!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_003 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 3.544762293347266e-01 1.76636e-13 1.48485e-11 2 6.782119933604619e-01 6.782119933600907e-01 3.71148e-13 1.65581e-11 3 1.053020676875888e+00 1.053020676874978e+00 9.09495e-13 1.08835e-11 ----------------------------------------------------------------------------------------------------- 2 O 1 4.383808085690745e-01 4.383808085695018e-01 4.27380e-13 6.45139e-12 2 -1.102183741677778e+00 -1.102183741676431e+00 1.34714e-12 1.51985e-11 3 -2.795273094005829e-01 -2.795273094003025e-01 2.80387e-13 3.52363e-12 ----------------------------------------------------------------------------------------------------- 3 O 1 -3.637600903093950e-01 -3.637600903091639e-01 2.31093e-13 1.62139e-11 2 2.058824150724778e-01 2.058824150740812e-01 1.60338e-12 8.34977e-12 3 3.642710397676693e-01 3.642710397678027e-01 1.33449e-13 2.67919e-12 ----------------------------------------------------------------------------------------------------- 4 O 1 -3.236782356228475e-01 -3.236782356268228e-01 3.97532e-12 5.76122e-12 2 -5.163851583609395e-01 -5.163851583619771e-01 1.03761e-12 1.71640e-12 3 -5.207041285185550e-01 -5.207041285193026e-01 7.47624e-13 5.94058e-12 ----------------------------------------------------------------------------------------------------- 5 O 1 -9.316566766991269e-02 -9.316566766972025e-02 1.92443e-13 3.72855e-12 2 6.365605344200138e-01 6.365605344199445e-01 6.92779e-14 1.99627e-11 3 -2.653585805127598e-01 -2.653585805126965e-01 6.33937e-14 1.21119e-11 ----------------------------------------------------------------------------------------------------- 6 O 1 -4.579237661143585e-01 -4.579237661137643e-01 5.94136e-13 2.50761e-12 2 -7.888453949773189e-01 -7.888453949771252e-01 1.93623e-13 6.48903e-12 3 5.121030940846576e-01 5.121030940845859e-01 7.17204e-14 2.21201e-12 ----------------------------------------------------------------------------------------------------- 7 O 1 -3.840553411671663e-01 -3.840553411673458e-01 1.79468e-13 5.71311e-11 * 2 4.041943293313921e-01 4.041943293314386e-01 4.64628e-14 6.99568e-12 3 -5.715114185203244e-01 -5.715114185200921e-01 2.32259e-13 2.24631e-12 ----------------------------------------------------------------------------------------------------- 8 O 1 5.202488672729206e-01 5.202488672672455e-01 5.67513e-12 2.17671e-11 2 2.022197486340458e-01 2.022197486346503e-01 6.04461e-13 8.83202e-12 3 3.872132783178666e-01 3.872132783178871e-01 2.04836e-14 2.57944e-12 ----------------------------------------------------------------------------------------------------- 9 O 1 2.916674083252479e-01 2.916674083250861e-01 1.61759e-13 1.71541e-12 2 8.585615356049230e-01 8.585615356057760e-01 8.52984e-13 3.64531e-12 3 5.152511730035348e-01 5.152511730036395e-01 1.04694e-13 4.50928e-12 ----------------------------------------------------------------------------------------------------- 10 O 1 -3.200197585342443e-01 -3.200197585345170e-01 2.72726e-13 8.86496e-12 2 -2.176159855816177e-01 -2.176159855832451e-01 1.62745e-12 3.75389e-12 3 -1.375834787986411e-01 -1.375834787991661e-01 5.25080e-13 8.91037e-13 ----------------------------------------------------------------------------------------------------- 11 O 1 -4.109841972458377e-01 -4.109841972439446e-01 1.89304e-12 2.82575e-11 2 3.820781382450900e-01 3.820781382494773e-01 4.38738e-12 1.57042e-11 3 -5.265930749920307e-01 -5.265930749939574e-01 1.92668e-12 8.14970e-12 ----------------------------------------------------------------------------------------------------- 12 O 1 1.853881278253071e-01 1.853881278249922e-01 3.14943e-13 1.57914e-11 2 -5.307946365254096e-01 -5.307946365255259e-01 1.16351e-13 7.28784e-12 3 -2.043808072138245e-01 -2.043808072137348e-01 8.97338e-14 1.16422e-11 ----------------------------------------------------------------------------------------------------- 13 O 1 1.528754721058768e-01 1.528754721039133e-01 1.96357e-12 2.74222e-12 2 4.970775111795115e-02 4.970775111871856e-02 7.67407e-13 5.35467e-12 3 -2.935329025282659e-01 -2.935329025280585e-01 2.07390e-13 1.03516e-11 ----------------------------------------------------------------------------------------------------- 14 O 1 2.790984009744525e-01 2.790984009741934e-01 2.59126e-13 2.41196e-12 2 -3.647985821065100e-01 -3.647985821066287e-01 1.18738e-13 3.46267e-12 3 2.120513641500836e-01 2.120513641498403e-01 2.43305e-13 5.97949e-12 ----------------------------------------------------------------------------------------------------- 15 O 1 1.466578277243260e-01 1.466578277246360e-01 3.09947e-13 8.87299e-11 * 2 8.403151351234558e-01 8.403151351234811e-01 2.53131e-14 2.84207e-11 3 -4.507778724140882e-01 -4.507778724210544e-01 6.96621e-12 4.46140e-11 ----------------------------------------------------------------------------------------------------- 16 O 1 -3.193259066848592e-01 -3.193259066833173e-01 1.54193e-12 3.16621e-11 2 4.286130370565326e-01 4.286130370589243e-01 2.39170e-12 3.71159e-12 3 3.997227642078189e-01 3.997227642087693e-01 9.50406e-13 1.71732e-11 ----------------------------------------------------------------------------------------------------- 17 O 1 9.368702947968534e-01 9.368702947979298e-01 1.07647e-12 1.33539e-11 2 5.020095799094257e-01 5.020095799084922e-01 9.33587e-13 2.54408e-12 3 6.703936798826700e-01 6.703936798815299e-01 1.14009e-12 3.46564e-11 ----------------------------------------------------------------------------------------------------- 18 O 1 -2.154781483738952e-01 -2.154781483733464e-01 5.48728e-13 9.97247e-12 2 -1.114911217356600e+00 -1.114911217355988e+00 6.11955e-13 1.06992e-11 3 5.770546994606595e-01 5.770546994552213e-01 5.43821e-12 7.56961e-12 ----------------------------------------------------------------------------------------------------- 19 O 1 -7.920090434053851e-01 -7.920090434066046e-01 1.21947e-12 6.20970e-12 2 1.106748713638046e+00 1.106748713638685e+00 6.39266e-13 8.85114e-12 3 -3.211723367918648e-01 -3.211723367921527e-01 2.87881e-13 1.20881e-12 ----------------------------------------------------------------------------------------------------- 20 O 1 5.408208795304209e-01 5.408208795302324e-01 1.88516e-13 2.97817e-12 2 -1.006215824634294e+00 -1.006215824634807e+00 5.12923e-13 4.70424e-12 3 -6.516100748217343e-01 -6.516100748220647e-01 3.30402e-13 2.27611e-11 ----------------------------------------------------------------------------------------------------- 21 O 1 1.326914059853742e+00 1.326914059852619e+00 1.12310e-12 3.59106e-11 2 1.886275855245637e-01 1.886275855237030e-01 8.60728e-13 7.12380e-12 3 4.334158653003810e-01 4.334158653005903e-01 2.09333e-13 1.01223e-11 ----------------------------------------------------------------------------------------------------- 22 O 1 -3.351529864259931e-01 -3.351529864263570e-01 3.63987e-13 1.68323e-11 2 -6.481669763463643e-01 -6.481669763454194e-01 9.44911e-13 1.48637e-12 3 7.339667652581491e-01 7.339667652584142e-01 2.65121e-13 1.94555e-12 ----------------------------------------------------------------------------------------------------- 23 O 1 -7.463727266190455e-01 -7.463727266194411e-01 3.95572e-13 5.46962e-12 2 4.051510106800210e-01 4.051510106801550e-01 1.33948e-13 2.08922e-12 3 -1.075788234133561e+00 -1.075788234135908e+00 2.34657e-12 2.00422e-11 ----------------------------------------------------------------------------------------------------- 24 O 1 -2.630874432115387e-01 -2.630874432115271e-01 1.16018e-14 1.10374e-11 2 -7.118582704473128e-01 -7.118582704475240e-01 2.11275e-13 1.78164e-11 3 -5.192548485352790e-01 -5.192548485359570e-01 6.78013e-13 1.63082e-11 ----------------------------------------------------------------------------------------------------- 25 O 1 -7.684534378258356e-01 -7.684534378284684e-01 2.63278e-12 5.79969e-12 2 -3.738040852124443e-01 -3.738040852083179e-01 4.12642e-12 1.51819e-11 3 -2.041811218723274e+00 -2.041811218727465e+00 4.19043e-12 1.33178e-11 ----------------------------------------------------------------------------------------------------- 26 O 1 -5.026732110694351e-01 -5.026732110694569e-01 2.18714e-14 4.88354e-12 2 2.168679119941843e-01 2.168679119937733e-01 4.10977e-13 8.76352e-12 3 5.983297324410417e-01 5.983297324429796e-01 1.93789e-12 1.24686e-11 ----------------------------------------------------------------------------------------------------- 27 O 1 6.133500879154542e-01 6.133500879183325e-01 2.87825e-12 6.29674e-12 2 5.607723523694561e-01 5.607723523689883e-01 4.67848e-13 2.50420e-11 3 7.265890385640932e-01 7.265890385644284e-01 3.35176e-13 1.00443e-11 ----------------------------------------------------------------------------------------------------- 28 O 1 4.562387583424430e-01 4.562387583432768e-01 8.33777e-13 3.49777e-11 2 4.602880591755202e-01 4.602880591752888e-01 2.31370e-13 3.06536e-11 3 6.019470659557806e-01 6.019470659552811e-01 4.99489e-13 4.93454e-11 ----------------------------------------------------------------------------------------------------- 29 O 1 7.127628089458303e-01 7.127628089406106e-01 5.21971e-12 2.87832e-11 2 -4.157231836068516e-02 -4.157231835194012e-02 8.74504e-12 9.77160e-12 3 4.588283693318305e-01 4.588283693422201e-01 1.03896e-11 5.50537e-12 ----------------------------------------------------------------------------------------------------- 30 O 1 -2.524679852671886e-01 -2.524679852658895e-01 1.29913e-12 1.04988e-11 2 -8.070690024582106e-01 -8.070690024587335e-01 5.22915e-13 1.12751e-11 3 1.936418494443141e-01 1.936418494433657e-01 9.48408e-13 2.37671e-05 * ----------------------------------------------------------------------------------------------------- 31 O 1 -3.574626722421883e-01 -3.574626722413318e-01 8.56482e-13 1.39024e-11 2 6.170567725839022e-01 6.170567725832437e-01 6.58584e-13 3.89990e-11 3 -4.612120330049997e-01 -4.612120330040953e-01 9.04388e-13 7.00218e-12 ----------------------------------------------------------------------------------------------------- 32 O 1 -4.967941372737754e-02 -4.967941373047262e-02 3.09508e-12 2.28505e-05 * 2 -5.196454097959788e-01 -5.196454097954580e-01 5.20806e-13 2.00950e-12 3 -1.169821371366537e-01 -1.169821371400584e-01 3.40472e-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 = ----------------------- = 2.10357e-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 1.387455943515335e+00 6.06182e-13 3.06977e-12 2 1.212178281451795e+00 1.212178281451569e+00 2.25597e-13 1.33071e-11 3 1.544165605006207e+00 1.544165605006188e+00 1.88738e-14 5.65770e-12 ----------------------------------------------------------------------------------------------------- 2 Zn 1 -7.831823816901013e-01 -7.831823816893051e-01 7.96252e-13 4.67371e-12 2 -6.898093558546141e-01 -6.898093558573540e-01 2.73992e-12 4.52349e-11 3 -1.671939675655949e+00 -1.671939675662468e+00 6.51923e-12 1.35808e-10 * ----------------------------------------------------------------------------------------------------- 3 Zn 1 5.658061052944857e-01 5.658061052958299e-01 1.34415e-12 2.76055e-11 2 -6.924863148052924e-01 -6.924863148118212e-01 6.52878e-12 3.23857e-10 * 3 2.429907587197443e-01 2.429907586887332e-01 3.10111e-11 4.98795e-11 ----------------------------------------------------------------------------------------------------- 4 Zn 1 -1.766360449489789e+00 -1.766360449490011e+00 2.22489e-13 3.47628e-10 * 2 -6.225284891861622e-01 -6.225284891871437e-01 9.81437e-13 1.03352e-11 3 3.852672509846398e-01 3.852672509843840e-01 2.55851e-13 7.09466e-12 ----------------------------------------------------------------------------------------------------- 5 Zn 1 8.231746568472837e-01 8.231746568458785e-01 1.40521e-12 5.52924e-12 2 1.538284112062795e+00 1.538284112060896e+00 1.89870e-12 5.09459e-12 3 1.306291864554139e+00 1.306291864554310e+00 1.70530e-13 1.46569e-11 ----------------------------------------------------------------------------------------------------- 6 Zn 1 -6.868355045302346e-01 -6.868355045305380e-01 3.03424e-13 2.99805e-12 2 -1.877731872697400e+00 -1.877731872697756e+00 3.55938e-13 1.64091e-11 3 -5.327835760868700e-01 -5.327835760866440e-01 2.26041e-13 3.41016e-12 ----------------------------------------------------------------------------------------------------- 7 Zn 1 -2.474574760670982e-01 -2.474574760670587e-01 3.94962e-14 6.45775e-12 2 7.132972075045847e-01 7.132972075038142e-01 7.70495e-13 4.89475e-12 3 -1.544295400228554e+00 -1.544295400229123e+00 5.68878e-13 9.86522e-12 ----------------------------------------------------------------------------------------------------- 8 Zn 1 3.284088928114814e-01 3.284088928124755e-01 9.94149e-13 2.07573e-11 2 -1.016418360477099e+00 -1.016418360476516e+00 5.83311e-13 1.44682e-11 3 5.756351558076976e-01 5.756351558071847e-01 5.12923e-13 3.77794e-11 ----------------------------------------------------------------------------------------------------- 9 Zn 1 7.591917283126987e-02 7.591917283151452e-02 2.44652e-13 2.40429e-12 2 -3.453995086663990e-01 -3.453995086664658e-01 6.67799e-14 1.78196e-12 3 1.378270880723071e+00 1.378270880723193e+00 1.21902e-13 2.70428e-12 ----------------------------------------------------------------------------------------------------- 10 Zn 1 -4.786855680392730e-01 -4.786855680392169e-01 5.61218e-14 1.11619e-11 2 1.169735530428382e+00 1.169735530429354e+00 9.71223e-13 1.00697e-12 3 2.074405128201571e-02 2.074405128268187e-02 6.66162e-13 4.20482e-12 ----------------------------------------------------------------------------------------------------- 11 Zn 1 4.586184758530426e-01 4.586184758560518e-01 3.00915e-12 6.86140e-12 2 -1.185390990145166e-01 -1.185390990149239e-01 4.07313e-13 5.51537e-12 3 4.205602347068594e-01 4.205602347065134e-01 3.46057e-13 5.46363e-12 ----------------------------------------------------------------------------------------------------- 12 Zn 1 7.614105850309971e-01 7.614105850303950e-01 6.02074e-13 1.04594e-12 2 -1.028679671985522e+00 -1.028679671985998e+00 4.75842e-13 2.12874e-12 3 -1.099056269622168e+00 -1.099056269622662e+00 4.94493e-13 5.65281e-12 ----------------------------------------------------------------------------------------------------- 13 Zn 1 5.643633593921128e-01 5.643633593929652e-01 8.52429e-13 1.89038e-12 2 -4.742369625344902e-01 -4.742369625349225e-01 4.32376e-13 9.37694e-13 3 -5.978621065587443e-02 -5.978621065619067e-02 3.16240e-13 1.61689e-11 ----------------------------------------------------------------------------------------------------- 14 Zn 1 -8.974322694387947e-01 -8.974322694380596e-01 7.35079e-13 2.23821e-12 2 -1.292604049304725e-01 -1.292604049308509e-01 3.78392e-13 1.06427e-11 3 8.559142357725962e-01 8.559142357719102e-01 6.86007e-13 1.04837e-11 ----------------------------------------------------------------------------------------------------- 15 Zn 1 5.200313403563397e-01 5.200313403553065e-01 1.03317e-12 2.38847e-11 2 1.840781123850060e+00 1.840781123843485e+00 6.57452e-12 1.73941e-11 3 -7.801324989340412e-01 -7.801324989339636e-01 7.76046e-14 6.79179e-12 ----------------------------------------------------------------------------------------------------- 16 Zn 1 1.561981996271089e+00 1.561981996272860e+00 1.77036e-12 2.06208e-11 2 4.607076244239839e-01 4.607076244185439e-01 5.44004e-12 4.83064e-12 3 -6.134596248049053e-01 -6.134596248038685e-01 1.03684e-12 6.08980e-11 ----------------------------------------------------------------------------------------------------- 17 Zn 1 7.447609397197253e-01 7.447609397198499e-01 1.24567e-13 2.37838e-11 2 1.367924400165833e+00 1.367924400165568e+00 2.65121e-13 1.60028e-12 3 -4.076667240794481e-02 -4.076667240915318e-02 1.20837e-12 1.91383e-11 ----------------------------------------------------------------------------------------------------- 18 Zn 1 1.050332164875114e+00 1.050332164824825e+00 5.02891e-11 1.23761e-10 * 2 1.358894270446024e+00 1.358894270405451e+00 4.05729e-11 1.90345e-10 * 3 -1.545224172427460e+00 -1.545224172422297e+00 5.16365e-12 6.53411e-11 ----------------------------------------------------------------------------------------------------- 19 Zn 1 2.168796734059457e+00 2.168796734059316e+00 1.40332e-13 2.82836e-11 2 -1.028529198223619e+00 -1.028529198224244e+00 6.25056e-13 1.10865e-11 3 -1.320104128110973e-01 -1.320104128091415e-01 1.95585e-12 1.12985e-11 ----------------------------------------------------------------------------------------------------- 20 Zn 1 -1.142905106894136e+00 -1.142905106894053e+00 8.26006e-14 1.90183e-11 2 1.025775132576163e+00 1.025775132577856e+00 1.69265e-12 1.86327e-11 3 4.717861833118395e-02 4.717861832862667e-02 2.55727e-12 3.36214e-11 ----------------------------------------------------------------------------------------------------- 21 Zn 1 -6.074292835349668e-01 -6.074292835515649e-01 1.65981e-11 4.14883e-11 2 9.307014007001559e-01 9.307014006863842e-01 1.37718e-11 1.63794e-10 * 3 8.830700135476941e-01 8.830700135499251e-01 2.23099e-12 2.18485e-07 * ----------------------------------------------------------------------------------------------------- 22 Zn 1 1.009424378665176e+00 1.009424378664433e+00 7.43405e-13 1.45650e-11 2 -3.467950188525368e+00 -3.467950188521639e+00 3.72902e-12 2.89155e-11 3 1.618321089153725e+00 1.618321089152422e+00 1.30362e-12 2.41502e-11 ----------------------------------------------------------------------------------------------------- 23 Zn 1 -1.057146727078867e+00 -1.057146727076616e+00 2.25131e-12 7.06679e-12 2 1.263305652495284e-01 1.263305652500055e-01 4.77146e-13 4.75214e-12 3 -9.528702143399039e-01 -9.528702143400168e-01 1.12910e-13 1.55230e-10 * ----------------------------------------------------------------------------------------------------- 24 Zn 1 -2.119020433869609e+00 -2.119020433869814e+00 2.05169e-13 9.26415e-12 2 -1.700539835514952e+00 -1.700539835512323e+00 2.62901e-12 3.09133e-11 3 -6.484687104669069e-01 -6.484687104664667e-01 4.40203e-13 1.54664e-11 ----------------------------------------------------------------------------------------------------- 25 Zn 1 -2.522880733899376e-01 -2.522880733907953e-01 8.57647e-13 6.79667e-12 2 -5.858254006424846e-01 -5.858254006422075e-01 2.77112e-13 1.07200e-11 3 5.870085884643365e-01 5.870085884598705e-01 4.46598e-12 1.01210e-11 ----------------------------------------------------------------------------------------------------- 26 Zn 1 4.057873003264181e-01 4.057873003263637e-01 5.44009e-14 6.21225e-13 2 2.473863425391427e-01 2.473863425393748e-01 2.32175e-13 2.86785e-11 3 2.955796162883332e-01 2.955796162868534e-01 1.47982e-12 1.26095e-11 ----------------------------------------------------------------------------------------------------- 27 Zn 1 -1.782195998003824e+00 -1.782195998004934e+00 1.10978e-12 2.06093e-11 2 -2.612552881687324e-01 -2.612552881679834e-01 7.49067e-13 3.61296e-11 3 -6.052245287333378e-01 -6.052245287318080e-01 1.52978e-12 6.34480e-07 * ----------------------------------------------------------------------------------------------------- 28 Zn 1 1.073673094067004e+00 1.073673094066254e+00 7.50067e-13 8.17835e-12 2 -8.338427611071138e-01 -8.338427611058021e-01 1.31162e-12 4.33398e-12 3 -2.227719241197510e-01 -2.227719241191417e-01 6.09235e-13 9.58403e-12 ----------------------------------------------------------------------------------------------------- 29 Zn 1 -2.176366189377651e+00 -2.176366189379056e+00 1.40465e-12 2.59655e-11 2 2.081115833684255e+00 2.081115833685088e+00 8.32667e-13 7.28928e-12 3 7.526582346208117e-01 7.526582346222787e-01 1.46694e-12 1.22169e-12 ----------------------------------------------------------------------------------------------------- 30 Zn 1 -7.582768213017571e-01 -7.582768213018036e-01 4.65183e-14 7.23910e-12 2 -6.929256098083764e-02 -6.929256098474103e-02 3.90339e-12 1.00736e-11 3 -4.386902951368039e-01 -4.386902951376624e-01 8.58535e-13 1.06663e-11 ----------------------------------------------------------------------------------------------------- 31 Zn 1 2.771386662689468e-01 2.771386662660911e-01 2.85572e-12 2.36594e-12 2 1.788309140938112e+00 1.788309140938207e+00 9.48130e-14 4.15179e-12 3 1.173860927803050e-01 1.173860927822119e-01 1.90689e-12 3.60610e-12 ----------------------------------------------------------------------------------------------------- 32 Zn 1 9.784984765201559e-01 9.784984765298496e-01 9.69369e-12 1.27177e-11 2 -9.190956927057415e-01 -9.190956927057655e-01 2.39808e-14 6.93656e-12 3 -1.435621043117912e-01 -1.435621043107546e-01 1.03662e-12 2.26480e-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 = ----------------------- = 1.27623e-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 -4.201728537535463e-01 8.15459e-13 1.69831e-12 2 -2.278472639348026e+00 -2.278472639348073e+00 4.66294e-14 1.35509e-11 3 -1.514526587997074e+00 -1.514526587997553e+00 4.79172e-13 8.64930e-12 ----------------------------------------------------------------------------------------------------- 2 Zn 1 5.202903644228710e-02 5.202903643984287e-02 2.44423e-12 1.19043e-11 2 -5.362375701766275e+00 -5.362375701768757e+00 2.48246e-12 1.39462e-11 3 -5.341696649404518e+00 -5.341696649402770e+00 1.74882e-12 1.54641e-11 ----------------------------------------------------------------------------------------------------- 3 Zn 1 -2.011783388091366e+00 -2.011783388091382e+00 1.59872e-14 3.17852e-11 2 -1.141423168202077e+00 -1.141423168193869e+00 8.20810e-12 1.19322e-10 3 9.033433780946183e-01 9.033433780917891e-01 2.82918e-12 1.07786e-11 ----------------------------------------------------------------------------------------------------- 4 Zn 1 -7.241574336483454e+00 -7.241574336468648e+00 1.48059e-11 4.01084e-11 2 -1.085189914486148e+01 -1.085189914485054e+01 1.09353e-11 5.33014e-11 3 4.312509137552827e+00 4.312509137552028e+00 7.99361e-13 5.77502e-11 ----------------------------------------------------------------------------------------------------- 5 O 1 -4.681272022244779e+00 -4.681272022241808e+00 2.97096e-12 1.23032e-10 2 -1.342380387041999e+01 -1.342380387041830e+01 1.69287e-12 8.72333e-11 3 -9.532652594787999e+00 -9.532652594783720e+00 4.27924e-12 8.85521e-10 * ----------------------------------------------------------------------------------------------------- 6 O 1 7.927474774711259e+00 7.927474774727568e+00 1.63096e-11 1.90732e-10 2 5.523524922970465e+00 5.523524922968138e+00 2.32792e-12 3.13163e-11 3 -1.144181649958458e+01 -1.144181649953645e+01 4.81251e-11 9.03668e-11 ----------------------------------------------------------------------------------------------------- 7 O 1 9.819715122098085e+00 9.819715122084204e+00 1.38805e-11 3.21609e-11 2 -6.726693671470649e+00 -6.726693671486808e+00 1.61595e-11 1.59676e-10 3 2.352755094349703e+00 2.352755094352269e+00 2.56550e-12 1.29699e-10 ----------------------------------------------------------------------------------------------------- 8 Zn 1 -1.316008143542672e+01 -1.316008143548043e+01 5.37064e-11 8.22276e-11 2 1.441041303335322e+00 1.441041303329436e+00 5.88574e-12 9.62845e-11 3 1.838326825551010e+01 1.838326825552256e+01 1.24558e-11 9.17346e-11 ----------------------------------------------------------------------------------------------------- 9 O 1 -2.211699502716578e+01 -2.211699502717407e+01 8.28493e-12 3.39302e-10 2 1.406730691609889e+00 1.406730691609233e+00 6.56808e-13 4.53408e-11 3 -2.116843137992283e+01 -2.116843137990897e+01 1.38591e-11 3.40904e-10 ----------------------------------------------------------------------------------------------------- 10 O 1 -1.151054800579302e+00 -1.151054800569337e+00 9.96492e-12 9.91984e-11 2 2.829671086701883e+00 2.829671086702425e+00 5.41789e-13 2.63580e-11 3 -2.253728867382020e+00 -2.253728867380651e+00 1.36913e-12 1.03975e-07 * ----------------------------------------------------------------------------------------------------- 11 O 1 2.653802885299807e+01 2.653802885300819e+01 1.01252e-11 9.34612e-11 2 1.517363053029825e+01 1.517363053028507e+01 1.31806e-11 7.87175e-11 3 2.248262512375019e+01 2.248262512375105e+01 8.59757e-13 2.88377e-10 ----------------------------------------------------------------------------------------------------- 12 O 1 1.638854350109260e-01 1.638854350126414e-01 1.71546e-12 6.15914e-11 2 3.094366083983946e+00 3.094366083986439e+00 2.49312e-12 1.40468e-10 3 -4.271497438913862e+00 -4.271497438913298e+00 5.63993e-13 1.12985e-11 ----------------------------------------------------------------------------------------------------- 13 O 1 -1.430361001034300e+00 -1.430361001029431e+00 4.86811e-12 1.36737e-10 2 3.298377328915425e+00 3.298377328915746e+00 3.20632e-13 3.64104e-11 3 -1.225310734076387e+01 -1.225310734077028e+01 6.40910e-12 1.20570e-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 8.602718430184453e+00 1.93321e-11 6.40092e-11 2 7.962290585723158e+00 7.962290585722791e+00 3.67706e-13 1.56302e-11 3 3.940193585150424e+00 3.940193585149283e+00 1.14042e-12 4.61706e-11 ----------------------------------------------------------------------------------------------------- 16 O 1 1.730443251429599e-01 1.730443251510293e-01 8.06943e-12 3.93892e-08 * 2 1.711189966018608e+00 1.711189966008232e+00 1.03764e-11 2.06517e-11 3 1.622984992887262e+00 1.622984992888046e+00 7.83151e-13 5.14944e-11 ----------------------------------------------------------------------------------------------------- 17 Zn 1 -4.304012151278665e-02 -4.304012150942472e-02 3.36194e-12 1.40773e-11 2 -1.362208341291364e-01 -1.362208341302212e-01 1.08483e-12 9.93328e-12 3 -1.232879884766350e+00 -1.232879884766160e+00 1.89404e-13 6.56515e-11 ----------------------------------------------------------------------------------------------------- 18 O 1 -2.274977975397933e+01 -2.274977975398580e+01 6.47304e-12 9.32623e-11 2 -3.372590284110099e+01 -3.372590284112596e+01 2.49685e-11 1.03661e-09 * 3 -1.382622457510811e+01 -1.382622457510607e+01 2.04103e-12 2.74802e-11 ----------------------------------------------------------------------------------------------------- 19 Zn 1 -2.480385520604535e-01 -2.480385520628633e-01 2.40977e-12 9.41186e-12 2 -3.072095642244240e+00 -3.072095642234023e+00 1.02163e-11 4.66081e-10 * 3 2.713251469960868e+00 2.713251469961666e+00 7.97584e-13 4.72182e-11 ----------------------------------------------------------------------------------------------------- 20 O 1 -2.169344618690483e+01 -2.169344618684595e+01 5.88791e-11 6.67484e-11 2 -1.238830901389407e+01 -1.238830901389663e+01 2.56151e-12 2.27912e-10 3 2.630987500825215e+01 2.630987500828983e+01 3.76801e-11 1.26757e-10 ----------------------------------------------------------------------------------------------------- 21 Zn 1 5.168294203723982e+00 5.168294203725600e+00 1.61826e-12 1.78337e-11 2 -8.995430285159685e+00 -8.995430285156058e+00 3.62732e-12 5.28768e-11 3 -2.912707953999816e+00 -2.912707954002839e+00 3.02336e-12 3.32627e-11 ----------------------------------------------------------------------------------------------------- 22 O 1 2.244510743375705e+01 2.244510743376193e+01 4.88143e-12 6.93785e-10 * 2 -1.893985712342388e+01 -1.893985712341095e+01 1.29319e-11 2.42831e-04 * 3 2.136163069490606e+00 2.136163069486255e+00 4.35119e-12 1.26841e-04 * ----------------------------------------------------------------------------------------------------- 23 Zn 1 -1.091945883410813e-01 -1.091945883421428e-01 1.06155e-12 1.21099e-11 2 -1.323099551557053e+00 -1.323099551556991e+00 6.12843e-14 6.70419e-12 3 9.824799875411091e-01 9.824799875390967e-01 2.01239e-12 2.40618e-11 ----------------------------------------------------------------------------------------------------- 24 Zn 1 2.665913657306318e+00 2.665913657286900e+00 1.94182e-11 9.16711e-11 2 -1.176714612825085e+00 -1.176714612823214e+00 1.87117e-12 4.45823e-11 3 1.083498641872007e+01 1.083498641872793e+01 7.86216e-12 1.27192e-10 ----------------------------------------------------------------------------------------------------- 25 O 1 -1.634654478910392e+01 -1.634654478908595e+01 1.79696e-11 1.15918e-10 2 -4.183182215866234e-01 -4.183182215747786e-01 1.18448e-11 1.00180e-10 3 -1.592518108577783e+01 -1.592518108578154e+01 3.70370e-12 2.75623e-10 ----------------------------------------------------------------------------------------------------- 26 O 1 1.038333246119539e+01 1.038333246121017e+01 1.47846e-11 5.03935e-11 2 1.374046599753459e+01 1.374046599751678e+01 1.78133e-11 8.66862e-11 3 -5.163562892664100e+00 -5.163562892662217e+00 1.88294e-12 2.15650e-11 ----------------------------------------------------------------------------------------------------- 27 Zn 1 4.953344390042912e+00 4.953344390046271e+00 3.35909e-12 1.63805e-10 2 -7.705136655012550e+00 -7.705136655019858e+00 7.30793e-12 7.84510e-11 3 1.075110470653562e+01 1.075110470655479e+01 1.91669e-11 6.69971e-11 ----------------------------------------------------------------------------------------------------- 28 Zn 1 -3.893020305444493e+00 -3.893020305445201e+00 7.07878e-13 2.38156e-11 2 8.592771983643443e+00 8.592771983639617e+00 3.82627e-12 5.19851e-11 3 3.816512806175805e+00 3.816512806173342e+00 2.46336e-12 5.13767e-11 ----------------------------------------------------------------------------------------------------- 29 O 1 1.062297493571326e+01 1.062297493572088e+01 7.61879e-12 1.06926e-10 2 5.852575957968151e+01 5.852575957968163e+01 1.20792e-13 1.13978e-10 3 -1.173256118867334e+01 -1.173256118868067e+01 7.32925e-12 6.09504e-11 ----------------------------------------------------------------------------------------------------- 30 Zn 1 1.020958702147031e-01 1.020958702157298e-01 1.02671e-12 2.40448e-11 2 5.596117434429995e-02 5.596117434509849e-02 7.98549e-13 9.67569e-12 3 1.297186327569149e-01 1.297186327565671e-01 3.47833e-13 3.16907e-11 ----------------------------------------------------------------------------------------------------- 31 Zn 1 3.590690458443074e+00 3.590690458439873e+00 3.20055e-12 1.30975e-11 2 1.363769311915983e+00 1.363769311914590e+00 1.39289e-12 4.11002e-11 3 3.289820130794859e+00 3.289820130786664e+00 8.19478e-12 5.25815e-11 ----------------------------------------------------------------------------------------------------- 32 Zn 1 4.087709775121218e+00 4.087709775127862e+00 6.64357e-12 4.94458e-11 2 2.946202430325000e+00 2.946202430331617e+00 6.61737e-12 3.92371e-11 3 3.608983142223199e+00 3.608983142223487e+00 2.87770e-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 = ----------------------- = 7.81117e-11 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 2.10357e-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 2.10357e-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.