!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 -2.914839537582453e+00 -2.914839537582411e+00 4.17444e-14 1.56453e-12 2 -2.954579911124476e+00 -2.954579911124776e+00 3.00648e-13 1.79918e-11 3 -3.520756618714180e+00 -3.520756618714486e+00 3.05533e-13 1.02545e-11 ----------------------------------------------------------------------------------------------------- 2 O 1 -1.435513714400145e+00 -1.435513714402177e+00 2.03171e-12 3.75033e-12 2 1.236460254552234e+00 1.236460254551132e+00 1.10179e-12 8.34488e-12 3 -4.584434790615901e+00 -4.584434790603860e+00 1.20401e-11 9.35341e-12 ----------------------------------------------------------------------------------------------------- 3 O 1 -3.885554602340995e-01 -3.885554602339312e-01 1.68365e-13 7.90362e-12 2 -3.879914508248583e+00 -3.879914508246610e+00 1.97309e-12 4.57279e-12 3 1.658255717601333e+00 1.658255717602133e+00 8.00027e-13 1.26863e-11 ----------------------------------------------------------------------------------------------------- 4 O 1 -3.810775432950808e+00 -3.810775432950753e+00 5.46230e-14 1.36580e-11 2 1.349037546947983e+00 1.349037546948104e+00 1.21680e-13 3.98637e-12 3 8.196998614139480e-01 8.196998614111685e-01 2.77955e-12 4.14591e-12 ----------------------------------------------------------------------------------------------------- 5 O 1 2.181900026207466e+00 2.181900026205320e+00 2.14539e-12 5.45910e-11 2 -4.737068282882851e+00 -4.737068282879032e+00 3.81917e-12 2.51275e-11 3 -3.533363538420645e+00 -3.533363538419833e+00 8.11351e-13 2.91367e-12 ----------------------------------------------------------------------------------------------------- 6 O 1 3.018668580536256e+00 3.018668580533132e+00 3.12372e-12 1.01417e-11 2 4.190095070095639e-01 4.190095070152307e-01 5.66674e-12 2.13886e-11 3 -3.823621538779812e+00 -3.823621538778792e+00 1.02007e-12 8.40039e-12 ----------------------------------------------------------------------------------------------------- 7 O 1 3.873832393509014e+00 3.873832393506369e+00 2.64544e-12 3.96883e-12 2 -6.322771485247257e+00 -6.322771485247156e+00 1.01252e-13 3.48290e-11 3 -2.887322954727534e+00 -2.887322954729010e+00 1.47571e-12 9.58256e-12 ----------------------------------------------------------------------------------------------------- 8 O 1 -1.540861051127143e+00 -1.540861051127834e+00 6.91225e-13 4.17599e-12 2 -1.648890257854445e+00 -1.648890257850734e+00 3.71081e-12 1.75044e-11 3 -5.206060918310029e-01 -5.206060918309495e-01 5.34017e-14 5.16776e-12 ----------------------------------------------------------------------------------------------------- 9 O 1 -4.154904595897042e+00 -4.154904595910659e+00 1.36167e-11 1.30311e-10 * 2 -2.377124700768964e+00 -2.377124700781725e+00 1.27609e-11 7.60476e-11 * 3 -5.868728706730220e+00 -5.868728706719264e+00 1.09557e-11 2.29496e-11 ----------------------------------------------------------------------------------------------------- 10 O 1 -1.752567936524843e-01 -1.752567936524075e-01 7.67997e-14 4.19470e-12 2 5.919875167716478e+00 5.919875167720251e+00 3.77298e-12 1.87264e-11 3 -5.123764700646353e+00 -5.123764700652502e+00 6.14886e-12 1.21316e-11 ----------------------------------------------------------------------------------------------------- 11 O 1 -2.309884527017751e+00 -2.309884527017936e+00 1.84297e-13 2.11862e-11 2 -1.993053191114316e+00 -1.993053191116322e+00 2.00528e-12 4.14246e-12 3 2.161475424831551e+00 2.161475424826591e+00 4.96003e-12 1.22271e-11 ----------------------------------------------------------------------------------------------------- 12 O 1 -4.086713409796285e+00 -4.086713409796008e+00 2.77112e-13 4.04299e-12 2 4.637906854526394e+00 4.637906854524933e+00 1.46105e-12 5.26956e-12 3 2.408607794166007e+00 2.408607794169474e+00 3.46745e-12 1.32943e-11 ----------------------------------------------------------------------------------------------------- 13 O 1 1.816194384405306e-01 1.816194384330589e-01 7.47163e-12 1.20586e-11 2 -1.762990170216829e+00 -1.762990170213761e+00 3.06821e-12 3.12110e-11 3 -8.663953706487998e+00 -8.663953706486099e+00 1.89893e-12 1.11005e-11 ----------------------------------------------------------------------------------------------------- 14 O 1 2.885555474580127e+00 2.885555474572125e+00 8.00204e-12 1.59552e-11 2 3.633808757744549e+00 3.633808757744903e+00 3.53939e-13 2.74079e-11 3 -3.200476978546070e+00 -3.200476978544873e+00 1.19726e-12 2.49054e-11 ----------------------------------------------------------------------------------------------------- 15 O 1 7.744470151147323e+00 7.744470151156407e+00 9.08429e-12 2.61077e-09 * 2 -1.141468089296968e+00 -1.141468089296849e+00 1.18572e-13 1.70044e-11 3 1.690231208356657e+00 1.690231208356179e+00 4.78062e-13 7.05169e-12 ----------------------------------------------------------------------------------------------------- 16 O 1 1.384001544352272e+00 1.384001544351751e+00 5.20917e-13 1.54923e-10 * 2 7.246437852645898e+00 7.246437852648008e+00 2.10942e-12 1.57065e-11 3 1.464355409260847e+00 1.464355409261498e+00 6.51257e-13 1.35339e-10 * ----------------------------------------------------------------------------------------------------- 17 O 1 -4.559552467739437e+00 -4.559552467739460e+00 2.30926e-14 5.19229e-12 2 -3.353280592758418e+00 -3.353280592756939e+00 1.47882e-12 7.24754e-12 3 -1.507482086951345e+00 -1.507482086955280e+00 3.93485e-12 1.98339e-11 ----------------------------------------------------------------------------------------------------- 18 O 1 4.502647334895743e-01 4.502647334904788e-01 9.04499e-13 2.34993e-11 2 8.930398357698615e-01 8.930398357656968e-01 4.16467e-12 2.70582e-10 * 3 -1.523232537068081e+00 -1.523232537064245e+00 3.83604e-12 6.99023e-11 ----------------------------------------------------------------------------------------------------- 19 O 1 1.802149157897218e+00 1.802149157897448e+00 2.30038e-13 4.80038e-12 2 -4.997117647030815e+00 -4.997117647035157e+00 4.34230e-12 6.86828e-12 3 4.239506866915455e+00 4.239506866918114e+00 2.65832e-12 8.12328e-12 ----------------------------------------------------------------------------------------------------- 20 O 1 -4.074594280251349e+00 -4.074594280245234e+00 6.11511e-12 1.49685e-11 2 1.389076206122171e+00 1.389076206126564e+00 4.39293e-12 7.18079e-11 3 3.753612564229364e+00 3.753612564230976e+00 1.61204e-12 3.42988e-11 ----------------------------------------------------------------------------------------------------- 21 O 1 -1.741632222759504e+00 -1.741632222762344e+00 2.83951e-12 5.93259e-12 2 -4.459529307742077e+00 -4.459529307734765e+00 7.31237e-12 9.18110e-12 3 1.297138543787693e+00 1.297138543787416e+00 2.76446e-13 2.44462e-11 ----------------------------------------------------------------------------------------------------- 22 O 1 5.219718579405694e+00 5.219718579413719e+00 8.02469e-12 2.41904e-11 2 2.838066720946621e+00 2.838066720940899e+00 5.72209e-12 1.05969e-11 3 2.795138352441753e+00 2.795138352439790e+00 1.96243e-12 1.94840e-11 ----------------------------------------------------------------------------------------------------- 23 O 1 2.341345553263071e+00 2.341345553264492e+00 1.42153e-12 9.50084e-12 2 -1.925823888699867e+00 -1.925823888699008e+00 8.59313e-13 2.80043e-12 3 3.008305128494126e+00 3.008305128494955e+00 8.29559e-13 1.60485e-11 ----------------------------------------------------------------------------------------------------- 24 O 1 7.635002458375226e-01 7.635002458391517e-01 1.62903e-12 1.60327e-12 2 -2.828445423196014e-01 -2.828445423148602e-01 4.74121e-12 6.39827e-12 3 4.120499257100811e+00 4.120499257099987e+00 8.24230e-13 2.22089e-11 ----------------------------------------------------------------------------------------------------- 25 O 1 -5.143669132886999e+00 -5.143669132885955e+00 1.04450e-12 1.65964e-10 * 2 -1.018735440139444e+00 -1.018735440139958e+00 5.14255e-13 6.18505e-12 3 -1.747143405031482e+00 -1.747143405017399e+00 1.40832e-11 1.77263e-11 ----------------------------------------------------------------------------------------------------- 26 O 1 -1.418942557412700e+00 -1.418942557412721e+00 2.06501e-14 6.88449e-12 2 5.899956863784028e+00 5.899956863781467e+00 2.56062e-12 2.71481e-11 3 -1.173917407717659e+00 -1.173917407708435e+00 9.22418e-12 2.32712e-11 ----------------------------------------------------------------------------------------------------- 27 O 1 1.192495363467946e+00 1.192495363466003e+00 1.94267e-12 5.04912e-11 2 -3.352926489965998e+00 -3.352926489977127e+00 1.11298e-11 1.30886e-11 3 5.383790043366459e+00 5.383790043358916e+00 7.54330e-12 5.83977e-12 ----------------------------------------------------------------------------------------------------- 28 O 1 -4.700216889874149e+00 -4.700216889873594e+00 5.55112e-13 4.69225e-12 2 4.796506390290523e+00 4.796506390290340e+00 1.82965e-13 5.57598e-12 3 3.059724830182100e+00 3.059724830181735e+00 3.64597e-13 2.11111e-11 ----------------------------------------------------------------------------------------------------- 29 O 1 -1.103250241288285e-01 -1.103250241228318e-01 5.99665e-12 1.51576e-11 2 -1.349123151338508e+00 -1.349123151334751e+00 3.75744e-12 1.21949e-11 3 1.193984423259027e+00 1.193984423257249e+00 1.77791e-12 6.21636e-12 ----------------------------------------------------------------------------------------------------- 30 O 1 3.579286498680666e+00 3.579286498679885e+00 7.81597e-13 1.31086e-11 2 4.100844727924449e+00 4.100844727921831e+00 2.61835e-12 2.25802e-11 3 -8.437804727831399e-02 -8.437804727969737e-02 1.38338e-12 5.97442e-12 ----------------------------------------------------------------------------------------------------- 31 O 1 4.356062077261766e+00 4.356062077261525e+00 2.41585e-13 5.28644e-12 2 -1.321241825683956e+00 -1.321241825685905e+00 1.94822e-12 9.61453e-12 3 4.210655217842859e+00 4.210655217843075e+00 2.15827e-13 1.36975e-11 ----------------------------------------------------------------------------------------------------- 32 O 1 1.591367279634725e+00 1.591367279633913e+00 8.11573e-13 8.57980e-12 2 4.518456796452623e+00 4.518456796450359e+00 2.26485e-12 2.86526e-12 3 4.498202466296607e+00 4.498202466296063e+00 5.43565e-13 3.09512e-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 = 29, direction = 1: |F_model - F_numer| error = ----------------------- = 5.43544e-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 -5.142743882304728e+00 -5.142743882304031e+00 6.97220e-13 9.06475e-12 2 -5.196967617356222e+00 -5.196967617357179e+00 9.57456e-13 3.07727e-11 3 -5.224877279157810e+00 -5.224877279157660e+00 1.50102e-13 1.15934e-11 ----------------------------------------------------------------------------------------------------- 2 Si 1 -3.543136843793576e+00 -3.543136843796445e+00 2.86882e-12 1.95524e-11 2 -1.883598066496959e+00 -1.883598066495813e+00 1.14553e-12 1.03193e-11 3 -1.105926124188836e+01 -1.105926124188814e+01 2.13163e-13 6.86562e-12 ----------------------------------------------------------------------------------------------------- 3 Si 1 -1.610013061351152e+00 -1.610013061348562e+00 2.59015e-12 1.86667e-10 * 2 -1.085803598862991e+01 -1.085803598862231e+01 7.60103e-12 3.13634e-11 3 -4.159139357751156e-01 -4.159139357848950e-01 9.77940e-12 5.51996e-11 ----------------------------------------------------------------------------------------------------- 4 Si 1 -1.088240184484558e+01 -1.088240184484572e+01 1.42109e-13 7.42247e-10 * 2 -1.257414301196638e+00 -1.257414301197756e+00 1.11733e-12 2.81137e-11 3 -1.124614177677133e+00 -1.124614177681690e+00 4.55702e-12 1.33653e-11 ----------------------------------------------------------------------------------------------------- 5 Si 1 9.307306905618502e-01 9.307306905631137e-01 1.26354e-12 5.57943e-12 2 -9.662717686970208e+00 -9.662717686969955e+00 2.52243e-13 1.72022e-11 3 -7.798178981862486e+00 -7.798178981862959e+00 4.73399e-13 2.29559e-11 ----------------------------------------------------------------------------------------------------- 6 Si 1 7.968497232227620e+00 7.968497232222732e+00 4.88853e-12 1.40323e-11 2 5.810375251985561e-01 5.810375252041386e-01 5.58253e-12 1.66859e-11 3 -9.341467261273529e+00 -9.341467261270799e+00 2.73026e-12 3.95133e-11 ----------------------------------------------------------------------------------------------------- 7 Si 1 8.127182811171460e+00 8.127182811166602e+00 4.85834e-12 1.32445e-11 2 -8.087991679261037e+00 -8.087991679264015e+00 2.97717e-12 1.86464e-11 3 4.402177872554998e-01 4.402177872558055e-01 3.05755e-13 1.42523e-11 ----------------------------------------------------------------------------------------------------- 8 Si 1 2.287100505220722e+00 2.287100505219294e+00 1.42775e-12 7.32081e-12 2 -1.206582104642745e+00 -1.206582104642069e+00 6.75904e-13 6.35305e-11 3 2.655447550936482e-02 2.655447550742797e-02 1.93685e-12 2.10408e-11 ----------------------------------------------------------------------------------------------------- 9 Si 1 -8.847444822698110e+00 -8.847444822695300e+00 2.81020e-12 5.55698e-11 2 1.515273720536943e-01 1.515273720469297e-01 6.76453e-12 5.60424e-12 3 -9.191343625758146e+00 -9.191343625751294e+00 6.85141e-12 2.00848e-09 * ----------------------------------------------------------------------------------------------------- 10 Si 1 -9.058814809528318e-01 -9.058814809515553e-01 1.27653e-12 1.94146e-11 2 9.977671360446111e+00 9.977671360442230e+00 3.88134e-12 2.47269e-11 3 -9.756029922590361e+00 -9.756029922578939e+00 1.14220e-11 1.38041e-11 ----------------------------------------------------------------------------------------------------- 11 Si 1 -6.909436157108271e-01 -6.909436157243595e-01 1.35324e-11 2.52378e-11 2 -1.412283714403606e+00 -1.412283714401850e+00 1.75682e-12 2.73808e-11 3 -1.460671664393586e+00 -1.460671664393252e+00 3.33733e-13 6.72933e-11 ----------------------------------------------------------------------------------------------------- 12 Si 1 -1.046422407638186e+01 -1.046422407638292e+01 1.06404e-12 3.26548e-11 2 8.906018709815653e+00 8.906018709819728e+00 4.07496e-12 2.34532e-11 3 -1.068501801915220e+00 -1.068501801914265e+00 9.55458e-13 4.19893e-11 ----------------------------------------------------------------------------------------------------- 13 Si 1 4.593030016485623e+00 4.593030016479617e+00 6.00675e-12 6.43929e-12 2 3.101845826784588e+00 3.101845826782288e+00 2.29994e-12 1.05587e-11 3 -1.028252150495855e+01 -1.028252150496409e+01 5.54223e-12 1.79288e-11 ----------------------------------------------------------------------------------------------------- 14 Si 1 4.204773802344643e+00 4.204773802346876e+00 2.23288e-12 1.62501e-11 2 3.498189369453470e+00 3.498189369453906e+00 4.36096e-13 1.99689e-11 3 -4.245253961123366e+00 -4.245253961124037e+00 6.71463e-13 3.84910e-11 ----------------------------------------------------------------------------------------------------- 15 Si 1 1.036788641899394e+01 1.036788641899227e+01 1.66622e-12 3.45679e-12 2 1.858857007915007e+00 1.858857007914908e+00 9.90319e-14 2.75202e-12 3 -2.943630265728644e+00 -2.943630265715023e+00 1.36211e-11 7.09997e-11 ----------------------------------------------------------------------------------------------------- 16 Si 1 3.167569244562067e+00 3.167569244565405e+00 3.33777e-12 5.11422e-11 2 1.029436452436544e+01 1.029436452435647e+01 8.97415e-12 1.40652e-11 3 -8.513033569797890e-01 -8.513033569872700e-01 7.48102e-12 6.63445e-09 * ----------------------------------------------------------------------------------------------------- 17 Si 1 -6.993213235539952e+00 -6.993213235535563e+00 4.38938e-12 4.24558e-11 2 -7.020995075464008e+00 -7.020995075471721e+00 7.71205e-12 7.62146e-12 3 1.326643913454048e+00 1.326643913453301e+00 7.46514e-13 3.10134e-11 ----------------------------------------------------------------------------------------------------- 18 Si 1 -2.910675748949470e+00 -2.910675748952038e+00 2.56772e-12 5.52567e-11 2 -1.914292264232933e+00 -1.914292264235161e+00 2.22755e-12 3.63063e-11 3 1.361757124839123e+00 1.361757124835054e+00 4.06875e-12 2.55533e-11 ----------------------------------------------------------------------------------------------------- 19 Si 1 -2.313304226227418e+00 -2.313304226235186e+00 7.76801e-12 9.67004e-12 2 -8.137888913480559e+00 -8.137888913477463e+00 3.09619e-12 1.22959e-11 3 7.651084504464611e+00 7.651084504455110e+00 9.50173e-12 2.06510e-11 ----------------------------------------------------------------------------------------------------- 20 Si 1 -8.007454495381289e+00 -8.007454495380809e+00 4.79616e-13 4.08740e-12 2 -2.714835421209407e+00 -2.714835421210111e+00 7.03437e-13 1.60800e-11 3 7.986685218788698e+00 7.986685218784728e+00 3.97016e-12 4.57903e-10 * ----------------------------------------------------------------------------------------------------- 21 Si 1 1.274676468632945e+00 1.274676468635808e+00 2.86327e-12 9.30145e-12 2 -1.195451954988824e+01 -1.195451954989057e+01 2.33058e-12 7.91029e-11 3 -4.669579430603625e-01 -4.669579430589206e-01 1.44196e-12 1.20713e-11 ----------------------------------------------------------------------------------------------------- 22 Si 1 1.012413767216213e+01 1.012413767215709e+01 5.04308e-12 1.85487e-11 2 -1.423072377957082e+00 -1.423072377955492e+00 1.58984e-12 1.12157e-11 3 -1.674071872234194e+00 -1.674071872236584e+00 2.39031e-12 1.57572e-11 ----------------------------------------------------------------------------------------------------- 23 Si 1 7.487688562845717e+00 7.487688562840614e+00 5.10347e-12 8.57536e-12 2 -7.448442075093299e+00 -7.448442075092488e+00 8.10907e-13 1.05933e-11 3 6.659265460432586e+00 6.659265460428835e+00 3.75078e-12 1.94467e-11 ----------------------------------------------------------------------------------------------------- 24 Si 1 4.590969700321206e-01 4.590969700465521e-01 1.44316e-11 1.46263e-11 2 -3.162607605294154e-01 -3.162607605319512e-01 2.53575e-12 1.35679e-11 3 1.242558324474189e+01 1.242558324474499e+01 3.10507e-12 1.43263e-11 ----------------------------------------------------------------------------------------------------- 25 Si 1 -1.273158623243448e+01 -1.273158623244110e+01 6.62581e-12 7.66125e-11 2 3.999519726833477e-01 3.999519726792265e-01 4.12120e-12 3.69781e-11 3 8.609553639641457e-03 8.609553639972499e-03 3.31042e-13 2.86241e-11 ----------------------------------------------------------------------------------------------------- 26 Si 1 -7.565941468228096e-01 -7.565941468508861e-01 2.80765e-11 3.76201e-10 * 2 1.248249071825724e+01 1.248249071825413e+01 3.11395e-12 1.08511e-10 3 2.815280112568316e+00 2.815280112566406e+00 1.90958e-12 1.64579e-10 ----------------------------------------------------------------------------------------------------- 27 Si 1 1.278238101075870e-01 1.278238101036630e-01 3.92403e-12 3.83288e-11 2 1.021303200539698e+00 1.021303200532464e+00 7.23488e-12 1.77274e-11 3 1.179091180754074e+01 1.179091180754044e+01 3.03757e-13 1.02062e-10 ----------------------------------------------------------------------------------------------------- 28 Si 1 -5.106386931535676e+00 -5.106386931544473e+00 8.79741e-12 6.70477e-11 2 6.360629356973222e+00 6.360629356971182e+00 2.04015e-12 6.91989e-11 3 5.680440572249495e+00 5.680440572247507e+00 1.98774e-12 4.48868e-11 ----------------------------------------------------------------------------------------------------- 29 Si 1 2.255160247980299e+00 2.255160247980284e+00 1.46549e-14 1.07264e-10 2 2.210374456025591e+00 2.210374456014450e+00 1.11413e-11 3.97235e-10 * 3 5.291533983340151e-01 5.291533983395315e-01 5.51637e-12 1.01867e-10 ----------------------------------------------------------------------------------------------------- 30 Si 1 7.486142573875342e+00 7.486142573872850e+00 2.49223e-12 5.07656e-11 2 7.492364452231652e+00 7.492364452230931e+00 7.21201e-13 3.42792e-11 3 1.149992467679179e+00 1.149992467688101e+00 8.92197e-12 1.40736e-11 ----------------------------------------------------------------------------------------------------- 31 Si 1 8.358434768772193e+00 8.358434768760016e+00 1.21769e-11 2.54264e-10 * 2 3.418540008160474e+00 3.418540008144604e+00 1.58700e-11 1.69850e-10 3 8.938870996006072e+00 8.938870996026459e+00 2.03872e-11 2.80114e-10 * ----------------------------------------------------------------------------------------------------- 32 Si 1 1.686072848953497e+00 1.686072848950061e+00 3.43658e-12 7.00666e-11 2 8.740731735908518e+00 8.740731735906323e+00 2.19558e-12 2.65103e-11 3 8.113548158873371e+00 8.113548158876677e+00 3.30580e-12 1.77955e-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 = 8, direction = 3: |F_model - F_numer| error = ----------------------- = 7.29387e-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. 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 O 1 -1.011204850265337e+00 -1.011204850265868e+00 5.30687e-13 3.76321e-12 2 -4.004298597180998e+00 -4.004298597180699e+00 2.99316e-13 9.81615e-12 3 -3.003134173008137e+00 -3.003134173009264e+00 1.12665e-12 3.11795e-12 ----------------------------------------------------------------------------------------------------- 2 O 1 4.108088178833615e+00 4.108088178834622e+00 1.00719e-12 1.72257e-10 * 2 -2.404371764178478e-01 -2.404371764171991e-01 6.48731e-13 5.62975e-11 * 3 1.320985237040628e+00 1.320985237038933e+00 1.69487e-12 7.26330e-12 ----------------------------------------------------------------------------------------------------- 3 O 1 4.245622351603664e+00 4.245622351604185e+00 5.21361e-13 4.06608e-12 2 -1.836123155215170e-01 -1.836123155223255e-01 8.08520e-13 8.74981e-12 3 -2.949065494120218e+00 -2.949065494120179e+00 3.86358e-14 6.41798e-12 ----------------------------------------------------------------------------------------------------- 4 O 1 -1.978808390392153e+00 -1.978808390392955e+00 8.01581e-13 9.69225e-12 2 2.443915264016139e+00 2.443915264015772e+00 3.67262e-13 1.94267e-11 3 3.734264588379923e+00 3.734264588379934e+00 1.06581e-14 1.68598e-11 ----------------------------------------------------------------------------------------------------- 5 Si 1 -8.106686534584739e+00 -8.106686534588007e+00 3.26850e-12 2.13696e-12 2 -2.893143002006603e+00 -2.893143002007162e+00 5.59108e-13 1.65201e-12 3 -3.037940070339500e+00 -3.037940070339708e+00 2.07390e-13 7.58460e-12 ----------------------------------------------------------------------------------------------------- 6 Si 1 2.954308551353901e+00 2.954308551354269e+00 3.67706e-13 5.72831e-12 2 7.277808837612438e+00 7.277808837612707e+00 2.68230e-13 2.31353e-11 3 -3.408165484855538e+00 -3.408165484855096e+00 4.41869e-13 3.93374e-12 ----------------------------------------------------------------------------------------------------- 7 Si 1 3.498338267934569e+00 3.498338267934152e+00 4.17444e-13 5.40368e-12 2 -3.734318707720230e+00 -3.734318707719702e+00 5.27578e-13 5.70211e-12 3 6.858433558962793e+00 6.858433558961034e+00 1.75948e-12 1.31841e-11 ----------------------------------------------------------------------------------------------------- 8 Si 1 -7.667319659087613e+00 -7.667319659089973e+00 2.35989e-12 4.55636e-12 2 1.997476444536508e+00 1.997476444534787e+00 1.72129e-12 3.11773e-12 3 5.535269868191297e+00 5.535269868189012e+00 2.28528e-12 6.13554e-12 ----------------------------------------------------------------------------------------------------- 9 O 1 1.397246578980897e+00 1.397246578981358e+00 4.60521e-13 1.08891e-11 2 4.375703169468770e+00 4.375703169471651e+00 2.88036e-12 9.33564e-12 3 1.527331002720627e+00 1.527331002720526e+00 1.00586e-13 2.74336e-12 ----------------------------------------------------------------------------------------------------- 10 Si 1 2.145470830297163e+00 2.145470830295176e+00 1.98730e-12 6.76925e-12 2 -9.589518264947940e-01 -9.589518264951641e-01 3.70037e-13 1.18761e-12 3 -3.625657538379989e+00 -3.625657538381319e+00 1.32916e-12 5.28022e-12 ----------------------------------------------------------------------------------------------------- 11 Si 1 1.519540619587980e+00 1.519540619589609e+00 1.62870e-12 7.47846e-13 2 -4.460562718858801e+00 -4.460562718858914e+00 1.12799e-13 5.47029e-12 3 2.090717857126149e+00 2.090717857126120e+00 2.88658e-14 9.94760e-12 ----------------------------------------------------------------------------------------------------- 12 Si 1 -2.872417825554306e+00 -2.872417825554608e+00 3.01981e-13 2.81997e-12 2 -7.655756727872424e-01 -7.655756727872959e-01 5.35127e-14 3.37785e-12 3 1.747545218788776e+00 1.747545218789521e+00 7.45626e-13 3.23541e-12 ----------------------------------------------------------------------------------------------------- 13 O 1 1.488987874978758e+00 1.488987874977023e+00 1.73483e-12 4.42362e-11 * 2 1.409244395482017e+00 1.409244395482355e+00 3.37730e-13 2.50577e-12 3 9.672601010382805e-01 9.672601010383096e-01 2.90878e-14 1.01567e-11 ----------------------------------------------------------------------------------------------------- 14 Si 1 -1.413781611087765e+00 -1.413781611087793e+00 2.77556e-14 7.74913e-12 2 -2.301547972277437e+00 -2.301547972275785e+00 1.65246e-12 9.95204e-13 3 2.285900023043991e+00 2.285900023044032e+00 4.13003e-14 3.63753e-12 ----------------------------------------------------------------------------------------------------- 15 O 1 1.032563120655636e+00 1.032563120655059e+00 5.77316e-13 1.41289e-11 2 -6.732154411215401e-01 -6.732154411220591e-01 5.19029e-13 2.52987e-12 3 -2.907759323118531e+00 -2.907759323117871e+00 6.60361e-13 1.31095e-11 ----------------------------------------------------------------------------------------------------- 16 O 1 -2.945216282278867e-01 -2.945216282287816e-01 8.94951e-13 1.34814e-12 2 2.643785499530547e+00 2.643785499528756e+00 1.79190e-12 7.22578e-12 3 -1.367463647867433e+00 -1.367463647866917e+00 5.16254e-13 8.38885e-13 ----------------------------------------------------------------------------------------------------- 17 Si 1 4.014567519864847e+00 4.014567519865630e+00 7.83373e-13 3.67884e-12 2 7.120408238442789e-01 7.120408238446674e-01 3.88467e-13 1.44795e-12 3 -4.917503244298596e+00 -4.917503244298667e+00 7.10543e-14 3.59268e-12 ----------------------------------------------------------------------------------------------------- 18 O 1 -3.617400209641432e-01 -3.617400209641020e-01 4.12448e-14 2.04520e-12 2 1.840449047237536e+00 1.840449047236600e+00 9.35918e-13 3.45501e-12 3 4.077524233823648e+00 4.077524233823483e+00 1.65201e-13 1.10374e-11 ----------------------------------------------------------------------------------------------------- 19 O 1 -1.900532652037869e+00 -1.900532652038627e+00 7.58504e-13 1.14886e-12 2 3.702847978157178e+00 3.702847978153577e+00 3.60068e-12 1.49778e-11 3 6.295491151880287e-01 6.295491151877615e-01 2.67231e-13 1.53744e-12 ----------------------------------------------------------------------------------------------------- 20 Si 1 4.365325608622359e-01 4.365325608620862e-01 1.49658e-13 4.17882e-12 2 -2.124942507988411e+00 -2.124942507988607e+00 1.95399e-13 4.81171e-12 3 -7.996179305765130e-01 -7.996179305755843e-01 9.28702e-13 2.87081e-12 ----------------------------------------------------------------------------------------------------- 21 O 1 5.348993882797674e+00 5.348993882796617e+00 1.05693e-12 8.45271e-11 * 2 1.908470322648897e+00 1.908470322649279e+00 3.81695e-13 2.25198e-12 3 8.628039255042743e-01 8.628039255040389e-01 2.35367e-13 2.77800e-11 * ----------------------------------------------------------------------------------------------------- 22 O 1 -1.219113280949669e+00 -1.219113280951159e+00 1.48925e-12 7.19580e-12 2 -5.310134345309874e+00 -5.310134345308577e+00 1.29674e-12 4.88587e-12 3 3.498031662163965e-01 3.498031662149653e-01 1.43124e-12 3.91909e-12 ----------------------------------------------------------------------------------------------------- 23 Si 1 1.452043602312521e+00 1.452043602311564e+00 9.56568e-13 8.86691e-12 2 6.465597053219696e-02 6.465597053226653e-02 6.95694e-14 2.20760e-12 3 -1.687385211059769e+00 -1.687385211058897e+00 8.71525e-13 6.19726e-13 ----------------------------------------------------------------------------------------------------- 24 Si 1 -1.615432662939871e-01 -1.615432662941953e-01 2.08195e-13 1.81932e-12 2 -7.282641810103008e-02 -7.282641810034964e-02 6.80442e-13 3.27854e-12 3 -3.758160331362616e+00 -3.758160331361993e+00 6.23057e-13 9.36096e-12 ----------------------------------------------------------------------------------------------------- 25 O 1 1.374687765535418e+00 1.374687765534856e+00 5.61995e-13 5.25779e-12 2 2.564539662605617e+00 2.564539662606334e+00 7.16760e-13 3.42482e-12 3 3.892326025669946e+00 3.892326025670173e+00 2.27374e-13 5.62794e-12 ----------------------------------------------------------------------------------------------------- 26 O 1 -1.817138856096840e+00 -1.817138856097241e+00 4.00124e-13 5.49250e-12 2 -1.623847674947491e+00 -1.623847674947639e+00 1.48104e-13 6.11822e-12 3 1.271323886669680e+00 1.271323886669352e+00 3.27960e-13 6.92335e-12 ----------------------------------------------------------------------------------------------------- 27 Si 1 1.295378794457015e+00 1.295378794457979e+00 9.63452e-13 4.34164e-12 2 1.384137223501303e-02 1.384137223474374e-02 2.69292e-13 7.75515e-13 3 -3.076705591641934e+00 -3.076705591641595e+00 3.38840e-13 6.81011e-12 ----------------------------------------------------------------------------------------------------- 28 Si 1 -2.182341893058840e+00 -2.182341893058295e+00 5.45786e-13 3.45270e-11 * 2 1.387271840046679e+00 1.387271840046840e+00 1.61204e-13 6.00830e-12 3 -2.380901266543344e+00 -2.380901266543242e+00 1.02141e-13 1.69642e-12 ----------------------------------------------------------------------------------------------------- 29 O 1 -2.774935190545917e+00 -2.774935190544960e+00 9.56124e-13 3.07310e-12 2 1.720728628665653e+00 1.720728628667433e+00 1.78013e-12 2.28395e-12 3 3.411011936606080e+00 3.411011936607154e+00 1.07381e-12 1.67244e-12 ----------------------------------------------------------------------------------------------------- 30 Si 1 -3.922453530873860e-01 -3.922453530874745e-01 8.85403e-14 2.65332e-12 2 -4.514445668172774e+00 -4.514445668172616e+00 1.58096e-13 4.80949e-12 3 -4.883827999693079e+00 -4.883827999691235e+00 1.84386e-12 1.27560e-11 ----------------------------------------------------------------------------------------------------- 31 O 1 -2.126631225006802e+00 -2.126631225007436e+00 6.33271e-13 7.96252e-12 2 1.702286491993879e+00 1.702286491994936e+00 1.05649e-12 2.57230e-11 3 1.756826382236398e+00 1.756826382236569e+00 1.70752e-13 5.39324e-12 ----------------------------------------------------------------------------------------------------- 32 Si 1 -3.140826281463482e-02 -3.140826281498040e-02 3.45578e-13 1.11301e-12 2 -1.903205703706760e+00 -1.903205703707554e+00 7.94476e-13 6.70320e-10 * 3 -5.155888203417174e-01 -5.155888203418700e-01 1.52656e-13 3.72824e-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 = 27, direction = 2: |F_model - F_numer| error = ----------------------- = 1.94556e-11 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 7.29387e-11 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 7.29387e-11 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.