!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 = 4.049999237060547 | (Configuration in file "config-Al.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Al 1 -9.907023776621369e-01 -9.907023776630721e-01 9.35252e-13 9.18772e-11 2 -8.409387718029135e-01 -8.409387718164836e-01 1.35700e-11 2.11958e-10 3 -1.435365330142223e+00 -1.435365330150329e+00 8.10574e-12 1.41128e-10 ----------------------------------------------------------------------------------------------------- 2 Al 1 -1.221143069176357e+00 -1.221143069199862e+00 2.35052e-11 8.47939e-11 2 3.821404235437338e+00 3.821404235429817e+00 7.52065e-12 1.30158e-10 3 -9.558593816407094e-01 -9.558593816455209e-01 4.81148e-12 2.65264e-10 ----------------------------------------------------------------------------------------------------- 3 Al 1 1.498530970716512e-01 1.498530970714251e-01 2.26125e-13 1.97769e-10 2 -1.357901430989078e+00 -1.357901430982321e+00 6.75771e-12 2.66420e-10 3 2.582424621297107e+00 2.582424621491267e+00 1.94160e-10 2.45536e-10 ----------------------------------------------------------------------------------------------------- 4 Al 1 -4.754679322004220e-01 -4.754679322051549e-01 4.73294e-12 3.53129e-10 2 1.489038913172877e+00 1.489038913210910e+00 3.80331e-11 2.99722e-10 3 1.125285605998026e+00 1.125285606023548e+00 2.55225e-11 1.46570e-10 ----------------------------------------------------------------------------------------------------- 5 Al 1 3.201478749240215e+00 3.201478749381264e+00 1.41049e-10 8.15663e-11 2 -2.212164378503045e+00 -2.212164378508725e+00 5.67990e-12 1.99829e-08 * 3 -5.801033624842251e-01 -5.801033624788097e-01 5.41545e-12 5.99467e-11 ----------------------------------------------------------------------------------------------------- 6 Al 1 1.103523247549951e-01 1.103523247434706e-01 1.15244e-11 1.19841e-10 2 -4.390031731964018e-02 -4.390031733434236e-02 1.47022e-11 2.59399e-10 3 -3.580153520969498e-01 -3.580153520878722e-01 9.07768e-12 1.89659e-10 ----------------------------------------------------------------------------------------------------- 7 Al 1 2.697822577644424e-01 2.697822577701263e-01 5.68384e-12 1.88680e-11 2 -3.230926755845382e+00 -3.230926755835417e+00 9.96447e-12 1.92147e-10 3 -4.748494181417836e+00 -4.748494181476373e+00 5.85372e-11 1.54928e-10 ----------------------------------------------------------------------------------------------------- 8 Al 1 -3.390650544964178e+00 -3.390650544991072e+00 2.68936e-11 9.29211e-09 * 2 -5.643793507499523e+00 -5.643793507508323e+00 8.80007e-12 6.10483e-09 * 3 1.942058753721118e-01 1.942058753729572e-01 8.45407e-13 3.24560e-10 ----------------------------------------------------------------------------------------------------- 9 Al 1 -8.393398595881901e-01 -8.393398595788989e-01 9.29123e-12 5.46710e-11 2 -1.748072264172166e+00 -1.748072264168591e+00 3.57447e-12 9.29703e-11 3 -1.638080985029202e+00 -1.638080985050322e+00 2.11196e-11 1.05584e-10 ----------------------------------------------------------------------------------------------------- 10 Al 1 -6.592567638724061e-01 -6.592567638539483e-01 1.84578e-11 3.45063e-11 2 2.120544636996459e+00 2.120544637054746e+00 5.82876e-11 8.19858e-09 * 3 -2.879011678918731e+00 -2.879011678922283e+00 3.55227e-12 1.13182e-10 ----------------------------------------------------------------------------------------------------- 11 Al 1 -1.578015960964711e+00 -1.578015960973307e+00 8.59535e-12 1.94712e-10 2 -3.241260982723117e+00 -3.241260982757768e+00 3.46509e-11 6.60832e-10 3 6.920637443561303e-01 6.920637443546296e-01 1.50069e-12 9.45797e-11 ----------------------------------------------------------------------------------------------------- 12 Al 1 -1.174791175781798e+00 -1.174791175782845e+00 1.04672e-12 2.72073e-11 2 2.008170271085344e+00 2.008170271076973e+00 8.37153e-12 7.09867e-09 * 3 6.890932008913743e-01 6.890932008969995e-01 5.62528e-12 1.64550e-09 ----------------------------------------------------------------------------------------------------- 13 Al 1 -2.029874034077138e+00 -2.029874034073444e+00 3.69349e-12 1.12518e-09 2 -1.990299223175747e+00 -1.990299223209027e+00 3.32807e-11 4.70888e-11 3 -7.641146381259895e+00 -7.641146381282145e+00 2.22498e-11 1.65172e-08 * ----------------------------------------------------------------------------------------------------- 14 Al 1 7.973876042228466e-01 7.973876042036578e-01 1.91888e-11 1.12510e-10 2 1.297813118171874e+00 1.297813118165729e+00 6.14575e-12 1.56595e-10 3 -4.277082729525781e-01 -4.277082729571935e-01 4.61542e-12 4.01866e-10 ----------------------------------------------------------------------------------------------------- 15 Al 1 7.618716388963165e+00 7.618716388925803e+00 3.73621e-11 1.11186e-09 2 3.132846067815828e-02 3.132846071346532e-02 3.53070e-11 5.73371e-11 3 1.843239909177074e+00 1.843239909190169e+00 1.30953e-11 7.35578e-10 ----------------------------------------------------------------------------------------------------- 16 Al 1 1.094440434639801e+00 1.094440434620816e+00 1.89846e-11 5.18370e-11 2 5.582948064181943e+00 5.582948064488995e+00 3.07051e-10 4.53661e-10 3 3.230793284196378e+00 3.230793284257722e+00 6.13438e-11 3.14857e-10 ----------------------------------------------------------------------------------------------------- 17 Al 1 -1.171624320944819e+00 -1.171624320940039e+00 4.78040e-12 2.34424e-11 2 -9.494887440194393e-01 -9.494887440122592e-01 7.18003e-12 4.86785e-11 3 -1.415369245630801e+00 -1.415369245669948e+00 3.91476e-11 1.50342e-08 * ----------------------------------------------------------------------------------------------------- 18 Al 1 1.186148859107004e+00 1.186148859106466e+00 5.37792e-13 2.57719e-10 2 1.861723003088564e+00 1.861723003107776e+00 1.92117e-11 2.54751e-10 3 -1.193525730883563e+00 -1.193525730864888e+00 1.86742e-11 3.00483e-10 ----------------------------------------------------------------------------------------------------- 19 Al 1 1.544947516865713e+00 1.544947516860001e+00 5.71143e-12 9.97227e-11 2 -1.358641049581913e+00 -1.358641049577400e+00 4.51217e-12 1.97261e-10 3 1.102123524735657e+00 1.102123524752278e+00 1.66211e-11 3.36537e-11 ----------------------------------------------------------------------------------------------------- 20 Al 1 -5.867311694975511e-01 -5.867311695055001e-01 7.94897e-12 8.46577e-11 2 1.614906155503853e+00 1.614906155493824e+00 1.00298e-11 7.33916e-10 3 7.887411293839131e-01 7.887411293762399e-01 7.67320e-12 2.47796e-10 ----------------------------------------------------------------------------------------------------- 21 Al 1 -3.637591733299395e+00 -3.637591733310156e+00 1.07616e-11 3.18560e-09 * 2 -1.486449114824219e+00 -1.486449114812620e+00 1.15989e-11 2.88610e-09 * 3 2.911119953112740e-03 2.911119957178549e-03 4.06581e-12 1.88356e-10 ----------------------------------------------------------------------------------------------------- 22 Al 1 2.253711477366049e+00 2.253711477422444e+00 5.63944e-11 3.09636e-10 2 4.730583187554649e+00 4.730583187537765e+00 1.68843e-11 4.53900e-09 * 3 2.556013546290155e+00 2.556013546402459e+00 1.12304e-10 8.43805e-10 ----------------------------------------------------------------------------------------------------- 23 Al 1 1.482099319139549e+00 1.482099319141704e+00 2.15539e-12 1.00132e-10 2 -6.192421459916138e-01 -6.192421459828578e-01 8.75600e-12 9.54548e-11 3 1.949996946976421e+00 1.949996947079472e+00 1.03051e-10 1.84541e-10 ----------------------------------------------------------------------------------------------------- 24 Al 1 -8.133422030164645e-01 -8.133422030746497e-01 5.81851e-11 1.41514e-10 2 1.313948768452333e+00 1.313948768437502e+00 1.48310e-11 1.67882e-10 3 4.664570614663575e-01 4.664570614675597e-01 1.20226e-12 7.11750e-11 ----------------------------------------------------------------------------------------------------- 25 Al 1 -2.297445489859230e+00 -2.297445489895789e+00 3.65588e-11 1.27540e-10 2 -2.412920352838063e+00 -2.412920352886288e+00 4.82250e-11 1.01934e-08 * 3 6.390098198664289e-01 6.390098198486021e-01 1.78269e-11 2.19450e-10 ----------------------------------------------------------------------------------------------------- 26 Al 1 7.605920095155315e-01 7.605920094795504e-01 3.59811e-11 1.71359e-10 2 3.108731310461170e+00 3.108731310463041e+00 1.87139e-12 4.53363e-10 3 -2.243417999333688e+00 -2.243417999350155e+00 1.64668e-11 1.83192e-10 ----------------------------------------------------------------------------------------------------- 27 Al 1 1.888369934324844e+00 1.888369934314492e+00 1.03524e-11 1.03876e-08 * 2 -5.740247522305749e+00 -5.740247522302255e+00 3.49409e-12 4.91258e-10 3 1.865679952599106e+00 1.865679952581922e+00 1.71836e-11 4.80525e-10 ----------------------------------------------------------------------------------------------------- 28 Al 1 -3.442149357402333e+00 -3.442149357439432e+00 3.70988e-11 3.73658e-09 * 2 2.789957844112873e+00 2.789957844129725e+00 1.68519e-11 7.43108e-10 3 6.522578793715355e-01 6.522578793782520e-01 6.71652e-12 3.74952e-10 ----------------------------------------------------------------------------------------------------- 29 Al 1 -1.606679422161905e+00 -1.606679422182388e+00 2.04829e-11 5.20831e-10 2 -1.110542271416175e+00 -1.110542271470323e+00 5.41482e-11 1.25262e-09 3 2.739904610795276e+00 2.739904610765818e+00 2.94582e-11 2.96918e-11 ----------------------------------------------------------------------------------------------------- 30 Al 1 8.915087796279519e-01 8.915087796275359e-01 4.16001e-13 1.84384e-10 2 1.840314136416332e+00 1.840314136413199e+00 3.13372e-12 9.76037e-11 3 5.521610206454079e-02 5.521610210218723e-02 3.76464e-11 1.21669e-10 ----------------------------------------------------------------------------------------------------- 31 Al 1 1.703142158009878e+00 1.703142157999635e+00 1.02438e-11 1.55062e-09 2 -1.464578186731400e+00 -1.464578186681258e+00 5.01412e-11 7.84243e-09 * 3 1.133322799471016e+00 1.133322799496535e+00 2.55194e-11 1.70239e-10 ----------------------------------------------------------------------------------------------------- 32 Al 1 9.622745038553979e-01 9.622745036610892e-01 1.94309e-10 2.45288e-10 2 1.839954914425411e+00 1.839954914158768e+00 2.66643e-10 8.18090e-10 3 1.207357167528682e+00 1.207357167538261e+00 9.57967e-12 8.96736e-11 ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as discontinuities. Maximum error obtained for particle = 21, direction = 3: |F_model - F_numer| error = ----------------------- = 1.39665e-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 = 4.480948448181152 | (Configuration in file "config-U.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 U 1 7.737746191187692e-01 7.737746190484553e-01 7.03139e-11 1.48230e-10 2 3.727679374911378e-01 3.727679374788126e-01 1.23253e-11 3.00547e-10 3 7.160420228892461e-01 7.160420229121338e-01 2.28877e-11 7.84786e-11 ----------------------------------------------------------------------------------------------------- 2 U 1 8.389910070076583e-01 8.389910069580389e-01 4.96194e-11 2.25155e-10 2 6.704251221050279e-01 6.704251220591034e-01 4.59245e-11 3.95748e-10 3 -2.195230551449948e+00 -2.195230551428616e+00 2.13327e-11 1.95488e-10 ----------------------------------------------------------------------------------------------------- 3 U 1 4.627182815401680e-01 4.627182815225228e-01 1.76452e-11 2.91175e-11 2 -2.020041776289787e+00 -2.020041776260383e+00 2.94040e-11 2.90781e-10 3 6.666366317363661e-01 6.666366317031902e-01 3.31759e-11 2.62969e-10 ----------------------------------------------------------------------------------------------------- 4 U 1 -2.238770410564400e+00 -2.238770410564046e+00 3.54383e-13 9.74225e-11 2 5.275011988777775e-01 5.275011988724254e-01 5.35205e-12 1.87668e-10 3 9.572740013378939e-01 9.572740013164819e-01 2.14120e-11 2.15668e-10 ----------------------------------------------------------------------------------------------------- 5 U 1 -5.195246256383010e-01 -5.195246256497462e-01 1.14452e-11 2.37683e-09 * 2 -1.878417099013280e-01 -1.878417099627007e-01 6.13727e-11 6.27309e-10 3 -3.607968573640586e-01 -3.607968573302027e-01 3.38559e-11 2.21607e-10 ----------------------------------------------------------------------------------------------------- 6 U 1 1.558874992374973e-01 1.558874992491429e-01 1.16456e-11 8.34905e-11 2 7.939337212194555e-01 7.939337212250420e-01 5.58653e-12 7.42407e-10 3 5.239145832347965e-02 5.239145830923884e-02 1.42408e-11 3.05061e-11 ----------------------------------------------------------------------------------------------------- 7 U 1 6.607335983974597e-01 6.607335984542929e-01 5.68332e-11 1.63742e-10 2 -4.421398475487831e-01 -4.421398474915370e-01 5.72461e-11 2.52787e-10 3 -5.671043598287880e-02 -5.671043596152493e-02 2.13539e-11 2.69966e-10 ----------------------------------------------------------------------------------------------------- 8 U 1 2.079041759222178e-01 2.079041759144323e-01 7.78549e-12 2.62094e-10 2 8.258734267723640e-01 8.258734267139172e-01 5.84468e-11 6.63311e-10 3 -5.854234955294032e-01 -5.854234954968511e-01 3.25521e-11 4.74255e-10 ----------------------------------------------------------------------------------------------------- 9 U 1 -1.214570981383122e+00 -1.214570981384453e+00 1.33116e-12 4.41758e-09 * 2 -2.953800088209609e+00 -2.953800088313151e+00 1.03542e-10 2.32814e-10 3 -3.116526762839834e+00 -3.116526762823462e+00 1.63727e-11 5.23539e-10 ----------------------------------------------------------------------------------------------------- 10 U 1 1.590509084668802e+00 1.590509084689235e+00 2.04330e-11 3.81759e-10 2 3.351163188840883e-01 3.351163188808339e-01 3.25434e-12 8.72870e-11 3 -3.550245355167235e-01 -3.550245354950325e-01 2.16910e-11 1.23725e-09 ----------------------------------------------------------------------------------------------------- 11 U 1 1.602539880819171e+00 1.602539880676686e+00 1.42485e-10 1.08075e-09 2 3.501075403664024e-01 3.501075404288563e-01 6.24539e-11 7.91583e-10 3 -7.663494853941002e-01 -7.663494854715350e-01 7.74348e-11 5.50503e-10 ----------------------------------------------------------------------------------------------------- 12 U 1 -1.297642862722792e+00 -1.297642862664819e+00 5.79730e-11 1.74804e-10 2 3.186829899623396e+00 3.186829899597742e+00 2.56546e-11 1.11297e-09 3 3.076792161497806e+00 3.076792161493469e+00 4.33786e-12 6.68944e-10 ----------------------------------------------------------------------------------------------------- 13 U 1 4.106986706140356e-01 4.106986707546528e-01 1.40617e-10 9.26176e-10 2 -1.586258855201655e-02 -1.586258860558489e-02 5.35683e-11 3.94997e-10 3 4.799960866431639e-01 4.799960866419654e-01 1.19849e-12 2.79664e-10 ----------------------------------------------------------------------------------------------------- 14 U 1 -1.010541991862126e+00 -1.010541991880648e+00 1.85221e-11 1.51501e-10 2 -8.403585170329583e-01 -8.403585169853686e-01 4.75897e-11 2.12158e-10 3 6.361252374865758e-01 6.361252375952979e-01 1.08722e-10 1.83388e-10 ----------------------------------------------------------------------------------------------------- 15 U 1 -4.660315264500208e-01 -4.660315264526380e-01 2.61724e-12 1.17915e-10 2 -3.771996499438389e-01 -3.771996499797472e-01 3.59083e-11 2.55014e-10 3 2.412706348909119e-01 2.412706349236464e-01 3.27345e-11 1.54564e-09 ----------------------------------------------------------------------------------------------------- 16 U 1 -1.189440846178729e+00 -1.189440846117387e+00 6.13423e-11 3.44282e-10 2 -2.391512255995713e-01 -2.391512256967604e-01 9.71892e-11 1.90252e-10 3 -9.495345203911081e-01 -9.495345204019841e-01 1.08760e-11 6.76226e-09 * ----------------------------------------------------------------------------------------------------- 17 U 1 -2.428509424042440e-01 -2.428509423993392e-01 4.90477e-12 6.92222e-10 2 -6.064796304370139e-01 -6.064796304381709e-01 1.15696e-12 6.31920e-09 * 3 -7.933713768148412e-01 -7.933713768362511e-01 2.14100e-11 1.17942e-10 ----------------------------------------------------------------------------------------------------- 18 U 1 -2.659311601435178e-02 -2.659311610055828e-02 8.62065e-11 2.36590e-09 * 2 -3.156098857145377e+00 -3.156098857177715e+00 3.23381e-11 7.59066e-10 3 -6.610402239475958e-01 -6.610402237015606e-01 2.46035e-10 5.25902e-10 ----------------------------------------------------------------------------------------------------- 19 U 1 1.048751620669489e+00 1.048751620675867e+00 6.37757e-12 3.15494e-09 * 2 -4.653938499112604e-01 -4.653938499267960e-01 1.55356e-11 1.87443e-10 3 4.015020333359516e-01 4.015020333362498e-01 2.98261e-13 1.84981e-10 ----------------------------------------------------------------------------------------------------- 20 U 1 -1.493451864813881e+00 -1.493451864886260e+00 7.23790e-11 1.98148e-10 2 -4.701532736305300e-01 -4.701532736545178e-01 2.39878e-11 7.41159e-10 3 1.297382150989302e+00 1.297382151069596e+00 8.02944e-11 3.49712e-09 * ----------------------------------------------------------------------------------------------------- 21 U 1 -2.710173287869145e+00 -2.710173287931192e+00 6.20473e-11 1.00850e-09 2 -1.962618431113823e+00 -1.962618431165101e+00 5.12781e-11 6.76317e-10 3 -8.323469468758061e-01 -8.323469468006611e-01 7.51450e-11 5.09986e-10 ----------------------------------------------------------------------------------------------------- 22 U 1 2.566899443853070e+00 2.566899443839150e+00 1.39195e-11 1.18138e-10 2 2.788518467213245e+00 2.788518467222892e+00 9.64739e-12 6.83984e-10 3 -2.998110349882697e+00 -2.998110349925784e+00 4.30864e-11 3.51292e-11 ----------------------------------------------------------------------------------------------------- 23 U 1 1.192641322385915e+00 1.192641322354267e+00 3.16487e-11 2.60128e-10 2 -1.957752652158672e+00 -1.957752652165816e+00 7.14406e-12 5.78289e-11 3 2.651174720191046e+00 2.651174720208975e+00 1.79283e-11 1.04194e-10 ----------------------------------------------------------------------------------------------------- 24 U 1 -1.803868006599077e+00 -1.803868006648426e+00 4.93490e-11 3.87831e-10 2 1.062171445863662e+00 1.062171445815286e+00 4.83762e-11 1.33138e-10 3 2.403032122854723e+00 2.403032122874381e+00 1.96581e-11 3.52119e-10 ----------------------------------------------------------------------------------------------------- 25 U 1 -2.461261032560194e+00 -2.461261032571566e+00 1.13718e-11 1.99531e-10 2 1.122114229994076e+00 1.122114229949135e+00 4.49409e-11 3.55565e-10 3 -9.786973414641024e-01 -9.786973411806213e-01 2.83481e-10 1.99775e-10 ----------------------------------------------------------------------------------------------------- 26 U 1 8.114536521499968e-01 8.114536520945946e-01 5.54021e-11 1.98611e-10 2 1.246079398062908e+00 1.246079398054688e+00 8.21987e-12 1.55858e-10 3 4.315307345972250e-01 4.315307345414001e-01 5.58249e-11 5.09268e-10 ----------------------------------------------------------------------------------------------------- 27 U 1 1.405606459564578e+00 1.405606459563548e+00 1.02962e-12 3.83212e-09 * 2 1.747509834450611e+00 1.747509834482465e+00 3.18545e-11 5.14128e-10 3 2.246379040680759e+00 2.246379040726761e+00 4.60023e-11 5.95755e-09 * ----------------------------------------------------------------------------------------------------- 28 U 1 6.589435245857321e-01 6.589435245418762e-01 4.38559e-11 5.95333e-11 2 -7.684076992427358e-01 -7.684076994036408e-01 1.60905e-10 8.96071e-10 3 -7.071261277786420e-01 -7.071261278020005e-01 2.33584e-11 4.40147e-10 ----------------------------------------------------------------------------------------------------- 29 U 1 2.532536662948137e+00 2.532536662861780e+00 8.63571e-11 6.19814e-10 2 2.323204549180249e+00 2.323204549325341e+00 1.45092e-10 9.63666e-10 3 -4.362530456206096e-01 -4.362530455348415e-01 8.57681e-11 3.84430e-10 ----------------------------------------------------------------------------------------------------- 30 U 1 5.334397293956887e-01 5.334397294264224e-01 3.07336e-11 1.26515e-10 2 -3.184418936587310e-01 -3.184418936425611e-01 1.61698e-11 4.85014e-10 3 5.787933252554119e-01 5.787933252532560e-01 2.15594e-12 6.15416e-10 ----------------------------------------------------------------------------------------------------- 31 U 1 -5.352155342195901e-01 -5.352155343232908e-01 1.03701e-10 3.90773e-10 2 3.086584235474599e-01 3.086584236044501e-01 5.69902e-11 2.24595e-10 3 -4.837493008206561e-01 -4.837493008216067e-01 9.50628e-13 1.16707e-11 ----------------------------------------------------------------------------------------------------- 32 U 1 -2.440922035984164e-01 -2.440922035888242e-01 9.59222e-12 7.45575e-11 2 -8.790698232758249e-01 -8.790698233037035e-01 2.78786e-11 1.40069e-10 3 -5.600310050368587e-01 -5.600310051703395e-01 1.33481e-10 5.42392e-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 = 13, direction = 2: |F_model - F_numer| error = ----------------------- = 3.37702e-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 = 4.4369704805720165 | (Configuration in file "config-AlU.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 U 1 9.566506297206394e-01 9.566506296646605e-01 5.59789e-11 7.46431e-11 2 9.320217335252033e-01 9.320217335365829e-01 1.13796e-11 1.17876e-10 3 7.815178900000884e-01 7.815178899861982e-01 1.38902e-11 4.98008e-11 ----------------------------------------------------------------------------------------------------- 2 Al 1 1.179982514946009e+00 1.179982515053990e+00 1.07981e-10 1.51154e-09 * 2 1.264433934546658e-03 1.264433991491313e-03 5.69447e-11 1.86229e-10 3 -6.220104623464988e-01 -6.220104623265386e-01 1.99603e-11 1.47585e-10 ----------------------------------------------------------------------------------------------------- 3 Al 1 1.645671856059443e+00 1.645671856031108e+00 2.83349e-11 9.39413e-11 2 -9.906856164596393e-01 -9.906856164130505e-01 4.65887e-11 7.84504e-10 3 -4.894232059217393e-01 -4.894232059150979e-01 6.64147e-12 5.53065e-11 ----------------------------------------------------------------------------------------------------- 4 U 1 -3.248784904087525e+00 -3.248784904094538e+00 7.01306e-12 3.58659e-10 2 -3.486186441505216e-01 -3.486186441419947e-01 8.52690e-12 4.42010e-10 3 -9.684028346357784e-01 -9.684028346231444e-01 1.26340e-11 5.64401e-10 ----------------------------------------------------------------------------------------------------- 5 U 1 -1.702699046665488e+00 -1.702699046651603e+00 1.38858e-11 1.69200e-10 2 -1.701215829542063e-01 -1.701215829565349e-01 2.32864e-12 4.07089e-11 3 5.756709749776336e-01 5.756709749712605e-01 6.37312e-12 3.80312e-11 ----------------------------------------------------------------------------------------------------- 6 Al 1 1.755079370294022e+00 1.755079370327371e+00 3.33491e-11 1.57095e-09 * 2 8.342708276726838e-01 8.342708276765637e-01 3.87990e-12 2.49025e-10 3 -1.855512345086605e+00 -1.855512345088963e+00 2.35767e-12 7.04434e-11 ----------------------------------------------------------------------------------------------------- 7 U 1 -6.432159581351141e-01 -6.432159581519882e-01 1.68741e-11 4.96922e-09 * 2 2.779408525634838e-01 2.779408525569155e-01 6.56836e-12 1.50194e-10 3 9.530795913762049e-01 9.530795913556817e-01 2.05232e-11 1.71150e-10 ----------------------------------------------------------------------------------------------------- 8 U 1 -4.888982777018218e+00 -4.888982777079798e+00 6.15801e-11 3.46009e-10 2 -1.224630032422310e+00 -1.224630032430228e+00 7.91833e-12 2.09830e-09 * 3 5.031602927336776e-01 5.031602926505742e-01 8.31034e-11 4.64649e-10 ----------------------------------------------------------------------------------------------------- 9 U 1 9.469930559352234e-01 9.469930559376777e-01 2.45426e-12 1.13583e-10 2 -7.461137784118216e-01 -7.461137784432128e-01 3.13912e-11 6.32607e-11 3 4.371326573166624e-01 4.371326573057789e-01 1.08835e-11 1.24747e-10 ----------------------------------------------------------------------------------------------------- 10 U 1 -1.596904975802705e+00 -1.596904975780117e+00 2.25875e-11 1.28896e-10 2 1.929686510971040e+00 1.929686510989472e+00 1.84324e-11 3.37639e-10 3 -1.696481743444002e+00 -1.696481743428559e+00 1.54432e-11 3.32170e-11 ----------------------------------------------------------------------------------------------------- 11 Al 1 1.358730217971569e+00 1.358730217976375e+00 4.80616e-12 3.44032e-10 2 -2.416677276120917e+00 -2.416677276130598e+00 9.68159e-12 7.16245e-10 3 4.240796312027133e-01 4.240796312066706e-01 3.95728e-12 4.91862e-09 * ----------------------------------------------------------------------------------------------------- 12 U 1 -1.657671455696932e+00 -1.657671455686505e+00 1.04272e-11 9.30895e-11 2 1.245085227106626e+00 1.245085226993866e+00 1.12760e-10 4.66617e-10 3 -2.025852038958516e-01 -2.025852038143876e-01 8.14639e-11 3.20201e-10 ----------------------------------------------------------------------------------------------------- 13 Al 1 5.288941912473557e-01 5.288941912365668e-01 1.07889e-11 7.98631e-11 2 -2.090706614955233e+00 -2.090706614951042e+00 4.19176e-12 7.62342e-09 * 3 -1.238936417328363e+00 -1.238936417338155e+00 9.79217e-12 3.21266e-10 ----------------------------------------------------------------------------------------------------- 14 Al 1 2.978136255529010e-01 2.978136255430605e-01 9.84052e-12 3.35094e-11 2 -5.012526389789904e-02 -5.012526389239364e-02 5.50539e-12 4.64407e-11 3 2.302005083774220e-01 2.302005083630270e-01 1.43950e-11 2.79497e-11 ----------------------------------------------------------------------------------------------------- 15 U 1 2.893629897978210e+00 2.893629897916343e+00 6.18670e-11 1.10826e-08 * 2 1.379224108290304e+00 1.379224108303386e+00 1.30826e-11 7.42668e-11 3 -2.667028714623411e+00 -2.667028714612504e+00 1.09068e-11 8.88946e-10 ----------------------------------------------------------------------------------------------------- 16 U 1 1.544832486329975e+00 1.544832486343859e+00 1.38838e-11 3.51212e-11 2 1.719992867525076e+00 1.719992867533450e+00 8.37441e-12 8.54552e-11 3 2.328797801241533e+00 2.328797801155993e+00 8.55405e-11 2.06723e-10 ----------------------------------------------------------------------------------------------------- 17 Al 1 2.366113045041152e-01 2.366113045025271e-01 1.58812e-12 5.57245e-11 2 2.224850768687168e-01 2.224850768627634e-01 5.95335e-12 2.74936e-11 3 -1.099560355996599e-02 -1.099560355658868e-02 3.37731e-12 5.63062e-11 ----------------------------------------------------------------------------------------------------- 18 Al 1 2.000005825675710e+00 2.000005825595596e+00 8.01141e-11 9.64396e-09 * 2 -9.198807548392793e-01 -9.198807547817375e-01 5.75419e-11 1.60442e-10 3 -1.240660267699046e+00 -1.240660267699215e+00 1.69420e-13 2.37783e-11 ----------------------------------------------------------------------------------------------------- 19 U 1 1.440840832597199e+00 1.440840832589769e+00 7.43006e-12 1.18276e-09 2 3.782973048618254e-01 3.782973048842503e-01 2.24248e-11 1.37760e-09 3 -5.826116065251701e-01 -5.826116065200743e-01 5.09581e-12 1.59713e-10 ----------------------------------------------------------------------------------------------------- 20 Al 1 -1.859255193397027e+00 -1.859255193422032e+00 2.50051e-11 2.47417e-10 2 -5.968952492246135e-01 -5.968952492434890e-01 1.88756e-11 2.06115e-10 3 5.863531943393326e-01 5.863531943282482e-01 1.10845e-11 2.05616e-10 ----------------------------------------------------------------------------------------------------- 21 Al 1 -5.419008008240360e-01 -5.419008008197326e-01 4.30345e-12 4.11547e-09 * 2 -2.117405021894072e-01 -2.117405021881370e-01 1.27026e-12 2.66705e-10 3 -5.723232524964301e-02 -5.723232525454153e-02 4.89853e-12 3.22450e-10 ----------------------------------------------------------------------------------------------------- 22 Al 1 1.444027713611721e+00 1.444027713615111e+00 3.38995e-12 3.71889e-10 2 -1.968460547598017e+00 -1.968460547697034e+00 9.90168e-11 1.98808e-10 3 2.539687256401758e+00 2.539687256397389e+00 4.36895e-12 2.50996e-10 ----------------------------------------------------------------------------------------------------- 23 Al 1 -4.584195254774114e-01 -4.584195254760084e-01 1.40299e-12 2.03114e-10 2 1.013039108928183e+00 1.013039108908517e+00 1.96660e-11 2.65632e-11 3 -6.727381158505784e-01 -6.727381158528408e-01 2.26241e-12 3.47645e-10 ----------------------------------------------------------------------------------------------------- 24 Al 1 -1.691345827006132e-01 -1.691345826396329e-01 6.09803e-11 3.83903e-10 2 -1.969365638827827e-01 -1.969365639863614e-01 1.03579e-10 1.47273e-10 3 2.038819586262999e-01 2.038819586113716e-01 1.49283e-11 1.99442e-10 ----------------------------------------------------------------------------------------------------- 25 Al 1 -1.282616795505898e+00 -1.282616795530761e+00 2.48623e-11 5.10592e-09 * 2 3.214938417993033e-01 3.214938417769272e-01 2.23761e-11 7.41559e-09 * 3 4.375706038719709e-01 4.375706038329196e-01 3.90513e-11 1.55480e-10 ----------------------------------------------------------------------------------------------------- 26 U 1 7.851170979605250e-01 7.851170980038548e-01 4.33298e-11 1.63793e-10 2 1.536480543533035e+00 1.536480543536011e+00 2.97584e-12 9.09086e-11 3 -1.385378821446868e+00 -1.385378821454530e+00 7.66143e-12 5.30799e-10 ----------------------------------------------------------------------------------------------------- 27 U 1 2.776263280619758e+00 2.776263280634580e+00 1.48224e-11 4.21719e-10 2 4.526386775558780e-01 4.526386775391700e-01 1.67080e-11 3.29406e-10 3 2.804360193872782e+00 2.804360193798831e+00 7.39511e-11 4.08291e-10 ----------------------------------------------------------------------------------------------------- 28 U 1 -1.076383705649197e-01 -1.076383705584494e-01 6.47024e-12 1.57261e-10 2 -9.135386804843770e-01 -9.135386804876120e-01 3.23497e-12 8.93030e-11 3 -6.552143064172048e-01 -6.552143064187714e-01 1.56664e-12 7.20345e-11 ----------------------------------------------------------------------------------------------------- 29 Al 1 -4.756557650609609e+00 -4.756557650548814e+00 6.07949e-11 7.56362e-10 2 -7.506159056141254e-02 -7.506159041453551e-02 1.46877e-10 4.85080e-11 3 1.884426008105750e+00 1.884426008096969e+00 8.78120e-12 4.52371e-10 ----------------------------------------------------------------------------------------------------- 30 U 1 6.625554776867888e-01 6.625554776691120e-01 1.76767e-11 1.53721e-10 2 1.634566277451841e+00 1.634566277441959e+00 9.88232e-12 9.61178e-09 * 3 -5.258797678265027e-01 -5.258797678497369e-01 2.32342e-11 4.25407e-09 * ----------------------------------------------------------------------------------------------------- 31 U 1 -7.741888223417439e-01 -7.741888222771272e-01 6.46168e-11 1.02250e-10 2 -6.119971270420164e-01 -6.119971270630790e-01 2.10626e-11 1.86547e-10 3 -2.417477789137685e-01 -2.417477790086826e-01 9.49142e-11 2.00474e-10 ----------------------------------------------------------------------------------------------------- 32 Al 1 1.234271480136075e+00 1.234271480109628e+00 2.64473e-11 3.92197e-10 2 -3.462975673932930e-01 -3.462975674010902e-01 7.79721e-12 6.58088e-11 3 4.229209583271673e-01 4.229209583266296e-01 5.37625e-13 2.48861e-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 = 2, direction = 2: |F_model - F_numer| error = ----------------------- = 4.50357e-08 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 4.50357e-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 4.50357e-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.