!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_LeeLee_2010_FeAl__MO_332211522050_002 Supported species : Al Fe 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 = 4.041934013366699 | (Configuration in file "config-Al.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Al 1 3.421627552046949e-01 3.421627552140153e-01 9.32043e-12 8.81789e-11 2 2.684865905542462e-03 2.684865885584988e-03 1.99575e-11 1.34207e-10 3 -5.822412687904121e-02 -5.822412690163317e-02 2.25920e-11 2.96015e-11 ----------------------------------------------------------------------------------------------------- 2 Al 1 -8.301188489797482e-01 -8.301188489647311e-01 1.50171e-11 1.81629e-10 2 8.687932417813409e-01 8.687932417847779e-01 3.43703e-12 2.14624e-09 * 3 3.403597791997932e-01 3.403597791926224e-01 7.17076e-12 6.09208e-11 ----------------------------------------------------------------------------------------------------- 3 Al 1 -1.549090962906239e-01 -1.549090962872169e-01 3.40700e-12 3.84947e-11 2 3.565172049833948e-01 3.565172049876938e-01 4.29901e-12 7.09312e-10 3 4.452855969004825e-03 4.452855981513538e-03 1.25087e-11 2.72276e-11 ----------------------------------------------------------------------------------------------------- 4 Al 1 5.054608802429119e-01 5.054608802251656e-01 1.77464e-11 7.92125e-11 2 2.123941624580624e-01 2.123941624685651e-01 1.05027e-11 1.01205e-10 3 3.608867338124708e-01 3.608867338491663e-01 3.66955e-11 1.12416e-10 ----------------------------------------------------------------------------------------------------- 5 Al 1 7.838285736497783e-01 7.838285736561087e-01 6.33038e-12 2.24977e-11 2 -4.066665881994418e-01 -4.066665882038900e-01 4.44816e-12 5.16346e-11 3 2.835897250034135e-01 2.835897250757718e-01 7.23584e-11 1.08090e-10 ----------------------------------------------------------------------------------------------------- 6 Al 1 -3.182359088070548e-01 -3.182359087923781e-01 1.46767e-11 2.92970e-11 2 2.473565429064959e-01 2.473565429177538e-01 1.12579e-11 1.24162e-10 3 2.367024155281387e-01 2.367024155319291e-01 3.79041e-12 7.00378e-10 ----------------------------------------------------------------------------------------------------- 7 Al 1 5.330776645106308e-01 5.330776645143235e-01 3.69271e-12 2.15124e-10 2 -1.265303936055062e+00 -1.265303936042269e+00 1.27935e-11 4.43162e-10 3 -1.664059852674135e+00 -1.664059852640307e+00 3.38278e-11 7.55971e-09 * ----------------------------------------------------------------------------------------------------- 8 Al 1 -1.106102765768292e+00 -1.106102765776464e+00 8.17213e-12 1.35476e-10 2 -5.786431552528933e-01 -5.786431552915623e-01 3.86690e-11 1.63932e-10 3 -3.976254646215626e-01 -3.976254645972029e-01 2.43596e-11 7.18102e-11 ----------------------------------------------------------------------------------------------------- 9 Al 1 1.154757113970890e-02 1.154757115311658e-02 1.34077e-11 1.78942e-10 2 -8.951085530454084e-01 -8.951085530547375e-01 9.32909e-12 4.76559e-10 3 -8.256673196619201e-01 -8.256673196939351e-01 3.20151e-11 6.84498e-11 ----------------------------------------------------------------------------------------------------- 10 Al 1 -5.940617298857083e-01 -5.940617299320099e-01 4.63016e-11 1.56380e-10 2 4.945734647228598e-01 4.945734647569671e-01 3.41072e-11 2.25918e-10 3 -7.395209650445473e-01 -7.395209650415115e-01 3.03579e-12 2.43183e-10 ----------------------------------------------------------------------------------------------------- 11 Al 1 -2.545585565648861e-01 -2.545585566296287e-01 6.47426e-11 3.38827e-10 2 -8.707854188315786e-01 -8.707854188052538e-01 2.63247e-11 2.69138e-11 3 8.100882807280941e-01 8.100882807110734e-01 1.70207e-11 5.29185e-10 ----------------------------------------------------------------------------------------------------- 12 Al 1 9.347404773093122e-02 9.347404774826741e-02 1.73362e-11 1.81031e-10 2 9.414913882260003e-01 9.414913882335001e-01 7.49978e-12 1.25499e-09 3 4.506103566584037e-01 4.506103566314462e-01 2.69574e-11 1.53567e-10 ----------------------------------------------------------------------------------------------------- 13 Al 1 -4.395996837971509e-01 -4.395996837944478e-01 2.70312e-12 1.51868e-10 2 -1.076082289699861e+00 -1.076082289696028e+00 3.83271e-12 8.12992e-10 3 -1.976587616330740e+00 -1.976587616340688e+00 9.94804e-12 4.52659e-09 * ----------------------------------------------------------------------------------------------------- 14 Al 1 -3.008974176982572e-02 -3.008974176255723e-02 7.26849e-12 1.39636e-09 2 1.923376313386332e-01 1.923376313393441e-01 7.10931e-13 2.36498e-10 3 3.262154839329902e-02 3.262154833972306e-02 5.35760e-11 2.20394e-10 ----------------------------------------------------------------------------------------------------- 15 Al 1 1.774239621035823e+00 1.774239621001755e+00 3.40672e-11 1.51029e-10 2 -4.684389635966641e-01 -4.684389635821232e-01 1.45410e-11 1.44984e-10 3 6.423592480696348e-01 6.423592481374656e-01 6.78307e-11 2.15666e-10 ----------------------------------------------------------------------------------------------------- 16 Al 1 6.154678876221233e-01 6.154678875985368e-01 2.35866e-11 4.46407e-10 2 1.347681653033961e+00 1.347681653041615e+00 7.65410e-12 4.31848e-09 * 3 8.770769467902998e-01 8.770769467927694e-01 2.46958e-12 8.34435e-10 ----------------------------------------------------------------------------------------------------- 17 Al 1 5.032650193424819e-02 5.032650193995582e-02 5.70764e-12 2.53588e-10 2 6.156218797134384e-02 6.156218797982426e-02 8.48042e-12 1.56010e-09 3 -5.910444345955491e-02 -5.910444345605883e-02 3.49609e-12 7.87560e-09 * ----------------------------------------------------------------------------------------------------- 18 Al 1 3.278939412964484e-01 3.278939412292376e-01 6.72108e-11 2.69393e-10 2 5.115728447725622e-01 5.115728447900002e-01 1.74381e-11 1.41781e-10 3 -1.726916745269419e-01 -1.726916745170838e-01 9.85806e-12 2.27563e-10 ----------------------------------------------------------------------------------------------------- 19 Al 1 3.503983694928400e-01 3.503983694763428e-01 1.64972e-11 1.62227e-10 2 6.332374425049112e-02 6.332374428772587e-02 3.72348e-11 5.74233e-11 3 -2.259876481988234e-01 -2.259876481992756e-01 4.52249e-13 6.92314e-11 ----------------------------------------------------------------------------------------------------- 20 Al 1 1.197459682079086e-01 1.197459681972889e-01 1.06197e-11 9.41377e-11 2 4.314491363324161e-01 4.314491363415829e-01 9.16678e-12 1.89926e-10 3 -1.475758965106769e-01 -1.475758965118358e-01 1.15888e-12 4.69971e-11 ----------------------------------------------------------------------------------------------------- 21 Al 1 -1.014728277895785e+00 -1.014728277918335e+00 2.25500e-11 7.66729e-11 2 9.179844528258480e-02 9.179844527173753e-02 1.08473e-11 2.11853e-10 3 6.380424290775545e-01 6.380424290556298e-01 2.19247e-11 3.21799e-10 ----------------------------------------------------------------------------------------------------- 22 Al 1 2.920303740607872e-01 2.920303740133708e-01 4.74164e-11 4.31850e-10 2 1.533747111289337e+00 1.533747111243081e+00 4.62559e-11 1.03951e-10 3 1.517047476493124e+00 1.517047476510158e+00 1.70335e-11 4.11748e-09 * ----------------------------------------------------------------------------------------------------- 23 Al 1 -2.652250431347256e-01 -2.652250431575469e-01 2.28212e-11 1.37017e-10 2 1.614763613566961e-01 1.614763613535779e-01 3.11823e-12 8.01724e-10 3 -3.031323261600296e-01 -3.031323261568131e-01 3.21643e-12 8.05261e-10 ----------------------------------------------------------------------------------------------------- 24 Al 1 1.820853905271868e-02 1.820853906608529e-02 1.33666e-11 1.91229e-10 2 -1.087408035869495e-01 -1.087408035936111e-01 6.66157e-12 1.27284e-09 3 -4.510481536596629e-01 -4.510481536352844e-01 2.43786e-11 5.18747e-10 ----------------------------------------------------------------------------------------------------- 25 Al 1 -1.823525584018393e-01 -1.823525583656261e-01 3.62132e-11 1.75894e-10 2 -7.142478377717680e-01 -7.142478377533047e-01 1.84633e-11 1.40804e-10 3 7.034881902330437e-01 7.034881902218509e-01 1.11927e-11 1.54794e-10 ----------------------------------------------------------------------------------------------------- 26 Al 1 -6.951391374998976e-01 -6.951391374656725e-01 3.42252e-11 1.62077e-09 * 2 4.449522384345632e-01 4.449522384133325e-01 2.12306e-11 2.80811e-11 3 -2.847930761819109e-01 -2.847930761478132e-01 3.40976e-11 4.06666e-10 ----------------------------------------------------------------------------------------------------- 27 Al 1 4.729838162040240e-01 4.729838162073517e-01 3.32767e-12 1.58924e-10 2 -2.000234467713951e+00 -2.000234467613532e+00 1.00420e-10 4.17736e-10 3 4.779814353512534e-03 4.779814370942621e-03 1.74301e-11 1.39776e-09 ----------------------------------------------------------------------------------------------------- 28 Al 1 -4.567208191267040e-01 -4.567208191317256e-01 5.02165e-12 1.88411e-10 2 6.462990845305345e-01 6.462990845232109e-01 7.32359e-12 1.34342e-10 3 -4.117347413472099e-01 -4.117347413556396e-01 8.42970e-12 1.94009e-10 ----------------------------------------------------------------------------------------------------- 29 Al 1 -3.738321474645545e-01 -3.738321475480065e-01 8.34520e-11 1.56717e-09 2 -7.330676212016853e-01 -7.330676212170505e-01 1.53652e-11 1.32508e-10 3 6.993810845538774e-01 6.993810845347080e-01 1.91693e-11 2.33682e-10 ----------------------------------------------------------------------------------------------------- 30 Al 1 -6.861677639795771e-02 -6.861677638095057e-02 1.70071e-11 9.22029e-11 2 6.349645344400621e-01 6.349645344573169e-01 1.72549e-11 5.02516e-10 3 -4.154900254077792e-01 -4.154900253855548e-01 2.22244e-11 5.17233e-11 ----------------------------------------------------------------------------------------------------- 31 Al 1 -4.892079588221049e-02 -4.892079589383816e-02 1.16277e-11 3.13117e-10 2 -9.138606173315145e-01 -9.138606173642180e-01 3.27035e-11 1.44162e-10 3 5.063761169737484e-01 5.063761169556145e-01 1.81339e-11 6.25669e-10 ----------------------------------------------------------------------------------------------------- 32 Al 1 5.423653762813858e-01 5.423653762507892e-01 3.05966e-11 5.81127e-09 * 2 7.862044082698962e-01 7.862044083145076e-01 4.46113e-11 8.40499e-11 3 2.538032882712257e-02 2.538032884389640e-02 1.67738e-11 1.12921e-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 = 1, direction = 2: |F_model - F_numer| error = ----------------------- = 7.43332e-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 = Fe | a0 = 3.611098289489746 | (Configuration in file "config-Fe.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Fe 1 6.869122780359000e-01 6.869122780259272e-01 9.97280e-12 6.81366e-12 2 6.775423324474170e-01 6.775423324486497e-01 1.23268e-12 1.11709e-10 3 6.871543232025207e-01 6.871543232014754e-01 1.04527e-12 5.95989e-11 ----------------------------------------------------------------------------------------------------- 2 Fe 1 3.700110072586406e-02 3.700110072746348e-02 1.59942e-12 2.57584e-10 2 3.550452260034828e-02 3.550452260582590e-02 5.47762e-12 1.71577e-11 3 1.081547058475869e+00 1.081547058447136e+00 2.87335e-11 1.01640e-10 ----------------------------------------------------------------------------------------------------- 3 Fe 1 -9.161188015175978e-01 -9.161188014856406e-01 3.19572e-11 1.35913e-10 2 8.067712373387783e-01 8.067712373345222e-01 4.25615e-12 4.03785e-11 3 -2.831490755617643e-01 -2.831490756069381e-01 4.51738e-11 1.88738e-10 ----------------------------------------------------------------------------------------------------- 4 Fe 1 6.572768486442921e-01 6.572768486078197e-01 3.64725e-11 9.53760e-11 2 3.819018679590463e-01 3.819018679589720e-01 7.43849e-14 2.80950e-09 * 3 -7.760189044783637e-01 -7.760189045259528e-01 4.75890e-11 5.97508e-11 ----------------------------------------------------------------------------------------------------- 5 Fe 1 -3.799268676016624e-01 -3.799268676599138e-01 5.82515e-11 8.62651e-11 2 -8.945330216689176e-01 -8.945330216747561e-01 5.83855e-12 9.65603e-10 3 -8.307971495695484e-01 -8.307971495798733e-01 1.03249e-11 2.90599e-10 ----------------------------------------------------------------------------------------------------- 6 Fe 1 9.993042665624521e-01 9.993042665948969e-01 3.24448e-11 1.32493e-10 2 7.945842138785660e-01 7.945842138219688e-01 5.65973e-11 2.84509e-10 3 -1.349337213654709e+00 -1.349337213694955e+00 4.02456e-11 4.95944e-10 ----------------------------------------------------------------------------------------------------- 7 Fe 1 1.850365125232871e+00 1.850365125235339e+00 2.46803e-12 1.63984e-10 2 -2.414231698393692e+00 -2.414231698399280e+00 5.58797e-12 9.89577e-11 3 1.203836436780581e+00 1.203836436791111e+00 1.05305e-11 1.82073e-10 ----------------------------------------------------------------------------------------------------- 8 Fe 1 -3.493030379206328e+00 -3.493030379183456e+00 2.28724e-11 3.18809e-10 2 2.320895437019085e+00 2.320895437102079e+00 8.29936e-11 3.96390e-11 3 6.495270127317460e-01 6.495270126829954e-01 4.87506e-11 4.53751e-10 ----------------------------------------------------------------------------------------------------- 9 Fe 1 6.197143093066225e-01 6.197143092977923e-01 8.83027e-12 6.51031e-11 2 2.209880656616792e-01 2.209880656499276e-01 1.17516e-11 2.14044e-11 3 1.221749312946572e+00 1.221749312940334e+00 6.23790e-12 2.30378e-11 ----------------------------------------------------------------------------------------------------- 10 Fe 1 -8.023879275522279e-01 -8.023879275641077e-01 1.18798e-11 8.35716e-11 2 -6.261608791041798e-01 -6.261608791125598e-01 8.37996e-12 3.57753e-09 * 3 -7.065573106437256e-01 -7.065573106376309e-01 6.09468e-12 3.47557e-10 ----------------------------------------------------------------------------------------------------- 11 Fe 1 -7.762520539717315e-01 -7.762520539982709e-01 2.65394e-11 9.02678e-11 2 1.608093851165350e+00 1.608093851153349e+00 1.20011e-11 6.89760e-10 3 -1.300460998501849e+00 -1.300460998539013e+00 3.71640e-11 3.28121e-10 ----------------------------------------------------------------------------------------------------- 12 Fe 1 6.530595707136606e-01 6.530595707088340e-01 4.82658e-12 1.11030e-10 2 -9.260761204981516e-01 -9.260761204897358e-01 8.41582e-12 5.70854e-11 3 4.169687403862563e-01 4.169687403794196e-01 6.83675e-12 7.33690e-10 ----------------------------------------------------------------------------------------------------- 13 Fe 1 -2.012055788896967e+00 -2.012055788958644e+00 6.16778e-11 1.21333e-10 2 -8.428992317272238e-01 -8.428992317093668e-01 1.78570e-11 2.34320e-10 3 -4.739835928546144e-02 -4.739835927707172e-02 8.38972e-12 8.52007e-11 ----------------------------------------------------------------------------------------------------- 14 Fe 1 1.587853021096175e+00 1.587853021094847e+00 1.32783e-12 3.23556e-10 2 1.371391964632991e+00 1.371391964657756e+00 2.47651e-11 2.19016e-10 3 -6.403608163398924e-01 -6.403608163411042e-01 1.21181e-12 3.30177e-10 ----------------------------------------------------------------------------------------------------- 15 Fe 1 8.667059327200882e-03 8.667059382885011e-03 5.56841e-11 1.07101e-09 2 -1.053947412184419e+00 -1.053947412203127e+00 1.87077e-11 3.46310e-10 3 -1.233854120468059e+00 -1.233854120462423e+00 5.63527e-12 4.78243e-10 ----------------------------------------------------------------------------------------------------- 16 Fe 1 8.446831207993817e-03 8.446831134988885e-03 7.30049e-11 1.15445e-09 2 -4.390576739087957e-01 -4.390576739024634e-01 6.33232e-12 9.68798e-11 3 1.712637673287720e+00 1.712637673300116e+00 1.23963e-11 3.31458e-10 ----------------------------------------------------------------------------------------------------- 17 Fe 1 5.349877525082049e-01 5.349877524524317e-01 5.57732e-11 4.94569e-11 2 -1.711492725594775e+00 -1.711492725586550e+00 8.22475e-12 1.14466e-10 3 -1.766970519262429e+00 -1.766970519268128e+00 5.69900e-12 5.41279e-10 ----------------------------------------------------------------------------------------------------- 18 Fe 1 -4.749087682111026e-01 -4.749087682170441e-01 5.94147e-12 3.70358e-10 2 -2.085501580913972e+00 -2.085501580840781e+00 7.31912e-11 2.71583e-10 3 1.048691787000501e+00 1.048691786966725e+00 3.37754e-11 5.84996e-10 ----------------------------------------------------------------------------------------------------- 19 Fe 1 3.795616037134072e-01 3.795616038579495e-01 1.44542e-10 1.61907e-10 2 7.191321218399294e-01 7.191321218432800e-01 3.35065e-12 1.66790e-10 3 -6.812922302160663e-01 -6.812922302501724e-01 3.41061e-11 1.39577e-10 ----------------------------------------------------------------------------------------------------- 20 Fe 1 -1.167365503138748e-01 -1.167365502940350e-01 1.98398e-11 1.79187e-07 * 2 1.972694764694076e+00 1.972694764668918e+00 2.51577e-11 1.23759e-10 3 1.695325868302859e+00 1.695325868305681e+00 2.82196e-12 4.65539e-12 ----------------------------------------------------------------------------------------------------- 21 Fe 1 -8.450270941539044e-01 -8.450270941693054e-01 1.54010e-11 3.44287e-10 2 -7.596047412109549e-01 -7.596047412062509e-01 4.70401e-12 8.47075e-11 3 -6.415852349003837e-01 -6.415852349561451e-01 5.57614e-11 5.88364e-10 ----------------------------------------------------------------------------------------------------- 22 Fe 1 1.260412831069654e+00 1.260412831070577e+00 9.23484e-13 1.20617e-10 2 -5.972638167331166e-01 -5.972638167707709e-01 3.76543e-11 8.91381e-11 3 8.675696507386045e-01 8.675696506963577e-01 4.22468e-11 1.42611e-08 * ----------------------------------------------------------------------------------------------------- 23 Fe 1 1.158315990928914e+00 1.158315990920301e+00 8.61311e-12 7.61666e-11 2 -6.000572579787414e-01 -6.000572580202053e-01 4.14638e-11 7.36945e-11 3 2.883824199889330e-01 2.883824199855123e-01 3.42071e-12 3.49789e-09 * ----------------------------------------------------------------------------------------------------- 24 Fe 1 -1.240660168348619e+00 -1.240660168385170e+00 3.65510e-11 1.61601e-09 2 8.132169979791952e-01 8.132169979420479e-01 3.71473e-11 3.46716e-09 * 3 6.520708575341623e-01 6.520708575124842e-01 2.16781e-11 4.81486e-11 ----------------------------------------------------------------------------------------------------- 25 Fe 1 -3.615543068772302e-01 -3.615543069265695e-01 4.93393e-11 9.34121e-11 2 -8.112691147115649e-01 -8.112691147213889e-01 9.82392e-12 8.03908e-10 3 -6.015881952997203e-01 -6.015881953717437e-01 7.20234e-11 4.72797e-10 ----------------------------------------------------------------------------------------------------- 26 Fe 1 4.363862305645658e-01 4.363862305659619e-01 1.39605e-12 4.67282e-09 * 2 -1.998414388980083e-01 -1.998414389249405e-01 2.69323e-11 2.27741e-10 3 -2.493678853251876e-01 -2.493678853509811e-01 2.57936e-11 2.92980e-09 * ----------------------------------------------------------------------------------------------------- 27 Fe 1 -3.249049191138263e-03 -3.249049197147558e-03 6.00930e-12 9.51759e-11 2 4.680899927939714e-01 4.680899927142802e-01 7.96912e-11 3.20890e-10 3 -2.135390375610013e-01 -2.135390375690251e-01 8.02383e-12 5.00417e-10 ----------------------------------------------------------------------------------------------------- 28 Fe 1 7.013319237414870e-01 7.013319237631607e-01 2.16737e-11 7.82080e-11 2 -3.233759629979375e-01 -3.233759629696961e-01 2.82414e-11 3.49204e-11 3 -4.104334052651841e-01 -4.104334052494354e-01 1.57486e-11 2.46914e-10 ----------------------------------------------------------------------------------------------------- 29 Fe 1 -1.540099451462839e-01 -1.540099451679696e-01 2.16857e-11 2.12121e-09 * 2 1.420245597194488e+00 1.420245597193974e+00 5.13811e-13 2.35176e-11 3 -6.407238339082285e-01 -6.407238338952606e-01 1.29680e-11 1.03655e-10 ----------------------------------------------------------------------------------------------------- 30 Fe 1 1.209732283827052e-01 1.209732283658302e-01 1.68749e-11 1.16133e-06 * 2 1.071068613583476e+00 1.071068613583526e+00 4.99600e-14 1.40053e-10 3 1.978254574855285e+00 1.978254574842198e+00 1.30871e-11 6.84715e-11 ----------------------------------------------------------------------------------------------------- 31 Fe 1 -1.364344197685735e-01 -1.364344197118222e-01 5.67513e-11 1.87939e-09 * 2 5.455885108754372e-01 5.455885108603165e-01 1.51208e-11 1.07729e-10 3 -4.003297736541368e-01 -4.003297737010320e-01 4.68952e-11 2.15579e-10 ----------------------------------------------------------------------------------------------------- 32 Fe 1 1.178214899527132e-02 1.178214898462804e-02 1.06433e-11 1.08865e-10 2 -9.423974151393871e-01 -9.423974151591015e-01 1.97143e-11 8.18428e-11 3 -7.299516523358990e-01 -7.299516523297970e-01 6.10201e-12 2.22580e-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 = 16, direction = 1: |F_model - F_numer| error = ----------------------- = 8.64288e-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 Fe | a0 = 3.7626323778658843 | (Configuration in file "config-AlFe.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Fe 1 2.231880039950049e-02 2.231880039656191e-02 2.93858e-12 1.32750e-11 2 2.648389394910570e-01 2.648389394901283e-01 9.28702e-13 9.76436e-11 3 -1.476472258127495e-03 -1.476472262525101e-03 4.39761e-12 7.35833e-12 ----------------------------------------------------------------------------------------------------- 2 Al 1 -6.007748035666831e-01 -6.007748035430138e-01 2.36693e-11 2.69493e-10 2 1.343397543340805e+00 1.343397543338290e+00 2.51510e-12 5.89158e-11 3 -9.873748427445063e-01 -9.873748427611768e-01 1.66706e-11 2.83788e-10 ----------------------------------------------------------------------------------------------------- 3 Fe 1 1.097187222339834e+00 1.097187222314929e+00 2.49047e-11 6.75315e-11 2 -6.176893202594201e-01 -6.176893202415631e-01 1.78570e-11 1.02535e-10 3 8.428320616918208e-01 8.428320617027844e-01 1.09636e-11 8.36397e-11 ----------------------------------------------------------------------------------------------------- 4 Al 1 -8.057366123866704e-01 -8.057366123596524e-01 2.70179e-11 4.31898e-10 2 1.262067092121021e+00 1.262067092112736e+00 8.28426e-12 8.75926e-11 3 1.076201458907571e+00 1.076201458879609e+00 2.79616e-11 8.71971e-11 ----------------------------------------------------------------------------------------------------- 5 Al 1 4.548526439373674e-01 4.548526439521529e-01 1.47856e-11 7.26423e-11 2 -1.023827286478161e+00 -1.023827286516729e+00 3.85685e-11 2.33811e-10 3 -1.925628039987793e-01 -1.925628040271612e-01 2.83819e-11 8.00633e-11 ----------------------------------------------------------------------------------------------------- 6 Al 1 7.586353494842512e-01 7.586353494968371e-01 1.25859e-11 4.01041e-11 2 5.268266834486806e-01 5.268266834451946e-01 3.48599e-12 2.94925e-10 3 -1.253349095447122e+00 -1.253349095442869e+00 4.25260e-12 2.88908e-10 ----------------------------------------------------------------------------------------------------- 7 Al 1 1.052030843549208e+00 1.052030843477041e+00 7.21667e-11 1.94837e-10 2 -9.088338283924133e-01 -9.088338284166326e-01 2.42193e-11 1.34764e-10 3 3.499183958266373e-01 3.499183958393359e-01 1.26986e-11 1.14283e-10 ----------------------------------------------------------------------------------------------------- 8 Al 1 -2.781558579436130e+00 -2.781558579443303e+00 7.17337e-12 1.89912e-10 2 -1.315420685736243e+00 -1.315420685690536e+00 4.57077e-11 1.31163e-08 * 3 6.622446648298678e-01 6.622446648918804e-01 6.20126e-11 1.49803e-09 * ----------------------------------------------------------------------------------------------------- 9 Fe 1 3.516383831194921e-01 3.516383831104284e-01 9.06364e-12 7.39871e-10 2 -6.266191969445537e-01 -6.266191969339776e-01 1.05761e-11 9.66616e-10 3 6.784724824752640e-01 6.784724824290185e-01 4.62456e-11 9.00369e-11 ----------------------------------------------------------------------------------------------------- 10 Al 1 -9.437250387679610e-01 -9.437250387922314e-01 2.42704e-11 1.16416e-10 2 1.103298919859725e+00 1.103298919847027e+00 1.26976e-11 6.38841e-10 3 2.982429761219674e-01 2.982429761179298e-01 4.03760e-12 1.78966e-10 ----------------------------------------------------------------------------------------------------- 11 Fe 1 1.770776385711662e+00 1.770776385662068e+00 4.95943e-11 3.41509e-10 2 -1.962717489330073e+00 -1.962717489437273e+00 1.07200e-10 3.53770e-10 3 -4.861900469863524e-01 -4.861900470156270e-01 2.92746e-11 7.67095e-11 ----------------------------------------------------------------------------------------------------- 12 Fe 1 -2.349658113661859e+00 -2.349658113662304e+00 4.44533e-13 4.30268e-10 2 1.670407420536828e+00 1.670407420586342e+00 4.95139e-11 3.35973e-10 3 -8.992618412829680e-01 -8.992618412898665e-01 6.89848e-12 4.61520e-12 ----------------------------------------------------------------------------------------------------- 13 Al 1 1.213746313552901e+00 1.213746313551298e+00 1.60227e-12 1.06789e-09 2 -4.247991501884638e-01 -4.247991502052488e-01 1.67850e-11 9.81911e-11 3 1.558253022742028e-02 1.558253025797669e-02 3.05564e-11 8.09570e-11 ----------------------------------------------------------------------------------------------------- 14 Fe 1 -5.519657022510248e-01 -5.519657022491943e-01 1.83054e-12 1.84031e-10 2 -7.729523639618120e-01 -7.729523639508035e-01 1.10085e-11 8.73768e-11 3 6.495986073930402e-01 6.495986073952458e-01 2.20557e-12 1.36617e-10 ----------------------------------------------------------------------------------------------------- 15 Al 1 1.969558919745289e+00 1.969558919716188e+00 2.91014e-11 1.01627e-08 * 2 3.297925671525263e+00 3.297925671570261e+00 4.49987e-11 2.33806e-10 3 -1.006491110934980e+00 -1.006491110920135e+00 1.48450e-11 1.30989e-10 ----------------------------------------------------------------------------------------------------- 16 Fe 1 -1.133976652551781e+00 -1.133976652523999e+00 2.77818e-11 8.33666e-11 2 -5.366219732544921e-01 -5.366219732125360e-01 4.19561e-11 2.55201e-09 * 3 -9.265312959109837e-01 -9.265312959069881e-01 3.99558e-12 7.09386e-11 ----------------------------------------------------------------------------------------------------- 17 Fe 1 5.124703819756490e-01 5.124703819916108e-01 1.59618e-11 1.07316e-10 2 6.510000647199342e-01 6.510000647146674e-01 5.26679e-12 1.14566e-10 3 3.626718910684866e-01 3.626718911454488e-01 7.69622e-11 1.67301e-10 ----------------------------------------------------------------------------------------------------- 18 Fe 1 -1.757559548016024e+00 -1.757559548053989e+00 3.79643e-11 4.58778e-10 2 -1.927223696523678e+00 -1.927223696455548e+00 6.81297e-11 1.64724e-10 3 -1.492814829262356e+00 -1.492814829235925e+00 2.64304e-11 1.03453e-10 ----------------------------------------------------------------------------------------------------- 19 Fe 1 -2.464681006056480e-01 -2.464681005832642e-01 2.23838e-11 1.18495e-10 2 -4.681647002208109e-02 -4.681647006408612e-02 4.20050e-11 2.57607e-10 3 -6.202547043235355e-01 -6.202547043204986e-01 3.03690e-12 3.25691e-10 ----------------------------------------------------------------------------------------------------- 20 Al 1 5.961374849282505e-01 5.961374849264263e-01 1.82421e-12 4.19776e-11 2 -3.870040836488956e-01 -3.870040836360227e-01 1.28729e-11 1.11028e-10 3 -6.216006561064485e-01 -6.216006561120151e-01 5.56655e-12 1.07239e-10 ----------------------------------------------------------------------------------------------------- 21 Al 1 -9.315134007783484e-01 -9.315134007256244e-01 5.27240e-11 1.67694e-10 2 8.855724850506211e-01 8.855724850217140e-01 2.89071e-11 1.62491e-10 3 1.390327347625271e+00 1.390327347561646e+00 6.36255e-11 7.40479e-10 ----------------------------------------------------------------------------------------------------- 22 Fe 1 4.405449423622823e-01 4.405449424381860e-01 7.59037e-11 1.52965e-10 2 -1.245193546121000e+00 -1.245193546108404e+00 1.25957e-11 4.80709e-09 * 3 8.869887561420114e-01 8.869887561470094e-01 4.99800e-12 5.53740e-11 ----------------------------------------------------------------------------------------------------- 23 Al 1 -5.804144619593016e-01 -5.804144620082581e-01 4.89565e-11 2.19053e-10 2 4.122236863188417e-01 4.122236863217670e-01 2.92527e-12 4.63740e-11 3 -7.884261353684603e-01 -7.884261353812076e-01 1.27474e-11 2.81299e-10 ----------------------------------------------------------------------------------------------------- 24 Fe 1 1.360054737940802e+00 1.360054737966957e+00 2.61555e-11 2.72809e-10 2 -1.784315407755960e+00 -1.784315407735381e+00 2.05784e-11 2.03539e-10 3 1.938725269994485e+00 1.938725269997067e+00 2.58127e-12 1.35098e-10 ----------------------------------------------------------------------------------------------------- 25 Fe 1 1.789033189325727e-01 1.789033189553327e-01 2.27600e-11 5.18410e-11 2 7.000971224998188e-01 7.000971224899247e-01 9.89409e-12 4.66057e-10 3 -4.923929634444450e-01 -4.923929634635461e-01 1.91011e-11 6.70414e-11 ----------------------------------------------------------------------------------------------------- 26 Al 1 -1.187661385305271e-01 -1.187661385055333e-01 2.49938e-11 5.79196e-09 * 2 -3.472039194164185e-01 -3.472039194160288e-01 3.89633e-13 4.33127e-10 3 1.055598516487691e+00 1.055598516490236e+00 2.54552e-12 4.65847e-10 ----------------------------------------------------------------------------------------------------- 27 Fe 1 -7.855670491563086e-01 -7.855670491762986e-01 1.99900e-11 8.65972e-11 2 1.059664848536609e+00 1.059664848530177e+00 6.43241e-12 6.30993e-10 3 1.002021148613835e+00 1.002021148636859e+00 2.30247e-11 8.34768e-11 ----------------------------------------------------------------------------------------------------- 28 Al 1 1.105246505066341e+00 1.105246505069750e+00 3.40905e-12 7.56206e-11 2 -7.203282041689626e-01 -7.203282041720390e-01 3.07643e-12 1.40831e-11 3 -9.023267300949807e-01 -9.023267301046936e-01 9.71290e-12 3.07067e-10 ----------------------------------------------------------------------------------------------------- 29 Al 1 5.436753040721731e-01 5.436753040697385e-01 2.43461e-12 2.98624e-11 2 2.200470428078594e+00 2.200470428046710e+00 3.18838e-11 5.05435e-09 * 3 -8.789915229643963e-01 -8.789915230174892e-01 5.30929e-11 4.30412e-10 ----------------------------------------------------------------------------------------------------- 30 Fe 1 3.770491962909429e-01 3.770491962639496e-01 2.69933e-11 7.48348e-11 2 -7.783975080171730e-01 -7.783975080208654e-01 3.69238e-12 1.40238e-10 3 9.367604161610377e-01 9.367604161653379e-01 4.30023e-12 7.89933e-10 ----------------------------------------------------------------------------------------------------- 31 Fe 1 -4.075743249782796e-01 -4.075743249771697e-01 1.10989e-12 2.64593e-10 2 2.869075743998949e-01 2.869075743724029e-01 2.74920e-11 1.27023e-10 3 -5.153391704034638e-01 -5.153391703910881e-01 1.23757e-11 4.66090e-09 * ----------------------------------------------------------------------------------------------------- 32 Al 1 1.904317932380279e-01 1.904317932427571e-01 4.72916e-12 2.05308e-11 2 -2.387343497078912e-01 -2.387343497078799e-01 1.13243e-14 3.15728e-09 * 3 -8.080230203450132e-02 -8.080230203208233e-02 2.41900e-12 4.19789e-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 = 1, direction = 3: |F_model - F_numer| error = ----------------------- = 2.97846e-09 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 8.64288e-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: B Comment: The letter grade B was assigned because the normalized error in the computation was 8.64288e-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.