!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_LiuAdams_1998_AlMg__MO_019873715786_000 Supported species : Al Mg 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 = 4.03203821182 | (Configuration in file "config-Al.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Al 1 1.745492965883887e-01 1.745492966159416e-01 2.75529e-11 7.93579e-10 2 -5.737835870407611e-02 -5.737835873608123e-02 3.20051e-11 9.66495e-10 3 -3.454238241669093e-01 -3.454238242914145e-01 1.24505e-10 6.41391e-10 ----------------------------------------------------------------------------------------------------- 2 Al 1 -3.667022987726067e-01 -3.667022988334943e-01 6.08876e-11 3.47252e-11 2 9.000702681727947e-01 9.000702681687680e-01 4.02667e-12 2.87633e-10 3 5.351015000612519e-01 5.351015000393217e-01 2.19302e-11 2.56005e-10 ----------------------------------------------------------------------------------------------------- 3 Al 1 3.212331600540416e-01 3.212331597451783e-01 3.08863e-10 2.91252e-09 2 2.575760900805757e-01 2.575760899354251e-01 1.45151e-10 5.66482e-10 3 6.663859768675762e-01 6.663859768191226e-01 4.84536e-11 8.73222e-09 * ----------------------------------------------------------------------------------------------------- 4 Al 1 5.711930411444953e-01 5.711930411870904e-01 4.25950e-11 8.30686e-10 2 3.176049921630680e-01 3.176049924311549e-01 2.68087e-10 1.00506e-09 3 7.084580694061070e-01 7.084580695386316e-01 1.32525e-10 1.52923e-10 ----------------------------------------------------------------------------------------------------- 5 Al 1 5.076152238645958e-01 5.076152238383194e-01 2.62764e-11 3.03535e-10 2 8.268987694240956e-02 8.268987696614291e-02 2.37333e-11 2.50051e-10 3 2.634604766403715e-01 2.634604766322344e-01 8.13705e-12 1.37975e-10 ----------------------------------------------------------------------------------------------------- 6 Al 1 -6.621526681378701e-01 -6.621526682769527e-01 1.39083e-10 1.34537e-09 2 5.088182076835632e-01 5.088182076159741e-01 6.75892e-11 5.71306e-10 3 5.690512564792181e-01 5.690512565143795e-01 3.51614e-11 1.31764e-10 ----------------------------------------------------------------------------------------------------- 7 Al 1 3.019009259296090e-01 3.019009258293698e-01 1.00239e-10 7.88279e-10 2 -1.793227219888173e+00 -1.793227219909410e+00 2.12368e-11 3.10700e-10 3 -2.167477304017990e+00 -2.167477303985136e+00 3.28533e-11 2.53329e-10 ----------------------------------------------------------------------------------------------------- 8 Al 1 -1.130883193527468e+00 -1.130883193509241e+00 1.82270e-11 6.80873e-10 2 -7.416010415885840e-01 -7.416010416918450e-01 1.03261e-10 3.26681e-10 3 -7.615399350139989e-01 -7.615399350045343e-01 9.46454e-12 4.27297e-10 ----------------------------------------------------------------------------------------------------- 9 Al 1 -2.555835384608245e-01 -2.555835385009430e-01 4.01185e-11 7.12913e-10 2 -1.280959115449786e+00 -1.280959115444669e+00 5.11680e-12 3.21706e-09 3 -1.039667378815132e+00 -1.039667378815533e+00 4.01457e-13 8.74261e-11 ----------------------------------------------------------------------------------------------------- 10 Al 1 -6.773034898865141e-01 -6.773034898660409e-01 2.04732e-11 7.45839e-11 2 9.631738539818102e-01 9.631738539754039e-01 6.40632e-12 2.45090e-11 3 -1.226824709594330e+00 -1.226824709598869e+00 4.53859e-12 2.04674e-10 ----------------------------------------------------------------------------------------------------- 11 Al 1 9.481906517647362e-01 9.481906521168028e-01 3.52067e-10 1.00016e-09 2 -1.335537740002253e+00 -1.335537739975527e+00 2.67264e-11 5.85314e-09 * 3 8.647202920731641e-01 8.647202922060853e-01 1.32921e-10 2.08100e-09 ----------------------------------------------------------------------------------------------------- 12 Al 1 3.318848001259531e-01 3.318848000315036e-01 9.44494e-11 1.14646e-10 2 1.145581353996014e+00 1.145581354010982e+00 1.49674e-11 7.53095e-11 3 6.747653187744387e-01 6.747653188501305e-01 7.56918e-11 6.53474e-10 ----------------------------------------------------------------------------------------------------- 13 Al 1 -1.140934169059186e+00 -1.140934168830008e+00 2.29177e-10 5.35052e-10 2 -1.993337492046910e+00 -1.993337492017714e+00 2.91958e-11 1.28036e-08 * 3 -2.127350448344605e+00 -2.127350448328955e+00 1.56501e-11 1.49071e-09 ----------------------------------------------------------------------------------------------------- 14 Al 1 1.978926861027136e-01 1.978926860003271e-01 1.02386e-10 1.08810e-09 2 7.511961969752931e-01 7.511961968958856e-01 7.94075e-11 6.99895e-10 3 -1.867316856579596e-01 -1.867316854808356e-01 1.77124e-10 1.55027e-09 ----------------------------------------------------------------------------------------------------- 15 Al 1 2.137010867328399e+00 2.137010867262930e+00 6.54699e-11 1.81451e-09 2 -9.582490485232171e-01 -9.582490485170438e-01 6.17328e-12 9.47440e-11 3 1.336014867797333e+00 1.336014867784558e+00 1.27749e-11 8.67122e-11 ----------------------------------------------------------------------------------------------------- 16 Al 1 6.859482557561545e-01 6.859482558123812e-01 5.62267e-11 9.81002e-10 2 1.475601224593951e+00 1.475601224617556e+00 2.36051e-11 3.95485e-09 3 1.232084834291436e+00 1.232084834270779e+00 2.06568e-11 5.11535e-09 * ----------------------------------------------------------------------------------------------------- 17 Al 1 5.349913436978825e-01 5.349913437527648e-01 5.48823e-11 4.78557e-10 2 4.605679021867334e-01 4.605679021833194e-01 3.41399e-12 4.53047e-10 3 -4.873604890331529e-01 -4.873604889419325e-01 9.12204e-11 2.99061e-10 ----------------------------------------------------------------------------------------------------- 18 Al 1 -6.410464437272665e-01 -6.410464437419190e-01 1.46525e-11 5.06760e-10 2 4.336179962186532e-01 4.336179957856243e-01 4.33029e-10 1.45022e-09 3 7.631694883950432e-01 7.631694875000087e-01 8.95034e-10 2.19331e-09 ----------------------------------------------------------------------------------------------------- 19 Al 1 3.225830008808654e-01 3.225830009303303e-01 4.94649e-11 1.83956e-10 2 2.958321868953727e-01 2.958321869020760e-01 6.70336e-12 4.53452e-11 3 -6.177641730145318e-01 -6.177641730018044e-01 1.27274e-11 7.74750e-11 ----------------------------------------------------------------------------------------------------- 20 Al 1 6.002428557623840e-01 6.002428556396989e-01 1.22685e-10 7.21693e-10 2 7.049374112207414e-01 7.049374112240540e-01 3.31257e-12 3.34636e-10 3 -5.362869675130268e-01 -5.362869675930084e-01 7.99816e-11 2.25438e-09 ----------------------------------------------------------------------------------------------------- 21 Al 1 -1.208017165764165e+00 -1.208017165732199e+00 3.19653e-11 2.74009e-10 2 6.872341484535345e-02 6.872341492620014e-02 8.08467e-11 2.11981e-10 3 5.449711736755080e-01 5.449711736152481e-01 6.02599e-11 1.45349e-09 ----------------------------------------------------------------------------------------------------- 22 Al 1 2.960385782946995e-01 2.960385784106823e-01 1.15983e-10 3.33514e-10 2 2.332210426747679e+00 2.332210426764966e+00 1.72871e-11 1.69697e-10 3 1.941136123265029e+00 1.941136123321794e+00 5.67641e-11 5.65952e-10 ----------------------------------------------------------------------------------------------------- 23 Al 1 -4.197224490390847e-01 -4.197224490405000e-01 1.41537e-12 1.26766e-10 2 4.766351669579696e-01 4.766351669889679e-01 3.09982e-11 3.33161e-11 3 -3.714831910430815e-01 -3.714831910854649e-01 4.23834e-11 1.66728e-10 ----------------------------------------------------------------------------------------------------- 24 Al 1 1.120683430812869e-01 1.120683430814506e-01 1.63661e-13 4.47724e-09 2 3.942063706471708e-01 3.942063701324199e-01 5.14751e-10 2.16328e-10 3 -6.861847957776781e-01 -6.861847958324951e-01 5.48170e-11 1.11821e-08 * ----------------------------------------------------------------------------------------------------- 25 Al 1 -4.117963065043309e-01 -4.117963065042315e-01 9.93650e-14 9.14163e-11 2 -8.612321907896970e-01 -8.612321898812545e-01 9.08443e-10 1.54026e-09 3 1.430969248292232e+00 1.430969248294898e+00 2.66609e-12 6.24427e-09 * ----------------------------------------------------------------------------------------------------- 26 Al 1 -1.079499746386281e+00 -1.079499746463532e+00 7.72511e-11 1.75438e-09 2 5.329775151084877e-01 5.329775152601485e-01 1.51661e-10 7.92667e-10 3 -1.215600074877310e+00 -1.215600074749161e+00 1.28149e-10 1.59132e-09 ----------------------------------------------------------------------------------------------------- 27 Al 1 1.043606742515981e+00 1.043606741962869e+00 5.53112e-10 9.18941e-10 2 -2.856270150601528e+00 -2.856270151096143e+00 4.94616e-10 3.68397e-09 3 -2.170293996788922e-01 -2.170293996781796e-01 7.12652e-13 2.17468e-10 ----------------------------------------------------------------------------------------------------- 28 Al 1 -1.053299311928501e+00 -1.053299311856219e+00 7.22817e-11 1.33392e-10 2 1.015963190901050e+00 1.015963190898182e+00 2.86859e-12 2.58155e-10 3 -4.695534095904398e-01 -4.695534096228695e-01 3.24297e-11 2.22509e-10 ----------------------------------------------------------------------------------------------------- 29 Al 1 -5.531537557694860e-01 -5.531537559035716e-01 1.34086e-10 3.05035e-10 2 -1.000683958437602e+00 -1.000683958465155e+00 2.75535e-11 1.01726e-09 3 6.406712949908231e-01 6.406712948498451e-01 1.40978e-10 1.52603e-09 ----------------------------------------------------------------------------------------------------- 30 Al 1 -3.459446957820463e-01 -3.459446957779908e-01 4.05553e-12 4.90862e-10 2 3.619690946827852e-01 3.619690947094014e-01 2.66162e-11 2.91913e-10 3 -2.469965278174237e-01 -2.469965277988214e-01 1.86023e-11 4.77135e-10 ----------------------------------------------------------------------------------------------------- 31 Al 1 1.285788152685821e-01 1.285788152771988e-01 8.61669e-12 1.18405e-10 2 -1.219922929924225e+00 -1.219922929891309e+00 3.29154e-11 1.11210e-10 3 -1.486873816913145e-02 -1.486873817741954e-02 8.28809e-12 1.13876e-10 ----------------------------------------------------------------------------------------------------- 32 Al 1 7.305106445848616e-01 7.305106446061667e-01 2.13051e-11 3.51320e-10 2 6.184465049545742e-01 6.184465049281461e-01 2.64281e-11 1.22253e-09 3 5.471831311160613e-01 5.471831311250126e-01 8.95128e-12 8.94018e-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 dicontinuities. Maximum error obtained for particle = 24, direction = 2: |F_model - F_numer| error = ----------------------- = 1.30579e-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 = Mg | a0 = 4.50575714111 | (Configuration in file "config-Mg.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Mg 1 -2.637776135658366e-01 -2.637776135813273e-01 1.54907e-11 1.22562e-10 2 -1.830895091721561e-01 -1.830895091787003e-01 6.54429e-12 2.68684e-11 3 -1.117024131780133e-01 -1.117024132479534e-01 6.99402e-11 5.69216e-10 ----------------------------------------------------------------------------------------------------- 2 Mg 1 7.103331252508179e-01 7.103331252494959e-01 1.32205e-12 2.79712e-10 2 6.247726297230530e-01 6.247726297229605e-01 9.24816e-14 1.46075e-10 3 -5.625196207804612e-01 -5.625196207851068e-01 4.64551e-12 1.45706e-10 ----------------------------------------------------------------------------------------------------- 3 Mg 1 7.172023545344690e-01 7.172023545611502e-01 2.66812e-11 1.77582e-10 2 -6.096836930699668e-01 -6.096836930894565e-01 1.94896e-11 5.47558e-11 3 7.172150653147349e-01 7.172150653962207e-01 8.14858e-11 3.66057e-10 ----------------------------------------------------------------------------------------------------- 4 Mg 1 -5.398916150231298e-01 -5.398916150021725e-01 2.09572e-11 8.69952e-11 2 7.285168570123093e-01 7.285168570164726e-01 4.16334e-12 2.94985e-11 3 7.538268943955817e-01 7.538268943934777e-01 2.10398e-12 1.41134e-10 ----------------------------------------------------------------------------------------------------- 5 Mg 1 -2.957102573501635e-01 -2.957102573502127e-01 4.91274e-14 1.52798e-10 2 2.992551917720945e-01 2.992551917171217e-01 5.49729e-11 1.44312e-10 3 2.440348046799173e-01 2.440348046909094e-01 1.09921e-11 2.72735e-12 ----------------------------------------------------------------------------------------------------- 6 Mg 1 -3.165397051857832e-01 -3.165397051782962e-01 7.48696e-12 1.13485e-11 2 1.415119565725207e-01 1.415119565987977e-01 2.62770e-11 8.01068e-11 3 2.722106963925839e-01 2.722106963770914e-01 1.54924e-11 1.32740e-10 ----------------------------------------------------------------------------------------------------- 7 Mg 1 -3.034947179718250e-01 -3.034947179739430e-01 2.11792e-12 5.41778e-11 2 4.112839184014625e-01 4.112839184020874e-01 6.24889e-13 2.27125e-10 3 2.183848400043619e-01 2.183848400052989e-01 9.37028e-13 2.75154e-10 ----------------------------------------------------------------------------------------------------- 8 Mg 1 2.634861724683905e-01 2.634861724871239e-01 1.87334e-11 8.19612e-11 2 -4.075597078335030e-01 -4.075597078332440e-01 2.59015e-13 1.92464e-11 3 1.275888764254975e-01 1.275888764330665e-01 7.56908e-12 9.39384e-11 ----------------------------------------------------------------------------------------------------- 9 Mg 1 3.217673776844181e-01 3.217673776724146e-01 1.20035e-11 4.88402e-11 2 -1.268266585421089e-02 -1.268266582237988e-02 3.18310e-11 1.20747e-10 3 2.542351384801220e-01 2.542351384800532e-01 6.87783e-14 2.43609e-10 ----------------------------------------------------------------------------------------------------- 10 Mg 1 -2.815771589663562e-01 -2.815771589576606e-01 8.69560e-12 6.21693e-11 2 1.896868530112391e-01 1.896868530196868e-01 8.44771e-12 1.73154e-09 * 3 1.351079733225135e-01 1.351079733331406e-01 1.06271e-11 1.45267e-10 ----------------------------------------------------------------------------------------------------- 11 Mg 1 -8.709808498692010e-01 -8.709808498783920e-01 9.19098e-12 1.58407e-11 2 -8.421426107780976e-01 -8.421426107805486e-01 2.45104e-12 5.52139e-11 3 6.151499095717048e-01 6.151499095741111e-01 2.40630e-12 1.26177e-10 ----------------------------------------------------------------------------------------------------- 12 Mg 1 3.789047968102047e-03 3.789047965861802e-03 2.24024e-12 1.53788e-11 2 -7.903188121281658e-02 -7.903188121082058e-02 1.99600e-12 1.78234e-10 3 -3.072741254145031e-01 -3.072741254220492e-01 7.54613e-12 5.45871e-11 ----------------------------------------------------------------------------------------------------- 13 Mg 1 6.332761052540370e-01 6.332761052471986e-01 6.83842e-12 2.80817e-10 2 -6.780628806489299e-01 -6.780628806884101e-01 3.94802e-11 1.28071e-09 * 3 -4.516993641161401e-01 -4.516993641690842e-01 5.29441e-11 1.80715e-10 ----------------------------------------------------------------------------------------------------- 14 Mg 1 4.337426899387045e-03 4.337426905414370e-03 6.02733e-12 2.89292e-11 2 -9.060675874922791e-02 -9.060675874970019e-02 4.72275e-13 7.17797e-11 3 2.840188287346005e-01 2.840188287350486e-01 4.48086e-13 2.25286e-11 ----------------------------------------------------------------------------------------------------- 15 Mg 1 -6.657968824102754e-02 -6.657968824269773e-02 1.67019e-12 2.98587e-11 2 2.397508695009845e-01 2.397508694716532e-01 2.93314e-11 4.70852e-10 3 -3.448533136299899e-01 -3.448533136377607e-01 7.77073e-12 1.92784e-09 * ----------------------------------------------------------------------------------------------------- 16 Mg 1 5.005528358582663e-01 5.005528358494418e-01 8.82450e-12 1.88083e-12 2 3.194232454824686e-01 3.194232454986133e-01 1.61448e-11 4.70783e-11 3 -1.367531088323949e-01 -1.367531088601933e-01 2.77985e-11 8.68558e-10 ----------------------------------------------------------------------------------------------------- 17 Mg 1 3.315342247697775e-01 3.315342247749747e-01 5.19718e-12 6.55997e-11 2 3.089470386464022e-01 3.089470386398370e-01 6.56514e-12 1.06416e-10 3 -2.182238203891166e-01 -2.182238203796684e-01 9.44819e-12 5.12977e-11 ----------------------------------------------------------------------------------------------------- 18 Mg 1 -1.066326155050270e+00 -1.066326155030492e+00 1.97780e-11 4.12722e-10 2 1.726171656598164e-01 1.726171656483093e-01 1.15071e-11 1.59581e-09 * 3 -1.292631046831232e+00 -1.292631046768305e+00 6.29274e-11 9.54001e-10 ----------------------------------------------------------------------------------------------------- 19 Mg 1 8.622166027023155e-02 8.622166027019162e-02 3.99264e-14 2.35321e-11 2 3.114802655896057e-01 3.114802656041688e-01 1.45631e-11 1.59956e-10 3 -1.735081349704919e-01 -1.735081349732822e-01 2.79027e-12 6.24972e-11 ----------------------------------------------------------------------------------------------------- 20 Mg 1 7.397964497364171e-02 7.397964503258082e-02 5.89391e-11 1.89554e-10 2 -5.046616722945259e-01 -5.046616723138563e-01 1.93304e-11 2.33653e-11 3 2.695327904480599e-01 2.695327904767902e-01 2.87303e-11 1.90643e-11 ----------------------------------------------------------------------------------------------------- 21 Mg 1 -1.065628114179692e-01 -1.065628114020878e-01 1.58814e-11 2.71487e-11 2 -1.670866137255445e-01 -1.670866136988559e-01 2.66886e-11 1.23493e-09 * 3 -6.023128169235514e-01 -6.023128169771762e-01 5.36248e-11 9.69100e-10 ----------------------------------------------------------------------------------------------------- 22 Mg 1 2.713102251975538e-01 2.713102252185765e-01 2.10227e-11 5.27301e-10 2 -2.675082316812625e-01 -2.675082316035143e-01 7.77482e-11 3.05648e-10 3 -8.646050753972918e-01 -8.646050752901420e-01 1.07150e-10 3.08873e-10 ----------------------------------------------------------------------------------------------------- 23 Mg 1 1.254011446604523e-02 1.254011446835866e-02 2.31342e-12 4.36249e-11 2 -3.017831651997151e-01 -3.017831651983202e-01 1.39488e-12 2.74332e-11 3 3.738962279562703e-01 3.738962279500271e-01 6.24312e-12 4.14832e-11 ----------------------------------------------------------------------------------------------------- 24 Mg 1 6.099245927245546e-01 6.099245927223480e-01 2.20657e-12 5.94261e-10 2 -3.511661071310295e-01 -3.511661071307906e-01 2.38920e-13 4.78332e-11 3 1.165373933736946e+00 1.165373933738818e+00 1.87161e-12 9.53366e-11 ----------------------------------------------------------------------------------------------------- 25 Mg 1 -5.621569090752239e-01 -5.621569090769545e-01 1.73062e-12 8.66993e-11 2 -9.289431003321366e-01 -9.289431003337524e-01 1.61582e-12 1.13107e-10 3 -1.281106233700643e+00 -1.281106233698486e+00 2.15716e-12 4.39653e-11 ----------------------------------------------------------------------------------------------------- 26 Mg 1 8.302201774345207e-01 8.302201774392606e-01 4.73988e-12 1.37656e-10 2 5.600166580809955e-01 5.600166580742910e-01 6.70453e-12 4.02286e-09 * 3 1.686154297111557e-01 1.686154297402332e-01 2.90774e-11 7.85608e-11 ----------------------------------------------------------------------------------------------------- 27 Mg 1 3.983682308316571e-01 3.983682308546827e-01 2.30256e-11 2.35036e-10 2 -2.346480975659587e-01 -2.346480975795671e-01 1.36084e-11 7.06933e-11 3 3.218410269764571e-01 3.218410270066799e-01 3.02228e-11 1.18905e-10 ----------------------------------------------------------------------------------------------------- 28 Mg 1 -2.461050278591317e-01 -2.461050278433730e-01 1.57586e-11 2.15728e-11 2 6.920314339389022e-01 6.920314339422433e-01 3.34111e-12 2.05597e-11 3 6.228037809453278e-01 6.228037809460354e-01 7.07545e-13 4.58127e-11 ----------------------------------------------------------------------------------------------------- 29 Mg 1 -7.484924647494513e-01 -7.484924647283201e-01 2.11312e-11 1.19795e-09 * 2 5.155228868010291e-01 5.155228867993381e-01 1.69098e-12 1.59158e-09 * 3 -1.666631424912979e-01 -1.666631424727409e-01 1.85570e-11 5.44505e-10 ----------------------------------------------------------------------------------------------------- 30 Mg 1 -2.578560749679164e-01 -2.578560749687303e-01 8.13904e-13 3.20621e-11 2 -3.110109805290037e-01 -3.110109805247972e-01 4.20652e-12 3.55111e-10 3 6.341344703394662e-02 6.341344704468597e-02 1.07394e-11 2.52173e-11 ----------------------------------------------------------------------------------------------------- 31 Mg 1 3.955846615882970e-01 3.955846615789544e-01 9.34253e-12 1.79143e-10 2 1.532372459326170e-01 1.532372459033062e-01 2.93108e-11 4.52899e-10 3 2.904096417784562e-01 2.904096417864191e-01 7.96291e-12 4.19795e-10 ----------------------------------------------------------------------------------------------------- 32 Mg 1 -2.383769288808827e-01 -2.383769288798842e-01 9.98479e-13 6.69331e-10 2 3.016134596525850e-01 3.016134596421667e-01 1.04183e-11 3.04790e-12 3 -3.838070892531099e-01 -3.838070892562214e-01 3.11157e-12 1.39232e-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 = 9, direction = 2: |F_model - F_numer| error = ----------------------- = 2.50980e-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 Mg | a0 = 4.10804131159 | (Configuration in file "config-AlMg.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Al 1 3.696830062554649e-01 3.696830062506496e-01 4.81531e-12 7.78150e-11 2 3.634297255132603e-02 3.634297254693393e-02 4.39210e-12 1.75649e-10 3 -6.107299117276030e-02 -6.107299118289450e-02 1.01342e-11 6.14295e-10 ----------------------------------------------------------------------------------------------------- 2 Al 1 -1.622388764701438e+00 -1.622388764721139e+00 1.97009e-11 2.16523e-10 2 -6.324992173286973e-01 -6.324992173315491e-01 2.85183e-12 2.01074e-08 * 3 -1.322409912717904e+00 -1.322409912835874e+00 1.17970e-10 5.24147e-10 ----------------------------------------------------------------------------------------------------- 3 Mg 1 -1.111568815755719e+00 -1.111568815719722e+00 3.59965e-11 1.00587e-10 2 -1.743711872705465e+00 -1.743711872703175e+00 2.29061e-12 6.26376e-08 * 3 9.764005039165943e-01 9.764005039093441e-01 7.25020e-12 2.40241e-08 * ----------------------------------------------------------------------------------------------------- 4 Mg 1 -2.959880828949655e-01 -2.959880828933422e-01 1.62326e-12 5.40695e-10 2 -5.672733776659720e-01 -5.672733777513906e-01 8.54187e-11 1.45449e-08 * 3 3.220213623398201e-01 3.220213618972848e-01 4.42535e-10 5.46709e-09 * ----------------------------------------------------------------------------------------------------- 5 Al 1 -1.421717556939534e+00 -1.421717556985532e+00 4.59981e-11 1.93094e-09 2 -1.566621154530822e+00 -1.566621154484229e+00 4.65923e-11 5.18303e-10 3 -1.277324360605717e+00 -1.277324359605892e+00 9.99825e-10 2.46828e-09 ----------------------------------------------------------------------------------------------------- 6 Al 1 1.210378566986142e+00 1.210378566858334e+00 1.27808e-10 7.74218e-10 2 1.355647985762706e+00 1.355647985509026e+00 2.53680e-10 6.70433e-10 3 3.770628943205027e-02 3.770628943623633e-02 4.18605e-12 7.29366e-11 ----------------------------------------------------------------------------------------------------- 7 Mg 1 5.588427622690211e-01 5.588427622731343e-01 4.11327e-12 2.11301e-08 * 2 -2.601219814435800e-02 -2.601219816643357e-02 2.20756e-11 5.29017e-10 3 9.939838394410079e-01 9.939838394274876e-01 1.35203e-11 5.68472e-11 ----------------------------------------------------------------------------------------------------- 8 Al 1 1.542174807436280e+00 1.542174807426650e+00 9.63074e-12 1.74337e-10 2 1.421583248121277e+00 1.421583248136549e+00 1.52718e-11 8.00682e-09 * 3 2.491021602849371e+00 2.491021602865538e+00 1.61671e-11 2.94505e-10 ----------------------------------------------------------------------------------------------------- 9 Mg 1 -2.908451459897088e+00 -2.908451459933654e+00 3.65654e-11 3.34863e-10 2 -1.196599785365335e+00 -1.196599785869962e+00 5.04628e-10 8.39370e-10 3 -2.677435658906339e+00 -2.677435658506533e+00 3.99806e-10 1.66061e-09 ----------------------------------------------------------------------------------------------------- 10 Mg 1 1.624189900894324e+00 1.624189900901435e+00 7.11076e-12 1.81653e-10 2 2.156638413312463e+00 2.156638413349916e+00 3.74523e-11 6.58737e-10 3 -1.092373751242984e+00 -1.092373751223465e+00 1.95191e-11 6.89254e-10 ----------------------------------------------------------------------------------------------------- 11 Al 1 2.290576189081870e+00 2.290576189091378e+00 9.50795e-12 4.72844e-10 2 -7.015779119266682e-01 -7.015779119412432e-01 1.45750e-11 4.52873e-10 3 3.627976639826192e+00 3.627976639868266e+00 4.20735e-11 4.30969e-09 ----------------------------------------------------------------------------------------------------- 12 Al 1 2.739378269150006e-02 2.739378273698998e-02 4.54899e-11 3.95528e-10 2 2.364640656320936e-01 2.364640656299753e-01 2.11825e-12 1.18187e-11 3 1.151108754453936e+00 1.151108754504935e+00 5.09990e-11 1.60736e-09 ----------------------------------------------------------------------------------------------------- 13 Mg 1 8.155090233867003e-01 8.155090233387383e-01 4.79620e-11 4.55728e-10 2 1.503480324864753e+00 1.503480324873596e+00 8.84337e-12 2.77789e-09 3 -6.737609569622622e-01 -6.737609569418909e-01 2.03714e-11 5.77992e-11 ----------------------------------------------------------------------------------------------------- 14 Mg 1 2.032939481682803e-01 2.032939481661656e-01 2.11473e-12 1.17193e-10 2 3.997909647229443e-01 3.997909647238840e-01 9.39693e-13 1.27900e-11 3 -8.657966108916066e-01 -8.657966108912296e-01 3.77032e-13 2.23232e-10 ----------------------------------------------------------------------------------------------------- 15 Al 1 -4.244523453238880e-01 -4.244523453216552e-01 2.23283e-12 3.49195e-10 2 -8.356938201414259e-01 -8.356938200612600e-01 8.01659e-11 1.36596e-09 3 3.731860934740798e-01 3.731860934740634e-01 1.64313e-14 7.70393e-11 ----------------------------------------------------------------------------------------------------- 16 Al 1 -9.425589442103144e-01 -9.425589441960001e-01 1.43143e-11 2.16526e-10 2 3.732459876980341e-01 3.732459867194273e-01 9.78607e-10 7.48480e-09 * 3 -2.270507908278166e-01 -2.270507909004041e-01 7.25875e-11 1.61246e-10 ----------------------------------------------------------------------------------------------------- 17 Al 1 3.784857133950351e-01 3.784857133904166e-01 4.61842e-12 9.11509e-11 2 -1.404868170155983e-01 -1.404868170174036e-01 1.80528e-12 1.59579e-10 3 -4.262555900571069e-01 -4.262555900601662e-01 3.05922e-12 2.33638e-10 ----------------------------------------------------------------------------------------------------- 18 Mg 1 6.301172017086281e-01 6.301172018052656e-01 9.66376e-11 1.72853e-10 2 7.153258956552817e-01 7.153258955628272e-01 9.24545e-11 7.63874e-10 3 -1.143767910157196e+00 -1.143767910183339e+00 2.61431e-11 2.99659e-09 ----------------------------------------------------------------------------------------------------- 19 Al 1 8.239970237241265e-01 8.239970237196927e-01 4.43379e-12 1.35209e-10 2 -5.854258364296813e-01 -5.854258364398502e-01 1.01690e-11 3.59186e-11 3 6.114030269616003e-02 6.114030272259375e-02 2.64337e-11 7.19693e-10 ----------------------------------------------------------------------------------------------------- 20 Mg 1 -7.024483776610410e-01 -7.024483775944811e-01 6.65599e-11 2.51301e-09 2 7.698891084695758e-01 7.698891084273071e-01 4.22687e-11 2.58369e-10 3 6.282135087737765e-01 6.282135087947792e-01 2.10028e-11 1.10982e-10 ----------------------------------------------------------------------------------------------------- 21 Al 1 -1.096655814732840e+00 -1.096655814724217e+00 8.62310e-12 1.15875e-09 2 -4.310361693348320e-01 -4.310361693273622e-01 7.46980e-12 4.49724e-10 3 -1.063809019991352e+00 -1.063809019864387e+00 1.26965e-10 5.33997e-09 * ----------------------------------------------------------------------------------------------------- 22 Mg 1 2.888686280580333e-01 2.888686281010750e-01 4.30417e-11 3.10851e-10 2 2.243167958303647e-02 2.243167958312969e-02 9.32171e-14 1.12554e-10 3 -8.472505499172467e-01 -8.472505498955470e-01 2.16996e-11 1.01983e-08 * ----------------------------------------------------------------------------------------------------- 23 Mg 1 6.322474038126626e-01 6.322474037924449e-01 2.02177e-11 3.27061e-09 2 -2.522282760959521e-01 -2.522282760957945e-01 1.57652e-13 3.19221e-10 3 4.113321165511798e-01 4.113321165554196e-01 4.23983e-12 7.68226e-11 ----------------------------------------------------------------------------------------------------- 24 Al 1 -8.332744964684007e-01 -8.332744964977526e-01 2.93520e-11 2.02942e-10 2 5.287908823888625e-01 5.287908823612369e-01 2.76256e-11 1.98858e-10 3 5.091373458734317e-01 5.091373458079126e-01 6.55191e-11 3.87743e-10 ----------------------------------------------------------------------------------------------------- 25 Mg 1 -9.498828328565814e-03 -9.498828375049190e-03 4.64834e-11 2.61508e-10 2 3.992217839488205e-01 3.992217839639201e-01 1.50996e-11 4.15064e-11 3 4.038185151325093e-01 4.038185151249382e-01 7.57117e-12 2.92820e-11 ----------------------------------------------------------------------------------------------------- 26 Al 1 -1.873400662754884e+00 -1.873400662753875e+00 1.00897e-12 2.74359e-08 * 2 1.011990468181295e+00 1.011990468169101e+00 1.21940e-11 1.45329e-10 3 -1.407744275736451e+00 -1.407744275720764e+00 1.56870e-11 1.12436e-10 ----------------------------------------------------------------------------------------------------- 27 Mg 1 -1.053433116242958e+00 -1.053433116200752e+00 4.22062e-11 2.87240e-10 2 -9.533338913191782e-01 -9.533338913176926e-01 1.48559e-12 3.04227e-10 3 7.933626819083854e-01 7.933626818557087e-01 5.26768e-11 5.38521e-10 ----------------------------------------------------------------------------------------------------- 28 Al 1 4.527425075799302e-01 4.527425075567206e-01 2.32097e-11 1.89761e-09 2 -3.329044393450364e-01 -3.329044393461006e-01 1.06426e-12 4.71257e-09 3 -3.201507338654943e-01 -3.201507339002303e-01 3.47360e-11 5.42623e-10 ----------------------------------------------------------------------------------------------------- 29 Mg 1 1.002193749303968e+00 1.002193749395931e+00 9.19631e-11 9.01488e-09 * 2 -2.682401282993275e+00 -2.682401282982697e+00 1.05778e-11 1.62670e-10 3 -8.586819699362783e-01 -8.586819699273616e-01 8.91676e-12 9.55790e-10 ----------------------------------------------------------------------------------------------------- 30 Mg 1 1.076742562594837e+00 1.076742562612903e+00 1.80658e-11 4.84439e-11 2 7.370587553336533e-01 7.370587553167846e-01 1.68687e-11 2.58874e-11 3 -6.113636397647446e-01 -6.113636397911681e-01 2.64235e-11 6.38966e-11 ----------------------------------------------------------------------------------------------------- 31 Al 1 -2.288888784626369e-01 -2.288888784726835e-01 1.00466e-11 5.02224e-08 * 2 -1.953579298136443e-01 -1.953579298096738e-01 3.97055e-12 1.73889e-10 3 6.394924308503466e-01 6.394924308269597e-01 2.33868e-11 1.24211e-10 ----------------------------------------------------------------------------------------------------- 32 Mg 1 5.972893670274703e-01 5.972893670561930e-01 2.87227e-11 1.33720e-09 2 1.175261443929819e+00 1.175261443943366e+00 1.35472e-11 1.01105e-10 3 1.456346735234421e+00 1.456346735243929e+00 9.50862e-12 5.30318e-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 dicontinuities. Maximum error obtained for particle = 25, direction = 1: |F_model - F_numer| error = ----------------------- = 4.89359e-09 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 4.89359e-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: A Comment: The letter grade A was assigned because the normalized error in the computation was 4.89359e-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.