!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_NakanoKaliaVashishta_1994_SiO__SM_503555646986_000 Supported species : O 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 = O | a0 = 8.375 | (Configuration in file "config-O.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 O 1 -2.914839537582459e+00 -2.914839537587238e+00 4.77929e-12 3.78311e-11 2 -2.954579911124477e+00 -2.954579911122234e+00 2.24354e-12 3.59486e-11 3 -3.520756618714179e+00 -3.520756618712013e+00 2.16538e-12 8.62865e-12 ----------------------------------------------------------------------------------------------------- 2 O 1 -1.435513714400140e+00 -1.435513714394669e+00 5.47051e-12 1.91207e-11 2 1.236460254552244e+00 1.236460254559421e+00 7.17693e-12 1.49425e-11 3 -4.584434790615907e+00 -4.584434790617673e+00 1.76570e-12 6.82387e-12 ----------------------------------------------------------------------------------------------------- 3 O 1 -3.885554602341043e-01 -3.885554602373166e-01 3.21232e-12 6.12366e-12 2 -3.879914508248584e+00 -3.879914508249358e+00 7.73603e-13 3.03992e-11 3 1.658255717601332e+00 1.658255717598640e+00 2.69118e-12 4.63385e-12 ----------------------------------------------------------------------------------------------------- 4 O 1 -3.810775432950825e+00 -3.810775432946783e+00 4.04121e-12 5.66303e-12 2 1.349037546947957e+00 1.349037546946564e+00 1.39266e-12 1.03153e-11 3 8.196998614139599e-01 8.196998614150242e-01 1.06426e-12 1.30952e-11 ----------------------------------------------------------------------------------------------------- 5 O 1 2.181900026207481e+00 2.181900026208234e+00 7.52731e-13 1.12896e-11 2 -4.737068282882858e+00 -4.737068282883815e+00 9.56568e-13 1.90568e-11 3 -3.533363538420638e+00 -3.533363538420706e+00 6.83897e-14 4.40270e-12 ----------------------------------------------------------------------------------------------------- 6 O 1 3.018668580536247e+00 3.018668580537092e+00 8.45546e-13 2.42451e-11 2 4.190095070095579e-01 4.190095070071019e-01 2.45598e-12 3.77057e-11 3 -3.823621538779791e+00 -3.823621538775916e+00 3.87468e-12 1.16755e-11 ----------------------------------------------------------------------------------------------------- 7 O 1 3.873832393509001e+00 3.873832393510146e+00 1.14531e-12 1.70788e-11 2 -6.322771485247278e+00 -6.322771485236896e+00 1.03819e-11 1.12097e-11 3 -2.887322954727592e+00 -2.887322954726223e+00 1.36913e-12 1.56133e-11 ----------------------------------------------------------------------------------------------------- 8 O 1 -1.540861051127101e+00 -1.540861051124906e+00 2.19491e-12 6.15770e-11 2 -1.648890257854447e+00 -1.648890257858936e+00 4.48930e-12 6.23190e-12 3 -5.206060918310319e-01 -5.206060918305857e-01 4.46199e-13 4.31166e-12 ----------------------------------------------------------------------------------------------------- 9 O 1 -4.154904595897043e+00 -4.154904595899381e+00 2.33769e-12 2.07647e-11 2 -2.377124700768972e+00 -2.377124700769906e+00 9.33476e-13 5.79323e-11 3 -5.868728706730257e+00 -5.868728706731088e+00 8.30447e-13 2.26654e-11 ----------------------------------------------------------------------------------------------------- 10 O 1 -1.752567936525088e-01 -1.752567936563953e-01 3.88653e-12 1.98843e-11 2 5.919875167716490e+00 5.919875167716563e+00 7.28306e-14 2.78382e-11 3 -5.123764700646372e+00 -5.123764700645206e+00 1.16529e-12 2.52252e-11 ----------------------------------------------------------------------------------------------------- 11 O 1 -2.309884527017705e+00 -2.309884527015569e+00 2.13607e-12 2.36819e-11 2 -1.993053191114291e+00 -1.993053191113476e+00 8.15792e-13 2.85791e-11 3 2.161475424831525e+00 2.161475424833465e+00 1.93978e-12 1.36970e-11 ----------------------------------------------------------------------------------------------------- 12 O 1 -4.086713409796305e+00 -4.086713409784569e+00 1.17364e-11 1.77334e-11 2 4.637906854526414e+00 4.637906854523587e+00 2.82707e-12 1.24754e-11 3 2.408607794166022e+00 2.408607794162757e+00 3.26494e-12 8.30314e-12 ----------------------------------------------------------------------------------------------------- 13 O 1 1.816194384405557e-01 1.816194384377871e-01 2.76859e-12 3.13968e-12 2 -1.762990170216834e+00 -1.762990170210359e+00 6.47460e-12 2.06133e-11 3 -8.663953706487945e+00 -8.663953706487099e+00 8.45546e-13 8.95106e-12 ----------------------------------------------------------------------------------------------------- 14 O 1 2.885555474580135e+00 2.885555474580092e+00 4.30767e-14 7.31015e-12 2 3.633808757744572e+00 3.633808757745911e+00 1.33937e-12 2.73208e-11 3 -3.200476978546097e+00 -3.200476978533513e+00 1.25837e-11 2.62261e-11 ----------------------------------------------------------------------------------------------------- 15 O 1 7.744470151147277e+00 7.744470151154953e+00 7.67653e-12 1.10987e-11 2 -1.141468089297017e+00 -1.141468089296983e+00 3.41949e-14 2.97546e-11 3 1.690231208356652e+00 1.690231208356828e+00 1.76081e-13 3.44436e-12 ----------------------------------------------------------------------------------------------------- 16 O 1 1.384001544352291e+00 1.384001544353414e+00 1.12266e-12 1.12335e-11 2 7.246437852645855e+00 7.246437852648951e+00 3.09619e-12 7.10187e-12 3 1.464355409260859e+00 1.464355409254881e+00 5.97788e-12 3.69398e-11 ----------------------------------------------------------------------------------------------------- 17 O 1 -4.559552467739406e+00 -4.559552467735948e+00 3.45857e-12 2.90274e-11 2 -3.353280592758396e+00 -3.353280592756656e+00 1.73994e-12 1.67590e-11 3 -1.507482086951314e+00 -1.507482086952473e+00 1.15907e-12 4.29123e-12 ----------------------------------------------------------------------------------------------------- 18 O 1 4.502647334895246e-01 4.502647334854999e-01 4.02472e-12 3.80167e-11 2 8.930398357698054e-01 8.930398357486298e-01 2.11756e-11 3.79868e-10 * 3 -1.523232537068064e+00 -1.523232537063675e+00 4.38938e-12 1.03241e-10 * ----------------------------------------------------------------------------------------------------- 19 O 1 1.802149157897163e+00 1.802149157897674e+00 5.10703e-13 3.35363e-11 2 -4.997117647030770e+00 -4.997117647047672e+00 1.69020e-11 2.56311e-11 3 4.239506866915423e+00 4.239506866909771e+00 5.65237e-12 1.30242e-11 ----------------------------------------------------------------------------------------------------- 20 O 1 -4.074594280251320e+00 -4.074594280246489e+00 4.83080e-12 1.10392e-11 2 1.389076206122128e+00 1.389076206123629e+00 1.50102e-12 1.13982e-11 3 3.753612564229343e+00 3.753612564237423e+00 8.08020e-12 1.72906e-11 ----------------------------------------------------------------------------------------------------- 21 O 1 -1.741632222759508e+00 -1.741632222767029e+00 7.52132e-12 1.37063e-10 * 2 -4.459529307742079e+00 -4.459529307741424e+00 6.54587e-13 2.69464e-11 3 1.297138543787706e+00 1.297138543787213e+00 4.93383e-13 6.08487e-11 ----------------------------------------------------------------------------------------------------- 22 O 1 5.219718579405704e+00 5.219718579408665e+00 2.96119e-12 3.09977e-09 * 2 2.838066720946677e+00 2.838066720947006e+00 3.28626e-13 1.52105e-11 3 2.795138352441769e+00 2.795138352445198e+00 3.42970e-12 4.97069e-12 ----------------------------------------------------------------------------------------------------- 23 O 1 2.341345553263073e+00 2.341345553257957e+00 5.11591e-12 1.11160e-11 2 -1.925823888699866e+00 -1.925823888701281e+00 1.41487e-12 1.32738e-12 3 3.008305128494141e+00 3.008305128493546e+00 5.95080e-13 1.45493e-11 ----------------------------------------------------------------------------------------------------- 24 O 1 7.635002458375540e-01 7.635002458304124e-01 7.14162e-12 1.05687e-11 2 -2.828445423196161e-01 -2.828445423168425e-01 2.77356e-12 1.71217e-11 3 4.120499257100830e+00 4.120499257097038e+00 3.79252e-12 3.46381e-11 ----------------------------------------------------------------------------------------------------- 25 O 1 -5.143669132887031e+00 -5.143669132888384e+00 1.35270e-12 1.67208e-11 2 -1.018735440139434e+00 -1.018735440151552e+00 1.21174e-11 2.28846e-11 3 -1.747143405031485e+00 -1.747143405032483e+00 9.98090e-13 2.19227e-11 ----------------------------------------------------------------------------------------------------- 26 O 1 -1.418942557412666e+00 -1.418942557412629e+00 3.68594e-14 3.84124e-11 2 5.899956863784011e+00 5.899956863784537e+00 5.25802e-13 2.90710e-11 3 -1.173917407717601e+00 -1.173917407722148e+00 4.54747e-12 1.01719e-11 ----------------------------------------------------------------------------------------------------- 27 O 1 1.192495363467937e+00 1.192495363470109e+00 2.17204e-12 3.42446e-10 * 2 -3.352926489965943e+00 -3.352926489964934e+00 1.00853e-12 2.04889e-11 3 5.383790043366455e+00 5.383790043357852e+00 8.60290e-12 8.83116e-12 ----------------------------------------------------------------------------------------------------- 28 O 1 -4.700216889874123e+00 -4.700216889867511e+00 6.61160e-12 1.03215e-11 2 4.796506390290502e+00 4.796506390290636e+00 1.34115e-13 7.87814e-12 3 3.059724830182106e+00 3.059724830180981e+00 1.12532e-12 4.67164e-11 ----------------------------------------------------------------------------------------------------- 29 O 1 -1.103250241288026e-01 -1.103250241291580e-01 3.55438e-13 2.31428e-11 2 -1.349123151338449e+00 -1.349123151342545e+00 4.09583e-12 1.93117e-11 3 1.193984423259048e+00 1.193984423260195e+00 1.14708e-12 1.08342e-11 ----------------------------------------------------------------------------------------------------- 30 O 1 3.579286498680657e+00 3.579286498680969e+00 3.11751e-13 1.77529e-11 2 4.100844727924430e+00 4.100844727927864e+00 3.43459e-12 5.42855e-12 3 -8.437804727829512e-02 -8.437804727798215e-02 3.12972e-13 1.25478e-11 ----------------------------------------------------------------------------------------------------- 31 O 1 4.356062077261758e+00 4.356062077251950e+00 9.80727e-12 5.08011e-11 2 -1.321241825683962e+00 -1.321241825684788e+00 8.26450e-13 9.80371e-12 3 4.210655217842825e+00 4.210655217839792e+00 3.03224e-12 7.28395e-12 ----------------------------------------------------------------------------------------------------- 32 O 1 1.591367279634691e+00 1.591367279634678e+00 1.31006e-14 4.74820e-12 2 4.518456796452632e+00 4.518456796451533e+00 1.09956e-12 2.55271e-11 3 4.498202466296572e+00 4.498202466293341e+00 3.23119e-12 2.16964e-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 dicontinuities. Maximum error obtained for particle = 10, direction = 1: |F_model - F_numer| error = ----------------------- = 2.21762e-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 = 8.375 | (Configuration in file "config-Si.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Si 1 -5.142743882304752e+00 -5.142743882304855e+00 1.03029e-13 2.61924e-11 2 -5.196967617356218e+00 -5.196967617364097e+00 7.87903e-12 5.92584e-11 3 -5.224877279157824e+00 -5.224877279160745e+00 2.92033e-12 1.26725e-11 ----------------------------------------------------------------------------------------------------- 2 Si 1 -3.543136843793592e+00 -3.543136843789067e+00 4.52438e-12 2.14984e-11 2 -1.883598066496945e+00 -1.883598066497321e+00 3.75255e-13 1.77605e-11 3 -1.105926124188833e+01 -1.105926124188261e+01 5.71276e-12 1.69186e-10 ----------------------------------------------------------------------------------------------------- 3 Si 1 -1.610013061351149e+00 -1.610013061371168e+00 2.00187e-11 4.37761e-11 2 -1.085803598862989e+01 -1.085803598861990e+01 9.99734e-12 2.70575e-11 3 -4.159139357750929e-01 -4.159139357792683e-01 4.17533e-12 1.04254e-11 ----------------------------------------------------------------------------------------------------- 4 Si 1 -1.088240184484555e+01 -1.088240184484655e+01 9.96536e-13 1.48128e-09 * 2 -1.257414301196613e+00 -1.257414301191254e+00 5.35882e-12 5.42477e-12 3 -1.124614177677144e+00 -1.124614177665496e+00 1.16482e-11 4.45814e-11 ----------------------------------------------------------------------------------------------------- 5 Si 1 9.307306905618591e-01 9.307306905511095e-01 1.07496e-11 1.08401e-11 2 -9.662717686970199e+00 -9.662717687007666e+00 3.74669e-11 4.53202e-11 3 -7.798178981862505e+00 -7.798178981863171e+00 6.66134e-13 3.16547e-12 ----------------------------------------------------------------------------------------------------- 6 Si 1 7.968497232227618e+00 7.968497232217596e+00 1.00213e-11 6.75993e-12 2 5.810375251985710e-01 5.810375251925187e-01 6.05227e-12 3.00983e-11 3 -9.341467261273539e+00 -9.341467261282592e+00 9.05231e-12 4.10765e-11 ----------------------------------------------------------------------------------------------------- 7 Si 1 8.127182811171480e+00 8.127182811169718e+00 1.76215e-12 1.45892e-11 2 -8.087991679261050e+00 -8.087991679263112e+00 2.06235e-12 4.48583e-11 3 4.402177872554998e-01 4.402177872574614e-01 1.96165e-12 3.80598e-11 ----------------------------------------------------------------------------------------------------- 8 Si 1 2.287100505220713e+00 2.287100505219172e+00 1.54099e-12 1.88195e-10 2 -1.206582104642721e+00 -1.206582104657816e+00 1.50948e-11 1.55843e-10 3 2.655447550936291e-02 2.655447550953148e-02 1.68570e-13 3.19303e-11 ----------------------------------------------------------------------------------------------------- 9 Si 1 -8.847444822698103e+00 -8.847444822702837e+00 4.73399e-12 2.59135e-11 2 1.515273720536842e-01 1.515273720428793e-01 1.08049e-11 4.81539e-11 3 -9.191343625758142e+00 -9.191343625759728e+00 1.58629e-12 1.65912e-11 ----------------------------------------------------------------------------------------------------- 10 Si 1 -9.058814809528526e-01 -9.058814809173563e-01 3.54963e-11 4.86610e-11 2 9.977671360446131e+00 9.977671360455059e+00 8.92797e-12 3.02194e-11 3 -9.756029922590393e+00 -9.756029922613845e+00 2.34515e-11 2.75442e-11 ----------------------------------------------------------------------------------------------------- 11 Si 1 -6.909436157108273e-01 -6.909436157758386e-01 6.50113e-11 6.33198e-11 2 -1.412283714403666e+00 -1.412283714414432e+00 1.07663e-11 3.44447e-11 3 -1.460671664393586e+00 -1.460671664389974e+00 3.61200e-12 4.25100e-11 ----------------------------------------------------------------------------------------------------- 12 Si 1 -1.046422407638187e+01 -1.046422407638275e+01 8.82849e-13 2.10516e-11 2 8.906018709815662e+00 8.906018709816230e+00 5.68434e-13 7.20508e-11 3 -1.068501801915227e+00 -1.068501801911269e+00 3.95750e-12 3.24980e-11 ----------------------------------------------------------------------------------------------------- 13 Si 1 4.593030016485638e+00 4.593030016483593e+00 2.04547e-12 1.83773e-11 2 3.101845826784559e+00 3.101845826776241e+00 8.31735e-12 1.36309e-11 3 -1.028252150495855e+01 -1.028252150496199e+01 3.43725e-12 1.11413e-11 ----------------------------------------------------------------------------------------------------- 14 Si 1 4.204773802344658e+00 4.204773802337284e+00 7.37366e-12 1.84048e-11 2 3.498189369453473e+00 3.498189369433339e+00 2.01341e-11 5.14961e-11 3 -4.245253961123383e+00 -4.245253961120414e+00 2.96829e-12 3.03430e-10 * ----------------------------------------------------------------------------------------------------- 15 Si 1 1.036788641899392e+01 1.036788641898210e+01 1.18234e-11 3.17222e-11 2 1.858857007914987e+00 1.858857007914315e+00 6.72129e-13 6.76461e-11 3 -2.943630265728649e+00 -2.943630265728020e+00 6.29274e-13 3.88738e-11 ----------------------------------------------------------------------------------------------------- 16 Si 1 3.167569244562102e+00 3.167569244556624e+00 5.47740e-12 2.12927e-11 2 1.029436452436544e+01 1.029436452437568e+01 1.02318e-11 3.07008e-11 3 -8.513033569797562e-01 -8.513033569866574e-01 6.90115e-12 4.82113e-11 ----------------------------------------------------------------------------------------------------- 17 Si 1 -6.993213235539946e+00 -6.993213235537157e+00 2.78888e-12 1.01734e-10 2 -7.020995075464026e+00 -7.020995075465692e+00 1.66533e-12 4.56168e-12 3 1.326643913454074e+00 1.326643913464790e+00 1.07165e-11 5.67124e-12 ----------------------------------------------------------------------------------------------------- 18 Si 1 -2.910675748949464e+00 -2.910675748931086e+00 1.83773e-11 1.34242e-10 2 -1.914292264232942e+00 -1.914292264224846e+00 8.09552e-12 4.57125e-11 3 1.361757124839124e+00 1.361757124848741e+00 9.61675e-12 4.57712e-11 ----------------------------------------------------------------------------------------------------- 19 Si 1 -2.313304226227419e+00 -2.313304226224153e+00 3.26672e-12 1.73221e-11 2 -8.137888913480532e+00 -8.137888913477893e+00 2.63967e-12 1.96589e-11 3 7.651084504464615e+00 7.651084504464121e+00 4.93827e-13 7.32637e-10 * ----------------------------------------------------------------------------------------------------- 20 Si 1 -8.007454495381289e+00 -8.007454495386076e+00 4.78728e-12 3.48255e-11 2 -2.714835421209431e+00 -2.714835421219767e+00 1.03366e-11 4.61102e-11 3 7.986685218788704e+00 7.986685218795889e+00 7.18448e-12 2.27365e-11 ----------------------------------------------------------------------------------------------------- 21 Si 1 1.274676468632901e+00 1.274676468628136e+00 4.76463e-12 3.51186e-12 2 -1.195451954988826e+01 -1.195451954989130e+01 3.03935e-12 4.13982e-10 * 3 -4.669579430603847e-01 -4.669579430677632e-01 7.37843e-12 1.61483e-10 ----------------------------------------------------------------------------------------------------- 22 Si 1 1.012413767216215e+01 1.012413767216068e+01 1.46727e-12 1.35612e-10 2 -1.423072377957055e+00 -1.423072377970390e+00 1.33353e-11 1.21762e-10 3 -1.674071872234244e+00 -1.674071872234745e+00 5.01599e-13 5.40394e-11 ----------------------------------------------------------------------------------------------------- 23 Si 1 7.487688562845769e+00 7.487688562842449e+00 3.32001e-12 1.42766e-11 2 -7.448442075093350e+00 -7.448442075093978e+00 6.27942e-13 5.02682e-11 3 6.659265460432603e+00 6.659265460431117e+00 1.48592e-12 3.30225e-11 ----------------------------------------------------------------------------------------------------- 24 Si 1 4.590969700320340e-01 4.590969700235138e-01 8.52018e-12 8.65187e-11 2 -3.162607605294097e-01 -3.162607605259398e-01 3.46989e-12 4.79545e-11 3 1.242558324474190e+01 1.242558324474084e+01 1.06049e-12 4.52438e-11 ----------------------------------------------------------------------------------------------------- 25 Si 1 -1.273158623243449e+01 -1.273158623243086e+01 3.62554e-12 7.24114e-11 2 3.999519726833398e-01 3.999519726803379e-01 3.00193e-12 3.24385e-11 3 8.609553639613951e-03 8.609553635981268e-03 3.63268e-12 7.14204e-11 ----------------------------------------------------------------------------------------------------- 26 Si 1 -7.565941468228042e-01 -7.565941468049163e-01 1.78879e-11 1.39680e-10 2 1.248249071825727e+01 1.248249071819537e+01 6.18972e-11 1.22350e-10 3 2.815280112568325e+00 2.815280112530268e+00 3.80571e-11 5.43982e-10 * ----------------------------------------------------------------------------------------------------- 27 Si 1 1.278238101076203e-01 1.278238101118283e-01 4.20797e-12 2.99151e-11 2 1.021303200539680e+00 1.021303200539184e+00 4.96048e-13 1.25677e-10 3 1.179091180754078e+01 1.179091180754216e+01 1.38023e-12 9.11804e-11 ----------------------------------------------------------------------------------------------------- 28 Si 1 -5.106386931535678e+00 -5.106386931536681e+00 1.00364e-12 1.39376e-10 2 6.360629356973232e+00 6.360629356969284e+00 3.94795e-12 1.35509e-11 3 5.680440572249506e+00 5.680440572238614e+00 1.08926e-11 3.32019e-11 ----------------------------------------------------------------------------------------------------- 29 Si 1 2.255160247980308e+00 2.255160247982839e+00 2.53131e-12 1.43559e-10 2 2.210374456025609e+00 2.210374455992131e+00 3.34781e-11 4.01106e-11 3 5.291533983340115e-01 5.291533983348551e-01 8.43547e-13 4.60996e-11 ----------------------------------------------------------------------------------------------------- 30 Si 1 7.486142573875336e+00 7.486142573887774e+00 1.24381e-11 6.67653e-11 2 7.492364452231646e+00 7.492364452222422e+00 9.22462e-12 2.34470e-11 3 1.149992467679180e+00 1.149992467718201e+00 3.90201e-11 9.34326e-11 ----------------------------------------------------------------------------------------------------- 31 Si 1 8.358434768772204e+00 8.358434768683056e+00 8.91482e-11 4.51047e-10 * 2 3.418540008160511e+00 3.418540008192008e+00 3.14970e-11 1.38150e-10 3 8.938870996006079e+00 8.938870995979087e+00 2.69917e-11 3.98135e-10 * ----------------------------------------------------------------------------------------------------- 32 Si 1 1.686072848953486e+00 1.686072848952604e+00 8.82405e-13 4.30740e-11 2 8.740731735908520e+00 8.740731735912259e+00 3.73923e-12 2.00355e-11 3 8.113548158873364e+00 8.113548158885532e+00 1.21680e-11 1.80496e-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 dicontinuities. Maximum error obtained for particle = 25, direction = 3: |F_model - F_numer| error = ----------------------- = 4.21936e-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 = O Si | a0 = 8.375 | (Configuration in file "config-OSi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Si 1 1.311866431116154e+00 1.311866431115558e+00 5.95746e-13 1.05005e-12 2 -2.585051436212676e+00 -2.585051436210483e+00 2.19336e-12 2.17648e-12 3 -1.071587837152259e+00 -1.071587837152354e+00 9.45910e-14 6.49014e-12 ----------------------------------------------------------------------------------------------------- 2 O 1 -3.071545670295467e+00 -3.071545670292561e+00 2.90523e-12 9.61009e-12 2 2.953915960410453e+00 2.953915960410319e+00 1.34115e-13 3.13749e-12 3 8.784635431555450e-01 8.784635431553801e-01 1.64868e-13 3.95939e-12 ----------------------------------------------------------------------------------------------------- 3 O 1 -4.417043335297271e+00 -4.417043335297983e+00 7.11431e-13 7.32037e-12 2 2.102829882304875e+00 2.102829882305417e+00 5.42677e-13 5.76161e-12 3 -4.402549472159581e+00 -4.402549472157169e+00 2.41229e-12 6.35492e-12 ----------------------------------------------------------------------------------------------------- 4 Si 1 -1.395174409432989e+00 -1.395174409432972e+00 1.75415e-14 1.60894e-12 2 -4.754659300913781e+00 -4.754659300915116e+00 1.33493e-12 4.08710e-10 * 3 5.438105545852479e+00 5.438105545852459e+00 2.04281e-14 8.26006e-12 ----------------------------------------------------------------------------------------------------- 5 Si 1 1.348939592085742e+00 1.348939592085773e+00 3.08642e-14 2.90967e-12 2 3.280088889437904e+00 3.280088889437108e+00 7.96696e-13 9.19709e-13 3 4.120362966423247e+00 4.120362966423238e+00 9.76996e-15 5.58931e-12 ----------------------------------------------------------------------------------------------------- 6 O 1 -1.489865889608909e+00 -1.489865889610148e+00 1.23968e-12 3.71192e-12 2 1.942755488327705e+00 1.942755488327180e+00 5.24247e-13 2.67177e-11 3 1.329014236280895e-01 1.329014236271559e-01 9.33559e-13 1.34098e-11 ----------------------------------------------------------------------------------------------------- 7 O 1 1.662018352845642e+00 1.662018352845712e+00 6.92779e-14 5.78182e-12 2 1.781825389676914e+00 1.781825389677582e+00 6.68132e-13 5.63349e-12 3 1.927287997113175e+00 1.927287997113826e+00 6.51035e-13 2.21245e-12 ----------------------------------------------------------------------------------------------------- 8 O 1 -6.381975253316244e-01 -6.381975253316908e-01 6.63913e-14 2.07434e-12 2 5.374011014880058e+00 5.374011014874895e+00 5.16209e-12 1.20606e-11 3 1.301869290888142e+00 1.301869290888357e+00 2.15161e-13 1.24434e-12 ----------------------------------------------------------------------------------------------------- 9 Si 1 -3.937998705092961e+00 -3.937998705091863e+00 1.09823e-12 2.51577e-12 2 -3.060107577862571e+00 -3.060107577862958e+00 3.86358e-13 1.02407e-12 3 -7.502973390500353e+00 -7.502973390500523e+00 1.70530e-13 1.45226e-11 ----------------------------------------------------------------------------------------------------- 10 Si 1 2.458708563141260e-02 2.458708563171112e-02 2.98522e-13 6.60804e-12 2 6.933604891470013e+00 6.933604891470397e+00 3.83693e-13 5.38236e-12 3 -6.844890103798806e+00 -6.844890103797723e+00 1.08358e-12 7.54152e-12 ----------------------------------------------------------------------------------------------------- 11 Si 1 1.644751152704772e+00 1.644751152705870e+00 1.09712e-12 8.06799e-12 2 -4.664630342735344e+00 -4.664630342735397e+00 5.32907e-14 1.68301e-11 3 9.455772063819619e+00 9.455772063818477e+00 1.14220e-12 2.79297e-11 ----------------------------------------------------------------------------------------------------- 12 Si 1 -5.349225372075220e+00 -5.349225372074927e+00 2.93099e-13 1.60130e-11 2 4.814196425842233e+00 4.814196425842682e+00 4.49418e-13 8.72991e-12 3 9.065980828724667e+00 9.065980828726012e+00 1.34470e-12 3.66995e-12 ----------------------------------------------------------------------------------------------------- 13 Si 1 4.447727016915080e+00 4.447727016913434e+00 1.64579e-12 2.12319e-11 2 -8.480525811541265e+00 -8.480525811543011e+00 1.74616e-12 4.62919e-12 3 -7.344815807154201e+00 -7.344815807156763e+00 2.56239e-12 3.16476e-11 ----------------------------------------------------------------------------------------------------- 14 O 1 -3.070192675038703e+00 -3.070192675039848e+00 1.14486e-12 1.05427e-11 2 -2.747261193677058e+00 -2.747261193677318e+00 2.59792e-13 2.87859e-12 3 2.867810194395020e+00 2.867810194394537e+00 4.82725e-13 5.02309e-12 ----------------------------------------------------------------------------------------------------- 15 Si 1 5.106199942026367e+00 5.106199942026874e+00 5.07150e-13 1.16120e-11 2 -1.391848456325343e-01 -1.391848456314074e-01 1.12690e-12 2.71775e-11 3 1.300565714009438e+00 1.300565714015430e+00 5.99165e-12 7.86775e-11 * ----------------------------------------------------------------------------------------------------- 16 Si 1 4.955148737867255e+00 4.955148737867055e+00 1.99840e-13 2.90790e-12 2 6.975418964189509e+00 6.975418964185893e+00 3.61577e-12 1.64986e-10 * 3 9.082380957598842e+00 9.082380957598939e+00 9.76996e-14 8.89955e-12 ----------------------------------------------------------------------------------------------------- 17 O 1 -4.709212718118616e-01 -4.709212718102411e-01 1.62048e-12 4.34558e-12 2 4.385139114969372e+00 4.385139114970203e+00 8.30447e-13 2.33413e-12 3 1.950990273121500e-01 1.950990273122604e-01 1.10439e-13 3.44527e-12 ----------------------------------------------------------------------------------------------------- 18 Si 1 2.947116015438741e+00 2.947116015438783e+00 4.17444e-14 3.05445e-12 2 -7.551403436581897e+00 -7.551403436582124e+00 2.27374e-13 4.97202e-12 3 -4.226752104829465e+00 -4.226752104827743e+00 1.72218e-12 1.05720e-11 ----------------------------------------------------------------------------------------------------- 19 O 1 1.187393840278446e-01 1.187393840294727e-01 1.62811e-12 3.11665e-12 2 3.917296394614512e+00 3.917296394614070e+00 4.41869e-13 8.22187e-12 3 1.639818476981778e+00 1.639818476982021e+00 2.43139e-13 2.73337e-12 ----------------------------------------------------------------------------------------------------- 20 Si 1 -3.033707585883249e+00 -3.033707585880945e+00 2.30349e-12 5.55556e-12 2 -3.624636853350549e+00 -3.624636853352115e+00 1.56630e-12 1.59668e-11 3 -1.435667782572927e+00 -1.435667782573090e+00 1.63203e-13 1.04534e-11 ----------------------------------------------------------------------------------------------------- 21 O 1 3.408636714741951e+00 3.408636714731821e+00 1.01297e-11 4.01545e-11 * 2 2.475808620269907e+00 2.475808620269376e+00 5.31131e-13 2.39979e-10 * 3 4.712152960218639e+00 4.712152960219967e+00 1.32783e-12 1.45612e-10 * ----------------------------------------------------------------------------------------------------- 22 Si 1 -7.280021472505342e-01 -7.280021472511521e-01 6.17839e-13 4.67437e-12 2 -9.169218999251190e-01 -9.169218999241057e-01 1.01330e-12 1.60547e-11 3 -6.582860744832233e+00 -6.582860744833194e+00 9.61009e-13 4.26326e-12 ----------------------------------------------------------------------------------------------------- 23 Si 1 1.405949692850722e+00 1.405949692851207e+00 4.84501e-13 8.02070e-12 2 -4.499425946086191e+00 -4.499425946085778e+00 4.13003e-13 8.56026e-12 3 1.358900231327846e+00 1.358900231327012e+00 8.34666e-13 7.00306e-12 ----------------------------------------------------------------------------------------------------- 24 Si 1 9.794354753867147e-01 9.794354753855123e-01 1.20237e-12 5.00266e-12 2 2.562169439309597e+00 2.562169439309285e+00 3.11751e-13 5.98055e-12 3 1.238902783457725e+00 1.238902783456601e+00 1.12421e-12 2.08789e-12 ----------------------------------------------------------------------------------------------------- 25 O 1 2.830780150708118e+00 2.830780150708274e+00 1.55431e-13 7.44693e-12 2 -3.513405191360290e+00 -3.513405191359473e+00 8.16680e-13 4.97469e-12 3 -4.663408181130272e+00 -4.663408181126973e+00 3.29958e-12 1.00941e-11 ----------------------------------------------------------------------------------------------------- 26 O 1 6.449404322005839e-02 6.449404321935628e-02 7.02105e-13 2.25418e-10 * 2 -1.320774143583021e+00 -1.320774143582952e+00 6.83897e-14 4.54969e-12 3 -6.746149040952759e+00 -6.746149040951519e+00 1.23990e-12 8.89333e-12 ----------------------------------------------------------------------------------------------------- 27 Si 1 -1.051057007497440e+00 -1.051057007499415e+00 1.97464e-12 1.01186e-11 2 9.559634772433897e+00 9.559634772433336e+00 5.61329e-13 2.24532e-12 3 -1.005893876341115e+00 -1.005893876340741e+00 3.73923e-13 7.14007e-12 ----------------------------------------------------------------------------------------------------- 28 O 1 -8.376702313683945e-02 -8.376702313519502e-02 1.64443e-12 2.34165e-12 2 -1.866830743018944e+00 -1.866830743019583e+00 6.38822e-13 2.07367e-12 3 2.136220020485738e+00 2.136220020486173e+00 4.35652e-13 4.63540e-12 ----------------------------------------------------------------------------------------------------- 29 O 1 -3.392759902526617e+00 -3.392759902525780e+00 8.36664e-13 2.82085e-12 2 -4.432534919314230e+00 -4.432534919312953e+00 1.27631e-12 4.41958e-12 3 -3.419590346520922e+00 -3.419590346520009e+00 9.13492e-13 1.00178e-11 ----------------------------------------------------------------------------------------------------- 30 O 1 1.769274164281436e+00 1.769274164281486e+00 4.95159e-14 7.72515e-12 2 1.340978916120696e+00 1.340978916121766e+00 1.07003e-12 9.81881e-13 3 -6.797570272634954e+00 -6.797570272635709e+00 7.54952e-13 1.27436e-11 ----------------------------------------------------------------------------------------------------- 31 O 1 -7.528464241198374e-02 -7.528464241212059e-02 1.36849e-13 1.54462e-11 2 -7.561425246734941e+00 -7.561425246734014e+00 9.27258e-13 9.00791e-12 3 2.824912551389904e+00 2.824912551389439e+00 4.65405e-13 1.25482e-11 ----------------------------------------------------------------------------------------------------- 32 O 1 -1.820920789156345e+00 -1.820920789156382e+00 3.61933e-14 4.95914e-12 2 1.319104724272766e+00 1.319104724270038e+00 2.72715e-12 9.63407e-12 3 2.367202383797808e+00 2.367202383797677e+00 1.31450e-13 1.65659e-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 dicontinuities. Maximum error obtained for particle = 28, direction = 1: |F_model - F_numer| error = ----------------------- = 1.96310e-11 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 4.21936e-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 4.21936e-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.