!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_000 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 3.421627552140151e-01 9.32021e-12 8.81787e-11 2 2.684865905542462e-03 2.684865885584985e-03 1.99575e-11 1.34207e-10 3 -5.822412687904121e-02 -5.822412690163311e-02 2.25919e-11 2.96015e-11 ----------------------------------------------------------------------------------------------------- 2 Al 1 -8.301188489797482e-01 -8.301188489647303e-01 1.50179e-11 1.81629e-10 2 8.687932417813409e-01 8.687932417847783e-01 3.43747e-12 2.14624e-09 * 3 3.403597791997932e-01 3.403597791926223e-01 7.17088e-12 6.09207e-11 ----------------------------------------------------------------------------------------------------- 3 Al 1 -1.549090962906239e-01 -1.549090962872167e-01 3.40711e-12 3.84947e-11 2 3.565172049833948e-01 3.565172049876941e-01 4.29923e-12 7.09312e-10 3 4.452855969004825e-03 4.452855981513536e-03 1.25087e-11 2.72276e-11 ----------------------------------------------------------------------------------------------------- 4 Al 1 5.054608802429119e-01 5.054608802251652e-01 1.77467e-11 7.92123e-11 2 2.123941624580624e-01 2.123941624685649e-01 1.05025e-11 1.01205e-10 3 3.608867338124708e-01 3.608867338491660e-01 3.66952e-11 1.12416e-10 ----------------------------------------------------------------------------------------------------- 5 Al 1 7.838285736497783e-01 7.838285736561079e-01 6.32960e-12 2.24974e-11 2 -4.066665881994418e-01 -4.066665882038896e-01 4.44783e-12 5.16344e-11 3 2.835897250034135e-01 2.835897250757716e-01 7.23582e-11 1.08090e-10 ----------------------------------------------------------------------------------------------------- 6 Al 1 -3.182359088070548e-01 -3.182359087923779e-01 1.46769e-11 2.92969e-11 2 2.473565429064959e-01 2.473565429177536e-01 1.12577e-11 1.24162e-10 3 2.367024155281387e-01 2.367024155319292e-01 3.79050e-12 7.00378e-10 ----------------------------------------------------------------------------------------------------- 7 Al 1 5.330776645106308e-01 5.330776645143230e-01 3.69227e-12 2.15124e-10 2 -1.265303936055062e+00 -1.265303936042270e+00 1.27929e-11 4.43162e-10 3 -1.664059852674135e+00 -1.664059852640307e+00 3.38274e-11 7.55971e-09 * ----------------------------------------------------------------------------------------------------- 8 Al 1 -1.106102765768292e+00 -1.106102765776463e+00 8.17124e-12 1.35474e-10 2 -5.786431552528933e-01 -5.786431552915616e-01 3.86683e-11 1.63932e-10 3 -3.976254646215626e-01 -3.976254645972026e-01 2.43600e-11 7.18103e-11 ----------------------------------------------------------------------------------------------------- 9 Al 1 1.154757113970890e-02 1.154757115311657e-02 1.34077e-11 1.78942e-10 2 -8.951085530454084e-01 -8.951085530547368e-01 9.32843e-12 4.76560e-10 3 -8.256673196619201e-01 -8.256673196939346e-01 3.20145e-11 6.84494e-11 ----------------------------------------------------------------------------------------------------- 10 Al 1 -5.940617298857083e-01 -5.940617299320096e-01 4.63013e-11 1.56381e-10 2 4.945734647228598e-01 4.945734647569668e-01 3.41069e-11 2.25917e-10 3 -7.395209650445473e-01 -7.395209650415109e-01 3.03646e-12 2.43183e-10 ----------------------------------------------------------------------------------------------------- 11 Al 1 -2.545585565648861e-01 -2.545585566296286e-01 6.47424e-11 3.38827e-10 2 -8.707854188315786e-01 -8.707854188052530e-01 2.63256e-11 2.69137e-11 3 8.100882807280941e-01 8.100882807110725e-01 1.70216e-11 5.29185e-10 ----------------------------------------------------------------------------------------------------- 12 Al 1 9.347404773093122e-02 9.347404774826734e-02 1.73361e-11 1.81031e-10 2 9.414913882260003e-01 9.414913882334992e-01 7.49889e-12 1.25499e-09 3 4.506103566584037e-01 4.506103566314458e-01 2.69579e-11 1.53567e-10 ----------------------------------------------------------------------------------------------------- 13 Al 1 -4.395996837971509e-01 -4.395996837945653e-01 2.58560e-12 1.53281e-10 2 -1.076082289699861e+00 -1.076082289696028e+00 3.83338e-12 8.12992e-10 3 -1.976587616330740e+00 -1.976587616340689e+00 9.94915e-12 4.52659e-09 * ----------------------------------------------------------------------------------------------------- 14 Al 1 -3.008974176982572e-02 -3.008974176255724e-02 7.26848e-12 1.39636e-09 2 1.923376313386332e-01 1.923376313393441e-01 7.10876e-13 2.36498e-10 3 3.262154839329902e-02 3.262154833972303e-02 5.35760e-11 2.20394e-10 ----------------------------------------------------------------------------------------------------- 15 Al 1 1.774239621035823e+00 1.774239621001754e+00 3.40690e-11 1.51029e-10 2 -4.684389635966641e-01 -4.684389635821227e-01 1.45414e-11 1.44984e-10 3 6.423592480696348e-01 6.423592481374650e-01 6.78302e-11 2.15666e-10 ----------------------------------------------------------------------------------------------------- 16 Al 1 6.154678876221233e-01 6.154678875985363e-01 2.35870e-11 4.46407e-10 2 1.347681653033961e+00 1.347681653041616e+00 7.65454e-12 4.31848e-09 * 3 8.770769467902998e-01 8.770769467927688e-01 2.46902e-12 8.34435e-10 ----------------------------------------------------------------------------------------------------- 17 Al 1 5.032650193424819e-02 5.032650193995578e-02 5.70759e-12 2.53588e-10 2 6.156218797134384e-02 6.156218797982429e-02 8.48045e-12 1.56010e-09 3 -5.910444345955491e-02 -5.910444345605886e-02 3.49606e-12 7.87560e-09 * ----------------------------------------------------------------------------------------------------- 18 Al 1 3.278939412964484e-01 3.278939412292375e-01 6.72110e-11 2.69393e-10 2 5.115728447725622e-01 5.115728447899996e-01 1.74375e-11 1.41781e-10 3 -1.726916745269419e-01 -1.726916745170837e-01 9.85820e-12 2.27563e-10 ----------------------------------------------------------------------------------------------------- 19 Al 1 3.503983694928400e-01 3.503983694763425e-01 1.64975e-11 1.62227e-10 2 6.332374425049112e-02 6.332374428772583e-02 3.72347e-11 5.74233e-11 3 -2.259876481988234e-01 -2.259876481992755e-01 4.52083e-13 6.92314e-11 ----------------------------------------------------------------------------------------------------- 20 Al 1 1.197459682079086e-01 1.197459681972888e-01 1.06198e-11 9.41377e-11 2 4.314491363324161e-01 4.314491363415824e-01 9.16633e-12 1.89926e-10 3 -1.475758965106769e-01 -1.475758965118357e-01 1.15880e-12 4.69969e-11 ----------------------------------------------------------------------------------------------------- 21 Al 1 -1.014728277895785e+00 -1.014728277918334e+00 2.25486e-11 7.66722e-11 2 9.179844528258480e-02 9.179844527173746e-02 1.08473e-11 2.11853e-10 3 6.380424290775545e-01 6.380424290556292e-01 2.19252e-11 3.21800e-10 ----------------------------------------------------------------------------------------------------- 22 Al 1 2.920303740607867e-01 2.920303740133706e-01 4.74162e-11 4.31851e-10 2 1.533747111289337e+00 1.533747111243082e+00 4.62550e-11 1.03949e-10 3 1.517047476493125e+00 1.517047476510159e+00 1.70339e-11 4.11748e-09 * ----------------------------------------------------------------------------------------------------- 23 Al 1 -2.652250431347256e-01 -2.652250431575466e-01 2.28210e-11 1.37017e-10 2 1.614763613566961e-01 1.614763613535777e-01 3.11842e-12 8.01724e-10 3 -3.031323261600296e-01 -3.031323261568133e-01 3.21626e-12 8.05261e-10 ----------------------------------------------------------------------------------------------------- 24 Al 1 1.820853905271912e-02 1.820853906608528e-02 1.33662e-11 1.91229e-10 2 -1.087408035869495e-01 -1.087408035936110e-01 6.66148e-12 1.27284e-09 3 -4.510481536596634e-01 -4.510481536352847e-01 2.43788e-11 5.18747e-10 ----------------------------------------------------------------------------------------------------- 25 Al 1 -1.823525584018393e-01 -1.823525583656259e-01 3.62134e-11 1.75894e-10 2 -7.142478377717680e-01 -7.142478377533041e-01 1.84639e-11 1.40804e-10 3 7.034881902330437e-01 7.034881902218505e-01 1.11932e-11 1.54793e-10 ----------------------------------------------------------------------------------------------------- 26 Al 1 -6.951391374998976e-01 -6.951391374656727e-01 3.42250e-11 1.62077e-09 * 2 4.449522384345632e-01 4.449522384133321e-01 2.12310e-11 2.80810e-11 3 -2.847930761819109e-01 -2.847930761478129e-01 3.40979e-11 4.06666e-10 ----------------------------------------------------------------------------------------------------- 27 Al 1 4.729838162040240e-01 4.729838162073512e-01 3.32723e-12 1.58924e-10 2 -2.000234467713951e+00 -2.000234467613530e+00 1.00421e-10 4.17738e-10 3 4.779814353512534e-03 4.779814370942623e-03 1.74301e-11 1.39776e-09 ----------------------------------------------------------------------------------------------------- 28 Al 1 -4.567208191267040e-01 -4.567208191317254e-01 5.02137e-12 1.88411e-10 2 6.462990845305345e-01 6.462990845232106e-01 7.32392e-12 1.34342e-10 3 -4.117347413472099e-01 -4.117347413556393e-01 8.42937e-12 1.94008e-10 ----------------------------------------------------------------------------------------------------- 29 Al 1 -3.738321474645545e-01 -3.738321475480062e-01 8.34517e-11 1.56717e-09 2 -7.330676212016853e-01 -7.330676212170506e-01 1.53653e-11 1.32509e-10 3 6.993810845538774e-01 6.993810845347074e-01 1.91700e-11 2.33681e-10 ----------------------------------------------------------------------------------------------------- 30 Al 1 -6.861677639795771e-02 -6.861677638095053e-02 1.70072e-11 9.22030e-11 2 6.349645344400621e-01 6.349645344573175e-01 1.72554e-11 5.02517e-10 3 -4.154900254077792e-01 -4.154900253855544e-01 2.22248e-11 5.17233e-11 ----------------------------------------------------------------------------------------------------- 31 Al 1 -4.892079588221049e-02 -4.892079589383812e-02 1.16276e-11 3.13117e-10 2 -9.138606173315145e-01 -9.138606173642174e-01 3.27030e-11 1.44162e-10 3 5.063761169737484e-01 5.063761169556140e-01 1.81344e-11 6.25669e-10 ----------------------------------------------------------------------------------------------------- 32 Al 1 5.423653762813858e-01 5.423653762507895e-01 3.05963e-11 5.81127e-09 * 2 7.862044082698962e-01 7.862044083145070e-01 4.46108e-11 8.40494e-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 6.869122780259266e-01 9.97347e-12 6.81344e-12 2 6.775423324474170e-01 6.775423324486491e-01 1.23213e-12 1.11708e-10 3 6.871543232025207e-01 6.871543232014747e-01 1.04594e-12 5.95998e-11 ----------------------------------------------------------------------------------------------------- 2 Fe 1 3.700110072586406e-02 3.700110072746344e-02 1.59938e-12 2.57584e-10 2 3.550452260034828e-02 3.550452260582582e-02 5.47754e-12 1.71577e-11 3 1.081547058475869e+00 1.081547058447135e+00 2.87343e-11 1.01642e-10 ----------------------------------------------------------------------------------------------------- 3 Fe 1 -9.161188015175978e-01 -9.161188014856398e-01 3.19580e-11 1.35913e-10 2 8.067712373387783e-01 8.067712373345214e-01 4.25693e-12 4.03785e-11 3 -2.831490755617643e-01 -2.831490756069379e-01 4.51735e-11 1.88738e-10 ----------------------------------------------------------------------------------------------------- 4 Fe 1 6.572768486442921e-01 6.572768486078193e-01 3.64728e-11 9.53757e-11 2 3.819018679590463e-01 3.819018679589721e-01 7.42184e-14 2.80950e-09 * 3 -7.760189044783637e-01 -7.760189045259520e-01 4.75883e-11 5.97506e-11 ----------------------------------------------------------------------------------------------------- 5 Fe 1 -3.799268676016624e-01 -3.799268676599136e-01 5.82512e-11 8.62652e-11 2 -8.945330216689176e-01 -8.945330216747553e-01 5.83777e-12 9.65603e-10 3 -8.307971495695484e-01 -8.307971495798725e-01 1.03241e-11 2.90599e-10 ----------------------------------------------------------------------------------------------------- 6 Fe 1 9.993042665624521e-01 9.993042665948961e-01 3.24440e-11 1.32493e-10 2 7.945842138785660e-01 7.945842138219682e-01 5.65978e-11 2.84509e-10 3 -1.349337213654709e+00 -1.349337213694954e+00 4.02447e-11 4.95944e-10 ----------------------------------------------------------------------------------------------------- 7 Fe 1 1.850365125232871e+00 1.850365125235338e+00 2.46647e-12 1.63986e-10 2 -2.414231698393692e+00 -2.414231698399278e+00 5.58620e-12 9.89608e-11 3 1.203836436780581e+00 1.203836436791110e+00 1.05294e-11 1.82074e-10 ----------------------------------------------------------------------------------------------------- 8 Fe 1 -3.493030379206328e+00 -3.493030379183453e+00 2.28750e-11 3.18811e-10 2 2.320895437019085e+00 2.320895437102077e+00 8.29918e-11 3.96385e-11 3 6.495270127317460e-01 6.495270126829948e-01 4.87511e-11 4.53750e-10 ----------------------------------------------------------------------------------------------------- 9 Fe 1 6.197143093066225e-01 6.197143092977917e-01 8.83082e-12 6.51027e-11 2 2.209880656616792e-01 2.209880656499274e-01 1.17518e-11 2.14044e-11 3 1.221749312946572e+00 1.221749312940332e+00 6.23923e-12 2.30382e-11 ----------------------------------------------------------------------------------------------------- 10 Fe 1 -8.023879275522279e-01 -8.023879275641072e-01 1.18793e-11 8.35718e-11 2 -6.261608791041798e-01 -6.261608791125602e-01 8.38041e-12 3.57753e-09 * 3 -7.065573106437256e-01 -7.065573106376313e-01 6.09435e-12 3.47556e-10 ----------------------------------------------------------------------------------------------------- 11 Fe 1 -7.762520539717315e-01 -7.762520539982701e-01 2.65387e-11 9.02678e-11 2 1.608093851165350e+00 1.608093851153350e+00 1.20008e-11 6.89761e-10 3 -1.300460998501849e+00 -1.300460998539013e+00 3.71632e-11 3.28121e-10 ----------------------------------------------------------------------------------------------------- 12 Fe 1 6.530595707136606e-01 6.530595707088334e-01 4.82725e-12 1.11029e-10 2 -9.260761204981516e-01 -9.260761204897350e-01 8.41660e-12 5.70849e-11 3 4.169687403862563e-01 4.169687403794198e-01 6.83653e-12 7.33691e-10 ----------------------------------------------------------------------------------------------------- 13 Fe 1 -2.012055788896967e+00 -2.012055788958642e+00 6.16756e-11 1.21335e-10 2 -8.428992317272238e-01 -8.428992317093660e-01 1.78578e-11 2.34320e-10 3 -4.739835928546144e-02 -4.739835927707169e-02 8.38975e-12 8.52006e-11 ----------------------------------------------------------------------------------------------------- 14 Fe 1 1.587853021096175e+00 1.587853021094845e+00 1.32960e-12 3.23558e-10 2 1.371391964632991e+00 1.371391964657755e+00 2.47642e-11 2.19016e-10 3 -6.403608163398924e-01 -6.403608163411036e-01 1.21125e-12 3.30177e-10 ----------------------------------------------------------------------------------------------------- 15 Fe 1 8.667059327200882e-03 8.667059382885004e-03 5.56841e-11 1.07101e-09 2 -1.053947412184419e+00 -1.053947412203126e+00 1.87066e-11 3.46311e-10 3 -1.233854120468059e+00 -1.233854120462423e+00 5.63594e-12 4.78243e-10 ----------------------------------------------------------------------------------------------------- 16 Fe 1 8.446831207993817e-03 8.446831134988876e-03 7.30049e-11 1.15445e-09 2 -4.390576739087957e-01 -4.390576739024627e-01 6.33299e-12 9.68801e-11 3 1.712637673287720e+00 1.712637673300115e+00 1.23948e-11 3.31458e-10 ----------------------------------------------------------------------------------------------------- 17 Fe 1 5.349877525082049e-01 5.349877524524308e-01 5.57741e-11 4.94572e-11 2 -1.711492725594775e+00 -1.711492725586549e+00 8.22609e-12 1.14466e-10 3 -1.766970519262429e+00 -1.766970519268126e+00 5.69722e-12 5.41279e-10 ----------------------------------------------------------------------------------------------------- 18 Fe 1 -4.749087682111026e-01 -4.749087682170438e-01 5.94114e-12 3.70358e-10 2 -2.085501580913972e+00 -2.085501580840779e+00 7.31935e-11 2.71584e-10 3 1.048691787000501e+00 1.048691786966725e+00 3.37761e-11 5.84996e-10 ----------------------------------------------------------------------------------------------------- 19 Fe 1 3.795616037134072e-01 3.795616038579491e-01 1.44542e-10 1.61907e-10 2 7.191321218399294e-01 7.191321218432793e-01 3.34999e-12 1.66790e-10 3 -6.812922302160663e-01 -6.812922302501718e-01 3.41055e-11 1.39577e-10 ----------------------------------------------------------------------------------------------------- 20 Fe 1 -1.167365503138748e-01 -1.167365502940351e-01 1.98397e-11 1.79187e-07 * 2 1.972694764694076e+00 1.972694764668917e+00 2.51590e-11 1.23759e-10 3 1.695325868302859e+00 1.695325868305684e+00 2.82485e-12 4.65983e-12 ----------------------------------------------------------------------------------------------------- 21 Fe 1 -8.450270941539044e-01 -8.450270941693048e-01 1.54003e-11 3.44287e-10 2 -7.596047412109549e-01 -7.596047412062502e-01 4.70468e-12 8.47074e-11 3 -6.415852349003837e-01 -6.415852349561444e-01 5.57607e-11 5.88363e-10 ----------------------------------------------------------------------------------------------------- 22 Fe 1 1.260412831069654e+00 1.260412831070576e+00 9.22595e-13 1.20618e-10 2 -5.972638167331166e-01 -5.972638167707702e-01 3.76537e-11 8.91381e-11 3 8.675696507386045e-01 8.675696506963582e-01 4.22463e-11 1.42611e-08 * ----------------------------------------------------------------------------------------------------- 23 Fe 1 1.158315990928914e+00 1.158315990920300e+00 8.61422e-12 7.61666e-11 2 -6.000572579787414e-01 -6.000572580202047e-01 4.14633e-11 7.36943e-11 3 2.883824199889330e-01 2.883824199855125e-01 3.42054e-12 3.49789e-09 * ----------------------------------------------------------------------------------------------------- 24 Fe 1 -1.240660168348619e+00 -1.240660168385171e+00 3.65517e-11 1.61601e-09 2 8.132169979791952e-01 8.132169979420482e-01 3.71471e-11 3.46716e-09 * 3 6.520708575341623e-01 6.520708575124834e-01 2.16789e-11 4.81489e-11 ----------------------------------------------------------------------------------------------------- 25 Fe 1 -3.615543068772302e-01 -3.615543069265691e-01 4.93389e-11 9.34117e-11 2 -8.112691147115649e-01 -8.112691147213882e-01 9.82325e-12 8.03908e-10 3 -6.015881952997203e-01 -6.015881953717432e-01 7.20229e-11 4.72797e-10 ----------------------------------------------------------------------------------------------------- 26 Fe 1 4.363862305645658e-01 4.363862305659621e-01 1.39627e-12 4.67282e-09 * 2 -1.998414388980083e-01 -1.998414389249404e-01 2.69321e-11 2.27741e-10 3 -2.493678853251876e-01 -2.493678853509813e-01 2.57937e-11 2.92980e-09 * ----------------------------------------------------------------------------------------------------- 27 Fe 1 -3.249049191138263e-03 -3.249049197147556e-03 6.00929e-12 9.51759e-11 2 4.680899927939714e-01 4.680899927142798e-01 7.96916e-11 3.20890e-10 3 -2.135390375610013e-01 -2.135390375690250e-01 8.02369e-12 5.00417e-10 ----------------------------------------------------------------------------------------------------- 28 Fe 1 7.013319237414870e-01 7.013319237631599e-01 2.16729e-11 7.82087e-11 2 -3.233759629979375e-01 -3.233759629696941e-01 2.82434e-11 3.49222e-11 3 -4.104334052651841e-01 -4.104334052494351e-01 1.57490e-11 2.46914e-10 ----------------------------------------------------------------------------------------------------- 29 Fe 1 -1.540099451462839e-01 -1.540099451679697e-01 2.16858e-11 2.12121e-09 * 2 1.420245597194488e+00 1.420245597193973e+00 5.14921e-13 2.35192e-11 3 -6.407238339082285e-01 -6.407238338952600e-01 1.29685e-11 1.03656e-10 ----------------------------------------------------------------------------------------------------- 30 Fe 1 1.209732283827052e-01 1.209732283658303e-01 1.68749e-11 1.16133e-06 * 2 1.071068613583476e+00 1.071068613583525e+00 4.90719e-14 1.40054e-10 3 1.978254574855285e+00 1.978254574842196e+00 1.30884e-11 6.84715e-11 ----------------------------------------------------------------------------------------------------- 31 Fe 1 -1.364344197685735e-01 -1.364344197118221e-01 5.67514e-11 1.87939e-09 * 2 5.455885108754372e-01 5.455885108603161e-01 1.51211e-11 1.07729e-10 3 -4.003297736541368e-01 -4.003297737010317e-01 4.68949e-11 2.15579e-10 ----------------------------------------------------------------------------------------------------- 32 Fe 1 1.178214899527132e-02 1.178214898462803e-02 1.06433e-11 1.08865e-10 2 -9.423974151393871e-01 -9.423974151591007e-01 1.97136e-11 8.18425e-11 3 -7.299516523358990e-01 -7.299516523297962e-01 6.10278e-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 2.231880039656189e-02 2.93860e-12 1.32750e-11 2 2.648389394910570e-01 2.648389394901282e-01 9.28868e-13 9.76434e-11 3 -1.476472258127495e-03 -1.476472262525099e-03 4.39760e-12 7.35833e-12 ----------------------------------------------------------------------------------------------------- 2 Al 1 -6.007748035666831e-01 -6.007748035430133e-01 2.36698e-11 2.69493e-10 2 1.343397543340805e+00 1.343397543338289e+00 2.51599e-12 5.89149e-11 3 -9.873748427445063e-01 -9.873748427611759e-01 1.66697e-11 2.83789e-10 ----------------------------------------------------------------------------------------------------- 3 Fe 1 1.097187222339834e+00 1.097187222314929e+00 2.49054e-11 6.75315e-11 2 -6.176893202594201e-01 -6.176893202415625e-01 1.78576e-11 1.02535e-10 3 8.428320616918208e-01 8.428320617027836e-01 1.09628e-11 8.36397e-11 ----------------------------------------------------------------------------------------------------- 4 Al 1 -8.057366123866704e-01 -8.057366123596518e-01 2.70186e-11 4.31898e-10 2 1.262067092121021e+00 1.262067092112735e+00 8.28537e-12 8.75915e-11 3 1.076201458907571e+00 1.076201458879608e+00 2.79627e-11 8.71978e-11 ----------------------------------------------------------------------------------------------------- 5 Al 1 4.548526439373674e-01 4.548526439521526e-01 1.47852e-11 7.26425e-11 2 -1.023827286478161e+00 -1.023827286516729e+00 3.85676e-11 2.33811e-10 3 -1.925628039987793e-01 -1.925628040271610e-01 2.83817e-11 8.00634e-11 ----------------------------------------------------------------------------------------------------- 6 Al 1 7.586353494842512e-01 7.586353494968363e-01 1.25852e-11 4.01036e-11 2 5.268266834486806e-01 5.268266834451942e-01 3.48632e-12 2.94925e-10 3 -1.253349095447122e+00 -1.253349095442868e+00 4.25393e-12 2.88907e-10 ----------------------------------------------------------------------------------------------------- 7 Al 1 1.052030843549208e+00 1.052030843477040e+00 7.21676e-11 1.94837e-10 2 -9.088338283924133e-01 -9.088338284166319e-01 2.42185e-11 1.34764e-10 3 3.499183958266373e-01 3.499183958393356e-01 1.26983e-11 1.14283e-10 ----------------------------------------------------------------------------------------------------- 8 Al 1 -2.781558579436130e+00 -2.781558579443301e+00 7.17160e-12 1.89910e-10 2 -1.315420685736243e+00 -1.315420685690537e+00 4.57068e-11 1.31163e-08 * 3 6.622446648298678e-01 6.622446648918799e-01 6.20122e-11 1.49803e-09 * ----------------------------------------------------------------------------------------------------- 9 Fe 1 3.516383831194921e-01 3.516383831104284e-01 9.06364e-12 7.39872e-10 2 -6.266191969445537e-01 -6.266191969339781e-01 1.05757e-11 9.66615e-10 3 6.784724824752640e-01 6.784724824290183e-01 4.62458e-11 9.00366e-11 ----------------------------------------------------------------------------------------------------- 10 Al 1 -9.437250387679610e-01 -9.437250387922305e-01 2.42695e-11 1.16416e-10 2 1.103298919859725e+00 1.103298919847026e+00 1.26985e-11 6.38840e-10 3 2.982429761219674e-01 2.982429761179295e-01 4.03788e-12 1.78966e-10 ----------------------------------------------------------------------------------------------------- 11 Fe 1 1.770776385711662e+00 1.770776385662066e+00 4.95968e-11 3.41510e-10 2 -1.962717489330073e+00 -1.962717489437267e+00 1.07194e-10 3.53766e-10 3 -4.861900469863524e-01 -4.861900470156268e-01 2.92745e-11 7.67100e-11 ----------------------------------------------------------------------------------------------------- 12 Fe 1 -2.349658113661859e+00 -2.349658113662302e+00 4.42757e-13 4.30267e-10 2 1.670407420536828e+00 1.670407420586345e+00 4.95168e-11 3.35978e-10 3 -8.992618412829680e-01 -8.992618412898656e-01 6.89759e-12 4.61542e-12 ----------------------------------------------------------------------------------------------------- 13 Al 1 1.213746313552901e+00 1.213746313551297e+00 1.60316e-12 1.06789e-09 2 -4.247991501884638e-01 -4.247991502052482e-01 1.67844e-11 9.81909e-11 3 1.558253022742028e-02 1.558253025797673e-02 3.05564e-11 8.09570e-11 ----------------------------------------------------------------------------------------------------- 14 Fe 1 -5.519657022510248e-01 -5.519657022491938e-01 1.83098e-12 1.84031e-10 2 -7.729523639618120e-01 -7.729523639508026e-01 1.10094e-11 8.73769e-11 3 6.495986073930402e-01 6.495986073952453e-01 2.20512e-12 1.36617e-10 ----------------------------------------------------------------------------------------------------- 15 Al 1 1.969558919745289e+00 1.969558919716189e+00 2.91005e-11 1.01627e-08 * 2 3.297925671525263e+00 3.297925671570259e+00 4.49960e-11 2.33808e-10 3 -1.006491110934980e+00 -1.006491110920134e+00 1.48459e-11 1.30988e-10 ----------------------------------------------------------------------------------------------------- 16 Fe 1 -1.133976652551781e+00 -1.133976652523998e+00 2.77827e-11 8.33678e-11 2 -5.366219732544921e-01 -5.366219732125362e-01 4.19559e-11 2.55201e-09 * 3 -9.265312959109837e-01 -9.265312959069874e-01 3.99636e-12 7.09384e-11 ----------------------------------------------------------------------------------------------------- 17 Fe 1 5.124703819756490e-01 5.124703819916102e-01 1.59612e-11 1.07316e-10 2 6.510000647199342e-01 6.510000647146671e-01 5.26712e-12 1.14565e-10 3 3.626718910684866e-01 3.626718911454486e-01 7.69620e-11 1.67301e-10 ----------------------------------------------------------------------------------------------------- 18 Fe 1 -1.757559548016024e+00 -1.757559548053987e+00 3.79630e-11 4.58778e-10 2 -1.927223696523678e+00 -1.927223696455546e+00 6.81313e-11 1.64724e-10 3 -1.492814829262356e+00 -1.492814829235927e+00 2.64284e-11 1.03450e-10 ----------------------------------------------------------------------------------------------------- 19 Fe 1 -2.464681006056480e-01 -2.464681005832640e-01 2.23840e-11 1.18495e-10 2 -4.681647002208109e-02 -4.681647006408607e-02 4.20050e-11 2.57607e-10 3 -6.202547043235355e-01 -6.202547043204981e-01 3.03735e-12 3.25691e-10 ----------------------------------------------------------------------------------------------------- 20 Al 1 5.961374849282505e-01 5.961374849264258e-01 1.82465e-12 4.19775e-11 2 -3.870040836488956e-01 -3.870040836360223e-01 1.28733e-11 1.11028e-10 3 -6.216006561064485e-01 -6.216006561120146e-01 5.56610e-12 1.07239e-10 ----------------------------------------------------------------------------------------------------- 21 Al 1 -9.315134007783484e-01 -9.315134007256235e-01 5.27249e-11 1.67694e-10 2 8.855724850506211e-01 8.855724850217129e-01 2.89082e-11 1.62492e-10 3 1.390327347625271e+00 1.390327347561645e+00 6.36264e-11 7.40479e-10 ----------------------------------------------------------------------------------------------------- 22 Fe 1 4.405449423622823e-01 4.405449424381856e-01 7.59033e-11 1.52965e-10 2 -1.245193546121000e+00 -1.245193546108404e+00 1.25950e-11 4.80709e-09 * 3 8.869887561420114e-01 8.869887561470087e-01 4.99722e-12 5.53740e-11 ----------------------------------------------------------------------------------------------------- 23 Al 1 -5.804144619593016e-01 -5.804144620082575e-01 4.89560e-11 2.19053e-10 2 4.122236863188417e-01 4.122236863217666e-01 2.92488e-12 4.63740e-11 3 -7.884261353684603e-01 -7.884261353812069e-01 1.27466e-11 2.81300e-10 ----------------------------------------------------------------------------------------------------- 24 Fe 1 1.360054737940802e+00 1.360054737966956e+00 2.61546e-11 2.72809e-10 2 -1.784315407755960e+00 -1.784315407735380e+00 2.05798e-11 2.03539e-10 3 1.938725269994485e+00 1.938725269997065e+00 2.57949e-12 1.35098e-10 ----------------------------------------------------------------------------------------------------- 25 Fe 1 1.789033189325727e-01 1.789033189553326e-01 2.27598e-11 5.18410e-11 2 7.000971224998188e-01 7.000971224899250e-01 9.89386e-12 4.66057e-10 3 -4.923929634444450e-01 -4.923929634635456e-01 1.91006e-11 6.70413e-11 ----------------------------------------------------------------------------------------------------- 26 Al 1 -1.187661385305271e-01 -1.187661385055333e-01 2.49938e-11 5.79196e-09 * 2 -3.472039194164185e-01 -3.472039194160285e-01 3.90021e-13 4.33127e-10 3 1.055598516487691e+00 1.055598516490235e+00 2.54463e-12 4.65846e-10 ----------------------------------------------------------------------------------------------------- 27 Fe 1 -7.855670491563086e-01 -7.855670491762978e-01 1.99892e-11 8.65972e-11 2 1.059664848536609e+00 1.059664848530176e+00 6.43330e-12 6.30993e-10 3 1.002021148613835e+00 1.002021148636858e+00 2.30238e-11 8.34757e-11 ----------------------------------------------------------------------------------------------------- 28 Al 1 1.105246505066341e+00 1.105246505069749e+00 3.40816e-12 7.56215e-11 2 -7.203282041689626e-01 -7.203282041720385e-01 3.07587e-12 1.40826e-11 3 -9.023267300949807e-01 -9.023267301046928e-01 9.71212e-12 3.07067e-10 ----------------------------------------------------------------------------------------------------- 29 Al 1 5.436753040721731e-01 5.436753040697382e-01 2.43494e-12 2.98622e-11 2 2.200470428078594e+00 2.200470428046711e+00 3.18829e-11 5.05435e-09 * 3 -8.789915229643963e-01 -8.789915230174884e-01 5.30921e-11 4.30412e-10 ----------------------------------------------------------------------------------------------------- 30 Fe 1 3.770491962909429e-01 3.770491962639492e-01 2.69936e-11 7.48350e-11 2 -7.783975080171730e-01 -7.783975080208647e-01 3.69171e-12 1.40237e-10 3 9.367604161610377e-01 9.367604161653371e-01 4.29945e-12 7.89934e-10 ----------------------------------------------------------------------------------------------------- 31 Fe 1 -4.075743249782796e-01 -4.075743249771699e-01 1.10967e-12 2.64593e-10 2 2.869075743998949e-01 2.869075743724027e-01 2.74922e-11 1.27023e-10 3 -5.153391704034638e-01 -5.153391703910883e-01 1.23754e-11 4.66090e-09 * ----------------------------------------------------------------------------------------------------- 32 Al 1 1.904317932380279e-01 1.904317932427570e-01 4.72905e-12 2.05308e-11 2 -2.387343497078912e-01 -2.387343497078800e-01 1.11855e-14 3.15728e-09 * 3 -8.080230203450132e-02 -8.080230203208226e-02 2.41906e-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 = ----------------------- = 2.97845e-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.