!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_Tersoff_PRB39_1989_GeSi__MO_350526375143_001 Supported species : Ge 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 = Ge | a0 = 4.02358818054 | (Configuration in file "config-Ge.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ge 1 6.060735949465059e+00 6.060735949476014e+00 1.09548e-11 6.56737e-11 2 3.041304174181285e+00 3.041304174179575e+00 1.71019e-12 2.95937e-11 3 1.987445885979059e+00 1.987445885981250e+00 2.19114e-12 1.43061e-11 ----------------------------------------------------------------------------------------------------- 2 Ge 1 -4.059738781400100e+00 -4.059738781403420e+00 3.32090e-12 3.83800e-11 2 5.018433045806563e-01 5.018433045859403e-01 5.28400e-12 3.38903e-11 3 3.037905524703559e+00 3.037905524704030e+00 4.70735e-13 4.37693e-10 * ----------------------------------------------------------------------------------------------------- 3 Ge 1 -1.078366292286802e+00 -1.078366292265673e+00 2.11291e-11 1.01406e-10 2 5.231383323833623e-01 5.231383323820571e-01 1.30518e-12 4.36550e-11 3 -3.884089201702008e+00 -3.884089201678350e+00 2.36575e-11 4.81136e-09 * ----------------------------------------------------------------------------------------------------- 4 Ge 1 4.467527525378248e+00 4.467527525394702e+00 1.64544e-11 4.10036e-11 2 4.814230425684723e+00 4.814230425685103e+00 3.80140e-13 8.40874e-11 3 1.975741975728414e+00 1.975741975727941e+00 4.73399e-13 1.45373e-11 ----------------------------------------------------------------------------------------------------- 5 Ge 1 -3.874214365923171e-01 -3.874214366005651e-01 8.24796e-12 2.26499e-11 2 6.156722907621687e-01 6.156722907641108e-01 1.94211e-12 3.46367e-11 3 2.134666091080269e+00 2.134666091080633e+00 3.63709e-13 1.44236e-11 ----------------------------------------------------------------------------------------------------- 6 Ge 1 -1.257840335701212e+00 -1.257840335697674e+00 3.53850e-12 2.98048e-11 2 2.457899312058906e-01 2.457899312020466e-01 3.84401e-12 2.85550e-11 3 1.553529631484126e+00 1.553529631470787e+00 1.33389e-11 1.28495e-11 ----------------------------------------------------------------------------------------------------- 7 Ge 1 1.049821748720391e-01 1.049821748865268e-01 1.44878e-11 2.76237e-11 2 -2.779692057293126e+00 -2.779692057286496e+00 6.62981e-12 1.33507e-11 3 -3.209360162583992e+00 -3.209360162583077e+00 9.14824e-13 7.94644e-11 ----------------------------------------------------------------------------------------------------- 8 Ge 1 -4.527506167566758e+00 -4.527506167578607e+00 1.18492e-11 1.88907e-09 * 2 -1.959066459046248e+00 -1.959066459134502e+00 8.82536e-11 1.00534e-09 * 3 6.363098602977557e-01 6.363098602984207e-01 6.65024e-13 1.81001e-10 ----------------------------------------------------------------------------------------------------- 9 Ge 1 -6.868886962425239e-02 -6.868886962692466e-02 2.67228e-12 7.08941e-11 2 -6.134625848188935e+00 -6.134625848191799e+00 2.86438e-12 7.53921e-11 3 1.574676468191079e+00 1.574676468189610e+00 1.46883e-12 4.22897e-11 ----------------------------------------------------------------------------------------------------- 10 Ge 1 -1.615433017777661e-04 -1.615432936865697e-04 8.09120e-12 3.50958e-11 2 1.185360623704758e+00 1.185360623714739e+00 9.98046e-12 2.43445e-11 3 -2.238301406460104e+00 -2.238301406461669e+00 1.56541e-12 2.75038e-11 ----------------------------------------------------------------------------------------------------- 11 Ge 1 -1.378509613056541e+00 -1.378509612527227e+00 5.29313e-10 8.60805e-10 * 2 -8.231510464049926e+00 -8.231510464036976e+00 1.29496e-11 4.13533e-09 * 3 7.221394050208954e-01 7.221394050222915e-01 1.39611e-12 4.47345e-11 ----------------------------------------------------------------------------------------------------- 12 Ge 1 -2.100736892750069e+00 -2.100736892747952e+00 2.11786e-12 1.21392e-10 2 2.292083313048324e+00 2.292083313049414e+00 1.09024e-12 1.00266e-11 3 2.033750501297111e+00 2.033750501340061e+00 4.29505e-11 2.35343e-10 ----------------------------------------------------------------------------------------------------- 13 Ge 1 -1.224354857975845e+00 -1.224354857981655e+00 5.81002e-12 5.25913e-11 2 -9.535089348267378e-01 -9.535089348234661e-01 3.27172e-12 1.47510e-10 3 -4.581518894781909e+00 -4.581518894780539e+00 1.37046e-12 4.28795e-11 ----------------------------------------------------------------------------------------------------- 14 Ge 1 -8.099286395658892e-01 -8.099286395657985e-01 9.07052e-14 1.03554e-10 2 6.996486416732975e-02 6.996486416681716e-02 5.12590e-13 1.53940e-11 3 8.831026984715916e-01 8.831026984767221e-01 5.13045e-12 5.01602e-11 ----------------------------------------------------------------------------------------------------- 15 Ge 1 5.224263511147270e+00 5.224263511149462e+00 2.19202e-12 5.48335e-11 2 5.950399915516488e-01 5.950399915516356e-01 1.32117e-14 6.12076e-11 3 2.885623487990816e+00 2.885623487991786e+00 9.70335e-13 6.12506e-11 ----------------------------------------------------------------------------------------------------- 16 Ge 1 3.594000470993798e+00 3.594000470978196e+00 1.56022e-11 3.68514e-11 2 4.118830670530174e+00 4.118830670525518e+00 4.65583e-12 7.09512e-11 3 4.045334756001014e-01 4.045334756027211e-01 2.61963e-12 6.33704e-12 ----------------------------------------------------------------------------------------------------- 17 Ge 1 3.453652844257727e-01 3.453652844363986e-01 1.06259e-11 2.81324e-10 * 2 3.176018850463901e+00 3.176018850529121e+00 6.52203e-11 2.29522e-10 3 -5.795318512820522e-01 -5.795318512743626e-01 7.68963e-12 1.66337e-10 ----------------------------------------------------------------------------------------------------- 18 Ge 1 1.247808054137756e+00 1.247808054184993e+00 4.72369e-11 1.01874e-09 * 2 3.348092727451592e+00 3.348092727474253e+00 2.26614e-11 2.43084e-10 3 -1.431478025089177e-01 -1.431478025183793e-01 9.46157e-12 5.00585e-11 ----------------------------------------------------------------------------------------------------- 19 Ge 1 3.860409298492239e+00 3.860409298490910e+00 1.32871e-12 2.39098e-11 2 4.785744855220368e+00 4.785744855218428e+00 1.93978e-12 2.80673e-11 3 -1.311286655224934e+00 -1.311286655232101e+00 7.16716e-12 2.37483e-11 ----------------------------------------------------------------------------------------------------- 20 Ge 1 5.866920949763412e+00 5.866920949769249e+00 5.83711e-12 2.06919e-11 2 1.703399229800738e-01 1.703399229780905e-01 1.98327e-12 3.94893e-11 3 -2.955908590067171e+00 -2.955908590074819e+00 7.64810e-12 3.70770e-11 ----------------------------------------------------------------------------------------------------- 21 Ge 1 -6.214435277050108e+00 -6.214435277032069e+00 1.80389e-11 5.85443e-11 2 3.128358913965188e+00 3.128358913963571e+00 1.61693e-12 2.25580e-11 3 4.460207318264775e+00 4.460207318258345e+00 6.43041e-12 5.24185e-11 ----------------------------------------------------------------------------------------------------- 22 Ge 1 4.636246280042402e-01 4.636246280166708e-01 1.24306e-11 8.95110e-11 2 3.853797801951308e+00 3.853797801959804e+00 8.49587e-12 4.23775e-10 * 3 5.595882431468854e-01 5.595882431586875e-01 1.18021e-11 9.16422e-11 ----------------------------------------------------------------------------------------------------- 23 Ge 1 -2.670596355458791e+00 -2.670596355458317e+00 4.74287e-13 1.63949e-11 2 2.088273129760969e+00 2.088273129765104e+00 4.13491e-12 4.16924e-11 3 1.054949703024406e+00 1.054949703020483e+00 3.92286e-12 1.27305e-11 ----------------------------------------------------------------------------------------------------- 24 Ge 1 5.931101055687289e-01 5.931101055682614e-01 4.67515e-13 4.01832e-11 2 -1.820128332988273e+00 -1.820128332982568e+00 5.70521e-12 4.68121e-11 3 -6.383697746098433e+00 -6.383697746100225e+00 1.79146e-12 9.09850e-12 ----------------------------------------------------------------------------------------------------- 25 Ge 1 9.466963465756904e-01 9.466963465814519e-01 5.76150e-12 1.97818e-11 2 -4.937183662425432e+00 -4.937183662419244e+00 6.18794e-12 2.72458e-11 3 -1.411426872855739e+00 -1.411426872864135e+00 8.39595e-12 1.49594e-10 ----------------------------------------------------------------------------------------------------- 26 Ge 1 -2.151274548153193e+00 -2.151274548146055e+00 7.13740e-12 2.68998e-11 2 1.906484099133010e+00 1.906484099131315e+00 1.69531e-12 4.56071e-11 3 6.993369335111556e-01 6.993369335045632e-01 6.59239e-12 4.45406e-11 ----------------------------------------------------------------------------------------------------- 27 Ge 1 -4.744270843931879e-01 -4.744270844171862e-01 2.39983e-11 3.43738e-11 2 -6.882657981092884e+00 -6.882657981088630e+00 4.25437e-12 2.86340e-11 3 9.244281352283373e-01 9.244281352424112e-01 1.40739e-11 2.24794e-11 ----------------------------------------------------------------------------------------------------- 28 Ge 1 -1.306290349813875e+00 -1.306290349819028e+00 5.15277e-12 7.97518e-11 2 1.458840586249220e+00 1.458840586240817e+00 8.40283e-12 1.88611e-10 3 -9.486186465309204e-01 -9.486186465307445e-01 1.75970e-13 3.72620e-11 ----------------------------------------------------------------------------------------------------- 29 Ge 1 4.940278568468901e-01 4.940278568371422e-01 9.74787e-12 7.49961e-10 * 2 -3.149581158794357e+00 -3.149581158805816e+00 1.14584e-11 1.06404e-11 3 2.236155841979906e-01 2.236155841895800e-01 8.41058e-12 2.33789e-11 ----------------------------------------------------------------------------------------------------- 30 Ge 1 -5.897176957723353e-01 -5.897176957713524e-01 9.82991e-13 6.63087e-11 2 -1.251676144083902e+00 -1.251676144084934e+00 1.03162e-12 2.60321e-11 3 -2.061765977911588e+00 -2.061765977914437e+00 2.84972e-12 4.24141e-11 ----------------------------------------------------------------------------------------------------- 31 Ge 1 -3.372473565223320e+00 -3.372473565206377e+00 1.69424e-11 5.20064e-11 2 -3.701671718596760e+00 -3.701671718601812e+00 5.05285e-12 1.10409e-11 3 1.151737165398914e+00 1.151737165402529e+00 3.61555e-12 2.50422e-11 ----------------------------------------------------------------------------------------------------- 32 Ge 1 4.029961500152277e-01 4.029961500204839e-01 5.25618e-12 2.67996e-11 2 -1.179060475893599e-01 -1.179060475863494e-01 3.01049e-12 2.04361e-11 3 8.053657193905468e-01 8.053657193930970e-01 2.55018e-12 3.99758e-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 = --------------------------------- = 5.00869e-08 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 = Si | a0 = 3.89748287201 | (Configuration in file "config-Si.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Si 1 2.711285960934940e+00 2.711285960933600e+00 1.34026e-12 2.49858e-11 2 1.009625721351990e+00 1.009625721351492e+00 4.97380e-13 2.04403e-11 3 3.076829291992824e+00 3.076829291990553e+00 2.27152e-12 6.25224e-11 ----------------------------------------------------------------------------------------------------- 2 Si 1 -1.388159386243284e+00 -1.388159386236518e+00 6.76637e-12 1.69114e-10 2 -2.907177501964942e+00 -2.907177501946272e+00 1.86704e-11 1.39460e-10 3 -1.345786119002540e+00 -1.345786118979508e+00 2.30322e-11 1.69262e-10 ----------------------------------------------------------------------------------------------------- 3 Si 1 -3.660428119021056e+00 -3.660428119012444e+00 8.61222e-12 8.24842e-11 2 -7.169435425466477e-01 -7.169435425461190e-01 5.28688e-13 6.74846e-10 * 3 -1.817180261366529e+00 -1.817180261356818e+00 9.71090e-12 4.72160e-11 ----------------------------------------------------------------------------------------------------- 4 Si 1 5.737147866426413e-01 5.737147866427936e-01 1.52323e-13 2.63171e-11 2 1.824188813770889e-01 1.824188813920611e-01 1.49723e-11 4.92645e-11 3 -4.228543040710164e-01 -4.228543040662556e-01 4.76086e-12 1.21284e-11 ----------------------------------------------------------------------------------------------------- 5 Si 1 1.534993485334459e+00 1.534993485329593e+00 4.86633e-12 1.69613e-11 2 1.366013081590215e+00 1.366013081590521e+00 3.05977e-13 1.77212e-11 3 2.030468573265182e+00 2.030468573269015e+00 3.83293e-12 8.94318e-09 * ----------------------------------------------------------------------------------------------------- 6 Si 1 -2.935465393636367e+00 -2.935465393625578e+00 1.07891e-11 7.15294e-12 2 1.839798152515192e+00 1.839798152527728e+00 1.25355e-11 7.17735e-11 3 1.906987173210938e+00 1.906987173189139e+00 2.17981e-11 5.41842e-11 ----------------------------------------------------------------------------------------------------- 7 Si 1 -4.088611280348359e+00 -4.088611280339466e+00 8.89333e-12 1.36025e-11 2 1.239837868240525e+00 1.239837868243332e+00 2.80642e-12 3.01390e-11 3 -2.824630494729452e+00 -2.824630494724452e+00 5.00000e-12 1.26219e-11 ----------------------------------------------------------------------------------------------------- 8 Si 1 2.621013602488981e+00 2.621013602451237e+00 3.77431e-11 4.07768e-10 2 -8.853245509212312e-01 -8.853245509304791e-01 9.24794e-12 2.50637e-10 3 2.913038985946772e+00 2.913038985953326e+00 6.55431e-12 4.22324e-11 ----------------------------------------------------------------------------------------------------- 9 Si 1 4.639670973730835e-01 4.639670973691369e-01 3.94662e-12 4.66370e-11 2 8.622473439374088e-01 8.622473439367578e-01 6.50924e-13 3.02267e-11 3 6.775212211145416e-01 6.775212211106256e-01 3.91598e-12 2.29401e-11 ----------------------------------------------------------------------------------------------------- 10 Si 1 1.051248188522374e+00 1.051248188519865e+00 2.50844e-12 2.77403e-11 2 3.239656676092506e+00 3.239656676091203e+00 1.30296e-12 5.83884e-11 3 -4.405546365105454e+00 -4.405546365103580e+00 1.87317e-12 2.57785e-11 ----------------------------------------------------------------------------------------------------- 11 Si 1 -3.136163620467233e+00 -3.136163620446924e+00 2.03082e-11 2.43029e-10 2 -6.169799023385271e+00 -6.169799023367824e+00 1.74465e-11 1.71226e-10 3 4.641915631943970e+00 4.641915631901046e+00 4.29239e-11 3.04729e-10 ----------------------------------------------------------------------------------------------------- 12 Si 1 -1.785044886898465e+00 -1.785044886903415e+00 4.95026e-12 3.79061e-11 2 -3.710481826165110e-01 -3.710481826141767e-01 2.33430e-12 5.72625e-11 3 -6.208165244517774e-01 -6.208165244419344e-01 9.84302e-12 2.56790e-11 ----------------------------------------------------------------------------------------------------- 13 Si 1 7.160177802149669e+00 7.160177802156604e+00 6.93490e-12 1.62548e-10 2 1.128067802767991e+00 1.128067802762363e+00 5.62728e-12 3.84341e-11 3 8.888653177062065e-01 8.888653176883817e-01 1.78247e-11 5.64845e-11 ----------------------------------------------------------------------------------------------------- 14 Si 1 -6.472514502238667e-01 -6.472514502238226e-01 4.40759e-14 2.31166e-11 2 -2.348683611548430e-02 -2.348683611632566e-02 8.41365e-13 5.49560e-12 3 5.837925785678154e-01 5.837925785684741e-01 6.58695e-13 9.05909e-12 ----------------------------------------------------------------------------------------------------- 15 Si 1 -1.339022157998879e+00 -1.339022157989463e+00 9.41647e-12 3.63383e-10 2 4.557132097680419e+00 4.557132097675039e+00 5.38058e-12 1.18350e-10 3 8.277820061608057e-01 8.277820061760511e-01 1.52455e-11 3.58067e-11 ----------------------------------------------------------------------------------------------------- 16 Si 1 3.295790465321564e+00 3.295790465382813e+00 6.12488e-11 3.41669e-10 2 -1.152328831590151e+00 -1.152328831597955e+00 7.80487e-12 7.34020e-11 3 2.994639453047058e+00 2.994639453055141e+00 8.08287e-12 5.80598e-11 ----------------------------------------------------------------------------------------------------- 17 Si 1 6.757217684182130e-01 6.757217684176194e-01 5.93525e-13 2.05144e-11 2 1.189624808769607e-01 1.189624808762569e-01 7.03854e-13 2.21516e-12 3 -5.892342102924926e-01 -5.892342102946988e-01 2.20624e-12 2.49134e-12 ----------------------------------------------------------------------------------------------------- 18 Si 1 -1.493081066237546e+00 -1.493081066197499e+00 4.00471e-11 1.68236e-10 2 -1.846863351326862e-01 -1.846863351418505e-01 9.16431e-12 3.24540e-10 3 3.122478229376903e+00 3.122478229377736e+00 8.33111e-13 5.10925e-11 ----------------------------------------------------------------------------------------------------- 19 Si 1 1.180556399249934e+00 1.180556399254375e+00 4.44067e-12 4.44167e-11 2 7.360107545968446e+00 7.360107545977536e+00 9.09051e-12 4.36149e-11 3 -4.064947543545856e+00 -4.064947543537027e+00 8.82938e-12 4.97575e-11 ----------------------------------------------------------------------------------------------------- 20 Si 1 2.817169470710330e+00 2.817169470708465e+00 1.86473e-12 7.68092e-11 2 -1.992814101379927e+00 -1.992814101378940e+00 9.87432e-13 3.33289e-12 3 2.161440523191759e-01 2.161440523126157e-01 6.56022e-12 3.98162e-11 ----------------------------------------------------------------------------------------------------- 21 Si 1 -5.386365548868574e+00 -5.386365548866925e+00 1.64935e-12 5.41238e-11 2 5.004067551949150e-02 5.004067552877878e-02 9.28728e-12 3.43168e-11 3 -1.314787518339791e+00 -1.314787518319222e+00 2.05693e-11 7.64349e-11 ----------------------------------------------------------------------------------------------------- 22 Si 1 2.710065699799797e-01 2.710065700069105e-01 2.69308e-11 9.86608e-11 2 1.791818062161676e+00 1.791818062157275e+00 4.40048e-12 4.35982e-10 3 -3.300135424407487e+00 -3.300135424375460e+00 3.20273e-11 4.27308e-10 ----------------------------------------------------------------------------------------------------- 23 Si 1 2.233295893135177e+00 2.233295893129801e+00 5.37570e-12 8.08060e-11 2 -5.968286462017733e-01 -5.968286461542471e-01 4.75262e-11 7.23761e-11 3 4.676422519126518e+00 4.676422519127525e+00 1.00631e-12 1.84661e-11 ----------------------------------------------------------------------------------------------------- 24 Si 1 -1.342271719654072e+00 -1.342271719656140e+00 2.06835e-12 1.80413e-10 2 2.928182242852087e+00 2.928182242846552e+00 5.53513e-12 4.80451e-11 3 -1.461022401781158e+00 -1.461022401781769e+00 6.10623e-13 2.58320e-11 ----------------------------------------------------------------------------------------------------- 25 Si 1 -1.925624580166069e+00 -1.925624580175004e+00 8.93485e-12 1.07366e-10 2 -3.883414680501414e+00 -3.883414680489714e+00 1.17004e-11 1.16779e-10 3 -5.583503401789451e+00 -5.583503401774343e+00 1.51079e-11 1.00951e-10 ----------------------------------------------------------------------------------------------------- 26 Si 1 2.218985571530445e+00 2.218985571559112e+00 2.86668e-11 1.12799e-09 * 2 2.252234978414712e+00 2.252234978424002e+00 9.29035e-12 5.39599e-11 3 1.510018089136535e+00 1.510018089125808e+00 1.07270e-11 4.95823e-11 ----------------------------------------------------------------------------------------------------- 27 Si 1 1.055330958851276e+01 1.055330958851262e+01 1.36779e-13 1.49157e-10 2 -4.797627971663010e+00 -4.797627971681659e+00 1.86491e-11 3.77203e-10 3 3.301669734269903e+00 3.301669734295432e+00 2.55298e-11 8.35176e-11 ----------------------------------------------------------------------------------------------------- 28 Si 1 5.892987610266545e-01 5.892987610234113e-01 3.24318e-12 5.79572e-11 2 -1.136527984873988e-01 -1.136527984813735e-01 6.02533e-12 4.76001e-11 3 -2.211803462035530e+00 -2.211803462037198e+00 1.66800e-12 4.29869e-11 ----------------------------------------------------------------------------------------------------- 29 Si 1 -3.821041099756691e+00 -3.821041099758681e+00 1.98908e-12 1.73372e-10 2 1.306155412390613e-02 1.306155411353490e-02 1.03712e-11 6.24366e-11 3 1.098256046051793e+00 1.098256046051037e+00 7.55840e-13 1.97620e-09 * ----------------------------------------------------------------------------------------------------- 30 Si 1 -4.269495192204058e+00 -4.269495192205595e+00 1.53744e-12 1.34844e-10 2 -4.354049077667260e+00 -4.354049077687907e+00 2.06466e-11 1.94706e-10 3 -5.296044485595488e+00 -5.296044485586940e+00 8.54783e-12 2.10836e-11 ----------------------------------------------------------------------------------------------------- 31 Si 1 -5.963771520031313e+00 -5.963771520027020e+00 4.29257e-12 2.43866e-10 2 5.788635906680416e-01 5.788635906609689e-01 7.07268e-12 6.77141e-11 3 6.807519159373271e-01 6.807519159392370e-01 1.90992e-12 5.59747e-11 ----------------------------------------------------------------------------------------------------- 32 Si 1 3.230261610424626e+00 3.230261610436947e+00 1.23217e-11 1.52598e-11 2 -2.368886675964956e+00 -2.368886675964315e+00 6.41709e-13 1.10942e-11 3 1.107116973397517e-01 1.107116973461840e-01 6.43226e-12 3.46630e-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 = 29, direction = 2: |F_model - F_numer| error = --------------------------------- = 7.94028e-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. MIXED STRUCTURE -- Species = Ge Si | a0 = 3.88511290578 | (Configuration in file "config-GeSi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Si 1 -1.814683425947205e+00 -1.814683425948061e+00 8.55982e-13 1.59326e-11 2 -1.482645401976226e+00 -1.482645401973479e+00 2.74691e-12 6.14473e-11 3 -2.321117607719381e+00 -2.321117607720570e+00 1.18971e-12 4.25393e-12 ----------------------------------------------------------------------------------------------------- 2 Ge 1 2.386925212548114e+00 2.386925212540640e+00 7.47313e-12 1.87703e-11 2 -2.992174065797961e+00 -2.992174065785576e+00 1.23856e-11 2.28773e-11 3 -3.765027454349720e+00 -3.765027454353094e+00 3.37463e-12 2.60307e-11 ----------------------------------------------------------------------------------------------------- 3 Ge 1 1.961665401914328e+00 1.961665401910478e+00 3.84981e-12 1.43097e-11 2 -1.844635295382068e+00 -1.844635295396919e+00 1.48510e-11 7.23455e-11 3 1.333082960869354e+00 1.333082960861294e+00 8.06066e-12 1.37790e-11 ----------------------------------------------------------------------------------------------------- 4 Si 1 -3.906078509376990e+00 -3.906078509390749e+00 1.37592e-11 2.09921e-11 2 -5.088600860698392e-01 -5.088600860613520e-01 8.48721e-12 6.70723e-11 3 1.635387664928625e+00 1.635387664919623e+00 9.00191e-12 2.67854e-10 ----------------------------------------------------------------------------------------------------- 5 Si 1 1.464740392622284e+00 1.464740392620264e+00 2.02038e-12 6.24174e-11 2 2.740372892958929e+00 2.740372892954879e+00 4.04965e-12 4.24416e-12 3 1.139747481559183e+00 1.139747481559425e+00 2.41807e-13 1.73377e-11 ----------------------------------------------------------------------------------------------------- 6 Si 1 -2.084666842587256e+00 -2.084666842587442e+00 1.86073e-13 4.83742e-11 2 -4.499412222400673e+00 -4.499412222398613e+00 2.05969e-12 5.28733e-11 3 2.369846140408562e+00 2.369846140406541e+00 2.02061e-12 2.34648e-11 ----------------------------------------------------------------------------------------------------- 7 Ge 1 -1.320948481265735e+00 -1.320948481267429e+00 1.69442e-12 3.41243e-11 2 5.604354098882489e+00 5.604354098870968e+00 1.15206e-11 4.76774e-12 3 -9.234391951885275e-01 -9.234391951810484e-01 7.47902e-12 9.46854e-12 ----------------------------------------------------------------------------------------------------- 8 Ge 1 2.158741834608477e+00 2.158741834417053e+00 1.91424e-10 2.07838e-09 * 2 -7.764157604702144e+00 -7.764157604597757e+00 1.04388e-10 3.18660e-10 3 4.719106090298143e+00 4.719106090277855e+00 2.02887e-11 9.54561e-11 ----------------------------------------------------------------------------------------------------- 9 Ge 1 -1.123316279945945e+00 -1.123316279944218e+00 1.72684e-12 5.81198e-10 * 2 6.060215926808696e+00 6.060215926810173e+00 1.47704e-12 3.06563e-10 3 -3.640580042003115e+00 -3.640580042002581e+00 5.34239e-13 4.48734e-11 ----------------------------------------------------------------------------------------------------- 10 Si 1 -2.102974145428191e+00 -2.102974145442845e+00 1.46541e-11 1.99468e-10 2 -4.652522786195221e+00 -4.652522786205014e+00 9.79306e-12 2.71907e-11 3 1.447257861510695e+00 1.447257861399048e+00 1.11648e-10 1.48624e-10 ----------------------------------------------------------------------------------------------------- 11 Ge 1 2.811824413314938e+00 2.811824412024684e+00 1.29025e-09 3.55125e-09 * 2 1.984627121079851e+00 1.984627121643906e+00 5.64055e-10 4.81353e-09 * 3 2.453183535247878e+00 2.453183535255554e+00 7.67608e-12 6.90137e-11 ----------------------------------------------------------------------------------------------------- 12 Si 1 -5.293846724086353e+00 -5.293846724119098e+00 3.27454e-11 4.11997e-10 * 2 -4.381989973996644e-01 -4.381989974197982e-01 2.01338e-11 5.23443e-09 * 3 -4.949315136679878e+00 -4.949315136674834e+00 5.04397e-12 2.89792e-10 ----------------------------------------------------------------------------------------------------- 13 Si 1 1.886508667033620e+00 1.886508667037689e+00 4.06875e-12 6.57374e-11 2 4.627329984842128e+00 4.627329984852759e+00 1.06306e-11 2.48003e-09 * 3 -1.907841543043572e+00 -1.907841543016834e+00 2.67384e-11 9.26261e-11 ----------------------------------------------------------------------------------------------------- 14 Si 1 -2.245516157430521e+00 -2.245516157427528e+00 2.99316e-12 2.73830e-11 2 -1.663399370164424e+00 -1.663399370165374e+00 9.50573e-13 2.66805e-10 3 7.499323453685725e-01 7.499323453674057e-01 1.16673e-12 7.08086e-11 ----------------------------------------------------------------------------------------------------- 15 Ge 1 6.434318097107096e+00 6.434318097108510e+00 1.41398e-12 2.01208e-11 2 -2.074829791599136e+00 -2.074829791591441e+00 7.69518e-12 7.12923e-11 3 3.477792385679539e+00 3.477792385658351e+00 2.11879e-11 1.68323e-10 ----------------------------------------------------------------------------------------------------- 16 Si 1 -1.789072208922681e+00 -1.789072208982617e+00 5.99361e-11 2.53169e-10 2 5.159027601559639e+00 5.159027601542737e+00 1.69020e-11 3.57705e-11 3 -4.458448793062679e+00 -4.458448793062053e+00 6.26166e-13 1.08932e-10 ----------------------------------------------------------------------------------------------------- 17 Ge 1 -3.188392953060210e+00 -3.188392953060825e+00 6.15064e-13 5.62586e-11 2 -2.606697687317610e+00 -2.606697687314343e+00 3.26628e-12 6.74327e-11 3 -1.550155009097791e+00 -1.550155009099712e+00 1.92069e-12 2.42193e-11 ----------------------------------------------------------------------------------------------------- 18 Si 1 1.655823342477224e+00 1.655823342422039e+00 5.51854e-11 7.17372e-10 * 2 2.649072228778696e+00 2.649072228780203e+00 1.50724e-12 5.17808e-11 3 -3.074580478690765e-01 -3.074580478701348e-01 1.05826e-12 5.98628e-11 ----------------------------------------------------------------------------------------------------- 19 Si 1 1.762339682496270e+00 1.762339682495458e+00 8.12239e-13 4.35056e-11 2 -1.197200025424845e+00 -1.197200025419555e+00 5.29021e-12 2.57090e-11 3 2.202145364726151e+00 2.202145364724273e+00 1.87805e-12 3.08944e-11 ----------------------------------------------------------------------------------------------------- 20 Si 1 -1.367065667485663e-01 -1.367065667476476e-01 9.18654e-13 4.36184e-11 2 4.633416187516433e+00 4.633416187526342e+00 9.90941e-12 6.48281e-11 3 -7.738636704130091e-01 -7.738636704097621e-01 3.24696e-12 4.07949e-11 ----------------------------------------------------------------------------------------------------- 21 Ge 1 2.089311511133104e-01 2.089311510388230e-01 7.44874e-11 6.23815e-06 * 2 1.627620120016137e+00 1.627620120057328e+00 4.11908e-11 2.65960e-10 3 -3.819700547353597e+00 -3.819700547351593e+00 2.00417e-12 3.71809e-11 ----------------------------------------------------------------------------------------------------- 22 Si 1 -3.686574876459694e+00 -3.686574876456497e+00 3.19611e-12 1.36866e-10 2 -1.313226739565914e+00 -1.313226739557763e+00 8.15170e-12 5.14362e-11 3 -1.801018172692938e+00 -1.801018172697440e+00 4.50151e-12 4.80338e-11 ----------------------------------------------------------------------------------------------------- 23 Si 1 -2.185989818145664e+00 -2.185989818144531e+00 1.13332e-12 5.03988e-11 2 4.918119477897066e+00 4.918119477893867e+00 3.19833e-12 3.88809e-11 3 -3.660370154717189e+00 -3.660370154718007e+00 8.18012e-13 1.31930e-11 ----------------------------------------------------------------------------------------------------- 24 Si 1 2.300964419558496e+00 2.300964419552223e+00 6.27320e-12 8.54277e-11 2 1.334519932181342e+00 1.334519932160058e+00 2.12839e-11 4.46847e-11 3 1.670347763610257e+00 1.670347763611365e+00 1.10822e-12 9.41796e-11 ----------------------------------------------------------------------------------------------------- 25 Ge 1 -2.358366879663986e+00 -2.358366879654907e+00 9.07896e-12 1.81766e-11 2 -2.350147386407833e+00 -2.350147386417861e+00 1.00280e-11 1.22168e-10 3 1.792776246022519e+00 1.792776246036923e+00 1.44043e-11 5.91264e-10 * ----------------------------------------------------------------------------------------------------- 26 Ge 1 5.351915129146612e+00 5.351915129164131e+00 1.75193e-11 5.66214e-11 2 2.561643261062407e+00 2.561643261059821e+00 2.58682e-12 1.55298e-12 3 5.884062743000736e+00 5.884062743004611e+00 3.87512e-12 4.29647e-11 ----------------------------------------------------------------------------------------------------- 27 Si 1 1.419745142853589e+00 1.419745142843988e+00 9.60121e-12 2.98557e-11 2 -2.757753902938347e+00 -2.757753902940189e+00 1.84164e-12 1.01870e-11 3 1.572525869474576e+00 1.572525869491242e+00 1.66662e-11 4.55151e-11 ----------------------------------------------------------------------------------------------------- 28 Ge 1 2.776005990803875e+00 2.776005990808395e+00 4.51994e-12 9.05356e-11 2 -1.713348544788537e+00 -1.713348544779701e+00 8.83604e-12 7.18761e-11 3 -1.430875299066685e+00 -1.430875299066167e+00 5.17586e-13 4.51159e-11 ----------------------------------------------------------------------------------------------------- 29 Ge 1 -1.976080520284639e+00 -1.976080520283161e+00 1.47748e-12 9.92317e-11 2 -4.180980131489113e+00 -4.180980131483489e+00 5.62395e-12 4.09912e-11 3 3.505576885407369e+00 3.505576885411793e+00 4.42446e-12 1.82356e-10 ----------------------------------------------------------------------------------------------------- 30 Ge 1 3.843607061647919e+00 3.843607061653459e+00 5.53957e-12 6.53788e-12 2 1.305103408406836e+00 1.305103408405942e+00 8.94174e-13 8.79494e-11 3 -1.960829054052182e+00 -1.960829054049915e+00 2.26663e-12 2.05103e-10 ----------------------------------------------------------------------------------------------------- 31 Ge 1 -7.233732146056495e-01 -7.233732146042516e-01 1.39788e-12 1.14033e-10 2 -2.811473506716747e-01 -2.811473506664379e-01 5.23681e-12 1.03763e-11 3 -3.543318873646517e-01 -3.543318873586568e-01 5.99487e-12 1.67041e-11 ----------------------------------------------------------------------------------------------------- 32 Ge 1 -2.487468335286881e+00 -2.487468335307748e+00 2.08678e-11 1.01607e-10 2 -8.840848516994052e-01 -8.840848517049921e-01 5.58686e-12 2.50373e-11 3 1.671600276561842e+00 1.671600276562384e+00 5.41789e-13 6.57685e-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 = 3: |F_model - F_numer| error = --------------------------------- = 7.71442e-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 = 5.00869e-08 Machine precision = 2.22045e-16 Grade: B Comment: The letter grade B was assigned because the normalized error in the computation was 5.00869e-08 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.