!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 : Tersoff_LAMMPS_Nord_Albe_Erhart_Nordlund_GaN__MO_612061685362_000 Supported species : Ga N 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 = Ga | a0 = 3.9710893631 | (Configuration in file "config-Ga.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ga 1 2.866867716964543e+00 2.866867716966130e+00 1.58717e-12 2.00280e-11 2 2.150124304596861e+00 2.150124304598541e+00 1.68043e-12 1.57736e-10 3 1.134031399880674e-01 1.134031399874468e-01 6.20587e-13 1.95297e-10 * ----------------------------------------------------------------------------------------------------- 2 Ga 1 -2.013599418731890e+00 -2.013599418729761e+00 2.12852e-12 9.62652e-12 2 4.632189900748294e-01 4.632189900707244e-01 4.10505e-12 7.18492e-12 3 1.115952570747216e+00 1.115952570746712e+00 5.04707e-13 2.27922e-11 ----------------------------------------------------------------------------------------------------- 3 Ga 1 -7.185913116431097e-01 -7.185913116422342e-01 8.75522e-13 1.63172e-11 2 2.431964975972220e+00 2.431964975967607e+00 4.61320e-12 7.53668e-11 3 -8.682884410189504e-01 -8.682884410163884e-01 2.56206e-12 2.53982e-11 ----------------------------------------------------------------------------------------------------- 4 Ga 1 2.207301399628999e+00 2.207301399628760e+00 2.38476e-13 1.38760e-10 2 4.260665546620340e-01 4.260665546703851e-01 8.35115e-12 2.00690e-10 * 3 -6.273786118922936e-01 -6.273786118861755e-01 6.11811e-12 2.61841e-11 ----------------------------------------------------------------------------------------------------- 5 Ga 1 1.599781549825919e+00 1.599781549823637e+00 2.28195e-12 2.30731e-11 2 1.525394675758097e+00 1.525394675756067e+00 2.03060e-12 1.64280e-11 3 3.997221160782829e+00 3.997221160784786e+00 1.95710e-12 2.50227e-11 ----------------------------------------------------------------------------------------------------- 6 Ga 1 -1.107776925617501e+00 -1.107776925607916e+00 9.58522e-12 1.12941e-11 2 3.589031651033426e-01 3.589031651026631e-01 6.79512e-13 1.96464e-11 3 1.494708950329622e+00 1.494708950329491e+00 1.31228e-13 6.52478e-12 ----------------------------------------------------------------------------------------------------- 7 Ga 1 -4.776063281739428e+00 -4.776063281736484e+00 2.94431e-12 1.05942e-11 2 1.897174251666277e-01 1.897174251681452e-01 1.51745e-12 1.58296e-11 3 -5.622136983759236e-01 -5.622136983720745e-01 3.84914e-12 1.02511e-10 ----------------------------------------------------------------------------------------------------- 8 Ga 1 8.610391027094757e-01 8.610391027075742e-01 1.90148e-12 2.87533e-10 * 2 -3.323255246816701e+00 -3.323255246818786e+00 2.08544e-12 1.69798e-10 3 -5.338928419010866e-02 -5.338928418715321e-02 2.95545e-12 1.82332e-11 ----------------------------------------------------------------------------------------------------- 9 Ga 1 9.836445466086229e-01 9.836445466096249e-01 1.00198e-12 1.97633e-10 * 2 -3.705790538704794e+00 -3.705790538719497e+00 1.47025e-11 2.27516e-11 3 3.278617125408223e+00 3.278617125410450e+00 2.22711e-12 1.29567e-11 ----------------------------------------------------------------------------------------------------- 10 Ga 1 -6.692132723100881e-01 -6.692132723108868e-01 7.98694e-13 1.80806e-11 2 3.721342097742220e-01 3.721342097753864e-01 1.16446e-12 1.55162e-10 3 -3.743311925841962e-01 -3.743311925853168e-01 1.12060e-12 3.36124e-11 ----------------------------------------------------------------------------------------------------- 11 Ga 1 -9.635004442456252e-01 -9.635004442489985e-01 3.37330e-12 1.20742e-10 2 -1.466619406639172e+00 -1.466619406633003e+00 6.16929e-12 6.67932e-12 3 -2.590756010846125e-02 -2.590756010709700e-02 1.36425e-12 3.82601e-11 ----------------------------------------------------------------------------------------------------- 12 Ga 1 2.139864530691272e-01 2.139864530656019e-01 3.52532e-12 3.52932e-11 2 -8.704177604798195e-02 -8.704177604736969e-02 6.12260e-13 2.41986e-11 3 -8.835977712491276e-01 -8.835977712468500e-01 2.27762e-12 3.97875e-11 ----------------------------------------------------------------------------------------------------- 13 Ga 1 6.887377759236886e-01 6.887377759283491e-01 4.66049e-12 7.10648e-11 2 7.472306279566359e-01 7.472306279572820e-01 6.46150e-13 5.61571e-11 3 -1.884319050382553e+00 -1.884319050380948e+00 1.60494e-12 3.19269e-11 ----------------------------------------------------------------------------------------------------- 14 Ga 1 -1.611669382010835e+00 -1.611669382013759e+00 2.92433e-12 3.04332e-11 2 -1.656310431346338e+00 -1.656310431348471e+00 2.13252e-12 1.55793e-11 3 1.505242684367760e-01 1.505242684379334e-01 1.15732e-12 8.52429e-12 ----------------------------------------------------------------------------------------------------- 15 Ga 1 1.059596363997300e+00 1.059596363997044e+00 2.56239e-13 2.18818e-11 2 -1.773427869969248e-02 -1.773427870343586e-02 3.74338e-12 1.44723e-11 3 -3.251316193841620e-01 -3.251316193840114e-01 1.50657e-13 2.08554e-11 ----------------------------------------------------------------------------------------------------- 16 Ga 1 6.751716756533204e-01 6.751716756484445e-01 4.87588e-12 1.60862e-11 2 1.716966436793415e+00 1.716966436789890e+00 3.52451e-12 3.77918e-11 3 -6.485768403321186e-01 -6.485768403373445e-01 5.22593e-12 3.10467e-11 ----------------------------------------------------------------------------------------------------- 17 Ga 1 1.819132804186137e+00 1.819132804185926e+00 2.11164e-13 4.24303e-11 2 1.776401761206148e+00 1.776401761210288e+00 4.13936e-12 2.12537e-11 3 2.532688250624714e-01 2.532688250718858e-01 9.41436e-12 1.63216e-11 ----------------------------------------------------------------------------------------------------- 18 Ga 1 3.943172133623133e-01 3.943172133625524e-01 2.39031e-13 5.14619e-11 2 -2.670106839120273e+00 -2.670106839104410e+00 1.58633e-11 5.00333e-11 3 2.215231410695209e-01 2.215231410567994e-01 1.27214e-11 1.41737e-10 ----------------------------------------------------------------------------------------------------- 19 Ga 1 2.208551597534566e+00 2.208551597543176e+00 8.61045e-12 4.39564e-11 2 2.124424392848433e+00 2.124424392838757e+00 9.67670e-12 4.70535e-11 3 -3.069170121752074e+00 -3.069170121748294e+00 3.78009e-12 2.05000e-11 ----------------------------------------------------------------------------------------------------- 20 Ga 1 2.083088389474739e+00 2.083088389484328e+00 9.58966e-12 1.20619e-11 2 3.827123922014037e-01 3.827123921965546e-01 4.84907e-12 1.75468e-11 3 -1.677577012825866e+00 -1.677577012820538e+00 5.32863e-12 7.12874e-12 ----------------------------------------------------------------------------------------------------- 21 Ga 1 -2.474765686877101e+00 -2.474765686869181e+00 7.91944e-12 3.88032e-11 2 3.475361597082774e+00 3.475361597085122e+00 2.34790e-12 4.07958e-11 3 1.285354791642615e+00 1.285354791646776e+00 4.16112e-12 5.31493e-11 ----------------------------------------------------------------------------------------------------- 22 Ga 1 -1.711916928230559e+00 -1.711916928226929e+00 3.62954e-12 5.44327e-11 2 1.610555761720910e+00 1.610555761724051e+00 3.14127e-12 4.84546e-11 3 3.595306135504697e-01 3.595306135522667e-01 1.79701e-12 8.51191e-11 ----------------------------------------------------------------------------------------------------- 23 Ga 1 -1.120681489824476e+00 -1.120681489830775e+00 6.29941e-12 5.68259e-11 2 9.983672261188640e-01 9.983672261184063e-01 4.57634e-13 9.77429e-12 3 -4.908466727366539e-01 -4.908466727394420e-01 2.78816e-12 1.11757e-11 ----------------------------------------------------------------------------------------------------- 24 Ga 1 -7.480960411226105e-01 -7.480960411274871e-01 4.87654e-12 5.69234e-12 2 -2.125844222148893e+00 -2.125844222151066e+00 2.17337e-12 9.48979e-11 3 -2.088366247545747e+00 -2.088366247547556e+00 1.80922e-12 5.12967e-12 ----------------------------------------------------------------------------------------------------- 25 Ga 1 1.188586844788123e-01 1.188586844766884e-01 2.12391e-12 8.46376e-11 2 -1.148226082166084e+00 -1.148226082175283e+00 9.19909e-12 8.59490e-12 3 9.597631457369759e-01 9.597631457213648e-01 1.56111e-11 9.30528e-11 ----------------------------------------------------------------------------------------------------- 26 Ga 1 -7.332930193209962e-01 -7.332930193234113e-01 2.41507e-12 5.87876e-11 2 2.306697209722463e-01 2.306697209728639e-01 6.17589e-13 3.44758e-12 3 -1.841581953272505e-01 -1.841581953285916e-01 1.34107e-12 5.55348e-11 ----------------------------------------------------------------------------------------------------- 27 Ga 1 2.569338151171708e+00 2.569338151181000e+00 9.29212e-12 6.00924e-11 2 -1.317204153894042e+00 -1.317204153896352e+00 2.31037e-12 5.39142e-11 3 -9.391151375895987e-01 -9.391151375901291e-01 5.30354e-13 6.93142e-11 ----------------------------------------------------------------------------------------------------- 28 Ga 1 -9.773858975039402e-01 -9.773858975162120e-01 1.22717e-11 4.43037e-11 2 8.987239638096600e-01 8.987239638093402e-01 3.19855e-13 2.35201e-12 3 -2.785974698172722e-01 -2.785974698257523e-01 8.48011e-12 1.42075e-11 ----------------------------------------------------------------------------------------------------- 29 Ga 1 -7.378418046493846e-01 -7.378418046490706e-01 3.14082e-13 1.89703e-10 * 2 -1.602669782448382e+00 -1.602669782453133e+00 4.75109e-12 5.03835e-11 3 1.154591315558751e+00 1.154591315545125e+00 1.36262e-11 9.64806e-12 ----------------------------------------------------------------------------------------------------- 30 Ga 1 -1.242560859507102e+00 -1.242560859510370e+00 3.26761e-12 1.39193e-11 2 9.168100061373356e-02 9.168100061566584e-02 1.93227e-12 1.17257e-11 3 1.679471070786006e+00 1.679471070788527e+00 2.52109e-12 2.51255e-11 ----------------------------------------------------------------------------------------------------- 31 Ga 1 6.824469948563557e-01 6.824469948572977e-01 9.41913e-13 3.53116e-11 2 -1.137931187586305e+00 -1.137931187588266e+00 1.96065e-12 5.07727e-11 3 -5.377894317183192e-01 -5.377894317175668e-01 7.52398e-13 1.75183e-11 ----------------------------------------------------------------------------------------------------- 32 Ga 1 5.750953438890138e-01 5.750953438855630e-01 3.45080e-12 1.97644e-11 2 -1.711885236813807e+00 -1.711885236811712e+00 2.09543e-12 4.31564e-11 3 -5.451757602688850e-01 -5.451757602560279e-01 1.28572e-11 2.74829e-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 = 15, direction = 2: |F_model - F_numer| error = --------------------------------- = 2.11081e-10 max{(|F_model|+|F_numer|)/2, 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 = N | a0 = 3.06042385101 | (Configuration in file "config-N.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 N 1 4.352241469593539e-01 4.352241469579594e-01 1.39444e-12 6.18450e-12 2 -5.920124933427154e-01 -5.920124933467728e-01 4.05731e-12 3.63749e-11 3 1.948607597718245e+00 1.948607597718341e+00 9.61453e-14 7.93876e-12 ----------------------------------------------------------------------------------------------------- 2 N 1 -7.735462050306758e-01 -7.735462050301977e-01 4.78173e-13 3.73224e-12 2 5.360553950477413e+00 5.360553950476078e+00 1.33493e-12 4.16591e-11 3 -8.779181216907348e-01 -8.779181216973739e-01 6.63913e-12 1.21416e-11 ----------------------------------------------------------------------------------------------------- 3 N 1 -1.639621600709235e+00 -1.639621600709621e+00 3.86136e-13 7.68208e-12 2 -1.330254981553723e+00 -1.330254981549701e+00 4.02278e-12 1.22111e-11 3 -4.870460209244849e-02 -4.870460209868199e-02 6.23350e-12 5.50120e-12 ----------------------------------------------------------------------------------------------------- 4 N 1 -2.880981414391245e-01 -2.880981414370409e-01 2.08367e-12 3.29585e-11 2 -1.973011899320282e+00 -1.973011899318835e+00 1.44706e-12 2.39919e-11 3 -1.483439754119385e+00 -1.483439754118339e+00 1.04627e-12 1.42661e-11 ----------------------------------------------------------------------------------------------------- 5 N 1 -2.606674736271362e+00 -2.606674736267357e+00 4.00568e-12 3.68856e-11 2 3.374965618340039e-01 3.374965618310619e-01 2.94209e-12 4.90452e-12 3 1.862379101964037e+00 1.862379101964634e+00 5.97078e-13 2.84015e-11 ----------------------------------------------------------------------------------------------------- 6 N 1 -4.589719371860447e-01 -4.589719371896831e-01 3.63842e-12 8.95856e-12 2 1.274932616099416e+00 1.274932616097852e+00 1.56408e-12 5.63061e-12 3 2.707933649085014e+00 2.707933649086366e+00 1.35136e-12 1.09486e-11 ----------------------------------------------------------------------------------------------------- 7 N 1 -1.468390648244413e+00 -1.468390648244907e+00 4.93827e-13 2.05673e-11 2 2.398083839019821e+00 2.398083839022815e+00 2.99405e-12 1.24745e-11 3 3.081073431029006e+00 3.081073431024219e+00 4.78639e-12 2.95710e-11 ----------------------------------------------------------------------------------------------------- 8 N 1 2.989627938749273e+00 2.989627938742734e+00 6.53833e-12 2.27285e-11 2 -1.678987114687508e+00 -1.678987114700652e+00 1.31444e-11 6.92491e-11 3 -2.091055932886320e+00 -2.091055932886388e+00 6.79456e-14 2.04174e-11 ----------------------------------------------------------------------------------------------------- 9 N 1 1.633181760911073e+00 1.633181760908685e+00 2.38831e-12 1.49405e-11 2 -3.430166930930751e-01 -3.430166930956229e-01 2.54780e-12 1.02997e-11 3 -4.770924912053475e-01 -4.770924912083274e-01 2.97989e-12 6.42442e-12 ----------------------------------------------------------------------------------------------------- 10 N 1 5.536480890789791e-02 5.536480890486804e-02 3.02987e-12 1.43198e-11 2 -1.914356845432999e+00 -1.914356845433046e+00 4.70735e-14 5.66818e-11 3 -9.027753410818138e-01 -9.027753410833397e-01 1.52589e-12 2.42619e-11 ----------------------------------------------------------------------------------------------------- 11 N 1 2.531641000444916e-01 2.531641000424124e-01 2.07923e-12 6.13849e-11 2 -4.083233721093686e-01 -4.083233721191016e-01 9.73299e-12 2.08401e-11 3 -5.555390839852833e-01 -5.555390839925695e-01 7.28617e-12 6.20820e-11 ----------------------------------------------------------------------------------------------------- 12 N 1 3.059543181203960e+00 3.059543181206632e+00 2.67120e-12 6.50369e-12 2 -1.188747491659041e+00 -1.188747491661489e+00 2.44760e-12 3.78164e-12 3 3.171329288032377e+00 3.171329288035262e+00 2.88525e-12 3.14571e-11 ----------------------------------------------------------------------------------------------------- 13 N 1 -1.575891996693511e+00 -1.575891996683165e+00 1.03457e-11 3.35050e-11 2 3.090934274667199e+00 3.090934274666200e+00 9.99201e-13 5.55280e-11 3 7.429537413077041e-01 7.429537413123665e-01 4.66238e-12 5.45497e-11 ----------------------------------------------------------------------------------------------------- 14 N 1 -1.129461878651857e+00 -1.129461878654172e+00 2.31482e-12 2.70912e-11 2 -1.528110069889086e+00 -1.528110069889019e+00 6.70575e-14 1.36386e-11 3 2.302526247897657e+00 2.302526247898125e+00 4.68070e-13 3.91998e-12 ----------------------------------------------------------------------------------------------------- 15 N 1 1.236789019647227e+00 1.236789019646585e+00 6.41487e-13 1.21496e-11 2 2.431281273533618e+00 2.431281273539549e+00 5.93170e-12 5.86611e-11 3 -2.814808545441852e+00 -2.814808545446318e+00 4.46621e-12 1.20113e-11 ----------------------------------------------------------------------------------------------------- 16 N 1 -8.605099118845549e-02 -8.605099118523246e-02 3.22303e-12 3.30662e-11 2 -1.510927401557391e+00 -1.510927401558104e+00 7.12763e-13 1.19271e-11 3 -5.187025020366850e-01 -5.187025020372447e-01 5.59663e-13 2.80839e-11 ----------------------------------------------------------------------------------------------------- 17 N 1 3.510758760144561e+00 3.510758760148026e+00 3.46523e-12 1.01625e-11 2 1.479103511667950e-01 1.479103511614271e-01 5.36782e-12 3.68734e-11 3 1.309304627043178e+00 1.309304627039924e+00 3.25451e-12 5.69944e-12 ----------------------------------------------------------------------------------------------------- 18 N 1 -7.949117248207382e-01 -7.949117248164033e-01 4.33498e-12 7.56901e-11 2 -2.391391606558523e+00 -2.391391606562367e+00 3.84448e-12 1.87491e-10 * 3 2.418716580067378e+00 2.418716580065624e+00 1.75326e-12 8.54263e-11 ----------------------------------------------------------------------------------------------------- 19 N 1 -1.003696933284574e+00 -1.003696933280052e+00 4.52238e-12 1.68310e-11 2 5.741772647064756e-01 5.741772647066739e-01 1.98286e-13 2.75127e-11 3 -2.816841877102484e+00 -2.816841877105321e+00 2.83729e-12 5.32854e-11 ----------------------------------------------------------------------------------------------------- 20 N 1 3.150721906324204e+00 3.150721906328318e+00 4.11404e-12 1.04743e-11 2 2.783561000343791e+00 2.783561000345465e+00 1.67422e-12 2.91296e-11 3 -6.962047032958969e-01 -6.962047032989767e-01 3.07976e-12 5.80819e-11 ----------------------------------------------------------------------------------------------------- 21 N 1 1.231982433493868e+00 1.231982433492859e+00 1.00897e-12 9.96621e-11 2 -1.845711105262671e+00 -1.845711105281434e+00 1.87625e-11 3.48293e-11 3 -7.346788534357684e-02 -7.346788534169252e-02 1.88433e-12 1.41362e-11 ----------------------------------------------------------------------------------------------------- 22 N 1 7.333081408667342e-01 7.333081408611409e-01 5.59330e-12 2.88467e-11 2 -2.330234992077090e+00 -2.330234992074260e+00 2.83062e-12 1.32636e-11 3 9.241210254236515e-02 9.241210254352099e-02 1.15584e-12 3.61287e-12 ----------------------------------------------------------------------------------------------------- 23 N 1 -1.870330427835315e+00 -1.870330427838984e+00 3.66818e-12 5.00511e-12 2 1.595497428292514e+00 1.595497428292891e+00 3.76588e-13 4.59166e-12 3 -2.821081873423049e+00 -2.821081873423469e+00 4.20552e-13 1.39577e-12 ----------------------------------------------------------------------------------------------------- 24 N 1 2.627450569671767e-02 2.627450570828956e-02 1.15719e-11 2.39693e-11 2 1.055716931234320e+00 1.055716931255779e+00 2.14591e-11 3.67339e-11 3 1.225022045060885e+00 1.225022045062561e+00 1.67577e-12 2.47813e-11 ----------------------------------------------------------------------------------------------------- 25 N 1 1.651088071069525e+00 1.651088070940513e+00 1.29013e-10 9.72514e-10 * 2 2.887860917886210e+00 2.887860917960933e+00 7.47233e-11 5.01239e-11 3 8.099669347046522e-01 8.099669346900160e-01 1.46362e-11 1.54988e-10 * ----------------------------------------------------------------------------------------------------- 26 N 1 -1.035616423224896e+00 -1.035616423206473e+00 1.84233e-11 4.41121e-10 * 2 -2.061250031684352e-02 -2.061250028633209e-02 3.05114e-11 1.02431e-10 3 -2.574839053663790e+00 -2.574839053662627e+00 1.16351e-12 2.48782e-10 * ----------------------------------------------------------------------------------------------------- 27 N 1 -4.789218962588214e+00 -4.789218962601479e+00 1.32641e-11 3.61906e-11 2 -2.370121898645353e+00 -2.370121898644815e+00 5.38680e-13 1.10349e-10 3 -9.030005210651212e-01 -9.030005210725336e-01 7.41240e-12 3.42488e-10 * ----------------------------------------------------------------------------------------------------- 28 N 1 4.921397748129367e-01 4.921397748121076e-01 8.29170e-13 1.72431e-11 2 -1.847042057129422e+00 -1.847042057129865e+00 4.42535e-13 3.05789e-11 3 -1.383253702609020e+00 -1.383253702608154e+00 8.66196e-13 3.89764e-11 ----------------------------------------------------------------------------------------------------- 29 N 1 -2.074909765280565e+00 -2.074909765278987e+00 1.57829e-12 7.57794e-12 2 1.172283929695279e+00 1.172283929692757e+00 2.52220e-12 2.38765e-11 3 -6.579322601623383e-01 -6.579322601777233e-01 1.53850e-11 8.79163e-11 ----------------------------------------------------------------------------------------------------- 30 N 1 -7.524065548417675e-01 -7.524065548348333e-01 6.93423e-12 2.25172e-11 2 -4.346960853039644e-01 -4.346960852967148e-01 7.24965e-12 3.65151e-11 3 -8.425054514718322e-02 -8.425054514750066e-02 3.17441e-13 3.48799e-11 ----------------------------------------------------------------------------------------------------- 31 N 1 7.903210339191031e-01 7.903210339232458e-01 4.14269e-12 3.47631e-11 2 -2.522600279387993e-01 -2.522600279471097e-01 8.31046e-12 1.53607e-11 3 1.466722186900807e+00 1.466722186898797e+00 2.01017e-12 1.63196e-11 ----------------------------------------------------------------------------------------------------- 32 N 1 1.098309344539828e+00 1.098309344541858e+00 2.02927e-12 2.41185e-12 2 -1.150471703078993e+00 -1.150471703073131e+00 5.86242e-12 2.78615e-11 3 -1.358038737000975e+00 -1.358038737000194e+00 7.81153e-13 4.57243e-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 = 26, direction = 2: |F_model - F_numer| error = --------------------------------- = 1.48024e-09 max{(|F_model|+|F_numer|)/2, 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 = Ga N | a0 = 3.4087673311 | (Configuration in file "config-GaN.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 N 1 -9.355284270963047e+00 -9.355284270960244e+00 2.80309e-12 4.67537e-12 2 -2.257189954886097e+00 -2.257189954884760e+00 1.33626e-12 1.26508e-11 3 -2.615589771917777e+00 -2.615589771918591e+00 8.14016e-13 7.33991e-12 ----------------------------------------------------------------------------------------------------- 2 N 1 -1.504734652819643e+01 -1.504734652820049e+01 4.05187e-12 5.65201e-11 2 -2.202621927329619e+00 -2.202621927320114e+00 9.50573e-12 1.03137e-10 * 3 -1.339052817218150e+01 -1.339052817217621e+01 5.29177e-12 1.23181e-10 * ----------------------------------------------------------------------------------------------------- 3 Ga 1 6.587821948406001e+00 6.587821948405507e+00 4.93827e-13 4.54392e-12 2 -1.055589478109060e+01 -1.055589478109052e+01 8.52651e-14 4.35740e-12 3 4.113761458258590e+00 4.113761458253205e+00 5.38503e-12 2.99369e-11 ----------------------------------------------------------------------------------------------------- 4 N 1 -4.669645049957492e+00 -4.669645049961267e+00 3.77476e-12 1.37419e-11 2 -3.106576092887022e+00 -3.106576092888677e+00 1.65512e-12 7.80012e-11 3 2.568415134122767e+00 2.568415134123355e+00 5.87974e-13 8.25962e-12 ----------------------------------------------------------------------------------------------------- 5 Ga 1 6.066808337299210e+00 6.066808337298895e+00 3.15303e-13 1.96962e-11 2 -9.104912288163623e+00 -9.104912288167856e+00 4.23306e-12 2.22506e-11 3 -4.610047132796228e+00 -4.610047132792827e+00 3.40084e-12 6.30607e-13 ----------------------------------------------------------------------------------------------------- 6 Ga 1 3.747649289410088e+00 3.747649289408835e+00 1.25278e-12 1.04947e-11 2 5.825106560079081e-02 5.825106560158386e-02 7.93053e-13 8.29338e-12 3 -4.317283736750793e+00 -4.317283736746070e+00 4.72333e-12 1.15818e-12 ----------------------------------------------------------------------------------------------------- 7 Ga 1 3.390201907061415e+00 3.390201907060896e+00 5.19584e-13 1.10933e-12 2 -6.774971232124143e+00 -6.774971232121117e+00 3.02602e-12 4.01990e-11 3 -1.078676784153163e+00 -1.078676784151422e+00 1.74016e-12 2.81064e-12 ----------------------------------------------------------------------------------------------------- 8 Ga 1 6.862295131237777e+00 6.862295131238021e+00 2.44249e-13 1.41505e-11 2 -1.629295633900089e+00 -1.629295633909495e+00 9.40514e-12 9.59499e-12 3 4.809760860203383e+00 4.809760860203157e+00 2.25597e-13 9.22284e-12 ----------------------------------------------------------------------------------------------------- 9 Ga 1 7.997681283322414e-01 7.997681283341580e-01 1.91658e-12 5.99243e-12 2 1.175623262015219e+00 1.175623262011787e+00 3.43259e-12 8.09397e-12 3 -4.664984443883710e-01 -4.664984443876513e-01 7.19702e-13 8.33522e-12 ----------------------------------------------------------------------------------------------------- 10 N 1 -1.775635463297438e+01 -1.775635463297562e+01 1.24345e-12 5.41398e-11 2 1.049747583635221e+01 1.049747583634956e+01 2.65032e-12 3.25304e-11 3 -4.411295041772557e+00 -4.411295041766600e+00 5.95701e-12 6.94111e-12 ----------------------------------------------------------------------------------------------------- 11 Ga 1 -3.761474431983225e+00 -3.761474431985894e+00 2.66853e-12 3.04721e-11 2 3.658644161099092e+00 3.658644161101623e+00 2.53131e-12 1.09126e-11 3 -8.272187743855214e+00 -8.272187743852836e+00 2.37854e-12 4.02842e-11 ----------------------------------------------------------------------------------------------------- 12 N 1 -3.436491100460128e+00 -3.436491100462503e+00 2.37455e-12 4.33609e-12 2 -6.913286887253971e-01 -6.913286887250788e-01 3.18301e-13 1.41790e-11 3 2.285078900754816e+00 2.285078900753693e+00 1.12221e-12 2.23941e-11 ----------------------------------------------------------------------------------------------------- 13 N 1 4.940087688473716e+00 4.940087688473455e+00 2.61124e-13 1.01294e-10 2 4.457405721863772e+00 4.457405721862946e+00 8.26006e-13 2.76286e-11 3 -2.077908558728527e+01 -2.077908558727512e+01 1.01537e-11 2.98108e-11 ----------------------------------------------------------------------------------------------------- 14 Ga 1 -1.997498889003263e+00 -1.997498889003133e+00 1.30562e-13 3.78853e-12 2 -1.681656915855867e+00 -1.681656915855004e+00 8.62865e-13 6.36580e-12 3 1.821328812247210e+00 1.821328812246399e+00 8.11351e-13 3.98392e-12 ----------------------------------------------------------------------------------------------------- 15 N 1 1.950964926380365e+01 1.950964926380711e+01 3.45324e-12 1.30093e-10 * 2 6.171617698460723e+00 6.171617698462241e+00 1.51879e-12 1.36176e-11 3 1.803018951070807e+01 1.803018951071041e+01 2.34479e-12 1.18515e-10 * ----------------------------------------------------------------------------------------------------- 16 N 1 5.121991403427574e+00 5.121991403421815e+00 5.75895e-12 2.49774e-11 2 1.135482232792697e+00 1.135482232793378e+00 6.81011e-13 8.30425e-12 3 5.062741675146108e+00 5.062741675144903e+00 1.20526e-12 4.77485e-12 ----------------------------------------------------------------------------------------------------- 17 N 1 -5.829105815646188e+00 -5.829105815646334e+00 1.45661e-13 2.09983e-11 2 4.640689365890909e+00 4.640689365890819e+00 8.97060e-14 2.02487e-11 3 1.278635364065279e-01 1.278635364029918e-01 3.53617e-12 8.63101e-12 ----------------------------------------------------------------------------------------------------- 18 N 1 -8.126305549254513e-01 -8.126305549248010e-01 6.50369e-13 1.13956e-11 2 -8.271798353990190e+00 -8.271798353992594e+00 2.40341e-12 5.56710e-12 3 3.581856954570990e+00 3.581856954574719e+00 3.72902e-12 2.05729e-11 ----------------------------------------------------------------------------------------------------- 19 N 1 4.490573773398062e-02 4.490573773362944e-02 3.51184e-13 6.26180e-12 2 2.046384809457571e+00 2.046384809457262e+00 3.08642e-13 5.29754e-12 3 3.340700265605373e-02 3.340700265602924e-02 2.44874e-14 1.97377e-12 ----------------------------------------------------------------------------------------------------- 20 Ga 1 -2.316715107372199e+00 -2.316715107374790e+00 2.59170e-12 4.47464e-12 2 -4.491543845595852e+00 -4.491543845593459e+00 2.39275e-12 3.32356e-12 3 1.241938404417455e+00 1.241938404417804e+00 3.48832e-13 3.60911e-12 ----------------------------------------------------------------------------------------------------- 21 N 1 -3.017955295096903e+01 -3.017955295096973e+01 6.99885e-13 1.07114e-11 2 -2.424410135677362e+01 -2.424410135677360e+01 1.77636e-14 4.55103e-11 3 -3.871541410962876e+00 -3.871541410963612e+00 7.35856e-13 6.29772e-11 ----------------------------------------------------------------------------------------------------- 22 N 1 3.102889817965395e+01 3.102889817965685e+01 2.89901e-12 6.44320e-11 2 2.406491813814864e+01 2.406491813814741e+01 1.23634e-12 2.22826e-11 3 -3.274888176870242e+00 -3.274888176888643e+00 1.84004e-11 2.95297e-11 ----------------------------------------------------------------------------------------------------- 23 Ga 1 4.432535078513665e+00 4.432535078512018e+00 1.64757e-12 8.58957e-12 2 -4.510319013618298e+00 -4.510319013618584e+00 2.86882e-13 1.91456e-11 3 2.742922937055939e+00 2.742922937052981e+00 2.95763e-12 2.20997e-11 ----------------------------------------------------------------------------------------------------- 24 Ga 1 -6.479906205393267e+00 -6.479906205394119e+00 8.52651e-13 9.91562e-12 2 -6.235339224139321e-01 -6.235339224125664e-01 1.36569e-12 7.22367e-12 3 1.200421581040164e+01 1.200421581040228e+01 6.39488e-13 2.29026e-11 ----------------------------------------------------------------------------------------------------- 25 N 1 -1.132005115538740e+01 -1.132005115539188e+01 4.47642e-12 1.57527e-11 2 -9.843959711232745e+00 -9.843959711240561e+00 7.81597e-12 1.34364e-11 3 -1.595473833666937e+01 -1.595473833667346e+01 4.09628e-12 3.06155e-11 ----------------------------------------------------------------------------------------------------- 26 Ga 1 7.712855807501920e+00 7.712855807499099e+00 2.82085e-12 6.20570e-12 2 9.302977683953868e+00 9.302977684001503e+00 4.76348e-11 4.02753e-11 3 -6.144522741223243e-01 -6.144522741271832e-01 4.85889e-12 5.26225e-05 * ----------------------------------------------------------------------------------------------------- 27 Ga 1 1.916696966356425e+00 1.916696966356639e+00 2.14495e-13 3.80285e-11 2 1.905887127440602e+00 1.905887127468650e+00 2.80487e-11 5.22785e-05 * 3 4.560616951966552e+00 4.560616951976979e+00 1.04272e-11 1.49813e-10 * ----------------------------------------------------------------------------------------------------- 28 N 1 -3.623749050693714e-01 -3.623749050694824e-01 1.11022e-13 6.60150e-12 2 1.101659426551463e+01 1.101659426551103e+01 3.60423e-12 1.39693e-11 3 1.485139753595833e+01 1.485139753596071e+01 2.38920e-12 3.08820e-11 ----------------------------------------------------------------------------------------------------- 29 Ga 1 5.695090214933717e+00 5.695090214932518e+00 1.19993e-12 2.12834e-11 2 3.598290939989850e+00 3.598290939995816e+00 5.96678e-12 4.00457e-11 3 4.108630740603199e+00 4.108630740601942e+00 1.25677e-12 2.89706e-11 ----------------------------------------------------------------------------------------------------- 30 Ga 1 8.114317697721657e-01 8.114317697744238e-01 2.25808e-12 7.37932e-12 2 2.230131713046772e+00 2.230131713046441e+00 3.31735e-13 7.93587e-12 3 -9.591551611228816e-01 -9.591551611209809e-01 1.90070e-12 2.51076e-11 ----------------------------------------------------------------------------------------------------- 31 Ga 1 2.743813088202377e+00 2.743813088201344e+00 1.03295e-12 7.10676e-12 2 5.296680688120497e+00 5.296680688120307e+00 1.90070e-13 1.34115e-11 3 4.731214762568414e+00 4.731214762570102e+00 1.68754e-12 5.51825e-11 ----------------------------------------------------------------------------------------------------- 32 N 1 1.911931658181037e+00 1.911931658179316e+00 1.72018e-12 4.30544e-11 2 -1.267350991160760e+00 -1.267350991159666e+00 1.09357e-12 4.76574e-12 3 -2.059373213197629e+00 -2.059373213197932e+00 3.02869e-13 6.49347e-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 dicontinuities. Maximum error obtained for particle = 17, direction = 3: |F_model - F_numer| error = --------------------------------- = 2.76558e-11 max{(|F_model|+|F_numer|)/2, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 1.48024e-09 Machine precision = 2.22045e-16 Grade: A Comment: The letter grade A was assigned because the normalized error in the computation was 1.48024e-09 compared with a machine precision of 2.22045e-16. The letter grade was based on 'score=log10(error/eps)', with ranges A=[0, 7.5], B=(7.5, 10.0], C=(10.0, 12.5], D=(12.5, 15.0), F>15.0. 'A' is the best grade, and 'F' indicates failure. 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.