!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_KimKimJung_2016_AlTi__MO_618133763375_000 Supported species : Al Ti random seed = 13 perturbation amplitude = 0.250 number unit cells per side = 2 ----------------------------------------------------------------------------------------------------- Comparison of analytical forces obtained from the model, the force computed as a numerical derivative of the energy, the difference between them, and the uncertainty in the numerical estimate of the force. The computed equilibrium lattice constant for the crystal (a0) is given in the heading. MONOATOMIC STRUCTURE -- Species = Al | a0 = 4.044651031494141 | (Configuration in file "config-Al.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Al 1 3.436525911965789e-01 3.436525911962103e-01 3.68594e-13 8.19412e-11 2 -2.618077135066970e-02 -2.618077134246379e-02 8.20592e-12 1.67646e-09 * 3 3.437088995681828e-02 3.437088997925107e-02 2.24328e-11 2.62628e-09 * ----------------------------------------------------------------------------------------------------- 2 Al 1 -8.101099691017800e-01 -8.101099690966305e-01 5.14955e-12 1.68933e-10 2 8.600115920378795e-01 8.600115920137965e-01 2.40830e-11 1.28895e-10 3 3.127577390207467e-01 3.127577390218405e-01 1.09385e-12 1.17592e-11 ----------------------------------------------------------------------------------------------------- 3 Al 1 -8.242116320851114e-02 -8.242116318379669e-02 2.47145e-11 3.47104e-10 2 -4.844087934567273e-02 -4.844087930977662e-02 3.58961e-11 6.65230e-10 3 -2.547485505583829e-01 -2.547485506184553e-01 6.00724e-11 7.57109e-11 ----------------------------------------------------------------------------------------------------- 4 Al 1 4.983906972712699e-01 4.983906972848870e-01 1.36171e-11 1.02367e-10 2 2.408671156367183e-01 2.408671156298007e-01 6.91761e-12 1.63044e-10 3 3.779437014996986e-01 3.779437014642161e-01 3.54825e-11 4.41834e-11 ----------------------------------------------------------------------------------------------------- 5 Al 1 7.931111417768137e-01 7.931111417728759e-01 3.93785e-12 8.10714e-10 2 -3.817072359932426e-01 -3.817072360144322e-01 2.11896e-11 1.56436e-10 3 2.806999037568573e-01 2.806999037432166e-01 1.36407e-11 1.21565e-10 ----------------------------------------------------------------------------------------------------- 6 Al 1 -3.438254917523603e-01 -3.438254917440490e-01 8.31124e-12 1.20342e-10 2 2.501153026637515e-01 2.501153026677563e-01 4.00480e-12 6.85927e-11 3 3.380287586210458e-01 3.380287586301083e-01 9.06247e-12 1.32820e-09 ----------------------------------------------------------------------------------------------------- 7 Al 1 2.574680736984308e-01 2.574680736849549e-01 1.34759e-11 1.47935e-10 2 -1.219046612242066e+00 -1.219046612262273e+00 2.02069e-11 1.19399e-10 3 -1.651118750217780e+00 -1.651118750225451e+00 7.67142e-12 5.05653e-11 ----------------------------------------------------------------------------------------------------- 8 Al 1 -7.221783476917665e-01 -7.221783476951721e-01 3.40561e-12 1.79329e-10 2 -4.748262701343214e-01 -4.748262701502547e-01 1.59334e-11 2.16145e-10 3 -7.562197728107218e-01 -7.562197727083421e-01 1.02380e-10 1.71668e-10 ----------------------------------------------------------------------------------------------------- 9 Al 1 4.288843075342455e-02 4.288843076266633e-02 9.24178e-12 1.75662e-10 2 -1.188167833067991e+00 -1.188167833071561e+00 3.57070e-12 1.94918e-10 3 -1.184618248272586e+00 -1.184618248282853e+00 1.02676e-11 8.25618e-10 ----------------------------------------------------------------------------------------------------- 10 Al 1 -5.398641278301508e-01 -5.398641278114602e-01 1.86906e-11 4.20999e-11 2 4.980765562423825e-01 4.980765562427283e-01 3.45834e-13 4.01855e-09 * 3 -7.222686140810005e-01 -7.222686140815984e-01 5.97855e-13 2.63556e-10 ----------------------------------------------------------------------------------------------------- 11 Al 1 -3.572753881359405e-01 -3.572753881240894e-01 1.18510e-11 2.49441e-10 2 -8.581020031994876e-01 -8.581020032398184e-01 4.03308e-11 9.57195e-10 3 7.845981306438090e-01 7.845981306785340e-01 3.47250e-11 3.09379e-09 * ----------------------------------------------------------------------------------------------------- 12 Al 1 2.596028907967807e-02 2.596028908163869e-02 1.96062e-12 5.06429e-10 2 1.245097728346232e+00 1.245097728349031e+00 2.79865e-12 2.40915e-10 3 7.763446163722213e-01 7.763446163819090e-01 9.68770e-12 1.22900e-10 ----------------------------------------------------------------------------------------------------- 13 Al 1 -5.365341876815753e-01 -5.365341876619384e-01 1.96370e-11 4.49160e-09 * 2 -1.200162143003767e+00 -1.200162142991065e+00 1.27012e-11 1.19191e-10 3 -1.957550015823236e+00 -1.957550015840926e+00 1.76898e-11 7.40811e-10 ----------------------------------------------------------------------------------------------------- 14 Al 1 8.988775541241351e-02 8.988775541787830e-02 5.46480e-12 1.17706e-10 2 4.855436320620268e-01 4.855436320565924e-01 5.43438e-12 3.38328e-11 3 -1.387144392266403e-01 -1.387144392390290e-01 1.23886e-11 3.84984e-09 * ----------------------------------------------------------------------------------------------------- 15 Al 1 1.761450954861486e+00 1.761450955001500e+00 1.40013e-10 9.01348e-11 2 -6.436069113377252e-01 -6.436069114161602e-01 7.84350e-11 1.15220e-10 3 7.520276859211168e-01 7.520276858964818e-01 2.46350e-11 4.92524e-10 ----------------------------------------------------------------------------------------------------- 16 Al 1 5.978494647491811e-01 5.978494647608826e-01 1.17015e-11 9.09575e-10 2 1.336599645526329e+00 1.336599645525807e+00 5.22027e-13 2.55521e-10 3 8.753612998807425e-01 8.753612999025497e-01 2.18072e-11 2.67636e-10 ----------------------------------------------------------------------------------------------------- 17 Al 1 4.232924879699108e-01 4.232924879359529e-01 3.39579e-11 6.89677e-11 2 3.604714258365112e-01 3.604714258296250e-01 6.88616e-12 3.47143e-10 3 -9.557916874994031e-02 -9.557916875452306e-02 4.58275e-12 1.08106e-11 ----------------------------------------------------------------------------------------------------- 18 Al 1 -5.049839872936553e-01 -5.049839872641192e-01 2.95362e-11 1.04749e-09 2 4.028593471328348e-01 4.028593472490808e-01 1.16246e-10 2.27078e-10 3 1.019487429191001e+00 1.019487429153298e+00 3.77032e-11 1.90332e-09 * ----------------------------------------------------------------------------------------------------- 19 Al 1 2.575143922018392e-01 2.575143922074540e-01 5.61479e-12 1.75903e-10 2 3.794699165459633e-01 3.794699165730739e-01 2.71106e-11 2.93275e-10 3 -4.713117181409814e-01 -4.713117181136348e-01 2.73466e-11 2.32076e-10 ----------------------------------------------------------------------------------------------------- 20 Al 1 4.062913644585930e-01 4.062913644644761e-01 5.88307e-12 4.80884e-11 2 3.113003992267839e-01 3.113003992204912e-01 6.29274e-12 1.62569e-10 3 -4.575010808376562e-01 -4.575010808420334e-01 4.37728e-12 4.64536e-11 ----------------------------------------------------------------------------------------------------- 21 Al 1 -9.520288286595396e-01 -9.520288286466925e-01 1.28472e-11 2.24339e-10 2 4.430035600900081e-02 4.430035607024967e-02 6.12489e-11 1.92895e-10 3 8.201315241913862e-01 8.201315242197188e-01 2.83326e-11 7.00064e-11 ----------------------------------------------------------------------------------------------------- 22 Al 1 2.873278695623234e-01 2.873278695771739e-01 1.48505e-11 6.94759e-11 2 1.511178729448910e+00 1.511178729463907e+00 1.49971e-11 1.22733e-10 3 1.447152316912314e+00 1.447152316861450e+00 5.08642e-11 7.78415e-11 ----------------------------------------------------------------------------------------------------- 23 Al 1 -3.449440560560186e-01 -3.449440560282421e-01 2.77764e-11 2.42792e-10 2 3.006117704353070e-01 3.006117704179173e-01 1.73896e-11 1.44226e-10 3 -3.734060708052642e-01 -3.734060707940491e-01 1.12151e-11 8.28370e-11 ----------------------------------------------------------------------------------------------------- 24 Al 1 7.546372080369666e-02 7.546372079054924e-02 1.31474e-11 1.30407e-10 2 -5.937016491823286e-04 -5.937016283486258e-04 2.08337e-11 1.91243e-10 3 -6.192852818154609e-01 -6.192852818132845e-01 2.17648e-12 4.35812e-10 ----------------------------------------------------------------------------------------------------- 25 Al 1 -3.619449613179131e-01 -3.619449612781920e-01 3.97211e-11 1.02935e-10 2 -8.543636737279424e-01 -8.543636737195478e-01 8.39462e-12 1.65954e-10 3 2.198724703597425e-01 2.198724704145961e-01 5.48536e-11 1.54118e-10 ----------------------------------------------------------------------------------------------------- 26 Al 1 -4.995059878592494e-01 -4.995059878823541e-01 2.31046e-11 6.46032e-11 2 1.019971309665033e+00 1.019971309705318e+00 4.02851e-11 1.45177e-10 3 -7.917960883788592e-01 -7.917960883524606e-01 2.63986e-11 4.49544e-10 ----------------------------------------------------------------------------------------------------- 27 Al 1 5.695347882850870e-01 5.695347883580122e-01 7.29252e-11 3.99764e-10 2 -2.394436846487052e+00 -2.394436846557654e+00 7.06026e-11 6.98572e-10 3 7.839688761011113e-01 7.839688760887318e-01 1.23795e-11 8.34128e-10 ----------------------------------------------------------------------------------------------------- 28 Al 1 -5.446234038934674e-01 -5.446234038991051e-01 5.63771e-12 2.84434e-10 2 6.944340251598240e-01 6.944340251942364e-01 3.44124e-11 4.67587e-10 3 -2.318279184599022e-01 -2.318279184578471e-01 2.05513e-12 3.27606e-11 ----------------------------------------------------------------------------------------------------- 29 Al 1 -2.440918629055693e-01 -2.440918630001891e-01 9.46198e-11 1.60357e-10 2 -7.057629502897574e-01 -7.057629502342889e-01 5.54685e-11 3.05303e-10 3 6.755891576608803e-01 6.755891576235395e-01 3.73408e-11 3.12854e-10 ----------------------------------------------------------------------------------------------------- 30 Al 1 -7.998225684720663e-02 -7.998225681942228e-02 2.77843e-11 1.07874e-10 2 6.365060183912106e-01 6.365060183865139e-01 4.69669e-12 2.07175e-10 3 -3.994794171810697e-01 -3.994794171559160e-01 2.51537e-11 2.15582e-09 * ----------------------------------------------------------------------------------------------------- 31 Al 1 -7.196129164542195e-02 -7.196129167388403e-02 2.84621e-11 8.12897e-10 2 -9.584853879201196e-01 -9.584853879101884e-01 9.93117e-12 2.37149e-10 3 4.908346456816607e-01 4.908346456861973e-01 4.53654e-12 1.73409e-10 ----------------------------------------------------------------------------------------------------- 32 Al 1 5.661912897993999e-01 5.661912898348106e-01 3.54107e-11 1.42812e-10 2 3.764683493822977e-01 3.764683494010941e-01 1.87965e-11 2.02827e-10 3 1.162559895883294e-01 1.162559895780405e-01 1.02888e-11 2.41228e-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 = 24, direction = 2: |F_model - F_numer| error = ----------------------- = 3.50912e-08 max{|F_numer|, eps} Comparison of analytical forces obtained from the model, the force computed as a numerical derivative of the energy, the difference between them, and the uncertainty in the numerical estimate of the force. The computed equilibrium lattice constant for the crystal (a0) is given in the heading. MONOATOMIC STRUCTURE -- Species = Ti | a0 = 4.133002281188965 | (Configuration in file "config-Ti.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ti 1 7.675625885449386e-01 7.675625885408406e-01 4.09806e-12 5.93393e-11 2 5.653083814092233e-01 5.653083814099495e-01 7.26197e-13 1.06088e-09 3 3.355336565239141e-01 3.355336565247670e-01 8.52873e-13 1.02490e-11 ----------------------------------------------------------------------------------------------------- 2 Ti 1 -6.046515951047416e-01 -6.046515951212068e-01 1.64652e-11 1.41149e-10 2 -6.414408390919082e-01 -6.414408390826711e-01 9.23706e-12 1.76512e-11 3 9.462278716192620e-01 9.462278716144947e-01 4.76730e-12 4.53909e-11 ----------------------------------------------------------------------------------------------------- 3 Ti 1 -1.585147782426391e-01 -1.585147782395050e-01 3.13408e-12 5.51656e-11 2 6.776333686783985e-01 6.776333686355486e-01 4.28499e-11 6.87900e-11 3 -7.552122161723959e-01 -7.552122161612168e-01 1.11791e-11 7.73407e-11 ----------------------------------------------------------------------------------------------------- 4 Ti 1 4.225071337955756e-01 4.225071337955220e-01 5.36238e-14 7.74442e-11 2 3.574328974834684e-01 3.574328974814440e-01 2.02444e-12 2.77734e-10 3 -9.030874799349077e-01 -9.030874799431371e-01 8.22942e-12 2.74496e-09 * ----------------------------------------------------------------------------------------------------- 5 Ti 1 -5.239383796809076e-01 -5.239383796816122e-01 7.04548e-13 5.82469e-10 2 -5.104107915266056e-01 -5.104107915009473e-01 2.56584e-11 3.21193e-11 3 -4.581405485363321e-01 -4.581405485072850e-01 2.90472e-11 3.16142e-11 ----------------------------------------------------------------------------------------------------- 6 Ti 1 6.110242735233143e-01 6.110242735104682e-01 1.28462e-11 6.70087e-11 2 4.025323023576271e-01 4.025323023393932e-01 1.82339e-11 1.70211e-10 3 -9.366119868537870e-01 -9.366119868545296e-01 7.42628e-13 3.74438e-10 ----------------------------------------------------------------------------------------------------- 7 Ti 1 1.100177336290097e+00 1.100177336364833e+00 7.47362e-11 1.39892e-10 2 -1.447184673629863e+00 -1.447184673613986e+00 1.58764e-11 1.08795e-10 3 7.872401140199619e-01 7.872401140253436e-01 5.38170e-12 1.56145e-10 ----------------------------------------------------------------------------------------------------- 8 Ti 1 -1.430355026262907e+00 -1.430355026177871e+00 8.50364e-11 3.77926e-10 2 1.535732200610306e+00 1.535732200633029e+00 2.27234e-11 8.51179e-11 3 6.032609886603527e-01 6.032609887104055e-01 5.00527e-11 2.70266e-10 ----------------------------------------------------------------------------------------------------- 9 Ti 1 5.930062181691036e-01 5.930062181650820e-01 4.02156e-12 4.28786e-11 2 -7.656242553726924e-03 -7.656242556391091e-03 2.66417e-12 5.61501e-11 3 6.178200094001355e-01 6.178200094072878e-01 7.15228e-12 5.81694e-11 ----------------------------------------------------------------------------------------------------- 10 Ti 1 -2.977049958136025e-01 -2.977049957758018e-01 3.78007e-11 1.00369e-10 2 -1.385981165917059e-01 -1.385981166203556e-01 2.86497e-11 3.32076e-11 3 -1.343967066075090e-01 -1.343967066206055e-01 1.30965e-11 7.70445e-11 ----------------------------------------------------------------------------------------------------- 11 Ti 1 -1.305032988191632e+00 -1.305032988157966e+00 3.36655e-11 6.37408e-11 2 1.150066372552321e+00 1.150066372638968e+00 8.66471e-11 2.89392e-10 3 -1.638350043593011e+00 -1.638350043603480e+00 1.04690e-11 4.73088e-11 ----------------------------------------------------------------------------------------------------- 12 Ti 1 4.193721032087573e-01 4.193721031735170e-01 3.52403e-11 1.68066e-10 2 -3.154081492977271e-01 -3.154081492871786e-01 1.05485e-11 3.30719e-11 3 -3.065431567162785e-01 -3.065431566854339e-01 3.08446e-11 7.68977e-11 ----------------------------------------------------------------------------------------------------- 13 Ti 1 -1.019880444936389e+00 -1.019880444945987e+00 9.59788e-12 3.53155e-11 2 -5.165678775687155e-01 -5.165678775476941e-01 2.10214e-11 2.02822e-10 3 3.222940911527363e-01 3.222940911648202e-01 1.20839e-11 2.88373e-11 ----------------------------------------------------------------------------------------------------- 14 Ti 1 1.269618160368051e+00 1.269618160345972e+00 2.20786e-11 4.40010e-11 2 1.215980578466699e+00 1.215980578486208e+00 1.95082e-11 8.56391e-11 3 -6.457940064302596e-01 -6.457940064358265e-01 5.56688e-12 1.12277e-10 ----------------------------------------------------------------------------------------------------- 15 Ti 1 -5.309973575427079e-02 -5.309973581107400e-02 5.68032e-11 6.49200e-09 * 2 -7.423017548445154e-01 -7.423017548145375e-01 2.99779e-11 1.20620e-10 3 -3.643241636649742e-01 -3.643241636674620e-01 2.48773e-12 4.52067e-11 ----------------------------------------------------------------------------------------------------- 16 Ti 1 -8.092547973422598e-01 -8.092547973482915e-01 6.03173e-12 4.64947e-11 2 -5.906007338407572e-01 -5.906007338776970e-01 3.69398e-11 4.40283e-11 3 9.750854738958082e-01 9.750854738941971e-01 1.61116e-12 1.36507e-09 * ----------------------------------------------------------------------------------------------------- 17 Ti 1 3.776984393445087e-01 3.776984393673251e-01 2.28164e-11 1.76268e-09 * 2 -1.016087286686854e+00 -1.016087286685126e+00 1.72795e-12 5.18878e-11 3 -9.863755569438241e-01 -9.863755569281825e-01 1.56416e-11 7.26315e-11 ----------------------------------------------------------------------------------------------------- 18 Ti 1 3.213994614527348e-01 3.213994614483202e-01 4.41464e-12 1.51193e-10 2 -7.953909859407406e-01 -7.953909859426386e-01 1.89793e-12 8.19006e-11 3 6.333642799704619e-01 6.333642799582990e-01 1.21628e-11 2.59401e-10 ----------------------------------------------------------------------------------------------------- 19 Ti 1 -5.680176940844611e-02 -5.680176945968510e-02 5.12390e-11 5.64518e-10 2 -5.251123775893469e-01 -5.251123776047913e-01 1.54444e-11 4.73803e-10 3 4.090962403556263e-01 4.090962403504629e-01 5.16337e-12 2.13112e-10 ----------------------------------------------------------------------------------------------------- 20 Ti 1 -4.932840977183899e-01 -4.932840976895805e-01 2.88094e-11 2.02590e-10 2 1.457741781110795e+00 1.457741781115594e+00 4.79949e-12 6.76365e-10 3 1.159746664933978e+00 1.159746664926430e+00 7.54818e-12 5.75970e-11 ----------------------------------------------------------------------------------------------------- 21 Ti 1 1.469091031997613e-01 1.469091031662535e-01 3.35078e-11 4.28239e-10 2 -7.372504310187383e-01 -7.372504309970099e-01 2.17284e-11 2.08754e-10 3 -5.162906262183938e-01 -5.162906261539302e-01 6.44637e-11 7.49972e-11 ----------------------------------------------------------------------------------------------------- 22 Ti 1 -1.341534662528259e+00 -1.341534662407830e+00 1.20428e-10 2.93501e-10 2 -1.258207530193166e+00 -1.258207530178492e+00 1.46736e-11 1.45856e-10 3 7.195015723632813e-01 7.195015723456325e-01 1.76488e-11 1.01621e-10 ----------------------------------------------------------------------------------------------------- 23 Ti 1 3.840913836309059e-01 3.840913836492204e-01 1.83144e-11 2.95900e-10 2 1.048018983664947e-01 1.048018983990755e-01 3.25808e-11 4.60610e-10 3 2.876302960563356e-01 2.876302960534574e-01 2.87820e-12 1.52406e-10 ----------------------------------------------------------------------------------------------------- 24 Ti 1 8.379712591102914e-01 8.379712592498776e-01 1.39586e-10 2.04946e-10 2 5.693268360491834e-01 5.693268361183833e-01 6.91999e-11 2.20028e-08 * 3 -5.636578168152394e-01 -5.636578167598900e-01 5.53494e-11 1.29133e-10 ----------------------------------------------------------------------------------------------------- 25 Ti 1 -1.589930440914477e+00 -1.589930440915898e+00 1.42175e-12 5.41143e-11 2 -1.077809369203738e+00 -1.077809369218389e+00 1.46512e-11 9.48148e-11 3 4.410285875852481e-01 4.410285875646454e-01 2.06027e-11 4.40094e-11 ----------------------------------------------------------------------------------------------------- 26 Ti 1 7.294682287086235e-01 7.294682287025337e-01 6.08980e-12 1.26118e-10 2 -3.436501674475735e-02 -3.436501676403738e-02 1.92800e-11 1.18243e-10 3 3.997985207708011e-01 3.997985207550922e-01 1.57089e-11 9.94549e-10 ----------------------------------------------------------------------------------------------------- 27 Ti 1 -5.528915248922370e-01 -5.528915248839412e-01 8.29581e-12 2.49992e-10 2 7.658195023387051e-01 7.658195023017473e-01 3.69578e-11 2.26217e-10 3 -5.012627081001851e-01 -5.012627081147533e-01 1.45681e-11 1.26421e-09 ----------------------------------------------------------------------------------------------------- 28 Ti 1 7.504886027379343e-01 7.504886027318289e-01 6.10534e-12 4.16448e-10 2 -4.136910032531682e-01 -4.136910032503393e-01 2.82890e-12 2.26749e-11 3 -4.914555709368151e-01 -4.914555709229280e-01 1.38871e-11 4.20422e-10 ----------------------------------------------------------------------------------------------------- 29 Ti 1 1.447392307215056e+00 1.447392307219772e+00 4.71578e-12 8.25293e-09 * 2 1.839812682214394e+00 1.839812682227620e+00 1.32261e-11 3.46634e-11 3 5.107524556221559e-01 5.107524556314265e-01 9.27058e-12 3.07525e-11 ----------------------------------------------------------------------------------------------------- 30 Ti 1 2.603691123465020e-01 2.603691123600410e-01 1.35389e-11 3.89102e-10 2 3.469927284878177e-01 3.469927285264687e-01 3.86510e-11 1.89974e-10 3 6.295552206039261e-01 6.295552206014816e-01 2.44449e-12 3.23248e-10 ----------------------------------------------------------------------------------------------------- 31 Ti 1 -2.170416852389117e-01 -2.170416852295851e-01 9.32651e-12 3.02499e-09 * 2 1.401860182038282e-01 1.401860182062181e-01 2.38992e-12 8.75186e-10 3 -1.509477186036264e-01 -1.509477186223597e-01 1.87333e-11 8.97041e-11 ----------------------------------------------------------------------------------------------------- 32 Ti 1 1.486121038391439e-02 1.486121037944245e-02 4.47193e-12 3.79739e-10 2 -3.612843687532289e-01 -3.612843688036863e-01 5.04573e-11 2.80145e-09 * 3 -4.254857374064451e-01 -4.254857373975228e-01 8.92236e-12 5.57979e-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 = 19, direction = 1: |F_model - F_numer| error = ----------------------- = 9.02067e-10 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 Ti | a0 = 4.054133614767579 | (Configuration in file "config-AlTi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ti 1 -1.579738613289648e+00 -1.579738613274946e+00 1.47022e-11 1.12848e-10 2 -5.739124667358767e-01 -5.739124667383413e-01 2.46458e-12 2.41130e-11 3 -1.828939380595599e+00 -1.828939380592080e+00 3.51896e-12 1.84079e-10 ----------------------------------------------------------------------------------------------------- 2 Ti 1 -4.121232189552413e+00 -4.121232189534647e+00 1.77662e-11 6.33165e-10 2 4.173999332243118e+00 4.173999332221468e+00 2.16493e-11 2.74576e-10 3 -1.777862028306120e+00 -1.777862028289061e+00 1.70588e-11 1.51825e-10 ----------------------------------------------------------------------------------------------------- 3 Al 1 1.132146214660629e+00 1.132146214669764e+00 9.13492e-12 1.63655e-10 2 -1.243473263955485e+00 -1.243473263983014e+00 2.75291e-11 9.53482e-12 3 3.116807708231650e+00 3.116807708218090e+00 1.35598e-11 3.30608e-10 ----------------------------------------------------------------------------------------------------- 4 Al 1 2.910386884987931e-01 2.910386885165089e-01 1.77159e-11 1.14655e-10 2 4.437348282084584e-01 4.437348282181705e-01 9.71212e-12 1.95736e-10 3 7.459759533585129e-01 7.459759533611279e-01 2.61502e-12 8.68033e-11 ----------------------------------------------------------------------------------------------------- 5 Al 1 2.955067321440380e+00 2.955067321427637e+00 1.27427e-11 1.01251e-10 2 -2.639964279015721e+00 -2.639964278994792e+00 2.09290e-11 2.97540e-11 3 -2.856310823646482e-01 -2.856310823927655e-01 2.81172e-11 3.58763e-10 ----------------------------------------------------------------------------------------------------- 6 Al 1 -1.092851120213208e-01 -1.092851120290457e-01 7.72496e-12 4.48242e-10 2 -1.826566186619824e-01 -1.826566186935627e-01 3.15803e-11 7.93212e-10 3 5.111927833076104e-01 5.111927833110259e-01 3.41549e-12 2.08689e-12 ----------------------------------------------------------------------------------------------------- 7 Ti 1 -3.008437434601159e-01 -3.008437434448500e-01 1.52658e-11 6.58082e-11 2 9.181407352448248e-01 9.181407353091096e-01 6.42848e-11 1.01681e-10 3 3.469831643050488e-01 3.469831643633240e-01 5.82752e-11 9.62901e-11 ----------------------------------------------------------------------------------------------------- 8 Ti 1 1.626314072755762e+00 1.626314072796746e+00 4.09845e-11 7.66918e-10 2 -1.732497853504449e+00 -1.732497853504696e+00 2.46247e-13 3.81647e-10 3 3.320412811311080e+00 3.320412811355090e+00 4.40097e-11 3.75003e-10 ----------------------------------------------------------------------------------------------------- 9 Ti 1 3.110879886170992e-03 3.110879854742800e-03 3.14282e-11 5.94736e-11 2 -6.308364326981416e-01 -6.308364326738992e-01 2.42424e-11 4.67308e-11 3 -9.366321079119705e-01 -9.366321079032331e-01 8.73734e-12 2.49739e-10 ----------------------------------------------------------------------------------------------------- 10 Ti 1 5.441935015856179e-01 5.441935015885337e-01 2.91589e-12 1.70978e-09 * 2 -3.087873619513445e-01 -3.087873619383638e-01 1.29807e-11 1.96695e-09 * 3 2.563226062342244e-01 2.563226062358706e-01 1.64613e-12 7.44484e-11 ----------------------------------------------------------------------------------------------------- 11 Al 1 1.348439671708725e+00 1.348439671687405e+00 2.13205e-11 3.34546e-10 2 -1.200371117723958e+00 -1.200371117675612e+00 4.83455e-11 2.04062e-10 3 -6.359096974718136e-02 -6.359096971541431e-02 3.17670e-11 3.06381e-10 ----------------------------------------------------------------------------------------------------- 12 Ti 1 -1.022684184477153e+00 -1.022684184473363e+00 3.78919e-12 1.11540e-09 2 1.152681888427758e+00 1.152681888553535e+00 1.25777e-10 1.41369e-10 3 2.544080409772114e-01 2.544080409770172e-01 1.94234e-13 1.59270e-10 ----------------------------------------------------------------------------------------------------- 13 Ti 1 6.084689921585172e-01 6.084689921548680e-01 3.64919e-12 2.06243e-10 2 2.544119840280764e+00 2.544119840259639e+00 2.11253e-11 1.29734e-10 3 -6.523697379317699e-01 -6.523697379250397e-01 6.73017e-12 5.91348e-10 ----------------------------------------------------------------------------------------------------- 14 Ti 1 -8.181187949181534e-01 -8.181187949125118e-01 5.64160e-12 5.17844e-11 2 -1.067217540224307e+00 -1.067217540218200e+00 6.10689e-12 1.06266e-10 3 9.150930023972672e-01 9.150930024040171e-01 6.74993e-12 5.59881e-11 ----------------------------------------------------------------------------------------------------- 15 Al 1 -9.101107462670012e-01 -9.101107462166607e-01 5.03405e-11 6.92872e-10 2 1.204720477247895e+00 1.204720477237795e+00 1.01008e-11 1.16510e-10 3 -9.599620633474522e-01 -9.599620633025276e-01 4.49245e-11 6.22753e-10 ----------------------------------------------------------------------------------------------------- 16 Al 1 3.064533450826447e-01 3.064533451205754e-01 3.79307e-11 6.19323e-11 2 1.001538006790076e+00 1.001538006724574e+00 6.55016e-11 2.96251e-10 3 -2.055810247714104e+00 -2.055810247722839e+00 8.73568e-12 1.65300e-10 ----------------------------------------------------------------------------------------------------- 17 Al 1 6.336650646643075e-01 6.336650646552899e-01 9.01756e-12 1.69405e-10 2 5.365021011996035e-01 5.365021012027169e-01 3.11340e-12 9.21477e-11 3 4.734639770151334e-01 4.734639770084768e-01 6.65668e-12 3.15557e-10 ----------------------------------------------------------------------------------------------------- 18 Al 1 -1.445404159005743e-01 -1.445404158933449e-01 7.22944e-12 6.28222e-09 * 2 -3.979424204033311e+00 -3.979424204006203e+00 2.71072e-11 5.77687e-10 3 -2.836814946078333e+00 -2.836814946168863e+00 9.05302e-11 4.15491e-10 ----------------------------------------------------------------------------------------------------- 19 Ti 1 -8.126094343788302e-01 -8.126094343374329e-01 4.13972e-11 2.15590e-09 * 2 -3.210695367900950e-01 -3.210695367367221e-01 5.33729e-11 5.67306e-11 3 -6.274844705586524e-01 -6.274844705577043e-01 9.48130e-13 2.01261e-10 ----------------------------------------------------------------------------------------------------- 20 Ti 1 -1.587048551544503e-01 -1.587048551630120e-01 8.56168e-12 4.06635e-11 2 -6.768624542281928e-01 -6.768624542294062e-01 1.21336e-12 1.36443e-09 * 3 -6.388771017839606e-01 -6.388771017438084e-01 4.01522e-11 1.95872e-09 * ----------------------------------------------------------------------------------------------------- 21 Al 1 -9.861648806004580e-01 -9.861648806151849e-01 1.47269e-11 1.58113e-10 2 6.594883591759961e-01 6.594883591283330e-01 4.76631e-11 1.01914e-10 3 -8.579240364488635e-01 -8.579240365894985e-01 1.40635e-10 1.87321e-10 ----------------------------------------------------------------------------------------------------- 22 Al 1 -5.989807794153758e-01 -5.989807794415352e-01 2.61594e-11 3.59954e-11 2 -1.065607615262547e+00 -1.065607615286837e+00 2.42906e-11 2.20367e-10 3 1.433842155493084e-01 1.433842154473263e-01 1.01982e-10 2.76436e-11 ----------------------------------------------------------------------------------------------------- 23 Al 1 3.200470911208279e-01 3.200470911110162e-01 9.81165e-12 2.97605e-11 2 3.556764425264579e-01 3.556764425178346e-01 8.62321e-12 1.39723e-10 3 2.463496119248922e-01 2.463496119109101e-01 1.39821e-11 4.15271e-09 * ----------------------------------------------------------------------------------------------------- 24 Al 1 1.067978387218879e+00 1.067978387202937e+00 1.59421e-11 3.67931e-09 * 2 9.995119139326506e-01 9.995119139320832e-01 5.67435e-13 1.76854e-10 3 -6.168070427550613e-01 -6.168070428697661e-01 1.14705e-10 2.88580e-10 ----------------------------------------------------------------------------------------------------- 25 Al 1 -2.470907744949368e+00 -2.470907744924501e+00 2.48672e-11 2.10801e-10 2 -9.479612335253893e-01 -9.479612335627903e-01 3.74010e-11 1.56092e-09 * 3 -8.627123446365097e-01 -8.627123445612997e-01 7.52099e-11 1.82636e-10 ----------------------------------------------------------------------------------------------------- 26 Al 1 1.721351586896253e+00 1.721351586882807e+00 1.34468e-11 3.00950e-10 2 1.417092651619854e+00 1.417092651608561e+00 1.12927e-11 1.58471e-11 3 -2.399923035701241e-01 -2.399923035578049e-01 1.23192e-11 2.45864e-10 ----------------------------------------------------------------------------------------------------- 27 Ti 1 1.688278332544277e+00 1.688278332540753e+00 3.52451e-12 1.22861e-08 * 2 2.756319546218479e+00 2.756319546392521e+00 1.74042e-10 8.39957e-10 3 3.624788155477438e+00 3.624788155524591e+00 4.71529e-11 7.08811e-11 ----------------------------------------------------------------------------------------------------- 28 Ti 1 -6.173552935457014e-01 -6.173552935542620e-01 8.56060e-12 5.97958e-11 2 1.899722669233366e-01 1.899722669315374e-01 8.20080e-12 3.78013e-11 3 6.681563863083910e-01 6.681563862949093e-01 1.34818e-11 8.36079e-11 ----------------------------------------------------------------------------------------------------- 29 Ti 1 8.778254873252705e-01 8.778254872971877e-01 2.80829e-11 3.77305e-10 2 -1.503738135028270e+00 -1.503738135068759e+00 4.04885e-11 4.77127e-11 3 5.387615061131580e-01 5.387615061468296e-01 3.36716e-11 3.06826e-11 ----------------------------------------------------------------------------------------------------- 30 Ti 1 1.060938401454140e+00 1.060938401470393e+00 1.62528e-11 6.33067e-11 2 1.144611626035662e+00 1.144611625956514e+00 7.91471e-11 1.27075e-10 3 -2.073224562038935e+00 -2.073224561983781e+00 5.51541e-11 1.81055e-09 * ----------------------------------------------------------------------------------------------------- 31 Ti 1 -2.161363867372010e-01 -2.161363867335237e-01 3.67725e-12 1.99964e-09 * 2 -1.176264422440079e+00 -1.176264422405495e+00 3.45839e-11 3.11690e-10 3 8.829663117113115e-01 8.829663117250629e-01 1.37514e-11 1.58211e-10 ----------------------------------------------------------------------------------------------------- 32 Al 1 -1.317903864333431e+00 -1.317903864346624e+00 1.31923e-11 2.05984e-10 2 -2.474654802957851e-01 -2.474654802909725e-01 4.81257e-12 8.18411e-11 3 1.269568191567045e+00 1.269568191571530e+00 4.48463e-12 1.01951e-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 = 9, direction = 1: |F_model - F_numer| error = ----------------------- = 1.01027e-08 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 3.50912e-08 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 3.50912e-08 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.