!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_000 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 -3.469958011346307e+00 3.98259e-12 4.94770e-10 2 -3.734842214395171e+00 -3.734842214387853e+00 7.31770e-12 1.45501e-11 3 -5.717425684710198e+00 -5.717425684712643e+00 2.44516e-12 2.21493e-10 ----------------------------------------------------------------------------------------------------- 2 Mo 1 4.672737901111168e-01 4.672737901108649e-01 2.51910e-13 1.59882e-10 2 4.664190437468855e+00 4.664190437459877e+00 8.97771e-12 4.34392e-10 3 -1.258901395971228e+00 -1.258901395972302e+00 1.07447e-12 6.04348e-11 ----------------------------------------------------------------------------------------------------- 3 Mo 1 6.636404506150435e+00 6.636404506155300e+00 4.86455e-12 5.35984e-10 2 -4.489812859602999e+00 -4.489812859593173e+00 9.82592e-12 8.21245e-11 3 4.657532045768531e+00 4.657532045777614e+00 9.08340e-12 1.04061e-10 ----------------------------------------------------------------------------------------------------- 4 Mo 1 -2.573597140460425e+00 -2.573597140461512e+00 1.08713e-12 9.40146e-11 2 7.125968330859084e+00 7.125968330859243e+00 1.58096e-13 2.81553e-11 3 3.251217998298293e+00 3.251217998300246e+00 1.95355e-12 1.96073e-10 ----------------------------------------------------------------------------------------------------- 5 Mo 1 1.989871192298843e+00 1.989871192318137e+00 1.92939e-11 8.59979e-11 2 7.833205913354344e-02 7.833205913443085e-02 8.87415e-13 1.33334e-11 3 1.421592502813756e+00 1.421592502815852e+00 2.09632e-12 3.25837e-11 ----------------------------------------------------------------------------------------------------- 6 Mo 1 -1.588253633233466e+00 -1.588253633232820e+00 6.46594e-13 2.48768e-11 2 -2.329420328867488e-02 -2.329420328993136e-02 1.25648e-12 1.13602e-11 3 1.389629044643742e+00 1.389629044640572e+00 3.16969e-12 1.39810e-10 ----------------------------------------------------------------------------------------------------- 7 Mo 1 1.299716230164057e+00 1.299716230165668e+00 1.61005e-12 6.35254e-11 2 -8.546473062404392e+00 -8.546473062434856e+00 3.04645e-11 2.24993e-10 3 -1.142261148206101e+01 -1.142261148206973e+01 8.71303e-12 2.34955e-10 ----------------------------------------------------------------------------------------------------- 8 Mo 1 -6.095860770920599e+00 -6.095860770941204e+00 2.06057e-11 8.02300e-11 2 -2.918922234815247e+00 -2.918922234831747e+00 1.64997e-11 4.77858e-11 3 -1.555418111845561e+00 -1.555418111832040e+00 1.35205e-11 1.57903e-10 ----------------------------------------------------------------------------------------------------- 9 Mo 1 8.690037661714228e-01 8.690037661592134e-01 1.22095e-11 6.08770e-11 2 -1.366327541115386e+00 -1.366327541114267e+00 1.11910e-12 6.07248e-12 3 1.812558011278077e-01 1.812558011317207e-01 3.91301e-12 1.73915e-10 ----------------------------------------------------------------------------------------------------- 10 Mo 1 1.270066959228213e-01 1.270066959292226e-01 6.40138e-12 7.69462e-11 2 9.230300346269235e-01 9.230300346325793e-01 5.65581e-12 3.19862e-10 3 -1.994081503729003e+00 -1.994081503719555e+00 9.44822e-12 6.68836e-11 ----------------------------------------------------------------------------------------------------- 11 Mo 1 1.056549448419652e+00 1.056549448447523e+00 2.78717e-11 1.21115e-10 2 -4.277520258666515e+00 -4.277520258663437e+00 3.07754e-12 2.08342e-10 3 -6.678282357441864e-01 -6.678282357292770e-01 1.49094e-11 5.51208e-10 ----------------------------------------------------------------------------------------------------- 12 Mo 1 -1.729666952040572e+00 -1.729666952034254e+00 6.31739e-12 4.66849e-10 2 2.842006739112185e+00 2.842006739114842e+00 2.65699e-12 2.74068e-10 3 4.089522963862481e-01 4.089522964010689e-01 1.48208e-11 1.26583e-10 ----------------------------------------------------------------------------------------------------- 13 Mo 1 -4.947225988454604e+00 -4.947225988460812e+00 6.20837e-12 4.42242e-11 2 -5.114336279486587e+00 -5.114336279479758e+00 6.82920e-12 2.52540e-10 3 -1.270592098611485e+01 -1.270592098610714e+01 7.71117e-12 1.84386e-10 ----------------------------------------------------------------------------------------------------- 14 Mo 1 -6.056706282211693e-03 -6.056706278403906e-03 3.80779e-12 9.15799e-11 2 -8.049133106376921e-02 -8.049133106894876e-02 5.17955e-12 5.98503e-11 3 2.210076516417416e-01 2.210076516251402e-01 1.66014e-11 7.03775e-11 ----------------------------------------------------------------------------------------------------- 15 Mo 1 1.414949942558408e+01 1.414949942552623e+01 5.78471e-11 1.04079e-09 * 2 -5.935513549178459e+00 -5.935513549197074e+00 1.86153e-11 1.56322e-10 3 1.157795195683269e+00 1.157795195682946e+00 3.22631e-13 1.22205e-09 * ----------------------------------------------------------------------------------------------------- 16 Mo 1 -5.638121606299395e+00 -5.638121606275095e+00 2.42997e-11 2.39170e-10 2 1.214654574978061e+01 1.214654574974153e+01 3.90816e-11 3.75534e-10 3 2.099518084142670e+00 2.099518084169349e+00 2.66791e-11 1.02787e-10 ----------------------------------------------------------------------------------------------------- 17 Mo 1 -8.297681710955684e+00 -8.297681710982316e+00 2.66311e-11 1.00513e-10 2 -7.195815893729206e+00 -7.195815893723736e+00 5.46940e-12 2.05799e-10 3 -9.970982070894632e+00 -9.970982070890626e+00 4.00568e-12 1.99025e-10 ----------------------------------------------------------------------------------------------------- 18 Mo 1 5.861152431900683e+00 5.861152431934674e+00 3.39906e-11 2.22910e-10 2 7.048492859964099e+00 7.048492859992666e+00 2.85674e-11 1.24624e-10 3 -5.053140162636408e+00 -5.053140162598492e+00 3.79163e-11 9.48653e-10 * ----------------------------------------------------------------------------------------------------- 19 Mo 1 1.147289268980055e+01 1.147289268969359e+01 1.06965e-10 2.50213e-09 * 2 -8.024528802398674e+00 -8.024528802471727e+00 7.30527e-11 2.14301e-10 3 5.983011665414979e+00 5.983011665406020e+00 8.95817e-12 3.75465e-10 ----------------------------------------------------------------------------------------------------- 20 Mo 1 -6.818847526755121e+00 -6.818847526794743e+00 3.96216e-11 1.07551e-10 2 1.118256073302173e+01 1.118256073299019e+01 3.15463e-11 1.11475e-10 3 7.488943998094989e+00 7.488943998033203e+00 6.17861e-11 2.94761e-10 ----------------------------------------------------------------------------------------------------- 21 Mo 1 -4.524849609417358e+00 -4.524849609418599e+00 1.24079e-12 2.82616e-10 2 -9.796416951871904e-01 -9.796416951856132e-01 1.57718e-12 1.27522e-10 3 3.241295095634385e+00 3.241295095624774e+00 9.61053e-12 1.26173e-10 ----------------------------------------------------------------------------------------------------- 22 Mo 1 3.689653929447224e+00 3.689653929444847e+00 2.37721e-12 1.99809e-10 2 9.349137627736875e+00 9.349137627763220e+00 2.63451e-11 8.20510e-10 * 3 9.900637982392780e+00 9.900637982445337e+00 5.25571e-11 2.00272e-10 ----------------------------------------------------------------------------------------------------- 23 Mo 1 -9.015825460788062e-01 -9.015825460776582e-01 1.14797e-12 1.94040e-11 2 1.105199924746193e+00 1.105199924748020e+00 1.82765e-12 2.59623e-11 3 -5.365954446010756e-01 -5.365954445998350e-01 1.24056e-12 6.74948e-11 ----------------------------------------------------------------------------------------------------- 24 Mo 1 5.908485853695867e-01 5.908485853616298e-01 7.95697e-12 6.65528e-11 2 3.118712226220154e-01 3.118712226137858e-01 8.22958e-12 1.53853e-10 3 -1.786007362684201e+00 -1.786007362679190e+00 5.01132e-12 2.46189e-10 ----------------------------------------------------------------------------------------------------- 25 Mo 1 -1.693873523543807e+00 -1.693873523571948e+00 2.81410e-11 9.13458e-11 2 -2.078255576071362e+00 -2.078255576054998e+00 1.63642e-11 4.92713e-11 3 3.290831842409379e+00 3.290831842410090e+00 7.10987e-13 1.49565e-11 ----------------------------------------------------------------------------------------------------- 26 Mo 1 -3.753362455119102e+00 -3.753362455120873e+00 1.77058e-12 1.16616e-10 2 4.334579399022308e+00 4.334579399037653e+00 1.53451e-11 2.53996e-10 3 -5.687973256261545e+00 -5.687973256252842e+00 8.70326e-12 1.22593e-10 ----------------------------------------------------------------------------------------------------- 27 Mo 1 2.184008747601005e+00 2.184008747586621e+00 1.43832e-11 1.32990e-10 2 -7.971547530137862e+00 -7.971547530108327e+00 2.95346e-11 1.46570e-10 3 1.635639064505511e+00 1.635639064539533e+00 3.40226e-11 1.06899e-10 ----------------------------------------------------------------------------------------------------- 28 Mo 1 -4.499194132421886e+00 -4.499194132428828e+00 6.94200e-12 7.05400e-11 2 3.513514665090940e+00 3.513514665097577e+00 6.63736e-12 1.16761e-09 * 3 -1.987774938557844e-01 -1.987774938644216e-01 8.63729e-12 4.23457e-11 ----------------------------------------------------------------------------------------------------- 29 Mo 1 -4.682944231585239e+00 -4.682944231579450e+00 5.78915e-12 3.39209e-10 2 -6.524263051546587e+00 -6.524263051482406e+00 6.41807e-11 8.14915e-10 * 3 1.458738426074389e+00 1.458738426101446e+00 2.70572e-11 2.59646e-09 * ----------------------------------------------------------------------------------------------------- 30 Mo 1 3.457314253012831e+00 3.457314253021956e+00 9.12515e-12 1.22871e-09 * 2 5.076750365982627e+00 5.076750365958034e+00 2.45928e-11 3.59727e-10 3 3.736845039695746e+00 3.736845039717570e+00 2.18243e-11 8.70836e-10 * ----------------------------------------------------------------------------------------------------- 31 Mo 1 3.379037998709621e+00 3.379037998694276e+00 1.53455e-11 2.00629e-10 2 -2.394308205725563e+00 -2.394308205731448e+00 5.88507e-12 2.61686e-10 3 3.229642884428854e+00 3.229642884410542e+00 1.83125e-11 2.37282e-10 ----------------------------------------------------------------------------------------------------- 32 Mo 1 3.990842854246671e+00 3.990842854245832e+00 8.38885e-13 7.19758e-11 2 1.953714139645656e+00 1.953714139636131e+00 9.52549e-12 2.30392e-10 3 3.801576571952613e+00 3.801576571906956e+00 4.56568e-11 1.01747e-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 = ----------------------- = 6.28689e-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 -2.850435671701048e+00 3.04734e-12 2.70441e-10 2 -1.833209710451657e+00 -1.833209710447029e+00 4.62830e-12 9.89289e-11 3 -3.784795154228642e+00 -3.784795154233338e+00 4.69624e-12 9.52349e-11 ----------------------------------------------------------------------------------------------------- 2 Pd 1 3.310679054363351e-02 3.310679055821694e-02 1.45834e-11 8.31249e-11 2 3.586137836736406e+00 3.586137836742219e+00 5.81224e-12 4.12384e-10 3 -2.272559205187682e+00 -2.272559205189331e+00 1.64890e-12 1.05565e-08 * ----------------------------------------------------------------------------------------------------- 3 Pd 1 2.728261905400740e+00 2.728261905397169e+00 3.57048e-12 2.24376e-10 2 -2.247506625961364e+00 -2.247506625946264e+00 1.50995e-11 2.86581e-10 3 3.588165759922695e+00 3.588165759930073e+00 7.37854e-12 8.94594e-10 ----------------------------------------------------------------------------------------------------- 4 Pd 1 -2.406755601006533e+00 -2.406755601004507e+00 2.02593e-12 2.80329e-10 2 2.213021143901563e+00 2.213021143868134e+00 3.34288e-11 1.98141e-08 * 3 2.734897648860147e+00 2.734897648876099e+00 1.59526e-11 5.54547e-10 ----------------------------------------------------------------------------------------------------- 5 Pd 1 2.035114031608392e+00 2.035114031635966e+00 2.75744e-11 5.49152e-11 2 -1.304425927270995e+00 -1.304425927304698e+00 3.37033e-11 6.12738e-10 3 -5.799376452470655e-01 -5.799376452515806e-01 4.51517e-12 7.95709e-11 ----------------------------------------------------------------------------------------------------- 6 Pd 1 -1.278910534059064e+00 -1.278910534124428e+00 6.53637e-11 1.50346e-10 2 1.101140201072091e+00 1.101140201084275e+00 1.21840e-11 3.68794e-11 3 1.991168705359913e-01 1.991168705399227e-01 3.93147e-12 2.90772e-10 ----------------------------------------------------------------------------------------------------- 7 Pd 1 1.272969279743257e+00 1.272969279735015e+00 8.24163e-12 1.04363e-09 2 -1.932802473708416e+00 -1.932802473711700e+00 3.28493e-12 1.07793e-10 3 1.420735274866385e+00 1.420735274854121e+00 1.22642e-11 4.27833e-10 ----------------------------------------------------------------------------------------------------- 8 Pd 1 2.184080196829655e+00 2.184080196828062e+00 1.59295e-12 2.23969e-10 2 -3.062079153833205e+00 -3.062079153916384e+00 8.31788e-11 2.74358e-08 * 3 -3.685300331077335e+00 -3.685300331032166e+00 4.51692e-11 2.15465e-10 ----------------------------------------------------------------------------------------------------- 9 Pd 1 7.600112375887095e-01 7.600112375989335e-01 1.02240e-11 1.10809e-10 2 1.546732743163435e-01 1.546732742898624e-01 2.64812e-11 1.64442e-10 3 1.471369116501849e-01 1.471369116070213e-01 4.31636e-11 5.36652e-09 * ----------------------------------------------------------------------------------------------------- 10 Pd 1 -4.968342424065773e-01 -4.968342423400169e-01 6.65604e-11 2.20613e-10 2 6.245148220386804e-01 6.245148220192068e-01 1.94735e-11 1.64176e-10 3 3.192685695898524e-01 3.192685695710395e-01 1.88129e-11 2.01488e-10 ----------------------------------------------------------------------------------------------------- 11 Pd 1 -3.202103292008047e+00 -3.202103292053929e+00 4.58815e-11 3.83464e-10 2 2.176615462808476e+00 2.176615462836116e+00 2.76401e-11 4.97395e-10 3 8.910370678415230e-01 8.910370678342517e-01 7.27129e-12 7.53161e-10 ----------------------------------------------------------------------------------------------------- 12 Pd 1 7.474254270592466e-01 7.474254271672516e-01 1.08005e-10 5.46397e-10 2 -1.040831313580068e+00 -1.040831313589215e+00 9.14624e-12 7.76827e-11 3 2.809736617524748e-01 2.809736617614160e-01 8.94118e-12 1.16019e-10 ----------------------------------------------------------------------------------------------------- 13 Pd 1 -1.385752386909760e-01 -1.385752387162021e-01 2.52261e-11 1.90117e-11 2 -2.565964369285453e+00 -2.565964369274339e+00 1.11142e-11 4.29168e-11 3 -9.019001926154429e-01 -9.019001926493759e-01 3.39331e-11 1.61726e-09 * ----------------------------------------------------------------------------------------------------- 14 Pd 1 8.860787448908400e-01 8.860787448834200e-01 7.42006e-12 4.11673e-10 2 7.301370385030953e-01 7.301370385168540e-01 1.37587e-11 3.67447e-11 3 8.754256163752095e-01 8.754256163671282e-01 8.08131e-12 1.71023e-10 ----------------------------------------------------------------------------------------------------- 15 Pd 1 -5.037810153497231e-01 -5.037810153836736e-01 3.39505e-11 1.75082e-10 2 1.836866006807029e-01 1.836866007014459e-01 2.07429e-11 3.31428e-10 3 -3.591482628257388e-01 -3.591482628251971e-01 5.41678e-13 2.79004e-10 ----------------------------------------------------------------------------------------------------- 16 Pd 1 2.412241512747229e-01 2.412241512820120e-01 7.28909e-12 1.93188e-10 2 -5.842370433081575e-01 -5.842370433123966e-01 4.23905e-12 1.36450e-10 3 -6.882668788424900e-01 -6.882668788406456e-01 1.84441e-12 3.05619e-11 ----------------------------------------------------------------------------------------------------- 17 Pd 1 3.568750355631934e-01 3.568750355902340e-01 2.70405e-11 1.61351e-10 2 4.850602644860502e-01 4.850602645000788e-01 1.40286e-11 1.49402e-10 3 -3.235752953499453e-01 -3.235752953924180e-01 4.24727e-11 1.14942e-10 ----------------------------------------------------------------------------------------------------- 18 Pd 1 -2.327479609391607e+00 -2.327479609304955e+00 8.66516e-11 5.77867e-11 2 1.964976022088963e-01 1.964976021344004e-01 7.44959e-11 6.19745e-10 3 4.456291223675419e-01 4.456291223313299e-01 3.62120e-11 1.61197e-10 ----------------------------------------------------------------------------------------------------- 19 Pd 1 4.650617378279323e-01 4.650617378573136e-01 2.93813e-11 1.91829e-10 2 4.746962666687139e-01 4.746962667180387e-01 4.93248e-11 7.64146e-10 3 -5.129896478996829e-01 -5.129896478851337e-01 1.45493e-11 1.09844e-10 ----------------------------------------------------------------------------------------------------- 20 Pd 1 4.861892544094755e-01 4.861892544136555e-01 4.17993e-12 1.52702e-10 2 3.522667225874140e-01 3.522667225944078e-01 6.99379e-12 1.34677e-10 3 -4.925017835616127e-01 -4.925017835644606e-01 2.84794e-12 7.52061e-11 ----------------------------------------------------------------------------------------------------- 21 Pd 1 8.074897962526639e-01 8.074897961755740e-01 7.70899e-11 1.03082e-09 2 -9.107599258061791e-01 -9.107599258515052e-01 4.53261e-11 5.61531e-10 3 1.431641910263963e+00 1.431641910247943e+00 1.60201e-11 3.12789e-10 ----------------------------------------------------------------------------------------------------- 22 Pd 1 3.621299867683347e-01 3.621299867943860e-01 2.60513e-11 9.73876e-11 2 7.690636589613958e-01 7.690636590238815e-01 6.24857e-11 5.20000e-11 3 -3.241103471510924e-01 -3.241103471679262e-01 1.68339e-11 5.33463e-10 ----------------------------------------------------------------------------------------------------- 23 Pd 1 -1.395679298184644e+00 -1.395679298196553e+00 1.19087e-11 6.70769e-10 2 5.459007766126480e-01 5.459007766017168e-01 1.09313e-11 1.04004e-10 3 -7.752354895308887e-01 -7.752354895390700e-01 8.18123e-12 7.01764e-11 ----------------------------------------------------------------------------------------------------- 24 Pd 1 3.809612671885456e-01 3.809612671293413e-01 5.92043e-11 1.69564e-10 2 -7.332666707947653e-01 -7.332666707603142e-01 3.44511e-11 5.61942e-11 3 5.910391853615273e-03 5.910391845030807e-03 8.58447e-12 2.55271e-10 ----------------------------------------------------------------------------------------------------- 25 Pd 1 1.345446159804251e-01 1.345446159830359e-01 2.61074e-12 1.90756e-10 2 1.203852990189834e+00 1.203852990160867e+00 2.89668e-11 1.83693e-10 3 7.537341053515451e-01 7.537341053885458e-01 3.70007e-11 8.74236e-11 ----------------------------------------------------------------------------------------------------- 26 Pd 1 -1.081992467193017e+00 -1.081992467229111e+00 3.60936e-11 2.25403e-10 2 -7.487199343010206e-02 -7.487199341212135e-02 1.79807e-11 3.28826e-10 3 3.388813025128651e-01 3.388813024964188e-01 1.64462e-11 1.12889e-10 ----------------------------------------------------------------------------------------------------- 27 Pd 1 1.427774560875438e+00 1.427774560844251e+00 3.11871e-11 6.68592e-10 2 -1.385067809712633e+00 -1.385067809853152e+00 1.40518e-10 1.01577e-09 3 7.116103724767887e-01 7.116103724420600e-01 3.47287e-11 3.35762e-10 ----------------------------------------------------------------------------------------------------- 28 Pd 1 8.248075730476478e-03 8.248075765248128e-03 3.47716e-11 2.83653e-10 2 -2.914551501617930e-01 -2.914551501951180e-01 3.33250e-11 1.66672e-10 3 -2.142330603428372e+00 -2.142330603374164e+00 5.42086e-11 5.41331e-11 ----------------------------------------------------------------------------------------------------- 29 Pd 1 1.275192447951562e+00 1.275192447960819e+00 9.25726e-12 7.16480e-11 2 4.314007378717900e+00 4.314007378732059e+00 1.41593e-11 2.28524e-10 3 3.566236004164134e+00 3.566236004142560e+00 2.15743e-11 4.43118e-10 ----------------------------------------------------------------------------------------------------- 30 Pd 1 1.594614371243088e+00 1.594614371232609e+00 1.04794e-11 1.92821e-10 2 2.157576976371658e-01 2.157576976304829e-01 6.68288e-12 4.04942e-11 3 -2.134799024188986e+00 -2.134799024090231e+00 9.87552e-11 4.06380e-10 ----------------------------------------------------------------------------------------------------- 31 Pd 1 -2.917128295120993e-01 -2.917128294720390e-01 4.00603e-11 7.51297e-11 2 -9.790479425206020e-01 -9.790479425808829e-01 6.02809e-11 3.13509e-10 3 1.303032971880096e-01 1.303032972131907e-01 2.51810e-11 3.78153e-10 ----------------------------------------------------------------------------------------------------- 32 Pd 1 -2.213093115230042e+00 -2.213093115221977e+00 8.06510e-12 2.60933e-10 2 -3.815036283019859e-01 -3.815036283468755e-01 4.48896e-11 5.56832e-10 3 1.136745973562050e+00 1.136745973597847e+00 3.57974e-11 3.29735e-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 -3.164777145754339e-01 1.04379e-11 2.99403e-11 2 -6.673929136940330e+00 -6.673929136936426e+00 3.90354e-12 1.66686e-10 3 -6.991205336304057e+00 -6.991205336302465e+00 1.59250e-12 2.56793e-09 ----------------------------------------------------------------------------------------------------- 2 Mo 1 7.839703152490755e-01 7.839703152638783e-01 1.48028e-11 1.26662e-10 2 -4.587996034884264e+00 -4.587996034883498e+00 7.65610e-13 7.41418e-10 3 -1.194147145062518e+00 -1.194147145061016e+00 1.50191e-12 9.31945e-10 ----------------------------------------------------------------------------------------------------- 3 Pd 1 -1.068337387043658e+00 -1.068337386981345e+00 6.23133e-11 3.71936e-10 2 -6.809604337673517e-01 -6.809604337792704e-01 1.19187e-11 1.18722e-10 3 1.369613856249885e-01 1.369613856253173e-01 3.28820e-13 1.40431e-08 * ----------------------------------------------------------------------------------------------------- 4 Pd 1 3.592345084793139e-02 3.592345084796091e-02 2.95250e-14 1.20203e-08 * 2 8.102351216263191e+00 8.102351216271826e+00 8.63487e-12 3.15275e-10 3 6.857033505757908e+00 6.857033505735008e+00 2.28999e-11 2.54778e-10 ----------------------------------------------------------------------------------------------------- 5 Pd 1 9.955585735266264e-01 9.955585734202878e-01 1.06339e-10 3.20657e-10 2 5.495250224849185e-01 5.495250224955694e-01 1.06509e-11 3.91122e-11 3 4.561719477571421e-02 4.561719471027334e-02 6.54409e-11 5.15499e-11 ----------------------------------------------------------------------------------------------------- 6 Pd 1 2.656872884713862e+00 2.656872884752475e+00 3.86131e-11 3.35493e-10 2 -2.298619797822723e+00 -2.298619797829420e+00 6.69731e-12 8.31462e-10 3 -9.153562531752911e-01 -9.153562531729068e-01 2.38431e-12 1.96729e-10 ----------------------------------------------------------------------------------------------------- 7 Pd 1 -7.899306272328305e-01 -7.899306273601761e-01 1.27346e-10 1.45415e-10 2 5.865990119812445e-01 5.865990119945104e-01 1.32658e-11 1.15570e-10 3 4.633618593454822e-01 4.633618593107195e-01 3.47627e-11 7.17011e-11 ----------------------------------------------------------------------------------------------------- 8 Pd 1 -9.173907053397256e-01 -9.173907052764002e-01 6.33253e-11 1.45172e-10 2 -5.346371942558485e+00 -5.346371942593205e+00 3.47198e-11 1.83329e-09 3 1.861461744732456e+00 1.861461744738329e+00 5.87375e-12 2.99964e-10 ----------------------------------------------------------------------------------------------------- 9 Mo 1 -6.601927894255477e+00 -6.601927894238752e+00 1.67244e-11 1.42556e-10 2 2.249020169947031e-01 2.249020169846786e-01 1.00245e-11 1.35680e-09 3 -4.057619652376124e+00 -4.057619652395918e+00 1.97948e-11 1.82617e-10 ----------------------------------------------------------------------------------------------------- 10 Pd 1 1.596369554141088e+00 1.596369554141931e+00 8.43325e-13 9.79556e-10 2 1.756992992559709e+00 1.756992992581624e+00 2.19156e-11 2.79377e-10 3 -1.222995368292619e+00 -1.222995368285907e+00 6.71152e-12 3.80833e-11 ----------------------------------------------------------------------------------------------------- 11 Pd 1 1.055569014651170e+01 1.055569014654180e+01 3.00986e-11 3.30775e-11 2 -7.773828829664894e+00 -7.773828829624565e+00 4.03286e-11 8.23031e-11 3 4.357515332860825e+00 4.357515332844892e+00 1.59330e-11 3.11120e-10 ----------------------------------------------------------------------------------------------------- 12 Mo 1 -1.005785137991291e+01 -1.005785137992208e+01 9.17488e-12 1.45030e-09 2 6.857604405483376e+00 6.857604405464368e+00 1.90079e-11 6.50511e-11 3 2.792132837704520e-01 2.792132837714186e-01 9.66616e-13 1.91594e-09 ----------------------------------------------------------------------------------------------------- 13 Mo 1 -6.254635165928280e-01 -6.254635165781685e-01 1.46595e-11 1.52889e-10 2 6.687716749472022e+00 6.687716749436637e+00 3.53850e-11 3.17051e-09 * 3 -3.729206835281773e+00 -3.729206835291760e+00 9.98668e-12 1.63826e-09 ----------------------------------------------------------------------------------------------------- 14 Mo 1 -4.871152059121121e-02 -4.871152059456998e-02 3.35877e-12 1.63479e-11 2 -5.590675344955023e-01 -5.590675345043866e-01 8.88434e-12 5.24946e-11 3 -2.459216033442978e-01 -2.459216033215263e-01 2.27715e-11 8.45374e-11 ----------------------------------------------------------------------------------------------------- 15 Mo 1 1.729844763763883e+01 1.729844763765371e+01 1.48752e-11 7.71660e-10 2 -4.794933669254700e+00 -4.794933669265586e+00 1.08855e-11 3.79206e-09 * 3 -1.224902376473437e+01 -1.224902376469139e+01 4.29843e-11 6.82400e-10 ----------------------------------------------------------------------------------------------------- 16 Pd 1 -1.097649958593322e+01 -1.097649958593845e+01 5.23137e-12 1.02486e-09 2 1.274301427227570e+01 1.274301427233180e+01 5.60991e-11 3.70175e-10 3 -7.629175653195686e+00 -7.629175653192001e+00 3.68505e-12 1.12233e-10 ----------------------------------------------------------------------------------------------------- 17 Mo 1 -3.952873029581650e+00 -3.952873029600891e+00 1.92406e-11 1.01676e-09 2 -6.058296813699592e+00 -6.058296813729059e+00 2.94671e-11 1.23086e-10 3 -5.929628694488819e+00 -5.929628694510204e+00 2.13847e-11 1.01318e-10 ----------------------------------------------------------------------------------------------------- 18 Mo 1 8.408168733486109e+00 8.408168733481112e+00 4.99689e-12 1.34980e-10 2 3.978415055344358e+00 3.978415055332729e+00 1.16294e-11 3.73018e-10 3 -6.849697835531602e+00 -6.849697835566174e+00 3.45723e-11 3.69085e-10 ----------------------------------------------------------------------------------------------------- 19 Mo 1 9.136279720583991e+00 9.136279720576161e+00 7.83018e-12 1.63729e-10 2 -8.294487346810692e+00 -8.294487346791810e+00 1.88827e-11 3.43920e-10 3 5.066139166944334e+00 5.066139166948633e+00 4.29967e-12 8.32632e-11 ----------------------------------------------------------------------------------------------------- 20 Mo 1 -1.014106998585686e+01 -1.014106998585600e+01 8.57980e-13 2.19591e-10 2 6.603172963970330e+00 6.603172963936307e+00 3.40226e-11 1.17145e-09 3 1.178795971323470e+01 1.178795971327701e+01 4.23110e-11 8.10721e-09 * ----------------------------------------------------------------------------------------------------- 21 Pd 1 2.912060564843284e+00 2.912060564965084e+00 1.21800e-10 5.29164e-10 2 -1.435932754329758e+00 -1.435932754332688e+00 2.92921e-12 1.89515e-09 3 -1.146337147236901e+00 -1.146337147202125e+00 3.47760e-11 1.87924e-10 ----------------------------------------------------------------------------------------------------- 22 Pd 1 2.149807445019738e+00 2.149807445005473e+00 1.42641e-11 9.64540e-11 2 -5.603956800607586e+00 -5.603956800601611e+00 5.97478e-12 7.40646e-10 3 3.742561340242696e+00 3.742561340265861e+00 2.31655e-11 4.75339e-10 ----------------------------------------------------------------------------------------------------- 23 Mo 1 2.415718350310390e-01 2.415718350186120e-01 1.24270e-11 2.48074e-10 2 -2.865454719159655e-02 -2.865454719618191e-02 4.58536e-12 1.56116e-09 3 -1.291699744239698e+00 -1.291699744192029e+00 4.76692e-11 1.24318e-10 ----------------------------------------------------------------------------------------------------- 24 Pd 1 -1.957081370051013e+00 -1.957081370008810e+00 4.22025e-11 3.47805e-10 2 6.184631588278670e-01 6.184631587509307e-01 7.69362e-11 1.69346e-10 3 6.789603567751289e-01 6.789603568037967e-01 2.86678e-11 4.23690e-10 ----------------------------------------------------------------------------------------------------- 25 Pd 1 -3.937537467221740e+00 -3.937537467220389e+00 1.35136e-12 6.45151e-11 2 7.043723242705718e+00 7.043723242731114e+00 2.53966e-11 2.72037e-10 3 -3.571212647111428e+00 -3.571212647189328e+00 7.78995e-11 4.10378e-11 ----------------------------------------------------------------------------------------------------- 26 Mo 1 1.996948898014194e+00 1.996948898059911e+00 4.57170e-11 1.31710e-09 2 2.170575674311679e+00 2.170575674346279e+00 3.45999e-11 3.10892e-10 3 1.645798231773115e+00 1.645798231769195e+00 3.91953e-12 7.38677e-09 * ----------------------------------------------------------------------------------------------------- 27 Pd 1 -4.011623188884103e+00 -4.011623188936624e+00 5.25207e-11 7.00377e-10 2 -6.224775022956003e+00 -6.224775023013101e+00 5.70983e-11 2.85563e-10 3 2.223056040953697e+00 2.223056040944540e+00 9.15712e-12 1.59341e-10 ----------------------------------------------------------------------------------------------------- 28 Pd 1 5.650999605378995e-01 5.650999605529676e-01 1.50682e-11 6.53531e-11 2 -5.444473318681770e-01 -5.444473318800281e-01 1.18512e-11 8.90766e-11 3 -6.169117913268592e-01 -6.169117913201247e-01 6.73450e-12 1.65677e-10 ----------------------------------------------------------------------------------------------------- 29 Mo 1 -1.274936792834548e+01 -1.274936792836730e+01 2.18225e-11 8.87486e-11 2 -6.562996022924080e+00 -6.562996022905557e+00 1.85230e-11 7.28040e-11 3 1.273177326796311e+01 1.273177326798793e+01 2.48264e-11 9.19904e-10 ----------------------------------------------------------------------------------------------------- 30 Mo 1 5.343480950206152e+00 5.343480950177717e+00 2.84350e-11 1.28228e-10 2 4.536869298013611e+00 4.536869298019652e+00 6.04050e-12 3.85203e-11 3 5.329665746911968e+00 5.329665746902177e+00 9.79128e-12 3.71712e-09 * ----------------------------------------------------------------------------------------------------- 31 Pd 1 -1.076177771799459e+00 -1.076177771797519e+00 1.94000e-12 6.83020e-10 2 6.408031019143912e-01 6.408031019079120e-01 6.47915e-12 1.46208e-09 3 -1.168471246238364e+00 -1.168471246293369e+00 5.50049e-11 1.63678e-10 ----------------------------------------------------------------------------------------------------- 32 Mo 1 4.552070402876514e+00 4.552070402908336e+00 3.18217e-11 6.66600e-10 2 4.368525837172914e+00 4.368525837136380e+00 3.65343e-11 3.80339e-10 3 1.601532546273841e+00 1.601532546240257e+00 3.35838e-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.