!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_ErhartJuslinGoy_2006_ZnO__MO_616776018688_004 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 = 3.410830497741699 | (Configuration in file "config-O.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 O 1 3.544762293345500e-01 3.544762293347264e-01 1.76470e-13 1.48486e-11 2 6.782119933604619e-01 6.782119933600911e-01 3.70814e-13 1.65572e-11 3 1.053020676875888e+00 1.053020676874978e+00 9.09939e-13 1.08833e-11 ----------------------------------------------------------------------------------------------------- 2 O 1 4.383808085690745e-01 4.383808085695021e-01 4.27658e-13 6.45139e-12 2 -1.102183741677778e+00 -1.102183741676430e+00 1.34759e-12 1.51976e-11 3 -2.795273094005829e-01 -2.795273094003027e-01 2.80165e-13 3.52407e-12 ----------------------------------------------------------------------------------------------------- 3 O 1 -3.637600903093950e-01 -3.637600903091642e-01 2.30815e-13 1.62136e-11 2 2.058824150724778e-01 2.058824150740813e-01 1.60352e-12 8.34977e-12 3 3.642710397676693e-01 3.642710397678028e-01 1.33560e-13 2.67941e-12 ----------------------------------------------------------------------------------------------------- 4 O 1 -3.236782356228475e-01 -3.236782356268230e-01 3.97554e-12 5.76161e-12 2 -5.163851583609395e-01 -5.163851583619768e-01 1.03739e-12 1.71652e-12 3 -5.207041285185550e-01 -5.207041285193030e-01 7.48068e-13 5.93980e-12 ----------------------------------------------------------------------------------------------------- 5 O 1 -9.316566766991269e-02 -9.316566766972031e-02 1.92374e-13 3.72850e-12 2 6.365605344200138e-01 6.365605344199449e-01 6.89448e-14 1.99628e-11 3 -2.653585805127598e-01 -2.653585805126963e-01 6.35603e-14 1.21119e-11 ----------------------------------------------------------------------------------------------------- 6 O 1 -4.579237661143585e-01 -4.579237661137641e-01 5.94358e-13 2.50755e-12 2 -7.888453949773189e-01 -7.888453949771249e-01 1.93956e-13 6.48903e-12 3 5.121030940846576e-01 5.121030940845858e-01 7.18314e-14 2.21190e-12 ----------------------------------------------------------------------------------------------------- 7 O 1 -3.840553411671663e-01 -3.840553411673461e-01 1.79745e-13 5.71311e-11 * 2 4.041943293313921e-01 4.041943293314389e-01 4.67959e-14 6.99574e-12 3 -5.715114185203244e-01 -5.715114185200925e-01 2.31926e-13 2.24631e-12 ----------------------------------------------------------------------------------------------------- 8 O 1 5.202488672729206e-01 5.202488672672458e-01 5.67479e-12 2.17680e-11 2 2.022197486340458e-01 2.022197486346504e-01 6.04572e-13 8.83202e-12 3 3.872132783178666e-01 3.872132783178873e-01 2.06501e-14 2.57955e-12 ----------------------------------------------------------------------------------------------------- 9 O 1 2.916674083252479e-01 2.916674083250863e-01 1.61593e-13 1.71546e-12 2 8.585615356049230e-01 8.585615356057765e-01 8.53539e-13 3.64553e-12 3 5.152511730035348e-01 5.152511730036399e-01 1.05027e-13 4.50928e-12 ----------------------------------------------------------------------------------------------------- 10 O 1 -3.200197585342443e-01 -3.200197585345169e-01 2.72615e-13 8.86502e-12 2 -2.176159855816177e-01 -2.176159855832453e-01 1.62761e-12 3.75397e-12 3 -1.375834787986411e-01 -1.375834787991663e-01 5.25274e-13 8.90982e-13 ----------------------------------------------------------------------------------------------------- 11 O 1 -4.109841972458377e-01 -4.109841972439449e-01 1.89282e-12 2.82575e-11 2 3.820781382450900e-01 3.820781382494776e-01 4.38766e-12 1.57043e-11 3 -5.265930749920307e-01 -5.265930749939576e-01 1.92690e-12 8.15015e-12 ----------------------------------------------------------------------------------------------------- 12 O 1 1.853881278253071e-01 1.853881278249921e-01 3.15026e-13 1.57914e-11 2 -5.307946365254096e-01 -5.307946365255263e-01 1.16684e-13 7.28695e-12 3 -2.043808072138245e-01 -2.043808072137349e-01 8.96228e-14 1.16423e-11 ----------------------------------------------------------------------------------------------------- 13 O 1 1.528754721058768e-01 1.528754721070649e-01 1.18802e-12 3.99306e-12 2 4.970775111795115e-02 4.970775111871859e-02 7.67442e-13 5.35465e-12 3 -2.935329025282659e-01 -2.935329025280584e-01 2.07501e-13 1.03513e-11 ----------------------------------------------------------------------------------------------------- 14 O 1 2.790984009744525e-01 2.790984009741933e-01 2.59237e-13 2.41202e-12 2 -3.647985821065100e-01 -3.647985821066289e-01 1.18849e-13 3.46256e-12 3 2.120513641500836e-01 2.120513641498402e-01 2.43416e-13 5.97949e-12 ----------------------------------------------------------------------------------------------------- 15 O 1 1.466578277243260e-01 1.466578277246360e-01 3.10030e-13 8.87298e-11 * 2 8.403151351234558e-01 8.403151351234817e-01 2.58682e-14 2.84207e-11 3 -4.507778724140882e-01 -4.507778724210550e-01 6.96682e-12 4.46144e-11 ----------------------------------------------------------------------------------------------------- 16 O 1 -3.193259066848592e-01 -3.193259066833172e-01 1.54204e-12 3.16621e-11 2 4.286130370565326e-01 4.286130370589247e-01 2.39209e-12 3.71170e-12 3 3.997227642078189e-01 3.997227642087290e-01 9.10161e-13 1.70537e-11 ----------------------------------------------------------------------------------------------------- 17 O 1 9.368702947968536e-01 9.368702947979305e-01 1.07692e-12 1.33545e-11 2 5.020095799094257e-01 5.020095799084925e-01 9.33253e-13 2.54408e-12 3 6.703936798826703e-01 6.703936798815303e-01 1.13998e-12 3.46564e-11 ----------------------------------------------------------------------------------------------------- 18 O 1 -2.154781483738952e-01 -2.154781483733466e-01 5.48533e-13 9.97247e-12 2 -1.114911217356600e+00 -1.114911217355989e+00 6.11067e-13 1.06988e-11 3 5.770546994606595e-01 5.770546994552201e-01 5.43932e-12 7.57105e-12 ----------------------------------------------------------------------------------------------------- 19 O 1 -7.920090434053856e-01 -7.920090434066051e-01 1.21947e-12 6.20948e-12 2 1.106748713638046e+00 1.106748713638685e+00 6.38822e-13 8.85114e-12 3 -3.211723367918650e-01 -3.211723367921528e-01 2.87770e-13 1.20859e-12 ----------------------------------------------------------------------------------------------------- 20 O 1 5.408208795304209e-01 5.408208795302329e-01 1.87961e-13 2.97729e-12 2 -1.006215824634294e+00 -1.006215824634806e+00 5.12257e-13 4.70357e-12 3 -6.516100748217343e-01 -6.516100748220650e-01 3.30735e-13 2.27608e-11 ----------------------------------------------------------------------------------------------------- 21 O 1 1.326914059853742e+00 1.326914059852621e+00 1.12177e-12 3.59097e-11 2 1.886275855245637e-01 1.886275855237029e-01 8.60811e-13 7.12386e-12 3 4.334158653003810e-01 4.334158653005906e-01 2.09610e-13 1.01222e-11 ----------------------------------------------------------------------------------------------------- 22 O 1 -3.351529864259931e-01 -3.351529864263573e-01 3.64264e-13 1.68326e-11 2 -6.481669763463643e-01 -6.481669763454208e-01 9.43579e-13 1.48548e-12 3 7.339667652581491e-01 7.339667652584146e-01 2.65565e-13 1.94555e-12 ----------------------------------------------------------------------------------------------------- 23 O 1 -7.463727266190455e-01 -7.463727266194417e-01 3.96128e-13 5.47029e-12 2 4.051510106800210e-01 4.051510106801552e-01 1.34170e-13 2.08894e-12 3 -1.075788234133561e+00 -1.075788234135908e+00 2.34612e-12 2.00422e-11 ----------------------------------------------------------------------------------------------------- 24 O 1 -2.630874432115387e-01 -2.630874432115271e-01 1.15463e-14 1.10369e-11 2 -7.118582704473128e-01 -7.118582704475239e-01 2.11164e-13 1.78161e-11 3 -5.192548485352790e-01 -5.192548485359574e-01 6.78346e-13 1.63073e-11 ----------------------------------------------------------------------------------------------------- 25 O 1 -7.684534378258356e-01 -7.684534378284689e-01 2.63323e-12 5.79958e-12 2 -3.738040852124443e-01 -3.738040852083181e-01 4.12620e-12 1.51821e-11 3 -2.041811218723274e+00 -2.041811218727466e+00 4.19176e-12 1.33178e-11 ----------------------------------------------------------------------------------------------------- 26 O 1 -5.026732110694351e-01 -5.026732110694573e-01 2.22045e-14 4.88354e-12 2 2.168679119941843e-01 2.168679119937735e-01 4.10783e-13 8.76357e-12 3 5.983297324410417e-01 5.983297324429798e-01 1.93812e-12 1.24687e-11 ----------------------------------------------------------------------------------------------------- 27 O 1 6.133500879154542e-01 6.133500879183329e-01 2.87870e-12 6.29730e-12 2 5.607723523694561e-01 5.607723523689887e-01 4.67404e-13 2.50422e-11 3 7.265890385640932e-01 7.265890385644291e-01 3.35953e-13 1.00437e-11 ----------------------------------------------------------------------------------------------------- 28 O 1 4.562387583424430e-01 4.562387583432766e-01 8.33555e-13 3.49777e-11 2 4.602880591755202e-01 4.602880591752891e-01 2.31037e-13 3.06536e-11 3 6.019470659557806e-01 6.019470659552815e-01 4.99156e-13 4.93456e-11 ----------------------------------------------------------------------------------------------------- 29 O 1 7.127628089458303e-01 7.127628089406112e-01 5.21916e-12 2.87824e-11 2 -4.157231836068516e-02 -4.157231835194021e-02 8.74495e-12 9.77150e-12 3 4.588283693318305e-01 4.588283693422202e-01 1.03896e-11 5.50510e-12 ----------------------------------------------------------------------------------------------------- 30 O 1 -2.524679852671886e-01 -2.524679852658896e-01 1.29896e-12 1.04988e-11 2 -8.070690024582106e-01 -8.070690024587331e-01 5.22582e-13 1.12756e-11 3 1.936418494443141e-01 1.936418494433656e-01 9.48491e-13 2.37671e-05 * ----------------------------------------------------------------------------------------------------- 31 O 1 -3.574626722421883e-01 -3.574626722413315e-01 8.56704e-13 1.39024e-11 2 6.170567725839022e-01 6.170567725832434e-01 6.58806e-13 3.89990e-11 3 -4.612120330049997e-01 -4.612120330040951e-01 9.04610e-13 7.00218e-12 ----------------------------------------------------------------------------------------------------- 32 O 1 -4.967941372737754e-02 -4.967941373047259e-02 3.09505e-12 2.28505e-05 * 2 -5.196454097959788e-01 -5.196454097954585e-01 5.20362e-13 2.00917e-12 3 -1.169821371366537e-01 -1.169821371400584e-01 3.40467e-12 2.52077e-05 * ----------------------------------------------------------------------------------------------------- * 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 = 29, direction = 2: |F_model - F_numer| error = ----------------------- = 2.10355e-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 = Zn | a0 = 3.8162460327148438 | (Configuration in file "config-Zn.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Zn 1 1.387455943515941e+00 1.387455943515336e+00 6.04850e-13 3.07021e-12 2 1.212178281451795e+00 1.212178281451570e+00 2.24931e-13 1.33060e-11 3 1.544165605006207e+00 1.544165605006189e+00 1.84297e-14 5.65903e-12 ----------------------------------------------------------------------------------------------------- 2 Zn 1 -7.831823816901013e-01 -7.831823816893055e-01 7.95808e-13 4.67404e-12 2 -6.898093558546141e-01 -6.898093558573545e-01 2.74036e-12 4.52347e-11 3 -1.671939675655949e+00 -1.671939675662469e+00 6.52034e-12 1.35808e-10 * ----------------------------------------------------------------------------------------------------- 3 Zn 1 5.658061052944857e-01 5.658061052958302e-01 1.34448e-12 2.76053e-11 2 -6.924863148052924e-01 -6.924863148118214e-01 6.52900e-12 3.23858e-10 * 3 2.429907587197443e-01 2.429907586887333e-01 3.10110e-11 4.98795e-11 ----------------------------------------------------------------------------------------------------- 4 Zn 1 -1.766360449489789e+00 -1.766360449490012e+00 2.23821e-13 3.47628e-10 * 2 -6.225284891861622e-01 -6.225284891871432e-01 9.80993e-13 1.03348e-11 3 3.852672509846398e-01 3.852672509843838e-01 2.56017e-13 7.09471e-12 ----------------------------------------------------------------------------------------------------- 5 Zn 1 8.231746568472837e-01 8.231746568458781e-01 1.40565e-12 5.52902e-12 2 1.538284112062795e+00 1.538284112060896e+00 1.89937e-12 5.09459e-12 3 1.306291864554139e+00 1.306291864554309e+00 1.69642e-13 1.46567e-11 ----------------------------------------------------------------------------------------------------- 6 Zn 1 -6.868355045302346e-01 -6.868355045305384e-01 3.03868e-13 2.99805e-12 2 -1.877731872697400e+00 -1.877731872697755e+00 3.55049e-13 1.64082e-11 3 -5.327835760868700e-01 -5.327835760866443e-01 2.25708e-13 3.41061e-12 ----------------------------------------------------------------------------------------------------- 7 Zn 1 -2.474574760670982e-01 -2.474574760670588e-01 3.93852e-14 6.45764e-12 2 7.132972075045847e-01 7.132972075038139e-01 7.70828e-13 4.89497e-12 3 -1.544295400228554e+00 -1.544295400229124e+00 5.70211e-13 9.86544e-12 ----------------------------------------------------------------------------------------------------- 8 Zn 1 3.284088928114814e-01 3.284088928124754e-01 9.94038e-13 2.07574e-11 2 -1.016418360477099e+00 -1.016418360476516e+00 5.82645e-13 1.44682e-11 3 5.756351558076976e-01 5.756351558071845e-01 5.13145e-13 3.77791e-11 ----------------------------------------------------------------------------------------------------- 9 Zn 1 7.591917283126987e-02 7.591917283151449e-02 2.44624e-13 2.40434e-12 2 -3.453995086663990e-01 -3.453995086664656e-01 6.66134e-14 1.78196e-12 3 1.378270880723071e+00 1.378270880723193e+00 1.21236e-13 2.70406e-12 ----------------------------------------------------------------------------------------------------- 10 Zn 1 -4.786855680392730e-01 -4.786855680392168e-01 5.62328e-14 1.11618e-11 2 1.169735530428382e+00 1.169735530429354e+00 9.72111e-13 1.00631e-12 3 2.074405128201571e-02 2.074405128268189e-02 6.66179e-13 4.20482e-12 ----------------------------------------------------------------------------------------------------- 11 Zn 1 4.586184758530426e-01 4.586184758560520e-01 3.00943e-12 6.86140e-12 2 -1.185390990145166e-01 -1.185390990149239e-01 4.07258e-13 5.51539e-12 3 4.205602347068594e-01 4.205602347065132e-01 3.46223e-13 5.46352e-12 ----------------------------------------------------------------------------------------------------- 12 Zn 1 7.614105850309971e-01 7.614105850303955e-01 6.01630e-13 1.04572e-12 2 -1.028679671985522e+00 -1.028679671985999e+00 4.76730e-13 2.12852e-12 3 -1.099056269622168e+00 -1.099056269622663e+00 4.95382e-13 5.65326e-12 ----------------------------------------------------------------------------------------------------- 13 Zn 1 5.643633593921128e-01 5.643633593929659e-01 8.53095e-13 1.89049e-12 2 -4.742369625344902e-01 -4.742369625349223e-01 4.32154e-13 9.37694e-13 3 -5.978621065587443e-02 -5.978621065619070e-02 3.16268e-13 1.61689e-11 ----------------------------------------------------------------------------------------------------- 14 Zn 1 -8.974322694387947e-01 -8.974322694380602e-01 7.34524e-13 2.23788e-12 2 -1.292604049304725e-01 -1.292604049308509e-01 3.78364e-13 1.06427e-11 3 8.559142357725962e-01 8.559142357719097e-01 6.86451e-13 1.04831e-11 ----------------------------------------------------------------------------------------------------- 15 Zn 1 5.200313403563397e-01 5.200313403553063e-01 1.03340e-12 2.38846e-11 2 1.840781123850060e+00 1.840781123843484e+00 6.57541e-12 1.73932e-11 3 -7.801324989340412e-01 -7.801324989339641e-01 7.71605e-14 6.79123e-12 ----------------------------------------------------------------------------------------------------- 16 Zn 1 1.561981996271089e+00 1.561981996272859e+00 1.76970e-12 2.06200e-11 2 4.607076244239839e-01 4.607076244185439e-01 5.44004e-12 4.83041e-12 3 -6.134596248049053e-01 -6.134596248038682e-01 1.03717e-12 6.08980e-11 ----------------------------------------------------------------------------------------------------- 17 Zn 1 7.447609397197253e-01 7.447609397198498e-01 1.24456e-13 2.37835e-11 2 1.367924400165833e+00 1.367924400165569e+00 2.64455e-13 1.60139e-12 3 -4.076667240794481e-02 -4.076667240915322e-02 1.20841e-12 1.91383e-11 ----------------------------------------------------------------------------------------------------- 18 Zn 1 1.050332164875114e+00 1.050332164824825e+00 5.02884e-11 1.23761e-10 * 2 1.358894270446024e+00 1.358894270405452e+00 4.05720e-11 1.90346e-10 * 3 -1.545224172427460e+00 -1.545224172422298e+00 5.16276e-12 6.53417e-11 ----------------------------------------------------------------------------------------------------- 19 Zn 1 2.168796734059456e+00 2.168796734059316e+00 1.40776e-13 2.82836e-11 2 -1.028529198223619e+00 -1.028529198224245e+00 6.25944e-13 1.10876e-11 3 -1.320104128110973e-01 -1.320104128091416e-01 1.95577e-12 1.12983e-11 ----------------------------------------------------------------------------------------------------- 20 Zn 1 -1.142905106894136e+00 -1.142905106894052e+00 8.32667e-14 1.90183e-11 2 1.025775132576163e+00 1.025775132577857e+00 1.69331e-12 1.86327e-11 3 4.717861833118395e-02 4.717861832862665e-02 2.55729e-12 3.36214e-11 ----------------------------------------------------------------------------------------------------- 21 Zn 1 -6.074292835349668e-01 -6.074292835515653e-01 1.65985e-11 4.14878e-11 2 9.307014007001559e-01 9.307014006863848e-01 1.37711e-11 1.63794e-10 * 3 8.830700135476941e-01 8.830700135499246e-01 2.23055e-12 2.18485e-07 * ----------------------------------------------------------------------------------------------------- 22 Zn 1 1.009424378665176e+00 1.009424378664432e+00 7.43849e-13 1.45646e-11 2 -3.467950188525368e+00 -3.467950188521641e+00 3.72724e-12 2.89151e-11 3 1.618321089153725e+00 1.618321089152421e+00 1.30451e-12 2.41502e-11 ----------------------------------------------------------------------------------------------------- 23 Zn 1 -1.057146727078867e+00 -1.057146727076617e+00 2.25064e-12 7.06679e-12 2 1.263305652495284e-01 1.263305652500057e-01 4.77257e-13 4.75228e-12 3 -9.528702143399039e-01 -9.528702143400164e-01 1.12466e-13 1.55230e-10 * ----------------------------------------------------------------------------------------------------- 24 Zn 1 -2.119020433869609e+00 -2.119020433869816e+00 2.06946e-13 9.26459e-12 2 -1.700539835514952e+00 -1.700539835512324e+00 2.62768e-12 3.09130e-11 3 -6.484687104669069e-01 -6.484687104664663e-01 4.40648e-13 1.54666e-11 ----------------------------------------------------------------------------------------------------- 25 Zn 1 -2.522880733899376e-01 -2.522880733907955e-01 8.57814e-13 6.79667e-12 2 -5.858254006424846e-01 -5.858254006422071e-01 2.77445e-13 1.07200e-11 3 5.870085884643365e-01 5.870085884598711e-01 4.46532e-12 1.01207e-11 ----------------------------------------------------------------------------------------------------- 26 Zn 1 4.057873003264181e-01 4.057873003263642e-01 5.39568e-14 6.21503e-13 2 2.473863425391427e-01 2.473863425393747e-01 2.32064e-13 2.86783e-11 3 2.955796162883332e-01 2.955796162868533e-01 1.47993e-12 1.26094e-11 ----------------------------------------------------------------------------------------------------- 27 Zn 1 -1.782195998003824e+00 -1.782195998004935e+00 1.11111e-12 2.06095e-11 2 -2.612552881687324e-01 -2.612552881679835e-01 7.48901e-13 3.61296e-11 3 -6.052245287333378e-01 -6.052245287318077e-01 1.53011e-12 6.34480e-07 * ----------------------------------------------------------------------------------------------------- 28 Zn 1 1.073673094067004e+00 1.073673094066255e+00 7.49178e-13 8.17835e-12 2 -8.338427611071138e-01 -8.338427611058027e-01 1.31106e-12 4.33487e-12 3 -2.227719241197510e-01 -2.227719241191416e-01 6.09346e-13 9.58403e-12 ----------------------------------------------------------------------------------------------------- 29 Zn 1 -2.176366189377651e+00 -2.176366189379058e+00 1.40643e-12 2.59641e-11 2 2.081115833684255e+00 2.081115833685089e+00 8.34444e-13 7.28972e-12 3 7.526582346208117e-01 7.526582346222792e-01 1.46749e-12 1.22191e-12 ----------------------------------------------------------------------------------------------------- 30 Zn 1 -7.582768213017571e-01 -7.582768213018043e-01 4.71845e-14 7.23899e-12 2 -6.929256098083764e-02 -6.929256098474099e-02 3.90335e-12 1.00735e-11 3 -4.386902951368039e-01 -4.386902951376626e-01 8.58702e-13 1.06661e-11 ----------------------------------------------------------------------------------------------------- 31 Zn 1 2.771386662689468e-01 2.771386662660910e-01 2.85588e-12 2.36583e-12 2 1.788309140938112e+00 1.788309140938208e+00 9.61453e-14 4.15024e-12 3 1.173860927803050e-01 1.173860927822119e-01 1.90696e-12 3.60614e-12 ----------------------------------------------------------------------------------------------------- 32 Zn 1 9.784984765201559e-01 9.784984765298502e-01 9.69436e-12 1.27177e-11 2 -9.190956927057415e-01 -9.190956927057661e-01 2.45359e-14 6.93656e-12 3 -1.435621043117912e-01 -1.435621043107545e-01 1.03667e-12 2.26474e-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 discontinuities. Maximum error obtained for particle = 3, direction = 3: |F_model - F_numer| error = ----------------------- = 1.27622e-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 Zn | a0 = 3.7960064813521055 | (Configuration in file "config-OZn.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Zn 1 -4.201728537527308e-01 -4.201728537535466e-01 8.15792e-13 1.69836e-12 2 -2.278472639348026e+00 -2.278472639348075e+00 4.84057e-14 1.35509e-11 3 -1.514526587997074e+00 -1.514526587997552e+00 4.78506e-13 8.64975e-12 ----------------------------------------------------------------------------------------------------- 2 Zn 1 5.202903644228710e-02 5.202903643984291e-02 2.44420e-12 1.19043e-11 2 -5.362375701766275e+00 -5.362375701768754e+00 2.47979e-12 1.39435e-11 3 -5.341696649404518e+00 -5.341696649402767e+00 1.75149e-12 1.54667e-11 ----------------------------------------------------------------------------------------------------- 3 Zn 1 -2.011783388091366e+00 -2.011783388091384e+00 1.73195e-14 3.17852e-11 2 -1.141423168202077e+00 -1.141423168193870e+00 8.20743e-12 1.19323e-10 3 9.033433780946183e-01 9.033433780917898e-01 2.82852e-12 1.07782e-11 ----------------------------------------------------------------------------------------------------- 4 Zn 1 -7.241574336483454e+00 -7.241574336468645e+00 1.48095e-11 4.01084e-11 2 -1.085189914486148e+01 -1.085189914485055e+01 1.09281e-11 5.33014e-11 3 4.312509137552827e+00 4.312509137552031e+00 7.95808e-13 5.77547e-11 ----------------------------------------------------------------------------------------------------- 5 O 1 -4.681272022244779e+00 -4.681272022241806e+00 2.97362e-12 1.23034e-10 2 -1.342380387041999e+01 -1.342380387041829e+01 1.69997e-12 8.72298e-11 3 -9.532652594787999e+00 -9.532652594783723e+00 4.27569e-12 8.85533e-10 * ----------------------------------------------------------------------------------------------------- 6 O 1 7.927474774711259e+00 7.927474774727574e+00 1.63149e-11 1.90732e-10 2 5.523524922970465e+00 5.523524922968141e+00 2.32436e-12 3.13145e-11 3 -1.144181649958458e+01 -1.144181649953645e+01 4.81215e-11 9.03757e-11 ----------------------------------------------------------------------------------------------------- 7 O 1 9.819715122098085e+00 9.819715122084197e+00 1.38876e-11 3.21592e-11 2 -6.726693671470649e+00 -6.726693671486814e+00 1.61648e-11 1.59678e-10 3 2.352755094349703e+00 2.352755094352271e+00 2.56728e-12 1.29699e-10 ----------------------------------------------------------------------------------------------------- 8 Zn 1 -1.316008143542672e+01 -1.316008143548044e+01 5.37153e-11 8.22276e-11 2 1.441041303335322e+00 1.441041303329437e+00 5.88440e-12 9.62839e-11 3 1.838326825551010e+01 1.838326825552255e+01 1.24487e-11 9.17346e-11 ----------------------------------------------------------------------------------------------------- 9 O 1 -2.211699502716578e+01 -2.211699502717406e+01 8.27427e-12 3.39298e-10 2 1.406730691609889e+00 1.406730691609232e+00 6.57474e-13 4.53404e-11 3 -2.116843137992283e+01 -2.116843137990896e+01 1.38698e-11 3.40908e-10 ----------------------------------------------------------------------------------------------------- 10 O 1 -1.151054800579302e+00 -1.151054800569337e+00 9.96536e-12 9.91986e-11 2 2.829671086701883e+00 2.829671086702426e+00 5.43121e-13 2.63558e-11 3 -2.253728867382020e+00 -2.253728867380649e+00 1.37046e-12 1.03975e-07 * ----------------------------------------------------------------------------------------------------- 11 O 1 2.653802885299807e+01 2.653802885300822e+01 1.01501e-11 9.34612e-11 2 1.517363053029825e+01 1.517363053028506e+01 1.31912e-11 7.87210e-11 3 2.248262512375019e+01 2.248262512375107e+01 8.77520e-13 2.88395e-10 ----------------------------------------------------------------------------------------------------- 12 O 1 1.638854350109260e-01 1.638854350126416e-01 1.71557e-12 6.15914e-11 2 3.094366083983946e+00 3.094366083986441e+00 2.49489e-12 1.40466e-10 3 -4.271497438913862e+00 -4.271497438913301e+00 5.60441e-13 1.12959e-11 ----------------------------------------------------------------------------------------------------- 13 O 1 -1.430361001034300e+00 -1.430361001029431e+00 4.86877e-12 1.36737e-10 2 3.298377328915425e+00 3.298377328915744e+00 3.18856e-13 3.64109e-11 3 -1.225310734076387e+01 -1.225310734077029e+01 6.41620e-12 1.20572e-10 ----------------------------------------------------------------------------------------------------- 14 O 1 0.000000000000000e+00 0.000000000000000e+00 0.00000e+00 0.00000e+00 2 0.000000000000000e+00 0.000000000000000e+00 0.00000e+00 0.00000e+00 3 0.000000000000000e+00 0.000000000000000e+00 0.00000e+00 0.00000e+00 ----------------------------------------------------------------------------------------------------- 15 Zn 1 8.602718430203785e+00 8.602718430184456e+00 1.93285e-11 6.40199e-11 2 7.962290585723158e+00 7.962290585722787e+00 3.71259e-13 1.56302e-11 3 3.940193585150424e+00 3.940193585149286e+00 1.13776e-12 4.61706e-11 ----------------------------------------------------------------------------------------------------- 16 O 1 1.730443251429599e-01 1.730443251510292e-01 8.06938e-12 3.93892e-08 * 2 1.711189966018608e+00 1.711189966008232e+00 1.03757e-11 2.06526e-11 3 1.622984992887262e+00 1.622984992888047e+00 7.84484e-13 5.14957e-11 ----------------------------------------------------------------------------------------------------- 17 Zn 1 -4.304012151278665e-02 -4.304012150942475e-02 3.36190e-12 1.40774e-11 2 -1.362208341291364e-01 -1.362208341302213e-01 1.08494e-12 9.93314e-12 3 -1.232879884766350e+00 -1.232879884766161e+00 1.88516e-13 6.56515e-11 ----------------------------------------------------------------------------------------------------- 18 O 1 -2.274977975397933e+01 -2.274977975398581e+01 6.48370e-12 9.32445e-11 2 -3.372590284110099e+01 -3.372590284112599e+01 2.50040e-11 1.03664e-09 * 3 -1.382622457510811e+01 -1.382622457510608e+01 2.03215e-12 2.74785e-11 ----------------------------------------------------------------------------------------------------- 19 Zn 1 -2.480385520604535e-01 -2.480385520628635e-01 2.40993e-12 9.41186e-12 2 -3.072095642244240e+00 -3.072095642234026e+00 1.02141e-11 4.66083e-10 * 3 2.713251469960868e+00 2.713251469961667e+00 7.99361e-13 4.72191e-11 ----------------------------------------------------------------------------------------------------- 20 O 1 -2.169344618690483e+01 -2.169344618684594e+01 5.88898e-11 6.67413e-11 2 -1.238830901389407e+01 -1.238830901389664e+01 2.56861e-12 2.27908e-10 3 2.630987500825215e+01 2.630987500828985e+01 3.77050e-11 1.26757e-10 ----------------------------------------------------------------------------------------------------- 21 Zn 1 5.168294203723982e+00 5.168294203725599e+00 1.61737e-12 1.78293e-11 2 -8.995430285159685e+00 -8.995430285156052e+00 3.63265e-12 5.28768e-11 3 -2.912707953999816e+00 -2.912707954002840e+00 3.02425e-12 3.32614e-11 ----------------------------------------------------------------------------------------------------- 22 O 1 2.244510743375705e+01 2.244510743376192e+01 4.87077e-12 6.93785e-10 * 2 -1.893985712342388e+01 -1.893985712341094e+01 1.29390e-11 2.42831e-04 * 3 2.136163069490606e+00 2.136163069486254e+00 4.35207e-12 1.26841e-04 * ----------------------------------------------------------------------------------------------------- 23 Zn 1 -1.091945883410813e-01 -1.091945883421430e-01 1.06172e-12 1.21100e-11 2 -1.323099551557053e+00 -1.323099551556992e+00 6.03961e-14 6.70464e-12 3 9.824799875411091e-01 9.824799875390973e-01 2.01184e-12 2.40612e-11 ----------------------------------------------------------------------------------------------------- 24 Zn 1 2.665913657306318e+00 2.665913657286902e+00 1.94165e-11 9.16720e-11 2 -1.176714612825085e+00 -1.176714612823215e+00 1.87050e-12 4.45797e-11 3 1.083498641872007e+01 1.083498641872794e+01 7.86926e-12 1.27196e-10 ----------------------------------------------------------------------------------------------------- 25 O 1 -1.634654478910392e+01 -1.634654478908596e+01 1.79590e-11 1.15918e-10 2 -4.183182215866234e-01 -4.183182215747789e-01 1.18445e-11 1.00180e-10 3 -1.592518108577783e+01 -1.592518108578155e+01 3.71436e-12 2.75623e-10 ----------------------------------------------------------------------------------------------------- 26 O 1 1.038333246119539e+01 1.038333246121018e+01 1.47899e-11 5.03917e-11 2 1.374046599753459e+01 1.374046599751679e+01 1.78044e-11 8.66933e-11 3 -5.163562892664100e+00 -5.163562892662220e+00 1.87939e-12 2.15650e-11 ----------------------------------------------------------------------------------------------------- 27 Zn 1 4.953344390042912e+00 4.953344390046274e+00 3.36176e-12 1.63804e-10 2 -7.705136655012550e+00 -7.705136655019865e+00 7.31415e-12 7.84466e-11 3 1.075110470653562e+01 1.075110470655476e+01 1.91385e-11 6.69722e-11 ----------------------------------------------------------------------------------------------------- 28 Zn 1 -3.893020305444493e+00 -3.893020305445203e+00 7.10543e-13 2.38156e-11 2 8.592771983643443e+00 8.592771983639613e+00 3.82983e-12 5.19869e-11 3 3.816512806175805e+00 3.816512806173341e+00 2.46425e-12 5.13776e-11 ----------------------------------------------------------------------------------------------------- 29 O 1 1.062297493571326e+01 1.062297493572087e+01 7.61524e-12 1.06921e-10 2 5.852575957968151e+01 5.852575957968161e+01 9.94760e-14 1.13985e-10 3 -1.173256118867334e+01 -1.173256118868067e+01 7.32392e-12 6.09504e-11 ----------------------------------------------------------------------------------------------------- 30 Zn 1 1.020958702147031e-01 1.020958702157299e-01 1.02680e-12 2.40448e-11 2 5.596117434429995e-02 5.596117434509851e-02 7.98570e-13 9.67568e-12 3 1.297186327569149e-01 1.297186327565672e-01 3.47666e-13 3.16907e-11 ----------------------------------------------------------------------------------------------------- 31 Zn 1 3.590690458443074e+00 3.590690458439876e+00 3.19744e-12 1.30966e-11 2 1.363769311915983e+00 1.363769311914591e+00 1.39244e-12 4.11007e-11 3 3.289820130794859e+00 3.289820130786662e+00 8.19700e-12 5.25824e-11 ----------------------------------------------------------------------------------------------------- 32 Zn 1 4.087709775121218e+00 4.087709775127860e+00 6.64180e-12 4.94458e-11 2 2.946202430325000e+00 2.946202430331616e+00 6.61560e-12 3.92357e-11 3 3.608983142223199e+00 3.608983142223489e+00 2.89990e-13 2.72435e-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 discontinuities. Maximum error obtained for particle = 17, direction = 1: |F_model - F_numer| error = ----------------------- = 7.81109e-11 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 2.10355e-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 2.10355e-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.