!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_JeongParkDo_2018_PdCu__MO_353393547686_000 Supported species : Cu Pd 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 = Cu | a0 = 3.6133155822753906 | (Configuration in file "config-Cu.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Cu 1 2.745433687208207e-01 2.745433687161436e-01 4.67715e-12 6.15731e-11 2 -5.595297648847753e-01 -5.595297649245038e-01 3.97284e-11 3.25020e-10 3 -8.170859671023030e-01 -8.170859671176192e-01 1.53162e-11 2.20837e-10 ----------------------------------------------------------------------------------------------------- 2 Cu 1 -2.230222686347155e+00 -2.230222686314774e+00 3.23817e-11 1.57899e-10 2 2.177954371071972e+00 2.177954371106551e+00 3.45790e-11 1.53645e-10 3 5.775715304866219e-01 5.775715305332612e-01 4.66392e-11 2.05713e-10 ----------------------------------------------------------------------------------------------------- 3 Cu 1 1.194281044769073e+00 1.194281044773458e+00 4.38494e-12 6.26389e-10 2 3.786803499447911e-01 3.786803499324733e-01 1.23178e-11 4.39165e-10 3 -4.266925713626413e-01 -4.266925713532196e-01 9.42163e-12 1.16779e-10 ----------------------------------------------------------------------------------------------------- 4 Cu 1 6.700123463837453e-01 6.700123463803819e-01 3.36342e-12 1.12308e-10 2 1.044210720545018e+00 1.044210720489050e+00 5.59677e-11 7.83729e-11 3 9.550673230539817e-01 9.550673230610778e-01 7.09610e-12 2.70342e-10 ----------------------------------------------------------------------------------------------------- 5 Cu 1 1.031674681423036e+00 1.031674681391090e+00 3.19458e-11 1.08713e-10 2 -2.212814585906744e+00 -2.212814585898530e+00 8.21387e-12 4.26060e-10 3 5.120032028576389e-01 5.120032028386731e-01 1.89658e-11 1.93237e-10 ----------------------------------------------------------------------------------------------------- 6 Cu 1 1.184312277755507e-01 1.184312277589409e-01 1.66098e-11 5.44247e-11 2 1.095462413796044e+00 1.095462413808180e+00 1.21358e-11 4.01730e-11 3 1.880277552720012e-01 1.880277552807427e-01 8.74156e-12 6.87617e-11 ----------------------------------------------------------------------------------------------------- 7 Cu 1 1.151446257847565e+00 1.151446257877485e+00 2.99198e-11 9.80529e-11 2 -3.122531011953475e+00 -3.122531011931359e+00 2.21161e-11 4.14522e-09 * 3 -3.229736513516150e+00 -3.229736513591577e+00 7.54268e-11 2.87543e-10 ----------------------------------------------------------------------------------------------------- 8 Cu 1 -2.152251730223598e+00 -2.152251730334140e+00 1.10542e-10 1.50621e-10 2 -7.771366761559770e-01 -7.771366761018507e-01 5.41264e-11 1.92914e-10 3 -7.346894013255745e-01 -7.346894014138238e-01 8.82493e-11 1.25939e-10 ----------------------------------------------------------------------------------------------------- 9 Cu 1 -1.278454963714754e-02 -1.278454965316751e-02 1.60200e-11 2.06101e-10 2 -1.202047295530907e+00 -1.202047295578739e+00 4.78324e-11 1.87210e-10 3 -3.636053923436480e-01 -3.636053923162731e-01 2.73748e-11 8.34658e-11 ----------------------------------------------------------------------------------------------------- 10 Cu 1 -1.265061614940256e+00 -1.265061614961753e+00 2.14970e-11 5.78889e-10 2 1.373322433433143e+00 1.373322433448471e+00 1.53275e-11 5.52813e-11 3 -1.513021768177937e+00 -1.513021768195470e+00 1.75335e-11 1.74422e-10 ----------------------------------------------------------------------------------------------------- 11 Cu 1 -3.660990698351381e-01 -3.660990698663776e-01 3.12395e-11 7.06517e-11 2 -1.526232170357089e+00 -1.526232170328580e+00 2.85090e-11 1.14129e-10 3 3.822280216556362e-01 3.822280215825142e-01 7.31221e-11 4.08509e-10 ----------------------------------------------------------------------------------------------------- 12 Cu 1 3.245282811282000e-01 3.245282811339181e-01 5.71809e-12 3.60237e-09 * 2 7.671034135700758e-01 7.671034135578488e-01 1.22270e-11 3.10664e-11 3 6.709628615812144e-01 6.709628615682091e-01 1.30054e-11 1.24917e-11 ----------------------------------------------------------------------------------------------------- 13 Cu 1 -1.171373895189430e+00 -1.171373895167207e+00 2.22231e-11 1.86825e-10 2 -2.577520288963591e+00 -2.577520288935507e+00 2.80842e-11 1.74096e-10 3 -3.321806466624346e+00 -3.321806466632267e+00 7.92033e-12 8.78191e-11 ----------------------------------------------------------------------------------------------------- 14 Cu 1 2.439248134576649e-01 2.439248134798909e-01 2.22260e-11 3.21808e-10 2 9.730162877019592e-01 9.730162877299506e-01 2.79914e-11 1.04954e-10 3 -1.608122652385942e-01 -1.608122652417431e-01 3.14890e-12 1.63887e-10 ----------------------------------------------------------------------------------------------------- 15 Cu 1 2.981312863600329e+00 2.981312863635524e+00 3.51950e-11 3.25566e-10 2 -1.424094652385910e+00 -1.424094652396020e+00 1.01099e-11 3.01719e-10 3 1.239371608774584e+00 1.239371608747802e+00 2.67819e-11 2.29272e-10 ----------------------------------------------------------------------------------------------------- 16 Cu 1 1.345763234601343e+00 1.345763234619304e+00 1.79607e-11 2.04435e-10 2 2.082462479797583e+00 2.082462479784237e+00 1.33462e-11 3.22009e-10 3 1.631424988328648e+00 1.631424988331876e+00 3.22875e-12 5.67824e-11 ----------------------------------------------------------------------------------------------------- 17 Cu 1 -6.766586107701242e-01 -6.766586107725612e-01 2.43694e-12 1.21061e-10 2 -6.174129212862314e-01 -6.174129213438994e-01 5.76680e-11 5.21335e-11 3 -4.965882476032390e-01 -4.965882476444887e-01 4.12497e-11 1.51423e-10 ----------------------------------------------------------------------------------------------------- 18 Cu 1 6.775174326517839e-01 6.775174326148481e-01 3.69358e-11 4.12625e-10 2 1.068562561119390e+00 1.068562561150022e+00 3.06326e-11 1.57695e-10 3 -2.710240835238834e-01 -2.710240834411166e-01 8.27668e-11 4.17093e-09 * ----------------------------------------------------------------------------------------------------- 19 Cu 1 5.306008197035287e-01 5.306008197157041e-01 1.21754e-11 4.76461e-11 2 2.035764162125822e-01 2.035764162240887e-01 1.15066e-11 7.37969e-11 3 -2.419493157197391e-01 -2.419493157207629e-01 1.02382e-12 1.24943e-10 ----------------------------------------------------------------------------------------------------- 20 Cu 1 1.573111748462076e-01 1.573111748567028e-01 1.04952e-11 8.16359e-10 2 1.159066785557503e+00 1.159066785545548e+00 1.19551e-11 1.13503e-10 3 2.442512749095372e-01 2.442512749208061e-01 1.12689e-11 3.24539e-10 ----------------------------------------------------------------------------------------------------- 21 Cu 1 -1.981172210585642e+00 -1.981172210624808e+00 3.91664e-11 9.95177e-10 2 -1.312654391456153e-01 -1.312654391454256e-01 1.89765e-13 1.46322e-10 3 1.717357649138300e+00 1.717357649077506e+00 6.07947e-11 7.76388e-11 ----------------------------------------------------------------------------------------------------- 22 Cu 1 1.133122666509827e+00 1.133122666511349e+00 1.52189e-12 7.82857e-09 * 2 3.124655684496089e+00 3.124655684542835e+00 4.67453e-11 1.27225e-10 3 2.741324876217243e+00 2.741324876230213e+00 1.29705e-11 2.45692e-10 ----------------------------------------------------------------------------------------------------- 23 Cu 1 -6.649646153601377e-01 -6.649646153541107e-01 6.02707e-12 2.58938e-11 2 4.975396011973452e-01 4.975396012173177e-01 1.99725e-11 5.23406e-11 3 -5.934434275821604e-01 -5.934434275791034e-01 3.05700e-12 5.04413e-10 ----------------------------------------------------------------------------------------------------- 24 Cu 1 4.480218754933397e-01 4.480218754898273e-01 3.51241e-12 1.44297e-10 2 -2.153418315219687e-01 -2.153418315100084e-01 1.19604e-11 4.30350e-09 * 3 -7.389792057128290e-01 -7.389792057143482e-01 1.51912e-12 1.43569e-10 ----------------------------------------------------------------------------------------------------- 25 Cu 1 -1.820532689497066e+00 -1.820532689513995e+00 1.69289e-11 1.21998e-10 2 -1.111381175651127e+00 -1.111381175692851e+00 4.17237e-11 7.19338e-11 3 2.132988572906090e-01 2.132988572529282e-01 3.76808e-11 9.23957e-10 ----------------------------------------------------------------------------------------------------- 26 Cu 1 -1.034976043577942e+00 -1.034976043555823e+00 2.21192e-11 7.43062e-10 2 1.595437540290724e+00 1.595437540311794e+00 2.10705e-11 1.19219e-09 * 3 -2.037243555365554e+00 -2.037243555371593e+00 6.03917e-12 6.12545e-10 ----------------------------------------------------------------------------------------------------- 27 Cu 1 2.081308897288959e+00 2.081308897292605e+00 3.64686e-12 6.06679e-11 2 -3.762635105707171e+00 -3.762635105707851e+00 6.80789e-13 1.05605e-09 * 3 1.498109220085966e+00 1.498109220034341e+00 5.16249e-11 1.87773e-10 ----------------------------------------------------------------------------------------------------- 28 Cu 1 -1.666025689469496e+00 -1.666025689450545e+00 1.89506e-11 9.86129e-11 2 1.770745250712004e+00 1.770745250707774e+00 4.22951e-12 1.18828e-10 3 -3.258037745002718e-01 -3.258037745192964e-01 1.90246e-11 1.49571e-10 ----------------------------------------------------------------------------------------------------- 29 Cu 1 -1.050777059357803e+00 -1.050777059397456e+00 3.96538e-11 1.57770e-09 * 2 -9.031986512648609e-01 -9.031986512804033e-01 1.55425e-11 1.36293e-10 3 1.872394017684995e-01 1.872394017790126e-01 1.05131e-11 5.18870e-10 ----------------------------------------------------------------------------------------------------- 30 Cu 1 -2.931838619255555e-01 -2.931838619422492e-01 1.66937e-11 4.20903e-10 2 8.245222101674619e-01 8.245222101623069e-01 5.15499e-12 2.59904e-10 3 5.521838361836374e-01 5.521838361837449e-01 1.07470e-13 9.59247e-10 ----------------------------------------------------------------------------------------------------- 31 Cu 1 7.780473056652787e-01 7.780473056705998e-01 5.32108e-12 1.39491e-10 2 -9.806249228608190e-01 -9.806249228627176e-01 1.89859e-12 1.77016e-10 3 7.261833815318425e-01 7.261833815482484e-01 1.64059e-11 3.38181e-10 ----------------------------------------------------------------------------------------------------- 32 Cu 1 1.244236034850240e+00 1.244236034824681e+00 2.55591e-11 4.51015e-11 2 9.874479739625741e-01 9.874479739780377e-01 1.54636e-11 1.77323e-10 3 1.235876166562912e+00 1.235876166546026e+00 1.68858e-11 2.43614e-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 = 9, direction = 1: |F_model - F_numer| error = ----------------------- = 1.25307e-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 = Pd | a0 = 3.889087677001953 | (Configuration in file "config-Pd.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Pd 1 -3.476145306477673e-01 -3.476145306605065e-01 1.27393e-11 1.27406e-10 2 1.344211090737855e+00 1.344211090750813e+00 1.29587e-11 2.83142e-11 3 -5.910798672298233e-01 -5.910798672288732e-01 9.50129e-13 1.00615e-10 ----------------------------------------------------------------------------------------------------- 2 Pd 1 -1.167317617784604e-01 -1.167317617836082e-01 5.14776e-12 3.40586e-10 2 5.202786097139147e-01 5.202786096990520e-01 1.48627e-11 8.00364e-11 3 -1.775867663512570e+00 -1.775867663498911e+00 1.36589e-11 3.52245e-11 ----------------------------------------------------------------------------------------------------- 3 Pd 1 1.941223837117150e+00 1.941223837117357e+00 2.06946e-13 1.76479e-10 2 -2.866248474728777e+00 -2.866248474558129e+00 1.70648e-10 2.97931e-11 3 3.036811193971499e+00 3.036811193979648e+00 8.14904e-12 1.08396e-10 ----------------------------------------------------------------------------------------------------- 4 Pd 1 -1.505431498871356e+00 -1.505431498902837e+00 3.14817e-11 1.31853e-10 2 6.260771890638065e-01 6.260771890012120e-01 6.25945e-11 1.12476e-10 3 3.694280794199694e-01 3.694280794307419e-01 1.07724e-11 1.00982e-10 ----------------------------------------------------------------------------------------------------- 5 Pd 1 3.739108336921559e-01 3.739108336850078e-01 7.14812e-12 7.02844e-11 2 -1.837450589624512e-01 -1.837450589544134e-01 8.03782e-12 1.17300e-10 3 -2.421374945969580e-01 -2.421374945977902e-01 8.32251e-13 1.04417e-10 ----------------------------------------------------------------------------------------------------- 6 Pd 1 -4.736126453333293e-01 -4.736126453275920e-01 5.73724e-12 5.68333e-09 * 2 1.384752772012318e+00 1.384752772024390e+00 1.20715e-11 3.85416e-11 3 -5.697503043996039e-01 -5.697503044063574e-01 6.75349e-12 1.50021e-10 ----------------------------------------------------------------------------------------------------- 7 Pd 1 1.037464393053447e+00 1.037464393050532e+00 2.91456e-12 1.09012e-09 * 2 -3.678955901615774e-01 -3.678955901786374e-01 1.70600e-11 4.94835e-10 3 -3.420390009530355e-01 -3.420390009854505e-01 3.24150e-11 5.01865e-11 ----------------------------------------------------------------------------------------------------- 8 Pd 1 2.376660811175187e+00 2.376660811089990e+00 8.51972e-11 3.30758e-10 2 1.639456637535984e+00 1.639456637550627e+00 1.46430e-11 1.05817e-10 3 -1.232410127721898e+00 -1.232410127736494e+00 1.45963e-11 3.87555e-10 ----------------------------------------------------------------------------------------------------- 9 Pd 1 -1.349185637575494e+00 -1.349185637551248e+00 2.42466e-11 4.54277e-11 2 -7.687324734104295e+00 -7.687324734135376e+00 3.10809e-11 6.81006e-10 3 -5.659779726292253e+00 -5.659779726327669e+00 3.54161e-11 3.52635e-10 ----------------------------------------------------------------------------------------------------- 10 Pd 1 1.840702416563755e+00 1.840702416565688e+00 1.93223e-12 4.17962e-09 * 2 1.547136867803088e+00 1.547136867801531e+00 1.55675e-12 1.77232e-11 3 -1.674959663763614e+00 -1.674959663749253e+00 1.43610e-11 4.01935e-09 * ----------------------------------------------------------------------------------------------------- 11 Pd 1 -2.842121592078442e+00 -2.842121592049594e+00 2.88485e-11 6.89848e-11 2 2.517671812192544e+00 2.517671812201452e+00 8.90843e-12 2.97183e-10 3 -5.414121716661381e+00 -5.414121716660983e+00 3.97904e-13 5.89884e-11 ----------------------------------------------------------------------------------------------------- 12 Pd 1 -8.132401756477783e-01 -8.132401756749856e-01 2.72073e-11 1.74498e-10 2 6.108997865478593e+00 6.108997865525213e+00 4.66196e-11 8.64297e-10 3 6.957758497650632e+00 6.957758497631785e+00 1.88471e-11 5.98726e-10 ----------------------------------------------------------------------------------------------------- 13 Pd 1 7.343051524013611e-01 7.343051524190543e-01 1.76932e-11 6.22450e-10 2 -4.567407137112524e-01 -4.567407137116154e-01 3.63043e-13 1.33671e-10 3 7.381501835647185e-01 7.381501835785802e-01 1.38617e-11 6.84965e-11 ----------------------------------------------------------------------------------------------------- 14 Pd 1 -6.655110339820992e-01 -6.655110339874467e-01 5.34750e-12 2.04063e-10 2 -6.695862593178128e-01 -6.695862593990238e-01 8.12110e-11 2.55738e-10 3 7.969753271018249e-01 7.969753270735623e-01 2.82626e-11 9.95231e-11 ----------------------------------------------------------------------------------------------------- 15 Pd 1 -4.741165797877007e-01 -4.741165797903485e-01 2.64783e-12 1.21149e-09 * 2 -1.722064227615796e-02 -1.722064227453538e-02 1.62258e-12 3.28978e-10 3 5.022115255021918e-01 5.022115254751143e-01 2.70776e-11 6.75127e-10 ----------------------------------------------------------------------------------------------------- 16 Pd 1 -4.291396387569250e+00 -4.291396387604075e+00 3.48246e-11 1.19041e-10 2 -4.832851370182850e-01 -4.832851370166227e-01 1.66228e-12 1.80954e-11 3 -4.574800350326756e+00 -4.574800350372509e+00 4.57527e-11 7.37668e-11 ----------------------------------------------------------------------------------------------------- 17 Pd 1 -3.842249994801860e-01 -3.842249994831865e-01 3.00054e-12 2.30726e-10 2 -2.381056263267129e-01 -2.381056263265288e-01 1.84130e-13 3.09140e-10 3 -8.950015305384889e-01 -8.950015305759110e-01 3.74222e-11 2.55658e-10 ----------------------------------------------------------------------------------------------------- 18 Pd 1 -1.910658681180346e+00 -1.910658681130281e+00 5.00648e-11 1.16956e-10 2 -6.435296784566397e+00 -6.435296784474089e+00 9.23075e-11 3.24562e-10 3 2.529025537978385e+00 2.529025537951605e+00 2.67799e-11 1.09956e-10 ----------------------------------------------------------------------------------------------------- 19 Pd 1 1.053391838634052e+00 1.053391838653584e+00 1.95315e-11 7.33309e-11 2 6.905705852095307e-01 6.905705852254466e-01 1.59158e-11 1.26929e-10 3 -6.170716068306463e-02 -6.170716068542761e-02 2.36298e-12 2.12591e-11 ----------------------------------------------------------------------------------------------------- 20 Pd 1 -4.035178659293858e-01 -4.035178659293088e-01 7.69385e-14 9.34430e-11 2 3.557927929338349e-01 3.557927929516458e-01 1.78109e-11 3.04248e-10 3 9.657491807916548e-01 9.657491807440148e-01 4.76400e-11 2.50228e-10 ----------------------------------------------------------------------------------------------------- 21 Pd 1 -4.561660671442865e+00 -4.561660671485146e+00 4.22817e-11 5.47614e-10 2 -2.101613203148189e+00 -2.101613203197944e+00 4.97549e-11 8.66391e-10 3 1.336920652431201e+00 1.336920652457614e+00 2.64131e-11 1.11274e-10 ----------------------------------------------------------------------------------------------------- 22 Pd 1 3.017409454143016e+00 3.017409454103590e+00 3.94262e-11 3.28924e-10 2 2.970186594269650e+00 2.970186594386223e+00 1.16573e-10 4.88420e-10 3 -3.803888030509441e+00 -3.803888030515624e+00 6.18305e-12 1.48126e-10 ----------------------------------------------------------------------------------------------------- 23 Pd 1 6.692171507872537e-01 6.692171507953382e-01 8.08442e-12 3.14034e-10 2 -2.000191686467669e+00 -2.000191686477696e+00 1.00266e-11 1.15707e-10 3 1.595819609457553e+00 1.595819609469422e+00 1.18694e-11 1.59249e-10 ----------------------------------------------------------------------------------------------------- 24 Pd 1 -3.575625577107599e+00 -3.575625577107429e+00 1.70086e-13 1.58938e-10 2 3.290141994749118e-02 3.290141998970519e-02 4.22140e-11 2.01027e-10 3 2.326378446747120e+00 2.326378446720830e+00 2.62901e-11 3.25352e-10 ----------------------------------------------------------------------------------------------------- 25 Pd 1 -3.076416348752029e+00 -3.076416348684134e+00 6.78941e-11 2.88203e-10 2 -1.015877633144636e+00 -1.015877633076715e+00 6.79208e-11 2.18009e-10 3 -6.344691756912385e-01 -6.344691756835812e-01 7.65732e-12 6.41588e-10 ----------------------------------------------------------------------------------------------------- 26 Pd 1 3.287119048531228e+00 3.287119048540843e+00 9.61586e-12 4.79283e-11 2 2.918688369789469e+00 2.918688369770399e+00 1.90701e-11 2.05051e-10 3 -3.454770368653621e+00 -3.454770368677566e+00 2.39453e-11 1.46066e-10 ----------------------------------------------------------------------------------------------------- 27 Pd 1 2.351953393632586e+00 2.351953393671294e+00 3.87081e-11 4.31481e-10 2 -1.628242646650685e+00 -1.628242646641962e+00 8.72302e-12 3.34897e-10 3 2.823447057096542e+00 2.823447057050287e+00 4.62559e-11 1.74640e-09 * ----------------------------------------------------------------------------------------------------- 28 Pd 1 -2.339452991917398e+00 -2.339452991902951e+00 1.44476e-11 4.48508e-11 2 1.881216490604544e-01 1.881216490612729e-01 8.18540e-13 1.10232e-10 3 1.503472094751875e+00 1.503472094751452e+00 4.22773e-13 9.06610e-11 ----------------------------------------------------------------------------------------------------- 29 Pd 1 7.681103125640566e+00 7.681103125613082e+00 2.74838e-11 5.36239e-10 2 4.601081752212470e+00 4.601081752179423e+00 3.30473e-11 9.53744e-11 3 3.029083956734376e+00 3.029083956675739e+00 5.86367e-11 2.99788e-10 ----------------------------------------------------------------------------------------------------- 30 Pd 1 3.686368550992134e+00 3.686368550983956e+00 8.17790e-12 9.68194e-09 * 2 -7.646543547391907e-01 -7.646543547028748e-01 3.63160e-11 4.00138e-10 3 3.333374566307628e+00 3.333374566301771e+00 5.85665e-12 1.72453e-10 ----------------------------------------------------------------------------------------------------- 31 Pd 1 3.315365654116426e-01 3.315365654061079e-01 5.53474e-12 2.27950e-10 2 -5.708978116530316e-01 -5.708978117215455e-01 6.85140e-11 6.14939e-11 3 -9.935774231670285e-01 -9.935774231661580e-01 8.70415e-13 1.37609e-10 ----------------------------------------------------------------------------------------------------- 32 Pd 1 -1.251847592694047e+00 -1.251847592695682e+00 1.63536e-12 8.65992e-11 2 4.100034901611771e-02 4.100034901596395e-02 1.53759e-13 2.56798e-11 3 7.575369519360409e-02 7.575369522571961e-02 3.21155e-11 2.74382e-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 = 24, direction = 2: |F_model - F_numer| error = ----------------------- = 1.28305e-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 = Cu Pd | a0 = 3.7345322617402417 | (Configuration in file "config-CuPd.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Pd 1 -2.390053583316846e+00 -2.390053583305283e+00 1.15632e-11 3.25988e-11 2 -2.684540192328028e+00 -2.684540192331986e+00 3.95772e-12 2.68176e-10 3 -7.443927134132683e-01 -7.443927134474204e-01 3.41521e-11 2.15706e-10 ----------------------------------------------------------------------------------------------------- 2 Pd 1 4.985556530673020e+00 4.985556530678560e+00 5.53957e-12 8.59472e-11 2 2.525511651596475e+00 2.525511651584745e+00 1.17302e-11 9.37449e-09 * 3 -3.416753533976876e+00 -3.416753533983407e+00 6.53033e-12 8.01563e-11 ----------------------------------------------------------------------------------------------------- 3 Cu 1 1.425801698129276e+00 1.425801698139789e+00 1.05131e-11 9.84826e-11 2 -2.084236789973640e+00 -2.084236789983401e+00 9.76019e-12 2.22499e-10 3 1.002423035314200e+00 1.002423035312647e+00 1.55298e-12 8.60962e-11 ----------------------------------------------------------------------------------------------------- 4 Pd 1 -3.598381993732801e+00 -3.598381993802954e+00 7.01528e-11 3.32266e-10 2 2.536198448301022e+00 2.536198448247704e+00 5.33187e-11 2.41567e-10 3 2.285387567107786e+00 2.285387567107859e+00 7.32747e-14 2.41533e-10 ----------------------------------------------------------------------------------------------------- 5 Cu 1 -2.372676028158593e+00 -2.372676028156623e+00 1.97087e-12 1.09850e-10 2 -2.460123314564815e-01 -2.460123314551560e-01 1.32552e-12 1.44243e-10 3 -1.345518031449528e+00 -1.345518031434115e+00 1.54123e-11 6.11293e-11 ----------------------------------------------------------------------------------------------------- 6 Cu 1 9.677644069681289e-01 9.677644068984157e-01 6.97132e-11 5.97451e-11 2 1.094787117070599e+00 1.094787117087679e+00 1.70806e-11 1.32658e-10 3 8.339795349380645e-02 8.339795345511332e-02 3.86931e-11 8.41724e-10 ----------------------------------------------------------------------------------------------------- 7 Cu 1 1.480500658832836e+00 1.480500658818799e+00 1.40372e-11 1.54992e-11 2 -3.581151370284998e-02 -3.581151370348529e-02 6.35311e-13 1.28814e-09 * 3 1.959425805484527e+00 1.959425805460102e+00 2.44254e-11 1.70960e-10 ----------------------------------------------------------------------------------------------------- 8 Pd 1 -4.036193584356372e-01 -4.036193584412239e-01 5.58664e-12 1.84310e-10 2 -1.460342291248372e+00 -1.460342291225139e+00 2.32332e-11 1.49466e-09 * 3 1.385622435206110e+00 1.385622435174758e+00 3.13518e-11 2.95738e-10 ----------------------------------------------------------------------------------------------------- 9 Cu 1 6.877885010301009e-01 6.877885010121794e-01 1.79216e-11 1.42677e-10 2 -8.239339834161596e-01 -8.239339834448264e-01 2.86667e-11 8.21163e-11 3 9.682677218102581e-02 9.682677215870215e-02 2.23237e-11 7.88519e-11 ----------------------------------------------------------------------------------------------------- 10 Pd 1 3.891376262320548e-01 3.891376262108371e-01 2.12177e-11 2.69757e-10 2 -2.321152477812215e-01 -2.321152477890368e-01 7.81530e-12 9.14684e-11 3 -2.859010976180550e-01 -2.859010976294195e-01 1.13645e-11 1.90290e-09 * ----------------------------------------------------------------------------------------------------- 11 Pd 1 -1.213032944975544e+00 -1.213032944929074e+00 4.64697e-11 5.12612e-10 2 1.912975025400425e+00 1.912975025415849e+00 1.54243e-11 3.32231e-10 3 2.780675240220195e+00 2.780675240247591e+00 2.73963e-11 4.35549e-11 ----------------------------------------------------------------------------------------------------- 12 Pd 1 -8.064866495855127e-01 -8.064866495868620e-01 1.34925e-12 8.39135e-11 2 4.189196552246663e-01 4.189196552631466e-01 3.84803e-11 1.54397e-10 3 -2.038330734647443e-01 -2.038330734417149e-01 2.30293e-11 1.79062e-10 ----------------------------------------------------------------------------------------------------- 13 Pd 1 -6.332479324901022e-01 -6.332479324880382e-01 2.06402e-12 3.22886e-10 2 7.248704506294885e-01 7.248704506535599e-01 2.40714e-11 1.26353e-10 3 -3.905772017358411e+00 -3.905772017349703e+00 8.70815e-12 2.20162e-11 ----------------------------------------------------------------------------------------------------- 14 Cu 1 -3.677932108031843e-01 -3.677932107824214e-01 2.07629e-11 3.07545e-10 2 -1.128881558879474e+00 -1.128881558879941e+00 4.67182e-13 1.21154e-10 3 9.129260027525649e-01 9.129260027577925e-01 5.22760e-12 4.07350e-11 ----------------------------------------------------------------------------------------------------- 15 Pd 1 2.310530452853837e+00 2.310530452842124e+00 1.17129e-11 3.98881e-11 2 2.314024819392484e-01 2.314024819407956e-01 1.54721e-12 1.64692e-10 3 4.191057805136942e-01 4.191057804974037e-01 1.62906e-11 3.92105e-10 ----------------------------------------------------------------------------------------------------- 16 Cu 1 -8.257679412805181e-01 -8.257679412791686e-01 1.34948e-12 5.30773e-10 2 5.570502315370001e-01 5.570502315301176e-01 6.88249e-12 8.67600e-10 3 4.500280057189131e-02 4.500280051366981e-02 5.82215e-11 1.72181e-10 ----------------------------------------------------------------------------------------------------- 17 Pd 1 8.237691611092876e-01 8.237691611000536e-01 9.23395e-12 3.45853e-11 2 1.811245608308614e-01 1.811245608184592e-01 1.24022e-11 2.79409e-11 3 6.435226905363036e-01 6.435226905320159e-01 4.28768e-12 6.83396e-11 ----------------------------------------------------------------------------------------------------- 18 Cu 1 -7.546531529232937e-01 -7.546531529438811e-01 2.05874e-11 8.03886e-09 * 2 -1.444443817654639e+00 -1.444443817660204e+00 5.56510e-12 9.61398e-11 3 4.857421419801444e-01 4.857421420306656e-01 5.05212e-11 5.97163e-11 ----------------------------------------------------------------------------------------------------- 19 Cu 1 -1.532186557584081e+00 -1.532186557565166e+00 1.89146e-11 1.00024e-10 2 5.815938671305869e-01 5.815938671645412e-01 3.39543e-11 2.31751e-10 3 5.630906489955656e-01 5.630906490122164e-01 1.66508e-11 1.63597e-09 * ----------------------------------------------------------------------------------------------------- 20 Cu 1 7.087136696410390e-01 7.087136696529732e-01 1.19342e-11 2.35342e-09 * 2 1.619268850833383e-01 1.619268850407682e-01 4.25701e-11 3.29179e-10 3 -8.869204455616927e-01 -8.869204455673071e-01 5.61440e-12 5.03060e-09 * ----------------------------------------------------------------------------------------------------- 21 Cu 1 -1.678928261086868e-02 -1.678928260804065e-02 2.82803e-12 6.02830e-11 2 -3.951640110556177e-01 -3.951640110167117e-01 3.89059e-11 4.31789e-10 3 -1.453337047516367e+00 -1.453337047521218e+00 4.85167e-12 4.50604e-11 ----------------------------------------------------------------------------------------------------- 22 Pd 1 -3.067617223231059e-03 -3.067617225574481e-03 2.34342e-12 2.01482e-10 2 1.071443406362231e-01 1.071443406652896e-01 2.90665e-11 2.53338e-10 3 1.087803445236774e+00 1.087803445174502e+00 6.22717e-11 1.56014e-10 ----------------------------------------------------------------------------------------------------- 23 Cu 1 -3.740209397495005e-01 -3.740209397614903e-01 1.19898e-11 1.02068e-10 2 1.611113915156421e+00 1.611113915161429e+00 5.00733e-12 4.92317e-12 3 -9.401089089632345e-01 -9.401089089675693e-01 4.33475e-12 7.10216e-11 ----------------------------------------------------------------------------------------------------- 24 Pd 1 7.429710098216953e-01 7.429710098132520e-01 8.44325e-12 3.31776e-09 * 2 -1.568890697475460e-01 -1.568890698004045e-01 5.28585e-11 6.08235e-10 3 -7.092028197887754e-01 -7.092028197798477e-01 8.92775e-12 2.25012e-10 ----------------------------------------------------------------------------------------------------- 25 Pd 1 -3.236538975897945e+00 -3.236538975893220e+00 4.72467e-12 5.29332e-11 2 -3.547643293868859e+00 -3.547643293893774e+00 2.49143e-11 3.65296e-10 3 9.546554368233823e-01 9.546554368811696e-01 5.77873e-11 9.35858e-09 * ----------------------------------------------------------------------------------------------------- 26 Pd 1 4.252147430643927e+00 4.252147430589719e+00 5.42073e-11 2.13757e-10 2 2.934351728090057e+00 2.934351728096728e+00 6.67111e-12 1.90958e-10 3 1.498629934019614e+00 1.498629934030898e+00 1.12841e-11 5.51644e-10 ----------------------------------------------------------------------------------------------------- 27 Cu 1 -1.802846359140353e-02 -1.802846359355936e-02 2.15583e-12 3.05895e-10 2 1.516361846594093e-01 1.516361846412933e-01 1.81160e-11 1.30237e-10 3 -7.243674233538879e-01 -7.243674233196781e-01 3.42099e-11 1.39957e-09 * ----------------------------------------------------------------------------------------------------- 28 Cu 1 8.406811930012281e-01 8.406811929515872e-01 4.96410e-11 7.05228e-11 2 -7.253869475905481e-01 -7.253869475976361e-01 7.08800e-12 3.06224e-10 3 -1.031479866959577e+00 -1.031479866969133e+00 9.55569e-12 1.97722e-09 * ----------------------------------------------------------------------------------------------------- 29 Cu 1 3.122923785303510e-01 3.122923785207420e-01 9.60892e-12 1.33688e-10 2 6.007617065684508e-01 6.007617065622359e-01 6.21492e-12 1.64725e-10 3 8.391315863484395e-01 8.391315863242534e-01 2.41861e-11 1.50699e-10 ----------------------------------------------------------------------------------------------------- 30 Pd 1 -6.910071683731772e-01 -6.910071682838876e-01 8.92896e-11 1.10511e-10 2 7.465794671826934e-01 7.465794671850680e-01 2.37455e-12 2.44035e-10 3 -1.285109112538078e+00 -1.285109112536910e+00 1.16840e-12 6.83349e-10 ----------------------------------------------------------------------------------------------------- 31 Pd 1 -8.006336883929123e-01 -8.006336883460889e-01 4.68233e-11 2.14890e-10 2 -1.246496608052518e+00 -1.246496608081058e+00 2.85401e-11 3.41328e-10 3 7.355035689102146e-01 7.355035688864883e-01 2.37264e-11 7.95882e-10 ----------------------------------------------------------------------------------------------------- 32 Cu 1 1.103307716583658e-01 1.103307716258418e-01 3.25240e-11 5.13588e-10 2 -8.660500602810116e-01 -8.660500602804785e-01 5.33129e-13 3.80402e-10 3 -8.461767537337428e-01 -8.461767537505375e-01 1.67947e-11 5.97122e-10 ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as discontinuities. Maximum error obtained for particle = 16, direction = 3: |F_model - F_numer| error = ----------------------- = 1.29373e-09 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 1.29373e-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 1.29373e-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.