!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_MahataMukhopadhyayAsleZaeem_2022_AlNi__MO_461927113651_000 Supported species : Al Ni 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 = Al | a0 = 4.045352935791016 | (Configuration in file "config-Al.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Al 1 3.548041680685760e-01 3.548041680648557e-01 3.72030e-12 6.38983e-11 2 -1.979541821913386e-01 -1.979541821893844e-01 1.95419e-12 1.34545e-10 3 -1.249763335377377e-01 -1.249763335417834e-01 4.04562e-12 1.91670e-10 ----------------------------------------------------------------------------------------------------- 2 Al 1 -3.828105259859831e-01 -3.828105259938359e-01 7.85277e-12 2.98224e-11 2 2.808503552424037e-01 2.808503552396895e-01 2.71422e-12 4.90618e-10 3 3.937728998956271e-01 3.937728998980740e-01 2.44693e-12 9.03523e-11 ----------------------------------------------------------------------------------------------------- 3 Al 1 2.195785889226337e-01 2.195785889086248e-01 1.40090e-11 3.33722e-10 2 2.971955171639380e-01 2.971955171946840e-01 3.07460e-11 1.43570e-10 3 -2.268827659836142e-01 -2.268827659846308e-01 1.01663e-12 3.41788e-11 ----------------------------------------------------------------------------------------------------- 4 Al 1 4.985231959375622e-01 4.985231959366739e-01 8.88289e-13 2.39578e-11 2 2.821284628831262e-01 2.821284629177303e-01 3.46042e-11 1.45165e-10 3 9.349800072499312e-01 9.349800072496954e-01 2.35811e-13 9.45510e-12 ----------------------------------------------------------------------------------------------------- 5 Al 1 1.259143817762180e-01 1.259143817816260e-01 5.40798e-12 7.39874e-11 2 1.545597474452404e-01 1.545597474229897e-01 2.22507e-11 5.15450e-11 3 2.544464920118835e-01 2.544464920171017e-01 5.21827e-12 2.18768e-10 ----------------------------------------------------------------------------------------------------- 6 Al 1 -3.447814091155694e-01 -3.447814091181693e-01 2.59992e-12 3.91444e-11 2 1.677849131475374e-01 1.677849131552226e-01 7.68524e-12 6.16913e-10 3 3.959493371581584e-01 3.959493371742812e-01 1.61228e-11 1.83600e-10 ----------------------------------------------------------------------------------------------------- 7 Al 1 3.917761060806403e-01 3.917761060788543e-01 1.78602e-12 6.09212e-11 2 -1.050468454014109e+00 -1.050468454000547e+00 1.35623e-11 4.13349e-11 3 -1.346563605121440e+00 -1.346563605140362e+00 1.89220e-11 1.23614e-10 ----------------------------------------------------------------------------------------------------- 8 Al 1 -1.270917562620351e+00 -1.270917562600525e+00 1.98259e-11 1.42873e-09 2 -4.916831320925911e-01 -4.916831320812803e-01 1.13108e-11 7.96701e-11 3 -7.766702148283622e-01 -7.766702148261957e-01 2.16649e-12 2.08558e-11 ----------------------------------------------------------------------------------------------------- 9 Al 1 5.325027937568184e-02 5.325027940546918e-02 2.97873e-11 1.59451e-09 2 -7.295492113327975e-01 -7.295492113284949e-01 4.30256e-12 3.72297e-11 3 -9.663302365559467e-01 -9.663302365614199e-01 5.47318e-12 1.15496e-09 ----------------------------------------------------------------------------------------------------- 10 Al 1 -4.512075069332687e-01 -4.512075069440737e-01 1.08050e-11 1.41492e-10 2 3.376030068190305e-01 3.376030068173588e-01 1.67172e-12 1.46330e-10 3 -5.439344659892820e-01 -5.439344659878012e-01 1.48082e-12 6.76920e-11 ----------------------------------------------------------------------------------------------------- 11 Al 1 -3.859620978717951e-01 -3.859620978603883e-01 1.14068e-11 1.47202e-09 2 -6.911662717639310e-01 -6.911662717565695e-01 7.36144e-12 2.02749e-10 3 9.820198268585850e-01 9.820198268835845e-01 2.49994e-11 3.87534e-11 ----------------------------------------------------------------------------------------------------- 12 Al 1 2.174883971459499e-01 2.174883971068446e-01 3.91053e-11 6.29604e-11 2 6.305658635514133e-01 6.305658635542855e-01 2.87215e-12 6.48249e-11 3 9.696819203799349e-01 9.696819203616355e-01 1.82995e-11 2.47863e-11 ----------------------------------------------------------------------------------------------------- 13 Al 1 -3.196617975290810e-01 -3.196617975383795e-01 9.29851e-12 1.20849e-11 2 -9.201811100519109e-01 -9.201811100413023e-01 1.06086e-11 2.57168e-10 3 -1.671573387853172e+00 -1.671573387848439e+00 4.73288e-12 5.18020e-10 ----------------------------------------------------------------------------------------------------- 14 Al 1 -1.498865111748279e-01 -1.498865111651453e-01 9.68262e-12 2.49725e-10 2 1.747258173733233e-01 1.747258173769704e-01 3.64711e-12 2.50937e-10 3 1.984416067909356e-01 1.984416067792725e-01 1.16631e-11 9.59770e-10 ----------------------------------------------------------------------------------------------------- 15 Al 1 1.459303618361486e+00 1.459303618317753e+00 4.37337e-11 7.55437e-10 2 -4.750336141689794e-01 -4.750336141598725e-01 9.10688e-12 4.80837e-11 3 4.137286984177123e-01 4.137286984298602e-01 1.21478e-11 6.48339e-11 ----------------------------------------------------------------------------------------------------- 16 Al 1 5.471579744265194e-01 5.471579744460291e-01 1.95097e-11 9.49073e-10 2 1.140951036480043e+00 1.140951036476587e+00 3.45612e-12 3.52277e-10 3 6.596703353924230e-01 6.596703354009303e-01 8.50731e-12 8.98043e-11 ----------------------------------------------------------------------------------------------------- 17 Al 1 -1.530982577083883e-01 -1.530982576977957e-01 1.05926e-11 1.09945e-09 2 -5.352390109714968e-02 -5.352390111660341e-02 1.94537e-11 1.18040e-10 3 -3.411762254921702e-01 -3.411762254557131e-01 3.64571e-11 9.06343e-11 ----------------------------------------------------------------------------------------------------- 18 Al 1 6.040125689960706e-01 6.040125690048859e-01 8.81528e-12 1.29050e-10 2 5.601133097577019e-01 5.601133097963433e-01 3.86414e-11 6.61143e-10 3 -8.031664820111213e-02 -8.031664820352620e-02 2.41407e-12 2.61341e-10 ----------------------------------------------------------------------------------------------------- 19 Al 1 3.931668049677153e-01 3.931668050070490e-01 3.93338e-11 1.91581e-09 * 2 1.487931597492048e-01 1.487931597576258e-01 8.42096e-12 9.25597e-10 3 4.366872837872462e-02 4.366872838535339e-02 6.62877e-12 6.65548e-11 ----------------------------------------------------------------------------------------------------- 20 Al 1 1.847381775883754e-01 1.847381775571533e-01 3.12221e-11 2.37143e-10 2 3.561659433840377e-01 3.561659434245771e-01 4.05394e-11 1.06150e-10 3 -1.868998417196852e-01 -1.868998417670512e-01 4.73659e-11 4.95193e-10 ----------------------------------------------------------------------------------------------------- 21 Al 1 -1.007427226733289e+00 -1.007427226681803e+00 5.14861e-11 1.36799e-10 2 5.441759628737277e-03 5.441759662094859e-03 3.33576e-11 8.68523e-11 3 5.889251281219731e-01 5.889251281227691e-01 7.96030e-13 1.06341e-10 ----------------------------------------------------------------------------------------------------- 22 Al 1 4.861499576684879e-01 4.861499576671688e-01 1.31906e-12 1.67225e-10 2 1.368181366963369e+00 1.368181366953786e+00 9.58322e-12 3.74943e-09 * 3 1.693010660929621e+00 1.693010660914057e+00 1.55642e-11 1.02693e-10 ----------------------------------------------------------------------------------------------------- 23 Al 1 -4.290147993876936e-01 -4.290147993142304e-01 7.34632e-11 1.23717e-10 2 3.272289941639407e-01 3.272289941718732e-01 7.93249e-12 4.76377e-11 3 -4.311632842734316e-01 -4.311632842795947e-01 6.16307e-12 2.05073e-10 ----------------------------------------------------------------------------------------------------- 24 Al 1 1.412384613336560e-01 1.412384613561327e-01 2.24767e-11 4.40843e-11 2 1.292520368476316e-01 1.292520368544656e-01 6.83406e-12 1.31819e-09 3 -5.392751323248175e-01 -5.392751323463683e-01 2.15508e-11 4.32453e-10 ----------------------------------------------------------------------------------------------------- 25 Al 1 -4.759482947926442e-01 -4.759482948423844e-01 4.97402e-11 1.97174e-09 * 2 -6.122182178720932e-01 -6.122182178839279e-01 1.18348e-11 7.53795e-10 3 -7.637783788636807e-01 -7.637783787519239e-01 1.11757e-10 1.24721e-10 ----------------------------------------------------------------------------------------------------- 26 Al 1 -6.888040290213251e-01 -6.888040290058082e-01 1.55169e-11 2.09595e-09 * 2 4.996788452339572e-01 4.996788452106948e-01 2.32624e-11 3.63234e-11 3 -6.859779287782010e-01 -6.859779287623654e-01 1.58356e-11 1.33576e-10 ----------------------------------------------------------------------------------------------------- 27 Al 1 6.879785537569647e-01 6.879785538270383e-01 7.00736e-11 1.20327e-09 2 -1.702669652435197e+00 -1.702669652475435e+00 4.02376e-11 2.61303e-10 3 4.445949571142562e-01 4.445949570893152e-01 2.49410e-11 3.21237e-12 ----------------------------------------------------------------------------------------------------- 28 Al 1 -4.410952186821632e-01 -4.410952186771496e-01 5.01366e-12 2.88712e-11 2 7.582722105342891e-01 7.582722105402219e-01 5.93281e-12 1.05185e-10 3 -6.565260940907452e-02 -6.565260940562312e-02 3.45141e-12 5.04729e-10 ----------------------------------------------------------------------------------------------------- 29 Al 1 -4.941823372713921e-01 -4.941823372696894e-01 1.70275e-12 2.65042e-10 2 -5.900415710375500e-01 -5.900415710726101e-01 3.50602e-11 5.42460e-10 3 8.636526999421063e-02 8.636527001448888e-02 2.02783e-11 2.65801e-09 * ----------------------------------------------------------------------------------------------------- 30 Al 1 -3.503509370746819e-01 -3.503509370657825e-01 8.89938e-12 4.96645e-11 2 -5.763272506989826e-02 -5.763272507467867e-02 4.78041e-12 5.31189e-11 3 1.456044761131044e-01 1.456044761116899e-01 1.41454e-12 6.38176e-11 ----------------------------------------------------------------------------------------------------- 31 Al 1 7.853608118820588e-01 7.853608119429181e-01 6.08593e-11 1.59591e-10 2 -8.555144500932561e-01 -8.555144500916473e-01 1.60882e-12 1.23825e-10 3 2.373128756385313e-01 2.373128756253332e-01 1.31982e-11 2.49400e-10 ----------------------------------------------------------------------------------------------------- 32 Al 1 1.947064656138567e-01 1.947064655905419e-01 2.33148e-11 1.73286e-09 2 8.081441468518755e-01 8.081441468343347e-01 1.75409e-11 2.52138e-10 3 3.089978384861130e-01 3.089978385041580e-01 1.80450e-11 1.58815e-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 = 21, direction = 2: |F_model - F_numer| error = ----------------------- = 6.12993e-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 = Ni | a0 = 3.5213918685913086 | (Configuration in file "config-Ni.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ni 1 1.759557225753005e-01 1.759557226085261e-01 3.32256e-11 4.17460e-09 * 2 1.115476928576525e-01 1.115476928890352e-01 3.13826e-11 7.79114e-11 3 7.618854243220473e-01 7.618854243096583e-01 1.23890e-11 6.08448e-11 ----------------------------------------------------------------------------------------------------- 2 Ni 1 -1.776262996475564e+00 -1.776262996469123e+00 6.44085e-12 6.67621e-10 2 -1.616342825372926e+00 -1.616342825360531e+00 1.23954e-11 1.77778e-10 3 7.002313772574813e-01 7.002313772872001e-01 2.97188e-11 6.60909e-11 ----------------------------------------------------------------------------------------------------- 3 Ni 1 3.452964041366294e-01 3.452964041212668e-01 1.53626e-11 1.24683e-10 2 1.252495964876790e+00 1.252495964876874e+00 8.41549e-14 2.57097e-10 3 -9.533538736874462e-01 -9.533538737003963e-01 1.29501e-11 5.48159e-10 ----------------------------------------------------------------------------------------------------- 4 Ni 1 1.057396270988673e+00 1.057396270957624e+00 3.10496e-11 2.44218e-10 2 -8.153209611956264e-01 -8.153209612017702e-01 6.14386e-12 1.83194e-10 3 3.370933641452982e-01 3.370933641186571e-01 2.66410e-11 3.60995e-10 ----------------------------------------------------------------------------------------------------- 5 Ni 1 -3.418827503451358e-01 -3.418827503553281e-01 1.01923e-11 1.64682e-11 2 1.011072764634318e+00 1.011072764632685e+00 1.63336e-12 5.44236e-11 3 9.894776905872612e-01 9.894776905941135e-01 6.85230e-12 2.58562e-10 ----------------------------------------------------------------------------------------------------- 6 Ni 1 -5.193526388653231e-01 -5.193526388539380e-01 1.13851e-11 2.51731e-10 2 -1.616110039103773e+00 -1.616110039112565e+00 8.79141e-12 6.95199e-11 3 -4.447871033083294e-01 -4.447871033048899e-01 3.43953e-12 1.32904e-10 ----------------------------------------------------------------------------------------------------- 7 Ni 1 5.548955595849436e-01 5.548955595822801e-01 2.66354e-12 1.06482e-10 2 5.360092715599436e-01 5.360092715488571e-01 1.10865e-11 1.00291e-10 3 -7.364072789758871e-01 -7.364072789789018e-01 3.01470e-12 2.28058e-09 * ----------------------------------------------------------------------------------------------------- 8 Ni 1 -1.185700663389084e+00 -1.185700663388446e+00 6.37490e-13 2.81003e-09 * 2 2.564800193104117e+00 2.564800193071891e+00 3.22258e-11 5.76992e-11 3 -5.243471893889277e+00 -5.243471893846747e+00 4.25295e-11 2.79573e-10 ----------------------------------------------------------------------------------------------------- 9 Ni 1 1.052780148956868e+00 1.052780148960405e+00 3.53761e-12 6.63125e-11 2 3.313419176964664e-01 3.313419177138160e-01 1.73496e-11 2.01992e-10 3 5.848216203797341e-01 5.848216204035154e-01 2.37813e-11 1.06704e-10 ----------------------------------------------------------------------------------------------------- 10 Ni 1 2.432996397657260e-01 2.432996397585499e-01 7.17607e-12 8.94185e-11 2 -9.255549445027120e-01 -9.255549445031800e-01 4.67959e-13 2.54142e-11 3 1.105234956884104e+00 1.105234956907035e+00 2.29305e-11 1.28593e-09 ----------------------------------------------------------------------------------------------------- 11 Ni 1 5.291814790439646e-01 5.291814790066569e-01 3.73077e-11 5.57514e-10 2 8.720327222461213e-01 8.720327222274438e-01 1.86775e-11 5.60624e-11 3 -6.157641589240295e-01 -6.157641589448518e-01 2.08223e-11 2.87224e-10 ----------------------------------------------------------------------------------------------------- 12 Ni 1 7.156705641038856e-01 7.156705640934337e-01 1.04520e-11 1.10180e-10 2 -1.230619026225352e+00 -1.230619026199878e+00 2.54736e-11 1.36563e-10 3 1.940632508858722e-01 1.940632509102576e-01 2.43854e-11 2.75353e-11 ----------------------------------------------------------------------------------------------------- 13 Ni 1 -1.826778459233683e-03 -1.826778455801136e-03 3.43255e-12 2.42571e-10 2 1.955204160829683e+00 1.955204160808439e+00 2.12441e-11 1.76207e-10 3 -1.865265199160065e+00 -1.865265199090125e+00 6.99396e-11 2.22558e-10 ----------------------------------------------------------------------------------------------------- 14 Ni 1 -7.364017680300224e-01 -7.364017680449699e-01 1.49475e-11 3.08372e-09 * 2 -1.296256973622309e+00 -1.296256973635782e+00 1.34732e-11 1.90099e-09 * 3 8.638555439358582e-01 8.638555439768019e-01 4.09437e-11 3.28279e-09 * ----------------------------------------------------------------------------------------------------- 15 Ni 1 3.308312622723369e+00 3.308312622712687e+00 1.06817e-11 7.89178e-11 2 2.816946950896755e-01 2.816946950915892e-01 1.91364e-12 7.10496e-11 3 1.784431661624470e+00 1.784431661581696e+00 4.27745e-11 1.48122e-09 ----------------------------------------------------------------------------------------------------- 16 Ni 1 -1.578346757573221e+00 -1.578346757586474e+00 1.32536e-11 1.68197e-09 * 2 2.748230254991067e+00 2.748230255031027e+00 3.99596e-11 3.07498e-10 3 -1.079380747417077e-02 -1.079380746288069e-02 1.12901e-11 1.30059e-10 ----------------------------------------------------------------------------------------------------- 17 Ni 1 6.790700633535568e-01 6.790700633547432e-01 1.18638e-12 4.96972e-11 2 1.133244069375132e+00 1.133244069397090e+00 2.19578e-11 1.88561e-10 3 5.069864662279687e-01 5.069864662093279e-01 1.86409e-11 3.89052e-10 ----------------------------------------------------------------------------------------------------- 18 Ni 1 -2.524627810678333e+00 -2.524627810637756e+00 4.05773e-11 7.07931e-11 2 -7.921912687318403e-01 -7.921912687339202e-01 2.07989e-12 5.34240e-11 3 -6.128944986736141e-01 -6.128944986539264e-01 1.96877e-11 4.61998e-10 ----------------------------------------------------------------------------------------------------- 19 Ni 1 -1.839909060232348e+00 -1.839909060237500e+00 5.15277e-12 1.85080e-10 2 -6.409136337821175e-01 -6.409136338061215e-01 2.40040e-11 2.08787e-09 * 3 -8.375265204806188e-01 -8.375265204912815e-01 1.06627e-11 1.01398e-09 ----------------------------------------------------------------------------------------------------- 20 Ni 1 9.705355429997685e-01 9.705355430084869e-01 8.71836e-12 1.73422e-10 2 -8.772545869008118e-02 -8.772545869026234e-02 1.81161e-13 2.39864e-10 3 -9.573946812858762e-01 -9.573946812991900e-01 1.33138e-11 1.20564e-10 ----------------------------------------------------------------------------------------------------- 21 Ni 1 -1.370850452371059e+00 -1.370850452368838e+00 2.22178e-12 8.04072e-11 2 -5.577259809868444e+00 -5.577259809892427e+00 2.39826e-11 2.69995e-10 3 3.771439774058876e+00 3.771439774076224e+00 1.73483e-11 1.58328e-10 ----------------------------------------------------------------------------------------------------- 22 Ni 1 4.092803448915777e+00 4.092803448912252e+00 3.52518e-12 2.81432e-10 2 -1.679136555927920e+00 -1.679136555918331e+00 9.58900e-12 1.87567e-10 3 -1.380466019057798e+00 -1.380466019008914e+00 4.88833e-11 3.77031e-09 * ----------------------------------------------------------------------------------------------------- 23 Ni 1 -7.450350211357495e-01 -7.450350211456657e-01 9.91618e-12 1.55956e-10 2 6.937228803121960e-01 6.937228803163132e-01 4.11726e-12 1.35392e-09 3 -1.017909054087560e+00 -1.017909054089306e+00 1.74594e-12 6.07632e-11 ----------------------------------------------------------------------------------------------------- 24 Ni 1 1.419179507836338e+00 1.419179507869160e+00 3.28217e-11 6.30355e-10 2 1.794253503355601e+00 1.794253503385046e+00 2.94451e-11 3.08534e-10 3 2.886677661789861e+00 2.886677661799600e+00 9.73888e-12 4.34537e-10 ----------------------------------------------------------------------------------------------------- 25 Ni 1 8.585277933883624e-01 8.585277933518796e-01 3.64828e-11 3.20836e-10 2 1.356476623228059e-01 1.356476623322229e-01 9.41699e-12 6.28782e-10 3 6.473655405554801e-01 6.473655405743949e-01 1.89148e-11 2.86928e-10 ----------------------------------------------------------------------------------------------------- 26 Ni 1 -1.593639832887426e+00 -1.593639832848274e+00 3.91518e-11 4.40160e-10 2 -1.102796909435162e+00 -1.102796909372857e+00 6.23053e-11 4.32526e-10 3 -4.984050262604085e+00 -4.984050262545215e+00 5.88702e-11 1.12756e-09 ----------------------------------------------------------------------------------------------------- 27 Ni 1 -7.872519711168721e-01 -7.872519711040084e-01 1.28637e-11 7.29676e-10 2 -2.370699043277291e-01 -2.370699044477156e-01 1.19986e-10 7.08615e-11 3 -6.991428262747187e-01 -6.991428262283477e-01 4.63710e-11 2.45772e-10 ----------------------------------------------------------------------------------------------------- 28 Ni 1 -1.103896222748408e+00 -1.103896222752198e+00 3.78986e-12 1.74672e-09 * 2 -6.827971426639555e-01 -6.827971426699397e-01 5.98421e-12 4.78271e-09 * 3 8.842493207752994e-01 8.842493207762323e-01 9.32920e-13 1.80669e-10 ----------------------------------------------------------------------------------------------------- 29 Ni 1 -2.849575706345259e+00 -2.849575706363291e+00 1.80318e-11 1.25927e-10 2 2.683902795350378e+00 2.683902795337758e+00 1.26197e-11 1.06148e-10 3 9.136720210559207e-01 9.136720207890483e-01 2.66872e-10 2.91461e-10 ----------------------------------------------------------------------------------------------------- 30 Ni 1 -1.125703649867791e+00 -1.125703649847126e+00 2.06655e-11 2.94251e-09 * 2 -3.381559154453909e-01 -3.381559154366494e-01 8.74156e-12 2.91694e-11 3 -6.850276870166228e-01 -6.850276870333193e-01 1.66965e-11 4.04239e-11 ----------------------------------------------------------------------------------------------------- 31 Ni 1 1.455653288133690e-01 1.455653287954704e-01 1.78986e-11 5.48755e-10 2 9.777662399804069e-01 9.777662399861941e-01 5.78715e-12 7.67842e-11 3 2.019532718097923e+00 2.019532718076466e+00 2.14575e-11 4.87796e-11 ----------------------------------------------------------------------------------------------------- 32 Ni 1 3.931793983334299e+00 3.931793983342116e+00 7.81730e-12 1.34532e-10 2 -4.447154196870139e-01 -4.447154196813725e-01 5.64143e-12 3.14884e-11 3 2.093236472316643e+00 2.093236472322404e+00 5.76073e-12 1.32233e-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 = 13, direction = 1: |F_model - F_numer| error = ----------------------- = 1.87902e-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 = Al Ni | a0 = 3.965119150131886 | (Configuration in file "config-AlNi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ni 1 6.310615903822105e-01 6.310615904290542e-01 4.68436e-11 3.52575e-10 2 1.122226604631495e-01 1.122226604676459e-01 4.49636e-12 2.63541e-10 3 -1.531238274057044e+00 -1.531238274069076e+00 1.20319e-11 5.62861e-10 ----------------------------------------------------------------------------------------------------- 2 Al 1 -4.094276445513222e-01 -4.094276445389832e-01 1.23390e-11 1.86873e-10 2 9.787502449576685e-01 9.787502449113302e-01 4.63383e-11 1.14828e-10 3 -5.131673274181456e-01 -5.131673274034263e-01 1.47193e-11 3.32967e-11 ----------------------------------------------------------------------------------------------------- 3 Ni 1 1.208267883078390e+00 1.208267883115587e+00 3.71976e-11 5.18776e-10 2 -2.642959036488050e+00 -2.642959036492875e+00 4.82503e-12 1.47616e-10 3 1.536971373638339e+00 1.536971373631617e+00 6.72240e-12 1.41841e-10 ----------------------------------------------------------------------------------------------------- 4 Al 1 -1.884644491659977e+00 -1.884644491642156e+00 1.78213e-11 4.03526e-09 * 2 3.115596170930758e+00 3.115596170946706e+00 1.59481e-11 5.04388e-11 3 1.592871628173986e+00 1.592871628210623e+00 3.66371e-11 6.02806e-09 * ----------------------------------------------------------------------------------------------------- 5 Al 1 5.459769503629095e-01 5.459769504179897e-01 5.50802e-11 3.47376e-10 2 -2.661555999118774e-01 -2.661555999157895e-01 3.91209e-12 8.46613e-11 3 2.562824782034117e-01 2.562824782033412e-01 7.04992e-14 1.21479e-10 ----------------------------------------------------------------------------------------------------- 6 Al 1 2.880910371435904e-02 2.880910370294699e-02 1.14121e-11 3.33016e-09 * 2 2.262343528117294e-01 2.262343528111777e-01 5.51670e-13 7.54273e-10 3 -3.501849390017858e-01 -3.501849390098973e-01 8.11157e-12 1.91476e-11 ----------------------------------------------------------------------------------------------------- 7 Al 1 -1.857227982833944e-01 -1.857227982554734e-01 2.79210e-11 5.93378e-10 2 -5.698710674048479e-01 -5.698710674219805e-01 1.71325e-11 4.13187e-10 3 -5.179983618755303e-01 -5.179983618769461e-01 1.41587e-12 1.55328e-10 ----------------------------------------------------------------------------------------------------- 8 Al 1 -1.444547931852244e+00 -1.444547931825977e+00 2.62672e-11 1.32583e-09 2 1.110686620299125e-01 1.110686620391303e-01 9.21777e-12 1.76753e-10 3 1.779014420680628e+00 1.779014420669397e+00 1.12317e-11 8.59781e-11 ----------------------------------------------------------------------------------------------------- 9 Ni 1 -1.055407884889433e+00 -1.055407884892018e+00 2.58527e-12 5.88782e-11 2 -9.851763478286105e-01 -9.851763478327203e-01 4.10982e-12 9.57515e-11 3 8.553687366088011e-01 8.553687366005868e-01 8.21432e-12 2.42992e-11 ----------------------------------------------------------------------------------------------------- 10 Al 1 1.510878895631022e+00 1.510878895632606e+00 1.58384e-12 3.08145e-11 2 1.955204210742903e+00 1.955204210712350e+00 3.05527e-11 4.65215e-11 3 4.336536323760659e-01 4.336536323557988e-01 2.02671e-11 9.98240e-11 ----------------------------------------------------------------------------------------------------- 11 Ni 1 -5.682281991115593e-01 -5.682281991267332e-01 1.51739e-11 5.99311e-11 2 -2.177680537064953e+00 -2.177680537011975e+00 5.29781e-11 1.30163e-10 3 -1.164066311785798e+00 -1.164066311761849e+00 2.39486e-11 1.75820e-10 ----------------------------------------------------------------------------------------------------- 12 Ni 1 -1.419903290248735e+00 -1.419903290275234e+00 2.64992e-11 9.51614e-11 2 -1.019719127651853e+00 -1.019719127651888e+00 3.50830e-14 7.81069e-11 3 -1.017132955986004e+00 -1.017132955986790e+00 7.85816e-13 6.93492e-11 ----------------------------------------------------------------------------------------------------- 13 Al 1 1.603624455947220e+00 1.603624455994963e+00 4.77425e-11 7.23352e-11 2 -7.258816164615979e-01 -7.258816164603742e-01 1.22369e-12 8.38872e-11 3 -1.853626341313242e-01 -1.853626341081469e-01 2.31773e-11 2.90401e-10 ----------------------------------------------------------------------------------------------------- 14 Ni 1 -1.179528599550424e+00 -1.179528599546807e+00 3.61688e-12 7.41035e-10 2 -5.795254387148466e-01 -5.795254387295570e-01 1.47103e-11 6.88660e-11 3 6.215312756763980e-01 6.215312756672440e-01 9.15401e-12 2.31926e-09 * ----------------------------------------------------------------------------------------------------- 15 Al 1 8.514228167863019e-01 8.514228167752270e-01 1.10749e-11 1.53245e-11 2 4.779153511988436e+00 4.779153511957620e+00 3.08154e-11 1.58157e-09 * 3 -1.273502059495371e+00 -1.273502059510003e+00 1.46325e-11 1.45959e-10 ----------------------------------------------------------------------------------------------------- 16 Ni 1 -8.981800475062950e-01 -8.981800475059513e-01 3.43725e-13 3.20779e-09 * 2 6.515205287433173e-02 6.515205285176118e-02 2.25706e-11 5.13816e-11 3 -6.280926327798911e-01 -6.280926327585757e-01 2.13154e-11 2.22246e-10 ----------------------------------------------------------------------------------------------------- 17 Ni 1 1.039212058571970e+00 1.039212058681139e+00 1.09169e-10 6.72649e-11 2 4.336983246776338e-01 4.336983246458214e-01 3.18124e-11 6.40096e-11 3 8.296549059804232e-01 8.296549059950133e-01 1.45901e-11 1.72291e-10 ----------------------------------------------------------------------------------------------------- 18 Ni 1 -2.696402374669055e+00 -2.696402374655430e+00 1.36247e-11 9.03224e-11 2 -7.520426617562119e-01 -7.520426618061328e-01 4.99208e-11 5.14052e-10 3 -8.536753432763866e-01 -8.536753432841176e-01 7.73104e-12 2.08357e-10 ----------------------------------------------------------------------------------------------------- 19 Ni 1 2.860913770142134e-01 2.860913770513331e-01 3.71197e-11 9.51427e-11 2 3.393194960489768e-02 3.393194963320833e-02 2.83106e-11 9.84872e-11 3 -6.339714301125440e-01 -6.339714300990457e-01 1.34983e-11 1.15806e-10 ----------------------------------------------------------------------------------------------------- 20 Al 1 8.948556158241026e-01 8.948556157510735e-01 7.30290e-11 3.33558e-10 2 1.132450377009747e+00 1.132450377025678e+00 1.59308e-11 1.04618e-10 3 -2.772877160026280e-01 -2.772877159943835e-01 8.24457e-12 1.11545e-10 ----------------------------------------------------------------------------------------------------- 21 Al 1 1.766183855067401e+00 1.766183855098876e+00 3.14750e-11 2.16823e-10 2 -8.531227223415161e-01 -8.531227223574698e-01 1.59537e-11 1.51043e-10 3 3.463715999270407e-01 3.463715999293759e-01 2.33519e-12 4.23577e-11 ----------------------------------------------------------------------------------------------------- 22 Ni 1 9.438538110442009e-01 9.438538110696755e-01 2.54746e-11 4.06585e-10 2 -4.145398153764607e+00 -4.145398153747148e+00 1.74580e-11 1.20629e-08 * 3 4.130253110888503e+00 4.130253110921354e+00 3.28519e-11 8.00551e-11 ----------------------------------------------------------------------------------------------------- 23 Al 1 -1.062864950112193e+00 -1.062864950137899e+00 2.57059e-11 9.43843e-11 2 5.581020499957602e-01 5.581020500013775e-01 5.61728e-12 7.83897e-11 3 -1.165292459869675e+00 -1.165292459832613e+00 3.70621e-11 1.36228e-10 ----------------------------------------------------------------------------------------------------- 24 Ni 1 5.203848289586510e-01 5.203848289621158e-01 3.46478e-12 5.17213e-10 2 -1.256235182615251e+00 -1.256235182652049e+00 3.67981e-11 2.54940e-10 3 1.521537562187756e+00 1.521537562224305e+00 3.65488e-11 1.32269e-10 ----------------------------------------------------------------------------------------------------- 25 Ni 1 7.152510597520353e-01 7.152510597457319e-01 6.30340e-12 1.39353e-10 2 1.190612682587712e+00 1.190612682579174e+00 8.53806e-12 8.09992e-11 3 -8.496501024459413e-01 -8.496501024787492e-01 3.28079e-11 7.07848e-11 ----------------------------------------------------------------------------------------------------- 26 Al 1 3.585799636028754e-01 3.585799635552127e-01 4.76627e-11 7.05890e-11 2 1.447360385834337e+00 1.447360385861348e+00 2.70108e-11 1.75421e-10 3 3.460501448366564e+00 3.460501448375348e+00 8.78408e-12 1.77658e-10 ----------------------------------------------------------------------------------------------------- 27 Ni 1 -3.661884916359288e+00 -3.661884916380114e+00 2.08256e-11 1.89237e-09 * 2 -7.182387844335980e-01 -7.182387843686604e-01 6.49376e-11 3.24048e-10 3 1.148432577250068e+00 1.148432577391686e+00 1.41618e-10 4.40876e-10 ----------------------------------------------------------------------------------------------------- 28 Al 1 8.232236533204879e-01 8.232236532993824e-01 2.11055e-11 1.57585e-11 2 -9.977813131549493e-01 -9.977813131166330e-01 3.83164e-11 6.02464e-11 3 -7.792342453029748e-01 -7.792342452978576e-01 5.11724e-12 1.23262e-10 ----------------------------------------------------------------------------------------------------- 29 Al 1 2.790415221859325e+00 2.790415221800496e+00 5.88298e-11 6.60251e-10 2 4.624501393395366e+00 4.624501393267076e+00 1.28290e-10 2.09512e-10 3 -4.937112528594741e+00 -4.937112528663914e+00 6.91731e-11 5.17870e-11 ----------------------------------------------------------------------------------------------------- 30 Ni 1 -9.666491171936589e-01 -9.666491171987552e-01 5.09637e-12 7.19185e-11 2 -2.401482463517066e+00 -2.401482463517362e+00 2.96208e-13 1.59064e-09 * 3 -4.226468543490148e-01 -4.226468543521640e-01 3.14926e-12 1.22937e-09 ----------------------------------------------------------------------------------------------------- 31 Ni 1 -2.269115231549364e-01 -2.269115231599132e-01 4.97680e-12 1.12320e-09 2 5.689106841717121e-01 5.689106841807335e-01 9.02145e-12 9.99856e-11 3 -2.005899999681671e-01 -2.005899999202121e-01 4.79550e-11 4.80105e-10 ----------------------------------------------------------------------------------------------------- 32 Al 1 1.142210628224839e+00 1.142210628215557e+00 9.28213e-12 4.21462e-09 * 2 -1.241679660966216e+00 -1.241679660973660e+00 7.44405e-12 7.91336e-11 3 -1.212238573505019e+00 -1.212238573503311e+00 1.70797e-12 2.39354e-09 * ----------------------------------------------------------------------------------------------------- * 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 = 19, direction = 2: |F_model - F_numer| error = ----------------------- = 8.34336e-10 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 6.12993e-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 6.12993e-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.