!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_001 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 2.745433687161438e-01 4.67698e-12 6.15731e-11 2 -5.595297648847753e-01 -5.595297649245043e-01 3.97290e-11 3.25020e-10 3 -8.170859671023030e-01 -8.170859671176197e-01 1.53167e-11 2.20837e-10 ----------------------------------------------------------------------------------------------------- 2 Cu 1 -2.230222686347155e+00 -2.230222686314775e+00 3.23803e-11 1.57899e-10 2 2.177954371071972e+00 2.177954371106551e+00 3.45799e-11 1.53648e-10 3 5.775715304866219e-01 5.775715305332615e-01 4.66396e-11 2.05713e-10 ----------------------------------------------------------------------------------------------------- 3 Cu 1 1.194281044769073e+00 1.194281044773459e+00 4.38516e-12 6.26391e-10 2 3.786803499447911e-01 3.786803499324736e-01 1.23175e-11 4.39165e-10 3 -4.266925713626413e-01 -4.266925713532199e-01 9.42135e-12 1.16780e-10 ----------------------------------------------------------------------------------------------------- 4 Cu 1 6.700123463837453e-01 6.700123463803821e-01 3.36320e-12 1.12308e-10 2 1.044210720545018e+00 1.044210720489051e+00 5.59663e-11 7.83731e-11 3 9.550673230539817e-01 9.550673230610784e-01 7.09677e-12 2.70342e-10 ----------------------------------------------------------------------------------------------------- 5 Cu 1 1.031674681423036e+00 1.031674681391091e+00 3.19451e-11 1.08713e-10 2 -2.212814585906744e+00 -2.212814585898532e+00 8.21210e-12 4.26056e-10 3 5.120032028576389e-01 5.120032028262610e-01 3.13779e-11 4.99816e-10 ----------------------------------------------------------------------------------------------------- 6 Cu 1 1.184312277755476e-01 1.184312277589410e-01 1.66066e-11 5.44247e-11 2 1.095462413796045e+00 1.095462413808181e+00 1.21358e-11 4.01741e-11 3 1.880277552720049e-01 1.880277552807429e-01 8.73795e-12 6.87616e-11 ----------------------------------------------------------------------------------------------------- 7 Cu 1 1.151446257847564e+00 1.151446257877485e+00 2.99210e-11 9.80527e-11 2 -3.122531011953475e+00 -3.122531011931358e+00 2.21170e-11 4.14522e-09 * 3 -3.229736513516150e+00 -3.229736513591579e+00 7.54290e-11 2.87543e-10 ----------------------------------------------------------------------------------------------------- 8 Cu 1 -2.152251730223595e+00 -2.152251730334143e+00 1.10548e-10 1.50623e-10 2 -7.771366761559781e-01 -7.771366761018510e-01 5.41271e-11 1.92913e-10 3 -7.346894013255783e-01 -7.346894014138244e-01 8.82462e-11 1.25939e-10 ----------------------------------------------------------------------------------------------------- 9 Cu 1 -1.278454963714754e-02 -1.278454965316752e-02 1.60200e-11 2.06101e-10 2 -1.202047295530907e+00 -1.202047295578740e+00 4.78328e-11 1.87210e-10 3 -3.636053923436480e-01 -3.636053923162735e-01 2.73745e-11 8.34657e-11 ----------------------------------------------------------------------------------------------------- 10 Cu 1 -1.265061614940256e+00 -1.265061614961754e+00 2.14979e-11 5.78890e-10 2 1.373322433433143e+00 1.373322433448471e+00 1.53284e-11 5.52813e-11 3 -1.513021768177937e+00 -1.513021768195471e+00 1.75346e-11 1.74421e-10 ----------------------------------------------------------------------------------------------------- 11 Cu 1 -3.660990698351381e-01 -3.660990698663779e-01 3.12398e-11 7.06516e-11 2 -1.526232170357089e+00 -1.526232170328581e+00 2.85079e-11 1.14130e-10 3 3.822280216556362e-01 3.822280215825145e-01 7.31217e-11 4.08509e-10 ----------------------------------------------------------------------------------------------------- 12 Cu 1 3.245282811282000e-01 3.245282811339180e-01 5.71798e-12 3.60237e-09 * 2 7.671034135700758e-01 7.671034135578494e-01 1.22264e-11 3.10659e-11 3 6.709628615812144e-01 6.709628615682095e-01 1.30049e-11 1.24917e-11 ----------------------------------------------------------------------------------------------------- 13 Cu 1 -1.171373895189430e+00 -1.171373895167208e+00 2.22222e-11 1.86826e-10 2 -2.577520288963591e+00 -2.577520288935509e+00 2.80824e-11 1.74096e-10 3 -3.321806466624346e+00 -3.321806466632269e+00 7.92255e-12 8.78191e-11 ----------------------------------------------------------------------------------------------------- 14 Cu 1 2.439248134576537e-01 2.439248134798910e-01 2.22373e-11 3.21808e-10 2 9.730162877019596e-01 9.730162877299513e-01 2.79917e-11 1.04954e-10 3 -1.608122652385846e-01 -1.608122652417432e-01 3.15861e-12 1.63887e-10 ----------------------------------------------------------------------------------------------------- 15 Cu 1 2.981312863600331e+00 2.981312863635526e+00 3.51950e-11 3.25563e-10 2 -1.424094652385917e+00 -1.424094652396021e+00 1.01033e-11 3.01719e-10 3 1.239371608774590e+00 1.239371608747803e+00 2.67875e-11 2.29271e-10 ----------------------------------------------------------------------------------------------------- 16 Cu 1 1.345763234601354e+00 1.345763234619305e+00 1.79505e-11 2.04436e-10 2 2.082462479797583e+00 2.082462479784239e+00 1.33444e-11 3.22007e-10 3 1.631424988328638e+00 1.631424988331877e+00 3.23963e-12 5.67824e-11 ----------------------------------------------------------------------------------------------------- 17 Cu 1 -6.766586107701242e-01 -6.766586107725615e-01 2.43727e-12 1.21061e-10 2 -6.174129212862314e-01 -6.174129213438996e-01 5.76682e-11 5.21332e-11 3 -4.965882476032390e-01 -4.965882476444890e-01 4.12500e-11 1.51423e-10 ----------------------------------------------------------------------------------------------------- 18 Cu 1 6.775174326517839e-01 6.775174326148484e-01 3.69355e-11 4.12625e-10 2 1.068562561119390e+00 1.068562561150023e+00 3.06331e-11 1.57696e-10 3 -2.710240835238834e-01 -2.710240834411164e-01 8.27670e-11 4.17093e-09 * ----------------------------------------------------------------------------------------------------- 19 Cu 1 5.306008197035287e-01 5.306008197157049e-01 1.21763e-11 4.76467e-11 2 2.035764162125822e-01 2.035764162240889e-01 1.15067e-11 7.37967e-11 3 -2.419493157197391e-01 -2.419493157207631e-01 1.02396e-12 1.24943e-10 ----------------------------------------------------------------------------------------------------- 20 Cu 1 1.573111748462076e-01 1.573111748567029e-01 1.04952e-11 8.16359e-10 2 1.159066785557503e+00 1.159066785545549e+00 1.19544e-11 1.13503e-10 3 2.442512749095372e-01 2.442512749208066e-01 1.12694e-11 3.24539e-10 ----------------------------------------------------------------------------------------------------- 21 Cu 1 -1.981172210585642e+00 -1.981172210624810e+00 3.91678e-11 9.95177e-10 2 -1.312654391456153e-01 -1.312654391454257e-01 1.89682e-13 1.46322e-10 3 1.717357649138300e+00 1.717357649077507e+00 6.07936e-11 7.76388e-11 ----------------------------------------------------------------------------------------------------- 22 Cu 1 1.133122666509826e+00 1.133122666511349e+00 1.52234e-12 7.82857e-09 * 2 3.124655684496097e+00 3.124655684543061e+00 4.69638e-11 1.27661e-10 3 2.741324876217236e+00 2.741324876230216e+00 1.29794e-11 2.45693e-10 ----------------------------------------------------------------------------------------------------- 23 Cu 1 -6.649646153601377e-01 -6.649646153541110e-01 6.02673e-12 2.58933e-11 2 4.975396011973452e-01 4.975396012173181e-01 1.99729e-11 5.23406e-11 3 -5.934434275821604e-01 -5.934434275791032e-01 3.05722e-12 5.04413e-10 ----------------------------------------------------------------------------------------------------- 24 Cu 1 4.480218754933388e-01 4.480218754898276e-01 3.51114e-12 1.44297e-10 2 -2.153418315219692e-01 -2.153418315100082e-01 1.19609e-11 4.30350e-09 * 3 -7.389792057128285e-01 -7.389792057143488e-01 1.52034e-12 1.43568e-10 ----------------------------------------------------------------------------------------------------- 25 Cu 1 -1.820532689497066e+00 -1.820532689513997e+00 1.69305e-11 1.21998e-10 2 -1.111381175651127e+00 -1.111381175692852e+00 4.17246e-11 7.19358e-11 3 2.132988572906090e-01 2.132988572529284e-01 3.76806e-11 9.23956e-10 ----------------------------------------------------------------------------------------------------- 26 Cu 1 -1.034976043577942e+00 -1.034976043555824e+00 2.21183e-11 7.43061e-10 2 1.595437540290724e+00 1.595437540311795e+00 2.10711e-11 1.19219e-09 * 3 -2.037243555365554e+00 -2.037243555371594e+00 6.04050e-12 6.12545e-10 ----------------------------------------------------------------------------------------------------- 27 Cu 1 2.081308897288973e+00 2.081308897292607e+00 3.63443e-12 6.06710e-11 2 -3.762635105707172e+00 -3.762635105707850e+00 6.77680e-13 1.05605e-09 * 3 1.498109220085952e+00 1.498109220034342e+00 5.16100e-11 1.87772e-10 ----------------------------------------------------------------------------------------------------- 28 Cu 1 -1.666025689469496e+00 -1.666025689450546e+00 1.89495e-11 9.86133e-11 2 1.770745250712004e+00 1.770745250707775e+00 4.22840e-12 1.18828e-10 3 -3.258037745002718e-01 -3.258037745192968e-01 1.90249e-11 1.49571e-10 ----------------------------------------------------------------------------------------------------- 29 Cu 1 -1.050777059357817e+00 -1.050777059231377e+00 1.26440e-10 2.52900e-10 2 -9.031986512648595e-01 -9.031986512804041e-01 1.55446e-11 1.36294e-10 3 1.872394017685128e-01 1.872394017790127e-01 1.04999e-11 5.18870e-10 ----------------------------------------------------------------------------------------------------- 30 Cu 1 -2.931838619255555e-01 -2.931838619422492e-01 1.66936e-11 4.20903e-10 2 8.245222101674619e-01 8.245222101623074e-01 5.15443e-12 2.59903e-10 3 5.521838361836374e-01 5.521838361837452e-01 1.07803e-13 9.59247e-10 ----------------------------------------------------------------------------------------------------- 31 Cu 1 7.780473056652790e-01 7.780473056706003e-01 5.32130e-12 1.39491e-10 2 -9.806249228608184e-01 -9.806249228627183e-01 1.89992e-12 1.77016e-10 3 7.261833815318426e-01 7.261833815482487e-01 1.64061e-11 3.38182e-10 ----------------------------------------------------------------------------------------------------- 32 Cu 1 1.244236034850240e+00 1.244236034824682e+00 2.55582e-11 4.51015e-11 2 9.874479739625741e-01 9.874479739780384e-01 1.54643e-11 1.77323e-10 3 1.235876166562912e+00 1.235876166546027e+00 1.68849e-11 2.43603e-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 -3.476145306605069e-01 1.27396e-11 1.27406e-10 2 1.344211090737855e+00 1.344211090750814e+00 1.29599e-11 2.83145e-11 3 -5.910798672298233e-01 -5.910798672288736e-01 9.49685e-13 1.00615e-10 ----------------------------------------------------------------------------------------------------- 2 Pd 1 -1.167317617784604e-01 -1.167317617836083e-01 5.14785e-12 3.40586e-10 2 5.202786097139147e-01 5.202786096990523e-01 1.48624e-11 8.00359e-11 3 -1.775867663512570e+00 -1.775867663498912e+00 1.36577e-11 3.52245e-11 ----------------------------------------------------------------------------------------------------- 3 Pd 1 1.941223837117150e+00 1.941223837117358e+00 2.08056e-13 1.76478e-10 2 -2.866248474728777e+00 -2.866248474558131e+00 1.70646e-10 2.97926e-11 3 3.036811193971499e+00 3.036811193979650e+00 8.15126e-12 1.08396e-10 ----------------------------------------------------------------------------------------------------- 4 Pd 1 -1.505431498871356e+00 -1.505431498902838e+00 3.14826e-11 1.31853e-10 2 6.260771890638065e-01 6.260771890012127e-01 6.25938e-11 1.12476e-10 3 3.694280794199694e-01 3.694280794307422e-01 1.07728e-11 1.00982e-10 ----------------------------------------------------------------------------------------------------- 5 Pd 1 3.739108336921559e-01 3.739108336850081e-01 7.14784e-12 7.02846e-11 2 -1.837450589624512e-01 -1.837450589544136e-01 8.03768e-12 1.17300e-10 3 -2.421374945969580e-01 -2.421374945977904e-01 8.32445e-13 1.04417e-10 ----------------------------------------------------------------------------------------------------- 6 Pd 1 -4.736126453333293e-01 -4.736126453275918e-01 5.73747e-12 5.68333e-09 * 2 1.384752772012318e+00 1.384752772024391e+00 1.20730e-11 3.85423e-11 3 -5.697503043996039e-01 -5.697503044063579e-01 6.75393e-12 1.50020e-10 ----------------------------------------------------------------------------------------------------- 7 Pd 1 1.037464393053447e+00 1.037464393050533e+00 2.91389e-12 1.09012e-09 * 2 -3.678955901615774e-01 -3.678955901786376e-01 1.70602e-11 4.94835e-10 3 -3.420390009530355e-01 -3.420390009854507e-01 3.24152e-11 5.01865e-11 ----------------------------------------------------------------------------------------------------- 8 Pd 1 2.376660811175187e+00 2.376660811089991e+00 8.51959e-11 3.30761e-10 2 1.639456637535984e+00 1.639456637550628e+00 1.46443e-11 1.05816e-10 3 -1.232410127721898e+00 -1.232410127736495e+00 1.45972e-11 3.87557e-10 ----------------------------------------------------------------------------------------------------- 9 Pd 1 -1.349185637575494e+00 -1.349185637551248e+00 2.42459e-11 4.54274e-11 2 -7.687324734104295e+00 -7.687324734172545e+00 6.82503e-11 3.61522e-10 3 -5.659779726292253e+00 -5.659779726327673e+00 3.54197e-11 3.52635e-10 ----------------------------------------------------------------------------------------------------- 10 Pd 1 1.840702416563755e+00 1.840702416565687e+00 1.93134e-12 4.17962e-09 * 2 1.547136867803088e+00 1.547136867801532e+00 1.55587e-12 1.77232e-11 3 -1.674959663763614e+00 -1.674959663749253e+00 1.43618e-11 4.01935e-09 * ----------------------------------------------------------------------------------------------------- 11 Pd 1 -2.842121592078442e+00 -2.842121592049596e+00 2.88467e-11 6.89866e-11 2 2.517671812192544e+00 2.517671812201453e+00 8.90932e-12 2.97181e-10 3 -5.414121716661381e+00 -5.414121716660987e+00 3.93463e-13 5.89822e-11 ----------------------------------------------------------------------------------------------------- 12 Pd 1 -8.132401756477783e-01 -8.132401756749859e-01 2.72076e-11 1.74497e-10 2 6.108997865478593e+00 6.108997865525216e+00 4.66231e-11 8.64296e-10 3 6.957758497650632e+00 6.957758497631788e+00 1.88436e-11 5.98728e-10 ----------------------------------------------------------------------------------------------------- 13 Pd 1 7.343051524013611e-01 7.343051524190544e-01 1.76933e-11 6.22451e-10 2 -4.567407137112524e-01 -4.567407137116157e-01 3.63376e-13 1.33671e-10 3 7.381501835647185e-01 7.381501835785809e-01 1.38624e-11 6.84967e-11 ----------------------------------------------------------------------------------------------------- 14 Pd 1 -6.655110339820992e-01 -6.655110339874472e-01 5.34794e-12 2.04064e-10 2 -6.695862593178128e-01 -6.695862593990244e-01 8.12116e-11 2.55738e-10 3 7.969753271018249e-01 7.969753270735628e-01 2.82622e-11 9.95229e-11 ----------------------------------------------------------------------------------------------------- 15 Pd 1 -4.741165797877007e-01 -4.741165797903488e-01 2.64816e-12 1.21149e-09 * 2 -1.722064227615796e-02 -1.722064227453539e-02 1.62256e-12 3.28978e-10 3 5.022115255021918e-01 5.022115254751146e-01 2.70772e-11 6.75127e-10 ----------------------------------------------------------------------------------------------------- 16 Pd 1 -4.291396387569250e+00 -4.291396387604077e+00 3.48273e-11 1.19040e-10 2 -4.832851370182850e-01 -4.832851370166231e-01 1.66189e-12 1.80954e-11 3 -4.574800350326756e+00 -4.574800350372511e+00 4.57554e-11 7.37650e-11 ----------------------------------------------------------------------------------------------------- 17 Pd 1 -3.842249994801860e-01 -3.842249994831868e-01 3.00082e-12 2.30727e-10 2 -2.381056263267129e-01 -2.381056263265290e-01 1.83936e-13 3.09140e-10 3 -8.950015305384889e-01 -8.950015305759117e-01 3.74228e-11 2.55658e-10 ----------------------------------------------------------------------------------------------------- 18 Pd 1 -1.910658681180346e+00 -1.910658681130283e+00 5.00633e-11 1.16957e-10 2 -6.435296784566397e+00 -6.435296784474099e+00 9.22977e-11 3.24556e-10 3 2.529025537978385e+00 2.529025537951608e+00 2.67772e-11 1.09953e-10 ----------------------------------------------------------------------------------------------------- 19 Pd 1 1.053391838634052e+00 1.053391838653585e+00 1.95324e-11 7.33316e-11 2 6.905705852095307e-01 6.905705852254471e-01 1.59164e-11 1.26930e-10 3 -6.170716068306463e-02 -6.170716068542766e-02 2.36303e-12 2.12591e-11 ----------------------------------------------------------------------------------------------------- 20 Pd 1 -4.035178659293858e-01 -4.035178659293092e-01 7.66054e-14 9.34431e-11 2 3.557927929338349e-01 3.557927929516461e-01 1.78113e-11 3.04248e-10 3 9.657491807916548e-01 9.657491807440155e-01 4.76393e-11 2.50228e-10 ----------------------------------------------------------------------------------------------------- 21 Pd 1 -4.561660671442865e+00 -4.561660671485151e+00 4.22862e-11 5.47613e-10 2 -2.101613203148189e+00 -2.101613203197946e+00 4.97566e-11 8.66392e-10 3 1.336920652431201e+00 1.336920652457615e+00 2.64142e-11 1.11274e-10 ----------------------------------------------------------------------------------------------------- 22 Pd 1 3.017409454143016e+00 3.017409454103592e+00 3.94236e-11 3.28921e-10 2 2.970186594269650e+00 2.970186594386228e+00 1.16577e-10 4.88424e-10 3 -3.803888030509441e+00 -3.803888030515627e+00 6.18572e-12 1.48126e-10 ----------------------------------------------------------------------------------------------------- 23 Pd 1 6.692171507872537e-01 6.692171507953387e-01 8.08498e-12 3.14035e-10 2 -2.000191686467669e+00 -2.000191686477697e+00 1.00280e-11 1.15707e-10 3 1.595819609457553e+00 1.595819609469423e+00 1.18705e-11 1.59248e-10 ----------------------------------------------------------------------------------------------------- 24 Pd 1 -3.575625577107599e+00 -3.575625577107431e+00 1.67866e-13 1.58936e-10 2 3.290141994749118e-02 3.290141998970521e-02 4.22140e-11 2.01027e-10 3 2.326378446747120e+00 2.326378446720831e+00 2.62892e-11 3.25354e-10 ----------------------------------------------------------------------------------------------------- 25 Pd 1 -3.076416348752029e+00 -3.076416348684136e+00 6.78924e-11 2.88199e-10 2 -1.015877633144636e+00 -1.015877633076716e+00 6.79199e-11 2.18010e-10 3 -6.344691756912385e-01 -6.344691756835814e-01 7.65710e-12 6.41587e-10 ----------------------------------------------------------------------------------------------------- 26 Pd 1 3.287119048531228e+00 3.287119048540846e+00 9.61853e-12 4.79261e-11 2 2.918688369789469e+00 2.918688369770401e+00 1.90674e-11 2.05051e-10 3 -3.454770368653621e+00 -3.454770368677569e+00 2.39480e-11 1.46068e-10 ----------------------------------------------------------------------------------------------------- 27 Pd 1 2.351953393632586e+00 2.351953393671296e+00 3.87099e-11 4.31481e-10 2 -1.628242646650685e+00 -1.628242646641963e+00 8.72213e-12 3.34897e-10 3 2.823447057096542e+00 2.823447057050288e+00 4.62546e-11 1.74640e-09 * ----------------------------------------------------------------------------------------------------- 28 Pd 1 -2.339452991917398e+00 -2.339452991902952e+00 1.44462e-11 4.48503e-11 2 1.881216490604544e-01 1.881216490612732e-01 8.18845e-13 1.10232e-10 3 1.503472094751875e+00 1.503472094751453e+00 4.21663e-13 9.06613e-11 ----------------------------------------------------------------------------------------------------- 29 Pd 1 7.681103125640566e+00 7.681103125613073e+00 2.74927e-11 5.36253e-10 2 4.601081752212470e+00 4.601081752179426e+00 3.30438e-11 9.53770e-11 3 3.029083956734376e+00 3.029083956675741e+00 5.86349e-11 2.99787e-10 ----------------------------------------------------------------------------------------------------- 30 Pd 1 3.686368550992134e+00 3.686368550983954e+00 8.17968e-12 9.68194e-09 * 2 -7.646543547391907e-01 -7.646543547028752e-01 3.63155e-11 4.00137e-10 3 3.333374566307628e+00 3.333374566301774e+00 5.85398e-12 1.72454e-10 ----------------------------------------------------------------------------------------------------- 31 Pd 1 3.315365654116426e-01 3.315365654061081e-01 5.53452e-12 2.27951e-10 2 -5.708978116530316e-01 -5.708978117215462e-01 6.85146e-11 6.14943e-11 3 -9.935774231670285e-01 -9.935774231661587e-01 8.69749e-13 1.37610e-10 ----------------------------------------------------------------------------------------------------- 32 Pd 1 -1.251847592694047e+00 -1.251847592695683e+00 1.63602e-12 8.65978e-11 2 4.100034901611771e-02 4.100034901596399e-02 1.53724e-13 2.56798e-11 3 7.575369519360409e-02 7.575369522571966e-02 3.21156e-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 -2.390053583305284e+00 1.15623e-11 3.25988e-11 2 -2.684540192328028e+00 -2.684540192331987e+00 3.95950e-12 2.68173e-10 3 -7.443927134132683e-01 -7.443927134474211e-01 3.41528e-11 2.15706e-10 ----------------------------------------------------------------------------------------------------- 2 Pd 1 4.985556530673020e+00 4.985556530678562e+00 5.54223e-12 8.59499e-11 2 2.525511651596475e+00 2.525511651584743e+00 1.17315e-11 9.37449e-09 * 3 -3.416753533976876e+00 -3.416753533983409e+00 6.53255e-12 8.01563e-11 ----------------------------------------------------------------------------------------------------- 3 Cu 1 1.425801698129276e+00 1.425801698139790e+00 1.05140e-11 9.84821e-11 2 -2.084236789973640e+00 -2.084236789983402e+00 9.76197e-12 2.22501e-10 3 1.002423035314200e+00 1.002423035312648e+00 1.55231e-12 8.60962e-11 ----------------------------------------------------------------------------------------------------- 4 Pd 1 -3.598381993732801e+00 -3.598381993802956e+00 7.01550e-11 3.32266e-10 2 2.536198448301022e+00 2.536198448247706e+00 5.33165e-11 2.41567e-10 3 2.285387567107786e+00 2.285387567107860e+00 7.41629e-14 2.41533e-10 ----------------------------------------------------------------------------------------------------- 5 Cu 1 -2.372676028158593e+00 -2.372676028156625e+00 1.96865e-12 1.09851e-10 2 -2.460123314564815e-01 -2.460123314551562e-01 1.32536e-12 1.44243e-10 3 -1.345518031449528e+00 -1.345518031434116e+00 1.54114e-11 6.11284e-11 ----------------------------------------------------------------------------------------------------- 6 Cu 1 9.677644069681289e-01 9.677644068984164e-01 6.97126e-11 5.97455e-11 2 1.094787117070599e+00 1.094787117087680e+00 1.70814e-11 1.32656e-10 3 8.339795349380645e-02 8.339795345511337e-02 3.86931e-11 8.41724e-10 ----------------------------------------------------------------------------------------------------- 7 Cu 1 1.480500658832836e+00 1.480500658818800e+00 1.40359e-11 1.54992e-11 2 -3.581151370284998e-02 -3.581151370348527e-02 6.35290e-13 1.28814e-09 * 3 1.959425805484527e+00 1.959425805460103e+00 2.44240e-11 1.70960e-10 ----------------------------------------------------------------------------------------------------- 8 Pd 1 -4.036193584356372e-01 -4.036193584412242e-01 5.58692e-12 1.84310e-10 2 -1.460342291248372e+00 -1.460342291225140e+00 2.32319e-11 1.49466e-09 * 3 1.385622435206110e+00 1.385622435174759e+00 3.13505e-11 2.95738e-10 ----------------------------------------------------------------------------------------------------- 9 Cu 1 6.877885010301009e-01 6.877885010121798e-01 1.79211e-11 1.42677e-10 2 -8.239339834161596e-01 -8.239339834448270e-01 2.86674e-11 8.21165e-11 3 9.682677218102581e-02 9.682677215870222e-02 2.23236e-11 7.88519e-11 ----------------------------------------------------------------------------------------------------- 10 Pd 1 3.891376262320548e-01 3.891376262108374e-01 2.12175e-11 2.69757e-10 2 -2.321152477812215e-01 -2.321152477890370e-01 7.81550e-12 9.14684e-11 3 -2.859010976180550e-01 -2.859010976294193e-01 1.13643e-11 1.90290e-09 * ----------------------------------------------------------------------------------------------------- 11 Pd 1 -1.213032944975544e+00 -1.213032944929075e+00 4.64691e-11 5.12614e-10 2 1.912975025400425e+00 1.912975025415850e+00 1.54254e-11 3.32230e-10 3 2.780675240220195e+00 2.780675240245186e+00 2.49911e-11 4.25371e-11 ----------------------------------------------------------------------------------------------------- 12 Pd 1 -8.064866495855127e-01 -8.064866495868627e-01 1.34992e-12 8.39137e-11 2 4.189196552246663e-01 4.189196552631469e-01 3.84806e-11 1.54397e-10 3 -2.038330734647443e-01 -2.038330734417154e-01 2.30289e-11 1.79062e-10 ----------------------------------------------------------------------------------------------------- 13 Pd 1 -6.332479324901022e-01 -6.332479324880389e-01 2.06335e-12 3.22885e-10 2 7.248704506294885e-01 7.248704506535605e-01 2.40720e-11 1.26353e-10 3 -3.905772017358411e+00 -3.905772017349706e+00 8.70459e-12 2.20206e-11 ----------------------------------------------------------------------------------------------------- 14 Cu 1 -3.677932108031843e-01 -3.677932107824212e-01 2.07632e-11 3.07545e-10 2 -1.128881558879474e+00 -1.128881558879942e+00 4.68070e-13 1.21153e-10 3 9.129260027525649e-01 9.129260027577932e-01 5.22837e-12 4.07346e-11 ----------------------------------------------------------------------------------------------------- 15 Pd 1 2.310530452853837e+00 2.310530452842125e+00 1.17120e-11 3.98854e-11 2 2.314024819392484e-01 2.314024819407957e-01 1.54737e-12 1.64692e-10 3 4.191057805136942e-01 4.191057804974040e-01 1.62902e-11 3.92105e-10 ----------------------------------------------------------------------------------------------------- 16 Cu 1 -8.257679412805181e-01 -8.257679412791691e-01 1.34903e-12 5.30773e-10 2 5.570502315370001e-01 5.570502315301179e-01 6.88216e-12 8.67599e-10 3 4.500280057189131e-02 4.500280051366984e-02 5.82215e-11 1.72181e-10 ----------------------------------------------------------------------------------------------------- 17 Pd 1 8.237691611092876e-01 8.237691611000543e-01 9.23328e-12 3.45859e-11 2 1.811245608308614e-01 1.811245608184592e-01 1.24021e-11 2.79409e-11 3 6.435226905363036e-01 6.435226905320165e-01 4.28713e-12 6.83401e-11 ----------------------------------------------------------------------------------------------------- 18 Cu 1 -7.546531529232937e-01 -7.546531529438807e-01 2.05870e-11 8.03886e-09 * 2 -1.444443817654639e+00 -1.444443817660205e+00 5.56599e-12 9.61398e-11 3 4.857421419801444e-01 4.857421420306659e-01 5.05215e-11 5.97163e-11 ----------------------------------------------------------------------------------------------------- 19 Cu 1 -1.532186557584081e+00 -1.532186557565167e+00 1.89135e-11 1.00024e-10 2 5.815938671305869e-01 5.815938671645414e-01 3.39545e-11 2.31751e-10 3 5.630906489955656e-01 5.630906490122161e-01 1.66505e-11 1.63597e-09 * ----------------------------------------------------------------------------------------------------- 20 Cu 1 7.087136696410390e-01 7.087136696529729e-01 1.19339e-11 2.35342e-09 * 2 1.619268850833383e-01 1.619268850407683e-01 4.25700e-11 3.29179e-10 3 -8.869204455616927e-01 -8.869204455673066e-01 5.61395e-12 5.03060e-09 * ----------------------------------------------------------------------------------------------------- 21 Cu 1 -1.678928261086868e-02 -1.678928260804066e-02 2.82802e-12 6.02830e-11 2 -3.951640110556177e-01 -3.951640110167121e-01 3.89056e-11 4.31788e-10 3 -1.453337047516367e+00 -1.453337047521220e+00 4.85278e-12 4.50602e-11 ----------------------------------------------------------------------------------------------------- 22 Pd 1 -3.067617223231059e-03 -3.067617225574483e-03 2.34342e-12 2.01482e-10 2 1.071443406362231e-01 1.071443406652897e-01 2.90666e-11 2.53338e-10 3 1.087803445236774e+00 1.087803445174503e+00 6.22715e-11 1.56015e-10 ----------------------------------------------------------------------------------------------------- 23 Cu 1 -3.740209397495005e-01 -3.740209397614906e-01 1.19901e-11 1.02068e-10 2 1.611113915156421e+00 1.611113915161430e+00 5.00822e-12 4.92340e-12 3 -9.401089089632345e-01 -9.401089089675699e-01 4.33542e-12 7.10223e-11 ----------------------------------------------------------------------------------------------------- 24 Pd 1 7.429710098216953e-01 7.429710098132517e-01 8.44358e-12 3.31776e-09 * 2 -1.568890697475460e-01 -1.568890698004046e-01 5.28586e-11 6.08235e-10 3 -7.092028197887754e-01 -7.092028197798482e-01 8.92719e-12 2.25013e-10 ----------------------------------------------------------------------------------------------------- 25 Pd 1 -3.236538975897945e+00 -3.236538975893220e+00 4.72422e-12 5.29363e-11 2 -3.547643293868859e+00 -3.547643293893776e+00 2.49170e-11 3.65294e-10 3 9.546554368233823e-01 9.546554368811691e-01 5.77868e-11 9.35858e-09 * ----------------------------------------------------------------------------------------------------- 26 Pd 1 4.252147430643927e+00 4.252147430589721e+00 5.42055e-11 2.13754e-10 2 2.934351728090057e+00 2.934351728096732e+00 6.67466e-12 1.90961e-10 3 1.498629934019614e+00 1.498629934030899e+00 1.12852e-11 5.51644e-10 ----------------------------------------------------------------------------------------------------- 27 Cu 1 -1.802846359140353e-02 -1.802846359355937e-02 2.15584e-12 3.05895e-10 2 1.516361846594093e-01 1.516361846412934e-01 1.81159e-11 1.30237e-10 3 -7.243674233538879e-01 -7.243674233196785e-01 3.42094e-11 1.39957e-09 * ----------------------------------------------------------------------------------------------------- 28 Cu 1 8.406811930012281e-01 8.406811929515877e-01 4.96404e-11 7.05230e-11 2 -7.253869475905481e-01 -7.253869475976366e-01 7.08844e-12 3.06224e-10 3 -1.031479866959577e+00 -1.031479866969132e+00 9.55525e-12 1.97722e-09 * ----------------------------------------------------------------------------------------------------- 29 Cu 1 3.122923785303510e-01 3.122923785207423e-01 9.60865e-12 1.33688e-10 2 6.007617065684508e-01 6.007617065622366e-01 6.21425e-12 1.64724e-10 3 8.391315863484395e-01 8.391315863242512e-01 2.41883e-11 1.50696e-10 ----------------------------------------------------------------------------------------------------- 30 Pd 1 -6.910071683731772e-01 -6.910071682838881e-01 8.92891e-11 1.10512e-10 2 7.465794671826934e-01 7.465794671850685e-01 2.37510e-12 2.44035e-10 3 -1.285109112538078e+00 -1.285109112536911e+00 1.16707e-12 6.83350e-10 ----------------------------------------------------------------------------------------------------- 31 Pd 1 -8.006336883929123e-01 -8.006336883460894e-01 4.68229e-11 2.14890e-10 2 -1.246496608052518e+00 -1.246496608081059e+00 2.85409e-11 3.41327e-10 3 7.355035689102146e-01 7.355035688864888e-01 2.37258e-11 7.95882e-10 ----------------------------------------------------------------------------------------------------- 32 Cu 1 1.103307716583658e-01 1.103307716258419e-01 3.25239e-11 5.13588e-10 2 -8.660500602810116e-01 -8.660500602804782e-01 5.33462e-13 3.80402e-10 3 -8.461767537337428e-01 -8.461767537505379e-01 1.67951e-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.