!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! VERIFICATION CHECK: vc-forces-numerical-derivative !!!!! !!!!! !!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Description: Comparison of the analytical forces obtained from the model with forces computed by numerical differentiation using Richardson extrapolation for a randomly distorted non-periodic structure based off the equilibrium face-centered cubic (fcc) structure. Separate configurations are tested for each species supported by the model, as well as one containing a random distribution of all species. Configurations used for testing are provided as auxiliary files. Author: Ellad Tadmor ----------------------------------------------------------------------------------------------------- Results for KIM Model : Sim_LAMMPS_Vashishta_VashishtaKaliaNakano_2007_SiC__SM_196548226654_000 Supported species : C Si 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 = 14.375 | (Configuration in file "config-C.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 C 1 -5.929862786624845e-01 -5.929862786629956e-01 5.11036e-13 2.25497e-12 2 -6.075992735276181e-01 -6.075992735275679e-01 5.01821e-14 5.35016e-13 3 -6.774264604657058e-01 -6.774264604653272e-01 3.78586e-13 2.13618e-12 ----------------------------------------------------------------------------------------------------- 2 C 1 -4.836970781529434e-02 -4.836970781529398e-02 3.60822e-16 1.68678e-12 2 9.631507973964426e-02 9.631507974069659e-02 1.05232e-12 3.75888e-12 3 -1.025213354361532e+00 -1.025213354361669e+00 1.37002e-13 8.73968e-13 ----------------------------------------------------------------------------------------------------- 3 C 1 1.140194148617754e-01 1.140194148622477e-01 4.72261e-13 2.70756e-13 2 -9.925713416602591e-01 -9.925713416595565e-01 7.02549e-13 4.38849e-12 3 2.497592722275882e-02 2.497592722282270e-02 6.38760e-14 2.43951e-12 ----------------------------------------------------------------------------------------------------- 4 C 1 -9.984310926053686e-01 -9.984310926049897e-01 3.78808e-13 5.64437e-12 2 1.469841683393654e-01 1.469841683390175e-01 3.47944e-13 3.31532e-12 3 1.783421723000776e-01 1.783421722998396e-01 2.37949e-13 3.41352e-11 * ----------------------------------------------------------------------------------------------------- 5 C 1 1.613357245556259e-01 1.613357245555969e-01 2.90046e-14 4.42812e-13 2 -8.778828621026304e-01 -8.778828621038453e-01 1.21481e-12 4.90519e-12 3 -7.362830474701210e-01 -7.362830474703681e-01 2.47136e-13 1.51545e-12 ----------------------------------------------------------------------------------------------------- 6 C 1 7.826724781738633e-01 7.826724781740617e-01 1.98397e-13 1.11344e-12 2 -7.788166625326676e-02 -7.788166625354070e-02 2.73948e-13 4.10255e-13 3 -8.355891587294072e-01 -8.355891587292881e-01 1.19127e-13 7.00107e-13 ----------------------------------------------------------------------------------------------------- 7 C 1 8.511770822528256e-01 8.511770822532888e-01 4.63185e-13 1.40565e-12 2 -9.480550935420504e-01 -9.480550935418942e-01 1.56208e-13 1.31262e-12 3 -2.689631212597667e-01 -2.689631212598466e-01 7.98805e-14 5.68323e-13 ----------------------------------------------------------------------------------------------------- 8 C 1 -1.705815258433843e-01 -1.705815258430926e-01 2.91739e-13 4.35790e-12 2 -1.683191737231258e-01 -1.683191737229768e-01 1.49020e-13 1.56372e-12 3 -4.096589335504164e-03 -4.096589335374624e-03 1.29540e-13 3.85966e-12 ----------------------------------------------------------------------------------------------------- 9 C 1 -7.572513687966598e-01 -7.572513687965330e-01 1.26787e-13 8.83071e-13 2 -8.212894650121089e-02 -8.212894650117467e-02 3.62210e-14 3.07393e-12 3 -9.303823183755584e-01 -9.303823183740768e-01 1.48159e-12 2.00208e-11 * ----------------------------------------------------------------------------------------------------- 10 C 1 -4.202560583943138e-03 -4.202560583741108e-03 2.02030e-13 9.02519e-13 2 8.867941497290128e-01 8.867941497264191e-01 2.59370e-12 5.84810e-12 3 -9.635024337605117e-01 -9.635024337644581e-01 3.94640e-12 7.62009e-11 * ----------------------------------------------------------------------------------------------------- 11 C 1 -1.720206197370548e-01 -1.720206197367311e-01 3.23713e-13 1.70150e-12 2 -2.239387300637178e-01 -2.239387300637258e-01 7.99361e-15 1.18933e-12 3 5.928258726994048e-02 5.928258726981004e-02 1.30444e-13 1.28173e-12 ----------------------------------------------------------------------------------------------------- 12 C 1 -8.607662912040984e-01 -8.607662912043614e-01 2.63012e-13 7.44860e-12 2 8.797132912726171e-01 8.797132912722248e-01 3.92353e-13 2.18203e-12 3 1.280733795377126e-01 1.280733795381986e-01 4.86000e-13 7.38631e-13 ----------------------------------------------------------------------------------------------------- 13 C 1 1.910534307822146e-02 1.910534307873292e-02 5.11462e-13 3.22453e-12 2 -5.655882528860456e-02 -5.655882528834952e-02 2.55046e-13 6.29510e-12 3 -1.259734091192119e+00 -1.259734091192099e+00 1.99840e-14 2.06879e-12 ----------------------------------------------------------------------------------------------------- 14 C 1 5.626676404130667e-01 5.626676404131179e-01 5.11813e-14 1.60172e-12 2 5.721132007965751e-01 5.721132007962463e-01 3.28848e-13 1.08680e-12 3 -5.106190798665803e-01 -5.106190798669653e-01 3.85025e-13 4.76286e-13 ----------------------------------------------------------------------------------------------------- 15 C 1 1.212904217398032e+00 1.212904217397693e+00 3.38174e-13 2.41696e-12 2 3.580075324606563e-02 3.580075324594934e-02 1.16289e-13 3.28288e-12 3 -8.591774732261470e-02 -8.591774732300503e-02 3.90327e-13 4.81309e-13 ----------------------------------------------------------------------------------------------------- 16 C 1 1.856785871102903e-01 1.856785871105378e-01 2.47496e-13 1.57974e-12 2 1.264668076211675e+00 1.264668076211626e+00 4.92939e-14 7.16538e-13 3 1.054329401653832e-01 1.054329401664662e-01 1.08299e-12 1.11953e-11 ----------------------------------------------------------------------------------------------------- 17 C 1 -8.573125561960081e-01 -8.573125561954476e-01 5.60552e-13 4.65983e-12 2 -6.899917723571427e-01 -6.899917723572355e-01 9.28146e-14 4.68403e-12 3 3.981301446504937e-03 3.981301446282095e-03 2.22842e-13 2.00218e-12 ----------------------------------------------------------------------------------------------------- 18 C 1 -1.132554046728119e-01 -1.132554046728480e-01 3.60961e-14 1.36131e-12 2 1.111561375129163e-01 1.111561375117154e-01 1.20087e-12 3.76790e-12 3 -1.409232737640263e-02 -1.409232737646275e-02 6.01203e-14 3.12245e-12 ----------------------------------------------------------------------------------------------------- 19 C 1 8.213323645256895e-02 8.213323645290521e-02 3.36259e-13 8.03035e-12 2 -8.287581159543593e-01 -8.287581159543729e-01 1.35447e-14 4.20219e-12 3 7.959750029448005e-01 7.959750029450690e-01 2.68452e-13 4.45399e-12 ----------------------------------------------------------------------------------------------------- 20 C 1 -7.366100436342859e-01 -7.366100436341090e-01 1.76970e-13 1.81499e-12 2 1.265805714939450e-01 1.265805714942344e-01 2.89324e-13 2.59534e-12 3 6.892067096334147e-01 6.892067096322629e-01 1.15175e-12 3.23364e-12 ----------------------------------------------------------------------------------------------------- 21 C 1 -7.984464707681539e-02 -7.984464707698896e-02 1.73569e-13 1.63486e-12 2 -1.035001807314791e+00 -1.035001807315159e+00 3.67928e-13 7.98157e-11 * 3 1.585483227773272e-01 1.585483227771415e-01 1.85713e-13 1.77841e-12 ----------------------------------------------------------------------------------------------------- 22 C 1 1.055194474158163e+00 1.055194474157802e+00 3.60822e-13 3.94174e-12 2 1.220388818436913e-01 1.220388818430414e-01 6.49897e-13 4.75147e-11 * 3 2.131959973546537e-01 2.131959973549058e-01 2.52132e-13 1.35184e-12 ----------------------------------------------------------------------------------------------------- 23 C 1 4.539194259721475e-01 4.539194259723709e-01 2.23432e-13 3.36714e-12 2 -4.860601377139585e-01 -4.860601377142075e-01 2.49079e-13 1.71707e-12 3 5.624104210093648e-01 5.624104210093360e-01 2.87548e-14 6.32716e-13 ----------------------------------------------------------------------------------------------------- 24 C 1 1.309190226154816e-02 1.309190226185422e-02 3.06057e-13 5.60006e-12 2 -1.043232345388374e-01 -1.043232345407201e-01 1.88269e-12 8.07457e-12 3 9.900790627869742e-01 9.900790627868387e-01 1.35558e-13 2.61291e-12 ----------------------------------------------------------------------------------------------------- 25 C 1 -1.056150946144222e+00 -1.056150946143371e+00 8.51097e-13 3.43126e-12 2 -1.716234989064962e-01 -1.716234989067703e-01 2.74114e-13 1.34970e-12 3 3.734554386822830e-02 3.734554386822620e-02 2.10248e-15 1.54980e-12 ----------------------------------------------------------------------------------------------------- 26 C 1 -1.394861867068695e-01 -1.394861867081801e-01 1.31056e-12 1.52475e-12 2 1.181375836925713e+00 1.181375836922977e+00 2.73581e-12 3.20965e-12 3 -1.781163833499834e-01 -1.781163833458479e-01 4.13558e-12 8.44014e-11 * ----------------------------------------------------------------------------------------------------- 27 C 1 1.039091427055205e-02 1.039091426996674e-02 5.85317e-13 1.98235e-11 * 2 -3.394052342344165e-01 -3.394052342347030e-01 2.86438e-13 9.84324e-13 3 1.033958898655541e+00 1.033958898656204e+00 6.62359e-13 1.62981e-12 ----------------------------------------------------------------------------------------------------- 28 C 1 -7.435654534052623e-01 -7.435654534048637e-01 3.98570e-13 1.77525e-12 2 6.596426880128955e-01 6.596426880131867e-01 2.91211e-13 5.62228e-12 3 5.592181226175688e-01 5.592181226177566e-01 1.87850e-13 5.05485e-13 ----------------------------------------------------------------------------------------------------- 29 C 1 -5.003792101560502e-02 -5.003792101581011e-02 2.05086e-13 7.04786e-12 2 -1.406885556259426e-01 -1.406885556269570e-01 1.01433e-12 2.41121e-12 3 1.478413848435924e-01 1.478413848437517e-01 1.59317e-13 3.50858e-13 ----------------------------------------------------------------------------------------------------- 30 C 1 7.833093320491447e-01 7.833093320491472e-01 2.55351e-15 2.17437e-12 2 8.980068278476404e-01 8.980068278468107e-01 8.29670e-13 5.19995e-12 3 7.023141789084647e-02 7.023141789097911e-02 1.32644e-13 2.66276e-12 ----------------------------------------------------------------------------------------------------- 31 C 1 8.777934581298281e-01 8.777934581300867e-01 2.58571e-13 2.49726e-11 * 2 -1.132784913313373e-02 -1.132784913278781e-02 3.45921e-13 2.16695e-12 3 8.290138363702183e-01 8.290138363700571e-01 1.61204e-13 1.34104e-12 ----------------------------------------------------------------------------------------------------- 32 C 1 2.154793729625155e-01 2.154793729623125e-01 2.02977e-13 6.30968e-13 2 8.609264554698044e-01 8.609264554702428e-01 4.38427e-13 9.31477e-14 3 9.028230841708990e-01 9.028230841758486e-01 4.94960e-12 2.77312e-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 = 17, direction = 3: |F_model - F_numer| error = ----------------------- = 5.59721e-11 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 = Si | a0 = 14.375 | (Configuration in file "config-Si.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Si 1 -5.494962554414040e-01 -5.494962554412957e-01 1.08358e-13 1.11048e-11 2 -4.911721155545180e-01 -4.911721155546634e-01 1.45384e-13 2.85189e-12 3 -4.618428890635775e-01 -4.618428890633737e-01 2.03781e-13 5.81818e-12 ----------------------------------------------------------------------------------------------------- 2 Si 1 -1.260741862133345e-01 -1.260741862131559e-01 1.78607e-13 1.75346e-12 2 9.303652051686429e-03 9.303652051467244e-03 2.19184e-13 1.77829e-12 3 -1.090649663017261e+00 -1.090649663017684e+00 4.22773e-13 2.03437e-12 ----------------------------------------------------------------------------------------------------- 3 Si 1 -7.017580212846304e-02 -7.017580212833416e-02 1.28883e-13 8.81434e-13 2 -1.072963391765375e+00 -1.072963391765987e+00 6.11733e-13 4.07852e-12 3 1.456376684905899e-01 1.456376684908646e-01 2.74752e-13 2.87420e-12 ----------------------------------------------------------------------------------------------------- 4 Si 1 -1.077084893554250e+00 -1.077084893554199e+00 5.12923e-14 8.43836e-12 2 -6.510157566263672e-02 -6.510157566401895e-02 1.38223e-12 5.39316e-12 3 -3.498521963070655e-03 -3.498521962304586e-03 7.66069e-13 1.89871e-11 * ----------------------------------------------------------------------------------------------------- 5 Si 1 3.072906139070338e-02 3.072906139039995e-02 3.03434e-13 8.90819e-13 2 -8.579432915117130e-01 -8.579432915120427e-01 3.29736e-13 3.39728e-12 3 -8.853937284743594e-01 -8.853937284731653e-01 1.19404e-12 1.17895e-12 ----------------------------------------------------------------------------------------------------- 6 Si 1 8.434518518950529e-01 8.434518518953144e-01 2.61458e-13 1.42297e-12 2 1.367174817010784e-01 1.367174817012231e-01 1.44662e-13 1.61238e-12 3 -9.514323669637114e-01 -9.514323669637422e-01 3.08642e-14 3.18301e-13 ----------------------------------------------------------------------------------------------------- 7 Si 1 8.401369507599605e-01 8.401369507596768e-01 2.83773e-13 3.09908e-12 2 -1.008517718455478e+00 -1.008517718456027e+00 5.49560e-13 1.75104e-12 3 6.241388323835312e-02 6.241388323892567e-02 5.72556e-13 9.53931e-13 ----------------------------------------------------------------------------------------------------- 8 Si 1 -6.732198154585552e-02 -6.732198154690336e-02 1.04784e-12 1.64467e-11 2 2.343145300072275e-02 2.343145300133264e-02 6.09898e-13 1.79794e-12 3 6.699029967802508e-02 6.699029967877591e-02 7.50830e-13 3.41809e-12 ----------------------------------------------------------------------------------------------------- 9 Si 1 -7.090291423665074e-01 -7.090291423667475e-01 2.40141e-13 2.75502e-12 2 1.179529206023387e-01 1.179529206022162e-01 1.22471e-13 1.51394e-12 3 -6.497680287258588e-01 -6.497680287257660e-01 9.28146e-14 1.56930e-12 ----------------------------------------------------------------------------------------------------- 10 Si 1 -3.203716004055307e-02 -3.203716004017844e-02 3.74631e-13 5.04805e-14 2 6.227159084508102e-01 6.227159084510194e-01 2.09277e-13 5.68212e-13 3 -6.145208099191982e-01 -6.145208099192488e-01 5.06262e-14 7.12430e-13 ----------------------------------------------------------------------------------------------------- 11 Si 1 -1.292842408911303e-01 -1.292842408916800e-01 5.49727e-13 1.05468e-12 2 2.649638073801708e-01 2.649638073800666e-01 1.04194e-13 2.59132e-12 3 -2.181374512848294e-01 -2.181374512843315e-01 4.97852e-13 1.52101e-12 ----------------------------------------------------------------------------------------------------- 12 Si 1 -6.694431065216736e-01 -6.694431065215489e-01 1.24678e-13 4.22562e-12 2 6.020021851324696e-01 6.020021851291114e-01 3.35820e-12 1.80654e-11 * 3 -7.231740077930934e-02 -7.231740077890604e-02 4.03302e-13 9.04984e-13 ----------------------------------------------------------------------------------------------------- 13 Si 1 1.527213832419269e-01 1.527213832418290e-01 9.79217e-14 7.13041e-13 2 2.293892259362142e-01 2.293892259360392e-01 1.75027e-13 2.89915e-12 3 -9.624239994019014e-01 -9.624239993983126e-01 3.58880e-12 4.58056e-12 ----------------------------------------------------------------------------------------------------- 14 Si 1 4.170134962309778e-01 4.170134962308065e-01 1.71252e-13 1.96820e-12 2 3.861671174562539e-01 3.861671174573554e-01 1.10151e-12 1.95632e-12 3 -4.198552261790660e-01 -4.198552261776453e-01 1.42070e-12 9.57301e-12 ----------------------------------------------------------------------------------------------------- 15 Si 1 9.921891943391584e-01 9.921891943387749e-01 3.83471e-13 5.25221e-11 * 2 2.370229583466094e-01 2.370229583461124e-01 4.96991e-13 2.11339e-12 3 -1.458108531389157e-01 -1.458108531395501e-01 6.34381e-13 3.51966e-12 ----------------------------------------------------------------------------------------------------- 16 Si 1 5.855567597123845e-02 5.855567597137371e-02 1.35253e-13 1.57850e-12 2 9.712048956055717e-01 9.712048956055255e-01 4.61853e-14 2.75422e-11 * 3 -2.102524427983111e-01 -2.102524428056820e-01 7.37091e-12 2.82234e-11 * ----------------------------------------------------------------------------------------------------- 17 Si 1 -7.552698816790637e-01 -7.552698816793169e-01 2.53131e-13 3.90377e-12 2 -8.201113244708983e-01 -8.201113244702224e-01 6.75904e-13 1.26354e-12 3 -4.750613158603312e-02 -4.750613158649627e-02 4.63150e-13 5.07745e-12 ----------------------------------------------------------------------------------------------------- 18 Si 1 1.614059128984824e-02 1.614059128940090e-02 4.47337e-13 1.87626e-12 2 -1.716323350005073e-01 -1.716323350004044e-01 1.02945e-13 3.63012e-12 3 -3.220785143221706e-02 -3.220785143111212e-02 1.10494e-12 1.20428e-11 ----------------------------------------------------------------------------------------------------- 19 Si 1 -1.169800362678375e-01 -1.169800362678951e-01 5.76067e-14 4.28138e-12 2 -8.024451553998942e-01 -8.024451553996375e-01 2.56795e-13 3.10978e-11 * 3 8.797053711783218e-01 8.797053711778766e-01 4.45199e-13 3.18412e-12 ----------------------------------------------------------------------------------------------------- 20 Si 1 -7.648424394623139e-01 -7.648424394627591e-01 4.45199e-13 2.56917e-12 2 -8.159089139717776e-02 -8.159089139723306e-02 5.53030e-14 3.35815e-13 3 7.983867150132234e-01 7.983867150142371e-01 1.01363e-12 2.29952e-07 * ----------------------------------------------------------------------------------------------------- 21 Si 1 -7.845953228829711e-02 -7.845953228847023e-02 1.73125e-13 1.51287e-12 2 -1.031820541796126e+00 -1.031820541796432e+00 3.05977e-13 1.49569e-12 3 -1.860791124567912e-01 -1.860791124566404e-01 1.50852e-13 9.39193e-13 ----------------------------------------------------------------------------------------------------- 22 Si 1 1.011205839539223e+00 1.011205839538479e+00 7.44071e-13 1.31095e-12 2 3.197797447287828e-02 3.197797447265509e-02 2.23190e-13 1.63770e-12 3 1.644820165508025e-01 1.644820165506929e-01 1.09662e-13 2.97271e-12 ----------------------------------------------------------------------------------------------------- 23 Si 1 6.850608091808794e-01 6.850608091808444e-01 3.49720e-14 4.58500e-12 2 -5.701782857110136e-01 -5.701782857103942e-01 6.19393e-13 3.50475e-12 3 6.697743050608489e-01 6.697743050608902e-01 4.13003e-14 4.33520e-12 ----------------------------------------------------------------------------------------------------- 24 Si 1 5.033228891730135e-02 5.033228891709827e-02 2.03081e-13 1.60418e-12 2 -4.631683994239882e-02 -4.631683994264077e-02 2.41945e-13 4.88441e-11 * 3 1.023900243238699e+00 1.023900243241772e+00 3.07332e-12 5.77804e-12 ----------------------------------------------------------------------------------------------------- 25 Si 1 -1.129309020110117e+00 -1.129309020110181e+00 6.43929e-14 7.57616e-13 2 1.185300789976149e-01 1.185300789978586e-01 2.43694e-13 6.39329e-12 3 -1.056439100341120e-01 -1.056439100343922e-01 2.80220e-13 8.97948e-12 ----------------------------------------------------------------------------------------------------- 26 Si 1 4.568067380921881e-02 4.568067380940138e-02 1.82576e-13 1.52880e-12 2 1.005889828419975e+00 1.005889828419365e+00 6.10179e-13 5.90861e-12 3 -2.443115366969794e-03 -2.443115366553960e-03 4.15834e-13 1.30894e-12 ----------------------------------------------------------------------------------------------------- 27 Si 1 2.959502590107763e-02 2.959502590147867e-02 4.01047e-13 1.35568e-12 2 1.477006974874099e-01 1.477006974868426e-01 5.67268e-13 2.79476e-12 3 1.095853214397562e+00 1.095853214397468e+00 9.41469e-14 3.62044e-12 ----------------------------------------------------------------------------------------------------- 28 Si 1 -5.866417174230796e-01 -5.866417174198177e-01 3.26184e-12 4.65605e-12 2 5.680667744386559e-01 5.680667744427050e-01 4.04909e-12 6.33416e-12 3 6.130858064771935e-01 6.130858064761479e-01 1.04561e-12 7.16205e-13 ----------------------------------------------------------------------------------------------------- 29 Si 1 1.052628589380334e-01 1.052628589380556e-01 2.21212e-14 1.69889e-12 2 5.030877849589682e-02 5.030877849622871e-02 3.31887e-13 5.10585e-12 3 1.556608573262892e-01 1.556608573262595e-01 2.96985e-14 3.98304e-12 ----------------------------------------------------------------------------------------------------- 30 Si 1 8.212826714139764e-01 8.212826714140894e-01 1.13021e-13 5.45852e-12 2 7.564031871284764e-01 7.564031871285034e-01 2.69784e-14 5.71698e-12 3 -4.492882515414298e-03 -4.492882513395057e-03 2.01924e-12 8.65979e-12 ----------------------------------------------------------------------------------------------------- 31 Si 1 8.025407616524173e-01 8.025407616523446e-01 7.27196e-14 7.08710e-11 * 2 6.767724903076744e-02 6.767724903094081e-02 1.73375e-13 2.97717e-12 3 6.298294093758717e-01 6.298294093767263e-01 8.54539e-13 3.47944e-13 ----------------------------------------------------------------------------------------------------- 32 Si 1 -4.044973853711323e-02 -4.044973853731092e-02 1.97689e-13 1.55242e-12 2 6.723672925321355e-01 6.723672925330930e-01 9.57567e-13 1.43918e-12 3 7.585565950751273e-01 7.585565950805236e-01 5.39635e-12 8.55681e-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 = 30, direction = 3: |F_model - F_numer| error = ----------------------- = 4.49431e-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. MIXED STRUCTURE -- Species = C Si | a0 = 14.375 | (Configuration in file "config-CSi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Si 1 4.782655405649986e-01 4.782655405652735e-01 2.74891e-13 1.11344e-12 2 5.823626687446593e-01 5.823626687450539e-01 3.94684e-13 1.45517e-12 3 5.376213710658821e-01 5.376213710659903e-01 1.08136e-13 9.38916e-13 ----------------------------------------------------------------------------------------------------- 2 C 1 -7.592225384690621e-03 -7.592225384731830e-03 4.12092e-14 5.34575e-13 2 -5.633393844596312e-01 -5.633393844598454e-01 2.14273e-13 1.19471e-12 3 -7.345899062860229e-01 -7.345899062863603e-01 3.37397e-13 2.61868e-12 ----------------------------------------------------------------------------------------------------- 3 C 1 7.739094409482468e-01 7.739094409490894e-01 8.42659e-13 4.36251e-12 2 1.151487032172055e-02 1.151487032177118e-02 5.06348e-14 7.06100e-13 3 -4.103610465885553e-01 -4.103610465912977e-01 2.74247e-12 7.17787e-12 * ----------------------------------------------------------------------------------------------------- 4 C 1 -5.768816658621976e-01 -5.768816658624636e-01 2.66009e-13 1.54610e-12 2 8.656515308773352e-02 8.656515308771154e-02 2.19824e-14 5.11202e-13 3 -2.193118016673728e-01 -2.193118016673098e-01 6.29774e-14 5.63244e-12 ----------------------------------------------------------------------------------------------------- 5 Si 1 -8.829614638938894e-02 -8.829614638928082e-02 1.08122e-13 5.91222e-13 2 3.070632426637317e-01 3.070632426637725e-01 4.08007e-14 9.74942e-13 3 2.677685263407339e-01 2.677685263407520e-01 1.81521e-14 1.00903e-12 ----------------------------------------------------------------------------------------------------- 6 C 1 -1.128316178772795e-01 -1.128316178773592e-01 7.96307e-14 6.20254e-13 2 -4.641794713077948e-01 -4.641794713087276e-01 9.32754e-13 1.01130e-12 3 -4.764099452034759e-01 -4.764099452034578e-01 1.80966e-14 9.86433e-13 ----------------------------------------------------------------------------------------------------- 7 C 1 -2.686238370645754e-01 -2.686238370646032e-01 2.78666e-14 7.54286e-13 2 5.959426012129143e-02 5.959426012126383e-02 2.76029e-14 6.20407e-13 3 2.006430799378071e-01 2.006430799376973e-01 1.09829e-13 3.77254e-13 ----------------------------------------------------------------------------------------------------- 8 Si 1 -1.559680028460070e-01 -1.559680028459624e-01 4.46032e-14 1.78710e-12 2 2.306833826621805e-01 2.306833826621925e-01 1.19904e-14 1.91763e-13 3 -1.028344707356766e+00 -1.028344707356839e+00 7.30527e-14 1.59628e-12 ----------------------------------------------------------------------------------------------------- 9 Si 1 9.123014914701645e-01 9.123014914706107e-01 4.46199e-13 5.83900e-12 * 2 1.642031940568464e-01 1.642031940568783e-01 3.19744e-14 1.62370e-14 3 8.864477293337995e-01 8.864477293341306e-01 3.31180e-13 9.15934e-13 ----------------------------------------------------------------------------------------------------- 10 C 1 -5.886648889002367e-01 -5.886648889002712e-01 3.45279e-14 2.18159e-12 2 1.563591017471935e-01 1.563591017471318e-01 6.16451e-14 7.44960e-14 3 -7.827328215079096e-01 -7.827328215079191e-01 9.54792e-15 3.85358e-13 ----------------------------------------------------------------------------------------------------- 11 C 1 3.209403673324611e-01 3.209403673326141e-01 1.53044e-13 4.65250e-12 2 -3.954786779605253e-01 -3.954786779605302e-01 4.88498e-15 1.13637e-12 3 1.170550090477902e+00 1.170550090477852e+00 5.01821e-14 5.05906e-12 ----------------------------------------------------------------------------------------------------- 12 C 1 -2.176345342018189e-01 -2.176345342018020e-01 1.69587e-14 1.47216e-13 2 3.145423385867294e-02 3.145423385868061e-02 7.67442e-15 6.20483e-13 3 -1.620916140217030e-01 -1.620916140216308e-01 7.21923e-14 6.66051e-13 ----------------------------------------------------------------------------------------------------- 13 C 1 2.557851318831650e-01 2.557851318828998e-01 2.65177e-13 4.01512e-13 2 -1.105626149230229e-01 -1.105626149230771e-01 5.42066e-14 5.84477e-13 3 -5.838093479002004e-01 -5.838093479003246e-01 1.24123e-13 7.00995e-13 ----------------------------------------------------------------------------------------------------- 14 Si 1 -6.427139160286445e-01 -6.427139160285972e-01 4.72955e-14 8.10907e-13 2 -6.580360082935142e-01 -6.580360082936074e-01 9.32587e-14 5.07150e-13 3 5.481224987956614e-01 5.481224987955925e-01 6.89448e-14 7.87592e-13 ----------------------------------------------------------------------------------------------------- 15 C 1 1.736356890946357e-01 1.736356890946521e-01 1.63758e-14 4.97880e-13 2 1.504934514204521e-01 1.504934514204963e-01 4.41869e-14 2.59986e-13 3 1.319656939897030e+00 1.319656939897351e+00 3.20410e-13 4.70823e-12 ----------------------------------------------------------------------------------------------------- 16 C 1 5.652021884678837e-01 5.652021884680023e-01 1.18572e-13 1.33449e-12 2 5.721053183966693e-01 5.721053183967687e-01 9.93650e-14 6.79834e-11 * 3 1.093686591840609e+00 1.093686591840552e+00 5.70655e-14 5.16875e-12 ----------------------------------------------------------------------------------------------------- 17 C 1 2.499749561585551e-01 2.499749561585826e-01 2.75335e-14 3.14332e-13 2 2.073821588921219e-01 2.073821588921104e-01 1.15186e-14 3.00482e-13 3 8.260880264799833e-01 8.260880264800992e-01 1.15907e-13 3.54772e-12 ----------------------------------------------------------------------------------------------------- 18 Si 1 -4.885244554250395e-01 -4.885244554251449e-01 1.05416e-13 5.39402e-13 2 -5.235600843934269e-01 -5.235600843933326e-01 9.43690e-14 1.72751e-13 3 -1.273072444531103e+00 -1.273072444531875e+00 7.72715e-13 2.14317e-12 ----------------------------------------------------------------------------------------------------- 19 Si 1 6.958684625387226e-01 6.958684625387219e-01 6.66134e-16 6.16396e-13 2 -2.417530925552839e-01 -2.417530925552143e-01 6.95555e-14 5.50893e-13 3 -2.544862835851560e-01 -2.544862835852379e-01 8.19345e-14 1.00087e-11 * ----------------------------------------------------------------------------------------------------- 20 Si 1 -7.950695327484703e-01 -7.950695327483441e-01 1.26121e-13 2.54030e-12 2 9.102789542068390e-03 9.102789542030067e-03 3.83235e-14 3.04820e-13 3 -1.580521916765558e-01 -1.580521916767217e-01 1.65923e-13 4.62974e-12 ----------------------------------------------------------------------------------------------------- 21 C 1 -4.853848967573334e-01 -4.853848967574274e-01 9.39249e-14 6.16618e-13 2 4.017929160519391e-01 4.017929160519422e-01 3.16414e-15 1.30890e-12 3 9.023374915773968e-02 9.023374915774383e-02 4.14946e-15 3.52843e-13 ----------------------------------------------------------------------------------------------------- 22 Si 1 -1.631982387360381e-01 -1.631982387360216e-01 1.65701e-14 5.54362e-13 2 -1.196817582601513e+00 -1.196817582601443e+00 6.99441e-14 1.75904e-12 3 7.127918264620381e-02 7.127918264626670e-02 6.28941e-14 3.16469e-13 ----------------------------------------------------------------------------------------------------- 23 C 1 4.983587963265134e-01 4.983587963270605e-01 5.47173e-13 8.91121e-13 2 5.801651073704800e-02 5.801651073701286e-02 3.51386e-14 1.83573e-12 3 5.752692848476004e-03 5.752692848437323e-03 3.86809e-14 4.89921e-14 ----------------------------------------------------------------------------------------------------- 24 C 1 -5.812512938858994e-01 -5.812512938855151e-01 3.84248e-13 3.55604e-13 2 1.022611546961832e+00 1.022611546962044e+00 2.12053e-13 5.83089e-13 3 -5.176901363336610e-01 -5.176901363337680e-01 1.07025e-13 1.81422e-12 ----------------------------------------------------------------------------------------------------- 25 C 1 6.757821252858194e-01 6.757821252857250e-01 9.43690e-14 6.69353e-13 2 4.346769077191209e-02 4.346769077186811e-02 4.39856e-14 5.44696e-13 3 1.423031078274692e+00 1.423031078275220e+00 5.28910e-13 7.34968e-13 ----------------------------------------------------------------------------------------------------- 26 Si 1 -6.035957991806205e-01 -6.035957991809047e-01 2.84217e-13 6.34159e-13 2 -1.056369217848061e-01 -1.056369217849817e-01 1.75568e-13 4.87624e-13 3 -1.513141348202230e+00 -1.513141348201784e+00 4.46310e-13 2.31104e-12 ----------------------------------------------------------------------------------------------------- 27 Si 1 1.314069285778378e-01 1.314069285779769e-01 1.39139e-13 1.59453e-12 2 -5.055468491428563e-01 -5.055468491429994e-01 1.43108e-13 1.16496e-12 3 4.722614843728498e-01 4.722614843728761e-01 2.63123e-14 7.21145e-13 ----------------------------------------------------------------------------------------------------- 28 Si 1 -5.346811056756802e-01 -5.346811056755892e-01 9.09273e-14 2.72826e-12 2 -8.061381986713627e-03 -8.061381986752264e-03 3.86375e-14 2.18481e-13 3 -4.505000436650813e-02 -4.505000436645525e-02 5.28813e-14 3.26079e-13 ----------------------------------------------------------------------------------------------------- 29 Si 1 -3.931561998766167e-02 -3.931561998750826e-02 1.53412e-13 5.36626e-13 2 -9.668179255255566e-03 -9.668179255278679e-03 2.31135e-14 1.77385e-12 3 -1.325118258612886e+00 -1.325118258612717e+00 1.69198e-13 2.34324e-12 ----------------------------------------------------------------------------------------------------- 30 Si 1 3.495548911644717e-01 3.495548911644023e-01 6.94445e-14 1.78263e-12 2 3.600073303607531e-01 3.600073303606476e-01 1.05471e-13 1.15308e-12 3 -9.388393574926576e-01 -9.388393574925304e-01 1.27121e-13 1.04472e-12 ----------------------------------------------------------------------------------------------------- 31 Si 1 2.596687128707562e-01 2.596687128707753e-01 1.90403e-14 1.71192e-11 * 2 -4.576561331579719e-01 -4.576561331580590e-01 8.70415e-14 1.96965e-12 3 7.776753713258402e-01 7.776753713265750e-01 7.34857e-13 1.88838e-12 ----------------------------------------------------------------------------------------------------- 32 Si 1 9.573054267351055e-03 9.573054267355019e-03 3.96384e-15 1.95557e-13 2 7.855165614234897e-01 7.855165614230878e-01 4.01901e-13 1.87682e-11 * 3 7.322828025375518e-01 7.322828025379367e-01 3.84803e-13 3.19234e-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 = 23, direction = 3: |F_model - F_numer| error = ----------------------- = 6.72396e-12 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 4.49431e-10 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 4.49431e-10 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.