!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! VERIFICATION CHECK: vc-forces-numerical-derivative !!!!! !!!!! !!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Description: Comparison of the analytical forces obtained from the model with forces computed by numerical differentiation using Richardson extrapolation for a randomly distorted non-periodic structure based off the equilibrium face-centered cubic (fcc) structure. Separate configurations are tested for each species supported by the model, as well as one containing a random distribution of all species. Configurations used for testing are provided as auxiliary files. Author: Ellad Tadmor ----------------------------------------------------------------------------------------------------- Results for KIM Model : Sim_LAMMPS_Vashishta_VashishtaKaliaRino_1990_SiO__SM_887826436433_000 Supported species : O Si 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 = O | a0 = 14.375 | (Configuration in file "config-O.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 O 1 -5.253233385799594e-01 -5.253233385801207e-01 1.61315e-13 2.25586e-12 2 -5.124313375843913e-01 -5.124313375841776e-01 2.13718e-13 5.90528e-13 3 -5.159799716867306e-01 -5.159799716873247e-01 5.94080e-13 7.08766e-13 ----------------------------------------------------------------------------------------------------- 2 O 1 -1.401668093455136e-01 -1.401668093462434e-01 7.29750e-13 8.19356e-12 2 -1.177467561114680e-01 -1.177467561113627e-01 1.05332e-13 2.16255e-12 3 -9.718277537902068e-01 -9.718277537897135e-01 4.93272e-13 3.36342e-12 ----------------------------------------------------------------------------------------------------- 3 O 1 -1.174601201188339e-01 -1.174601201199490e-01 1.11507e-12 2.85434e-12 2 -9.429377302575077e-01 -9.429377302579164e-01 4.08673e-13 6.14730e-13 3 -1.018618647419905e-01 -1.018618647416824e-01 3.08184e-13 1.01086e-12 ----------------------------------------------------------------------------------------------------- 4 O 1 -9.591464689575514e-01 -9.591464689588828e-01 1.33138e-12 3.27577e-11 * 2 -1.149777528118398e-01 -1.149777528082426e-01 3.59715e-12 5.74948e-12 3 -1.114647967848923e-01 -1.114647967851516e-01 2.59237e-13 5.52336e-13 ----------------------------------------------------------------------------------------------------- 5 O 1 1.571315057020510e-01 1.571315057020598e-01 8.79852e-15 1.03827e-11 2 -7.814133024046048e-01 -7.814133024065447e-01 1.93989e-12 2.62534e-12 3 -6.940711140030530e-01 -6.940711140028023e-01 2.50688e-13 7.72715e-13 ----------------------------------------------------------------------------------------------------- 6 O 1 6.997838576703116e-01 6.997838576693333e-01 9.78329e-13 6.25833e-13 2 -1.309795955072723e-01 -1.309795955071326e-01 1.39694e-13 3.40708e-12 3 -7.404894731283005e-01 -7.404894731276652e-01 6.35270e-13 1.19504e-12 ----------------------------------------------------------------------------------------------------- 7 O 1 7.318642462260390e-01 7.318642462259319e-01 1.07025e-13 7.51421e-12 2 -7.947370816210070e-01 -7.947370816205563e-01 4.50640e-13 4.76064e-13 3 -1.705173556975249e-01 -1.705173556979292e-01 4.04371e-13 1.31685e-11 ----------------------------------------------------------------------------------------------------- 8 O 1 1.228388982618003e-01 1.228388982620263e-01 2.25930e-13 6.81698e-12 2 -2.608197904133652e-01 -2.608197904147971e-01 1.43191e-12 8.65835e-12 3 -1.239402660256642e-01 -1.239402660229039e-01 2.76022e-12 2.92187e-12 ----------------------------------------------------------------------------------------------------- 9 O 1 -6.884259667439437e-01 -6.884259667439774e-01 3.36398e-14 7.84928e-13 2 1.467930514095406e-01 1.467930514105489e-01 1.00836e-12 3.53392e-12 3 -7.697752049056138e-01 -7.697752049043233e-01 1.29052e-12 2.75178e-11 * ----------------------------------------------------------------------------------------------------- 10 O 1 -1.638260242190035e-01 -1.638260242192898e-01 2.86271e-13 4.75520e-12 2 7.527571934604947e-01 7.527571934595236e-01 9.71112e-13 3.78231e-12 3 -7.537456643657323e-01 -7.537456643657542e-01 2.18714e-14 1.78396e-11 ----------------------------------------------------------------------------------------------------- 11 O 1 -2.372037865624036e-01 -2.372037865632166e-01 8.12989e-13 5.49305e-12 2 1.463971906035373e-01 1.463971906066308e-01 3.09353e-12 1.41996e-10 * 3 -1.612578876304201e-01 -1.612578876411985e-01 1.07784e-11 5.57945e-11 * ----------------------------------------------------------------------------------------------------- 12 O 1 -7.277118928241624e-01 -7.277118928239833e-01 1.79079e-13 1.21114e-12 2 7.116808467105223e-01 7.116808467120070e-01 1.48470e-12 9.91718e-12 3 -1.188633018601459e-01 -1.188633018591427e-01 1.00325e-12 2.30706e-12 ----------------------------------------------------------------------------------------------------- 13 O 1 1.385740794924117e-01 1.385740794934117e-01 9.99978e-13 1.68252e-12 2 1.073370876494277e-01 1.073370876478231e-01 1.60462e-12 5.23126e-12 3 -1.058607290365372e+00 -1.058607290365165e+00 2.07834e-13 1.35714e-12 ----------------------------------------------------------------------------------------------------- 14 O 1 5.312229916230342e-01 5.312229916227335e-01 3.00759e-13 3.11795e-12 2 5.210516938383992e-01 5.210516938394987e-01 1.09945e-12 1.28628e-11 3 -5.111987356343823e-01 -5.111987356317306e-01 2.65177e-12 4.69635e-12 ----------------------------------------------------------------------------------------------------- 15 O 1 1.040760674281451e+00 1.040760674280942e+00 5.08926e-13 3.17302e-12 2 1.179479643134701e-01 1.179479643135480e-01 7.78405e-14 3.63612e-13 3 -1.456216037756026e-01 -1.456216037763887e-01 7.86121e-13 1.06963e-10 * ----------------------------------------------------------------------------------------------------- 16 O 1 1.406566065106979e-01 1.406566065102818e-01 4.16167e-13 8.91676e-13 2 1.040210747197604e+00 1.040210747196896e+00 7.08766e-13 1.51656e-11 3 -1.210107865312378e-01 -1.210107865319037e-01 6.65884e-13 5.67446e-12 ----------------------------------------------------------------------------------------------------- 17 O 1 -7.654000793153015e-01 -7.654000793151898e-01 1.11688e-13 1.06574e-11 2 -6.956509261785980e-01 -6.956509261781669e-01 4.31100e-13 1.83126e-11 3 3.660777537732130e-02 3.660777537841600e-02 1.09470e-12 1.06515e-11 ----------------------------------------------------------------------------------------------------- 18 O 1 -1.157078916348599e-01 -1.157078916357236e-01 8.63726e-13 2.03544e-12 2 -1.463909646714454e-01 -1.463909646724792e-01 1.03373e-12 1.75890e-12 3 2.022466352964363e-01 2.022466352966837e-01 2.47441e-13 3.17060e-12 ----------------------------------------------------------------------------------------------------- 19 O 1 -8.452114945504879e-03 -8.452114945692745e-03 1.87865e-13 6.21482e-14 2 -7.424062119827755e-01 -7.424062119829880e-01 2.12497e-13 7.89557e-12 3 7.066326292841439e-01 7.066326292847671e-01 6.23168e-13 7.40789e-11 * ----------------------------------------------------------------------------------------------------- 20 O 1 -7.037167291976812e-01 -7.037167291974447e-01 2.36589e-13 1.81244e-12 2 -1.428798026549786e-02 -1.428798026534141e-02 1.56450e-13 4.24375e-12 3 7.162793110352215e-01 7.162793110349114e-01 3.10085e-13 1.45839e-12 ----------------------------------------------------------------------------------------------------- 21 O 1 9.461941700778659e-02 9.461941700806326e-02 2.76668e-13 1.66803e-12 2 -9.213653946871163e-01 -9.213653946872928e-01 1.76525e-13 6.96132e-12 3 1.841749533576878e-01 1.841749533577753e-01 8.75688e-14 1.27846e-11 ----------------------------------------------------------------------------------------------------- 22 O 1 9.469855531553651e-01 9.469855531551156e-01 2.49578e-13 4.61997e-12 2 -8.320260779197144e-02 -8.320260778922589e-02 2.74555e-12 1.55335e-11 3 2.184524557418372e-01 2.184524557422267e-01 3.89550e-13 7.97834e-13 ----------------------------------------------------------------------------------------------------- 23 O 1 4.917023068619603e-01 4.917023068618215e-01 1.38778e-13 2.39342e-12 2 -4.495185036186526e-01 -4.495185036182990e-01 3.53662e-13 1.00420e-12 3 5.173759684931813e-01 5.173759684939389e-01 7.57505e-13 1.16263e-12 ----------------------------------------------------------------------------------------------------- 24 O 1 1.131614423679465e-01 1.131614423663828e-01 1.56364e-12 1.09363e-11 2 -1.221279854180371e-01 -1.221279854177544e-01 2.82691e-13 5.48922e-12 3 9.218652527724243e-01 9.218652527725738e-01 1.49547e-13 2.82285e-12 ----------------------------------------------------------------------------------------------------- 25 O 1 -9.574619532173738e-01 -9.574619532168920e-01 4.81837e-13 2.75513e-12 2 1.227627073031218e-01 1.227627073035086e-01 3.86788e-13 3.51034e-12 3 1.599571540363704e-01 1.599571540363542e-01 1.61537e-14 4.21344e-12 ----------------------------------------------------------------------------------------------------- 26 O 1 -2.005175532645584e-01 -2.005175532675756e-01 3.01725e-12 5.30745e-12 2 1.011614738035540e+00 1.011614738036010e+00 4.70068e-13 2.76446e-12 3 9.041295275820421e-02 9.041295275868141e-02 4.77202e-13 3.85389e-11 * ----------------------------------------------------------------------------------------------------- 27 O 1 -1.229177946145133e-01 -1.229177946147846e-01 2.71325e-13 3.47397e-12 2 -1.105312418116525e-02 -1.105312418144340e-02 2.78151e-13 6.95756e-12 3 9.303799926378002e-01 9.303799926378790e-01 7.87148e-14 2.47757e-12 ----------------------------------------------------------------------------------------------------- 28 O 1 -5.769054876743851e-01 -5.769054876747677e-01 3.82583e-13 2.89702e-12 2 5.359064489854438e-01 5.359064489859661e-01 5.22249e-13 2.18403e-12 3 4.918152105649387e-01 4.918152105647299e-01 2.08722e-13 5.93470e-12 ----------------------------------------------------------------------------------------------------- 29 O 1 1.382188910111126e-01 1.382188910105749e-01 5.37737e-13 6.61005e-12 2 5.087163468228370e-02 5.087163468152717e-02 7.56534e-13 5.23764e-12 3 2.428777334834064e-01 2.428777334851989e-01 1.79254e-12 1.04059e-11 ----------------------------------------------------------------------------------------------------- 30 O 1 7.550226725695630e-01 7.550226725684126e-01 1.15041e-12 1.17697e-11 2 7.695985747774351e-01 7.695985747770570e-01 3.78142e-13 7.49178e-13 3 1.197716474162242e-01 1.197716474161061e-01 1.18100e-13 1.75476e-11 ----------------------------------------------------------------------------------------------------- 31 O 1 7.464605060942310e-01 7.464605060942699e-01 3.89688e-14 1.80611e-12 2 5.309943783737642e-02 5.309943783747677e-02 1.00357e-13 2.57372e-12 3 7.486739154983830e-01 7.486739154973195e-01 1.06348e-12 1.12788e-12 ----------------------------------------------------------------------------------------------------- 32 O 1 1.613403623797876e-01 1.613403623793618e-01 4.25882e-13 2.08680e-12 2 7.540177287025185e-01 7.540177287022248e-01 2.93654e-13 8.65530e-13 3 7.827094831732894e-01 7.827094831728409e-01 4.48419e-13 6.67710e-12 ----------------------------------------------------------------------------------------------------- * 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 = 22, direction = 2: |F_model - F_numer| error = ----------------------- = 3.29984e-11 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 = Si | a0 = 14.375 | (Configuration in file "config-Si.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Si 1 -2.025844469347067e+00 -2.025844469343827e+00 3.24007e-12 6.69598e-12 2 -2.113881580511684e+00 -2.113881580513253e+00 1.56852e-12 6.16573e-12 3 -2.111296073112017e+00 -2.111296073111818e+00 1.99396e-13 6.31628e-12 ----------------------------------------------------------------------------------------------------- 2 Si 1 3.271909024875834e-03 3.271909027412577e-03 2.53674e-12 6.64011e-11 * 2 -5.632048680286185e-01 -5.632048680284855e-01 1.33005e-13 2.28400e-11 3 -3.634574134659300e+00 -3.634574134655443e+00 3.85691e-12 8.97149e-12 ----------------------------------------------------------------------------------------------------- 3 Si 1 -1.609336110337179e-01 -1.609336110334020e-01 3.15969e-13 6.74630e-12 2 -3.856681587249987e+00 -3.856681587249882e+00 1.05249e-13 1.50773e-11 3 -6.064134314321340e-01 -6.064134314296361e-01 2.49789e-12 1.41580e-11 ----------------------------------------------------------------------------------------------------- 4 Si 1 -3.846004673208203e+00 -3.846004673210499e+00 2.29594e-12 1.29399e-11 2 -5.638106466903718e-01 -5.638106466882005e-01 2.17137e-12 4.52549e-12 3 -4.322436790066976e-01 -4.322436790037070e-01 2.99061e-12 8.23719e-12 ----------------------------------------------------------------------------------------------------- 5 Si 1 2.621498639740416e-01 2.621498639734717e-01 5.69877e-13 6.09679e-12 2 -2.725425797205922e+00 -2.725425797207281e+00 1.35891e-12 5.11990e-12 3 -2.724418046364204e+00 -2.724418046373948e+00 9.74376e-12 2.05405e-11 ----------------------------------------------------------------------------------------------------- 6 Si 1 2.679811480061763e+00 2.679811480065171e+00 3.40794e-12 1.98441e-11 2 -4.161934033830562e-01 -4.161934033832901e-01 2.33924e-13 1.84957e-11 3 -2.757913306342189e+00 -2.757913306342020e+00 1.69198e-13 5.04174e-12 ----------------------------------------------------------------------------------------------------- 7 Si 1 2.787145819734752e+00 2.787145819734612e+00 1.39888e-13 7.61657e-12 2 -2.845913469408945e+00 -2.845913469410108e+00 1.16263e-12 5.58487e-12 3 -4.577273257216509e-01 -4.577273257207015e-01 9.49352e-13 7.16383e-12 ----------------------------------------------------------------------------------------------------- 8 Si 1 4.278336257356496e-01 4.278336257344897e-01 1.15985e-12 4.36323e-12 2 -2.151812261909919e-01 -2.151812261946585e-01 3.66651e-12 5.38602e-12 3 -6.786197607654370e-01 -6.786197607647015e-01 7.35412e-13 9.14535e-12 ----------------------------------------------------------------------------------------------------- 9 Si 1 -3.106360746384199e+00 -3.106360746384031e+00 1.67866e-13 6.60583e-12 2 4.364460466323022e-01 4.364460466291559e-01 3.14632e-12 9.84096e-12 3 -2.961226821444981e+00 -2.961226821445893e+00 9.12159e-13 5.67413e-12 ----------------------------------------------------------------------------------------------------- 10 Si 1 -1.466764646929894e-01 -1.466764646949338e-01 1.94444e-12 6.71535e-12 2 2.734006004224542e+00 2.734006004223630e+00 9.12603e-13 3.41669e-10 * 3 -3.124168827654020e+00 -3.124168827651370e+00 2.65077e-12 1.65374e-11 ----------------------------------------------------------------------------------------------------- 11 Si 1 2.659736227133399e-01 2.659736226963995e-01 1.69404e-11 9.50956e-12 2 4.002255370572076e-01 4.002255370569655e-01 2.42084e-13 6.03467e-12 3 -5.669286882197841e-01 -5.669286882156591e-01 4.12503e-12 7.96629e-12 ----------------------------------------------------------------------------------------------------- 12 Si 1 -3.249063829016506e+00 -3.249063829019103e+00 2.59659e-12 4.00657e-12 2 3.136866451200660e+00 3.136866451199306e+00 1.35403e-12 1.48908e-11 3 -5.091220493582533e-01 -5.091220493586376e-01 3.84248e-13 4.15392e-11 ----------------------------------------------------------------------------------------------------- 13 Si 1 4.498484199793692e-01 4.498484199796791e-01 3.09919e-13 3.55327e-11 2 6.187705918292852e-01 6.187705918293718e-01 8.65974e-14 2.98406e-12 3 -3.384087858113390e+00 -3.384087858111944e+00 1.44551e-12 5.57243e-12 ----------------------------------------------------------------------------------------------------- 14 Si 1 1.899858575995819e+00 1.899858575999678e+00 3.85825e-12 8.51985e-12 2 1.939655305213462e+00 1.939655305215319e+00 1.85696e-12 1.86295e-12 3 -1.868384015533824e+00 -1.868384015533255e+00 5.68878e-13 1.34242e-11 ----------------------------------------------------------------------------------------------------- 15 Si 1 3.391819889067293e+00 3.391819889050232e+00 1.70615e-11 2.50555e-11 2 7.086996073438133e-01 7.086996073397259e-01 4.08740e-12 1.21331e-11 3 -6.704827820885829e-01 -6.704827821048548e-01 1.62719e-11 2.39652e-11 ----------------------------------------------------------------------------------------------------- 16 Si 1 6.918331157365110e-01 6.918331157354809e-01 1.03006e-12 8.59357e-12 2 3.332447592129040e+00 3.332447592125847e+00 3.19345e-12 2.55509e-10 * 3 -5.042939360304953e-01 -5.042939360345752e-01 4.07985e-12 8.70851e-11 * ----------------------------------------------------------------------------------------------------- 17 Si 1 -3.117334703063256e+00 -3.117334703073841e+00 1.05849e-11 7.50484e-11 * 2 -3.233778520648071e+00 -3.233778520648626e+00 5.54667e-13 7.09344e-12 3 5.132906385483513e-01 5.132906385496058e-01 1.25444e-12 1.21238e-10 * ----------------------------------------------------------------------------------------------------- 18 Si 1 6.287153021191612e-02 6.287153021095400e-02 9.62119e-13 4.61058e-10 * 2 -6.809516646751462e-01 -6.809516646742447e-01 9.01501e-13 9.97291e-12 3 2.996852067970603e-01 2.996852068017685e-01 4.70818e-12 3.36420e-12 ----------------------------------------------------------------------------------------------------- 19 Si 1 -3.145324201385885e-01 -3.145324201371362e-01 1.45228e-12 3.29448e-12 2 -2.918258063734912e+00 -2.918258063735789e+00 8.77076e-13 1.39238e-10 * 3 3.072444697997475e+00 3.072444697994497e+00 2.97806e-12 1.33773e-11 ----------------------------------------------------------------------------------------------------- 20 Si 1 -3.363261662107584e+00 -3.363261662110570e+00 2.98517e-12 1.18083e-11 2 -6.985380058294599e-01 -6.985380058324148e-01 2.95486e-12 1.01624e-11 3 3.138048961995678e+00 3.138048961993172e+00 2.50555e-12 9.72955e-12 ----------------------------------------------------------------------------------------------------- 21 Si 1 3.834701616199394e-01 3.834701616199395e-01 1.66533e-16 1.84880e-12 2 -3.766010491955459e+00 -3.766010491949971e+00 5.48761e-12 5.73408e-12 3 4.854542456256863e-01 4.854542456225598e-01 3.12644e-12 1.19432e-11 ----------------------------------------------------------------------------------------------------- 22 Si 1 3.846639355078319e+00 3.846639355092155e+00 1.38365e-11 2.15179e-11 2 -5.769176748174553e-01 -5.769176748193409e-01 1.88560e-12 3.34277e-12 3 2.272864709074220e-01 2.272864709059547e-01 1.46735e-12 2.22015e-11 ----------------------------------------------------------------------------------------------------- 23 Si 1 2.110661839709376e+00 2.110661839705637e+00 3.73923e-12 1.20042e-11 2 -2.113761652153537e+00 -2.113761652152970e+00 5.67102e-13 2.62466e-10 * 3 2.052350776078006e+00 2.052350776077717e+00 2.89102e-13 1.51363e-11 ----------------------------------------------------------------------------------------------------- 24 Si 1 6.841173429089387e-02 6.841173428363186e-02 7.26201e-12 1.72234e-11 2 -4.449291263862140e-01 -4.449291263862228e-01 8.82627e-15 1.99354e-11 3 3.768780007558547e+00 3.768780007555979e+00 2.56861e-12 1.43459e-11 ----------------------------------------------------------------------------------------------------- 25 Si 1 -4.102872978948633e+00 -4.102872978944355e+00 4.27836e-12 1.69518e-11 2 6.293081989005964e-01 6.293081988993887e-01 1.20770e-12 1.75417e-11 3 3.321412689624044e-01 3.321412689552397e-01 7.16466e-12 5.41894e-12 ----------------------------------------------------------------------------------------------------- 26 Si 1 -1.220758978356215e-01 -1.220758978364308e-01 8.09297e-13 9.74869e-12 2 3.896229863416828e+00 3.896229863418970e+00 2.14140e-12 1.17848e-11 3 5.542282257525972e-01 5.542282257529010e-01 3.03757e-13 1.70387e-11 ----------------------------------------------------------------------------------------------------- 27 Si 1 -2.793602786351868e-02 -2.793602786391220e-02 3.93525e-13 6.48034e-12 2 5.917032848481033e-01 5.917032848470860e-01 1.01730e-12 2.51128e-11 3 3.907734556326829e+00 3.907734556325792e+00 1.03695e-12 1.34599e-11 ----------------------------------------------------------------------------------------------------- 28 Si 1 -2.126905287810311e+00 -2.126905287813007e+00 2.69651e-12 2.14881e-11 2 2.190161381549903e+00 2.190161381548037e+00 1.86651e-12 2.75553e-11 3 2.316665737230158e+00 2.316665737230807e+00 6.49703e-13 3.67972e-12 ----------------------------------------------------------------------------------------------------- 29 Si 1 4.206256710956212e-01 4.206256710958396e-01 2.18436e-13 6.58434e-12 2 7.565838428475207e-01 7.565838428492846e-01 1.76392e-12 4.12214e-11 3 8.798606490559480e-02 8.798606490755100e-02 1.95620e-12 4.81100e-12 ----------------------------------------------------------------------------------------------------- 30 Si 1 2.646907516494675e+00 2.646907516494464e+00 2.10942e-13 2.23426e-11 2 2.913308063475679e+00 2.913308063474700e+00 9.78773e-13 4.67404e-12 3 3.066732536501466e-01 3.066732536469042e-01 3.24246e-12 6.01164e-12 ----------------------------------------------------------------------------------------------------- 31 Si 1 2.892176852424070e+00 2.892176852426486e+00 2.41629e-12 2.69962e-12 2 7.105555835162906e-01 7.105555835183307e-01 2.04015e-12 1.25119e-11 3 2.965833366761893e+00 2.965833366764629e+00 2.73603e-12 6.79323e-12 ----------------------------------------------------------------------------------------------------- 32 Si 1 4.184917885019701e-01 4.184917885043232e-01 2.35312e-12 1.68893e-12 2 2.738470424684595e+00 2.738470424681604e+00 2.99183e-12 5.38960e-11 3 2.963297256749112e+00 2.963297256748044e+00 1.06803e-12 4.25646e-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 = 24, direction = 1: |F_model - F_numer| error = ----------------------- = 1.06152e-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. MIXED STRUCTURE -- Species = O Si | a0 = 14.375 | (Configuration in file "config-OSi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 O 1 4.363348948684421e-01 4.363348948682592e-01 1.82854e-13 1.11833e-12 2 9.694514775791429e-01 9.694514775791804e-01 3.75255e-14 1.10412e-12 3 4.650959674830917e-01 4.650959674825211e-01 5.70599e-13 5.73097e-13 ----------------------------------------------------------------------------------------------------- 2 Si 1 1.119045542134660e+00 1.119045542133895e+00 7.64944e-13 1.37956e-12 2 -9.399711634732256e-01 -9.399711634708203e-01 2.40530e-12 1.20675e-10 * 3 -1.208889602099186e+00 -1.208889602100171e+00 9.84990e-13 3.46900e-12 ----------------------------------------------------------------------------------------------------- 3 O 1 -3.195633005956429e-01 -3.195633005956681e-01 2.52021e-14 6.26832e-13 2 1.324011771095552e+00 1.324011771095417e+00 1.34781e-13 1.25921e-12 3 7.662220730556898e-01 7.662220730561056e-01 4.15779e-13 1.36813e-12 ----------------------------------------------------------------------------------------------------- 4 Si 1 -1.594547300688715e+00 -1.594547300688643e+00 7.23865e-14 2.00218e-12 2 -2.192625889106713e+00 -2.192625889103426e+00 3.28626e-12 4.23084e-12 3 -1.788498901161496e+00 -1.788498901161387e+00 1.08802e-13 1.33757e-11 ----------------------------------------------------------------------------------------------------- 5 Si 1 1.556247292637836e+00 1.556247292637992e+00 1.55875e-13 5.31797e-13 2 4.045784420391466e-01 4.045784420395850e-01 4.38372e-13 6.61748e-13 3 9.282987904386791e-01 9.282987904388127e-01 1.33560e-13 3.52052e-12 ----------------------------------------------------------------------------------------------------- 6 O 1 -2.051127640963101e-01 -2.051127640962803e-01 2.98650e-14 5.01904e-13 2 -4.970050280481346e-01 -4.970050280483288e-01 1.94234e-13 1.74570e-11 * 3 -6.731629343008528e-01 -6.731629343005607e-01 2.92100e-13 7.72027e-12 ----------------------------------------------------------------------------------------------------- 7 O 1 -5.751568007913084e-01 -5.751568007914006e-01 9.22595e-14 1.17140e-12 2 -5.940762443527302e-01 -5.940762443526864e-01 4.38538e-14 2.53020e-13 3 -1.938143625242380e-01 -1.938143625247503e-01 5.12257e-13 1.43197e-12 ----------------------------------------------------------------------------------------------------- 8 O 1 -2.050216573742911e+00 -2.050216573743168e+00 2.57572e-13 1.35492e-12 2 -5.823935633406593e-01 -5.823935633399865e-01 6.72795e-13 1.22602e-12 3 -1.026661464890413e-02 -1.026661464916486e-02 2.60734e-13 1.14393e-12 ----------------------------------------------------------------------------------------------------- 9 Si 1 -9.414880917212040e-01 -9.414880917204602e-01 7.43738e-13 1.69686e-12 2 8.499979066272842e-01 8.499979066269365e-01 3.47722e-13 1.19771e-12 3 -2.352112472273469e+00 -2.352112472273093e+00 3.76144e-13 2.67120e-12 ----------------------------------------------------------------------------------------------------- 10 O 1 -4.651091174942067e-01 -4.651091174945512e-01 3.44502e-13 2.74114e-12 2 -6.877448406042534e-01 -6.877448406040667e-01 1.86740e-13 7.42517e-13 3 9.940865634629203e-01 9.940865634637970e-01 8.76632e-13 1.87073e-12 ----------------------------------------------------------------------------------------------------- 11 Si 1 3.603148678688810e+00 3.603148678689044e+00 2.34035e-13 2.52953e-12 2 1.048040791821489e+00 1.048040791821498e+00 8.65974e-15 1.41420e-12 3 -4.995770325471184e-01 -4.995770325463186e-01 7.99860e-13 9.11271e-13 ----------------------------------------------------------------------------------------------------- 12 Si 1 -1.900576533201472e-01 -1.900576533217726e-01 1.62545e-12 4.99012e-12 2 2.474106448164431e+00 2.474106448164074e+00 3.57492e-13 6.92779e-13 3 -3.551886536751422e-01 -3.551886536749312e-01 2.10942e-13 8.80296e-13 ----------------------------------------------------------------------------------------------------- 13 O 1 -1.037511422350022e+00 -1.037511422350594e+00 5.71765e-13 2.16338e-12 2 6.170703272230067e-01 6.170703272227953e-01 2.11386e-13 9.64118e-13 3 6.499344025475416e-02 6.499344025465811e-02 9.60482e-14 1.03853e-12 ----------------------------------------------------------------------------------------------------- 14 Si 1 1.467235157956853e-01 1.467235157957766e-01 9.12881e-14 6.48873e-12 2 -1.008779930263122e+00 -1.008779930262872e+00 2.50022e-13 5.41589e-12 3 -1.471791542212141e-01 -1.471791542212456e-01 3.15581e-14 4.41036e-13 ----------------------------------------------------------------------------------------------------- 15 O 1 -6.114233890032535e-02 -6.114233889972025e-02 6.05106e-13 1.00050e-11 2 1.196609517701170e+00 1.196609517703251e+00 2.08100e-12 2.53109e-12 3 -4.692346786307021e-01 -4.692346786300710e-01 6.31106e-13 1.18971e-11 ----------------------------------------------------------------------------------------------------- 16 Si 1 7.395256923560188e-01 7.395256923559672e-01 5.16254e-14 9.88765e-13 2 -6.069344815692981e-01 -6.069344815695039e-01 2.05835e-13 1.31006e-12 3 1.441527362648571e+00 1.441527362649929e+00 1.35847e-12 4.44866e-12 ----------------------------------------------------------------------------------------------------- 17 Si 1 -5.220511587454096e-01 -5.220511587456844e-01 2.74780e-13 1.19071e-12 2 -2.839774049796916e+00 -2.839774049796840e+00 7.59393e-14 1.59561e-12 3 1.678666882447496e-02 1.678666882463158e-02 1.56621e-13 4.53512e-13 ----------------------------------------------------------------------------------------------------- 18 Si 1 2.552380487941408e+00 2.552380487941814e+00 4.06342e-13 6.24389e-13 2 -9.136175760193784e-01 -9.136175760192593e-01 1.19127e-13 6.60805e-13 3 -6.748739500777647e-01 -6.748739500771471e-01 6.17617e-13 4.87599e-12 ----------------------------------------------------------------------------------------------------- 19 O 1 -1.921772531122884e-01 -1.921772531122793e-01 9.07607e-15 1.17525e-11 2 1.478869948785309e+00 1.478869948784557e+00 7.51621e-13 1.29696e-12 3 -1.121692528031836e+00 -1.121692528032087e+00 2.50910e-13 5.39790e-13 ----------------------------------------------------------------------------------------------------- 20 Si 1 -1.167710257382521e+00 -1.167710257384909e+00 2.38765e-12 8.72635e-14 2 -1.593063937492250e+00 -1.593063937492426e+00 1.76081e-13 2.51887e-12 3 2.510864219206670e+00 2.510864219204676e+00 1.99352e-12 9.87699e-12 ----------------------------------------------------------------------------------------------------- 21 Si 1 1.998675329605474e+00 1.998675329605907e+00 4.32987e-13 1.23301e-12 2 -9.908574789346656e-01 -9.908574789346181e-01 4.75175e-14 1.03562e-12 3 -5.591071914155319e-01 -5.591071914151260e-01 4.05898e-13 1.76548e-12 ----------------------------------------------------------------------------------------------------- 22 O 1 -6.851016793344300e-01 -6.851016793343364e-01 9.35918e-14 4.20508e-12 2 -6.001846235032710e-01 -6.001846235032849e-01 1.39888e-14 2.29183e-12 3 6.224098614005158e-01 6.224098614014955e-01 9.79661e-13 1.91691e-12 ----------------------------------------------------------------------------------------------------- 23 O 1 -9.079616237140959e-01 -9.079616237139456e-01 1.50324e-13 2.53353e-13 2 8.528911644063492e-02 8.528911643893936e-02 1.69556e-12 2.12506e-12 3 -1.165379493877259e-01 -1.165379493888166e-01 1.09061e-12 5.68730e-11 * ----------------------------------------------------------------------------------------------------- 24 Si 1 2.795049669150072e+00 2.795049669150156e+00 8.39329e-14 3.64198e-12 2 2.112890624595463e-01 2.112890624593894e-01 1.56875e-13 1.90070e-12 3 6.387004018834753e-01 6.387004018834181e-01 5.71765e-14 3.22586e-12 ----------------------------------------------------------------------------------------------------- 25 Si 1 -1.815646687142982e+00 -1.815646687142441e+00 5.40457e-13 1.51634e-12 2 1.206202195301732e+00 1.206202195303696e+00 1.96376e-12 2.70584e-12 3 2.462581125292467e-01 2.462581125301026e-01 8.55899e-13 7.54535e-12 ----------------------------------------------------------------------------------------------------- 26 O 1 -1.202374558512191e+00 -1.202374558512205e+00 1.37668e-14 8.51985e-13 2 -1.060469873979593e+00 -1.060469873979191e+00 4.01679e-13 4.46843e-12 3 -5.306036237373402e-01 -5.306036237369114e-01 4.28768e-13 3.33122e-12 ----------------------------------------------------------------------------------------------------- 27 Si 1 2.604616004370509e+00 2.604616004372397e+00 1.88782e-12 2.48113e-12 2 2.195499181924991e+00 2.195499181925185e+00 1.93623e-13 7.33680e-12 3 9.744730879821164e-01 9.744730879842846e-01 2.16815e-12 5.49294e-12 ----------------------------------------------------------------------------------------------------- 28 Si 1 -3.829631441427982e-01 -3.829631441421496e-01 6.48592e-13 4.22895e-12 2 1.917983112570583e+00 1.917983112569770e+00 8.12461e-13 6.79878e-12 3 8.536922635610292e-01 8.536922635608080e-01 2.21267e-13 1.15663e-12 ----------------------------------------------------------------------------------------------------- 29 O 1 -2.037221125163530e+00 -2.037221125163173e+00 3.57048e-13 7.12896e-12 2 -6.410644314741795e-01 -6.410644314745754e-01 3.95906e-13 1.64946e-12 3 1.477559316455679e-02 1.477559316460796e-02 5.11709e-14 8.93930e-12 ----------------------------------------------------------------------------------------------------- 30 O 1 -9.417206392548702e-02 -9.417206392592406e-02 4.37039e-13 2.94875e-12 2 5.924855785457699e-01 5.924855785454105e-01 3.59379e-13 1.44385e-12 3 -7.890393454324295e-01 -7.890393454339422e-01 1.51268e-12 7.39531e-12 ----------------------------------------------------------------------------------------------------- 31 O 1 -2.517628414560251e-01 -2.517628414558242e-01 2.00839e-13 1.50208e-12 2 -5.647036454752360e-01 -5.647036454749383e-01 2.97651e-13 1.84297e-13 3 5.929257011633142e-01 5.929257011632981e-01 1.60982e-14 1.82276e-12 ----------------------------------------------------------------------------------------------------- 32 O 1 -8.526993512163644e-01 -8.526993512167913e-01 4.26881e-13 6.54088e-12 2 -2.582181208461639e-01 -2.582181208466096e-01 4.45644e-13 4.88831e-13 3 3.586688871058459e-01 3.586688871055032e-01 3.42726e-13 6.93900e-12 ----------------------------------------------------------------------------------------------------- * 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 = 8, direction = 3: |F_model - F_numer| error = ----------------------- = 2.53963e-11 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 1.06152e-10 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 1.06152e-10 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.