!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 : EAM_Dynamo_MishinMehlPapaconstantopoulos_2002_NiAl__MO_109933561507_005 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 = 4.0515266418457045 | (Configuration in file "config-Al.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Al 1 5.344203440739886e-02 5.344203436034337e-02 4.70555e-11 2.57435e-10 2 -1.841151957609842e-01 -1.841151958208943e-01 5.99101e-11 1.12907e-10 3 -5.187490858726385e-01 -5.187490858453233e-01 2.73152e-11 1.56275e-10 ----------------------------------------------------------------------------------------------------- 2 Al 1 -1.311416289221876e+00 -1.311416289174964e+00 4.69118e-11 6.23732e-11 2 2.437587281248413e+00 2.437587281233514e+00 1.48983e-11 1.98167e-10 3 1.254095243268217e-01 1.254095243282835e-01 1.46175e-12 1.30024e-09 ----------------------------------------------------------------------------------------------------- 3 Al 1 3.349247020685331e-01 3.349247021627791e-01 9.42460e-11 2.55947e-10 2 -5.708355018572877e-01 -5.708355018652159e-01 7.92821e-12 9.17646e-11 3 7.483768682018094e-01 7.483768681856442e-01 1.61652e-11 1.16901e-10 ----------------------------------------------------------------------------------------------------- 4 Al 1 2.049191648416258e-01 2.049191647783777e-01 6.32480e-11 3.47352e-10 2 5.327586939533455e-01 5.327586940198514e-01 6.65059e-11 5.07411e-10 3 6.735427529908876e-01 6.735427530316674e-01 4.07798e-11 9.30619e-11 ----------------------------------------------------------------------------------------------------- 5 Al 1 1.747391575935598e+00 1.747391575915881e+00 1.97167e-11 1.85429e-10 2 -1.206946116690337e+00 -1.206946116840012e+00 1.49675e-10 1.74647e-08 * 3 2.599214130824289e-01 2.599214130795413e-01 2.88758e-12 1.13050e-09 ----------------------------------------------------------------------------------------------------- 6 Al 1 -6.274188327138144e-01 -6.274188327294167e-01 1.56023e-11 1.01407e-10 2 6.211281368154130e-01 6.211281368056148e-01 9.79816e-12 1.67566e-10 3 5.150760459751856e-01 5.150760458779043e-01 9.72813e-11 4.38125e-10 ----------------------------------------------------------------------------------------------------- 7 Al 1 4.137743232537494e-01 4.137743232793280e-01 2.55787e-11 8.83208e-11 2 -3.374672879417996e+00 -3.374672879351587e+00 6.64087e-11 1.70711e-09 3 -3.791115903311918e+00 -3.791115903447714e+00 1.35795e-10 1.27721e-09 ----------------------------------------------------------------------------------------------------- 8 Al 1 -2.082067886582847e+00 -2.082067886655374e+00 7.25264e-11 2.47255e-10 2 -1.006690834458815e+00 -1.006690834318318e+00 1.40497e-10 1.59491e-09 3 -7.400879949267399e-01 -7.400879949392878e-01 1.25479e-11 8.41734e-10 ----------------------------------------------------------------------------------------------------- 9 Al 1 -4.771210260270097e-01 -4.771210260157580e-01 1.12517e-11 2.35597e-10 2 -1.488336336975120e+00 -1.488336337015619e+00 4.04989e-11 1.11319e-10 3 -1.957019264971695e+00 -1.957019264882049e+00 8.96456e-11 9.81922e-10 ----------------------------------------------------------------------------------------------------- 10 Al 1 -9.080397694522522e-01 -9.080397692567403e-01 1.95512e-10 2.04290e-10 2 3.772461749830370e-01 3.772461749382997e-01 4.47373e-11 3.64219e-10 3 -1.238192647171832e+00 -1.238192647159070e+00 1.27620e-11 1.43401e-09 ----------------------------------------------------------------------------------------------------- 11 Al 1 4.206052861035923e+00 4.206052861100164e+00 6.42411e-11 3.23448e-10 2 -1.480863291351119e+00 -1.480863291288400e+00 6.27194e-11 2.59996e-09 * 3 -8.811498414998116e-01 -8.811498414704095e-01 2.94020e-11 4.45293e-10 ----------------------------------------------------------------------------------------------------- 12 Al 1 -1.614740837002562e-01 -1.614740836925787e-01 7.67750e-12 1.20741e-09 2 2.400057041453751e+00 2.400057041538390e+00 8.46394e-11 1.82012e-09 3 6.080178490788568e-01 6.080178490844965e-01 5.63971e-12 1.81410e-10 ----------------------------------------------------------------------------------------------------- 13 Al 1 -2.356793734103964e+00 -2.356793734106741e+00 2.77778e-12 5.51496e-10 2 -2.305322067798909e+00 -2.305322067799282e+00 3.73035e-13 1.22038e-09 3 -3.666801245813528e+00 -3.666801245711375e+00 1.02153e-10 3.67390e-10 ----------------------------------------------------------------------------------------------------- 14 Al 1 -2.570950603148871e-02 -2.570950603100623e-02 4.82482e-13 4.96836e-10 2 2.022719418716475e-01 2.022719418801182e-01 8.47064e-12 3.91967e-10 3 3.550397305606419e-01 3.550397305630786e-01 2.43672e-12 3.05350e-10 ----------------------------------------------------------------------------------------------------- 15 Al 1 3.756131957148358e+00 3.756131957105052e+00 4.33062e-11 5.94534e-10 2 -6.376346574354506e-01 -6.376346574742549e-01 3.88043e-11 5.49078e-10 3 1.383109423124325e+00 1.383109423084379e+00 3.99458e-11 2.73025e-10 ----------------------------------------------------------------------------------------------------- 16 Al 1 6.949699060253399e-01 6.949699060708320e-01 4.54921e-11 4.83907e-10 2 2.074436885343597e+00 2.074436885355082e+00 1.14855e-11 4.66132e-10 3 1.890331863477870e+00 1.890331863287138e+00 1.90731e-10 2.07454e-10 ----------------------------------------------------------------------------------------------------- 17 Al 1 4.509035047723686e-02 4.509035051077034e-02 3.35335e-11 2.90832e-10 2 -7.837211342685364e-01 -7.837211343796661e-01 1.11130e-10 3.36099e-10 3 -1.469808248161500e+00 -1.469808248194086e+00 3.25855e-11 5.46778e-11 ----------------------------------------------------------------------------------------------------- 18 Al 1 2.282419106905740e-01 2.282419106332213e-01 5.73526e-11 6.95401e-10 2 1.377500938877445e+00 1.377500938996541e+00 1.19096e-10 4.58473e-10 3 8.332368481162066e-01 8.332368480269053e-01 8.93012e-11 1.63278e-10 ----------------------------------------------------------------------------------------------------- 19 Al 1 1.031346136844462e+00 1.031346136896009e+00 5.15474e-11 1.04794e-09 2 -1.108427066267260e-01 -1.108427065528899e-01 7.38361e-11 3.08449e-10 3 -4.342963965320391e-01 -4.342963965146713e-01 1.73677e-11 5.68104e-10 ----------------------------------------------------------------------------------------------------- 20 Al 1 1.707728970851486e-01 1.707728971139277e-01 2.87792e-11 4.46981e-10 2 2.010623673131653e+00 2.010623673150541e+00 1.88884e-11 3.21827e-10 3 5.361704314874782e-01 5.361704314950682e-01 7.58993e-12 1.34678e-10 ----------------------------------------------------------------------------------------------------- 21 Al 1 -3.190595981972620e+00 -3.190595981801787e+00 1.70832e-10 4.67164e-10 2 6.075616845683309e-02 6.075616841658364e-02 4.02494e-11 4.15397e-10 3 -8.171495217262881e-01 -8.171495216939282e-01 3.23599e-11 2.55936e-10 ----------------------------------------------------------------------------------------------------- 22 Al 1 6.498885499031133e-01 6.498885499184354e-01 1.53221e-11 8.12973e-10 2 4.125630233499862e+00 4.125630233608958e+00 1.09096e-10 1.72022e-10 3 2.972617656509514e+00 2.972617656445686e+00 6.38281e-11 1.98030e-10 ----------------------------------------------------------------------------------------------------- 23 Al 1 1.368514164921445e+00 1.368514164888313e+00 3.31317e-11 8.84263e-10 2 1.168429265104093e-02 1.168429270945183e-02 5.84109e-11 1.81006e-10 3 1.740213508893250e+00 1.740213508923134e+00 2.98843e-11 1.65414e-09 ----------------------------------------------------------------------------------------------------- 24 Al 1 -5.884722357518275e-01 -5.884722358360420e-01 8.42145e-11 2.50355e-10 2 4.466592869432168e-01 4.466592869556692e-01 1.24524e-11 1.58792e-09 3 -8.466574983250588e-01 -8.466574982442642e-01 8.07946e-11 3.07298e-10 ----------------------------------------------------------------------------------------------------- 25 Al 1 -2.185105635033450e+00 -2.185105635135013e+00 1.01563e-10 1.04816e-09 2 -1.320226838462276e+00 -1.320226838467644e+00 5.36837e-12 2.72780e-10 3 3.713915419776959e+00 3.713915420001140e+00 2.24181e-10 7.09868e-10 ----------------------------------------------------------------------------------------------------- 26 Al 1 -8.269294374546512e-01 -8.269294375377865e-01 8.31353e-11 1.10465e-09 2 1.654164869579282e+00 1.654164869584569e+00 5.28666e-12 1.42037e-10 3 -2.033034426870129e+00 -2.033034426815877e+00 5.42526e-11 8.36624e-10 ----------------------------------------------------------------------------------------------------- 27 Al 1 1.986568317940168e+00 1.986568317737388e+00 2.02781e-10 6.16641e-10 2 -5.300369171747014e+00 -5.300369171767190e+00 2.01759e-11 7.05364e-10 3 6.180006551565898e-01 6.180006551676084e-01 1.10186e-11 8.01219e-10 ----------------------------------------------------------------------------------------------------- 28 Al 1 -2.376053897069286e+00 -2.376053896932791e+00 1.36495e-10 8.05935e-10 2 2.204860806564152e+00 2.204860806663208e+00 9.90568e-11 1.12750e-09 3 -2.231379342893244e-01 -2.231379344031057e-01 1.13781e-10 1.61459e-10 ----------------------------------------------------------------------------------------------------- 29 Al 1 -1.113538392904615e+00 -1.113538392868083e+00 3.65317e-11 1.15941e-09 2 -1.073522425357593e+00 -1.073522425463554e+00 1.05962e-10 5.34097e-10 3 6.019731643087812e-01 6.019731643390477e-01 3.02665e-11 5.85167e-10 ----------------------------------------------------------------------------------------------------- 30 Al 1 -4.771116344225323e-01 -4.771116343191928e-01 1.03340e-10 3.81498e-10 2 4.948393159207840e-01 4.948393159245444e-01 3.76049e-12 2.43366e-10 3 1.917199832869518e-01 1.917199833269556e-01 4.00038e-11 5.13671e-10 ----------------------------------------------------------------------------------------------------- 31 Al 1 9.908655653960513e-01 9.908655654859664e-01 8.99151e-11 5.79439e-10 2 -1.134565426620022e+00 -1.134565426614135e+00 5.88729e-12 9.33500e-10 3 2.979628934330992e-01 2.979628933539787e-01 7.91205e-11 2.62013e-10 ----------------------------------------------------------------------------------------------------- 32 Al 1 8.249539244677662e-01 8.249539242338682e-01 2.33898e-10 8.38547e-10 2 9.464588435347153e-01 9.464588435338671e-01 8.48210e-13 1.82712e-10 3 5.525639776848458e-01 5.525639777921304e-01 1.07285e-10 4.12594e-10 ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as discontinuities. Maximum error obtained for particle = 23, direction = 2: |F_model - F_numer| error = ----------------------- = 4.99910e-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 = 3.4524641036987305 | (Configuration in file "config-Ni.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ni 1 1.407304288928021e+00 1.407304288865171e+00 6.28491e-11 8.22061e-10 2 1.035545812769842e+00 1.035545812867804e+00 9.79621e-11 5.74593e-10 3 1.400598491963059e+00 1.400598491970778e+00 7.71960e-12 1.75295e-11 ----------------------------------------------------------------------------------------------------- 2 Ni 1 -4.119659934235415e+00 -4.119659934366131e+00 1.30716e-10 1.38021e-09 2 2.571851976826644e+00 2.571851976954658e+00 1.28014e-10 7.78117e-10 3 -8.591653858351261e-01 -8.591653858373133e-01 2.18714e-12 8.15770e-09 * ----------------------------------------------------------------------------------------------------- 3 Ni 1 1.388405455980457e+00 1.388405456088720e+00 1.08263e-10 7.84115e-10 2 9.147631719445460e-01 9.147631720438845e-01 9.93384e-11 1.67688e-09 3 -9.962511689064999e-01 -9.962511688714076e-01 3.50923e-11 2.88474e-10 ----------------------------------------------------------------------------------------------------- 4 Ni 1 1.548775965696494e+00 1.548775965712009e+00 1.55154e-11 2.24837e-09 2 1.094204415370860e+00 1.094204415270272e+00 1.00588e-10 8.65867e-10 3 -8.784552307725879e-01 -8.784552308134358e-01 4.08479e-11 5.12360e-10 ----------------------------------------------------------------------------------------------------- 5 Ni 1 1.801819270026632e+00 1.801819270021661e+00 4.97069e-12 9.85225e-10 2 -6.426176830492001e+00 -6.426176830450137e+00 4.18643e-11 6.93129e-10 3 -3.745884563317671e+00 -3.745884563332481e+00 1.48099e-11 7.20591e-10 ----------------------------------------------------------------------------------------------------- 6 Ni 1 1.860293894791069e+00 1.860293894763551e+00 2.75182e-11 9.94202e-10 2 -2.711012446650642e+00 -2.711012446553624e+00 9.70188e-11 1.91233e-10 3 1.965364941064494e-01 1.965364941031438e-01 3.30561e-12 1.90074e-09 ----------------------------------------------------------------------------------------------------- 7 Ni 1 -1.859753428862983e+00 -1.859753428998471e+00 1.35489e-10 4.97898e-10 2 1.698131943336185e+00 1.698131943268138e+00 6.80473e-11 3.39738e-10 3 2.227705424951462e-02 2.227705416872576e-02 8.07889e-11 4.84625e-10 ----------------------------------------------------------------------------------------------------- 8 Ni 1 9.778046471104036e-01 9.778046472315227e-01 1.21119e-10 6.76345e-10 2 4.254740488722611e+00 4.254740488969006e+00 2.46395e-10 5.11614e-10 3 8.113718430164816e+00 8.113718430088603e+00 7.62128e-11 1.50141e-09 ----------------------------------------------------------------------------------------------------- 9 Ni 1 1.746032929288361e+00 1.746032929721737e+00 4.33376e-10 8.59655e-10 2 -5.396343887406917e-02 -5.396343883436660e-02 3.97026e-11 5.28132e-10 3 1.978733420130232e+00 1.978733420119438e+00 1.07947e-11 4.34650e-10 ----------------------------------------------------------------------------------------------------- 10 Ni 1 3.227753411897272e-02 3.227753405452687e-02 6.44459e-11 5.43916e-10 2 -1.491700372515234e+00 -1.491700372381919e+00 1.33315e-10 9.49034e-10 3 1.942018751682217e+00 1.942018751631429e+00 5.07876e-11 1.25113e-09 ----------------------------------------------------------------------------------------------------- 11 Ni 1 -8.280930814557579e-02 -8.280930802403058e-02 1.21545e-10 6.95034e-10 2 1.662351812489585e-01 1.662351811204365e-01 1.28522e-10 5.11160e-10 3 -5.439621445861832e-01 -5.439621445645668e-01 2.16164e-11 1.97204e-09 ----------------------------------------------------------------------------------------------------- 12 Ni 1 1.417905592941127e+00 1.417905592893710e+00 4.74174e-11 9.31404e-10 2 -1.832615649565053e+00 -1.832615649242807e+00 3.22246e-10 6.11792e-10 3 -2.171463766707984e-01 -2.171463766802940e-01 9.49560e-12 2.39217e-09 ----------------------------------------------------------------------------------------------------- 13 Ni 1 -4.715647798521779e+00 -4.715647798496255e+00 2.55245e-11 3.14263e-09 2 3.061021899992955e+00 3.061021900003252e+00 1.02971e-11 4.51818e-10 3 -1.362662289015535e+00 -1.362662289036022e+00 2.04876e-11 4.18834e-10 ----------------------------------------------------------------------------------------------------- 14 Ni 1 3.400542395396343e+00 3.400542395372762e+00 2.35807e-11 9.96753e-10 2 -8.749106264624009e-01 -8.749106265869787e-01 1.24578e-10 2.27239e-09 3 -2.696870767886150e+00 -2.696870768734686e+00 8.48535e-10 1.15355e-09 ----------------------------------------------------------------------------------------------------- 15 Ni 1 1.082281515964952e+00 1.082281515949181e+00 1.57716e-11 5.95320e-10 2 2.192937639736818e+00 2.192937639750038e+00 1.32205e-11 8.74121e-10 3 -1.120016096161927e+00 -1.120016096240348e+00 7.84210e-11 2.86594e-09 ----------------------------------------------------------------------------------------------------- 16 Ni 1 -5.890788845909984e+00 -5.890788845828316e+00 8.16671e-11 3.16855e-10 2 -1.052525539183783e+00 -1.052525539253833e+00 7.00497e-11 4.39823e-10 3 4.387766507551147e+00 4.387766507558742e+00 7.59481e-12 8.12754e-10 ----------------------------------------------------------------------------------------------------- 17 Ni 1 -1.427586366402441e+00 -1.427586366680724e+00 2.78283e-10 1.60112e-10 2 -6.859697772089109e-01 -6.859697772640502e-01 5.51392e-11 2.22317e-09 3 2.156466089743890e+00 2.156466089694154e+00 4.97353e-11 3.15854e-10 ----------------------------------------------------------------------------------------------------- 18 Ni 1 2.638110996120996e+00 2.638110996403981e+00 2.82985e-10 7.38199e-10 2 2.296532974017734e+00 2.296532974340302e+00 3.22568e-10 1.20973e-09 3 -2.335443344959524e+00 -2.335443344902349e+00 5.71756e-11 3.12973e-10 ----------------------------------------------------------------------------------------------------- 19 Ni 1 1.192941368057737e+00 1.192941368114552e+00 5.68150e-11 1.00319e-09 2 -9.881993976616268e-01 -9.881993977592216e-01 9.75948e-11 4.19291e-10 3 -5.061831275840977e-01 -5.061831275856842e-01 1.58651e-12 6.78911e-10 ----------------------------------------------------------------------------------------------------- 20 Ni 1 -4.665907039642002e-01 -4.665907040245689e-01 6.03687e-11 3.22910e-10 2 8.235337601267688e-01 8.235337599827035e-01 1.44065e-10 6.43037e-10 3 4.508475561545577e-01 4.508475562638485e-01 1.09291e-10 2.34990e-10 ----------------------------------------------------------------------------------------------------- 21 Ni 1 -8.357671476817368e-01 -8.357671478881711e-01 2.06434e-10 3.18880e-09 2 1.001957618642770e+00 1.001957618681245e+00 3.84748e-11 9.02936e-11 3 -7.408814363078758e-01 -7.408814362554951e-01 5.23808e-11 1.31645e-09 ----------------------------------------------------------------------------------------------------- 22 Ni 1 -5.543988972823991e-01 -5.543988972343981e-01 4.80010e-11 5.55615e-10 2 -2.554782463586421e+00 -2.554782463395246e+00 1.91175e-10 8.15454e-11 3 3.131238265688175e+00 3.131238265672581e+00 1.55933e-11 2.47197e-10 ----------------------------------------------------------------------------------------------------- 23 Ni 1 -9.755081845942699e-01 -9.755081847381566e-01 1.43887e-10 6.40886e-10 2 1.461357040873595e+00 1.461357040911772e+00 3.81772e-11 2.43464e-10 3 -1.172445561352941e+00 -1.172445561339006e+00 1.39353e-11 1.92637e-10 ----------------------------------------------------------------------------------------------------- 24 Ni 1 1.472764883954898e+00 1.472764883982827e+00 2.79294e-11 2.46548e-08 * 2 -1.512447607539193e+00 -1.512447607704687e+00 1.65494e-10 2.05888e-10 3 -2.268640271033758e-01 -2.268640272471247e-01 1.43749e-10 6.66423e-10 ----------------------------------------------------------------------------------------------------- 25 Ni 1 1.457982277668433e+00 1.457982277453709e+00 2.14724e-10 7.64319e-10 2 1.182719133704400e+00 1.182719133709278e+00 4.87788e-12 1.16536e-08 * 3 -7.099512624870905e-01 -7.099512624329842e-01 5.41063e-11 1.63432e-10 ----------------------------------------------------------------------------------------------------- 26 Ni 1 3.758968389213233e-01 3.758968388556730e-01 6.56503e-11 1.26821e-09 2 -1.653997312434867e+00 -1.653997312388938e+00 4.59288e-11 7.65933e-10 3 -1.257870811985985e+00 -1.257870811704978e+00 2.81007e-10 2.80896e-10 ----------------------------------------------------------------------------------------------------- 27 Ni 1 -5.758527647116798e+00 -5.758527647131117e+00 1.43183e-11 1.06083e-09 2 -9.107849072449790e-01 -9.107849078646706e-01 6.19692e-10 1.19769e-09 3 1.276915840901968e+00 1.276915840914501e+00 1.25329e-11 2.37844e-10 ----------------------------------------------------------------------------------------------------- 28 Ni 1 9.543545443698642e-01 9.543545444687067e-01 9.88425e-11 4.44295e-10 2 -1.282976224302852e+00 -1.282976224355229e+00 5.23770e-11 1.16841e-09 3 -7.650798173580280e-01 -7.650798173656818e-01 7.65377e-12 2.06361e-10 ----------------------------------------------------------------------------------------------------- 29 Ni 1 2.817095820832086e+00 2.817095820939278e+00 1.07192e-10 2.29933e-10 2 1.246946366783496e-01 1.246946368397143e-01 1.61365e-10 4.75586e-10 3 -3.919884316639876e+00 -3.919884316858054e+00 2.18177e-10 1.11381e-09 ----------------------------------------------------------------------------------------------------- 30 Ni 1 -1.061148246149334e+00 -1.061148246341127e+00 1.91793e-10 1.31616e-08 * 2 -7.837273689219678e-01 -7.837273689007769e-01 2.11909e-11 1.94405e-09 3 8.952343163894059e-01 8.952343163061568e-01 8.32491e-11 5.62763e-10 ----------------------------------------------------------------------------------------------------- 31 Ni 1 -1.809413537660680e+00 -1.809413537744327e+00 8.36469e-11 6.32937e-10 2 -2.844718168323873e-01 -2.844718168830899e-01 5.07026e-11 2.28077e-10 3 -1.829294064693310e+00 -1.829294064873561e+00 1.80252e-10 3.41390e-10 ----------------------------------------------------------------------------------------------------- 32 Ni 1 1.985009826359426e+00 1.985009826208809e+00 1.50618e-10 4.87899e-10 2 1.220034085483353e+00 1.220034085514205e+00 3.08518e-11 5.92405e-10 3 -6.803942510084633e-02 -6.803942513200772e-02 3.11614e-11 7.97112e-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 = 7, direction = 3: |F_model - F_numer| error = ----------------------- = 3.62655e-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 = 3.7322173316731826 | (Configuration in file "config-AlNi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ni 1 1.256474359042349e+00 1.256474359051573e+00 9.22418e-12 9.09819e-09 * 2 9.180952223432876e-01 9.180952223275235e-01 1.57641e-11 2.63399e-10 3 1.418980478389051e+00 1.418980478391246e+00 2.19536e-12 9.10865e-11 ----------------------------------------------------------------------------------------------------- 2 Al 1 1.823176019657221e+00 1.823176019715905e+00 5.86842e-11 2.39615e-10 2 2.868655796857105e-02 2.868655796264696e-02 5.92409e-12 7.36087e-10 3 -1.651626090313160e+00 -1.651626090324370e+00 1.12104e-11 2.42169e-10 ----------------------------------------------------------------------------------------------------- 3 Ni 1 4.782004028130414e-01 4.782004029984156e-01 1.85374e-10 1.78517e-09 2 1.487269814854538e+00 1.487269814951820e+00 9.72820e-11 1.70065e-10 3 6.898825311304067e-02 6.898825292892351e-02 1.84117e-10 1.22826e-09 ----------------------------------------------------------------------------------------------------- 4 Al 1 -1.368588299662494e+00 -1.368588299537522e+00 1.24972e-10 1.18918e-09 2 -1.269024019293322e+00 -1.269024019210131e+00 8.31906e-11 1.71733e-09 3 -2.232400510845025e-01 -2.232400510328407e-01 5.16619e-11 1.11774e-08 * ----------------------------------------------------------------------------------------------------- 5 Al 1 -4.707124858856411e+00 -4.707124858899323e+00 4.29115e-11 1.81456e-10 2 -1.426349099274804e+00 -1.426349099122812e+00 1.51992e-10 1.42092e-09 3 -1.894746924649417e+00 -1.894746924632452e+00 1.69651e-11 1.79892e-10 ----------------------------------------------------------------------------------------------------- 6 Al 1 6.215181816430648e+00 6.215181816392755e+00 3.78924e-11 2.55607e-09 2 -2.840896223379436e+00 -2.840896223373813e+00 5.62350e-12 2.70041e-09 3 -1.431882724504705e+00 -1.431882724555475e+00 5.07705e-11 1.24098e-09 ----------------------------------------------------------------------------------------------------- 7 Ni 1 1.500736117280190e+00 1.500736117523943e+00 2.43753e-10 1.28392e-09 2 7.380198472724230e-01 7.380198472602848e-01 1.21382e-11 4.36223e-10 3 3.836678107865353e+00 3.836678108022999e+00 1.57647e-10 6.98799e-10 ----------------------------------------------------------------------------------------------------- 8 Al 1 -2.707910867465725e+00 -2.707910867740916e+00 2.75191e-10 3.82688e-10 2 -3.209217529467781e+00 -3.209217529556726e+00 8.89449e-11 6.43495e-10 3 1.580772082472718e+00 1.580772082475127e+00 2.40830e-12 5.48811e-10 ----------------------------------------------------------------------------------------------------- 9 Ni 1 1.177069789593882e+00 1.177069789580811e+00 1.30707e-11 7.82531e-10 2 6.957956776988193e-01 6.957956777134323e-01 1.46130e-11 6.58775e-10 3 8.987803657216714e-01 8.987803659219492e-01 2.00278e-10 1.03346e-09 ----------------------------------------------------------------------------------------------------- 10 Al 1 1.284462208451129e-01 1.284462206532072e-01 1.91906e-10 4.38951e-10 2 -1.209971231688450e+00 -1.209971231743862e+00 5.54126e-11 2.88704e-10 3 2.598279794575717e-01 2.598279795678312e-01 1.10259e-10 3.44187e-10 ----------------------------------------------------------------------------------------------------- 11 Ni 1 -8.762373166582590e-01 -8.762373167893043e-01 1.31045e-10 3.92077e-09 * 2 -5.632921414138673e-01 -5.632921414677164e-01 5.38491e-11 2.30893e-10 3 -1.722666997746071e-01 -1.722666998170787e-01 4.24717e-11 2.46802e-10 ----------------------------------------------------------------------------------------------------- 12 Ni 1 1.101147837124094e+00 1.101147837171156e+00 4.70624e-11 3.17816e-10 2 -1.878444778421926e+00 -1.878444778365673e+00 5.62526e-11 2.02200e-10 3 7.186149894081540e-01 7.186149893438359e-01 6.43181e-11 3.17027e-10 ----------------------------------------------------------------------------------------------------- 13 Al 1 -5.268034380588259e+00 -5.268034380610488e+00 2.22293e-11 2.34742e-10 2 3.172455418000075e+00 3.172455417927742e+00 7.23328e-11 6.99720e-10 3 -3.078449721717729e+00 -3.078449721653203e+00 6.45262e-11 2.17178e-09 ----------------------------------------------------------------------------------------------------- 14 Ni 1 -2.067968765855910e-01 -2.067968766155781e-01 2.99871e-11 4.97486e-10 2 1.433863429136799e-01 1.433863428347127e-01 7.89673e-11 1.12070e-09 3 2.418818100807680e-01 2.418818101485347e-01 6.77666e-11 3.19241e-10 ----------------------------------------------------------------------------------------------------- 15 Al 1 4.181574408319014e+00 4.181574408372045e+00 5.30314e-11 8.95493e-10 2 1.088584901570098e+00 1.088584901263560e+00 3.06538e-10 8.60086e-10 3 3.656030795552685e+00 3.656030795525859e+00 2.68257e-11 3.05125e-10 ----------------------------------------------------------------------------------------------------- 16 Al 1 -2.403738609518923e+00 -2.403738609508067e+00 1.08558e-11 1.44500e-10 2 6.539303320487042e-01 6.539303320822709e-01 3.35667e-11 3.08453e-10 3 4.765823759186739e-01 4.765823759302560e-01 1.15821e-11 1.02956e-09 ----------------------------------------------------------------------------------------------------- 17 Al 1 1.049858833670842e+00 1.049858833672724e+00 1.88183e-12 2.96748e-09 2 2.702514532302067e-01 2.702514533235958e-01 9.33891e-11 1.33249e-09 3 4.445711115397816e-01 4.445711113424120e-01 1.97370e-10 1.87223e-09 ----------------------------------------------------------------------------------------------------- 18 Al 1 7.996158278849901e-01 7.996158278551033e-01 2.98868e-11 1.22056e-09 2 -5.996014039907388e+00 -5.996014040225915e+00 3.18527e-10 1.02177e-09 3 -4.000664172076657e+00 -4.000664172210497e+00 1.33840e-10 2.83976e-10 ----------------------------------------------------------------------------------------------------- 19 Ni 1 1.267737857311715e+00 1.267737857350641e+00 3.89266e-11 1.14931e-09 2 3.243299837228296e-01 3.243299837714077e-01 4.85781e-11 9.37017e-10 3 -1.335515245477232e+00 -1.335515245424272e+00 5.29599e-11 2.54961e-10 ----------------------------------------------------------------------------------------------------- 20 Al 1 -1.564592897632229e+00 -1.564592897398047e+00 2.34181e-10 4.38414e-10 2 -7.620438431187151e-01 -7.620438432107479e-01 9.20328e-11 5.04445e-10 3 3.849383021954221e-01 3.849383022581009e-01 6.26789e-11 4.24196e-10 ----------------------------------------------------------------------------------------------------- 21 Ni 1 -8.562949017302537e-02 -8.562949020923483e-02 3.62095e-11 8.47178e-11 2 1.572986313144004e+00 1.572986313093105e+00 5.08986e-11 1.49725e-09 3 3.668822160910735e-02 3.668822167756703e-02 6.84597e-11 3.22638e-10 ----------------------------------------------------------------------------------------------------- 22 Ni 1 -2.072825737482206e+00 -2.072825737594338e+00 1.12133e-10 3.16831e-10 2 -1.416255875631033e-01 -1.416255874737068e-01 8.93965e-11 7.57417e-10 3 -1.706688006798080e-01 -1.706688006304908e-01 4.93171e-11 9.62311e-10 ----------------------------------------------------------------------------------------------------- 23 Ni 1 -1.053074776490346e+00 -1.053074776364160e+00 1.26186e-10 1.32696e-09 2 1.381838670119587e+00 1.381838670009807e+00 1.09780e-10 1.08211e-09 3 -1.464312058500463e+00 -1.464312058413858e+00 8.66041e-11 4.60370e-10 ----------------------------------------------------------------------------------------------------- 24 Al 1 1.145675091197393e+00 1.145675091245081e+00 4.76883e-11 3.26477e-10 2 -6.508394809043376e-01 -6.508394809310233e-01 2.66857e-11 2.69660e-10 3 -1.274170577427793e+00 -1.274170577462662e+00 3.48683e-11 1.48500e-09 ----------------------------------------------------------------------------------------------------- 25 Al 1 -1.954494646673101e+00 -1.954494646632834e+00 4.02671e-11 4.29511e-10 2 4.460507478888169e+00 4.460507478993717e+00 1.05548e-10 8.85398e-11 3 5.175928411135403e-01 5.175928410503046e-01 6.32357e-11 8.30801e-10 ----------------------------------------------------------------------------------------------------- 26 Ni 1 1.680953313443972e+00 1.680953313480428e+00 3.64559e-11 5.10342e-10 2 -6.834495520405657e-01 -6.834495517926913e-01 2.47874e-10 6.29482e-10 3 -1.952966330863662e+00 -1.952966330826840e+00 3.68217e-11 2.36636e-09 ----------------------------------------------------------------------------------------------------- 27 Al 1 1.552110863366996e+00 1.552110863277188e+00 8.98082e-11 6.14039e-10 2 5.457300867017866e+00 5.457300866976848e+00 4.10179e-11 4.56188e-10 3 4.594520814637757e+00 4.594520814631578e+00 6.17817e-12 1.96875e-10 ----------------------------------------------------------------------------------------------------- 28 Ni 1 6.466068712642073e-02 6.466068707424029e-02 5.21804e-11 5.09137e-10 2 -1.099895549587729e+00 -1.099895549579636e+00 8.09219e-12 4.73848e-10 3 -2.488313002704191e-01 -2.488313003014283e-01 3.10093e-11 1.86981e-10 ----------------------------------------------------------------------------------------------------- 29 Ni 1 1.135653503612979e+00 1.135653503441427e+00 1.71552e-10 1.58178e-09 2 1.664835311522081e+00 1.664835311616789e+00 9.47080e-11 8.58982e-11 3 1.210733495332168e+00 1.210733495322923e+00 9.24505e-12 4.58416e-10 ----------------------------------------------------------------------------------------------------- 30 Al 1 -5.195857291045449e-01 -5.195857291392372e-01 3.46922e-11 3.56756e-09 2 -5.925266593575229e-01 -5.925266593696868e-01 1.21639e-11 3.94782e-10 3 1.793334755055874e+00 1.793334755299900e+00 2.44027e-10 2.14842e-10 ----------------------------------------------------------------------------------------------------- 31 Ni 1 -9.228866482934275e-01 -9.228866483277955e-01 3.43681e-11 1.33809e-10 2 -6.406403107661527e-01 -6.406403106510593e-01 1.15093e-10 4.36289e-10 3 -1.634583669751189e+00 -1.634583669446213e+00 3.04976e-10 4.46556e-10 ----------------------------------------------------------------------------------------------------- 32 Ni 1 -8.467518135363146e-01 -8.467518136032988e-01 6.69842e-11 4.55648e-10 2 -1.094044146129836e+00 -1.094044146162051e+00 3.22145e-11 3.43060e-10 3 -1.605592412371993e+00 -1.605592412149956e+00 2.22037e-10 1.84776e-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 = 3, direction = 3: |F_model - F_numer| error = ----------------------- = 2.66882e-09 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 4.99910e-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 4.99910e-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.