!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! VERIFICATION CHECK: vc-forces-numerical-derivative !!!!! !!!!! !!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Description: Comparison of the analytical forces obtained from the model with forces computed by numerical differentiation using Richardson extrapolation for a randomly distorted non-periodic structure based off the equilibrium face-centered cubic (fcc) structure. Separate configurations are tested for each species supported by the model, as well as one containing a random distribution of all species. Configurations used for testing are provided as auxiliary files. Author: Ellad Tadmor ----------------------------------------------------------------------------------------------------- Results for KIM Model : MEAM_LAMMPS_KimSeolJi_2017_PtTi__MO_280985530673_000 Supported species : Pt Ti 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 = Pt | a0 = 3.9173717498779297 | (Configuration in file "config-Pt.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Pt 1 1.247861347458405e+00 1.247861347449688e+00 8.71703e-12 1.60936e-11 2 -9.151697336696690e-01 -9.151697336859853e-01 1.63163e-11 3.38614e-10 3 -8.349459620108962e-01 -8.349459620406657e-01 2.97695e-11 1.99672e-10 ----------------------------------------------------------------------------------------------------- 2 Pt 1 -3.690038216176190e+00 -3.690038216187514e+00 1.13243e-11 1.80356e-10 2 3.186831058826325e+00 3.186831058858021e+00 3.16960e-11 1.53932e-10 3 4.957926096341080e-01 4.957926096385694e-01 4.46138e-12 3.61813e-09 * ----------------------------------------------------------------------------------------------------- 3 Pt 1 4.364622393606138e-02 4.364622393034786e-02 5.71352e-12 2.55898e-09 * 2 1.213737496879875e+00 1.213737496858274e+00 2.16007e-11 3.50198e-11 3 -3.997025611917893e-01 -3.997025611962518e-01 4.46254e-12 6.28671e-11 ----------------------------------------------------------------------------------------------------- 4 Pt 1 1.113220310682871e+00 1.113220310702174e+00 1.93037e-11 1.12917e-10 2 2.137823830259976e+00 2.137823830305520e+00 4.55436e-11 4.31339e-10 3 1.900889450193399e+00 1.900889450110456e+00 8.29432e-11 8.82478e-10 ----------------------------------------------------------------------------------------------------- 5 Pt 1 2.552601769428423e+00 2.552601769477549e+00 4.91256e-11 4.19304e-10 2 -2.902441288675303e+00 -2.902441288730761e+00 5.54574e-11 1.37633e-10 3 1.006696186424698e+00 1.006696186400013e+00 2.46851e-11 2.02134e-10 ----------------------------------------------------------------------------------------------------- 6 Pt 1 -2.133466533050409e-01 -2.133466532565901e-01 4.84508e-11 5.46972e-11 2 8.507437604097992e-01 8.507437604234587e-01 1.36595e-11 9.30765e-11 3 3.788945945843959e-01 3.788945944720743e-01 1.12322e-10 5.53351e-10 ----------------------------------------------------------------------------------------------------- 7 Pt 1 1.142302059247453e+00 1.142302059258506e+00 1.10532e-11 2.68314e-10 2 -4.347874396158183e+00 -4.347874396243533e+00 8.53504e-11 1.82807e-10 3 -4.967752112533624e+00 -4.967752112556292e+00 2.26681e-11 1.37904e-10 ----------------------------------------------------------------------------------------------------- 8 Pt 1 -4.011407039923783e+00 -4.011407039926905e+00 3.12195e-12 3.82953e-10 2 -2.059478912364463e+00 -2.059478912336004e+00 2.84595e-11 6.80900e-11 3 -3.207531302423729e-01 -3.207531302549085e-01 1.25356e-11 1.07388e-08 * ----------------------------------------------------------------------------------------------------- 9 Pt 1 2.766083978951625e-01 2.766083979140067e-01 1.88442e-11 4.08162e-11 2 -1.142829689247633e+00 -1.142829689280324e+00 3.26910e-11 1.41235e-10 3 2.552064025221627e-01 2.552064025068151e-01 1.53476e-11 1.05674e-10 ----------------------------------------------------------------------------------------------------- 10 Pt 1 -2.193073024290793e+00 -2.193073024286033e+00 4.75975e-12 4.25186e-10 2 1.881576681455919e+00 1.881576681515937e+00 6.00182e-11 7.97853e-10 3 -2.500829600883678e+00 -2.500829600950306e+00 6.66276e-11 1.77265e-10 ----------------------------------------------------------------------------------------------------- 11 Pt 1 -1.701372000834832e+00 -1.701372000901604e+00 6.67724e-11 5.19379e-10 2 -3.425297935053175e+00 -3.425297935052323e+00 8.52207e-13 7.71556e-11 3 8.689732133971817e-01 8.689732134022181e-01 5.03642e-12 3.36473e-10 ----------------------------------------------------------------------------------------------------- 12 Pt 1 4.808266899872886e-01 4.808266900211689e-01 3.38803e-11 2.23076e-10 2 6.961909864389406e-01 6.961909864413320e-01 2.39142e-12 6.10390e-10 3 -7.453998913287714e-01 -7.453998913198344e-01 8.93696e-12 6.43820e-10 ----------------------------------------------------------------------------------------------------- 13 Pt 1 -2.252923063192334e+00 -2.252923062982338e+00 2.09996e-10 6.56111e-10 2 -4.015142397914195e+00 -4.015142397881571e+00 3.26237e-11 2.40074e-09 * 3 -6.571042994015174e+00 -6.571042994030045e+00 1.48708e-11 5.31202e-08 * ----------------------------------------------------------------------------------------------------- 14 Pt 1 -5.375084699633181e-02 -5.375084696927416e-02 2.70577e-11 3.14808e-10 2 1.737690323335475e+00 1.737690323355194e+00 1.97189e-11 1.58074e-09 3 4.482656442346368e-01 4.482656442142979e-01 2.03388e-11 3.59361e-11 ----------------------------------------------------------------------------------------------------- 15 Pt 1 6.679623184477896e+00 6.679623184346395e+00 1.31501e-10 1.07678e-09 2 -1.774214280210991e+00 -1.774214280179100e+00 3.18914e-11 7.19754e-10 3 3.160737704811130e+00 3.160737704805691e+00 5.43965e-12 2.81107e-10 ----------------------------------------------------------------------------------------------------- 16 Pt 1 3.633468790433233e+00 3.633468790402894e+00 3.03388e-11 4.86037e-10 2 5.461396508445701e+00 5.461396508141228e+00 3.04473e-10 2.02074e-09 3 8.184798942589951e-01 8.184798944930126e-01 2.34017e-10 1.83402e-09 ----------------------------------------------------------------------------------------------------- 17 Pt 1 7.956170698504978e-01 7.956170698504782e-01 1.96509e-14 1.92575e-10 2 7.488417339564937e-01 7.488417339565939e-01 1.00253e-13 5.10768e-10 3 3.436378375464971e-02 3.436378379045236e-02 3.58026e-11 3.55297e-10 ----------------------------------------------------------------------------------------------------- 18 Pt 1 3.397841776731590e-01 3.397841775955213e-01 7.76377e-11 2.82807e-10 2 1.109922785488012e+00 1.109922785523940e+00 3.59281e-11 2.04013e-10 3 -1.589078510018119e+00 -1.589078510018746e+00 6.26832e-13 1.71007e-10 ----------------------------------------------------------------------------------------------------- 19 Pt 1 6.146494388191345e-01 6.146494387838424e-01 3.52921e-11 4.35167e-10 2 -1.752234553262043e-01 -1.752234554112024e-01 8.49980e-11 1.41665e-10 3 1.503473450567429e-01 1.503473450592686e-01 2.52573e-12 6.94897e-11 ----------------------------------------------------------------------------------------------------- 20 Pt 1 4.794119032085006e-01 4.794119032674926e-01 5.89920e-11 1.24782e-09 2 4.974540730878041e-01 4.974540730560560e-01 3.17481e-11 2.51872e-10 3 -9.827819111962783e-01 -9.827819111359877e-01 6.02907e-11 5.55447e-10 ----------------------------------------------------------------------------------------------------- 21 Pt 1 -2.027419880318759e+00 -2.027419880314293e+00 4.46576e-12 1.96334e-09 2 1.012818265039347e+00 1.012818265056641e+00 1.72939e-11 2.72233e-10 3 2.055563923158481e+00 2.055563923154134e+00 4.34675e-12 2.63967e-10 ----------------------------------------------------------------------------------------------------- 22 Pt 1 1.027263834666951e+00 1.027263834646852e+00 2.00990e-11 1.46800e-10 2 4.115149836205262e+00 4.115149836242615e+00 3.73532e-11 5.95958e-10 3 4.131142776156675e+00 4.131142776191523e+00 3.48477e-11 1.04045e-08 * ----------------------------------------------------------------------------------------------------- 23 Pt 1 -1.039986495584836e+00 -1.039986495609954e+00 2.51177e-11 1.56966e-10 2 9.359286749821955e-01 9.359286749600780e-01 2.21174e-11 2.93717e-11 3 -8.803218133969818e-01 -8.803218134211199e-01 2.41381e-11 2.10165e-10 ----------------------------------------------------------------------------------------------------- 24 Pt 1 1.435001260063938e-01 1.435001259582860e-01 4.81078e-11 5.96029e-11 2 -1.263632050196128e-02 -1.263632049054291e-02 1.14184e-11 3.21517e-10 3 -9.919775206428868e-01 -9.919775206577887e-01 1.49019e-11 3.80495e-11 ----------------------------------------------------------------------------------------------------- 25 Pt 1 -1.352282579461965e+00 -1.352282579471861e+00 9.89631e-12 1.48739e-10 2 -1.981246515172121e+00 -1.981246515033658e+00 1.38463e-10 5.63208e-10 3 1.898006643961781e+00 1.898006643974261e+00 1.24805e-11 4.11960e-10 ----------------------------------------------------------------------------------------------------- 26 Pt 1 -2.666557776667926e+00 -2.666557776366822e+00 3.01104e-10 8.33127e-10 2 1.986968934654848e+00 1.986968934690095e+00 3.52467e-11 1.69452e-10 3 2.562284268404181e+00 2.562284268339920e+00 6.42606e-11 2.18429e-10 ----------------------------------------------------------------------------------------------------- 27 Pt 1 2.820431850277254e+00 2.820431850262620e+00 1.46341e-11 9.22729e-11 2 -5.138203105727959e+00 -5.138203105778214e+00 5.02549e-11 3.31891e-10 3 6.015151822598725e-01 6.015151822824305e-01 2.25580e-11 1.92006e-10 ----------------------------------------------------------------------------------------------------- 28 Pt 1 -1.737040109616617e+00 -1.737040109653776e+00 3.71594e-11 1.12806e-10 2 2.594844285990028e+00 2.594844285974092e+00 1.59366e-11 5.22298e-11 3 -1.940592013614002e+00 -1.940592013610096e+00 3.90532e-12 1.24041e-10 ----------------------------------------------------------------------------------------------------- 29 Pt 1 -4.864586143491532e-01 -4.864586143079117e-01 4.12415e-11 2.61715e-09 * 2 -1.435972806620595e+00 -1.435972806499774e+00 1.20821e-10 1.04324e-09 3 2.870884932746383e+00 2.870884932724566e+00 2.18163e-11 2.19429e-10 ----------------------------------------------------------------------------------------------------- 30 Pt 1 -1.046668412012437e+00 -1.046668412009646e+00 2.79088e-12 9.02043e-11 2 1.940140169906038e+00 1.940140169903185e+00 2.85238e-12 9.37206e-10 3 -1.675112816624559e+00 -1.675112816578042e+00 4.65168e-11 7.57927e-11 ----------------------------------------------------------------------------------------------------- 31 Pt 1 1.191176966660146e-01 1.191176966576609e-01 8.35375e-12 3.03315e-09 * 2 -3.140939071507922e+00 -3.140939071476858e+00 3.10645e-11 1.24586e-09 3 1.870043096428923e+00 1.870043096397753e+00 3.11708e-11 1.22770e-09 ----------------------------------------------------------------------------------------------------- 32 Pt 1 9.623898420162982e-01 9.623898420194001e-01 3.10196e-12 2.83447e-11 2 3.586105027883337e-01 3.586105027792567e-01 9.07702e-12 2.67936e-10 3 -1.107796814289265e+00 -1.107796814279501e+00 9.76397e-12 2.56251e-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 = 3: |F_model - F_numer| error = ----------------------- = 1.04187e-09 max{|F_numer|, eps} Comparison of analytical forces obtained from the model, the force computed as a numerical derivative of the energy, the difference between them, and the uncertainty in the numerical estimate of the force. The computed equilibrium lattice constant for the crystal (a0) is given in the heading. MONOATOMIC STRUCTURE -- Species = Ti | a0 = 4.133002281188965 | (Configuration in file "config-Ti.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ti 1 -5.315780300225935e-01 -5.315780300242583e-01 1.66478e-12 6.63146e-10 2 1.822198028812791e-01 1.822198028853743e-01 4.09522e-12 3.13674e-11 3 -6.727728271923678e-01 -6.727728271959549e-01 3.58713e-12 5.96035e-10 ----------------------------------------------------------------------------------------------------- 2 Ti 1 -2.133678237852970e-01 -2.133678237708045e-01 1.44924e-11 3.63684e-11 2 -7.935462708765018e-01 -7.935462708776314e-01 1.12965e-12 3.15586e-09 * 3 5.430224754394917e-01 5.430224754401876e-01 6.95888e-13 7.08410e-11 ----------------------------------------------------------------------------------------------------- 3 Ti 1 1.297205627818916e+00 1.297205627816945e+00 1.97087e-12 6.18406e-10 2 3.495713858926880e-01 3.495713858872094e-01 5.47856e-12 1.36404e-09 * 3 7.155983743211529e-01 7.155983743104509e-01 1.07020e-11 3.12998e-09 * ----------------------------------------------------------------------------------------------------- 4 Ti 1 2.768862693452518e-01 2.768862693636369e-01 1.83851e-11 9.35373e-11 2 9.600914233217848e-01 9.600914232893107e-01 3.24740e-11 1.74450e-10 3 -1.354066369619682e+00 -1.354066369624037e+00 4.35540e-12 6.97069e-11 ----------------------------------------------------------------------------------------------------- 5 Ti 1 -6.846260927994611e-01 -6.846260927873677e-01 1.20933e-11 9.11845e-11 2 2.300745980108850e-01 2.300745980061733e-01 4.71173e-12 1.29385e-11 3 -1.752340900318416e-01 -1.752340900158680e-01 1.59736e-11 6.87913e-11 ----------------------------------------------------------------------------------------------------- 6 Ti 1 -1.405454273227142e-01 -1.405454273319010e-01 9.18682e-12 4.10609e-11 2 4.117545601958619e-01 4.117545601891097e-01 6.75227e-12 1.39041e-10 3 -5.294784198490907e-02 -5.294784198774948e-02 2.84042e-12 5.15551e-10 ----------------------------------------------------------------------------------------------------- 7 Ti 1 5.914835805345294e-01 5.914835805436727e-01 9.14324e-12 1.07003e-09 * 2 4.428503151258358e-01 4.428503151017259e-01 2.41099e-11 4.30509e-11 3 6.529416768066165e-02 6.529416765595586e-02 2.47058e-11 6.10839e-11 ----------------------------------------------------------------------------------------------------- 8 Ti 1 -6.387442392746462e-02 -6.387442393545610e-02 7.99148e-12 2.68607e-10 2 -1.825737737319120e+00 -1.825737737346785e+00 2.76648e-11 1.26932e-10 3 -5.084884217067174e-01 -5.084884217256206e-01 1.89032e-11 4.56408e-11 ----------------------------------------------------------------------------------------------------- 9 Ti 1 -4.972258624692409e-01 -4.972258624635312e-01 5.70965e-12 1.91131e-10 2 -2.786364885998369e-01 -2.786364885815876e-01 1.82493e-11 6.40297e-11 3 -7.834042996398291e-02 -7.834042996192971e-02 2.05320e-12 4.58879e-11 ----------------------------------------------------------------------------------------------------- 10 Ti 1 -1.884988108712304e-01 -1.884988107761201e-01 9.51103e-11 3.52809e-10 2 7.686190575849204e-01 7.686190575949630e-01 1.00425e-11 1.86052e-10 3 -1.880145441043587e-01 -1.880145441071527e-01 2.79396e-12 1.57562e-11 ----------------------------------------------------------------------------------------------------- 11 Ti 1 2.754129220161984e+00 2.754129220186055e+00 2.40710e-11 8.19682e-11 2 -1.209960266083981e+00 -1.209960266131505e+00 4.75240e-11 1.49222e-10 3 -1.603213279007494e+00 -1.603213279019621e+00 1.21265e-11 2.41656e-11 ----------------------------------------------------------------------------------------------------- 12 Ti 1 -1.782941760353536e+00 -1.782941760340859e+00 1.26772e-11 3.10598e-11 2 1.871487451240335e+00 1.871487451243129e+00 2.79332e-12 7.66498e-11 3 1.794026305282465e-01 1.794026305373062e-01 9.05970e-12 1.75497e-11 ----------------------------------------------------------------------------------------------------- 13 Ti 1 1.128165386278421e+00 1.128165386222079e+00 5.63420e-11 7.99609e-11 2 -1.465565081331992e-01 -1.465565081355044e-01 2.30521e-12 1.47460e-10 3 5.413732943960174e-01 5.413732943974594e-01 1.44196e-12 1.41154e-10 ----------------------------------------------------------------------------------------------------- 14 Ti 1 -7.027190893025006e-01 -7.027190892995901e-01 2.91045e-12 4.63172e-11 2 -7.968473678032606e-01 -7.968473678042985e-01 1.03795e-12 1.48732e-10 3 6.461599579658611e-01 6.461599579593339e-01 6.52722e-12 1.91359e-11 ----------------------------------------------------------------------------------------------------- 15 Ti 1 8.559834870823467e-01 8.559834870821985e-01 1.48215e-13 2.40855e-10 2 1.490303852557426e+00 1.490303852552549e+00 4.87699e-12 1.68705e-10 3 -1.044730397600391e+00 -1.044730397606249e+00 5.85731e-12 1.79198e-10 ----------------------------------------------------------------------------------------------------- 16 Ti 1 3.472766196025874e-01 3.472766196114959e-01 8.90843e-12 5.32048e-11 2 -3.632562978612447e-01 -3.632562978242033e-01 3.70414e-11 4.70085e-11 3 -3.648714986972245e-01 -3.648714986878807e-01 9.34386e-12 7.08021e-11 ----------------------------------------------------------------------------------------------------- 17 Ti 1 1.366115557099931e-01 1.366115557233772e-01 1.33842e-11 1.04507e-10 2 -5.659599961990378e-01 -5.659599961901222e-01 8.91565e-12 4.76801e-11 3 1.179133545405895e+00 1.179133545412718e+00 6.82321e-12 3.49481e-09 * ----------------------------------------------------------------------------------------------------- 18 Ti 1 -2.123044593972719e+00 -2.123044594002403e+00 2.96838e-11 2.91280e-10 2 -5.774495166651397e-01 -5.774495165935108e-01 7.16288e-11 2.35096e-10 3 -1.729479421162498e+00 -1.729479421259105e+00 9.66069e-11 5.69692e-09 * ----------------------------------------------------------------------------------------------------- 19 Ti 1 -7.756471414631780e-01 -7.756471414756987e-01 1.25207e-11 5.01119e-11 2 -1.834151858662109e+00 -1.834151858680629e+00 1.85203e-11 2.23278e-10 3 2.877117722802792e-01 2.877117722713922e-01 8.88700e-12 7.06017e-10 ----------------------------------------------------------------------------------------------------- 20 Ti 1 -5.043930454190576e-01 -5.043930453991529e-01 1.99047e-11 1.71326e-10 2 6.120928255450300e-02 6.120928257707491e-02 2.25719e-11 8.90990e-11 3 1.034706691655617e-01 1.034706691334485e-01 3.21132e-11 2.86991e-10 ----------------------------------------------------------------------------------------------------- 21 Ti 1 -5.764320612347035e-01 -5.764320612338797e-01 8.23785e-13 4.84500e-10 2 6.058690632312083e-01 6.058690632501428e-01 1.89345e-11 1.63984e-10 3 4.613075603793034e-01 4.613075603931117e-01 1.38082e-11 2.59905e-10 ----------------------------------------------------------------------------------------------------- 22 Ti 1 -5.811268367021224e-01 -5.811268367175607e-01 1.54383e-11 7.48005e-11 2 -1.597085604880277e+00 -1.597085604876269e+00 4.00813e-12 1.61892e-10 3 -1.464701123338464e+00 -1.464701123324924e+00 1.35405e-11 1.25555e-10 ----------------------------------------------------------------------------------------------------- 23 Ti 1 4.459774714360115e-01 4.459774714527392e-01 1.67277e-11 9.84537e-11 2 1.933143218941030e-02 1.933143214820378e-02 4.12065e-11 9.50946e-11 3 5.397494713054642e-01 5.397494712310668e-01 7.43975e-11 4.20458e-10 ----------------------------------------------------------------------------------------------------- 24 Ti 1 2.444265327418036e+00 2.444265327446245e+00 2.82094e-11 5.51833e-10 2 4.306377027434453e-01 4.306377027364445e-01 7.00079e-12 1.31957e-10 3 1.202873880320915e+00 1.202873880305374e+00 1.55411e-11 2.04471e-10 ----------------------------------------------------------------------------------------------------- 25 Ti 1 -1.592038888986184e+00 -1.592038889004893e+00 1.87086e-11 1.17500e-10 2 9.794882093216302e-01 9.794882093086985e-01 1.29317e-11 2.26082e-09 * 3 1.955399743836895e+00 1.955399743877888e+00 4.09932e-11 1.03612e-10 ----------------------------------------------------------------------------------------------------- 26 Ti 1 -6.291013183188774e-01 -6.291013183494598e-01 3.05824e-11 1.57196e-10 2 -7.769123115364487e-01 -7.769123115050635e-01 3.13852e-11 3.04248e-10 3 6.174253955905652e-02 6.174253950976324e-02 4.92933e-11 1.54855e-10 ----------------------------------------------------------------------------------------------------- 27 Ti 1 -1.544520516030095e+00 -1.544520516086143e+00 5.60476e-11 1.25608e-09 * 2 -3.386644419582391e-01 -3.386644419673012e-01 9.06214e-12 2.88479e-10 3 -1.448126822859646e-01 -1.448126822829402e-01 3.02436e-12 1.15944e-10 ----------------------------------------------------------------------------------------------------- 28 Ti 1 3.833965106204565e-01 3.833965106692236e-01 4.87671e-11 4.51680e-10 2 -3.640807640297598e-01 -3.640807640394736e-01 9.71390e-12 2.83814e-11 3 -4.077053406730064e-01 -4.077053407033843e-01 3.03779e-11 1.66075e-10 ----------------------------------------------------------------------------------------------------- 29 Ti 1 1.587981895280347e+00 1.587981895322625e+00 4.22771e-11 3.92962e-10 2 1.243830948136182e+00 1.243830948106351e+00 2.98308e-11 1.39109e-10 3 -4.479127622203301e-01 -4.479127622614952e-01 4.11651e-11 9.89075e-10 * ----------------------------------------------------------------------------------------------------- 30 Ti 1 -2.030980303874015e-01 -2.030980303891967e-01 1.79520e-12 1.61805e-09 * 2 1.665935207698527e-02 1.665935207084058e-02 6.14469e-12 1.20820e-09 * 3 3.045178254766018e-01 3.045178254789260e-01 2.32420e-12 1.37151e-10 ----------------------------------------------------------------------------------------------------- 31 Ti 1 -1.469541638671836e-01 -1.469541638662025e-01 9.81104e-13 8.12347e-11 2 6.682966674859563e-01 6.682966674839621e-01 1.99418e-12 1.15746e-10 3 1.288024288728384e+00 1.288024288742491e+00 1.41067e-11 2.14455e-11 ----------------------------------------------------------------------------------------------------- 32 Ti 1 1.232370965946681e+00 1.232370965946152e+00 5.28910e-13 2.96669e-11 2 7.365503260578188e-01 7.365503260576101e-01 2.08722e-13 2.11745e-10 3 1.625088327994458e-01 1.625088327851689e-01 1.42769e-11 8.82722e-10 ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as discontinuities. Maximum error obtained for particle = 23, direction = 2: |F_model - F_numer| error = ----------------------- = 2.13158e-09 max{|F_numer|, eps} Comparison of analytical forces obtained from the model, the force computed as a numerical derivative of the energy, the difference between them, and the uncertainty in the numerical estimate of the force. The computed equilibrium lattice constant for the crystal (a0) is given in the heading. MIXED STRUCTURE -- Species = Pt Ti | a0 = 3.983040968627028 | (Configuration in file "config-PtTi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Pt 1 3.576285651356950e-01 3.576285651253525e-01 1.03425e-11 2.55917e-10 2 -5.746284399774871e-01 -5.746284399599058e-01 1.75814e-11 3.47127e-10 3 -7.995807891963523e-01 -7.995807891567931e-01 3.95592e-11 8.63705e-10 ----------------------------------------------------------------------------------------------------- 2 Ti 1 -9.191875660511727e-01 -9.191875660604211e-01 9.24838e-12 9.95121e-11 2 -4.284828755125223e-01 -4.284828754630316e-01 4.94907e-11 2.62959e-10 3 5.841557942845663e-01 5.841557942873933e-01 2.82696e-12 1.66240e-10 ----------------------------------------------------------------------------------------------------- 3 Ti 1 5.581750344263967e-01 5.581750344392575e-01 1.28608e-11 1.75835e-10 2 -7.957036442345369e-01 -7.957036441794009e-01 5.51360e-11 4.36722e-10 3 -1.968313806915567e+00 -1.968313806928987e+00 1.34199e-11 1.18213e-10 ----------------------------------------------------------------------------------------------------- 4 Pt 1 -1.516712087393731e+00 -1.516712087399430e+00 5.69855e-12 1.15590e-10 2 4.863382300502404e+00 4.863382300513666e+00 1.12621e-11 5.89172e-10 3 -4.405766412231109e+00 -4.405766412222273e+00 8.83560e-12 2.35090e-10 ----------------------------------------------------------------------------------------------------- 5 Ti 1 -2.501925371944509e-01 -2.501925371789350e-01 1.55159e-11 2.55754e-10 2 4.499095593451188e-01 4.499095593437666e-01 1.35220e-12 1.46503e-09 3 -3.328588238235323e-01 -3.328588238158516e-01 7.68074e-12 7.04071e-11 ----------------------------------------------------------------------------------------------------- 6 Pt 1 -1.207315557062986e+00 -1.207315557041801e+00 2.11853e-11 6.45526e-11 2 7.196507751490268e-01 7.196507751440673e-01 4.95948e-12 6.46009e-11 3 5.087102731486091e-01 5.087102731103510e-01 3.82581e-11 3.36627e-11 ----------------------------------------------------------------------------------------------------- 7 Ti 1 7.697779721265259e-01 7.697779721351459e-01 8.61999e-12 1.61117e-10 2 -6.723019283292668e-01 -6.723019283654016e-01 3.61348e-11 6.44729e-11 3 6.194758780302030e-01 6.194758779786428e-01 5.15602e-11 2.34742e-09 * ----------------------------------------------------------------------------------------------------- 8 Ti 1 -1.448984393930920e+00 -1.448984393903030e+00 2.78897e-11 4.72460e-11 2 -9.744515741379505e-01 -9.744515742160152e-01 7.80648e-11 3.25327e-10 3 -2.070312550726405e+00 -2.070312550734869e+00 8.46434e-12 1.96936e-09 * ----------------------------------------------------------------------------------------------------- 9 Pt 1 6.135577277496453e-01 6.135577278374564e-01 8.78111e-11 2.32043e-10 2 -7.934261244492190e-01 -7.934261244710045e-01 2.17855e-11 1.16978e-11 3 4.651647463707047e-01 4.651647463810799e-01 1.03753e-11 1.75175e-09 ----------------------------------------------------------------------------------------------------- 10 Ti 1 -1.949236542935912e+00 -1.949236542866357e+00 6.95553e-11 1.13824e-08 * 2 7.094552163478308e-01 7.094552163382827e-01 9.54814e-12 2.76142e-09 * 3 -6.809431049655720e-01 -6.809431049203065e-01 4.52655e-11 1.56710e-10 ----------------------------------------------------------------------------------------------------- 11 Pt 1 9.936327441301668e-01 9.936327440565851e-01 7.35817e-11 7.35251e-10 2 3.859705339693879e-01 3.859705339777573e-01 8.36947e-12 1.09109e-10 3 -1.777415724393317e+00 -1.777415724345763e+00 4.75540e-11 3.76445e-10 ----------------------------------------------------------------------------------------------------- 12 Ti 1 4.836254879753808e-01 4.836254879501746e-01 2.52062e-11 7.44487e-10 2 5.766492291454735e-01 5.766492291404222e-01 5.05129e-12 2.19714e-10 3 -6.201017584767484e-01 -6.201017584081642e-01 6.85842e-11 3.24067e-11 ----------------------------------------------------------------------------------------------------- 13 Ti 1 9.250124419667818e-01 9.250124419253383e-01 4.14435e-11 2.22441e-10 2 -1.897491692749241e+00 -1.897491692761755e+00 1.25144e-11 2.19248e-10 3 -1.005288573162081e+00 -1.005288573162515e+00 4.33653e-13 6.74198e-11 ----------------------------------------------------------------------------------------------------- 14 Pt 1 6.596395990346867e-01 6.596395990312777e-01 3.40905e-12 9.27111e-11 2 -2.826922463426264e-01 -2.826922463032670e-01 3.93593e-11 3.15756e-10 3 8.686744060922892e-01 8.686744061815894e-01 8.93002e-11 9.41997e-10 ----------------------------------------------------------------------------------------------------- 15 Ti 1 1.433854298900032e+00 1.433854298950829e+00 5.07969e-11 1.27578e-09 2 2.332179730732737e+00 2.332179730767432e+00 3.46949e-11 2.29181e-10 3 -2.149656266400060e+00 -2.149656266434623e+00 3.45630e-11 3.09219e-10 ----------------------------------------------------------------------------------------------------- 16 Ti 1 1.080304858524174e+00 1.080304858530142e+00 5.96767e-12 4.73733e-10 2 1.491919801618984e-01 1.491919801402687e-01 2.16298e-11 1.86893e-10 3 1.768873936081094e+00 1.768873936101320e+00 2.02263e-11 1.71177e-09 ----------------------------------------------------------------------------------------------------- 17 Pt 1 -1.662060084057254e+00 -1.662060084061588e+00 4.33364e-12 3.59910e-11 2 -3.677160317085044e+00 -3.677160317086483e+00 1.43885e-12 2.27026e-10 3 3.995772739146771e+00 3.995772739075007e+00 7.17644e-11 1.36618e-10 ----------------------------------------------------------------------------------------------------- 18 Pt 1 2.534449009679506e+00 2.534449009662127e+00 1.73799e-11 6.79616e-11 2 2.227630826926707e+00 2.227630826949620e+00 2.29132e-11 1.55716e-10 3 2.960172732945884e+00 2.960172732920328e+00 2.55551e-11 2.04444e-10 ----------------------------------------------------------------------------------------------------- 19 Pt 1 -1.449353362779218e+00 -1.449353362763175e+00 1.60427e-11 5.37929e-10 2 4.092635858359912e-01 4.092635858382710e-01 2.27984e-12 9.58298e-11 3 1.105814303933745e+00 1.105814303948010e+00 1.42650e-11 2.15943e-10 ----------------------------------------------------------------------------------------------------- 20 Pt 1 1.022411476827176e+00 1.022411476805126e+00 2.20497e-11 6.37222e-10 2 2.594415927961584e-01 2.594415928007839e-01 4.62552e-12 7.98214e-09 * 3 -5.026515076454358e-01 -5.026515076143273e-01 3.11084e-11 1.38723e-10 ----------------------------------------------------------------------------------------------------- 21 Ti 1 2.143698238715211e+00 2.143698238826734e+00 1.11522e-10 4.71325e-10 2 2.264940788630548e-01 2.264940788796272e-01 1.65724e-11 3.65421e-10 3 -1.037655159150802e-01 -1.037655158807599e-01 3.43203e-11 2.21639e-10 ----------------------------------------------------------------------------------------------------- 22 Ti 1 5.304804150432206e-01 5.304804150193687e-01 2.38519e-11 5.52187e-10 2 1.306686790030311e+00 1.306686790047344e+00 1.70324e-11 2.79558e-09 * 3 -1.260600871429193e+00 -1.260600871439695e+00 1.05018e-11 8.26454e-11 ----------------------------------------------------------------------------------------------------- 23 Pt 1 -5.407400559222986e-01 -5.407400558992517e-01 2.30469e-11 1.03129e-10 2 -2.860358801649795e+00 -2.860358801648103e+00 1.69242e-12 9.87939e-11 3 2.446138189905973e+00 2.446138189919508e+00 1.35350e-11 1.40350e-10 ----------------------------------------------------------------------------------------------------- 24 Pt 1 2.986373224138171e-01 2.986373224211513e-01 7.33413e-12 1.32589e-10 2 -1.991432167463270e+00 -1.991432167634020e+00 1.70750e-10 7.31017e-10 3 2.193083670212174e+00 2.193083670229058e+00 1.68834e-11 7.84841e-10 ----------------------------------------------------------------------------------------------------- 25 Ti 1 -1.116915674970970e+00 -1.116915674964315e+00 6.65490e-12 9.02868e-09 * 2 -1.930652078120325e+00 -1.930652078096537e+00 2.37881e-11 1.94432e-10 3 2.363630235271952e+00 2.363630235275737e+00 3.78542e-12 1.83793e-10 ----------------------------------------------------------------------------------------------------- 26 Pt 1 -4.480202228179234e-01 -4.480202228201008e-01 2.17742e-12 1.42403e-10 2 -1.749235422571782e-01 -1.749235421927099e-01 6.44683e-11 3.41706e-10 3 2.830822308635065e-01 2.830822308377685e-01 2.57381e-11 4.12715e-10 ----------------------------------------------------------------------------------------------------- 27 Pt 1 -5.503282114494372e-01 -5.503282114645174e-01 1.50802e-11 1.90770e-10 2 1.922310577546414e-01 1.922310578035254e-01 4.88840e-11 6.71777e-10 3 -8.331593902261706e-01 -8.331593901700615e-01 5.61091e-11 5.43370e-10 ----------------------------------------------------------------------------------------------------- 28 Ti 1 1.133429143508236e+00 1.133429143508916e+00 6.79901e-13 2.64232e-10 2 -6.668449831568457e-01 -6.668449831549446e-01 1.90115e-12 1.75616e-10 3 -6.906657283368174e-01 -6.906657283413989e-01 4.58156e-12 1.70691e-11 ----------------------------------------------------------------------------------------------------- 29 Pt 1 -2.449927782847181e+00 -2.449927782927135e+00 7.99538e-11 1.17372e-10 2 3.491363496259001e+00 3.491363496284343e+00 2.53424e-11 1.11519e-10 3 -2.217331290576382e+00 -2.217331290570484e+00 5.89795e-12 1.98418e-10 ----------------------------------------------------------------------------------------------------- 30 Ti 1 -2.234417156196503e-01 -2.234417156227318e-01 3.08151e-12 4.41575e-09 * 2 1.777599571982734e-01 1.777599571842907e-01 1.39826e-11 1.17187e-10 3 -1.167662663034983e+00 -1.167662663026930e+00 8.05289e-12 1.53792e-09 ----------------------------------------------------------------------------------------------------- 31 Pt 1 1.187503276366287e+00 1.187503276408612e+00 4.23255e-11 3.93576e-11 2 -1.290008739281490e+00 -1.290008739267118e+00 1.43721e-11 1.89593e-10 3 1.850250621166268e+00 1.850250621150374e+00 1.58942e-11 3.41253e-10 ----------------------------------------------------------------------------------------------------- 32 Ti 1 -9.934018174898348e-01 -9.934018174707241e-01 1.91107e-11 9.76526e-10 2 5.332984437287804e-01 5.332984437194395e-01 9.34097e-12 1.77473e-10 3 5.730750200010652e-01 5.730750199895127e-01 1.15525e-11 6.34830e-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 = 26, direction = 2: |F_model - F_numer| error = ----------------------- = 3.68552e-10 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 2.13158e-09 Machine precision = 2.22045e-16 Note: Lower grades can reflect errors in the analytical forces, a lack of smoothness in the potential, or loss of precision in the numerical derivative computation. Grade: A Comment: The letter grade A was assigned because the normalized error in the computation was 2.13158e-09 compared with a machine precision of 2.22045e-16. The letter grade was based on 'score=log10(error/eps)', with ranges A=[0, 7.5], B=(7.5, 10.0], C=(10.0, 12.5], D=(12.5, 15.0), F>15.0. 'A' is the best grade, and 'F' indicates failure.