!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 : Sim_LAMMPS_MEAM_PascuetFernandez_2015_AlU__SM_721930391003_000 Supported species : Al U 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 = 4.04999923706 | (Configuration in file "config-Al.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Al 1 -9.907023776620999e-01 -9.907023776572706e-01 4.82925e-12 1.66671e-10 2 -8.409387718028949e-01 -8.409387717961592e-01 6.73572e-12 3.83878e-10 3 -1.435365330142179e+00 -1.435365330116499e+00 2.56797e-11 3.82659e-10 ----------------------------------------------------------------------------------------------------- 2 Al 1 -1.221143069176313e+00 -1.221143069198132e+00 2.18188e-11 7.28910e-11 2 3.821404235437257e+00 3.821404235443436e+00 6.17817e-12 3.03189e-11 3 -9.558593816407172e-01 -9.558593816503901e-01 9.67293e-12 1.50469e-10 ----------------------------------------------------------------------------------------------------- 3 Al 1 1.498530970717200e-01 1.498530970708299e-01 8.90094e-13 1.50318e-10 2 -1.357901430989100e+00 -1.357901430900772e+00 8.83280e-11 3.01325e-10 3 2.582424621296951e+00 2.582424621356505e+00 5.95533e-11 1.64424e-10 ----------------------------------------------------------------------------------------------------- 4 Al 1 -4.754679322004540e-01 -4.754679321856063e-01 1.48477e-11 5.36852e-10 2 1.489038913172857e+00 1.489038913183702e+00 1.08444e-11 7.37275e-11 3 1.125285605998005e+00 1.125285605981184e+00 1.68205e-11 2.42117e-10 ----------------------------------------------------------------------------------------------------- 5 Al 1 3.201478749240101e+00 3.201478749288678e+00 4.85767e-11 5.15566e-10 2 -2.212164378503009e+00 -2.212164378528006e+00 2.49973e-11 3.77725e-11 3 -5.801033624841800e-01 -5.801033624811476e-01 3.03246e-12 1.31402e-10 ----------------------------------------------------------------------------------------------------- 6 Al 1 1.103523247549971e-01 1.103523247434011e-01 1.15960e-11 8.26494e-11 2 -4.390031731965222e-02 -4.390031730040692e-02 1.92453e-11 6.61197e-11 3 -3.580153520969560e-01 -3.580153520976972e-01 7.41240e-13 3.05967e-11 ----------------------------------------------------------------------------------------------------- 7 Al 1 2.697822577644087e-01 2.697822577641610e-01 2.47635e-13 6.73209e-11 2 -3.230926755845450e+00 -3.230926755841825e+00 3.62510e-12 6.88288e-10 3 -4.748494181417855e+00 -4.748494181394092e+00 2.37632e-11 6.42813e-10 ----------------------------------------------------------------------------------------------------- 8 Al 1 -3.390650544964166e+00 -3.390650544979127e+00 1.49609e-11 1.67432e-10 2 -5.643793507499534e+00 -5.643793507498597e+00 9.37028e-13 2.51663e-10 3 1.942058753721330e-01 1.942058753991019e-01 2.69690e-11 7.19894e-10 ----------------------------------------------------------------------------------------------------- 9 Al 1 -8.393398595883159e-01 -8.393398595969839e-01 8.66796e-12 1.30728e-10 2 -1.748072264172183e+00 -1.748072264179525e+00 7.34124e-12 4.30584e-11 3 -1.638080985029238e+00 -1.638080985016369e+00 1.28695e-11 8.89731e-11 ----------------------------------------------------------------------------------------------------- 10 Al 1 -6.592567638722902e-01 -6.592567638590998e-01 1.31903e-11 2.09652e-10 2 2.120544636996605e+00 2.120544636957232e+00 3.93734e-11 1.12043e-10 3 -2.879011678918793e+00 -2.879011678917976e+00 8.17568e-13 3.21521e-11 ----------------------------------------------------------------------------------------------------- 11 Al 1 -1.578015960964735e+00 -1.578015960976628e+00 1.18929e-11 5.75311e-11 2 -3.241260982723316e+00 -3.241260982711391e+00 1.19247e-11 9.80602e-11 3 6.920637443562663e-01 6.920637443610947e-01 4.82847e-12 1.15392e-10 ----------------------------------------------------------------------------------------------------- 12 Al 1 -1.174791175781867e+00 -1.174791175786329e+00 4.46199e-12 2.09548e-11 2 2.008170271085370e+00 2.008170271118553e+00 3.31828e-11 9.02336e-11 3 6.890932008913375e-01 6.890932008924884e-01 1.15086e-12 1.66305e-11 ----------------------------------------------------------------------------------------------------- 13 Al 1 -2.029874034077064e+00 -2.029874034114702e+00 3.76379e-11 4.12989e-10 2 -1.990299223175701e+00 -1.990299223174965e+00 7.35412e-13 1.88527e-11 3 -7.641146381259950e+00 -7.641146381207287e+00 5.26628e-11 1.61098e-09 * ----------------------------------------------------------------------------------------------------- 14 Al 1 7.973876042228190e-01 7.973876041766518e-01 4.61672e-11 1.40306e-10 2 1.297813118171871e+00 1.297813118160656e+00 1.12146e-11 5.95244e-11 3 -4.277082729525649e-01 -4.277082729524850e-01 7.98250e-14 6.18309e-10 ----------------------------------------------------------------------------------------------------- 15 Al 1 7.618716388963178e+00 7.618716388998025e+00 3.48468e-11 1.49018e-10 2 3.132846067813206e-02 3.132846070980545e-02 3.16734e-11 5.69783e-11 3 1.843239909177103e+00 1.843239909160255e+00 1.68483e-11 1.47879e-10 ----------------------------------------------------------------------------------------------------- 16 Al 1 1.094440434639833e+00 1.094440434651663e+00 1.18301e-11 1.96890e-10 2 5.582948064182059e+00 5.582948064157049e+00 2.50102e-11 2.57461e-10 3 3.230793284196341e+00 3.230793284197077e+00 7.35856e-13 2.27629e-10 ----------------------------------------------------------------------------------------------------- 17 Al 1 -1.171624320944884e+00 -1.171624320923692e+00 2.11917e-11 3.46059e-11 2 -9.494887440194903e-01 -9.494887440162298e-01 3.26050e-12 2.62004e-11 3 -1.415369245630792e+00 -1.415369245625882e+00 4.90941e-12 6.00765e-10 ----------------------------------------------------------------------------------------------------- 18 Al 1 1.186148859107035e+00 1.186148859131958e+00 2.49230e-11 2.47974e-10 2 1.861723003088717e+00 1.861723003025311e+00 6.34053e-11 7.35552e-11 3 -1.193525730883573e+00 -1.193525730796632e+00 8.69413e-11 7.50342e-11 ----------------------------------------------------------------------------------------------------- 19 Al 1 1.544947516865701e+00 1.544947516863714e+00 1.98663e-12 2.26216e-10 2 -1.358641049581994e+00 -1.358641049595269e+00 1.32749e-11 3.50086e-10 3 1.102123524735712e+00 1.102123524736194e+00 4.81393e-13 6.01461e-11 ----------------------------------------------------------------------------------------------------- 20 Al 1 -5.867311694975903e-01 -5.867311695008652e-01 3.27494e-12 2.10850e-10 2 1.614906155503890e+00 1.614906155503501e+00 3.89244e-13 8.09719e-11 3 7.887411293839418e-01 7.887411293910613e-01 7.11953e-12 6.78227e-10 ----------------------------------------------------------------------------------------------------- 21 Al 1 -3.637591733299276e+00 -3.637591733291857e+00 7.41851e-12 7.21592e-11 2 -1.486449114824193e+00 -1.486449114807136e+00 1.70566e-11 1.07329e-10 3 2.911119953096499e-03 2.911119938091881e-03 1.50046e-11 1.16434e-10 ----------------------------------------------------------------------------------------------------- 22 Al 1 2.253711477366040e+00 2.253711477295018e+00 7.10227e-11 7.47122e-11 2 4.730583187554657e+00 4.730583187519128e+00 3.55298e-11 2.25910e-10 3 2.556013546290227e+00 2.556013546334027e+00 4.37992e-11 2.46009e-10 ----------------------------------------------------------------------------------------------------- 23 Al 1 1.482099319139557e+00 1.482099319141682e+00 2.12497e-12 4.04061e-11 2 -6.192421459916075e-01 -6.192421459789160e-01 1.26915e-11 2.49825e-10 3 1.949996946976368e+00 1.949996946970163e+00 6.20570e-12 1.37722e-10 ----------------------------------------------------------------------------------------------------- 24 Al 1 -8.133422030164688e-01 -8.133422030111294e-01 5.33940e-12 5.56512e-10 2 1.313948768452406e+00 1.313948768410619e+00 4.17872e-11 3.84548e-10 3 4.664570614663626e-01 4.664570614459677e-01 2.03949e-11 1.90973e-10 ----------------------------------------------------------------------------------------------------- 25 Al 1 -2.297445489859305e+00 -2.297445489861099e+00 1.79412e-12 1.39685e-10 2 -2.412920352838175e+00 -2.412920352820134e+00 1.80407e-11 1.32920e-11 3 6.390098198664087e-01 6.390098198524830e-01 1.39257e-11 8.33557e-10 ----------------------------------------------------------------------------------------------------- 26 Al 1 7.605920095156870e-01 7.605920094969351e-01 1.87519e-11 4.52678e-10 2 3.108731310461208e+00 3.108731310482991e+00 2.17835e-11 3.13804e-10 3 -2.243417999333603e+00 -2.243417999326847e+00 6.75593e-12 6.49210e-11 ----------------------------------------------------------------------------------------------------- 27 Al 1 1.888369934325004e+00 1.888369934316491e+00 8.51319e-12 1.48218e-10 2 -5.740247522305810e+00 -5.740247522314317e+00 8.50697e-12 1.21628e-09 * 3 1.865679952599098e+00 1.865679952620058e+00 2.09599e-11 2.15453e-10 ----------------------------------------------------------------------------------------------------- 28 Al 1 -3.442149357402423e+00 -3.442149357388776e+00 1.36464e-11 3.54035e-10 2 2.789957844112980e+00 2.789957844115128e+00 2.14762e-12 1.08122e-10 3 6.522578793715811e-01 6.522578793636383e-01 7.94276e-12 6.12181e-10 ----------------------------------------------------------------------------------------------------- 29 Al 1 -1.606679422161909e+00 -1.606679422082708e+00 7.92011e-11 2.03235e-09 * 2 -1.110542271416137e+00 -1.110542271469644e+00 5.35063e-11 9.69367e-11 3 2.739904610795333e+00 2.739904610865144e+00 6.98117e-11 4.75941e-10 ----------------------------------------------------------------------------------------------------- 30 Al 1 8.915087796279004e-01 8.915087796318325e-01 3.93208e-12 4.86509e-11 2 1.840314136416279e+00 1.840314136442797e+00 2.65175e-11 9.26876e-11 3 5.521610206449257e-02 5.521610205800206e-02 6.49052e-12 2.84089e-10 ----------------------------------------------------------------------------------------------------- 31 Al 1 1.703142158009893e+00 1.703142157973073e+00 3.68203e-11 8.00680e-10 2 -1.464578186731421e+00 -1.464578186876364e+00 1.44943e-10 6.89905e-10 3 1.133322799471028e+00 1.133322799456375e+00 1.46527e-11 1.02919e-09 ----------------------------------------------------------------------------------------------------- 32 Al 1 9.622745038552830e-01 9.622745037865659e-01 6.87171e-11 9.72336e-11 2 1.839954914425381e+00 1.839954914481567e+00 5.61868e-11 4.28115e-11 3 1.207357167528611e+00 1.207357167501875e+00 2.67366e-11 1.95455e-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 dicontinuities. Maximum error obtained for particle = 21, direction = 3: |F_model - F_numer| error = ----------------------- = 5.15424e-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 = U | a0 = 4.48094844818 | (Configuration in file "config-U.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 U 1 7.737746191187378e-01 7.737746191165131e-01 2.22466e-12 1.27875e-10 2 3.727679374910933e-01 3.727679375470475e-01 5.59541e-11 1.64917e-10 3 7.160420228892177e-01 7.160420228790946e-01 1.01231e-11 1.04979e-10 ----------------------------------------------------------------------------------------------------- 2 U 1 8.389910070076888e-01 8.389910069756681e-01 3.20207e-11 8.53337e-11 2 6.704251221050338e-01 6.704251220758253e-01 2.92085e-11 2.07184e-10 3 -2.195230551449988e+00 -2.195230551475627e+00 2.56386e-11 1.96971e-10 ----------------------------------------------------------------------------------------------------- 3 U 1 4.627182815401047e-01 4.627182815166178e-01 2.34869e-11 2.79679e-09 * 2 -2.020041776289710e+00 -2.020041776312678e+00 2.29678e-11 4.12637e-10 3 6.666366317364517e-01 6.666366317310309e-01 5.42077e-12 1.68370e-10 ----------------------------------------------------------------------------------------------------- 4 U 1 -2.238770410564359e+00 -2.238770410547347e+00 1.70117e-11 5.31193e-11 2 5.275011988776758e-01 5.275011988193583e-01 5.83175e-11 3.00358e-10 3 9.572740013379875e-01 9.572740013605203e-01 2.25329e-11 1.24050e-10 ----------------------------------------------------------------------------------------------------- 5 U 1 -5.195246256382858e-01 -5.195246256179398e-01 2.03461e-11 6.42004e-11 2 -1.878417099013407e-01 -1.878417099000283e-01 1.31237e-12 6.61792e-09 * 3 -3.607968573640912e-01 -3.607968573571333e-01 6.95788e-12 9.98722e-11 ----------------------------------------------------------------------------------------------------- 6 U 1 1.558874992375105e-01 1.558874992386669e-01 1.15646e-12 1.50521e-10 2 7.939337212194417e-01 7.939337212251234e-01 5.68168e-12 1.66997e-10 3 5.239145832348241e-02 5.239145824338210e-02 8.01003e-11 4.49750e-10 ----------------------------------------------------------------------------------------------------- 7 U 1 6.607335983974609e-01 6.607335984815249e-01 8.40640e-11 1.02247e-09 2 -4.421398475487746e-01 -4.421398475666836e-01 1.79091e-11 1.84610e-10 3 -5.671043598287998e-02 -5.671043596388149e-02 1.89985e-11 8.70009e-11 ----------------------------------------------------------------------------------------------------- 8 U 1 2.079041759222387e-01 2.079041759296492e-01 7.41052e-12 3.64970e-10 2 8.258734267723681e-01 8.258734268201778e-01 4.78098e-11 5.89410e-10 3 -5.854234955293631e-01 -5.854234954447536e-01 8.46095e-11 1.87921e-10 ----------------------------------------------------------------------------------------------------- 9 U 1 -1.214570981383073e+00 -1.214570981390638e+00 7.56573e-12 7.45430e-11 2 -2.953800088209448e+00 -2.953800088187724e+00 2.17231e-11 3.20727e-10 3 -3.116526762839697e+00 -3.116526762898808e+00 5.91114e-11 9.24598e-11 ----------------------------------------------------------------------------------------------------- 10 U 1 1.590509084668759e+00 1.590509084661919e+00 6.84008e-12 1.11769e-10 2 3.351163188840945e-01 3.351163188267300e-01 5.73645e-11 4.87906e-10 3 -3.550245355166763e-01 -3.550245354951542e-01 2.15221e-11 1.33076e-10 ----------------------------------------------------------------------------------------------------- 11 U 1 1.602539880819199e+00 1.602539880797749e+00 2.14500e-11 2.77490e-10 2 3.501075403664660e-01 3.501075403265581e-01 3.99079e-11 4.46965e-10 3 -7.663494853941086e-01 -7.663494854313172e-01 3.72086e-11 8.13138e-11 ----------------------------------------------------------------------------------------------------- 12 U 1 -1.297642862722798e+00 -1.297642862791313e+00 6.85147e-11 1.49317e-10 2 3.186829899623265e+00 3.186829899607155e+00 1.61098e-11 6.12521e-10 3 3.076792161497657e+00 3.076792161400917e+00 9.67399e-11 1.88595e-10 ----------------------------------------------------------------------------------------------------- 13 U 1 4.106986706140459e-01 4.106986705845879e-01 2.94579e-11 1.42328e-10 2 -1.586258855199639e-02 -1.586258853609002e-02 1.59064e-11 8.93918e-11 3 4.799960866431972e-01 4.799960866465829e-01 3.38579e-12 8.71546e-11 ----------------------------------------------------------------------------------------------------- 14 U 1 -1.010541991862131e+00 -1.010541991847572e+00 1.45588e-11 6.44005e-10 2 -8.403585170329622e-01 -8.403585170393505e-01 6.38833e-12 2.17034e-10 3 6.361252374865621e-01 6.361252375407142e-01 5.41520e-11 2.62090e-10 ----------------------------------------------------------------------------------------------------- 15 U 1 -4.660315264500546e-01 -4.660315265076203e-01 5.75656e-11 3.84026e-10 2 -3.771996499438662e-01 -3.771996498812460e-01 6.26202e-11 1.18057e-09 3 2.412706348909115e-01 2.412706349908346e-01 9.99232e-11 1.17934e-10 ----------------------------------------------------------------------------------------------------- 16 U 1 -1.189440846179001e+00 -1.189440846131323e+00 4.76783e-11 1.68557e-09 * 2 -2.391512255996149e-01 -2.391512255195984e-01 8.00165e-11 5.31034e-10 3 -9.495345203913296e-01 -9.495345204758124e-01 8.44829e-11 5.04491e-10 ----------------------------------------------------------------------------------------------------- 17 U 1 -2.428509424042763e-01 -2.428509424139835e-01 9.70712e-12 2.56387e-11 2 -6.064796304369879e-01 -6.064796304604283e-01 2.34404e-11 1.98277e-10 3 -7.933713768149538e-01 -7.933713768488369e-01 3.38830e-11 1.32578e-10 ----------------------------------------------------------------------------------------------------- 18 U 1 -2.659311601443915e-02 -2.659311589620441e-02 1.18235e-10 1.20290e-09 2 -3.156098857145536e+00 -3.156098857139111e+00 6.42419e-12 5.18211e-10 3 -6.610402239476811e-01 -6.610402240010853e-01 5.34042e-11 4.02145e-10 ----------------------------------------------------------------------------------------------------- 19 U 1 1.048751620669540e+00 1.048751620667822e+00 1.71774e-12 8.95510e-11 2 -4.653938499113020e-01 -4.653938499205865e-01 9.28452e-12 2.33966e-10 3 4.015020333360241e-01 4.015020333367374e-01 7.13318e-13 8.78431e-11 ----------------------------------------------------------------------------------------------------- 20 U 1 -1.493451864813946e+00 -1.493451864919550e+00 1.05604e-10 6.01685e-10 2 -4.701532736305876e-01 -4.701532736343455e-01 3.75794e-12 3.85323e-11 3 1.297382150989412e+00 1.297382151026061e+00 3.66491e-11 2.05477e-10 ----------------------------------------------------------------------------------------------------- 21 U 1 -2.710173287869174e+00 -2.710173287944774e+00 7.56000e-11 2.21103e-10 2 -1.962618431113823e+00 -1.962618431113195e+00 6.27942e-13 4.89084e-11 3 -8.323469468758292e-01 -8.323469467491480e-01 1.26681e-10 2.11309e-09 * ----------------------------------------------------------------------------------------------------- 22 U 1 2.566899443853068e+00 2.566899443835208e+00 1.78595e-11 9.28785e-10 2 2.788518467213278e+00 2.788518467218967e+00 5.68878e-12 1.84414e-10 3 -2.998110349882717e+00 -2.998110349847502e+00 3.52145e-11 6.12412e-10 ----------------------------------------------------------------------------------------------------- 23 U 1 1.192641322385943e+00 1.192641322357780e+00 2.81630e-11 1.01985e-10 2 -1.957752652158681e+00 -1.957752652175385e+00 1.67046e-11 5.78799e-11 3 2.651174720191088e+00 2.651174720187810e+00 3.27827e-12 1.86964e-10 ----------------------------------------------------------------------------------------------------- 24 U 1 -1.803868006599037e+00 -1.803868006624039e+00 2.50016e-11 8.02356e-10 2 1.062171445863650e+00 1.062171445828491e+00 3.51585e-11 2.34624e-10 3 2.403032122854739e+00 2.403032122897789e+00 4.30500e-11 5.55791e-11 ----------------------------------------------------------------------------------------------------- 25 U 1 -2.461261032560147e+00 -2.461261032552623e+00 7.52420e-12 1.93606e-10 2 1.122114229994220e+00 1.122114230192491e+00 1.98271e-10 1.24849e-10 3 -9.786973414641384e-01 -9.786973415609554e-01 9.68170e-11 4.03558e-10 ----------------------------------------------------------------------------------------------------- 26 U 1 8.114536521499822e-01 8.114536521355127e-01 1.44695e-11 4.63763e-10 2 1.246079398062871e+00 1.246079398064697e+00 1.82609e-12 2.98556e-10 3 4.315307345972171e-01 4.315307345846368e-01 1.25803e-11 4.23816e-10 ----------------------------------------------------------------------------------------------------- 27 U 1 1.405606459564520e+00 1.405606459560207e+00 4.31277e-12 3.28673e-10 2 1.747509834450644e+00 1.747509834441363e+00 9.28169e-12 1.59656e-10 3 2.246379040680715e+00 2.246379040747067e+00 6.63518e-11 4.70442e-10 ----------------------------------------------------------------------------------------------------- 28 U 1 6.589435245857341e-01 6.589435245992248e-01 1.34907e-11 2.48097e-10 2 -7.684076992427514e-01 -7.684076992161458e-01 2.66056e-11 1.91713e-10 3 -7.071261277786500e-01 -7.071261277503985e-01 2.82515e-11 1.05720e-09 ----------------------------------------------------------------------------------------------------- 29 U 1 2.532536662948256e+00 2.532536662909627e+00 3.86291e-11 9.25843e-10 2 2.323204549180336e+00 2.323204549169941e+00 1.03952e-11 1.38119e-10 3 -4.362530456206555e-01 -4.362530456998889e-01 7.92334e-11 1.57891e-10 ----------------------------------------------------------------------------------------------------- 30 U 1 5.334397293959506e-01 5.334397293845672e-01 1.13834e-11 2.19415e-10 2 -3.184418936586803e-01 -3.184418936664341e-01 7.75385e-12 4.32872e-10 3 5.787933252555956e-01 5.787933254944958e-01 2.38900e-10 8.02891e-10 ----------------------------------------------------------------------------------------------------- 31 U 1 -5.352155342195974e-01 -5.352155342261171e-01 6.51967e-12 3.45490e-10 2 3.086584235474426e-01 3.086584235503406e-01 2.89807e-12 1.52497e-10 3 -4.837493008206616e-01 -4.837493008454545e-01 2.47929e-11 2.31635e-10 ----------------------------------------------------------------------------------------------------- 32 U 1 -2.440922035984242e-01 -2.440922036269560e-01 2.85318e-11 2.97867e-10 2 -8.790698232758175e-01 -8.790698232591665e-01 1.66510e-11 6.72794e-11 3 -5.600310050368400e-01 -5.600310049981341e-01 3.87059e-11 1.70230e-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 dicontinuities. Maximum error obtained for particle = 18, direction = 1: |F_model - F_numer| error = ----------------------- = 4.44607e-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 U | a0 = 4.49776321318 | (Configuration in file "config-AlU.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 U 1 -8.970743449735116e-02 -8.970743449182439e-02 5.52677e-12 3.40296e-10 2 3.972384377735050e-01 3.972384377671825e-01 6.32250e-12 4.98990e-11 3 -4.390638743337029e-01 -4.390638743256949e-01 8.00804e-12 3.22615e-11 ----------------------------------------------------------------------------------------------------- 2 U 1 -3.789575202707377e-01 -3.789575202714375e-01 6.99829e-13 2.61625e-10 2 1.528773475390841e+00 1.528773475350677e+00 4.01641e-11 7.41143e-11 3 -4.275804149105860e+00 -4.275804149074142e+00 3.17177e-11 1.75548e-10 ----------------------------------------------------------------------------------------------------- 3 Al 1 2.465168621226219e+00 2.465168621253092e+00 2.68732e-11 1.11096e-10 2 -5.100011504812843e+00 -5.100011504792643e+00 2.02007e-11 1.14266e-10 3 3.795155156369724e+00 3.795155156374570e+00 4.84635e-12 1.58211e-11 ----------------------------------------------------------------------------------------------------- 4 U 1 -3.589826652655736e+00 -3.589826652792536e+00 1.36800e-10 1.19493e-10 2 2.856005456069355e+00 2.856005456102672e+00 3.33169e-11 1.71453e-10 3 1.353912313395263e+00 1.353912313394278e+00 9.85212e-13 2.31598e-10 ----------------------------------------------------------------------------------------------------- 5 Al 1 5.821407097680294e-02 5.821407096835896e-02 8.44397e-12 4.17978e-10 2 -3.406672289822744e+00 -3.406672289836854e+00 1.41092e-11 4.94758e-10 3 -1.344552471431054e+00 -1.344552471413799e+00 1.72555e-11 1.20108e-10 ----------------------------------------------------------------------------------------------------- 6 Al 1 2.245782171783910e+00 2.245782171771499e+00 1.24114e-11 1.43800e-09 * 2 9.017404377645450e-01 9.017404377394649e-01 2.50802e-11 4.49226e-11 3 -1.754921285369179e+00 -1.754921285397008e+00 2.78293e-11 1.13518e-10 ----------------------------------------------------------------------------------------------------- 7 U 1 1.100725118707182e+00 1.100725118690759e+00 1.64233e-11 6.15782e-10 2 -2.433250338116830e+00 -2.433250338123499e+00 6.66889e-12 2.57611e-10 3 -1.486367234487777e+00 -1.486367234449958e+00 3.78186e-11 1.79823e-10 ----------------------------------------------------------------------------------------------------- 8 U 1 -2.303138845592349e+00 -2.303138845610029e+00 1.76801e-11 2.48803e-09 * 2 9.071047936290363e-01 9.071047936246861e-01 4.35019e-12 4.33583e-10 3 2.644592009622699e+00 2.644592009666402e+00 4.37024e-11 1.00834e-10 ----------------------------------------------------------------------------------------------------- 9 Al 1 2.284555337392340e-01 2.284555337541244e-01 1.48903e-11 4.65430e-10 2 8.696207065656539e-01 8.696207065575589e-01 8.09508e-12 3.47862e-10 3 2.670226132395838e-01 2.670226132539033e-01 1.43195e-11 1.22418e-10 ----------------------------------------------------------------------------------------------------- 10 U 1 -1.530557041117228e-01 -1.530557041563110e-01 4.45882e-11 4.84680e-11 2 -5.171744408730486e-01 -5.171744408882759e-01 1.52273e-11 4.38928e-11 3 4.830587028039684e-01 4.830587027918857e-01 1.20827e-11 1.65789e-10 ----------------------------------------------------------------------------------------------------- 11 U 1 -2.970770675789745e+00 -2.970770675739591e+00 5.01537e-11 5.29661e-10 2 -9.062848092448674e-01 -9.062848092329017e-01 1.19658e-11 1.77074e-10 3 -1.808337803283225e+00 -1.808337803322018e+00 3.87932e-11 5.09724e-10 ----------------------------------------------------------------------------------------------------- 12 Al 1 1.314214830694785e+00 1.314214830697182e+00 2.39697e-12 3.72857e-11 2 -8.916643610719863e-01 -8.916643610772061e-01 5.21982e-12 2.17671e-11 3 1.857442162340668e-01 1.857442162246251e-01 9.44173e-12 1.31832e-10 ----------------------------------------------------------------------------------------------------- 13 U 1 5.542343316600061e-01 5.542343316539839e-01 6.02218e-12 1.65521e-10 2 1.497562496740262e+00 1.497562496744336e+00 4.07430e-12 1.72743e-10 3 -3.351090493599795e-01 -3.351090493579106e-01 2.06890e-12 6.13353e-10 ----------------------------------------------------------------------------------------------------- 14 Al 1 -1.241422545398563e+00 -1.241422545404720e+00 6.15707e-12 1.43253e-10 2 -9.493640080268095e-01 -9.493640080611353e-01 3.43258e-11 1.53839e-10 3 5.986377933699617e-01 5.986377933575627e-01 1.23990e-11 1.51200e-10 ----------------------------------------------------------------------------------------------------- 15 Al 1 1.306343011181081e+00 1.306343011189508e+00 8.42704e-12 7.27647e-11 2 2.792282195991397e+00 2.792282195978036e+00 1.33613e-11 2.11152e-10 3 -1.261800074624659e+00 -1.261800074627681e+00 3.02203e-12 1.08535e-09 ----------------------------------------------------------------------------------------------------- 16 Al 1 3.163933307776403e+00 3.163933307756103e+00 2.03002e-11 2.41599e-10 2 2.500892910024993e+00 2.500892910057513e+00 3.25202e-11 7.08336e-11 3 -1.864624301886134e+00 -1.864624301987634e+00 1.01499e-10 4.53779e-10 ----------------------------------------------------------------------------------------------------- 17 U 1 1.867144389247269e+00 1.867144389251982e+00 4.71334e-12 1.28351e-11 2 1.794140698311588e-01 1.794140698165466e-01 1.46121e-11 7.16344e-10 3 8.101556480738266e-02 8.101556479254153e-02 1.48411e-11 2.48438e-10 ----------------------------------------------------------------------------------------------------- 18 Al 1 -1.433737806677532e+00 -1.433737806717689e+00 4.01570e-11 1.12527e-10 2 -5.917187916006776e+00 -5.917187915977211e+00 2.95657e-11 6.91630e-10 3 2.938347892967964e-01 2.938347893304706e-01 3.36742e-11 8.08688e-10 ----------------------------------------------------------------------------------------------------- 19 U 1 1.177741158439367e+00 1.177741158437615e+00 1.75149e-12 3.01221e-10 2 1.362103031076023e+00 1.362103031058668e+00 1.73555e-11 3.86096e-10 3 -1.942818761574595e+00 -1.942818761517805e+00 5.67906e-11 3.11822e-11 ----------------------------------------------------------------------------------------------------- 20 Al 1 3.050563301907000e-01 3.050563301913785e-01 6.78513e-13 7.69017e-11 2 -4.446167784812231e-01 -4.446167785229387e-01 4.17156e-11 2.89616e-10 3 1.624215507604333e+00 1.624215507666859e+00 6.25255e-11 6.62701e-11 ----------------------------------------------------------------------------------------------------- 21 Al 1 -2.289220017089075e+00 -2.289220017099442e+00 1.03668e-11 1.06550e-10 2 -5.146823246023893e-01 -5.146823246042564e-01 1.86717e-12 5.78787e-11 3 1.283359505249642e+00 1.283359505195484e+00 5.41580e-11 9.80815e-11 ----------------------------------------------------------------------------------------------------- 22 U 1 1.428030576056116e+00 1.428030576052870e+00 3.24651e-12 3.80755e-10 2 7.357097077936752e-01 7.357097077920661e-01 1.60905e-12 3.36824e-10 3 3.377264203797872e+00 3.377264203795626e+00 2.24576e-12 8.98736e-10 ----------------------------------------------------------------------------------------------------- 23 U 1 -1.501737159088868e+00 -1.501737159090664e+00 1.79634e-12 8.85545e-11 2 1.229943673031581e+00 1.229943673048706e+00 1.71247e-11 2.02180e-09 * 3 -1.243866136685842e+00 -1.243866136676661e+00 9.18177e-12 2.67714e-10 ----------------------------------------------------------------------------------------------------- 24 Al 1 -1.473479869345034e-01 -1.473479869561403e-01 2.16369e-11 4.43024e-10 2 -3.452849528075913e+00 -3.452849528117292e+00 4.13793e-11 1.94286e-10 3 2.607925953660393e+00 2.607925953657841e+00 2.55262e-12 1.55489e-11 ----------------------------------------------------------------------------------------------------- 25 U 1 -4.364881247129850e+00 -4.364881247196692e+00 6.68416e-11 5.18810e-10 2 1.021152343989226e+00 1.021152344060712e+00 7.14857e-11 2.33535e-10 3 -3.890805749516255e+00 -3.890805749523849e+00 7.59437e-12 1.16731e-10 ----------------------------------------------------------------------------------------------------- 26 U 1 -2.233583277535996e+00 -2.233583277603490e+00 6.74945e-11 6.03768e-10 2 2.893657953664120e+00 2.893657953657334e+00 6.78613e-12 3.19834e-10 3 -1.333279348370823e+00 -1.333279348406238e+00 3.54141e-11 2.49270e-10 ----------------------------------------------------------------------------------------------------- 27 Al 1 1.286314196302841e+00 1.286314196314760e+00 1.19187e-11 9.80300e-11 2 -8.815358742226247e-01 -8.815358741550281e-01 6.75966e-11 1.24091e-09 3 4.813022304545618e+00 4.813022304507322e+00 3.82965e-11 2.31222e-09 * ----------------------------------------------------------------------------------------------------- 28 Al 1 -2.206155079027524e-01 -2.206155078963327e-01 6.41967e-12 1.59296e-10 2 2.277464267613014e-01 2.277464267715883e-01 1.02869e-11 1.08589e-10 3 -1.189854724842923e-01 -1.189854725044787e-01 2.01864e-11 7.69323e-11 ----------------------------------------------------------------------------------------------------- 29 U 1 2.880584443710604e+00 2.880584443670610e+00 3.99933e-11 1.88709e-10 2 3.233090361661833e+00 3.233090361596592e+00 6.52407e-11 1.96434e-10 3 -1.058341390611345e+00 -1.058341390624819e+00 1.34732e-11 1.12307e-10 ----------------------------------------------------------------------------------------------------- 30 Al 1 3.500797230731805e-01 3.500797230446681e-01 2.85125e-11 3.57690e-10 2 1.940108814480344e+00 1.940108814485138e+00 4.79439e-12 5.91402e-11 3 -2.209224892729676e+00 -2.209224892728931e+00 7.44738e-13 1.44817e-10 ----------------------------------------------------------------------------------------------------- 31 U 1 5.100001183340921e-01 5.100001183571985e-01 2.31064e-11 1.16772e-10 2 -2.150525525355717e+00 -2.150525525342089e+00 1.36287e-11 1.46679e-10 3 1.355813105364373e+00 1.355813105326354e+00 3.80189e-11 8.30402e-11 ----------------------------------------------------------------------------------------------------- 32 Al 1 6.759804475749855e-01 6.759804475655854e-01 9.40015e-12 5.51609e-10 2 4.916724064749197e-01 4.916724064483822e-01 2.65375e-11 1.08822e-10 3 1.603328256492724e+00 1.603328256537765e+00 4.50406e-11 8.71725e-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 dicontinuities. Maximum error obtained for particle = 10, direction = 1: |F_model - F_numer| error = ----------------------- = 2.91320e-10 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 5.15424e-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 5.15424e-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.