85497e-10 3 3.910121337610080e-01 3.910121342978320e-01 5.36824e-10 3.45922e-09 ----------------------------------------------------------------------------------------------------- 6 Cu 1 -3.357182339444783e-01 -3.357182337723877e-01 1.72091e-10 4.32464e-10 2 -9.291306653849815e-01 -9.291306651865879e-01 1.98394e-10 2.67656e-09 3 3.649261626909206e-01 3.649261627308408e-01 3.99202e-11 1.30498e-09 ----------------------------------------------------------------------------------------------------- 7 Cu 1 -4.102399058507198e-01 -4.102399057350022e-01 1.15718e-10 2.37847e-09 2 1.078771308157445e+00 1.078771306522842e+00 1.63460e-09 3.92997e-09 3 1.635507251864781e-01 1.635507244065965e-01 7.79882e-10 3.97256e-09 ----------------------------------------------------------------------------------------------------- 8 Cu 1 1.356948966158221e+00 1.356948965827367e+00 3.30853e-10 4.25233e-09 2 -5.500143988146811e-01 -5.500143991025852e-01 2.87904e-10 2.10714e-09 3 8.737714843173787e-01 8.737714842183549e-01 9.90238e-11 1.03014e-09 ----------------------------------------------------------------------------------------------------- 9 Cu 1 1.649685840532728e+00 1.649685839254477e+00 1.27825e-09 1.43330e-09 2 -3.111065736101948e-01 -3.111065734777300e-01 1.32465e-10 1.02738e-09 3 1.338526417496578e+00 1.338526417913188e+00 4.16610e-10 9.54961e-10 ----------------------------------------------------------------------------------------------------- 10 Cu 1 -5.239001065972630e-01 -5.239001063012386e-01 2.96024e-10 3.37542e-09 2 -1.228102631924546e+00 -1.228102632115158e+00 1.90612e-10 7.07085e-10 3 1.157290409315531e+00 1.157290409110923e+00 2.04608e-10 7.07788e-09 ----------------------------------------------------------------------------------------------------- 11 Cu 1 -2.877899565428402e+00 -2.877899564950833e+00 4.77569e-10 6.24884e-09 2 5.797750773697203e-01 5.797750769959076e-01 3.73813e-10 3.75576e-09 3 6.961584403710613e-01 6.961584396798667e-01 6.91195e-10 1.32972e-08 * ----------------------------------------------------------------------------------------------------- 12 Cu 1 1.023503285743624e+00 1.023503285744854e+00 1.22991e-12 2.54428e-09 2 -7.604351529351427e-01 -7.604351525786807e-01 3.56462e-10 1.61587e-09 3 -5.104109894544311e-01 -5.104109894450825e-01 9.34863e-12 7.16998e-09 ----------------------------------------------------------------------------------------------------- 13 Cu 1 -2.930553309813737e-01 -2.930553311634602e-01 1.82087e-10 1.32602e-09 2 1.050747193549459e+00 1.050747194479685e+00 9.30226e-10 1.36493e-09 3 -2.141748705851665e+00 -2.141748704935897e+00 9.15768e-10 1.49296e-09 ----------------------------------------------------------------------------------------------------- 14 Cu 1 -8.996714666470261e-01 -8.996714669266523e-01 2.79626e-10 1.82102e-09 2 -9.220096050272351e-01 -9.220096050612657e-01 3.40307e-11 1.10355e-09 3 9.143288364081241e-01 9.143288360244969e-01 3.83627e-10 1.19610e-09 ----------------------------------------------------------------------------------------------------- 15 Cu 1 6.836757357655142e-01 6.836757352097137e-01 5.55801e-10 3.76380e-09 2 4.438795968522053e-01 4.438795965486637e-01 3.03542e-10 3.67251e-09 3 1.544480329012581e+00 1.544480328739113e+00 2.73468e-10 2.93591e-09 ----------------------------------------------------------------------------------------------------- 16 Cu 1 5.749960966250098e-01 5.749960961258312e-01 4.99179e-10 9.72813e-09 2 8.959296563318585e-01 8.959296567279001e-01 3.96042e-10 2.80509e-09 3 -1.778733416965621e+00 -1.778733417218672e+00 2.53052e-10 5.79542e-10 ----------------------------------------------------------------------------------------------------- 17 Cu 1 -1.513805297100274e+00 -1.513805297116197e+00 1.59233e-11 5.04152e-09 2 -2.169038127072048e+00 -2.169038126543762e+00 5.28286e-10 2.02982e-09 3 6.169256719379759e-01 6.169256720203805e-01 8.24046e-11 2.51569e-09 ----------------------------------------------------------------------------------------------------- 18 Cu 1 1.651979080309680e+00 1.651979080274062e+00 3.56182e-11 4.07453e-09 2 2.666768592868893e+00 2.666768593385392e+00 5.16499e-10 5.38118e-09 3 -1.043535904281593e+00 -1.043535904266204e+00 1.53888e-11 4.23139e-09 ----------------------------------------------------------------------------------------------------- 19 Cu 1 1.344183120912997e+00 1.344183121546407e+00 6.33410e-10 1.39354e-09 2 -7.138274775570164e-01 -7.138274770629413e-01 4.94075e-10 5.69094e-09 3 6.853961111290516e-01 6.853961111229866e-01 6.06504e-12 1.93768e-09 ----------------------------------------------------------------------------------------------------- 20 Cu 1 -7.062673244861389e-01 -7.062673238643554e-01 6.21784e-10 2.25582e-09 2 1.402208559140760e+00 1.402208559096020e+00 4.47391e-11 1.96157e-09 3 1.004275358587459e+00 1.004275358728421e+00 1.40962e-10 8.06749e-09 ----------------------------------------------------------------------------------------------------- 21 Cu 1 -8.881403001667857e-01 -8.881402996099087e-01 5.56877e-10 6.14778e-09 2 -9.377476791583815e-01 -9.377476793991627e-01 2.40781e-10 4.03907e-09 3 1.240037155136141e-01 1.240037141496142e-01 1.36400e-09 3.53022e-09 ----------------------------------------------------------------------------------------------------- 22 Cu 1 7.672053177944763e-01 7.672053176084356e-01 1.86041e-10 2.38955e-09 2 1.257297375388801e+00 1.257297377712646e+00 2.32384e-09 5.96089e-09 3 -1.085131011360610e+00 -1.085131011761105e+00 4.00495e-10 1.74585e-09 ----------------------------------------------------------------------------------------------------- 23 Cu 1 3.349828214326694e-01 3.349828216286030e-01 1.95934e-10 1.85997e-09 2 -5.686860072379993e-01 -5.686860070979597e-01 1.40040e-10 2.27085e-09 3 -1.684676478287322e-01 -1.684676481604839e-01 3.31752e-10 2.47418e-09 ----------------------------------------------------------------------------------------------------- 24 Cu 1 -1.825459035743539e+00 -1.825459035558621e+00 1.84919e-10 1.38087e-09 2 1.469226007187240e+00 1.469226006810915e+00 3.76325e-10 4.57712e-09 3 -5.390126714388818e-03 -5.390126748133404e-03 3.37446e-11 5.43244e-09 ----------------------------------------------------------------------------------------------------- 25 Cu 1 5.860123132045930e-01 5.860123143964533e-01 1.19186e-09 2.73921e-09 2 -5.611074648471093e-01 -5.611074645477493e-01 2.99360e-10 4.01160e-10 3 -9.778427274131971e-01 -9.778427274580199e-01 4.48228e-11 7.00634e-10 ----------------------------------------------------------------------------------------------------- 26 Cu 1 -9.012847702020492e-01 -9.012847702873965e-01 8.53473e-11 5.92654e-10 2 -9.417317455938981e-01 -9.417317456875907e-01 9.36926e-11 4.45341e-09 3 1.879918536293088e+00 1.879918536052845e+00 2.40243e-10 3.37576e-09 ----------------------------------------------------------------------------------------------------- 27 Cu 1 2.237556187785103e+00 2.237556187580671e+00 2.04432e-10 1.86655e-09 2 -8.226138902795300e-01 -8.226138904322774e-01 1.52747e-10 2.57517e-09 3 -1.012042291514023e+00 -1.012042291446184e+00 6.78393e-11 2.40911e-09 ----------------------------------------------------------------------------------------------------- 28 Cu 1 -4.221034532816290e-02 -4.221034523971643e-02 8.84465e-11 5.07709e-10 2 5.393843821662088e-01 5.393843820368666e-01 1.29342e-10 1.04072e-09 3 -6.852196123001257e-01 -6.852196121832940e-01 1.16832e-10 2.09309e-09 ----------------------------------------------------------------------------------------------------- 29 Cu 1 5.916938505720456e-01 5.916938523749247e-01 1.80288e-09 8.48361e-09 2 2.896544648221839e-01 2.896544648080520e-01 1.41320e-11 4.09398e-09 3 2.349123020540771e+00 2.349123019911261e+00 6.29510e-10 3.61884e-09 ----------------------------------------------------------------------------------------------------- 30 Cu 1 4.965430765961674e-01 4.965430766086814e-01 1.25140e-11 5.73822e-09 2 -9.226397163709888e-01 -9.226397177474405e-01 1.37645e-09 5.27549e-09 3 5.146641567548297e-01 5.146641574380125e-01 6.83183e-10 2.19024e-09 ----------------------------------------------------------------------------------------------------- 31 Cu 1 -8.576299446723766e-01 -8.576299427551830e-01 1.91719e-09 6.98508e-10 2 -6.459522604857380e-01 -6.459522612589831e-01 7.73245e-10 1.21274e-08 3 -1.380514955689316e+00 -1.380514956708056e+00 1.01874e-09 7.78536e-09 ----------------------------------------------------------------------------------------------------- 32 Cu 1 -1.340562571315271e+00 -1.340562573181423e+00 1.86615e-09 6.51653e-10 2 -8.358857180551179e-01 -8.358857173623866e-01 6.92731e-10 6.42686e-09 3 -8.675525725979315e-01 -8.675525726942490e-01 9.63175e-11 1.42111e-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 = 21, direction = 3: |F_model - F_numer| error = ----------------------- = 1.09997e-08 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 = 3.808666483326852 | (Configuration in file "config-AlCu.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Al 1 8.056192150315818e-01 8.056192150155975e-01 1.59843e-11 7.44689e-10 2 1.455097442543497e-01 1.455097439256789e-01 3.28671e-10 3.05477e-09 3 1.109696597313450e-01 1.109696594775423e-01 2.53803e-10 5.76860e-09 ----------------------------------------------------------------------------------------------------- 2 Cu 1 -6.236425180099940e-01 -6.236425175328734e-01 4.77121e-10 7.79468e-10 2 5.292159221730024e-02 5.292159256469145e-02 3.47391e-10 1.24825e-09 3 9.369851477665668e-01 9.369851479500380e-01 1.83471e-10 5.57525e-10 ----------------------------------------------------------------------------------------------------- 3 Cu 1 -6.811924660841805e-01 -6.811924660614436e-01 2.27369e-11 9.95093e-10 2 4.291211565389044e-01 4.291211563089677e-01 2.29937e-10 3.66024e-10 3 -5.312608785947485e-01 -5.312608784266220e-01 1.68127e-10 4.14177e-09 ----------------------------------------------------------------------------------------------------- 4 Cu 1 8.147962105096082e-01 8.147962114348734e-01 9.25265e-10 2.25642e-09 2 1.145128607966607e+00 1.145128608683202e+00 7.16595e-10 4.76656e-09 3 5.722507739838552e-01 5.722507737421959e-01 2.41659e-10 3.95745e-09 ----------------------------------------------------------------------------------------------------- 5 Cu 1 2.415336983209515e-01 2.415336985038867e-01 1.82935e-10 2.39272e-09 2 7.462775334975298e-01 7.462775337151158e-01 2.17586e-10 6.61166e-10 3 1.283675500597061e+00 1.283675500550219e+00 4.68416e-11 1.07573e-09 ----------------------------------------------------------------------------------------------------- 6 Cu 1 -2.030361989273949e-01 -2.030361992835585e-01 3.56164e-10 9.88756e-10 2 -1.137629854376883e+00 -1.137629853927757e+00 4.49127e-10 1.55074e-09 3 -5.799254553477627e-01 -5.799254560159357e-01 6.68173e-10 2.65906e-09 ----------------------------------------------------------------------------------------------------- 7 Cu 1 -9.535021563121645e-01 -9.535021564432141e-01 1.31050e-10 3.70124e-09 2 9.872957599581389e-01 9.872957599166147e-01 4.15242e-11 4.55218e-10 3 -3.558601177138681e-01 -3.558601182135578e-01 4.99690e-10 1.95925e-09 ----------------------------------------------------------------------------------------------------- 8 Cu 1 -6.424213565009969e-01 -6.424213571535282e-01 6.52531e-10 7.73955e-09 2 -1.240761693064954e+00 -1.240761693013696e+00 5.12583e-11 2.60315e-09 3 1.483813817353104e+00 1.483813817697481e+00 3.44377e-10 2.65005e-09 ----------------------------------------------------------------------------------------------------- 9 Cu 1 1.110515421198966e+00 1.110515420828231e+00 3.70735e-10 1.48867e-09 2 -2.883281862755256e-01 -2.883281860215089e-01 2.54017e-10 3.68846e-09 3 9.278780067125578e-01 9.278780077119959e-01 9.99438e-10 1.74732e-09 ----------------------------------------------------------------------------------------------------- 10 Al 1 2.633403610423688e-02 2.633403604831021e-02 5.59267e-11 3.50752e-09 2 -4.333038926781010e-01 -4.333038930273090e-01 3.49208e-10 6.29396e-09 3 5.231746080904754e-01 5.231746078657007e-01 2.24775e-10 5.81228e-09 ----------------------------------------------------------------------------------------------------- 11 Al 1 -5.750439212218325e-01 -5.750439217448446e-01 5.23012e-10 1.12806e-09 2 -1.819027613827082e+00 -1.819027614272464e+00 4.45382e-10 2.41126e-09 3 -1.368319084438067e+00 -1.368319082975334e+00 1.46273e-09 6.58549e-09 ----------------------------------------------------------------------------------------------------- 12 Al 1 -3.226817352145837e-01 -3.226817356705409e-01 4.55957e-10 1.41941e-08 2 -6.931324066071346e-01 -6.931324060728379e-01 5.34297e-10 5.18735e-09 3 -6.592614405754580e-01 -6.592614409394699e-01 3.64012e-10 2.39452e-09 ----------------------------------------------------------------------------------------------------- 13 Al 1 -5.384155447956370e-01 -5.384155447918890e-01 3.74800e-12 3.80821e-10 2 5.195476842546320e-01 5.195476841010155e-01 1.53617e-10 1.53123e-09 3 -1.215349175915525e+00 -1.215349176034267e+00 1.18742e-10 5.85306e-09 ----------------------------------------------------------------------------------------------------- 14 Al 1 -4.950538369656076e-01 -4.950538369170325e-01 4.85751e-11 2.12712e-09 2 -4.438714626906304e-01 -4.438714626006651e-01 8.99653e-11 1.74691e-09 3 7.985752235126002e-01 7.985752236817023e-01 1.69102e-10 9.52712e-09 ----------------------------------------------------------------------------------------------------- 15 Al 1 1.520146672101170e+00 1.520146671869223e+00 2.31946e-10 1.41533e-09 2 6.762337951637597e-01 6.762337930758365e-01 2.08792e-09 7.53071e-09 3 4.154441205304605e-01 4.154441206321440e-01 1.01683e-10 8.93085e-10 ----------------------------------------------------------------------------------------------------- 16 Cu 1 -4.612586989652821e-01 -4.612586991574557e-01 1.92174e-10 5.46763e-09 2 1.436235041560129e+00 1.436235041839999e+00 2.79871e-10 1.20991e-09 3 -1.339208214503259e+00 -1.339208215299297e+00 7.96037e-10 1.66024e-09 ----------------------------------------------------------------------------------------------------- 17 Al 1 1.106616016604927e-01 1.106616024831815e-01 8.22689e-10 2.05979e-09 2 1.482354448171631e-01 1.482354455145016e-01 6.97339e-10 2.68604e-09 3 -8.409073781645121e-01 -8.409073778238921e-01 3.40620e-10 3.24438e-09 ----------------------------------------------------------------------------------------------------- 18 Al 1 -2.832710972973927e-01 -2.832710984957900e-01 1.19840e-09 9.09949e-09 2 9.772797988676052e-01 9.772797997514578e-01 8.83853e-10 8.59143e-07 * 3 -1.179809549561311e+00 -1.179809549205818e+00 3.55493e-10 1.44656e-09 ----------------------------------------------------------------------------------------------------- 19 Al 1 7.473827612647170e-01 7.473827621153091e-01 8.50592e-10 4.29730e-09 2 -2.198740004207268e-01 -2.198740002098854e-01 2.10841e-10 3.57409e-09 3 7.118605216302509e-01 7.118605224544750e-01 8.24224e-10 2.53837e-09 ----------------------------------------------------------------------------------------------------- 20 Al 1 -5.866624623511998e-01 -5.866624622324366e-01 1.18763e-10 1.07975e-09 2 3.368383410108151e-01 3.368383413661649e-01 3.55350e-10 2.96949e-10 3 -4.411159648641474e-01 -4.411159646348637e-01 2.29284e-10 5.08105e-09 ----------------------------------------------------------------------------------------------------- 21 Al 1 9.904765953594304e-01 9.904765947720692e-01 5.87361e-10 2.97476e-09 2 -3.158835730103673e-01 -3.158835727655553e-01 2.44812e-10 3.54760e-09 3 -5.338437438547960e-01 -5.338437436761413e-01 1.78655e-10 2.35978e-09 ----------------------------------------------------------------------------------------------------- 22 Cu 1 -8.321622302369655e-01 -8.321622315064862e-01 1.26952e-09 3.55097e-09 2 -5.384808260016135e-01 -5.384808245678364e-01 1.43378e-09 2.27619e-09 3 6.330356125511077e-01 6.330356118054992e-01 7.45609e-10 1.46484e-08 ----------------------------------------------------------------------------------------------------- 23 Cu 1 -8.906589943183245e-01 -8.906589943553341e-01 3.70096e-11 2.72365e-10 2 1.231706693237209e+00 1.231706692823334e+00 4.13875e-10 1.26616e-09 3 -1.140658513872195e+00 -1.140658514663637e+00 7.91443e-10 3.52891e-09 ----------------------------------------------------------------------------------------------------- 24 Al 1 1.907615968405305e-01 1.907615955905825e-01 1.24995e-09 9.83029e-09 2 -1.152916770221473e+00 -1.152916769794678e+00 4.26795e-10 6.86715e-10 3 2.866277845821469e-01 2.866277825688751e-01 2.01327e-09 2.63308e-09 ----------------------------------------------------------------------------------------------------- 25 Cu 1 5.682859851611431e-01 5.682859850574485e-01 1.03695e-10 9.12570e-07 * 2 5.047414346492946e-01 5.047414326707830e-01 1.97851e-09 1.91681e-08 * 3 5.126659622132637e-01 5.126659636828388e-01 1.46958e-09 3.48928e-09 ----------------------------------------------------------------------------------------------------- 26 Cu 1 5.752982776345100e-03 5.752983492387305e-03 7.16042e-10 4.82686e-09 2 2.862482119302924e-01 2.862482114168012e-01 5.13491e-10 4.89236e-09 3 2.810343280030017e+00 2.810343279883839e+00 1.46178e-10 2.70491e-09 ----------------------------------------------------------------------------------------------------- 27 Al 1 -6.670024372566095e-02 -6.670024377605331e-02 5.03924e-11 1.93126e-09 2 1.768434895498147e+00 1.768434895253105e+00 2.45042e-10 8.13068e-10 3 -8.741312951128805e-01 -8.741312950944405e-01 1.84399e-11 2.61398e-09 ----------------------------------------------------------------------------------------------------- 28 Cu 1 1.129130157250567e+00 1.129130157276961e+00 2.63940e-11 2.59488e-09 2 -1.511684066768231e+00 -1.511684066503580e+00 2.64651e-10 4.48019e-09 3 -1.461215722602302e+00 -1.461215722530582e+00 7.17209e-11 4.88871e-09 ----------------------------------------------------------------------------------------------------- 29 Cu 1 -9.603215009907830e-01 -9.603215015503821e-01 5.59599e-10 1.91950e-09 2 -1.968215078260424e+00 -1.968215077742775e+00 5.17648e-10 4.27366e-09 3 1.102153007778882e+00 1.102153008392694e+00 6.13812e-10 5.65812e-09 ----------------------------------------------------------------------------------------------------- 30 Al 1 6.046538710530234e-01 6.046538707366915e-01 3.16332e-10 9.66471e-09 2 8.848718929222301e-01 8.848718905636057e-01 2.35862e-09 8.99233e-09 3 6.965499234428209e-01 6.965499233129844e-01 1.29836e-10 6.96603e-09 ----------------------------------------------------------------------------------------------------- 31 Al 1 -2.060651068493129e-01 -2.060651068450087e-01 4.30422e-12 8.52698e-09 2 9.734977997288572e-01 9.734977997739485e-01 4.50913e-11 9.25643e-09 3 -3.710344975982753e-01 -3.710344970573187e-01 5.40957e-10 2.92028e-09 ----------------------------------------------------------------------------------------------------- 32 Cu 1 4.560392641345482e-01 4.560392643677199e-01 2.33172e-10 5.09651e-10 2 -1.487016003869813e+00 -1.487016005046204e+00 1.17639e-09 3.61962e-09 3 -9.141019177874066e-01 -9.141019180657487e-01 2.78342e-10 3.44226e-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 = 26, direction = 1: |F_model - F_numer| error = ----------------------- = 1.24464e-07 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 1.24464e-07 Machine precision = 2.22045e-16 Note: Lower grades can reflect errors in the analytical forces, a lack of smoothness in the potential, or loss of precision in the numerical derivative computation. Grade: B Comment: The letter grade B was assigned because the normalized error in the computation was 1.24464e-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.