!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 : Tersoff_LAMMPS_Erhart_Juslin_Goy_Nordlund_Mueller_Albe_ZnO__MO_616776018688_001 Supported species : O Zn 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 = 3.41083049774 | (Configuration in file "config-O.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 O 1 3.544762293345422e-01 3.544762293354733e-01 9.31144e-13 1.98797e-12 2 6.782119933604599e-01 6.782119933604055e-01 5.44009e-14 7.54397e-12 3 1.053020676875884e+00 1.053020676876163e+00 2.78444e-13 4.47442e-12 ----------------------------------------------------------------------------------------------------- 2 O 1 4.383808085690839e-01 4.383808085702532e-01 1.16929e-12 1.44173e-11 2 -1.102183741677779e+00 -1.102183741677732e+00 4.68514e-14 1.35669e-11 3 -2.795273094005876e-01 -2.795273093994173e-01 1.17023e-12 6.34293e-12 ----------------------------------------------------------------------------------------------------- 3 O 1 -3.637600903094002e-01 -3.637600903100504e-01 6.50147e-13 1.94061e-11 2 2.058824150724632e-01 2.058824150719960e-01 4.67265e-13 2.92980e-11 3 3.642710397676759e-01 3.642710397690478e-01 1.37190e-12 3.95028e-12 ----------------------------------------------------------------------------------------------------- 4 O 1 -3.236782356228449e-01 -3.236782356236023e-01 7.57339e-13 9.87471e-12 2 -5.163851583609422e-01 -5.163851583613603e-01 4.18110e-13 1.94466e-11 3 -5.207041285185564e-01 -5.207041285185390e-01 1.74305e-14 7.22855e-12 ----------------------------------------------------------------------------------------------------- 5 O 1 -9.316566766991449e-02 -9.316566766974597e-02 1.68518e-13 2.71823e-12 2 6.365605344200193e-01 6.365605344189462e-01 1.07303e-12 1.52467e-11 3 -2.653585805127707e-01 -2.653585805126818e-01 8.88734e-14 1.02182e-11 ----------------------------------------------------------------------------------------------------- 6 O 1 -4.579237661143611e-01 -4.579237661149543e-01 5.93137e-13 6.22741e-12 2 -7.888453949773192e-01 -7.888453949772462e-01 7.30527e-14 2.20157e-13 3 5.121030940846557e-01 5.121030940844514e-01 2.04281e-13 5.46185e-12 ----------------------------------------------------------------------------------------------------- 7 O 1 -3.840553411671624e-01 -3.840553411670270e-01 1.35392e-13 9.35141e-13 2 4.041943293313965e-01 4.041943293313084e-01 8.80962e-14 1.18038e-11 3 -5.715114185203166e-01 -5.715114185204571e-01 1.40443e-13 3.36478e-11 ----------------------------------------------------------------------------------------------------- 8 O 1 5.202488672729232e-01 5.202488672729553e-01 3.20854e-14 3.21562e-11 2 2.022197486340384e-01 2.022197486330524e-01 9.85934e-13 1.48634e-12 3 3.872132783178733e-01 3.872132783193387e-01 1.46538e-12 1.04844e-11 ----------------------------------------------------------------------------------------------------- 9 O 1 2.916674083252461e-01 2.916674083259929e-01 7.46792e-13 7.11692e-12 2 8.585615356049199e-01 8.585615356048621e-01 5.77316e-14 7.70051e-13 3 5.152511730035353e-01 5.152511730044155e-01 8.80185e-13 4.85167e-13 ----------------------------------------------------------------------------------------------------- 10 O 1 -3.200197585342476e-01 -3.200197585334835e-01 7.64055e-13 2.68502e-12 2 -2.176159855816099e-01 -2.176159855813323e-01 2.77584e-13 1.27567e-11 3 -1.375834787986435e-01 -1.375834787997922e-01 1.14872e-12 7.68885e-12 ----------------------------------------------------------------------------------------------------- 11 O 1 -4.109841972458355e-01 -4.109841972460059e-01 1.70419e-13 1.66234e-11 2 3.820781382450973e-01 3.820781382450240e-01 7.32747e-14 2.29710e-11 3 -5.265930749920351e-01 -5.265930749943935e-01 2.35834e-12 9.55058e-12 ----------------------------------------------------------------------------------------------------- 12 O 1 1.853881278253135e-01 1.853881278245678e-01 7.45626e-13 3.25187e-12 2 -5.307946365254121e-01 -5.307946365259253e-01 5.13145e-13 1.71919e-11 3 -2.043808072138273e-01 -2.043808072138499e-01 2.25930e-14 5.50252e-12 ----------------------------------------------------------------------------------------------------- 13 O 1 1.528754721058862e-01 1.528754721036786e-01 2.20765e-12 1.70771e-11 2 4.970775111795737e-02 4.970775111779421e-02 1.63161e-13 6.34975e-12 3 -2.935329025282781e-01 -2.935329025296425e-01 1.36441e-12 3.68600e-12 ----------------------------------------------------------------------------------------------------- 14 O 1 2.790984009744470e-01 2.790984009758712e-01 1.42425e-12 1.28206e-11 2 -3.647985821064980e-01 -3.647985821080352e-01 1.53721e-12 3.65776e-11 3 2.120513641500651e-01 2.120513641500287e-01 3.64431e-14 6.70713e-13 ----------------------------------------------------------------------------------------------------- 15 O 1 1.466578277243311e-01 1.466578277191352e-01 5.19593e-12 5.00019e-06 * 2 8.403151351234197e-01 8.403151351219125e-01 1.50724e-12 8.07721e-12 3 -4.507778724140580e-01 -4.507778724060240e-01 8.03407e-12 4.15334e-11 ----------------------------------------------------------------------------------------------------- 16 O 1 -3.193259066848608e-01 -3.193259066866511e-01 1.79029e-12 1.59812e-10 * 2 4.286130370565362e-01 4.286130370546478e-01 1.88843e-12 1.99516e-11 3 3.997227642078285e-01 3.997227642025706e-01 5.25785e-12 1.07255e-11 ----------------------------------------------------------------------------------------------------- 17 O 1 9.368702947968554e-01 9.368702947964686e-01 3.86802e-13 2.03870e-12 2 5.020095799094311e-01 5.020095799094313e-01 2.22045e-16 5.08615e-12 3 6.703936798826785e-01 6.703936798817816e-01 8.96949e-13 5.60685e-12 ----------------------------------------------------------------------------------------------------- 18 O 1 -2.154781483738790e-01 -2.154781483724587e-01 1.42025e-12 9.96844e-12 2 -1.114911217356586e+00 -1.114911217354735e+00 1.85141e-12 4.92340e-12 3 5.770546994606565e-01 5.770546994636072e-01 2.95075e-12 1.10044e-11 ----------------------------------------------------------------------------------------------------- 19 O 1 -7.920090434053884e-01 -7.920090434048310e-01 5.57332e-13 1.14664e-11 2 1.106748713638054e+00 1.106748713637770e+00 2.84217e-13 2.25020e-12 3 -3.211723367918693e-01 -3.211723367920532e-01 1.83908e-13 5.26984e-12 ----------------------------------------------------------------------------------------------------- 20 O 1 5.408208795304176e-01 5.408208795314747e-01 1.05715e-12 3.47100e-12 2 -1.006215824634307e+00 -1.006215824633738e+00 5.69322e-13 3.82006e-12 3 -6.516100748217348e-01 -6.516100748216870e-01 4.78506e-14 3.46145e-12 ----------------------------------------------------------------------------------------------------- 21 O 1 1.326914059853727e+00 1.326914059853499e+00 2.28262e-13 1.96576e-12 2 1.886275855245644e-01 1.886275855240642e-01 5.00183e-13 7.14617e-12 3 4.334158653003820e-01 4.334158652997339e-01 6.48148e-13 9.09495e-12 ----------------------------------------------------------------------------------------------------- 22 O 1 -3.351529864259971e-01 -3.351529864239426e-01 2.05447e-12 1.36485e-11 2 -6.481669763463548e-01 -6.481669763450668e-01 1.28797e-12 2.69940e-12 3 7.339667652581440e-01 7.339667652587620e-01 6.18061e-13 4.25648e-12 ----------------------------------------------------------------------------------------------------- 23 O 1 -7.463727266190437e-01 -7.463727266184584e-01 5.85310e-13 3.81040e-12 2 4.051510106800308e-01 4.051510106800550e-01 2.42029e-14 7.94037e-12 3 -1.075788234133563e+00 -1.075788234133589e+00 2.55351e-14 1.05098e-11 ----------------------------------------------------------------------------------------------------- 24 O 1 -2.630874432115472e-01 -2.630874432119968e-01 4.49585e-13 7.76285e-12 2 -7.118582704473072e-01 -7.118582704477214e-01 4.14224e-13 3.93512e-11 3 -5.192548485352821e-01 -5.192548485342661e-01 1.01608e-12 4.23731e-11 ----------------------------------------------------------------------------------------------------- 25 O 1 -7.684534378258353e-01 -7.684534378276907e-01 1.85540e-12 1.05639e-11 2 -3.738040852124558e-01 -3.738040852110795e-01 1.37629e-12 1.77211e-11 3 -2.041811218723283e+00 -2.041811218720505e+00 2.77778e-12 1.61706e-11 ----------------------------------------------------------------------------------------------------- 26 O 1 -5.026732110694370e-01 -5.026732110704111e-01 9.74110e-13 1.00022e-11 2 2.168679119941941e-01 2.168679119941809e-01 1.32117e-14 1.15120e-11 3 5.983297324410388e-01 5.983297324410551e-01 1.63203e-14 1.02655e-11 ----------------------------------------------------------------------------------------------------- 27 O 1 6.133500879154822e-01 6.133500879151690e-01 3.13194e-13 2.80044e-11 2 5.607723523694119e-01 5.607723523699286e-01 5.16698e-13 1.06858e-11 3 7.265890385641117e-01 7.265890385662485e-01 2.13674e-12 5.32524e-10 * ----------------------------------------------------------------------------------------------------- 28 O 1 4.562387583424267e-01 4.562387583437632e-01 1.33643e-12 9.36717e-12 2 4.602880591755509e-01 4.602880591761009e-01 5.50060e-13 9.36989e-12 3 6.019470659557953e-01 6.019470659533916e-01 2.40363e-12 2.46789e-10 * ----------------------------------------------------------------------------------------------------- 29 O 1 7.127628089458325e-01 7.127628089476579e-01 1.82532e-12 7.63950e-11 * 2 -4.157231836069247e-02 -4.157231836044738e-02 2.45089e-13 3.11876e-13 3 4.588283693318264e-01 4.588283693345122e-01 2.68580e-12 2.89341e-11 ----------------------------------------------------------------------------------------------------- 30 O 1 -2.524679852671904e-01 -2.524679852671763e-01 1.41553e-14 1.23688e-11 2 -8.070690024582122e-01 -8.070690024607913e-01 2.57905e-12 3.98781e-12 3 1.936418494443126e-01 1.936418494411795e-01 3.13319e-12 1.48898e-11 ----------------------------------------------------------------------------------------------------- 31 O 1 -3.574626722421898e-01 -3.574626722425223e-01 3.32456e-13 1.12984e-11 2 6.170567725839063e-01 6.170567725857917e-01 1.88538e-12 1.25415e-11 3 -4.612120330050005e-01 -4.612120330071501e-01 2.14956e-12 5.80641e-12 ----------------------------------------------------------------------------------------------------- 32 O 1 -4.967941372738033e-02 -4.967941372334234e-02 4.03799e-12 5.28613e-11 * 2 -5.196454097959771e-01 -5.196454097971021e-01 1.12499e-12 8.34632e-12 3 -1.169821371366573e-01 -1.169821371448493e-01 8.19196e-12 1.81927e-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 = 32, direction = 3: |F_model - F_numer| error = --------------------------------- = 7.00275e-11 max{(|F_model|+|F_numer|)/2, 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 = Zn | a0 = 3.81624603271 | (Configuration in file "config-Zn.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Zn 1 1.387455943515948e+00 1.387455943515483e+00 4.65183e-13 5.15366e-12 2 1.212178281451802e+00 1.212178281450475e+00 1.32649e-12 1.16418e-12 3 1.544165605006206e+00 1.544165605005920e+00 2.85993e-13 1.79123e-12 ----------------------------------------------------------------------------------------------------- 2 Zn 1 -7.831823816900912e-01 -7.831823816986928e-01 8.60156e-12 3.13657e-11 2 -6.898093558546148e-01 -6.898093558587403e-01 4.12548e-12 1.19888e-10 * 3 -1.671939675655980e+00 -1.671939675656023e+00 4.26326e-14 1.81154e-09 * ----------------------------------------------------------------------------------------------------- 3 Zn 1 5.658061052944574e-01 5.658061052936679e-01 7.89480e-13 6.66434e-12 2 -6.924863148053220e-01 -6.924863147924675e-01 1.28545e-11 8.54035e-11 * 3 2.429907587197752e-01 2.429907587398021e-01 2.00269e-11 1.40922e-10 * ----------------------------------------------------------------------------------------------------- 4 Zn 1 -1.766360449489808e+00 -1.766360449491118e+00 1.30940e-12 3.53051e-12 2 -6.225284891861605e-01 -6.225284891850975e-01 1.06304e-12 5.63805e-12 3 3.852672509846421e-01 3.852672509863362e-01 1.69409e-12 7.18969e-12 ----------------------------------------------------------------------------------------------------- 5 Zn 1 8.231746568473001e-01 8.231746568461313e-01 1.16873e-12 7.07345e-12 2 1.538284112062821e+00 1.538284112064284e+00 1.46283e-12 5.84288e-12 3 1.306291864554170e+00 1.306291864552916e+00 1.25389e-12 4.00213e-12 ----------------------------------------------------------------------------------------------------- 6 Zn 1 -6.868355045302460e-01 -6.868355045286323e-01 1.61371e-12 7.04725e-12 2 -1.877731872697413e+00 -1.877731872697690e+00 2.76668e-13 4.57168e-12 3 -5.327835760868646e-01 -5.327835760875692e-01 7.04659e-13 9.97258e-12 ----------------------------------------------------------------------------------------------------- 7 Zn 1 -2.474574760671156e-01 -2.474574760666377e-01 4.77868e-13 9.21435e-12 2 7.132972075045927e-01 7.132972075042371e-01 3.55604e-13 5.31013e-11 3 -1.544295400228589e+00 -1.544295400229105e+00 5.16254e-13 1.71596e-12 ----------------------------------------------------------------------------------------------------- 8 Zn 1 3.284088928114902e-01 3.284088928127716e-01 1.28136e-12 4.77160e-11 2 -1.016418360477092e+00 -1.016418360476843e+00 2.48468e-13 2.15383e-12 3 5.756351558076732e-01 5.756351558076510e-01 2.22045e-14 9.52849e-12 ----------------------------------------------------------------------------------------------------- 9 Zn 1 7.591917283126562e-02 7.591917283078264e-02 4.82975e-13 5.73774e-12 2 -3.453995086664034e-01 -3.453995086668299e-01 4.26492e-13 4.89819e-12 3 1.378270880723069e+00 1.378270880724489e+00 1.41998e-12 3.01448e-12 ----------------------------------------------------------------------------------------------------- 10 Zn 1 -4.786855680392649e-01 -4.786855680384124e-01 8.52429e-13 3.21287e-12 2 1.169735530428402e+00 1.169735530427922e+00 4.79838e-13 1.74660e-12 3 2.074405128200057e-02 2.074405128071032e-02 1.29025e-12 6.24484e-12 ----------------------------------------------------------------------------------------------------- 11 Zn 1 4.586184758530483e-01 4.586184758532338e-01 1.85518e-13 1.54997e-11 2 -1.185390990145055e-01 -1.185390990213990e-01 6.89354e-12 9.03297e-12 3 4.205602347068804e-01 4.205602347064391e-01 4.41314e-13 1.76112e-11 ----------------------------------------------------------------------------------------------------- 12 Zn 1 7.614105850309977e-01 7.614105850351869e-01 4.18920e-12 5.60663e-12 2 -1.028679671985528e+00 -1.028679671984149e+00 1.37956e-12 4.24549e-12 3 -1.099056269622168e+00 -1.099056269622075e+00 9.23706e-14 5.18274e-12 ----------------------------------------------------------------------------------------------------- 13 Zn 1 5.643633593921205e-01 5.643633593922998e-01 1.79301e-13 1.66889e-12 2 -4.742369625344968e-01 -4.742369625339211e-01 5.75762e-13 6.66672e-12 3 -5.978621065587141e-02 -5.978621065512014e-02 7.51260e-13 1.24070e-10 * ----------------------------------------------------------------------------------------------------- 14 Zn 1 -8.974322694388026e-01 -8.974322694398453e-01 1.04272e-12 7.96574e-12 2 -1.292604049304794e-01 -1.292604049289718e-01 1.50754e-12 1.68604e-12 3 8.559142357726001e-01 8.559142357721885e-01 4.11560e-13 4.78895e-12 ----------------------------------------------------------------------------------------------------- 15 Zn 1 5.200313403563327e-01 5.200313403516803e-01 4.65239e-12 1.10706e-10 * 2 1.840781123850026e+00 1.840781123847060e+00 2.96585e-12 7.97673e-12 3 -7.801324989340060e-01 -7.801324989346250e-01 6.18949e-13 5.00811e-12 ----------------------------------------------------------------------------------------------------- 16 Zn 1 1.561981996271083e+00 1.561981996269128e+00 1.95421e-12 3.94307e-12 2 4.607076244239870e-01 4.607076244241594e-01 1.72362e-13 1.19991e-11 3 -6.134596248049021e-01 -6.134596247988284e-01 6.07370e-12 3.47000e-11 ----------------------------------------------------------------------------------------------------- 17 Zn 1 7.447609397197381e-01 7.447609397179401e-01 1.79801e-12 9.46898e-12 2 1.367924400165832e+00 1.367924400166185e+00 3.53051e-13 1.01179e-11 3 -4.076667240795604e-02 -4.076667240809696e-02 1.40922e-13 2.54866e-12 ----------------------------------------------------------------------------------------------------- 18 Zn 1 1.050332164875116e+00 1.050332164875360e+00 2.43805e-13 2.61235e-11 2 1.358894270446001e+00 1.358894270454820e+00 8.81850e-12 2.79603e-10 * 3 -1.545224172427458e+00 -1.545224172426395e+00 1.06315e-12 3.20004e-11 ----------------------------------------------------------------------------------------------------- 19 Zn 1 2.168796734059467e+00 2.168796734057040e+00 2.42650e-12 3.68416e-12 2 -1.028529198223615e+00 -1.028529198221982e+00 1.63247e-12 5.68323e-12 3 -1.320104128111086e-01 -1.320104128127465e-01 1.63783e-12 3.21479e-12 ----------------------------------------------------------------------------------------------------- 20 Zn 1 -1.142905106894137e+00 -1.142905106891288e+00 2.84928e-12 6.70153e-12 2 1.025775132576161e+00 1.025775132567361e+00 8.80007e-12 1.19715e-11 3 4.717861833118651e-02 4.717861833123668e-02 5.01682e-14 2.38179e-11 ----------------------------------------------------------------------------------------------------- 21 Zn 1 -6.074292835349784e-01 -6.074292835381472e-01 3.16880e-12 2.38698e-11 2 9.307014007001477e-01 9.307014007015291e-01 1.38134e-12 1.49132e-10 * 3 8.830700135477187e-01 8.830700135605154e-01 1.27967e-11 2.92079e-11 ----------------------------------------------------------------------------------------------------- 22 Zn 1 1.009424378665188e+00 1.009424378665505e+00 3.17302e-13 1.20530e-11 2 -3.467950188525338e+00 -3.467950188519196e+00 6.14175e-12 9.56653e-11 * 3 1.618321089153690e+00 1.618321089155933e+00 2.24243e-12 2.09646e-11 ----------------------------------------------------------------------------------------------------- 23 Zn 1 -1.057146727078865e+00 -1.057146727078766e+00 9.92539e-14 5.01399e-12 2 1.263305652495272e-01 1.263305652487072e-01 8.19955e-13 1.30953e-11 3 -9.528702143399057e-01 -9.528702143364119e-01 3.49376e-12 1.32133e-11 ----------------------------------------------------------------------------------------------------- 24 Zn 1 -2.119020433869625e+00 -2.119020433866870e+00 2.75513e-12 1.13221e-11 2 -1.700539835514961e+00 -1.700539835514849e+00 1.12355e-13 1.68121e-11 3 -6.484687104669048e-01 -6.484687104709678e-01 4.06297e-12 1.53577e-11 ----------------------------------------------------------------------------------------------------- 25 Zn 1 -2.522880733899371e-01 -2.522880733885682e-01 1.36890e-12 2.49383e-11 2 -5.858254006424900e-01 -5.858254006424778e-01 1.22125e-14 6.75420e-10 * 3 5.870085884643381e-01 5.870085884617761e-01 2.56206e-12 2.60070e-11 ----------------------------------------------------------------------------------------------------- 26 Zn 1 4.057873003264222e-01 4.057873003273127e-01 8.90510e-13 8.77609e-12 2 2.473863425391414e-01 2.473863425387255e-01 4.15945e-13 1.08615e-11 3 2.955796162883138e-01 2.955796162878808e-01 4.33042e-13 3.16103e-12 ----------------------------------------------------------------------------------------------------- 27 Zn 1 -1.782195998003815e+00 -1.782195998003173e+00 6.41709e-13 1.02045e-11 2 -2.612552881687285e-01 -2.612552881736847e-01 4.95620e-12 5.04685e-11 3 -6.052245287333281e-01 -6.052245287336357e-01 3.07643e-13 9.15744e-11 * ----------------------------------------------------------------------------------------------------- 28 Zn 1 1.073673094067001e+00 1.073673094064513e+00 2.48779e-12 1.95595e-11 2 -8.338427611071091e-01 -8.338427611069800e-01 1.29119e-13 2.00250e-11 3 -2.227719241197501e-01 -2.227719241206003e-01 8.50237e-13 1.08754e-11 ----------------------------------------------------------------------------------------------------- 29 Zn 1 -2.176366189377655e+00 -2.176366189378270e+00 6.14619e-13 6.16351e-12 2 2.081115833684255e+00 2.081115833686954e+00 2.69829e-12 2.14424e-11 3 7.526582346208175e-01 7.526582346198823e-01 9.35141e-13 6.25799e-12 ----------------------------------------------------------------------------------------------------- 30 Zn 1 -7.582768213017425e-01 -7.582768213047865e-01 3.04401e-12 6.71574e-12 2 -6.929256098082465e-02 -6.929256098230344e-02 1.47879e-12 5.90646e-12 3 -4.386902951368061e-01 -4.386902951361945e-01 6.11677e-13 4.69071e-11 ----------------------------------------------------------------------------------------------------- 31 Zn 1 2.771386662689629e-01 2.771386662680365e-01 9.26481e-13 1.08599e-11 2 1.788309140938118e+00 1.788309140938524e+00 4.05453e-13 1.03244e-11 3 1.173860927803009e-01 1.173860927801911e-01 1.09801e-13 8.37201e-12 ----------------------------------------------------------------------------------------------------- 32 Zn 1 9.784984765201472e-01 9.784984765191422e-01 1.00497e-12 7.30660e-12 2 -9.190956927057399e-01 -9.190956926968874e-01 8.85247e-12 2.29436e-11 3 -1.435621043117835e-01 -1.435621043099701e-01 1.81344e-12 8.67478e-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 = 10, direction = 3: |F_model - F_numer| error = --------------------------------- = 6.21983e-11 max{(|F_model|+|F_numer|)/2, 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 Zn | a0 = 3.73549228692 | (Configuration in file "config-OZn.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 O 1 -1.953877900169383e-02 -1.953877900116063e-02 5.33198e-13 1.01970e-11 2 5.147773430323250e-01 5.147773430306080e-01 1.71707e-12 5.19744e-11 3 6.323670064772083e-01 6.323670064746510e-01 2.55729e-12 2.37437e-11 ----------------------------------------------------------------------------------------------------- 2 Zn 1 -1.036936581203809e+01 -1.036936581202952e+01 8.56737e-12 8.26272e-11 2 -7.450872176569788e-02 -7.450872176053974e-02 5.15814e-12 8.62949e-11 3 -1.062659652511179e+01 -1.062659652511205e+01 2.57572e-13 2.99725e-11 ----------------------------------------------------------------------------------------------------- 3 O 1 2.208446728820070e+00 2.208446728819697e+00 3.72591e-13 2.95475e-11 2 -5.843255248047939e+00 -5.843255248055883e+00 7.94476e-12 1.53024e-11 3 -4.656145924558475e+00 -4.656145924562665e+00 4.19043e-12 2.15588e-11 ----------------------------------------------------------------------------------------------------- 4 Zn 1 -4.359568579473944e+00 -4.359568579474977e+00 1.03295e-12 2.34275e-11 2 9.618470301710845e-01 9.618470301616505e-01 9.43401e-12 4.19587e-12 3 -5.428344703771470e-01 -5.428344703708962e-01 6.25089e-12 5.13224e-11 ----------------------------------------------------------------------------------------------------- 5 Zn 1 -4.082205102263158e+00 -4.082205102249639e+00 1.35190e-11 1.32969e-10 2 -1.550583047186320e+01 -1.550583047186035e+01 2.84928e-12 2.13074e-11 3 -7.960444690322661e+00 -7.960444690324455e+00 1.79412e-12 1.44555e-10 ----------------------------------------------------------------------------------------------------- 6 O 1 1.364247254015887e+01 1.364247254012866e+01 3.02158e-11 7.08464e-11 2 1.111334897086630e+00 1.111334897055080e+00 3.15499e-11 1.23382e-10 3 -4.979103696092794e+00 -4.979103696094228e+00 1.43352e-12 5.38183e-11 ----------------------------------------------------------------------------------------------------- 7 O 1 9.084986228299567e+00 9.084986228295511e+00 4.05542e-12 6.08686e-11 2 -2.092302654984629e+01 -2.092302654979722e+01 4.90772e-11 8.80503e-07 * 3 -9.078376976934530e+00 -9.078376976944844e+00 1.03135e-11 9.41274e-11 ----------------------------------------------------------------------------------------------------- 8 O 1 -2.358447798071464e+00 -2.358447798069189e+00 2.27418e-12 1.32676e-11 2 -3.072427464804687e-01 -3.072427464593379e-01 2.11308e-11 3.53518e-10 * 3 1.671276197800920e+01 1.671276197801047e+01 1.27542e-12 2.21508e-10 ----------------------------------------------------------------------------------------------------- 9 Zn 1 -2.224441734923596e-01 -2.224441734946479e-01 2.28836e-12 3.25248e-12 2 4.644847166805758e-01 4.644847166795933e-01 9.82547e-13 3.88772e-11 3 9.447059011653547e-02 9.447059011428993e-02 2.24554e-12 2.94795e-11 ----------------------------------------------------------------------------------------------------- 10 O 1 -1.559318721416597e+00 -1.559318721419307e+00 2.71072e-12 4.81193e-12 2 -2.188308432543574e-01 -2.188308432486470e-01 5.71043e-12 1.45282e-10 3 1.704398924545317e+00 1.704398924550158e+00 4.84124e-12 2.65497e-11 ----------------------------------------------------------------------------------------------------- 11 Zn 1 -1.875901668970987e+01 -1.875901668970060e+01 9.26548e-12 1.54223e-11 2 8.710134629238780e+00 8.710134629243941e+00 5.16032e-12 1.77511e-11 3 6.373777997857689e+00 6.373777997864983e+00 7.29461e-12 8.95177e-11 ----------------------------------------------------------------------------------------------------- 12 Zn 1 1.730516437718675e+00 1.730516437718343e+00 3.32845e-13 5.39750e-11 2 -1.065447125863947e+00 -1.065447125862228e+00 1.71863e-12 6.38813e-11 3 -5.428843231686448e-01 -5.428843231636559e-01 4.98890e-12 8.58302e-12 ----------------------------------------------------------------------------------------------------- 13 O 1 1.786819778547710e+00 1.786819778550929e+00 3.21876e-12 1.45401e-11 2 7.943853979202264e+00 7.943853979196976e+00 5.28821e-12 3.93404e-10 * 3 -1.265647020588445e+01 -1.265647020588315e+01 1.30562e-12 8.05578e-11 ----------------------------------------------------------------------------------------------------- 14 Zn 1 1.119420616169453e+01 1.119420616169013e+01 4.39293e-12 3.38218e-11 2 1.158821212843819e+01 1.158821212844034e+01 2.14939e-12 2.78515e-11 3 -1.207100172693328e+01 -1.207100172692951e+01 3.76588e-12 2.90541e-11 ----------------------------------------------------------------------------------------------------- 15 O 1 8.420988733736277e+00 8.420988733732438e+00 3.83871e-12 1.00483e-10 2 -9.971430665791308e+00 -9.971430665790512e+00 7.95808e-13 2.86242e-11 3 4.378002520903318e+00 4.378002520896578e+00 6.74039e-12 5.15499e-11 ----------------------------------------------------------------------------------------------------- 16 Zn 1 -9.609111465243469e+00 -9.609111465242776e+00 6.92779e-13 2.61302e-11 2 1.128584668653384e+01 1.128584668653676e+01 2.91855e-12 5.17311e-11 3 8.877368435957321e+00 8.877368435961330e+00 4.00924e-12 1.94613e-09 * ----------------------------------------------------------------------------------------------------- 17 Zn 1 -2.051680884098489e+00 -2.051680884093599e+00 4.89031e-12 2.78004e-11 2 -3.840350945669949e-01 -3.840350945680157e-01 1.02085e-12 1.59114e-11 3 1.159827548020592e+00 1.159827548021231e+00 6.39488e-13 6.54632e-12 ----------------------------------------------------------------------------------------------------- 18 Zn 1 -2.703014851271878e+00 -2.703014851270038e+00 1.84031e-12 6.92513e-12 2 3.867446721878135e+00 3.867446721871738e+00 6.39711e-12 5.36460e-12 3 3.891505780396990e+00 3.891505780398380e+00 1.39000e-12 7.82294e-11 ----------------------------------------------------------------------------------------------------- 19 O 1 -1.329407393177375e+00 -1.329407393183668e+00 6.29297e-12 1.92997e-11 2 -2.652175911244320e+00 -2.652175911242215e+00 2.10498e-12 2.36033e-12 3 3.660814086663611e+00 3.660814086661663e+00 1.94866e-12 1.46936e-11 ----------------------------------------------------------------------------------------------------- 20 Zn 1 -1.230743629050632e+00 -1.230743629055132e+00 4.49996e-12 4.41844e-11 2 -1.100114808302240e+00 -1.100114808302761e+00 5.20473e-13 3.52482e-11 3 1.027578469995671e+00 1.027578469990766e+00 4.90474e-12 4.69467e-11 ----------------------------------------------------------------------------------------------------- 21 Zn 1 -2.558245418012328e+00 -2.558245418015106e+00 2.77778e-12 9.82574e-11 2 -3.976631615346597e+00 -3.976631615344981e+00 1.61560e-12 8.61440e-11 3 -1.187637338796408e-03 -1.187637337840159e-03 9.56249e-13 3.04706e-11 ----------------------------------------------------------------------------------------------------- 22 O 1 9.656081325743594e+00 9.656081325734245e+00 9.34897e-12 4.95106e-11 2 2.270388266809161e+01 2.270388266809184e+01 2.30926e-13 1.83071e-11 3 3.944997635627350e+00 3.944997635611686e+00 1.56644e-11 5.76641e-11 ----------------------------------------------------------------------------------------------------- 23 O 1 -5.230143594562719e-02 -5.230143594669322e-02 1.06602e-12 2.06208e-11 2 -1.016746982667616e+01 -1.016746982668615e+01 9.98845e-12 5.55662e-11 3 1.141465324793130e+01 1.141465324793588e+01 4.57234e-12 1.00213e-10 ----------------------------------------------------------------------------------------------------- 24 Zn 1 1.778089037235680e+00 1.778089037233279e+00 2.40075e-12 2.95117e-11 2 -3.745090703258980e-02 -3.745090703098591e-02 1.60388e-12 2.78168e-11 3 1.409491206883018e+00 1.409491206881445e+00 1.57319e-12 4.75311e-11 ----------------------------------------------------------------------------------------------------- 25 Zn 1 4.385367178541530e-01 4.385367178503612e-01 3.79174e-12 2.54198e-11 2 1.660511919080843e+00 1.660511919079664e+00 1.17928e-12 1.99545e-11 3 -3.848862750400500e-01 -3.848862750393999e-01 6.50147e-13 2.27653e-11 ----------------------------------------------------------------------------------------------------- 26 O 1 -1.070330983831872e+01 -1.070330983831814e+01 5.77316e-13 1.43547e-11 2 8.157046063128256e+00 8.157046063127680e+00 5.75540e-13 1.13047e-11 3 -4.661080252758628e+00 -4.661080252768504e+00 9.87566e-12 2.58487e-11 ----------------------------------------------------------------------------------------------------- 27 Zn 1 9.878909797722857e-01 9.878909797767855e-01 4.49984e-12 3.61014e-10 * 2 4.947431064412852e+00 4.947431064418174e+00 5.32197e-12 9.40901e-11 3 -2.221968000482380e-01 -2.221968000479383e-01 2.99649e-13 2.16712e-11 ----------------------------------------------------------------------------------------------------- 28 Zn 1 4.625868016834028e-01 4.625868016832231e-01 1.79745e-13 1.41958e-11 2 -1.537125605819491e+00 -1.537125605819428e+00 6.37268e-14 9.33209e-12 3 -1.298801998029359e+00 -1.298801998029867e+00 5.07816e-13 2.55196e-12 ----------------------------------------------------------------------------------------------------- 29 O 1 -3.166038358641031e+00 -3.166038358666959e+00 2.59277e-11 5.08944e-11 2 -1.803344409472463e+01 -1.803344409472144e+01 3.19389e-12 7.05320e-11 3 -1.731319635662254e+00 -1.731319635661425e+00 8.29559e-13 3.08440e-11 ----------------------------------------------------------------------------------------------------- 30 O 1 8.436612576637588e+00 8.436612576631422e+00 6.16573e-12 2.50839e-11 2 1.029378141741606e+01 1.029378141740535e+01 1.07150e-11 4.61018e-11 3 -1.613888907667252e+00 -1.613888907681343e+00 1.40901e-11 2.81451e-10 * ----------------------------------------------------------------------------------------------------- 31 O 1 3.694118613978218e+00 3.694118613976563e+00 1.65512e-12 5.23981e-12 2 -3.495095245607858e-01 -3.495095245585321e-01 2.25370e-12 7.14261e-11 3 3.178505583638410e+00 3.178505583638088e+00 3.22853e-13 2.34790e-12 ----------------------------------------------------------------------------------------------------- 32 O 1 1.611406267346094e+00 1.611406267344113e+00 1.98108e-12 9.95397e-11 2 -2.063061503204394e+00 -2.063061503206147e+00 1.75371e-12 4.01621e-11 3 4.566699032904870e+00 4.566699032913519e+00 8.64908e-12 4.84537e-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 = 21, direction = 3: |F_model - F_numer| error = --------------------------------- = 8.05169e-10 max{(|F_model|+|F_numer|)/2, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 8.05169e-10 Machine precision = 2.22045e-16 Grade: A Comment: The letter grade A was assigned because the normalized error in the computation was 8.05169e-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. 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.