!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_ErhartAlbe_2005_SiC__MO_903987585848_004 Supported species : C Si random seed = 13 perturbation amplitude = 0.250 number unit cells per side = 2 ----------------------------------------------------------------------------------------------------- Comparison of analytical forces obtained from the model, the force computed as a numerical derivative of the energy, the difference between them, and the uncertainty in the numerical estimate of the force. The computed equilibrium lattice constant for the crystal (a0) is given in the heading. MONOATOMIC STRUCTURE -- Species = C | a0 = 2.7390480041503906 | (Configuration in file "config-C.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 C 1 4.656005012238298e+00 4.656005012244125e+00 5.82734e-12 2.17124e-11 2 2.245485965009833e+00 2.245485965008435e+00 1.39799e-12 6.13318e-11 3 4.843987465750926e+00 4.843987465753850e+00 2.92388e-12 3.56701e-11 ----------------------------------------------------------------------------------------------------- 2 C 1 -3.240984834649639e+00 -3.240984834645440e+00 4.19842e-12 2.29567e-11 2 1.868060163220397e+00 1.868060163221438e+00 1.04095e-12 7.02438e-11 3 -4.898656183237594e-02 -4.898656182116239e-02 1.12136e-11 1.46788e-11 ----------------------------------------------------------------------------------------------------- 3 C 1 6.849838506532921e+00 6.849838506545758e+00 1.28368e-11 2.42437e-11 2 -6.267667733438691e+00 -6.267667733436705e+00 1.98686e-12 2.90035e-11 3 -7.231110696392816e+00 -7.231110696353396e+00 3.94209e-11 2.70468e-11 ----------------------------------------------------------------------------------------------------- 4 C 1 -3.683460474942790e+00 -3.683460474941539e+00 1.25100e-12 1.89595e-11 2 1.210404916371791e+01 1.210404916373099e+01 1.30811e-11 2.28049e-11 3 -6.047482396542826e+00 -6.047482396537849e+00 4.97646e-12 2.87885e-11 ----------------------------------------------------------------------------------------------------- 5 C 1 -1.925286498811293e+00 -1.925286498818115e+00 6.82188e-12 6.55487e-11 2 1.834328196488703e+00 1.834328196488816e+00 1.13465e-13 2.47349e-11 3 2.293878373380918e+00 2.293878373377582e+00 3.33600e-12 7.25158e-11 ----------------------------------------------------------------------------------------------------- 6 C 1 -1.355828259414555e+00 -1.355828259417527e+00 2.97229e-12 1.44078e-11 2 -4.001382642240371e+00 -4.001382642243468e+00 3.09708e-12 1.39897e-11 3 1.306964970857941e+00 1.306964970843739e+00 1.42020e-11 1.44281e-10 ----------------------------------------------------------------------------------------------------- 7 C 1 -1.667098110664015e+00 -1.667098110666482e+00 2.46692e-12 2.31559e-11 2 -6.181506345204323e+00 -6.181506345201695e+00 2.62723e-12 2.10408e-10 * 3 -1.257192103023361e+01 -1.257192103023223e+01 1.38023e-12 4.22151e-11 ----------------------------------------------------------------------------------------------------- 8 C 1 -2.637829118548693e+00 -2.637829118556347e+00 7.65477e-12 6.39040e-11 2 2.631332247765855e+00 2.631332247766763e+00 9.07718e-13 1.22879e-10 3 6.333157871672387e+00 6.333157871677084e+00 4.69758e-12 1.79419e-10 ----------------------------------------------------------------------------------------------------- 9 C 1 -1.079354458916211e+00 -1.079354458918633e+00 2.42162e-12 2.29039e-11 2 -3.745731400833101e+00 -3.745731400832240e+00 8.60645e-13 2.52158e-11 3 3.046883388879180e+00 3.046883388881667e+00 2.48646e-12 1.63143e-10 ----------------------------------------------------------------------------------------------------- 10 C 1 -4.029410785873956e+00 -4.029410785867502e+00 6.45350e-12 1.53886e-11 2 8.804346408814016e-01 8.804346408809858e-01 4.15779e-13 1.94900e-12 3 -2.429547796433460e+00 -2.429547796432895e+00 5.65326e-13 1.31406e-10 ----------------------------------------------------------------------------------------------------- 11 C 1 -6.608884219732448e-01 -6.608884219647464e-01 8.49842e-12 3.87522e-11 2 -1.377065134038647e+01 -1.377065134038226e+01 4.21174e-12 2.78373e-11 3 -6.283995316604410e+00 -6.283995316603735e+00 6.75016e-13 8.67484e-12 ----------------------------------------------------------------------------------------------------- 12 C 1 -1.540049415309755e+00 -1.540049415300178e+00 9.57656e-12 2.90512e-11 2 1.772488456988390e+00 1.772488456992322e+00 3.93197e-12 1.24185e-11 3 -5.216682536718962e-01 -5.216682536815598e-01 9.66360e-12 6.07697e-11 ----------------------------------------------------------------------------------------------------- 13 C 1 -4.240427326388718e+00 -4.240427326391996e+00 3.27738e-12 1.91962e-11 2 -3.118823690808053e+00 -3.118823690822244e+00 1.41904e-11 2.68816e-11 3 -1.153084433503150e+01 -1.153084433503499e+01 3.49232e-12 1.73197e-10 ----------------------------------------------------------------------------------------------------- 14 C 1 2.708129386576210e+00 2.708129386575831e+00 3.78808e-13 5.18776e-11 2 2.873778049027021e-01 2.873778049015362e-01 1.16590e-12 4.17555e-13 3 -2.292413274335261e+00 -2.292413274332397e+00 2.86304e-12 9.34719e-12 ----------------------------------------------------------------------------------------------------- 15 C 1 1.053410688532436e+01 1.053410688531828e+01 6.07692e-12 6.13518e-11 2 2.167899322623552e+00 2.167899322620260e+00 3.29248e-12 3.27010e-11 3 4.940953644486552e+00 4.940953644491473e+00 4.92051e-12 5.17586e-11 ----------------------------------------------------------------------------------------------------- 16 C 1 -5.824188989013712e-01 -5.824188988872566e-01 1.41146e-11 2.01438e-11 2 7.358126375216433e+00 7.358126375217941e+00 1.50724e-12 6.20481e-12 3 4.216431049325707e+00 4.216431049332798e+00 7.09122e-12 1.16001e-10 ----------------------------------------------------------------------------------------------------- 17 C 1 -6.300009085683228e+00 -6.300009085681553e+00 1.67510e-12 6.66871e-11 2 -2.916541750196980e+00 -2.916541750192418e+00 4.56213e-12 1.04749e-10 3 -1.840539132435065e+00 -1.840539132425364e+00 9.70091e-12 2.48672e-11 ----------------------------------------------------------------------------------------------------- 18 C 1 2.499477892977823e+00 2.499477892971543e+00 6.28031e-12 1.06541e-10 2 7.084495235680427e+00 7.084495235685393e+00 4.96669e-12 2.57186e-10 * 3 -4.095641844707487e+00 -4.095641844707646e+00 1.58984e-13 4.65086e-11 ----------------------------------------------------------------------------------------------------- 19 C 1 1.014959301854789e+01 1.014959301856410e+01 1.62110e-11 4.67253e-11 2 -2.867380306354548e+00 -2.867380306356083e+00 1.53477e-12 2.17399e-11 3 3.205196988502298e+00 3.205196988506877e+00 4.57900e-12 3.35536e-11 ----------------------------------------------------------------------------------------------------- 20 C 1 -7.208305867997927e-01 -7.208305867981535e-01 1.63924e-12 1.82542e-11 2 9.032337740050961e-01 9.032337740046389e-01 4.57190e-13 6.26710e-12 3 1.138470365916528e+00 1.138470365916891e+00 3.63043e-13 2.37033e-11 ----------------------------------------------------------------------------------------------------- 21 C 1 -6.326196110720780e+00 -6.326196110722236e+00 1.45572e-12 1.31160e-10 2 -3.571465329837320e+00 -3.571465329844528e+00 7.20890e-12 1.95683e-10 3 6.759809632124723e+00 6.759809632124386e+00 3.36620e-13 1.08205e-10 ----------------------------------------------------------------------------------------------------- 22 C 1 3.419649453252021e+00 3.419649453252414e+00 3.92575e-13 4.22937e-11 2 4.422919077742633e+00 4.422919077744556e+00 1.92291e-12 4.03855e-11 3 9.307033364611035e+00 9.307033364605138e+00 5.89750e-12 2.85549e-11 ----------------------------------------------------------------------------------------------------- 23 C 1 -2.822378908274390e+00 -2.822378908260566e+00 1.38236e-11 2.78546e-11 2 2.547541635221055e+00 2.547541635224150e+00 3.09486e-12 4.06311e-11 3 -2.454115272543896e+00 -2.454115272551736e+00 7.83951e-12 1.09698e-10 ----------------------------------------------------------------------------------------------------- 24 C 1 6.927772956424141e+00 6.927772956412481e+00 1.16600e-11 2.92752e-11 2 5.095731498162410e+00 5.095731498157754e+00 4.65583e-12 1.19215e-10 3 -1.530458042863133e+00 -1.530458042861222e+00 1.91114e-12 2.07963e-11 ----------------------------------------------------------------------------------------------------- 25 C 1 -2.445581146191013e-01 -2.445581146188607e-01 2.40669e-13 1.08584e-10 2 -4.068959111734037e+00 -4.068959111718393e+00 1.56435e-11 1.72697e-11 3 -2.110905230690796e+00 -2.110905230686849e+00 3.94662e-12 3.27955e-11 ----------------------------------------------------------------------------------------------------- 26 C 1 -1.025267968272156e+00 -1.025267968276000e+00 3.84448e-12 1.68783e-10 2 4.717767538145799e+00 4.717767538153522e+00 7.72271e-12 4.13118e-11 3 2.231962648427373e+00 2.231962648423760e+00 3.61267e-12 8.58424e-11 ----------------------------------------------------------------------------------------------------- 27 C 1 5.836290914798020e+00 5.836290914810759e+00 1.27383e-11 3.21103e-11 2 -4.810953027191385e+00 -4.810953027191252e+00 1.33227e-13 8.47766e-11 3 2.803414068154803e+00 2.803414068158917e+00 4.11449e-12 6.16720e-11 ----------------------------------------------------------------------------------------------------- 28 C 1 -7.394668411310737e+00 -7.394668411314173e+00 3.43636e-12 3.05054e-11 2 5.593176157532843e+00 5.593176157530869e+00 1.97442e-12 2.37756e-11 3 3.012358118745806e-01 3.012358118831525e-01 8.57187e-12 1.01156e-11 ----------------------------------------------------------------------------------------------------- 29 C 1 7.590992670061102e-01 7.590992670044863e-01 1.62392e-12 3.13916e-11 2 -4.767615581535100e+00 -4.767615581529459e+00 5.64171e-12 3.95417e-11 3 -1.215616216227394e+00 -1.215616216225035e+00 2.35922e-12 1.61491e-11 ----------------------------------------------------------------------------------------------------- 30 C 1 1.996115199278598e+00 1.996115199278462e+00 1.36335e-13 7.47780e-12 2 2.719437586411763e-01 2.719437586417788e-01 6.02518e-13 1.25533e-11 3 -1.247642291241628e+00 -1.247642291236667e+00 4.96025e-12 4.08293e-11 ----------------------------------------------------------------------------------------------------- 31 C 1 -5.610524063993372e+00 -5.610524064001762e+00 8.38973e-12 1.16405e-11 2 -5.323819875286969e+00 -5.323819875283689e+00 3.27915e-12 3.17826e-11 3 5.451881919994625e+00 5.451881919992312e+00 2.31282e-12 3.81011e-11 ----------------------------------------------------------------------------------------------------- 32 C 1 7.513913611114118e-01 7.513913611167004e-01 5.28855e-12 1.02915e-11 2 1.626107123100726e+00 1.626107123090531e+00 1.01945e-11 7.53650e-11 3 5.271626127827987e+00 5.271626127823526e+00 4.46043e-12 1.62208e-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 = 2, direction = 3: |F_model - F_numer| error = ----------------------- = 2.28911e-10 max{|F_numer|, eps} Comparison of analytical forces obtained from the model, the force computed as a numerical derivative of the energy, the difference between them, and the uncertainty in the numerical estimate of the force. The computed equilibrium lattice constant for the crystal (a0) is given in the heading. MONOATOMIC STRUCTURE -- Species = Si | a0 = 3.8463315963745117 | (Configuration in file "config-Si.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Si 1 5.120228101542475e+00 5.120228101539696e+00 2.77911e-12 1.48894e-11 2 3.393276701829042e+00 3.393276701828246e+00 7.96252e-13 3.00822e-11 3 7.166916026352578e+00 7.166916026359567e+00 6.98908e-12 3.84581e-11 ----------------------------------------------------------------------------------------------------- 2 Si 1 -4.319794633861901e+00 -4.319794633866220e+00 4.31921e-12 1.86260e-11 2 6.778729509997539e-01 6.778729510007734e-01 1.01952e-12 2.03024e-11 3 1.210930928180508e+00 1.210930928182860e+00 2.35145e-12 2.99629e-11 ----------------------------------------------------------------------------------------------------- 3 Si 1 -3.311238562823384e+00 -3.311238562824397e+00 1.01297e-12 1.13061e-10 2 1.767538326347310e+00 1.767538326347437e+00 1.27010e-13 1.67284e-11 3 -3.372786151738698e+00 -3.372786151736031e+00 2.66676e-12 1.53879e-10 ----------------------------------------------------------------------------------------------------- 4 Si 1 3.253108951815418e+00 3.253108951830542e+00 1.51243e-11 4.97820e-11 2 9.138613240048959e-01 9.138613240039098e-01 9.86100e-13 4.70906e-11 3 3.277580016496399e+00 3.277580016497214e+00 8.14904e-13 1.17575e-10 ----------------------------------------------------------------------------------------------------- 5 Si 1 5.138793606883010e+00 5.138793606884764e+00 1.75415e-12 2.57367e-11 2 3.987408671932655e+00 3.987408671932303e+00 3.51275e-13 2.47344e-11 3 6.768210195901059e+00 6.768210195905449e+00 4.39027e-12 1.90381e-11 ----------------------------------------------------------------------------------------------------- 6 Si 1 -4.097705283998383e+00 -4.097705283999226e+00 8.43769e-13 3.06333e-12 2 -2.640829895487638e+00 -2.640829895493213e+00 5.57465e-12 3.56906e-11 3 3.615053971407697e+00 3.615053971407364e+00 3.33067e-13 9.43512e-12 ----------------------------------------------------------------------------------------------------- 7 Si 1 -2.577972054465171e+00 -2.577972054485352e+00 2.01812e-11 2.76126e-11 2 3.485233497210870e+00 3.485233497202791e+00 8.07976e-12 1.63514e-11 3 -2.290945757187036e+00 -2.290945757187864e+00 8.28670e-13 1.06576e-10 ----------------------------------------------------------------------------------------------------- 8 Si 1 -1.382287037615318e+00 -1.382287037594525e+00 2.07929e-11 7.78178e-11 2 1.210098497533004e-02 1.210098496443789e-02 1.08922e-11 2.16044e-11 3 -4.549195058560623e-01 -4.549195058503429e-01 5.71937e-12 1.52613e-10 ----------------------------------------------------------------------------------------------------- 9 Si 1 5.307644572263460e+00 5.307644572262680e+00 7.80709e-13 2.26361e-11 2 1.621423263354708e+00 1.621423263361017e+00 6.30918e-12 1.30753e-11 3 3.242218557070053e+00 3.242218557072304e+00 2.25109e-12 1.22058e-11 ----------------------------------------------------------------------------------------------------- 10 Si 1 -3.758917851459276e+00 -3.758917851458419e+00 8.57092e-13 5.49107e-11 2 -5.561909586165817e+00 -5.561909586159109e+00 6.70841e-12 1.53211e-11 3 6.201846955656844e+00 6.201846955654417e+00 2.42739e-12 6.21521e-11 ----------------------------------------------------------------------------------------------------- 11 Si 1 -5.260728464901328e+00 -5.260728464907470e+00 6.14264e-12 1.57843e-10 2 2.731999226749061e+00 2.731999226746622e+00 2.43983e-12 7.76863e-11 3 -2.899232832979876e+00 -2.899232832986895e+00 7.01972e-12 1.53424e-11 ----------------------------------------------------------------------------------------------------- 12 Si 1 7.087336623516650e+00 7.087336623521073e+00 4.42313e-12 3.67102e-11 2 -6.327038939233703e+00 -6.327038939248371e+00 1.46674e-11 5.94547e-11 3 -4.486303028589720e+00 -4.486303028587059e+00 2.66098e-12 7.03571e-11 ----------------------------------------------------------------------------------------------------- 13 Si 1 -7.897728093148417e+00 -7.897728093136981e+00 1.14362e-11 9.46887e-12 2 4.720610143740858e-01 4.720610143684626e-01 5.62322e-12 7.70561e-12 3 -3.424633101104135e+00 -3.424633101099384e+00 4.75087e-12 9.57412e-12 ----------------------------------------------------------------------------------------------------- 14 Si 1 -1.100575504364702e+00 -1.100575504363836e+00 8.66196e-13 5.91381e-10 * 2 -1.166142504014258e-01 -1.166142504014408e-01 1.50019e-14 7.18417e-12 3 1.177044965756959e+00 1.177044965754570e+00 2.38898e-12 5.20850e-12 ----------------------------------------------------------------------------------------------------- 15 Si 1 5.408514972671228e+00 5.408514972653514e+00 1.77147e-11 2.01682e-10 2 -2.919163684706197e+00 -2.919163684699161e+00 7.03615e-12 8.62821e-11 3 4.556462195280303e+00 4.556462195284036e+00 3.73301e-12 1.13802e-11 ----------------------------------------------------------------------------------------------------- 16 Si 1 -2.991247545011865e+00 -2.991247545006384e+00 5.48095e-12 5.31163e-10 * 2 3.082685736523944e+00 3.082685736520195e+00 3.74900e-12 7.33591e-12 3 3.292431975413331e-01 3.292431975384885e-01 2.84456e-12 1.62822e-10 ----------------------------------------------------------------------------------------------------- 17 Si 1 6.715821560734618e+00 6.715821560731685e+00 2.93277e-12 5.45235e-11 2 6.372852553876648e+00 6.372852553885703e+00 9.05498e-12 3.05693e-11 3 3.718307920572234e-01 3.718307920615219e-01 4.29856e-12 2.27247e-11 ----------------------------------------------------------------------------------------------------- 18 Si 1 -3.610347070168903e+00 -3.610347070167784e+00 1.11955e-12 9.91096e-11 2 -6.141735258066495e-01 -6.141735258153634e-01 8.71392e-12 6.39925e-11 3 1.010963483356909e+00 1.010963483356454e+00 4.54081e-13 1.38904e-09 * ----------------------------------------------------------------------------------------------------- 19 Si 1 -4.258449680064627e+00 -4.258449680066657e+00 2.02949e-12 2.98241e-11 2 -2.157374250535051e+00 -2.157374250539539e+00 4.48797e-12 1.08824e-10 3 -2.812043846040902e+00 -2.812043846047650e+00 6.74838e-12 1.05030e-10 ----------------------------------------------------------------------------------------------------- 20 Si 1 3.486193056104812e+00 3.486193056108218e+00 3.40661e-12 7.24483e-11 2 2.785849442523540e+00 2.785849442526089e+00 2.54863e-12 1.26916e-11 3 -5.687845584510582e+00 -5.687845584507847e+00 2.73559e-12 1.57942e-10 ----------------------------------------------------------------------------------------------------- 21 Si 1 1.347818524356851e+00 1.347818524353513e+00 3.33844e-12 3.02098e-11 2 2.490183843477706e+00 2.490183843484736e+00 7.02993e-12 2.74474e-11 3 1.932083839443195e+00 1.932083839437844e+00 5.35105e-12 6.35378e-11 ----------------------------------------------------------------------------------------------------- 22 Si 1 1.563371817459724e-01 1.563371817463670e-01 3.94573e-13 1.96168e-12 2 -6.574787662549018e+00 -6.574787662538298e+00 1.07203e-11 6.17826e-11 3 3.307339909610139e+00 3.307339909607381e+00 2.75779e-12 3.82308e-11 ----------------------------------------------------------------------------------------------------- 23 Si 1 -2.588390172335044e+00 -2.588390172336378e+00 1.33404e-12 2.50697e-11 2 5.427053792619445e+00 5.427053792619339e+00 1.05693e-13 3.02993e-11 3 -6.808057334750193e+00 -6.808057334723632e+00 2.65610e-11 4.53202e-11 ----------------------------------------------------------------------------------------------------- 24 Si 1 8.419500917244807e-01 8.419500917139423e-01 1.05383e-11 2.69119e-11 2 4.634218407549217e+00 4.634218407542257e+00 6.95977e-12 1.24879e-10 3 -2.354033241436913e+00 -2.354033241439577e+00 2.66409e-12 2.62506e-11 ----------------------------------------------------------------------------------------------------- 25 Si 1 4.505350506099204e+00 4.505350506095336e+00 3.86802e-12 1.23769e-10 2 -5.803948460371637e+00 -5.803948460366589e+00 5.04841e-12 1.37428e-11 3 -4.043420370547777e+00 -4.043420370550882e+00 3.10507e-12 2.40513e-10 ----------------------------------------------------------------------------------------------------- 26 Si 1 -3.629061818574677e+00 -3.629061818570486e+00 4.19087e-12 9.71840e-11 2 1.749303996418989e+00 1.749303996432045e+00 1.30567e-11 1.37278e-10 3 1.391800484262253e+00 1.391800484242135e+00 2.01184e-11 1.92331e-10 ----------------------------------------------------------------------------------------------------- 27 Si 1 -4.391848132897709e+00 -4.391848132907160e+00 9.45111e-12 2.67688e-11 2 -2.226603210225140e+00 -2.226603210223389e+00 1.75104e-12 1.22703e-10 3 -4.100677594806277e+00 -4.100677594797441e+00 8.83649e-12 1.81011e-11 ----------------------------------------------------------------------------------------------------- 28 Si 1 5.522070175995070e+00 5.522070175994150e+00 9.20153e-13 8.50235e-11 2 -3.989027505616666e+00 -3.989027505632258e+00 1.55924e-11 5.50870e-11 3 -1.731960298193560e+00 -1.731960298188935e+00 4.62452e-12 1.45937e-11 ----------------------------------------------------------------------------------------------------- 29 Si 1 3.235136459327017e+00 3.235136459341801e+00 1.47846e-11 2.72106e-10 2 -2.626983972775147e+00 -2.626983972785766e+00 1.06191e-11 1.42914e-10 3 2.507994264235485e-01 2.507994264261081e-01 2.55967e-12 1.21393e-10 ----------------------------------------------------------------------------------------------------- 30 Si 1 -8.101502813242311e-01 -8.101502813195157e-01 4.71534e-12 3.24907e-12 2 -2.096098428771310e+00 -2.096098428779159e+00 7.84928e-12 5.11764e-11 3 -1.165424914182873e+00 -1.165424914170808e+00 1.20648e-11 1.30364e-10 ----------------------------------------------------------------------------------------------------- 31 Si 1 -4.228757944919027e+00 -4.228757944911425e+00 7.60281e-12 4.58922e-12 2 -4.392869421563380e-01 -4.392869421497437e-01 6.59428e-12 9.93842e-11 3 -1.300545528140787e+00 -1.300545528140915e+00 1.28120e-13 5.88498e-11 ----------------------------------------------------------------------------------------------------- 32 Si 1 3.088895747153697e+00 3.088895747153776e+00 7.90479e-14 1.15597e-10 2 -1.511083419965476e+00 -1.511083419962091e+00 3.38463e-12 4.13090e-11 3 1.122504145268375e+00 1.122504145271575e+00 3.19988e-12 1.91449e-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 = 2: |F_model - F_numer| error = ----------------------- = 9.00105e-10 max{|F_numer|, eps} Comparison of analytical forces obtained from the model, the force computed as a numerical derivative of the energy, the difference between them, and the uncertainty in the numerical estimate of the force. The computed equilibrium lattice constant for the crystal (a0) is given in the heading. MIXED STRUCTURE -- Species = C Si | a0 = 3.3845016139794097 | (Configuration in file "config-CSi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Si 1 -4.429385738561099e+00 -4.429385738588948e+00 2.78488e-11 8.96376e-11 2 -3.610794773847990e+00 -3.610794773860977e+00 1.29878e-11 2.88878e-09 3 -3.534850893418047e+00 -3.534850893265012e+00 1.53035e-10 2.70847e-09 ----------------------------------------------------------------------------------------------------- 2 Si 1 -2.343184890787960e+00 -2.343184891045604e+00 2.57645e-10 6.64624e-09 2 7.347020885370153e+00 7.347020885356618e+00 1.35350e-11 9.22437e-10 3 -3.205648073679431e+00 -3.205648073743717e+00 6.42855e-11 3.23625e-09 ----------------------------------------------------------------------------------------------------- 3 Si 1 -2.289248685915231e+00 -2.289248685731809e+00 1.83422e-10 5.40134e-09 2 1.429379579193597e+00 1.429379578546597e+00 6.47000e-10 4.60402e-09 3 1.248292546578046e+01 1.248292546630743e+01 5.26970e-10 9.57836e-10 ----------------------------------------------------------------------------------------------------- 4 C 1 5.572216077641707e+00 5.572216077712064e+00 7.03571e-11 2.90868e-09 2 6.551580070924273e+00 6.551580070607545e+00 3.16728e-10 9.99219e-10 3 3.207655128866616e+00 3.207655128897156e+00 3.05391e-11 1.07518e-09 ----------------------------------------------------------------------------------------------------- 5 Si 1 5.550590904500809e+00 5.550590904499296e+00 1.51257e-12 1.17484e-09 2 -8.100148891899799e+00 -8.100148891607628e+00 2.92172e-10 5.58391e-09 3 -8.044341551412042e+00 -8.044341550990127e+00 4.21915e-10 7.16025e-10 ----------------------------------------------------------------------------------------------------- 6 C 1 -9.400482639569676e-01 -9.400482634388628e-01 5.18105e-10 2.92045e-09 2 1.264353795205283e+00 1.264353795114719e+00 9.05633e-11 6.48727e-09 3 3.521894996170722e+00 3.521894996087617e+00 8.31046e-11 3.36253e-09 ----------------------------------------------------------------------------------------------------- 7 C 1 3.495802677492472e-01 3.495802683672656e-01 6.18018e-10 2.54853e-09 2 -1.582437382141413e+00 -1.582437382037979e+00 1.03434e-10 2.22159e-09 3 -8.285676151554764e-01 -8.285676150940935e-01 6.13829e-11 2.45060e-09 ----------------------------------------------------------------------------------------------------- 8 Si 1 -7.526544979739126e-01 -7.526544980724821e-01 9.85695e-11 1.30540e-09 2 7.226391246751295e+00 7.226391247415251e+00 6.63956e-10 1.90544e-09 3 8.922252728946257e+00 8.922252729100530e+00 1.54273e-10 1.51953e-09 ----------------------------------------------------------------------------------------------------- 9 C 1 3.611767844274600e+00 3.611767844216752e+00 5.78484e-11 1.50432e-09 2 -2.697196766223743e+00 -2.697196766212727e+00 1.10170e-11 6.65828e-10 3 4.755921984215343e-01 4.755921985451814e-01 1.23647e-10 1.55920e-11 ----------------------------------------------------------------------------------------------------- 10 Si 1 3.733771169699545e-01 3.733771176805303e-01 7.10576e-10 3.28768e-09 2 -8.095772962422069e-01 -8.095772966794675e-01 4.37261e-10 3.79963e-08 * 3 -1.811633719408361e+00 -1.811633717994078e+00 1.41428e-09 1.07930e-09 ----------------------------------------------------------------------------------------------------- 11 C 1 -3.948028211313099e+00 -3.948028212869575e+00 1.55648e-09 1.66621e-09 2 -5.081940596684008e+00 -5.081940596074173e+00 6.09836e-10 4.87407e-09 3 9.330093682476676e-01 9.330093684779590e-01 2.30291e-10 4.33868e-09 ----------------------------------------------------------------------------------------------------- 12 Si 1 -9.623513340788594e-01 -9.623513342126337e-01 1.33774e-10 4.95930e-09 2 4.169059974635914e+00 4.169059974279758e+00 3.56156e-10 1.39396e-09 3 -6.168262659085827e+00 -6.168262658714387e+00 3.71440e-10 2.20265e-09 ----------------------------------------------------------------------------------------------------- 13 C 1 1.125118320640175e+00 1.125118320808773e+00 1.68598e-10 1.65089e-09 2 1.226470910201157e+00 1.226470908428985e+00 1.77217e-09 2.19951e-09 3 -3.775126573062368e+00 -3.775126571418666e+00 1.64370e-09 1.08634e-08 ----------------------------------------------------------------------------------------------------- 14 Si 1 -2.398893606218402e+00 -2.398893606027326e+00 1.91076e-10 7.52697e-10 2 -1.823607013279014e+00 -1.823607013309819e+00 3.08054e-11 2.01842e-09 3 -1.333632835098528e+00 -1.333632834793258e+00 3.05270e-10 1.56227e-09 ----------------------------------------------------------------------------------------------------- 15 Si 1 3.424633477508195e+00 3.424633477641814e+00 1.33619e-10 8.35399e-10 2 -3.311077883467980e+00 -3.311077883562656e+00 9.46758e-11 7.96341e-09 3 -5.865714993910704e+00 -5.865714994152093e+00 2.41389e-10 9.11860e-09 ----------------------------------------------------------------------------------------------------- 16 Si 1 -2.954605375528089e+00 -2.954605375289629e+00 2.38460e-10 5.89612e-09 2 8.914382886314359e+00 8.914382887549454e+00 1.23510e-09 2.95691e-09 3 2.054544108902513e+00 2.054544108811631e+00 9.08824e-11 2.06423e-09 ----------------------------------------------------------------------------------------------------- 17 C 1 3.558484338900397e+00 3.558484338752203e+00 1.48193e-10 5.85752e-10 2 -4.337428375585369e-01 -4.337428376824422e-01 1.23905e-10 2.99374e-10 3 -3.713087272682360e+00 -3.713087272570974e+00 1.11386e-10 5.84474e-10 ----------------------------------------------------------------------------------------------------- 18 C 1 -3.798207460969324e+00 -3.798207462217938e+00 1.24861e-09 1.12055e-08 2 -7.131160153705214e+00 -7.131160154496621e+00 7.91407e-10 3.72273e-08 * 3 5.042152898338379e+00 5.042152897832647e+00 5.05732e-10 3.97578e-09 ----------------------------------------------------------------------------------------------------- 19 C 1 7.398962524293021e-01 7.398962524249081e-01 4.39404e-12 6.50683e-11 2 4.573404652507292e+00 4.573404652499222e+00 8.06999e-12 8.85754e-11 3 -4.525613767339923e+00 -4.525613767342803e+00 2.87947e-12 1.39054e-10 ----------------------------------------------------------------------------------------------------- 20 C 1 -1.504780179516252e-01 -1.504780180366723e-01 8.50471e-11 9.88087e-09 2 -3.769764806285597e+00 -3.769764806132714e+00 1.52883e-10 7.02544e-09 3 -3.197191159961561e+00 -3.197191159395099e+00 5.66461e-10 1.32720e-08 ----------------------------------------------------------------------------------------------------- 21 C 1 2.206334902933893e+00 2.206334903290050e+00 3.56156e-10 2.74918e-08 * 2 1.680215414613905e+00 1.680215414279441e+00 3.34463e-10 3.73592e-09 3 -4.070934629638165e-01 -4.070934627924853e-01 1.71331e-10 9.86236e-09 ----------------------------------------------------------------------------------------------------- 22 Si 1 2.099060122236834e+00 2.099060121694198e+00 5.42635e-10 4.72275e-09 2 5.429342878299483e+00 5.429342879152508e+00 8.53025e-10 1.26206e-09 3 7.967028245203687e-01 7.967028253663493e-01 8.45981e-10 1.73229e-08 ----------------------------------------------------------------------------------------------------- 23 Si 1 -9.460036478894382e+00 -9.460036481377946e+00 2.48356e-09 6.02582e-09 2 -1.879480818161554e+00 -1.879480818488180e+00 3.26626e-10 1.28647e-09 3 -3.711974507136053e-01 -3.711974506247551e-01 8.88502e-11 2.33492e-09 ----------------------------------------------------------------------------------------------------- 24 C 1 6.846250374867995e+00 6.846250374644079e+00 2.23916e-10 2.71909e-08 * 2 7.099297447255389e+00 7.099297447028049e+00 2.27340e-10 1.13913e-08 3 -6.592321202615956e-02 -6.592321240340752e-02 3.77248e-10 7.24667e-09 ----------------------------------------------------------------------------------------------------- 25 Si 1 -8.946150052079522e+00 -8.946150047704540e+00 4.37498e-09 2.84343e-08 * 2 -7.891491122250726e+00 -7.891491128691211e+00 6.44048e-09 1.55082e-08 3 -5.115165795106035e+00 -5.115165795408680e+00 3.02645e-10 7.96891e-09 ----------------------------------------------------------------------------------------------------- 26 C 1 9.695199044282264e+00 9.695199044158356e+00 1.23908e-10 5.34389e-09 2 3.205306015619055e+00 3.205306015445681e+00 1.73373e-10 3.07906e-09 3 5.870848161560743e+00 5.870848161699308e+00 1.38565e-10 3.53450e-09 ----------------------------------------------------------------------------------------------------- 27 Si 1 1.452405054043679e+01 1.452405054050721e+01 7.04148e-11 9.27959e-09 2 -1.280848294973502e+00 -1.280848294836754e+00 1.36747e-10 1.52425e-09 3 8.885971369857304e+00 8.885971369609246e+00 2.48058e-10 2.16403e-09 ----------------------------------------------------------------------------------------------------- 28 Si 1 -2.304958113256527e-01 -2.304958112235627e-01 1.02090e-10 2.49751e-09 2 4.322720504222384e+00 4.322720504245343e+00 2.29585e-11 1.56600e-09 3 2.386064553674107e+00 2.386064553948886e+00 2.74779e-10 1.49577e-09 ----------------------------------------------------------------------------------------------------- 29 Si 1 1.451220730651389e+00 1.451220730529522e+00 1.21867e-10 2.58794e-08 * 2 -6.739729004625231e+00 -6.739729003387110e+00 1.23812e-09 2.33748e-09 3 6.490447800830826e+00 6.490447801066997e+00 2.36171e-10 2.33503e-09 ----------------------------------------------------------------------------------------------------- 30 C 1 -2.382484508127014e+00 -2.382484507886651e+00 2.40363e-10 1.43839e-09 2 -9.628356593143694e-02 -9.628356530605649e-02 6.25380e-10 1.61396e-09 3 -4.574594817130160e-01 -4.574594820332131e-01 3.20197e-10 1.90034e-09 ----------------------------------------------------------------------------------------------------- 31 C 1 -7.624097363674887e+00 -7.624097363444236e+00 2.30651e-10 6.73402e-09 2 -9.263893840800629e+00 -9.263893840240026e+00 5.60602e-10 1.35745e-09 3 -3.087422776374448e+00 -3.087422776387176e+00 1.27289e-11 3.37643e-09 ----------------------------------------------------------------------------------------------------- 32 C 1 -7.517430018667523e+00 -7.517430018769662e+00 1.02140e-10 1.15751e-09 2 1.064248786965067e+00 1.064248786970562e+00 5.49516e-12 4.10671e-10 3 -5.562128311005784e+00 -5.562128310982890e+00 2.28946e-11 1.00382e-09 ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as discontinuities. Maximum error obtained for particle = 30, direction = 2: |F_model - F_numer| error = ----------------------- = 6.49519e-09 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 6.49519e-09 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 6.49519e-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.