!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_AgrawalMirzaeifar_2021_CuC__MO_028979335952_000 Supported species : C Cu 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 = C | a0 = 6.991379737854004 | (Configuration in file "config-C.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 C 1 8.258394776640116e-01 8.258394776635903e-01 4.21219e-13 6.42624e-11 2 5.976025136050812e-01 5.976025136042555e-01 8.25673e-13 7.43317e-12 3 -6.098399978343692e-02 -6.098399978318064e-02 2.56288e-13 8.80161e-12 ----------------------------------------------------------------------------------------------------- 2 C 1 -8.791074994983462e-01 -8.791074995054734e-01 7.12719e-12 4.51129e-05 * 2 -5.919044982700780e-01 -5.919044982750655e-01 4.98757e-12 2.51792e-11 3 6.531021672921546e-02 6.531021673003441e-02 8.18956e-13 1.66948e-10 * ----------------------------------------------------------------------------------------------------- 3 C 1 -1.582342326464571e-01 -1.582342326467237e-01 2.66537e-13 6.17185e-09 * 2 1.577289825823262e-02 1.577289825773370e-02 4.98927e-13 5.21713e-12 3 2.078080370398921e-02 2.078080370489881e-02 9.09599e-13 3.38856e-11 ----------------------------------------------------------------------------------------------------- 4 C 1 8.514244985275229e-02 8.514244985264305e-02 1.09246e-13 2.07026e-12 2 2.049716533116665e-02 2.049716533028515e-02 8.81500e-13 3.74666e-12 3 4.762186660551175e-02 4.762186660568812e-02 1.76373e-13 6.78173e-12 ----------------------------------------------------------------------------------------------------- 5 C 1 1.476814300255702e-01 1.476814300259857e-01 4.15529e-13 2.94844e-11 2 -5.057580563871372e-02 -5.057580563916314e-02 4.49418e-13 1.16678e-11 3 -1.135475323468385e-01 -1.135475323472472e-01 4.08687e-13 4.67517e-09 * ----------------------------------------------------------------------------------------------------- 6 C 1 -5.236419468678840e-02 -5.236419468641215e-02 3.76255e-13 7.67390e-12 2 1.650535507617290e-02 1.650535507620497e-02 3.20716e-14 1.45554e-11 3 -3.943943936620993e-02 -3.943943936587926e-02 3.30666e-13 5.98326e-12 ----------------------------------------------------------------------------------------------------- 7 C 1 -2.156006244740231e-02 -2.156006244684155e-02 5.60756e-13 4.47805e-12 2 -7.395475381111283e-02 -7.395475381025768e-02 8.55149e-13 1.45250e-11 3 3.904727585625550e-02 3.904727585389849e-02 2.35702e-12 6.13206e-11 ----------------------------------------------------------------------------------------------------- 8 C 1 8.906641778766840e-02 8.906641778312871e-02 4.53969e-12 5.81040e-11 2 -3.416204999776118e-01 -3.416204999767979e-01 8.13904e-13 3.05700e-11 3 2.407744004348982e-01 2.407744004332641e-01 1.63414e-12 8.16261e-12 ----------------------------------------------------------------------------------------------------- 9 C 1 2.819767884304472e-02 2.819767884387899e-02 8.34274e-13 1.33303e-11 2 -4.471573605742035e-02 -4.471573605698521e-02 4.35131e-13 3.61523e-12 3 1.326171835581864e-01 1.326171835598104e-01 1.62395e-12 1.69285e-11 ----------------------------------------------------------------------------------------------------- 10 C 1 1.051835807647419e-02 1.051835807661784e-02 1.43642e-13 2.02462e-12 2 3.528468484489286e-02 3.528468484517498e-02 2.82122e-13 5.18408e-12 3 1.755329802971048e-02 1.755329802990952e-02 1.99046e-13 3.82193e-12 ----------------------------------------------------------------------------------------------------- 11 C 1 -5.148292867433791e-01 -5.148292867402310e-01 3.14815e-12 1.07293e-11 2 6.609391612983926e-01 6.609391612925830e-01 5.80958e-12 2.36123e-11 3 -2.090053652619870e-01 -2.090053652636890e-01 1.70200e-12 9.36440e-11 ----------------------------------------------------------------------------------------------------- 12 C 1 6.108588669824314e-01 6.108588669844683e-01 2.03693e-12 2.76182e-11 2 -5.307163581062456e-01 -5.307163581065922e-01 3.46612e-13 5.27023e-12 3 -4.761052175011338e-02 -4.761052175117052e-02 1.05713e-12 1.28591e-10 ----------------------------------------------------------------------------------------------------- 13 C 1 -6.894574175942079e-02 -6.894574176075770e-02 1.33690e-12 6.66249e-12 2 1.226523340666204e-01 1.226523340665582e-01 6.22696e-14 2.08964e-09 * 3 -6.972050375602087e-02 -6.972050375858263e-02 2.56176e-12 3.06590e-11 ----------------------------------------------------------------------------------------------------- 14 C 1 -5.482828687609932e-02 -5.482828687249535e-02 3.60397e-12 5.25196e-12 2 -2.837009955726297e-02 -2.837009955719340e-02 6.95659e-14 3.57974e-13 3 6.400946557980482e-02 6.400946557946220e-02 3.42615e-13 2.78266e-11 ----------------------------------------------------------------------------------------------------- 15 C 1 -3.712629114050458e-03 -3.712629114456983e-03 4.06525e-13 2.17053e-12 2 2.711094951946806e-02 2.711094952126955e-02 1.80149e-12 1.32383e-11 3 -1.598794905208470e-02 -1.598794905185419e-02 2.30510e-13 7.46937e-11 ----------------------------------------------------------------------------------------------------- 16 C 1 1.814830700230119e-01 1.814830700213705e-01 1.64144e-12 4.04454e-12 2 -1.212362065777298e-01 -1.212362065780969e-01 3.67054e-13 8.36807e-12 3 -1.168783791522475e-01 -1.168783791494786e-01 2.76891e-12 5.02452e-09 * ----------------------------------------------------------------------------------------------------- 17 C 1 1.264930764713167e-01 1.264930764716943e-01 3.77559e-13 9.67593e-12 2 3.412849732560434e-02 3.412849732584692e-02 2.42584e-13 3.93785e-12 3 2.968960429154473e-02 2.968960429116886e-02 3.75869e-13 1.87242e-12 ----------------------------------------------------------------------------------------------------- 18 C 1 -1.524705827672094e-01 -1.524705827672846e-01 7.52176e-14 5.73974e-12 2 -2.351123924160096e-02 -2.351123924173722e-02 1.36263e-13 7.89149e-12 3 8.143816578632536e-02 8.143816578782473e-02 1.49937e-12 4.23244e-11 ----------------------------------------------------------------------------------------------------- 19 C 1 1.000182178646888e+00 1.000182178644334e+00 2.55440e-12 4.07275e-07 * 2 1.180437320370296e+00 1.180437320370171e+00 1.24123e-13 1.29916e-10 3 -4.086400334174108e-02 -4.086400334255722e-02 8.16146e-13 3.40573e-12 ----------------------------------------------------------------------------------------------------- 20 C 1 8.084248966642750e-02 8.084248966635764e-02 6.98608e-14 7.26659e-12 2 -1.086343007009104e-02 -1.086343007073687e-02 6.45824e-13 1.76592e-11 3 -1.946225290183934e-02 -1.946225290179628e-02 4.30593e-14 2.37946e-11 ----------------------------------------------------------------------------------------------------- 21 C 1 4.306851281189024e-02 4.306851281138482e-02 5.05422e-13 1.09964e-11 2 2.516336053463494e-01 2.516336053463646e-01 1.51545e-14 9.75103e-12 3 -1.500099078907086e-01 -1.500099078903929e-01 3.15636e-13 2.43530e-12 ----------------------------------------------------------------------------------------------------- 22 C 1 -1.330611299033981e-01 -1.330611299050954e-01 1.69728e-12 3.78615e-11 2 2.695025251561089e-02 2.695025251640533e-02 7.94441e-13 1.20512e-11 3 3.968535605522062e-02 3.968535605626955e-02 1.04892e-12 4.19605e-12 ----------------------------------------------------------------------------------------------------- 23 C 1 4.981194101684448e-02 4.981194101649820e-02 3.46272e-13 1.86495e-11 2 -2.430870876848009e-02 -2.430870876855896e-02 7.88779e-14 5.26179e-12 3 3.514992717609168e-02 3.514992717559923e-02 4.92453e-13 3.84769e-13 ----------------------------------------------------------------------------------------------------- 24 C 1 -1.073762952081834e+00 -1.073762952066075e+00 1.57585e-11 4.63408e-07 * 2 -1.159618527330481e+00 -1.159618527344738e+00 1.42573e-11 9.96914e-12 3 -7.532586017693500e-02 -7.532586017697787e-02 4.28685e-14 3.34655e-12 ----------------------------------------------------------------------------------------------------- 25 C 1 3.569976036211582e-02 3.569976036107584e-02 1.03998e-12 7.15367e-12 2 1.590383295242743e-02 1.590383295435328e-02 1.92585e-12 5.04976e-12 3 1.540199272444724e-01 1.540199272442717e-01 2.00728e-13 6.41459e-12 ----------------------------------------------------------------------------------------------------- 26 C 1 -6.845300737880246e-01 -6.845300737870360e-01 9.88543e-13 9.98053e-11 2 -9.300873212653887e-02 -9.300873212556003e-02 9.78842e-13 3.59028e-11 3 5.798224232707095e-01 5.798224232705327e-01 1.76859e-13 5.67768e-09 * ----------------------------------------------------------------------------------------------------- 27 C 1 1.030758317254827e-01 1.030758317250442e-01 4.38538e-13 2.03573e-12 2 -5.313373405023411e-02 -5.313373405024348e-02 9.37445e-15 1.36781e-11 3 -1.044687996401539e-01 -1.044687996386358e-01 1.51811e-12 4.85363e-12 ----------------------------------------------------------------------------------------------------- 28 C 1 3.742317280177724e-01 3.742317280174615e-01 3.10973e-13 6.17361e-11 2 9.581611823551822e-02 9.581611823638589e-02 8.67667e-13 7.32232e-11 3 -5.110939770087514e-01 -5.110939770118059e-01 3.05456e-12 1.35389e-08 * ----------------------------------------------------------------------------------------------------- 29 C 1 2.135920941583127e-02 2.135920941308483e-02 2.74645e-12 1.46744e-12 2 1.358932756374530e-01 1.358932756426606e-01 5.20753e-12 3.11645e-12 3 6.158396488005156e-02 6.158396488038659e-02 3.35038e-13 2.61589e-12 ----------------------------------------------------------------------------------------------------- 30 C 1 -7.863958409125009e-02 -7.863958409173444e-02 4.84349e-13 1.62893e-12 2 4.968282098637045e-02 4.968282098640205e-02 3.16067e-14 4.73226e-12 3 2.260263246442421e-02 2.260263246560165e-02 1.17744e-12 2.30331e-12 ----------------------------------------------------------------------------------------------------- 31 C 1 8.247121405380935e-02 8.247121405554779e-02 1.73844e-12 5.77377e-11 2 -1.288303927859597e-01 -1.288303927855544e-01 4.05342e-13 4.65264e-12 3 8.799075230818836e-03 8.799075230648953e-03 1.69883e-13 4.80710e-11 ----------------------------------------------------------------------------------------------------- 32 C 1 -1.997743503968394e-02 -1.997743503958081e-02 1.03133e-13 2.12828e-12 2 -1.044206300009573e-02 -1.044206300181142e-02 1.71569e-12 1.02725e-11 3 -6.610709546816292e-02 -6.610709546830563e-02 1.42719e-13 5.53745e-12 ----------------------------------------------------------------------------------------------------- * 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 = 32, direction = 2: |F_model - F_numer| error = ----------------------- = 1.64305e-10 max{|F_numer|, eps} Comparison of analytical forces obtained from the model, the force computed as a numerical derivative of the energy, the difference between them, and the uncertainty in the numerical estimate of the force. The computed equilibrium lattice constant for the crystal (a0) is given in the heading. MONOATOMIC STRUCTURE -- Species = Cu | a0 = 3.6150131225585938 | (Configuration in file "config-Cu.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Cu 1 6.799504206929191e-01 6.799504206951941e-01 2.27496e-12 2.18083e-11 2 8.420832120060049e-01 8.420832120109207e-01 4.91585e-12 6.60571e-10 3 7.745217230166229e-01 7.745217230046795e-01 1.19434e-11 8.68055e-11 ----------------------------------------------------------------------------------------------------- 2 Cu 1 -6.544262583074202e-01 -6.544262583187308e-01 1.13106e-11 4.24386e-11 2 -6.202149512472864e-01 -6.202149512723423e-01 2.50558e-11 1.60858e-10 3 2.497924023046773e-01 2.497924023904833e-01 8.58059e-11 8.28847e-11 ----------------------------------------------------------------------------------------------------- 3 Cu 1 1.741770176974608e+00 1.741770176992907e+00 1.82983e-11 2.32709e-11 2 -4.799931989313427e-01 -4.799931989456584e-01 1.43157e-11 1.46473e-10 3 -2.837121044519147e+00 -2.837121044525144e+00 5.99742e-12 6.43094e-11 ----------------------------------------------------------------------------------------------------- 4 Cu 1 -1.077142238006957e+00 -1.077142238019570e+00 1.26130e-11 6.26556e-10 2 -3.211947030929260e+00 -3.211947030922915e+00 6.34559e-12 3.46954e-11 3 -6.658128234936248e-01 -6.658128234945440e-01 9.19154e-13 7.67923e-10 ----------------------------------------------------------------------------------------------------- 5 Cu 1 -1.504754722959802e+00 -1.504754722944067e+00 1.57343e-11 2.25944e-10 2 -7.263466142055683e-01 -7.263466142036360e-01 1.93234e-12 1.13651e-10 3 -7.600145292513913e-01 -7.600145292612394e-01 9.84801e-12 1.19483e-10 ----------------------------------------------------------------------------------------------------- 6 Cu 1 1.395554004005561e+00 1.395554004092217e+00 8.66567e-11 2.90149e-10 2 -6.827727639084049e-01 -6.827727638783652e-01 3.00397e-11 2.62847e-10 3 -1.678115238219327e+00 -1.678115238216274e+00 3.05245e-12 1.76282e-10 ----------------------------------------------------------------------------------------------------- 7 Cu 1 1.149013130149375e+00 1.149013130152511e+00 3.13594e-12 1.91864e-10 2 -5.710506865177655e-01 -5.710506865251688e-01 7.40330e-12 1.42788e-10 3 1.850322787948774e+00 1.850322787934432e+00 1.43416e-11 7.90485e-11 ----------------------------------------------------------------------------------------------------- 8 Cu 1 3.455419473327959e-01 3.455419473215284e-01 1.12675e-11 1.56707e-10 2 2.733000319963952e-01 2.733000320045129e-01 8.11762e-12 4.08792e-10 3 -3.386855294344912e-01 -3.386855294500429e-01 1.55518e-11 4.19321e-10 ----------------------------------------------------------------------------------------------------- 9 Cu 1 -2.207833135133918e+00 -2.207833135120429e+00 1.34888e-11 4.74425e-11 2 1.150577024744599e+00 1.150577024756253e+00 1.16540e-11 1.33625e-10 3 -3.586921473724053e+00 -3.586921473745811e+00 2.17577e-11 1.11020e-10 ----------------------------------------------------------------------------------------------------- 10 Cu 1 4.814861445957738e-01 4.814861445844418e-01 1.13320e-11 1.63553e-10 2 4.068095688748099e-01 4.068095688776180e-01 2.80814e-12 1.01209e-10 3 -4.925618294220050e-01 -4.925618293873680e-01 3.46370e-11 4.84379e-11 ----------------------------------------------------------------------------------------------------- 11 Cu 1 4.204104666941245e+00 4.204104666957186e+00 1.59410e-11 7.59091e-11 2 3.239514614557280e-01 3.239514614664386e-01 1.07107e-11 3.67446e-10 3 2.072560419573850e+00 2.072560419586318e+00 1.24682e-11 1.97720e-10 ----------------------------------------------------------------------------------------------------- 12 Cu 1 -2.006327936324372e-01 -2.006327936185979e-01 1.38393e-11 2.34134e-10 2 -5.570859765727620e-03 -5.570859789016214e-03 2.32886e-11 1.97637e-10 3 2.136166685371153e-01 2.136166685403329e-01 3.21765e-12 3.25505e-10 ----------------------------------------------------------------------------------------------------- 13 Cu 1 -1.570043718861324e+00 -1.570043718801958e+00 5.93658e-11 4.95401e-10 2 2.115566749899970e+00 2.115566749889453e+00 1.05174e-11 4.70486e-10 3 -4.780505314226403e-01 -4.780505314203903e-01 2.24998e-12 7.36680e-11 ----------------------------------------------------------------------------------------------------- 14 Cu 1 -1.427964014071583e-01 -1.427964014100761e-01 2.91778e-12 1.17290e-10 2 -4.779003912508166e-01 -4.779003912715725e-01 2.07558e-11 1.25321e-09 3 1.129627853715126e-02 1.129627853839286e-02 1.24161e-12 1.14080e-11 ----------------------------------------------------------------------------------------------------- 15 Cu 1 6.218052149082830e-01 6.218052149285358e-01 2.02528e-11 1.00618e-10 2 1.317310928298467e+00 1.317310928236487e+00 6.19791e-11 6.22634e-10 3 9.147575379569194e-01 9.147575379347349e-01 2.21845e-11 1.83069e-10 ----------------------------------------------------------------------------------------------------- 16 Cu 1 -9.129351945434826e-01 -9.129351945551852e-01 1.17026e-11 8.43879e-11 2 9.010937866016381e-01 9.010937866037627e-01 2.12463e-12 7.24112e-11 3 -8.518858648097786e-01 -8.518858647997647e-01 1.00139e-11 7.92661e-11 ----------------------------------------------------------------------------------------------------- 17 Cu 1 -2.890610666241660e+00 -2.890610666252126e+00 1.04663e-11 1.45835e-10 2 -1.615309863395324e+00 -1.615309863388875e+00 6.44929e-12 2.78504e-11 3 1.801613949213319e+00 1.801613949228598e+00 1.52793e-11 6.48634e-10 ----------------------------------------------------------------------------------------------------- 18 Cu 1 3.047086314057633e+00 3.047086314041371e+00 1.62617e-11 2.49325e-10 2 1.351951993153838e+00 1.351951993111835e+00 4.20026e-11 1.68052e-10 3 1.330446038014808e+00 1.330446038039414e+00 2.46059e-11 5.74123e-10 ----------------------------------------------------------------------------------------------------- 19 Cu 1 6.705356094281191e-01 6.705356094283779e-01 2.58793e-13 3.56432e-11 2 -7.530815366671566e-01 -7.530815366715310e-01 4.37439e-12 2.08615e-09 * 3 -3.549264024769025e-01 -3.549264024726917e-01 4.21080e-12 2.96853e-11 ----------------------------------------------------------------------------------------------------- 20 Cu 1 -7.955435296042319e-01 -7.955435296007921e-01 3.43980e-12 7.04725e-11 2 1.028446668607738e+00 1.028446668622269e+00 1.45304e-11 9.63071e-10 3 1.057863858004279e-01 1.057863857851638e-01 1.52641e-11 1.32508e-10 ----------------------------------------------------------------------------------------------------- 21 Cu 1 -1.375105989799766e-01 -1.375105989597811e-01 2.01955e-11 1.21229e-09 2 -5.251505699026182e-01 -5.251505698785974e-01 2.40208e-11 4.42029e-10 3 6.794807427028627e-01 6.794807426582952e-01 4.45676e-11 1.76645e-10 ----------------------------------------------------------------------------------------------------- 22 Cu 1 2.545182629239968e-02 2.545182629720156e-02 4.80188e-12 1.57605e-10 2 -1.118688622369008e+00 -1.118688622370388e+00 1.38023e-12 8.73490e-11 3 -1.566189949473394e-01 -1.566189949391295e-01 8.20988e-12 5.70299e-10 ----------------------------------------------------------------------------------------------------- 23 Cu 1 -6.142402615896205e-01 -6.142402615890342e-01 5.86309e-13 4.50390e-11 2 7.021513858219179e-01 7.021513858379413e-01 1.60234e-11 5.49539e-11 3 -6.509563578906388e-01 -6.509563578823299e-01 8.30891e-12 8.25348e-11 ----------------------------------------------------------------------------------------------------- 24 Cu 1 7.535408883750634e-02 7.535408884730650e-02 9.80016e-12 5.09309e-09 * 2 2.460023407494014e-01 2.460023406805589e-01 6.88425e-11 1.72461e-10 3 3.139402437556068e-02 3.139402440727736e-02 3.17167e-11 5.41240e-10 ----------------------------------------------------------------------------------------------------- 25 Cu 1 -1.668056714289598e+00 -1.668056714298034e+00 8.43681e-12 4.37765e-11 2 2.370765341091379e+00 2.370765341083314e+00 8.06466e-12 4.01919e-10 3 2.692088903260118e+00 2.692088903253045e+00 7.07256e-12 8.70986e-09 * ----------------------------------------------------------------------------------------------------- 26 Cu 1 -4.516935357597889e-02 -4.516935363438073e-02 5.84018e-11 1.66752e-10 2 2.644826039351636e+00 2.644826039334709e+00 1.69265e-11 1.29379e-10 3 -3.350153845541704e+00 -3.350153845557168e+00 1.54641e-11 2.98125e-10 ----------------------------------------------------------------------------------------------------- 27 Cu 1 -7.575850462897754e-02 -7.575850460990081e-02 1.90767e-11 5.55338e-10 2 -2.997060021271414e+00 -2.997060021242365e+00 2.90492e-11 1.67003e-10 3 1.738085131712278e+00 1.738085131701206e+00 1.10718e-11 4.09044e-10 ----------------------------------------------------------------------------------------------------- 28 Cu 1 4.123224575325975e-02 4.123224575580509e-02 2.54534e-12 7.56857e-11 2 -5.244795119923016e-01 -5.244795119709033e-01 2.13983e-11 4.91776e-10 3 -4.204673664927908e-01 -4.204673664904278e-01 2.36294e-12 6.82341e-11 ----------------------------------------------------------------------------------------------------- 29 Cu 1 -7.287254986547397e-01 -7.287254986839447e-01 2.92050e-11 1.71041e-10 2 -2.115731538223272e+00 -2.115731538195177e+00 2.80953e-11 1.67097e-10 3 1.375674922120639e+00 1.375674922052852e+00 6.77867e-11 1.68341e-10 ----------------------------------------------------------------------------------------------------- 30 Cu 1 5.287552400252663e-01 5.287552400481695e-01 2.29032e-11 5.77079e-09 * 2 1.846286855663877e-02 1.846286858037116e-02 2.37324e-11 3.43128e-10 3 -6.505593207162002e-01 -6.505593207139134e-01 2.28673e-12 1.43394e-09 * ----------------------------------------------------------------------------------------------------- 31 Cu 1 7.934655380344772e-01 7.934655380523292e-01 1.78521e-11 6.16716e-10 2 -2.545997406994903e-01 -2.545997407920080e-01 9.25177e-11 3.17123e-10 3 6.988729668516408e-01 6.988729668608832e-01 9.24238e-12 2.07906e-10 ----------------------------------------------------------------------------------------------------- 32 Cu 1 -5.749269776119423e-01 -5.749269776196523e-01 7.70994e-12 1.50763e-10 2 9.865985000665944e-01 9.865985000634635e-01 3.13094e-12 3.65225e-11 3 7.325402704352699e-01 7.325402704274809e-01 7.78899e-12 3.63403e-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 = 12, direction = 2: |F_model - F_numer| error = ----------------------- = 4.18043e-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 = C Cu | a0 = 7.1593151807785045 | (Configuration in file "config-CCu.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Cu 1 1.606592707681221e+00 1.606592707681968e+00 7.46736e-13 4.19945e-10 2 1.510808012667279e+00 1.510808012656497e+00 1.07820e-11 1.96099e-11 3 2.885954076812468e+00 2.885954076817755e+00 5.28688e-12 5.74594e-11 ----------------------------------------------------------------------------------------------------- 2 C 1 1.291606355448209e+00 1.291606355365919e+00 8.22904e-11 4.78677e-11 2 -2.910303682283011e+00 -2.910303682273836e+00 9.17444e-12 1.15715e-10 3 -3.356955666177119e-01 -3.356955666066673e-01 1.10447e-11 1.13946e-09 * ----------------------------------------------------------------------------------------------------- 3 C 1 -5.516852086831248e-01 -5.516852086709507e-01 1.21740e-11 8.22149e-11 2 -2.053844216188114e+00 -2.053844216191412e+00 3.29736e-12 1.10861e-10 3 -1.602954900253231e+00 -1.602954900249469e+00 3.76210e-12 9.84925e-11 ----------------------------------------------------------------------------------------------------- 4 C 1 -1.950132739861349e+00 -1.950132739861038e+00 3.11751e-13 7.04636e-12 2 6.993046199163374e+00 6.993046199189556e+00 2.61817e-11 8.50031e-11 3 -5.867091930513060e+00 -5.867091930543624e+00 3.05640e-11 2.92442e-11 ----------------------------------------------------------------------------------------------------- 5 C 1 1.892033250956646e+00 1.892033250950464e+00 6.18194e-12 4.46354e-11 2 1.691436886081594e+00 1.691436886081574e+00 2.04281e-14 5.08420e-11 3 9.877449366945024e-01 9.877449366905602e-01 3.94218e-12 4.28719e-10 ----------------------------------------------------------------------------------------------------- 6 Cu 1 -2.675717606226592e-01 -2.675717606221522e-01 5.07094e-13 7.45596e-11 2 -6.149828908125859e-01 -6.149828908044022e-01 8.18379e-12 3.46964e-10 3 -4.398643630876105e-01 -4.398643630721146e-01 1.54958e-11 7.63670e-11 ----------------------------------------------------------------------------------------------------- 7 Cu 1 1.136386692883038e+00 1.136386692877958e+00 5.07994e-12 1.33609e-10 2 -1.006490195675533e+00 -1.006490195682535e+00 7.00173e-12 1.16143e-11 3 -3.303807526287328e+00 -3.303807526273477e+00 1.38511e-11 1.21893e-10 ----------------------------------------------------------------------------------------------------- 8 Cu 1 -2.182809034772654e+00 -2.182809034755971e+00 1.66831e-11 7.63456e-11 2 -1.003818195214134e+00 -1.003818195200228e+00 1.39058e-11 1.75949e-10 3 3.333183781624222e-01 3.333183781725021e-01 1.00800e-11 2.70700e-10 ----------------------------------------------------------------------------------------------------- 9 Cu 1 -2.665834419360769e+00 -2.665834419354741e+00 6.02851e-12 1.40308e-10 2 3.103072992427324e-01 3.103072991939677e-01 4.87647e-11 8.31094e-11 3 2.106632907911981e+00 2.106632907885864e+00 2.61169e-11 4.25087e-11 ----------------------------------------------------------------------------------------------------- 10 Cu 1 -9.313845165835750e-01 -9.313845165357940e-01 4.77810e-11 1.37669e-10 2 -5.214964887041600e-01 -5.214964886668897e-01 3.72703e-11 1.53978e-10 3 1.485487869160421e+00 1.485487869163119e+00 2.69829e-12 1.01320e-10 ----------------------------------------------------------------------------------------------------- 11 C 1 4.121405217198223e-01 4.121405217597722e-01 3.99499e-11 4.46251e-11 2 -4.453152290529608e+00 -4.453152290528073e+00 1.53477e-12 3.27822e-10 3 2.352306637596986e+00 2.352306637603130e+00 6.14442e-12 7.05880e-11 ----------------------------------------------------------------------------------------------------- 12 C 1 6.740371149450677e-01 6.740371149426652e-01 2.40252e-12 6.84601e-11 2 3.886130425468292e-01 3.886130425756220e-01 2.87928e-11 2.01630e-10 3 -2.554980503493738e+00 -2.554980503508198e+00 1.44595e-11 3.43801e-10 ----------------------------------------------------------------------------------------------------- 13 C 1 5.311912858390712e-01 5.311912858460374e-01 6.96621e-12 1.19088e-10 2 -2.680612673222453e-01 -2.680612673248473e-01 2.60192e-12 2.27781e-11 3 -1.731611688310692e+00 -1.731611688301163e+00 9.52904e-12 1.13643e-10 ----------------------------------------------------------------------------------------------------- 14 C 1 -6.420845846335718e-01 -6.420845846343182e-01 7.46403e-13 1.83448e-11 2 -7.212371204169119e-01 -7.212371204132003e-01 3.71159e-12 7.01353e-11 3 2.485707453095784e+00 2.485707453077151e+00 1.86327e-11 7.53139e-10 ----------------------------------------------------------------------------------------------------- 15 Cu 1 9.379447380561372e-01 9.379447380501619e-01 5.97533e-12 2.25543e-10 2 1.606009538549154e+00 1.606009538562027e+00 1.28733e-11 1.07338e-09 * 3 -2.062068526531113e+00 -2.062068526515676e+00 1.54370e-11 3.94258e-10 ----------------------------------------------------------------------------------------------------- 16 Cu 1 -2.855601620348230e-01 -2.855601620268418e-01 7.98117e-12 4.38538e-11 2 -4.359115254730054e-01 -4.359115255085215e-01 3.55161e-11 1.26396e-10 3 -9.839710604381665e-01 -9.839710604484243e-01 1.02578e-11 7.66615e-10 ----------------------------------------------------------------------------------------------------- 17 C 1 -7.031965500268702e-01 -7.031965500106117e-01 1.62586e-11 1.72731e-11 2 3.741965322442371e-01 3.741965322476734e-01 3.43625e-12 4.87959e-11 3 2.509592567056717e+00 2.509592567051317e+00 5.40012e-12 5.50875e-11 ----------------------------------------------------------------------------------------------------- 18 C 1 5.313929642920464e+00 5.313929642852243e+00 6.82210e-11 1.49351e-10 2 -1.230644134978666e+00 -1.230644134972198e+00 6.46727e-12 4.44023e-12 3 2.620106397281187e+00 2.620106397322224e+00 4.10370e-11 2.47798e-10 ----------------------------------------------------------------------------------------------------- 19 Cu 1 1.286527216260682e+00 1.286527216269506e+00 8.82316e-12 5.51606e-10 2 -2.062432541502678e+00 -2.062432541502657e+00 2.04281e-14 2.19274e-09 * 3 5.807868178433169e-01 5.807868178439894e-01 6.72573e-13 1.18935e-10 ----------------------------------------------------------------------------------------------------- 20 Cu 1 -4.438180869227721e-01 -4.438180868576622e-01 6.51099e-11 1.90657e-10 2 2.116044100602152e+00 2.116044100558153e+00 4.39990e-11 7.52411e-11 3 -5.437478897961507e+00 -5.437478897998079e+00 3.65716e-11 1.13209e-10 ----------------------------------------------------------------------------------------------------- 21 Cu 1 -2.361216662194217e+00 -2.361216662194194e+00 2.35367e-14 1.31324e-10 2 -1.296356197182419e+00 -1.296356197184674e+00 2.25486e-12 2.54646e-10 3 2.796999253070211e+00 2.796999253035555e+00 3.46554e-11 3.85820e-10 ----------------------------------------------------------------------------------------------------- 22 Cu 1 2.143146756087375e+00 2.143146756078608e+00 8.76721e-12 1.39398e-10 2 1.425596379350919e+00 1.425596379313107e+00 3.78120e-11 9.66027e-10 * 3 1.826753776971981e+00 1.826753776982595e+00 1.06140e-11 1.40986e-10 ----------------------------------------------------------------------------------------------------- 23 C 1 -8.561032427286515e-01 -8.561032427559394e-01 2.72879e-11 1.18233e-10 2 9.284265129398379e-01 9.284265129112044e-01 2.86335e-11 4.21323e-11 3 -1.966623938080784e+00 -1.966623938066409e+00 1.43745e-11 1.85609e-10 ----------------------------------------------------------------------------------------------------- 24 C 1 1.788320896647522e+00 1.788320896643723e+00 3.79941e-12 7.54052e-10 2 -1.772589692084534e+00 -1.772589692134881e+00 5.03471e-11 9.61504e-11 3 -1.825011337855861e-01 -1.825011338040646e-01 1.84786e-11 3.47453e-10 ----------------------------------------------------------------------------------------------------- 25 C 1 -4.343871357884109e+00 -4.343871357899264e+00 1.51550e-11 1.77931e-10 2 -7.429640429703986e-01 -7.429640429618081e-01 8.59057e-12 1.04069e-10 3 2.655425172494765e+00 2.655425172475272e+00 1.94933e-11 3.43050e-10 ----------------------------------------------------------------------------------------------------- 26 C 1 1.138464080386000e+00 1.138464080400206e+00 1.42060e-11 6.76630e-11 2 2.471369787071053e+00 2.471369787048141e+00 2.29119e-11 1.37952e-10 3 1.175820598765120e+00 1.175820598745524e+00 1.95961e-11 1.60392e-09 * ----------------------------------------------------------------------------------------------------- 27 C 1 -1.497266729870433e+00 -1.497266729864364e+00 6.06870e-12 1.20318e-10 2 2.277352049251189e+00 2.277352049246065e+00 5.12435e-12 8.14622e-10 3 -7.661882566146505e-02 -7.661882563945006e-02 2.20150e-11 7.68547e-11 ----------------------------------------------------------------------------------------------------- 28 Cu 1 1.490065324409466e+00 1.490065324405927e+00 3.53984e-12 7.02276e-11 2 -9.181073538521738e-01 -9.181073538502841e-01 1.88971e-12 1.15300e-10 3 -1.347951192611210e+00 -1.347951192609732e+00 1.47860e-12 1.33444e-10 ----------------------------------------------------------------------------------------------------- 29 Cu 1 -1.156416061923336e+00 -1.156416061957944e+00 3.46079e-11 4.36704e-09 * 2 -2.423554644648516e+00 -2.423554644617111e+00 3.14055e-11 4.77378e-11 3 1.867069473514286e+00 1.867069473416572e+00 9.77145e-11 1.91597e-09 * ----------------------------------------------------------------------------------------------------- 30 Cu 1 1.362266992956317e+00 1.362266992963270e+00 6.95222e-12 2.04747e-11 2 8.911646903081855e-01 8.911646903186579e-01 1.04724e-11 1.25203e-11 3 1.845025031141015e+00 1.845025031138616e+00 2.39875e-12 6.54561e-11 ----------------------------------------------------------------------------------------------------- 31 C 1 -1.166502119967857e+00 -1.166502119981189e+00 1.33320e-11 6.71182e-10 2 1.981440030421546e+00 1.981440030422668e+00 1.12288e-12 5.35341e-11 3 -2.166786868229422e+00 -2.166786868252460e+00 2.30385e-11 1.59317e-09 * ----------------------------------------------------------------------------------------------------- 32 Cu 1 -9.992003391262693e-01 -9.992003391247478e-01 1.52145e-12 4.22390e-11 2 -5.298645806013905e-01 -5.298645805874755e-01 1.39150e-11 7.88233e-11 3 -4.547244257105382e-01 -4.547244257053621e-01 5.17608e-12 8.89055e-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 = 27, direction = 3: |F_model - F_numer| error = ----------------------- = 2.87331e-10 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 4.18043e-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 4.18043e-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.