!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_002 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 1.247861347449689e+00 8.71614e-12 1.60936e-11 2 -9.151697336696690e-01 -9.151697336859861e-01 1.63171e-11 3.38614e-10 3 -8.349459620108962e-01 -8.349459620406664e-01 2.97702e-11 1.99671e-10 ----------------------------------------------------------------------------------------------------- 2 Pt 1 -3.690038216176190e+00 -3.690038216187517e+00 1.13274e-11 1.80356e-10 2 3.186831058826325e+00 3.186831058858024e+00 3.16991e-11 1.53932e-10 3 4.957926096341080e-01 4.957926096385691e-01 4.46110e-12 3.61813e-09 * ----------------------------------------------------------------------------------------------------- 3 Pt 1 4.364622393606138e-02 4.364622393034782e-02 5.71355e-12 2.55898e-09 * 2 1.213737496879875e+00 1.213737496858275e+00 2.15996e-11 3.50209e-11 3 -3.997025611917893e-01 -3.997025611962522e-01 4.46293e-12 6.28670e-11 ----------------------------------------------------------------------------------------------------- 4 Pt 1 1.113220310682871e+00 1.113220310702175e+00 1.93046e-11 1.12918e-10 2 2.137823830259976e+00 2.137823830305522e+00 4.55458e-11 4.31338e-10 3 1.900889450193399e+00 1.900889450110458e+00 8.29417e-11 8.82479e-10 ----------------------------------------------------------------------------------------------------- 5 Pt 1 2.552601769428423e+00 2.552601769477551e+00 4.91274e-11 4.19305e-10 2 -2.902441288675303e+00 -2.902441288730764e+00 5.54605e-11 1.37632e-10 3 1.006696186424698e+00 1.006696186400014e+00 2.46843e-11 2.02135e-10 ----------------------------------------------------------------------------------------------------- 6 Pt 1 -2.133466533050409e-01 -2.133466532565904e-01 4.84505e-11 5.46972e-11 2 8.507437604097992e-01 8.507437604234593e-01 1.36602e-11 9.30762e-11 3 3.788945945843959e-01 3.788945944720747e-01 1.12321e-10 5.53351e-10 ----------------------------------------------------------------------------------------------------- 7 Pt 1 1.142302059247453e+00 1.142302059258507e+00 1.10540e-11 2.68313e-10 2 -4.347874396158183e+00 -4.347874396243537e+00 8.53539e-11 1.82809e-10 3 -4.967752112533624e+00 -4.967752112556298e+00 2.26743e-11 1.37896e-10 ----------------------------------------------------------------------------------------------------- 8 Pt 1 -4.011407039923783e+00 -4.011407039926907e+00 3.12461e-12 3.82953e-10 2 -2.059478912364463e+00 -2.059478912335997e+00 2.84661e-11 6.80971e-11 3 -3.207531302423729e-01 -3.207531302549083e-01 1.25354e-11 1.07388e-08 * ----------------------------------------------------------------------------------------------------- 9 Pt 1 2.766083978951625e-01 2.766083979140069e-01 1.88444e-11 4.08162e-11 2 -1.142829689247633e+00 -1.142829689280325e+00 3.26921e-11 1.41234e-10 3 2.552064025221627e-01 2.552064025068154e-01 1.53473e-11 1.05674e-10 ----------------------------------------------------------------------------------------------------- 10 Pt 1 -2.193073024290793e+00 -2.193073024286035e+00 4.75753e-12 4.25186e-10 2 1.881576681455919e+00 1.881576681515938e+00 6.00195e-11 7.97852e-10 3 -2.500829600883678e+00 -2.500829600950306e+00 6.66280e-11 1.77263e-10 ----------------------------------------------------------------------------------------------------- 11 Pt 1 -1.701372000834832e+00 -1.701372000901606e+00 6.67739e-11 5.19379e-10 2 -3.425297935053175e+00 -3.425297935052327e+00 8.47766e-13 7.71574e-11 3 8.689732133971817e-01 8.689732134022187e-01 5.03697e-12 3.36473e-10 ----------------------------------------------------------------------------------------------------- 12 Pt 1 4.808266899872886e-01 4.808266900211693e-01 3.38807e-11 2.23076e-10 2 6.961909864389406e-01 6.961909864413326e-01 2.39198e-12 6.10390e-10 3 -7.453998913287714e-01 -7.453998913198352e-01 8.93619e-12 6.43820e-10 ----------------------------------------------------------------------------------------------------- 13 Pt 1 -2.252923063192334e+00 -2.252923062982340e+00 2.09994e-10 6.56111e-10 2 -4.015142397914195e+00 -4.015142397881575e+00 3.26201e-11 2.40074e-09 * 3 -6.571042994015174e+00 -6.571042994030042e+00 1.48672e-11 5.31202e-08 * ----------------------------------------------------------------------------------------------------- 14 Pt 1 -5.375084699633181e-02 -5.375084696927421e-02 2.70576e-11 3.14808e-10 2 1.737690323335475e+00 1.737690323355195e+00 1.97204e-11 1.58074e-09 3 4.482656442346368e-01 4.482656442142983e-01 2.03385e-11 3.59362e-11 ----------------------------------------------------------------------------------------------------- 15 Pt 1 6.679623184477896e+00 6.679623184346402e+00 1.31495e-10 1.07678e-09 2 -1.774214280210991e+00 -1.774214280179102e+00 3.18896e-11 7.19754e-10 3 3.160737704811130e+00 3.160737704805693e+00 5.43787e-12 2.81110e-10 ----------------------------------------------------------------------------------------------------- 16 Pt 1 3.633468790433233e+00 3.633468790402896e+00 3.03371e-11 4.86038e-10 2 5.461396508445701e+00 5.461396508141232e+00 3.04469e-10 2.02075e-09 3 8.184798942589951e-01 8.184798944930132e-01 2.34018e-10 1.83402e-09 ----------------------------------------------------------------------------------------------------- 17 Pt 1 7.956170698504978e-01 7.956170698504790e-01 1.88738e-14 1.92576e-10 2 7.488417339564937e-01 7.488417339565945e-01 1.00808e-13 5.10768e-10 3 3.436378375464971e-02 3.436378379045239e-02 3.58027e-11 3.55297e-10 ----------------------------------------------------------------------------------------------------- 18 Pt 1 3.397841776731590e-01 3.397841775955215e-01 7.76375e-11 2.82807e-10 2 1.109922785488012e+00 1.109922785523941e+00 3.59293e-11 2.04015e-10 3 -1.589078510018119e+00 -1.589078510018747e+00 6.28386e-13 1.71007e-10 ----------------------------------------------------------------------------------------------------- 19 Pt 1 6.146494388191345e-01 6.146494387838430e-01 3.52914e-11 4.35167e-10 2 -1.752234553262043e-01 -1.752234554112025e-01 8.49982e-11 1.41665e-10 3 1.503473450567429e-01 1.503473450592687e-01 2.52581e-12 6.94897e-11 ----------------------------------------------------------------------------------------------------- 20 Pt 1 4.794119032085006e-01 4.794119032674930e-01 5.89924e-11 1.24782e-09 2 4.974540730878041e-01 4.974540730560564e-01 3.17477e-11 2.51872e-10 3 -9.827819111962783e-01 -9.827819111359888e-01 6.02896e-11 5.55447e-10 ----------------------------------------------------------------------------------------------------- 21 Pt 1 -2.027419880318759e+00 -2.027419880314295e+00 4.46398e-12 1.96334e-09 2 1.012818265039347e+00 1.012818265056642e+00 1.72951e-11 2.72233e-10 3 2.055563923158481e+00 2.055563923154135e+00 4.34541e-12 2.63967e-10 ----------------------------------------------------------------------------------------------------- 22 Pt 1 1.027263834666951e+00 1.027263834646853e+00 2.00979e-11 1.46800e-10 2 4.115149836205262e+00 4.115149836242618e+00 3.73559e-11 5.95958e-10 3 4.131142776156675e+00 4.131142776191521e+00 3.48459e-11 1.04045e-08 * ----------------------------------------------------------------------------------------------------- 23 Pt 1 -1.039986495584836e+00 -1.039986495609955e+00 2.51186e-11 1.56965e-10 2 9.359286749821955e-01 9.359286749600788e-01 2.21166e-11 2.93717e-11 3 -8.803218133969818e-01 -8.803218134211207e-01 2.41389e-11 2.10165e-10 ----------------------------------------------------------------------------------------------------- 24 Pt 1 1.435001260063938e-01 1.435001259582861e-01 4.81078e-11 5.96027e-11 2 -1.263632050196128e-02 -1.263632049054293e-02 1.14184e-11 3.21517e-10 3 -9.919775206428868e-01 -9.919775206577893e-01 1.49025e-11 3.80495e-11 ----------------------------------------------------------------------------------------------------- 25 Pt 1 -1.352282579461965e+00 -1.352282579471862e+00 9.89719e-12 1.48739e-10 2 -1.981246515172121e+00 -1.981246515033660e+00 1.38461e-10 5.63207e-10 3 1.898006643961781e+00 1.898006643974263e+00 1.24820e-11 4.11960e-10 ----------------------------------------------------------------------------------------------------- 26 Pt 1 -2.666557776667926e+00 -2.666557776366823e+00 3.01103e-10 8.33125e-10 2 1.986968934654848e+00 1.986968934690096e+00 3.52480e-11 1.69451e-10 3 2.562284268404181e+00 2.562284268339923e+00 6.42579e-11 2.18429e-10 ----------------------------------------------------------------------------------------------------- 27 Pt 1 2.820431850277254e+00 2.820431850262620e+00 1.46336e-11 9.22702e-11 2 -5.138203105727959e+00 -5.138203105778217e+00 5.02585e-11 3.31896e-10 3 6.015151822598725e-01 6.015151822824311e-01 2.25585e-11 1.92005e-10 ----------------------------------------------------------------------------------------------------- 28 Pt 1 -1.737040109616617e+00 -1.737040109653778e+00 3.71607e-11 1.12806e-10 2 2.594844285990028e+00 2.594844285974094e+00 1.59344e-11 5.22284e-11 3 -1.940592013614002e+00 -1.940592013610098e+00 3.90377e-12 1.24042e-10 ----------------------------------------------------------------------------------------------------- 29 Pt 1 -4.864586143491532e-01 -4.864586143079122e-01 4.12410e-11 2.61715e-09 * 2 -1.435972806620595e+00 -1.435972806499775e+00 1.20820e-10 1.04324e-09 3 2.870884932746383e+00 2.870884932724568e+00 2.18146e-11 2.19429e-10 ----------------------------------------------------------------------------------------------------- 30 Pt 1 -1.046668412012437e+00 -1.046668412009647e+00 2.78977e-12 9.02047e-11 2 1.940140169906038e+00 1.940140169903187e+00 2.85083e-12 9.37206e-10 3 -1.675112816624559e+00 -1.675112816578044e+00 4.65152e-11 7.57927e-11 ----------------------------------------------------------------------------------------------------- 31 Pt 1 1.191176966660146e-01 1.191176966576608e-01 8.35380e-12 3.03315e-09 * 2 -3.140939071507922e+00 -3.140939071476860e+00 3.10623e-11 1.24587e-09 3 1.870043096428923e+00 1.870043096397754e+00 3.11691e-11 1.22770e-09 ----------------------------------------------------------------------------------------------------- 32 Pt 1 9.623898420162982e-01 9.623898420194010e-01 3.10285e-12 2.83447e-11 2 3.586105027883337e-01 3.586105027792570e-01 9.07674e-12 2.67936e-10 3 -1.107796814289265e+00 -1.107796814279502e+00 9.76286e-12 2.56259e-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 -5.315780300225940e-01 -5.315780300242580e-01 1.66400e-12 6.63146e-10 2 1.822198028812787e-01 1.822198028853745e-01 4.09581e-12 3.13675e-11 3 -6.727728271923683e-01 -6.727728271959545e-01 3.58624e-12 5.96035e-10 ----------------------------------------------------------------------------------------------------- 2 Ti 1 -2.133678237852969e-01 -2.133678237708048e-01 1.44921e-11 3.63684e-11 2 -7.935462708765015e-01 -7.935462708776310e-01 1.12943e-12 3.15586e-09 * 3 5.430224754394917e-01 5.430224754401880e-01 6.96332e-13 7.08413e-11 ----------------------------------------------------------------------------------------------------- 3 Ti 1 1.297205627818916e+00 1.297205627816946e+00 1.97020e-12 6.18406e-10 2 3.495713858926880e-01 3.495713858872093e-01 5.47873e-12 1.36404e-09 * 3 7.155983743211533e-01 7.155983743104506e-01 1.07027e-11 3.12998e-09 * ----------------------------------------------------------------------------------------------------- 4 Ti 1 2.768862693452518e-01 2.768862693636372e-01 1.83854e-11 9.35371e-11 2 9.600914233217848e-01 9.600914232893114e-01 3.24734e-11 1.74449e-10 3 -1.354066369619682e+00 -1.354066369624038e+00 4.35629e-12 6.97067e-11 ----------------------------------------------------------------------------------------------------- 5 Ti 1 -6.846260927994611e-01 -6.846260927873681e-01 1.20930e-11 9.11851e-11 2 2.300745980108850e-01 2.300745980061735e-01 4.71156e-12 1.29387e-11 3 -1.752340900318416e-01 -1.752340900134996e-01 1.83420e-11 4.89599e-10 ----------------------------------------------------------------------------------------------------- 6 Ti 1 -1.405454273227142e-01 -1.405454273257546e-01 3.04040e-12 1.07044e-10 2 4.117545601958619e-01 4.117545601891100e-01 6.75193e-12 1.39041e-10 3 -5.294784198490907e-02 -5.294784198774953e-02 2.84046e-12 5.15551e-10 ----------------------------------------------------------------------------------------------------- 7 Ti 1 5.914835805345294e-01 5.914835805436724e-01 9.14302e-12 1.07003e-09 * 2 4.428503151258358e-01 4.428503151017263e-01 2.41095e-11 4.30509e-11 3 6.529416768066165e-02 6.529416765595589e-02 2.47058e-11 6.10839e-11 ----------------------------------------------------------------------------------------------------- 8 Ti 1 -6.387442392746467e-02 -6.387442393545614e-02 7.99147e-12 2.68607e-10 2 -1.825737737319121e+00 -1.825737737335068e+00 1.59472e-11 8.79656e-11 3 -5.084884217067174e-01 -5.084884217256210e-01 1.89037e-11 4.56405e-11 ----------------------------------------------------------------------------------------------------- 9 Ti 1 -4.972258624692409e-01 -4.972258624635318e-01 5.70910e-12 1.91131e-10 2 -2.786364885998369e-01 -2.786364885815878e-01 1.82491e-11 6.40292e-11 3 -7.834042996398291e-02 -7.834042995704263e-02 6.94028e-12 1.49046e-10 ----------------------------------------------------------------------------------------------------- 10 Ti 1 -1.884988108712304e-01 -1.884988107675128e-01 1.03718e-10 2.28127e-10 2 7.686190575849204e-01 7.686190575949637e-01 1.00433e-11 1.86052e-10 3 -1.880145441043587e-01 -1.880145441071528e-01 2.79410e-12 1.57562e-11 ----------------------------------------------------------------------------------------------------- 11 Ti 1 2.754129220161984e+00 2.754129220186057e+00 2.40732e-11 8.19700e-11 2 -1.209960266083981e+00 -1.209960266131506e+00 4.75251e-11 1.49221e-10 3 -1.603213279007494e+00 -1.603213279019622e+00 1.21281e-11 2.41660e-11 ----------------------------------------------------------------------------------------------------- 12 Ti 1 -1.782941760353536e+00 -1.782941760340861e+00 1.26754e-11 3.10598e-11 2 1.871487451240335e+00 1.871487451243130e+00 2.79488e-12 7.66491e-11 3 1.794026305282465e-01 1.794026305373063e-01 9.05981e-12 1.75497e-11 ----------------------------------------------------------------------------------------------------- 13 Ti 1 1.128165386278421e+00 1.128165386222080e+00 5.63414e-11 7.99607e-11 2 -1.465565081331992e-01 -1.465565081355046e-01 2.30532e-12 1.47460e-10 3 5.413732943960174e-01 5.413732943974598e-01 1.44240e-12 1.41153e-10 ----------------------------------------------------------------------------------------------------- 14 Ti 1 -7.027190893025006e-01 -7.027190892995907e-01 2.90989e-12 4.63182e-11 2 -7.968473678032605e-01 -7.968473678040786e-01 8.18123e-13 1.43183e-10 3 6.461599579658610e-01 6.461599579718345e-01 5.97344e-12 1.85465e-11 ----------------------------------------------------------------------------------------------------- 15 Ti 1 8.559834870823467e-01 8.559834870821993e-01 1.47438e-13 2.40855e-10 2 1.490303852557426e+00 1.490303852552550e+00 4.87566e-12 1.68707e-10 3 -1.044730397600391e+00 -1.044730397606250e+00 5.85887e-12 1.79198e-10 ----------------------------------------------------------------------------------------------------- 16 Ti 1 3.472766196025875e-01 3.472766196009128e-01 1.67472e-12 2.08955e-11 2 -3.632562978612447e-01 -3.632562978896668e-01 2.84222e-11 8.81273e-11 3 -3.648714986972245e-01 -3.648714986878810e-01 9.34353e-12 7.08018e-11 ----------------------------------------------------------------------------------------------------- 17 Ti 1 1.366115557099931e-01 1.366115557284178e-01 1.84247e-11 1.13080e-10 2 -5.659599961990376e-01 -5.659599961901225e-01 8.91509e-12 4.76805e-11 3 1.179133545405895e+00 1.179133545412718e+00 6.82299e-12 3.49481e-09 * ----------------------------------------------------------------------------------------------------- 18 Ti 1 -2.123044593972719e+00 -2.123044594002760e+00 3.00409e-11 2.31181e-10 2 -5.774495166651394e-01 -5.774495165935112e-01 7.16283e-11 2.35097e-10 3 -1.729479421162498e+00 -1.729479421259120e+00 9.66220e-11 5.69782e-09 * ----------------------------------------------------------------------------------------------------- 19 Ti 1 -7.756471414631780e-01 -7.756471414492139e-01 1.39642e-11 2.10558e-09 * 2 -1.834151858662109e+00 -1.834151858676077e+00 1.39682e-11 2.59995e-09 * 3 2.877117722802792e-01 2.877117722886960e-01 8.41677e-12 1.96019e-10 ----------------------------------------------------------------------------------------------------- 20 Ti 1 -5.043930454190575e-01 -5.043930454614310e-01 4.23735e-11 3.26288e-10 2 6.120928255450300e-02 6.120928259493085e-02 4.04278e-11 1.39558e-10 3 1.034706691655616e-01 1.034706691351529e-01 3.04087e-11 3.21961e-10 ----------------------------------------------------------------------------------------------------- 21 Ti 1 -5.764320612347035e-01 -5.764320612338802e-01 8.23230e-13 4.84500e-10 2 6.058690632312083e-01 6.058690632501426e-01 1.89343e-11 1.63984e-10 3 4.613075603793034e-01 4.613075603936039e-01 1.43005e-11 2.59398e-10 ----------------------------------------------------------------------------------------------------- 22 Ti 1 -5.811268367021224e-01 -5.811268367175609e-01 1.54385e-11 7.48002e-11 2 -1.597085604880277e+00 -1.597085604876270e+00 4.00679e-12 1.61893e-10 3 -1.464701123338464e+00 -1.464701123324925e+00 1.35394e-11 1.25554e-10 ----------------------------------------------------------------------------------------------------- 23 Ti 1 4.459774714360115e-01 4.459774714467605e-01 1.07490e-11 1.73778e-10 2 1.933143218941030e-02 1.933143222276083e-02 3.33505e-11 1.75217e-10 3 5.397494713054642e-01 5.397494713589132e-01 5.34489e-11 2.03140e-10 ----------------------------------------------------------------------------------------------------- 24 Ti 1 2.444265327418036e+00 2.444265327426859e+00 8.82272e-12 2.30688e-10 2 4.306377027434453e-01 4.306377027296004e-01 1.38449e-11 1.27501e-10 3 1.202873880320915e+00 1.202873880306534e+00 1.43812e-11 1.35343e-10 ----------------------------------------------------------------------------------------------------- 25 Ti 1 -1.592038888986184e+00 -1.592038888996041e+00 9.85700e-12 1.88999e-09 * 2 9.794882093216302e-01 9.794882093289210e-01 7.29083e-12 3.26221e-10 3 1.955399743836895e+00 1.955399743877889e+00 4.09948e-11 1.03614e-10 ----------------------------------------------------------------------------------------------------- 26 Ti 1 -6.291013183188774e-01 -6.291013183494604e-01 3.05830e-11 1.57196e-10 2 -7.769123115364487e-01 -7.769123115198577e-01 1.65910e-11 3.01471e-10 3 6.174253955905652e-02 6.174253962372230e-02 6.46658e-11 9.62607e-10 ----------------------------------------------------------------------------------------------------- 27 Ti 1 -1.544520516030095e+00 -1.544520516011626e+00 1.84694e-11 1.25862e-10 2 -3.386644419582391e-01 -3.386644418984389e-01 5.98002e-11 3.12022e-10 3 -1.448126822859646e-01 -1.448126822899761e-01 4.01151e-12 3.09986e-09 * ----------------------------------------------------------------------------------------------------- 28 Ti 1 3.833965106204565e-01 3.833965105492844e-01 7.11721e-11 5.83761e-11 2 -3.640807640297598e-01 -3.640807639820888e-01 4.76709e-11 5.15148e-11 3 -4.077053406730064e-01 -4.077053406050006e-01 6.80058e-11 1.13320e-10 ----------------------------------------------------------------------------------------------------- 29 Ti 1 1.587981895280347e+00 1.587981895322626e+00 4.22782e-11 3.92962e-10 2 1.243830948136182e+00 1.243830948106352e+00 2.98299e-11 1.39110e-10 3 -4.479127622203301e-01 -4.479127621406762e-01 7.96538e-11 1.14082e-10 ----------------------------------------------------------------------------------------------------- 30 Ti 1 -2.030980303874016e-01 -2.030980303852722e-01 2.12935e-12 1.62107e-09 * 2 1.665935207698527e-02 1.665935207084057e-02 6.14470e-12 1.20820e-09 * 3 3.045178254766018e-01 3.045178254757292e-01 8.72580e-13 5.85365e-11 ----------------------------------------------------------------------------------------------------- 31 Ti 1 -1.469541638671836e-01 -1.469541638803483e-01 1.31647e-11 1.71334e-11 2 6.682966674859563e-01 6.682966674823323e-01 3.62399e-12 1.46702e-10 3 1.288024288728384e+00 1.288024288733196e+00 4.81237e-12 3.14180e-11 ----------------------------------------------------------------------------------------------------- 32 Ti 1 1.232370965946681e+00 1.232370965970688e+00 2.40077e-11 1.86936e-10 2 7.365503260578188e-01 7.365503260760178e-01 1.81990e-11 3.61414e-09 * 3 1.625088327994458e-01 1.625088327851639e-01 1.42819e-11 8.81827e-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 = ----------------------- = 1.72520e-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 3.576285651253527e-01 1.03423e-11 2.55916e-10 2 -5.746284399774871e-01 -5.746284399599062e-01 1.75809e-11 3.47127e-10 3 -7.995807891963523e-01 -7.995807891567939e-01 3.95585e-11 8.63705e-10 ----------------------------------------------------------------------------------------------------- 2 Ti 1 -9.191875660511727e-01 -9.191875660604220e-01 9.24927e-12 9.95122e-11 2 -4.284828755125223e-01 -4.284828754630319e-01 4.94904e-11 2.62959e-10 3 5.841557942845663e-01 5.841557942873937e-01 2.82740e-12 1.66239e-10 ----------------------------------------------------------------------------------------------------- 3 Ti 1 5.581750344263967e-01 5.581750344392581e-01 1.28614e-11 1.75835e-10 2 -7.957036442345369e-01 -7.957036441794015e-01 5.51353e-11 4.36722e-10 3 -1.968313806915567e+00 -1.968313806928988e+00 1.34213e-11 1.18214e-10 ----------------------------------------------------------------------------------------------------- 4 Pt 1 -1.516712087393731e+00 -1.516712087399431e+00 5.69966e-12 1.15590e-10 2 4.863382300502404e+00 4.863382300513670e+00 1.12665e-11 5.89176e-10 3 -4.405766412231109e+00 -4.405766412222277e+00 8.83205e-12 2.35095e-10 ----------------------------------------------------------------------------------------------------- 5 Ti 1 -2.501925371944509e-01 -2.501925371789353e-01 1.55156e-11 2.55755e-10 2 4.499095593451188e-01 4.499095593437664e-01 1.35242e-12 1.46503e-09 3 -3.328588238235323e-01 -3.328588238158519e-01 7.68047e-12 7.04069e-11 ----------------------------------------------------------------------------------------------------- 6 Pt 1 -1.207315557062986e+00 -1.207315557041802e+00 2.11842e-11 6.45530e-11 2 7.196507751490268e-01 7.196507751440679e-01 4.95881e-12 6.46011e-11 3 5.087102731486091e-01 5.087102731103513e-01 3.82577e-11 3.36625e-11 ----------------------------------------------------------------------------------------------------- 7 Ti 1 7.697779721265259e-01 7.697779721351468e-01 8.62088e-12 1.61117e-10 2 -6.723019283292668e-01 -6.723019283654020e-01 3.61352e-11 6.44729e-11 3 6.194758780302030e-01 6.194758779786425e-01 5.15605e-11 2.34742e-09 * ----------------------------------------------------------------------------------------------------- 8 Ti 1 -1.448984393930920e+00 -1.448984393903032e+00 2.78886e-11 4.72449e-11 2 -9.744515741379505e-01 -9.744515742160160e-01 7.80656e-11 3.25327e-10 3 -2.070312550726405e+00 -2.070312550734868e+00 8.46301e-12 1.96936e-09 * ----------------------------------------------------------------------------------------------------- 9 Pt 1 6.135577277496453e-01 6.135577278374569e-01 8.78115e-11 2.32043e-10 2 -7.934261244492190e-01 -7.934261244710050e-01 2.17860e-11 1.16975e-11 3 4.651647463707047e-01 4.651647463810802e-01 1.03756e-11 1.75175e-09 ----------------------------------------------------------------------------------------------------- 10 Ti 1 -1.949236542935912e+00 -1.949236542866356e+00 6.95561e-11 1.13824e-08 * 2 7.094552163478308e-01 7.094552163382822e-01 9.54858e-12 2.76142e-09 * 3 -6.809431049655720e-01 -6.809431049203007e-01 4.52712e-11 1.56716e-10 ----------------------------------------------------------------------------------------------------- 11 Pt 1 9.936327441301668e-01 9.936327440565859e-01 7.35809e-11 7.35251e-10 2 3.859705339693879e-01 3.859705339777576e-01 8.36975e-12 1.09109e-10 3 -1.777415724393317e+00 -1.777415724345764e+00 4.75526e-11 3.76444e-10 ----------------------------------------------------------------------------------------------------- 12 Ti 1 4.836254879753808e-01 4.836254879501750e-01 2.52058e-11 7.44487e-10 2 5.766492291454735e-01 5.766492291404225e-01 5.05096e-12 2.19714e-10 3 -6.201017584767484e-01 -6.201017584081647e-01 6.85837e-11 3.24070e-11 ----------------------------------------------------------------------------------------------------- 13 Ti 1 9.250124419667818e-01 9.250124419253388e-01 4.14430e-11 2.22442e-10 2 -1.897491692749241e+00 -1.897491692761756e+00 1.25158e-11 2.19248e-10 3 -1.005288573162081e+00 -1.005288573162516e+00 4.34541e-13 6.74201e-11 ----------------------------------------------------------------------------------------------------- 14 Pt 1 6.596395990346867e-01 6.596395990312784e-01 3.40827e-12 9.27121e-11 2 -2.826922463426264e-01 -2.826922463032672e-01 3.93591e-11 3.15756e-10 3 8.686744060922892e-01 8.686744061815890e-01 8.92998e-11 9.41997e-10 ----------------------------------------------------------------------------------------------------- 15 Ti 1 1.433854298900032e+00 1.433854298950830e+00 5.07983e-11 1.27578e-09 2 2.332179730732737e+00 2.332179730767435e+00 3.46976e-11 2.29184e-10 3 -2.149656266400060e+00 -2.149656266434624e+00 3.45648e-11 3.09221e-10 ----------------------------------------------------------------------------------------------------- 16 Ti 1 1.080304858524174e+00 1.080304858530142e+00 5.96723e-12 4.73733e-10 2 1.491919801618984e-01 1.491919801402687e-01 2.16297e-11 1.86892e-10 3 1.768873936081094e+00 1.768873936101321e+00 2.02276e-11 1.71177e-09 ----------------------------------------------------------------------------------------------------- 17 Pt 1 -1.662060084057254e+00 -1.662060084061589e+00 4.33520e-12 3.59910e-11 2 -3.677160317085044e+00 -3.677160317086486e+00 1.44196e-12 2.27026e-10 3 3.995772739146771e+00 3.995772739076096e+00 7.06750e-11 1.36736e-10 ----------------------------------------------------------------------------------------------------- 18 Pt 1 2.534449009679506e+00 2.534449009662129e+00 1.73777e-11 6.79630e-11 2 2.227630826926707e+00 2.227630826949624e+00 2.29172e-11 1.55714e-10 3 2.960172732945884e+00 2.960172732920331e+00 2.55524e-11 2.04447e-10 ----------------------------------------------------------------------------------------------------- 19 Pt 1 -1.449353362779218e+00 -1.449353362763177e+00 1.60416e-11 5.37929e-10 2 4.092635858359913e-01 4.092635858382714e-01 2.28018e-12 9.58295e-11 3 1.105814303933746e+00 1.105814303948011e+00 1.42655e-11 2.15943e-10 ----------------------------------------------------------------------------------------------------- 20 Pt 1 1.022411476827176e+00 1.022411476805127e+00 2.20486e-11 6.37223e-10 2 2.594415927961582e-01 2.594415928007838e-01 4.62552e-12 7.98214e-09 * 3 -5.026515076454356e-01 -5.026515076143279e-01 3.11078e-11 1.38723e-10 ----------------------------------------------------------------------------------------------------- 21 Ti 1 2.143698238715211e+00 2.143698238826735e+00 1.11524e-10 4.71325e-10 2 2.264940788630548e-01 2.264940788796274e-01 1.65726e-11 3.65421e-10 3 -1.037655159150802e-01 -1.037655158807600e-01 3.43202e-11 2.21639e-10 ----------------------------------------------------------------------------------------------------- 22 Ti 1 5.304804150432206e-01 5.304804150193690e-01 2.38516e-11 5.52187e-10 2 1.306686790030311e+00 1.306686790047343e+00 1.70315e-11 2.79558e-09 * 3 -1.260600871429193e+00 -1.260600871439696e+00 1.05027e-11 8.26461e-11 ----------------------------------------------------------------------------------------------------- 23 Pt 1 -5.407400559222986e-01 -5.407400558992522e-01 2.30463e-11 1.03128e-10 2 -2.860358801649795e+00 -2.860358801648105e+00 1.69020e-12 9.87952e-11 3 2.446138189905973e+00 2.446138189919511e+00 1.35376e-11 1.40350e-10 ----------------------------------------------------------------------------------------------------- 24 Pt 1 2.986373224138171e-01 2.986373224211515e-01 7.33436e-12 1.32589e-10 2 -1.991432167463270e+00 -1.991432167634022e+00 1.70752e-10 7.31017e-10 3 2.193083670212174e+00 2.193083670229059e+00 1.68852e-11 7.84841e-10 ----------------------------------------------------------------------------------------------------- 25 Ti 1 -1.116915674970970e+00 -1.116915674967591e+00 3.37885e-12 2.11280e-10 2 -1.930652078120325e+00 -1.930652078096538e+00 2.37868e-11 1.94432e-10 3 2.363630235271952e+00 2.363630235275738e+00 3.78630e-12 1.83793e-10 ----------------------------------------------------------------------------------------------------- 26 Pt 1 -4.480202228179234e-01 -4.480202228201012e-01 2.17781e-12 1.42403e-10 2 -1.749235422571782e-01 -1.749235421927100e-01 6.44682e-11 3.41706e-10 3 2.830822308635065e-01 2.830822308377687e-01 2.57379e-11 4.12715e-10 ----------------------------------------------------------------------------------------------------- 27 Pt 1 -5.503282114494374e-01 -5.503282114645179e-01 1.50805e-11 1.90770e-10 2 1.922310577546416e-01 1.922310578035256e-01 4.88840e-11 6.71777e-10 3 -8.331593902261707e-01 -8.331593901700622e-01 5.61085e-11 5.43370e-10 ----------------------------------------------------------------------------------------------------- 28 Ti 1 1.133429143508236e+00 1.133429143508915e+00 6.79234e-13 2.64231e-10 2 -6.668449831568457e-01 -6.668449831549442e-01 1.90148e-12 1.75616e-10 3 -6.906657283368174e-01 -6.906657283413996e-01 4.58222e-12 1.70696e-11 ----------------------------------------------------------------------------------------------------- 29 Pt 1 -2.449927782847181e+00 -2.449927782927137e+00 7.99556e-11 1.17374e-10 2 3.491363496259001e+00 3.491363496284347e+00 2.53459e-11 1.11519e-10 3 -2.217331290576382e+00 -2.217331290570487e+00 5.89528e-12 1.98417e-10 ----------------------------------------------------------------------------------------------------- 30 Ti 1 -2.234417156196503e-01 -2.234417156227317e-01 3.08140e-12 4.41575e-09 * 2 1.777599571982734e-01 1.777599571842909e-01 1.39825e-11 1.17187e-10 3 -1.167662663034983e+00 -1.167662663026930e+00 8.05311e-12 1.53793e-09 ----------------------------------------------------------------------------------------------------- 31 Pt 1 1.187503276366287e+00 1.187503276408613e+00 4.23264e-11 3.93579e-11 2 -1.290008739281490e+00 -1.290008739267119e+00 1.43709e-11 1.89593e-10 3 1.850250621166268e+00 1.850250621150375e+00 1.58928e-11 3.41254e-10 ----------------------------------------------------------------------------------------------------- 32 Ti 1 -9.934018174898349e-01 -9.934018174707249e-01 1.91100e-11 9.76526e-10 2 5.332984437287804e-01 5.332984437194398e-01 9.34064e-12 1.77472e-10 3 5.730750200010652e-01 5.730750199895130e-01 1.15522e-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 = ----------------------- = 3.68551e-10 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 1.72520e-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 1.72520e-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.