!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 : MEAM_LAMMPS_JeongParkDo_2018_PdMo__MO_356501945107_002 Supported species : Mo Pd 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 = Mo | a0 = 3.9763078689575195 | (Configuration in file "config-Mo.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Mo 1 -3.469958011342324e+00 -3.469958011346305e+00 3.98126e-12 4.94770e-10 2 -3.734842214395171e+00 -3.734842214387856e+00 7.31459e-12 1.45488e-11 3 -5.717425684710198e+00 -5.717425684712648e+00 2.44960e-12 2.21489e-10 ----------------------------------------------------------------------------------------------------- 2 Mo 1 4.672737901111168e-01 4.672737901108652e-01 2.51577e-13 1.59883e-10 2 4.664190437468855e+00 4.664190437459874e+00 8.98037e-12 4.34394e-10 3 -1.258901395971228e+00 -1.258901395972303e+00 1.07558e-12 6.04352e-11 ----------------------------------------------------------------------------------------------------- 3 Mo 1 6.636404506150435e+00 6.636404506155296e+00 4.86100e-12 5.35985e-10 2 -4.489812859602999e+00 -4.489812859593177e+00 9.82237e-12 8.21281e-11 3 4.657532045768531e+00 4.657532045777618e+00 9.08695e-12 1.04061e-10 ----------------------------------------------------------------------------------------------------- 4 Mo 1 -2.573597140460425e+00 -2.573597140461512e+00 1.08713e-12 9.40128e-11 2 7.125968330859084e+00 7.125968330859246e+00 1.61648e-13 2.81526e-11 3 3.251217998298293e+00 3.251217998300249e+00 1.95621e-12 1.96072e-10 ----------------------------------------------------------------------------------------------------- 5 Mo 1 1.989871192298843e+00 1.989871192318139e+00 1.92961e-11 8.59970e-11 2 7.833205913354344e-02 7.833205913443092e-02 8.87485e-13 1.33334e-11 3 1.421592502813756e+00 1.421592502815853e+00 2.09721e-12 3.25837e-11 ----------------------------------------------------------------------------------------------------- 6 Mo 1 -1.588253633233466e+00 -1.588253633232821e+00 6.45040e-13 2.48772e-11 2 -2.329420328867488e-02 -2.329420328993138e-02 1.25651e-12 1.13602e-11 3 1.389629044643742e+00 1.389629044640572e+00 3.17035e-12 1.39810e-10 ----------------------------------------------------------------------------------------------------- 7 Mo 1 1.299716230164057e+00 1.299716230165667e+00 1.60938e-12 6.35254e-11 2 -8.546473062404392e+00 -8.546473062434863e+00 3.04716e-11 2.24988e-10 3 -1.142261148206101e+01 -1.142261148206974e+01 8.72369e-12 2.34937e-10 ----------------------------------------------------------------------------------------------------- 8 Mo 1 -6.095860770920599e+00 -6.095860770941211e+00 2.06128e-11 8.02265e-11 2 -2.918922234815247e+00 -2.918922234831750e+00 1.65024e-11 4.77853e-11 3 -1.555418111845561e+00 -1.555418111832039e+00 1.35214e-11 1.57903e-10 ----------------------------------------------------------------------------------------------------- 9 Mo 1 8.690037661714228e-01 8.690037661592140e-01 1.22088e-11 6.08775e-11 2 -1.366327541115386e+00 -1.366327541114269e+00 1.11711e-12 6.07225e-12 3 1.812558011278077e-01 1.812558011317209e-01 3.91315e-12 1.73915e-10 ----------------------------------------------------------------------------------------------------- 10 Mo 1 1.270066959228213e-01 1.270066959292227e-01 6.40146e-12 7.69462e-11 2 9.230300346269235e-01 9.230300346325788e-01 5.65537e-12 3.19862e-10 3 -1.994081503729003e+00 -1.994081503719557e+00 9.44689e-12 6.68827e-11 ----------------------------------------------------------------------------------------------------- 11 Mo 1 1.056549448419652e+00 1.056549448447524e+00 2.78728e-11 1.21117e-10 2 -4.277520258666515e+00 -4.277520258663441e+00 3.07399e-12 2.08345e-10 3 -6.678282357441864e-01 -6.678282357292765e-01 1.49099e-11 5.51209e-10 ----------------------------------------------------------------------------------------------------- 12 Mo 1 -1.729666952040572e+00 -1.729666952034254e+00 6.31806e-12 4.66850e-10 2 2.842006739112185e+00 2.842006739114840e+00 2.65477e-12 2.74067e-10 3 4.089522963862481e-01 4.089522964010693e-01 1.48212e-11 1.26583e-10 ----------------------------------------------------------------------------------------------------- 13 Mo 1 -4.947225988454604e+00 -4.947225988460816e+00 6.21192e-12 4.42189e-11 2 -5.114336279486587e+00 -5.114336279479762e+00 6.82565e-12 2.52540e-10 3 -1.270592098611485e+01 -1.270592098610715e+01 7.70051e-12 1.84395e-10 ----------------------------------------------------------------------------------------------------- 14 Mo 1 -6.056706282211693e-03 -6.056706278403903e-03 3.80779e-12 9.15799e-11 2 -8.049133106376921e-02 -8.049133106894885e-02 5.17963e-12 5.98503e-11 3 2.210076516417416e-01 2.210076516251404e-01 1.66012e-11 7.03775e-11 ----------------------------------------------------------------------------------------------------- 15 Mo 1 1.414949942558408e+01 1.414949942552622e+01 5.78542e-11 1.04079e-09 * 2 -5.935513549178459e+00 -5.935513549197077e+00 1.86189e-11 1.56320e-10 3 1.157795195683269e+00 1.157795195682946e+00 3.23297e-13 1.22205e-09 * ----------------------------------------------------------------------------------------------------- 16 Mo 1 -5.638121606299395e+00 -5.638121606275099e+00 2.42952e-11 2.39169e-10 2 1.214654574978061e+01 1.214654574974155e+01 3.90585e-11 3.75522e-10 3 2.099518084142670e+00 2.099518084169350e+00 2.66804e-11 1.02787e-10 ----------------------------------------------------------------------------------------------------- 17 Mo 1 -8.297681710955684e+00 -8.297681710982324e+00 2.66400e-11 1.00517e-10 2 -7.195815893729206e+00 -7.195815893723744e+00 5.46230e-12 2.05800e-10 3 -9.970982070894632e+00 -9.970982070890633e+00 3.99858e-12 1.99018e-10 ----------------------------------------------------------------------------------------------------- 18 Mo 1 5.861152431900683e+00 5.861152431934680e+00 3.39968e-11 2.22909e-10 2 7.048492859964099e+00 7.048492859992673e+00 2.85745e-11 1.24627e-10 3 -5.053140162636408e+00 -5.053140162598490e+00 3.79181e-11 9.48653e-10 * ----------------------------------------------------------------------------------------------------- 19 Mo 1 1.147289268980055e+01 1.147289268969359e+01 1.06956e-10 2.50214e-09 * 2 -8.024528802398674e+00 -8.024528802471732e+00 7.30580e-11 2.14301e-10 3 5.983011665414979e+00 5.983011665406025e+00 8.95373e-12 3.75470e-10 ----------------------------------------------------------------------------------------------------- 20 Mo 1 -6.818847526755121e+00 -6.818847526794748e+00 3.96270e-11 1.07550e-10 2 1.118256073302173e+01 1.118256073299020e+01 3.15339e-11 1.11466e-10 3 7.488943998094989e+00 7.488943998033208e+00 6.17808e-11 2.94763e-10 ----------------------------------------------------------------------------------------------------- 21 Mo 1 -4.524849609417358e+00 -4.524849609418601e+00 1.24345e-12 2.82614e-10 2 -9.796416951871904e-01 -9.796416951856132e-01 1.57718e-12 1.27523e-10 3 3.241295095634385e+00 3.241295095624777e+00 9.60743e-12 1.26176e-10 ----------------------------------------------------------------------------------------------------- 22 Mo 1 3.689653929447224e+00 3.689653929444850e+00 2.37366e-12 1.99810e-10 2 9.349137627736875e+00 9.349137627763227e+00 2.63523e-11 8.20517e-10 * 3 9.900637982392780e+00 9.900637982445348e+00 5.25677e-11 2.00286e-10 ----------------------------------------------------------------------------------------------------- 23 Mo 1 -9.015825460788062e-01 -9.015825460776582e-01 1.14797e-12 1.94049e-11 2 1.105199924746193e+00 1.105199924748020e+00 1.82743e-12 2.59612e-11 3 -5.365954446010756e-01 -5.365954445998354e-01 1.24012e-12 6.74951e-11 ----------------------------------------------------------------------------------------------------- 24 Mo 1 5.908485853695870e-01 5.908485853616302e-01 7.95675e-12 6.65525e-11 2 3.118712226220152e-01 3.118712226137856e-01 8.22953e-12 1.53853e-10 3 -1.786007362684201e+00 -1.786007362679192e+00 5.00977e-12 2.46189e-10 ----------------------------------------------------------------------------------------------------- 25 Mo 1 -1.693873523543807e+00 -1.693873523571950e+00 2.81428e-11 9.13460e-11 2 -2.078255576071362e+00 -2.078255576054998e+00 1.63642e-11 4.92699e-11 3 3.290831842409379e+00 3.290831842410090e+00 7.11875e-13 1.49534e-11 ----------------------------------------------------------------------------------------------------- 26 Mo 1 -3.753362455119102e+00 -3.753362455120876e+00 1.77369e-12 1.16617e-10 2 4.334579399022308e+00 4.334579399037658e+00 1.53495e-11 2.53992e-10 3 -5.687973256261545e+00 -5.687973256252846e+00 8.69882e-12 1.22593e-10 ----------------------------------------------------------------------------------------------------- 27 Mo 1 2.184008747601005e+00 2.184008747586624e+00 1.43809e-11 1.32990e-10 2 -7.971547530137862e+00 -7.971547530108335e+00 2.95266e-11 1.46564e-10 3 1.635639064505511e+00 1.635639064539533e+00 3.40219e-11 1.06899e-10 ----------------------------------------------------------------------------------------------------- 28 Mo 1 -4.499194132421886e+00 -4.499194132428831e+00 6.94467e-12 7.05400e-11 2 3.513514665090940e+00 3.513514665097575e+00 6.63558e-12 1.16761e-09 * 3 -1.987774938557844e-01 -1.987774938644218e-01 8.63748e-12 4.23457e-11 ----------------------------------------------------------------------------------------------------- 29 Mo 1 -4.682944231585239e+00 -4.682944231579453e+00 5.78559e-12 3.39210e-10 2 -6.524263051546587e+00 -6.524263051482403e+00 6.41842e-11 8.14915e-10 * 3 1.458738426074389e+00 1.458738426101445e+00 2.70566e-11 2.59646e-09 * ----------------------------------------------------------------------------------------------------- 30 Mo 1 3.457314253012831e+00 3.457314253021959e+00 9.12825e-12 1.22871e-09 * 2 5.076750365982627e+00 5.076750365958039e+00 2.45883e-11 3.59724e-10 3 3.736845039695746e+00 3.736845039717568e+00 2.18221e-11 8.70836e-10 * ----------------------------------------------------------------------------------------------------- 31 Mo 1 3.379037998709621e+00 3.379037998694274e+00 1.53473e-11 2.00629e-10 2 -2.394308205725563e+00 -2.394308205731449e+00 5.88640e-12 2.61687e-10 3 3.229642884428854e+00 3.229642884410540e+00 1.83142e-11 2.37283e-10 ----------------------------------------------------------------------------------------------------- 32 Mo 1 3.990842854246671e+00 3.990842854245835e+00 8.35332e-13 7.19713e-11 2 1.953714139645656e+00 1.953714139636129e+00 9.52660e-12 2.30392e-10 3 3.801576571952613e+00 3.801576571906959e+00 4.56537e-11 1.01745e-10 ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as discontinuities. Maximum error obtained for particle = 14, direction = 1: |F_model - F_numer| error = ----------------------- = 6.28690e-10 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 = Pd | a0 = 3.889087677001953 | (Configuration in file "config-Pd.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Pd 1 -2.850435671698001e+00 -2.850435671701051e+00 3.05045e-12 2.70441e-10 2 -1.833209710451657e+00 -1.833209710447030e+00 4.62674e-12 9.89289e-11 3 -3.784795154228642e+00 -3.784795154233342e+00 4.69980e-12 9.52354e-11 ----------------------------------------------------------------------------------------------------- 2 Pd 1 3.310679054363351e-02 3.310679055821696e-02 1.45835e-11 8.31250e-11 2 3.586137836736406e+00 3.586137836742221e+00 5.81490e-12 4.12384e-10 3 -2.272559205187682e+00 -2.272559205189330e+00 1.64802e-12 1.05565e-08 * ----------------------------------------------------------------------------------------------------- 3 Pd 1 2.728261905400740e+00 2.728261905397171e+00 3.56826e-12 2.24373e-10 2 -2.247506625961364e+00 -2.247506625946266e+00 1.50977e-11 2.86578e-10 3 3.588165759922695e+00 3.588165759930076e+00 7.38121e-12 8.94596e-10 ----------------------------------------------------------------------------------------------------- 4 Pd 1 -2.406755601006533e+00 -2.406755601004509e+00 2.02460e-12 2.80330e-10 2 2.213021143901563e+00 2.213021143868133e+00 3.34297e-11 1.98141e-08 * 3 2.734897648860147e+00 2.734897648876101e+00 1.59548e-11 5.54547e-10 ----------------------------------------------------------------------------------------------------- 5 Pd 1 2.035114031608392e+00 2.035114031635968e+00 2.75762e-11 5.49174e-11 2 -1.304425927270995e+00 -1.304425927304699e+00 3.37042e-11 6.12737e-10 3 -5.799376452470655e-01 -5.799376452515811e-01 4.51561e-12 7.95708e-11 ----------------------------------------------------------------------------------------------------- 6 Pd 1 -1.278910534059064e+00 -1.278910534124429e+00 6.53650e-11 1.50347e-10 2 1.101140201072091e+00 1.101140201084275e+00 1.21847e-11 3.68789e-11 3 1.991168705359913e-01 1.991168705399229e-01 3.93166e-12 2.90772e-10 ----------------------------------------------------------------------------------------------------- 7 Pd 1 1.272969279743257e+00 1.272969279735016e+00 8.24052e-12 1.04363e-09 2 -1.932802473708416e+00 -1.932802473711702e+00 3.28670e-12 1.07793e-10 3 1.420735274866385e+00 1.420735274854123e+00 1.22626e-11 4.27835e-10 ----------------------------------------------------------------------------------------------------- 8 Pd 1 2.184080196829655e+00 2.184080196828064e+00 1.59073e-12 2.23968e-10 2 -3.062079153833205e+00 -3.062079153916383e+00 8.31775e-11 2.74358e-08 * 3 -3.685300331077335e+00 -3.685300331032169e+00 4.51656e-11 2.15466e-10 ----------------------------------------------------------------------------------------------------- 9 Pd 1 7.600112375887095e-01 7.600112375989340e-01 1.02245e-11 1.10809e-10 2 1.546732743163435e-01 1.546732742898625e-01 2.64810e-11 1.64442e-10 3 1.471369116501849e-01 1.471369116070213e-01 4.31636e-11 5.36652e-09 * ----------------------------------------------------------------------------------------------------- 10 Pd 1 -4.968342424065773e-01 -4.968342423400177e-01 6.65595e-11 2.20613e-10 2 6.245148220386804e-01 6.245148220192072e-01 1.94732e-11 1.64176e-10 3 3.192685695898524e-01 3.192685695710397e-01 1.88127e-11 2.01488e-10 ----------------------------------------------------------------------------------------------------- 11 Pd 1 -3.202103292008047e+00 -3.202103292053931e+00 4.58833e-11 3.83463e-10 2 2.176615462808476e+00 2.176615462836118e+00 2.76419e-11 4.97393e-10 3 8.910370678415230e-01 8.910370678342525e-01 7.27052e-12 7.53161e-10 ----------------------------------------------------------------------------------------------------- 12 Pd 1 7.474254270592466e-01 7.474254271672522e-01 1.08006e-10 5.46397e-10 2 -1.040831313580068e+00 -1.040831313589216e+00 9.14735e-12 7.76819e-11 3 2.809736617524748e-01 2.809736617614172e-01 8.94246e-12 1.16018e-10 ----------------------------------------------------------------------------------------------------- 13 Pd 1 -1.385752386909760e-01 -1.385752387162023e-01 2.52263e-11 1.90118e-11 2 -2.565964369285453e+00 -2.565964369274341e+00 1.11124e-11 4.29168e-11 3 -9.019001926154429e-01 -9.019001926493755e-01 3.39326e-11 1.61726e-09 * ----------------------------------------------------------------------------------------------------- 14 Pd 1 8.860787448908400e-01 8.860787448834209e-01 7.41918e-12 4.11673e-10 2 7.301370385030953e-01 7.301370385168546e-01 1.37593e-11 3.67448e-11 3 8.754256163752095e-01 8.754256163671287e-01 8.08087e-12 1.71024e-10 ----------------------------------------------------------------------------------------------------- 15 Pd 1 -5.037810153497231e-01 -5.037810153836741e-01 3.39511e-11 1.75083e-10 2 1.836866006807029e-01 1.836866007014460e-01 2.07431e-11 3.31428e-10 3 -3.591482628257388e-01 -3.591482628251975e-01 5.41289e-13 2.79005e-10 ----------------------------------------------------------------------------------------------------- 16 Pd 1 2.412241512747229e-01 2.412241512820121e-01 7.28925e-12 1.93189e-10 2 -5.842370433081575e-01 -5.842370433123971e-01 4.23961e-12 1.36450e-10 3 -6.882668788424900e-01 -6.882668788406461e-01 1.84397e-12 3.05617e-11 ----------------------------------------------------------------------------------------------------- 17 Pd 1 3.568750355631934e-01 3.568750355902343e-01 2.70409e-11 1.61352e-10 2 4.850602644860502e-01 4.850602645000792e-01 1.40290e-11 1.49402e-10 3 -3.235752953499453e-01 -3.235752953924181e-01 4.24728e-11 1.14942e-10 ----------------------------------------------------------------------------------------------------- 18 Pd 1 -2.327479609391607e+00 -2.327479609304957e+00 8.66498e-11 5.77876e-11 2 1.964976022088963e-01 1.964976021344006e-01 7.44957e-11 6.19745e-10 3 4.456291223675419e-01 4.456291223313303e-01 3.62116e-11 1.61197e-10 ----------------------------------------------------------------------------------------------------- 19 Pd 1 4.650617378279323e-01 4.650617378573140e-01 2.93818e-11 1.91828e-10 2 4.746962666687139e-01 4.746962667180392e-01 4.93253e-11 7.64146e-10 3 -5.129896478996829e-01 -5.129896478851340e-01 1.45489e-11 1.09844e-10 ----------------------------------------------------------------------------------------------------- 20 Pd 1 4.861892544094755e-01 4.861892544136558e-01 4.18032e-12 1.52702e-10 2 3.522667225874140e-01 3.522667225944083e-01 6.99429e-12 1.34677e-10 3 -4.925017835616127e-01 -4.925017835644610e-01 2.84833e-12 7.52067e-11 ----------------------------------------------------------------------------------------------------- 21 Pd 1 8.074897962526639e-01 8.074897961755744e-01 7.70896e-11 1.03082e-09 2 -9.107599258061791e-01 -9.107599258515059e-01 4.53267e-11 5.61531e-10 3 1.431641910263963e+00 1.431641910247944e+00 1.60190e-11 3.12790e-10 ----------------------------------------------------------------------------------------------------- 22 Pd 1 3.621299867683347e-01 3.621299867943862e-01 2.60515e-11 9.73877e-11 2 7.690636589613958e-01 7.690636590238820e-01 6.24861e-11 5.19996e-11 3 -3.241103471510924e-01 -3.241103471679266e-01 1.68343e-11 5.33463e-10 ----------------------------------------------------------------------------------------------------- 23 Pd 1 -1.395679298184644e+00 -1.395679298196552e+00 1.19078e-11 6.70769e-10 2 5.459007766126480e-01 5.459007766017173e-01 1.09307e-11 1.04003e-10 3 -7.752354895308887e-01 -7.752354895390706e-01 8.18190e-12 7.01768e-11 ----------------------------------------------------------------------------------------------------- 24 Pd 1 3.809612671885456e-01 3.809612671293417e-01 5.92039e-11 1.69564e-10 2 -7.332666707947653e-01 -7.332666707603152e-01 3.44501e-11 5.61939e-11 3 5.910391853615273e-03 5.910391845030812e-03 8.58446e-12 2.55271e-10 ----------------------------------------------------------------------------------------------------- 25 Pd 1 1.345446159804251e-01 1.345446159830359e-01 2.61083e-12 1.90756e-10 2 1.203852990189834e+00 1.203852990160868e+00 2.89659e-11 1.83694e-10 3 7.537341053515451e-01 7.537341053885465e-01 3.70014e-11 8.74236e-11 ----------------------------------------------------------------------------------------------------- 26 Pd 1 -1.081992467193017e+00 -1.081992467229112e+00 3.60945e-11 2.25403e-10 2 -7.487199343010206e-02 -7.487199341212140e-02 1.79807e-11 3.28826e-10 3 3.388813025128651e-01 3.388813024964191e-01 1.64460e-11 1.12889e-10 ----------------------------------------------------------------------------------------------------- 27 Pd 1 1.427774560875438e+00 1.427774560844252e+00 3.11857e-11 6.68593e-10 2 -1.385067809712633e+00 -1.385067809853153e+00 1.40520e-10 1.01577e-09 3 7.116103724767887e-01 7.116103724420606e-01 3.47281e-11 3.35762e-10 ----------------------------------------------------------------------------------------------------- 28 Pd 1 8.248075730476478e-03 8.248075765248135e-03 3.47717e-11 2.83653e-10 2 -2.914551501617930e-01 -2.914551501951183e-01 3.33253e-11 1.66672e-10 3 -2.142330603428372e+00 -2.142330603374170e+00 5.42020e-11 5.41376e-11 ----------------------------------------------------------------------------------------------------- 29 Pd 1 1.275192447951562e+00 1.275192447960820e+00 9.25859e-12 7.16480e-11 2 4.314007378717900e+00 4.314007378732063e+00 1.41629e-11 2.28527e-10 3 3.566236004164134e+00 3.566236004142564e+00 2.15703e-11 4.43119e-10 ----------------------------------------------------------------------------------------------------- 30 Pd 1 1.594614371243088e+00 1.594614371232611e+00 1.04778e-11 1.92821e-10 2 2.157576976371658e-01 2.157576976304831e-01 6.68268e-12 4.04940e-11 3 -2.134799024188986e+00 -2.134799024090233e+00 9.87534e-11 4.06379e-10 ----------------------------------------------------------------------------------------------------- 31 Pd 1 -2.917128295120993e-01 -2.917128294720392e-01 4.00601e-11 7.51298e-11 2 -9.790479425206020e-01 -9.790479425808836e-01 6.02816e-11 3.13509e-10 3 1.303032971880096e-01 1.303032972131908e-01 2.51811e-11 3.78153e-10 ----------------------------------------------------------------------------------------------------- 32 Pd 1 -2.213093115230042e+00 -2.213093115221978e+00 8.06377e-12 2.60932e-10 2 -3.815036283019859e-01 -3.815036283468758e-01 4.48899e-11 5.56832e-10 3 1.136745973562050e+00 1.136745973597848e+00 3.57983e-11 3.29733e-10 ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as discontinuities. Maximum error obtained for particle = 28, direction = 1: |F_model - F_numer| error = ----------------------- = 4.21573e-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 = Mo Pd | a0 = 3.9230529541082433 | (Configuration in file "config-MoPd.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Mo 1 -3.164777145858719e-01 -3.164777145754342e-01 1.04377e-11 2.99403e-11 2 -6.673929136940330e+00 -6.673929136936430e+00 3.89910e-12 1.66688e-10 3 -6.991205336304057e+00 -6.991205336302461e+00 1.59606e-12 2.56793e-09 ----------------------------------------------------------------------------------------------------- 2 Mo 1 7.839703152490755e-01 7.839703152638789e-01 1.48035e-11 1.26662e-10 2 -4.587996034884264e+00 -4.587996034883502e+00 7.62057e-13 7.41418e-10 3 -1.194147145062518e+00 -1.194147145061017e+00 1.50080e-12 9.31944e-10 ----------------------------------------------------------------------------------------------------- 3 Pd 1 -1.068337387043658e+00 -1.068337386981346e+00 6.23126e-11 3.71936e-10 2 -6.809604337673517e-01 -6.809604337792711e-01 1.19194e-11 1.18722e-10 3 1.369613856249885e-01 1.369613856253172e-01 3.28654e-13 1.40431e-08 * ----------------------------------------------------------------------------------------------------- 4 Pd 1 3.592345084793139e-02 3.592345084796089e-02 2.95042e-14 1.20203e-08 * 2 8.102351216263191e+00 8.102351216271833e+00 8.64198e-12 3.15268e-10 3 6.857033505757908e+00 6.857033505735012e+00 2.28955e-11 2.54780e-10 ----------------------------------------------------------------------------------------------------- 5 Pd 1 9.955585735266264e-01 9.955585734202884e-01 1.06338e-10 3.20657e-10 2 5.495250224849185e-01 5.495250224955698e-01 1.06513e-11 3.91117e-11 3 4.561719477571421e-02 4.561719471027337e-02 6.54408e-11 5.15499e-11 ----------------------------------------------------------------------------------------------------- 6 Pd 1 2.656872884713862e+00 2.656872884752477e+00 3.86149e-11 3.35493e-10 2 -2.298619797822723e+00 -2.298619797829422e+00 6.69909e-12 8.31461e-10 3 -9.153562531752911e-01 -9.153562531729075e-01 2.38365e-12 1.96728e-10 ----------------------------------------------------------------------------------------------------- 7 Pd 1 -7.899306272328305e-01 -7.899306273601766e-01 1.27346e-10 1.45415e-10 2 5.865990119812445e-01 5.865990119945107e-01 1.32662e-11 1.15570e-10 3 4.633618593454822e-01 4.633618593107199e-01 3.47623e-11 7.17008e-11 ----------------------------------------------------------------------------------------------------- 8 Pd 1 -9.173907053397256e-01 -9.173907052764011e-01 6.33245e-11 1.45172e-10 2 -5.346371942558485e+00 -5.346371942593210e+00 3.47251e-11 1.83329e-09 3 1.861461744732456e+00 1.861461744738331e+00 5.87530e-12 2.99963e-10 ----------------------------------------------------------------------------------------------------- 9 Mo 1 -6.601927894255477e+00 -6.601927894238757e+00 1.67200e-11 1.42553e-10 2 2.249020169947031e-01 2.249020169846788e-01 1.00243e-11 1.35680e-09 3 -4.057619652376124e+00 -4.057619652395921e+00 1.97975e-11 1.82613e-10 ----------------------------------------------------------------------------------------------------- 10 Pd 1 1.596369554141088e+00 1.596369554141930e+00 8.42659e-13 9.79556e-10 2 1.756992992559709e+00 1.756992992581625e+00 2.19169e-11 2.79376e-10 3 -1.222995368292619e+00 -1.222995368285908e+00 6.71085e-12 3.80844e-11 ----------------------------------------------------------------------------------------------------- 11 Pd 1 1.055569014651170e+01 1.055569014654180e+01 3.01057e-11 3.30740e-11 2 -7.773828829664894e+00 -7.773828829624573e+00 4.03215e-11 8.23031e-11 3 4.357515332860825e+00 4.357515332844896e+00 1.59295e-11 3.11116e-10 ----------------------------------------------------------------------------------------------------- 12 Mo 1 -1.005785137991291e+01 -1.005785137992209e+01 9.18021e-12 1.45029e-09 2 6.857604405483376e+00 6.857604405464374e+00 1.90017e-11 6.50511e-11 3 2.792132837704520e-01 2.792132837714185e-01 9.66505e-13 1.91594e-09 ----------------------------------------------------------------------------------------------------- 13 Mo 1 -6.254635165928280e-01 -6.254635165781691e-01 1.46588e-11 1.52888e-10 2 6.687716749472022e+00 6.687716749436634e+00 3.53886e-11 3.17051e-09 * 3 -3.729206835281773e+00 -3.729206835291758e+00 9.98490e-12 1.63826e-09 ----------------------------------------------------------------------------------------------------- 14 Mo 1 -4.871152059121121e-02 -4.871152059457003e-02 3.35882e-12 1.63479e-11 2 -5.590675344955023e-01 -5.590675345043864e-01 8.88412e-12 5.24946e-11 3 -2.459216033442978e-01 -2.459216033215265e-01 2.27713e-11 8.45374e-11 ----------------------------------------------------------------------------------------------------- 15 Mo 1 1.729844763763883e+01 1.729844763765370e+01 1.48681e-11 7.71667e-10 2 -4.794933669254700e+00 -4.794933669265583e+00 1.08829e-11 3.79206e-09 * 3 -1.224902376473437e+01 -1.224902376469138e+01 4.29896e-11 6.82400e-10 ----------------------------------------------------------------------------------------------------- 16 Pd 1 -1.097649958593322e+01 -1.097649958593846e+01 5.24025e-12 1.02488e-09 2 1.274301427227570e+01 1.274301427233181e+01 5.61098e-11 3.70180e-10 3 -7.629175653195686e+00 -7.629175653191997e+00 3.68860e-12 1.12231e-10 ----------------------------------------------------------------------------------------------------- 17 Mo 1 -3.952873029581650e+00 -3.952873029600889e+00 1.92384e-11 1.01676e-09 2 -6.058296813699592e+00 -6.058296813729062e+00 2.94706e-11 1.23091e-10 3 -5.929628694488819e+00 -5.929628694510210e+00 2.13909e-11 1.01319e-10 ----------------------------------------------------------------------------------------------------- 18 Mo 1 8.408168733486109e+00 8.408168733481119e+00 4.98979e-12 1.34982e-10 2 3.978415055344358e+00 3.978415055332733e+00 1.16249e-11 3.73015e-10 3 -6.849697835531602e+00 -6.849697835566182e+00 3.45795e-11 3.69085e-10 ----------------------------------------------------------------------------------------------------- 19 Mo 1 9.136279720583991e+00 9.136279720576166e+00 7.82485e-12 1.63729e-10 2 -8.294487346810692e+00 -8.294487346791806e+00 1.88862e-11 3.43922e-10 3 5.066139166944334e+00 5.066139166948638e+00 4.30411e-12 8.32641e-11 ----------------------------------------------------------------------------------------------------- 20 Mo 1 -1.014106998585686e+01 -1.014106998585601e+01 8.49099e-13 2.19593e-10 2 6.603172963970330e+00 6.603172963936313e+00 3.40172e-11 1.17146e-09 3 1.178795971323470e+01 1.178795971327700e+01 4.23039e-11 8.10721e-09 * ----------------------------------------------------------------------------------------------------- 21 Pd 1 2.912060564843284e+00 2.912060564965087e+00 1.21803e-10 5.29165e-10 2 -1.435932754329758e+00 -1.435932754332689e+00 2.93032e-12 1.89515e-09 3 -1.146337147236901e+00 -1.146337147202126e+00 3.47751e-11 1.87924e-10 ----------------------------------------------------------------------------------------------------- 22 Pd 1 2.149807445019738e+00 2.149807445005475e+00 1.42628e-11 9.64557e-11 2 -5.603956800607586e+00 -5.603956800601607e+00 5.97833e-12 7.40647e-10 3 3.742561340242696e+00 3.742561340265865e+00 2.31690e-11 4.75337e-10 ----------------------------------------------------------------------------------------------------- 23 Mo 1 2.415718350310390e-01 2.415718350186122e-01 1.24268e-11 2.48075e-10 2 -2.865454719159655e-02 -2.865454719618189e-02 4.58535e-12 1.56116e-09 3 -1.291699744239698e+00 -1.291699744192030e+00 4.76685e-11 1.24319e-10 ----------------------------------------------------------------------------------------------------- 24 Pd 1 -1.957081370051013e+00 -1.957081370008812e+00 4.22007e-11 3.47804e-10 2 6.184631588278670e-01 6.184631587509309e-01 7.69360e-11 1.69347e-10 3 6.789603567751289e-01 6.789603568037973e-01 2.86684e-11 4.23690e-10 ----------------------------------------------------------------------------------------------------- 25 Pd 1 -3.937537467221740e+00 -3.937537467220394e+00 1.34648e-12 6.45155e-11 2 7.043723242705718e+00 7.043723242731120e+00 2.54019e-11 2.72036e-10 3 -3.571212647111428e+00 -3.571212647189330e+00 7.79021e-11 4.10409e-11 ----------------------------------------------------------------------------------------------------- 26 Mo 1 1.996948898014194e+00 1.996948898059913e+00 4.57188e-11 1.31710e-09 2 2.170575674311679e+00 2.170575674346281e+00 3.46025e-11 3.10891e-10 3 1.645798231773115e+00 1.645798231769195e+00 3.92020e-12 7.38677e-09 * ----------------------------------------------------------------------------------------------------- 27 Pd 1 -4.011623188884103e+00 -4.011623188936627e+00 5.25242e-11 7.00381e-10 2 -6.224775022956003e+00 -6.224775023013091e+00 5.70886e-11 2.85547e-10 3 2.223056040953697e+00 2.223056040944542e+00 9.15490e-12 1.59343e-10 ----------------------------------------------------------------------------------------------------- 28 Pd 1 5.650999605378995e-01 5.650999605529681e-01 1.50686e-11 6.53528e-11 2 -5.444473318681770e-01 -5.444473318800287e-01 1.18517e-11 8.90769e-11 3 -6.169117913268592e-01 -6.169117913201252e-01 6.73406e-12 1.65676e-10 ----------------------------------------------------------------------------------------------------- 29 Mo 1 -1.274936792834548e+01 -1.274936792836731e+01 2.18314e-11 8.87450e-11 2 -6.562996022924080e+00 -6.562996022905561e+00 1.85185e-11 7.28031e-11 3 1.273177326796311e+01 1.273177326798793e+01 2.48210e-11 9.19913e-10 ----------------------------------------------------------------------------------------------------- 30 Mo 1 5.343480950206152e+00 5.343480950177722e+00 2.84297e-11 1.28226e-10 2 4.536869298013611e+00 4.536869298019657e+00 6.04583e-12 3.85239e-11 3 5.329665746911968e+00 5.329665746902174e+00 9.79394e-12 3.71712e-09 * ----------------------------------------------------------------------------------------------------- 31 Pd 1 -1.076177771799459e+00 -1.076177771797520e+00 1.93889e-12 6.83021e-10 2 6.408031019143912e-01 6.408031019079125e-01 6.47871e-12 1.46208e-09 3 -1.168471246238364e+00 -1.168471246293370e+00 5.50058e-11 1.63677e-10 ----------------------------------------------------------------------------------------------------- 32 Mo 1 4.552070402876514e+00 4.552070402908339e+00 3.18252e-11 6.66603e-10 2 4.368525837172914e+00 4.368525837136383e+00 3.65308e-11 3.80342e-10 3 1.601532546273841e+00 1.601532546240257e+00 3.35847e-11 1.03608e-10 ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as discontinuities. Maximum error obtained for particle = 5, direction = 3: |F_model - F_numer| error = ----------------------- = 1.43457e-09 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 4.21573e-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 4.21573e-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.