!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_005 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 4.656005012244128e+00 5.83000e-12 2.17124e-11 2 2.245485965009833e+00 2.245485965008434e+00 1.39888e-12 6.13332e-11 3 4.843987465750926e+00 4.843987465753852e+00 2.92566e-12 3.56710e-11 ----------------------------------------------------------------------------------------------------- 2 C 1 -3.240984834649639e+00 -3.240984834645439e+00 4.20020e-12 2.29567e-11 2 1.868060163220397e+00 1.868060163221439e+00 1.04228e-12 7.02418e-11 3 -4.898656183237594e-02 -4.898656182116242e-02 1.12135e-11 1.46788e-11 ----------------------------------------------------------------------------------------------------- 3 C 1 6.849838506532921e+00 6.849838506545755e+00 1.28333e-11 2.42437e-11 2 -6.267667733438691e+00 -6.267667733436709e+00 1.98241e-12 2.90052e-11 3 -7.231110696392816e+00 -7.231110696353398e+00 3.94182e-11 2.70433e-11 ----------------------------------------------------------------------------------------------------- 4 C 1 -3.683460474942790e+00 -3.683460474941542e+00 1.24833e-12 1.89595e-11 2 1.210404916371791e+01 1.210404916373100e+01 1.30900e-11 2.27995e-11 3 -6.047482396542826e+00 -6.047482396537853e+00 4.97291e-12 2.87903e-11 ----------------------------------------------------------------------------------------------------- 5 C 1 -1.925286498811293e+00 -1.925286498818114e+00 6.82077e-12 6.55491e-11 2 1.834328196488703e+00 1.834328196488817e+00 1.14353e-13 2.47362e-11 3 2.293878373380918e+00 2.293878373377584e+00 3.33467e-12 7.25149e-11 ----------------------------------------------------------------------------------------------------- 6 C 1 -1.355828259414555e+00 -1.355828259417528e+00 2.97318e-12 1.44083e-11 2 -4.001382642240371e+00 -4.001382642243466e+00 3.09530e-12 1.39870e-11 3 1.306964970857941e+00 1.306964970843740e+00 1.42013e-11 1.44282e-10 ----------------------------------------------------------------------------------------------------- 7 C 1 -1.667098110664015e+00 -1.667098110666483e+00 2.46847e-12 2.31559e-11 2 -6.181506345204323e+00 -6.181506345201699e+00 2.62368e-12 2.10417e-10 * 3 -1.257192103023361e+01 -1.257192103023224e+01 1.37135e-12 4.22080e-11 ----------------------------------------------------------------------------------------------------- 8 C 1 -2.637829118548693e+00 -2.637829118556349e+00 7.65654e-12 6.39040e-11 2 2.631332247765855e+00 2.631332247766762e+00 9.06830e-13 1.22880e-10 3 6.333157871672387e+00 6.333157871677090e+00 4.70290e-12 1.79424e-10 ----------------------------------------------------------------------------------------------------- 9 C 1 -1.079354458916211e+00 -1.079354458918634e+00 2.42228e-12 2.29057e-11 2 -3.745731400833101e+00 -3.745731400832238e+00 8.62421e-13 2.52158e-11 3 3.046883388879180e+00 3.046883388881668e+00 2.48779e-12 1.63143e-10 ----------------------------------------------------------------------------------------------------- 10 C 1 -4.029410785873956e+00 -4.029410785867505e+00 6.45084e-12 1.53886e-11 2 8.804346408814016e-01 8.804346408809863e-01 4.15223e-13 1.94900e-12 3 -2.429547796433460e+00 -2.429547796432896e+00 5.63993e-13 1.31409e-10 ----------------------------------------------------------------------------------------------------- 11 C 1 -6.608884219732448e-01 -6.608884219647468e-01 8.49798e-12 3.87531e-11 2 -1.377065134038647e+01 -1.377065134038226e+01 4.20819e-12 2.78444e-11 3 -6.283995316604410e+00 -6.283995316603741e+00 6.69687e-13 8.67040e-12 ----------------------------------------------------------------------------------------------------- 12 C 1 -1.540049415309755e+00 -1.540049415300180e+00 9.57523e-12 2.90505e-11 2 1.772488456988390e+00 1.772488456992321e+00 3.93130e-12 1.24187e-11 3 -5.216682536718962e-01 -5.216682536815596e-01 9.66338e-12 6.07694e-11 ----------------------------------------------------------------------------------------------------- 13 C 1 -4.240427326388718e+00 -4.240427326391998e+00 3.28004e-12 1.91909e-11 2 -3.118823690808053e+00 -3.118823690822242e+00 1.41887e-11 2.68825e-11 3 -1.153084433503150e+01 -1.153084433503499e+01 3.48699e-12 1.73193e-10 ----------------------------------------------------------------------------------------------------- 14 C 1 2.708129386576210e+00 2.708129386575830e+00 3.79696e-13 5.18794e-11 2 2.873778049027021e-01 2.873778049015365e-01 1.16568e-12 4.18221e-13 3 -2.292413274335261e+00 -2.292413274332463e+00 2.79732e-12 9.28280e-12 ----------------------------------------------------------------------------------------------------- 15 C 1 1.053410688532436e+01 1.053410688531828e+01 6.08402e-12 6.13589e-11 2 2.167899322623552e+00 2.167899322620261e+00 3.29070e-12 3.27014e-11 3 4.940953644486552e+00 4.940953644491477e+00 4.92406e-12 5.17568e-11 ----------------------------------------------------------------------------------------------------- 16 C 1 -5.824188989013712e-01 -5.824188988872567e-01 1.41145e-11 2.01441e-11 2 7.358126375216433e+00 7.358126375217937e+00 1.50369e-12 6.20481e-12 3 4.216431049325707e+00 4.216431049332797e+00 7.08944e-12 1.16002e-10 ----------------------------------------------------------------------------------------------------- 17 C 1 -6.300009085683228e+00 -6.300009085681549e+00 1.67866e-12 6.66871e-11 2 -2.916541750196980e+00 -2.916541750192419e+00 4.56035e-12 1.04751e-10 3 -1.840539132435065e+00 -1.840539132425365e+00 9.70002e-12 2.48674e-11 ----------------------------------------------------------------------------------------------------- 18 C 1 2.499477892977823e+00 2.499477892971544e+00 6.27898e-12 1.06541e-10 2 7.084495235680427e+00 7.084495235685390e+00 4.96314e-12 2.57186e-10 * 3 -4.095641844707487e+00 -4.095641844707648e+00 1.61648e-13 4.65086e-11 ----------------------------------------------------------------------------------------------------- 19 C 1 1.014959301854789e+01 1.014959301856410e+01 1.62057e-11 4.67129e-11 2 -2.867380306354548e+00 -2.867380306356085e+00 1.53699e-12 2.17413e-11 3 3.205196988502298e+00 3.205196988506875e+00 4.57767e-12 3.35527e-11 ----------------------------------------------------------------------------------------------------- 20 C 1 -7.208305867997927e-01 -7.208305867981539e-01 1.63880e-12 1.82544e-11 2 9.032337740050961e-01 9.032337740046384e-01 4.57634e-13 6.26710e-12 3 1.138470365916528e+00 1.138470365916890e+00 3.62599e-13 2.37035e-11 ----------------------------------------------------------------------------------------------------- 21 C 1 -6.326196110720780e+00 -6.326196110722233e+00 1.45217e-12 1.31166e-10 2 -3.571465329837320e+00 -3.571465329844527e+00 7.20712e-12 1.95683e-10 3 6.759809632124723e+00 6.759809632124392e+00 3.31291e-13 1.08202e-10 ----------------------------------------------------------------------------------------------------- 22 C 1 3.419649453252021e+00 3.419649453252412e+00 3.90799e-13 4.22937e-11 2 4.422919077742633e+00 4.422919077744560e+00 1.92646e-12 4.03917e-11 3 9.307033364611035e+00 9.307033364605143e+00 5.89218e-12 2.85656e-11 ----------------------------------------------------------------------------------------------------- 23 C 1 -2.822378908274390e+00 -2.822378908260565e+00 1.38245e-11 2.78528e-11 2 2.547541635221055e+00 2.547541635224149e+00 3.09397e-12 4.06302e-11 3 -2.454115272543896e+00 -2.454115272551737e+00 7.84039e-12 1.09695e-10 ----------------------------------------------------------------------------------------------------- 24 C 1 6.927772956424141e+00 6.927772956412488e+00 1.16529e-11 2.92726e-11 2 5.095731498162410e+00 5.095731498157757e+00 4.65228e-12 1.19208e-10 3 -1.530458042863133e+00 -1.530458042861222e+00 1.91136e-12 2.07971e-11 ----------------------------------------------------------------------------------------------------- 25 C 1 -2.445581146191013e-01 -2.445581146188608e-01 2.40502e-13 1.08584e-10 2 -4.068959111734037e+00 -4.068959111718391e+00 1.56453e-11 1.72697e-11 3 -2.110905230690796e+00 -2.110905230686851e+00 3.94484e-12 3.27929e-11 ----------------------------------------------------------------------------------------------------- 26 C 1 -1.025267968272156e+00 -1.025267968276001e+00 3.84515e-12 1.68783e-10 2 4.717767538145799e+00 4.717767538153525e+00 7.72538e-12 4.13056e-11 3 2.231962648427373e+00 2.231962648423762e+00 3.61045e-12 8.58429e-11 ----------------------------------------------------------------------------------------------------- 27 C 1 5.836290914798020e+00 5.836290914810764e+00 1.27436e-11 3.21121e-11 2 -4.810953027191385e+00 -4.810953027191256e+00 1.28786e-13 8.47766e-11 3 2.803414068154803e+00 2.803414068158916e+00 4.11315e-12 6.16711e-11 ----------------------------------------------------------------------------------------------------- 28 C 1 -7.394668411310737e+00 -7.394668411314178e+00 3.44080e-12 3.05072e-11 2 5.593176157532843e+00 5.593176157530866e+00 1.97709e-12 2.37783e-11 3 3.012358118745806e-01 3.012358118831527e-01 8.57209e-12 1.01158e-11 ----------------------------------------------------------------------------------------------------- 29 C 1 7.590992670061102e-01 7.590992670044868e-01 1.62337e-12 3.13918e-11 2 -4.767615581535100e+00 -4.767615581529456e+00 5.64437e-12 3.95408e-11 3 -1.215616216227394e+00 -1.215616216225036e+00 2.35811e-12 1.61493e-11 ----------------------------------------------------------------------------------------------------- 30 C 1 1.996115199278598e+00 1.996115199278464e+00 1.34115e-13 7.47868e-12 2 2.719437586411763e-01 2.719437586417789e-01 6.02685e-13 1.25532e-11 3 -1.247642291241628e+00 -1.247642291236668e+00 4.95959e-12 4.08285e-11 ----------------------------------------------------------------------------------------------------- 31 C 1 -5.610524063993372e+00 -5.610524064001916e+00 8.54428e-12 3.07843e-12 2 -5.323819875286969e+00 -5.323819875283687e+00 3.28182e-12 3.17826e-11 3 5.451881919994625e+00 5.451881919992315e+00 2.30926e-12 3.81011e-11 ----------------------------------------------------------------------------------------------------- 32 C 1 7.513913611114118e-01 7.513913611167009e-01 5.28910e-12 1.02918e-11 2 1.626107123100726e+00 1.626107123090533e+00 1.01932e-11 7.53635e-11 3 5.271626127827987e+00 5.271626127823525e+00 4.46132e-12 1.62164e-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 = ----------------------- = 2.28910e-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 5.120228101539698e+00 2.77733e-12 1.48912e-11 2 3.393276701829042e+00 3.393276701828244e+00 7.98028e-13 3.00822e-11 3 7.166916026352578e+00 7.166916026359565e+00 6.98641e-12 3.84626e-11 ----------------------------------------------------------------------------------------------------- 2 Si 1 -4.319794633861901e+00 -4.319794633866224e+00 4.32365e-12 1.86242e-11 2 6.778729509997539e-01 6.778729510007738e-01 1.01996e-12 2.03024e-11 3 1.210930928180508e+00 1.210930928182861e+00 2.35234e-12 2.99629e-11 ----------------------------------------------------------------------------------------------------- 3 Si 1 -3.311238562823384e+00 -3.311238562824399e+00 1.01430e-12 1.13061e-10 2 1.767538326347310e+00 1.767538326347438e+00 1.28342e-13 1.67291e-11 3 -3.372786151738698e+00 -3.372786151736033e+00 2.66454e-12 1.53879e-10 ----------------------------------------------------------------------------------------------------- 4 Si 1 3.253108951815418e+00 3.253108951830540e+00 1.51226e-11 4.97820e-11 2 9.138613240048959e-01 9.138613240037740e-01 1.12199e-12 3.68746e-11 3 3.277580016496399e+00 3.277580016497212e+00 8.13127e-13 1.17575e-10 ----------------------------------------------------------------------------------------------------- 5 Si 1 5.138793606883010e+00 5.138793606884765e+00 1.75504e-12 2.57305e-11 2 3.987408671932655e+00 3.987408671932302e+00 3.53051e-13 2.47344e-11 3 6.768210195901059e+00 6.768210195905453e+00 4.39471e-12 1.90328e-11 ----------------------------------------------------------------------------------------------------- 6 Si 1 -4.097705283998383e+00 -4.097705283999226e+00 8.43769e-13 3.06510e-12 2 -2.640829895487638e+00 -2.640829895493215e+00 5.57732e-12 3.56906e-11 3 3.615053971407697e+00 3.615053971407366e+00 3.30846e-13 9.43601e-12 ----------------------------------------------------------------------------------------------------- 7 Si 1 -2.577972054465171e+00 -2.577972054485353e+00 2.01825e-11 2.76130e-11 2 3.485233497210870e+00 3.485233497202791e+00 8.07931e-12 1.63536e-11 3 -2.290945757187036e+00 -2.290945757187863e+00 8.27338e-13 1.06576e-10 ----------------------------------------------------------------------------------------------------- 8 Si 1 -1.382287037615318e+00 -1.382287037594524e+00 2.07938e-11 7.78178e-11 2 1.210098497533004e-02 1.210098496443789e-02 1.08922e-11 2.16044e-11 3 -4.549195058560623e-01 -4.549195058503427e-01 5.71959e-12 1.52613e-10 ----------------------------------------------------------------------------------------------------- 9 Si 1 5.307644572263460e+00 5.307644572262677e+00 7.83373e-13 2.26406e-11 2 1.621423263354708e+00 1.621423263361017e+00 6.30829e-12 1.30753e-11 3 3.242218557070053e+00 3.242218557072307e+00 2.25375e-12 1.22093e-11 ----------------------------------------------------------------------------------------------------- 10 Si 1 -3.758917851459276e+00 -3.758917851458417e+00 8.58869e-13 5.49099e-11 2 -5.561909586165817e+00 -5.561909586159111e+00 6.70575e-12 1.53166e-11 3 6.201846955656844e+00 6.201846955654414e+00 2.43006e-12 6.21529e-11 ----------------------------------------------------------------------------------------------------- 11 Si 1 -5.260728464901328e+00 -5.260728464907475e+00 6.14708e-12 1.57840e-10 2 2.731999226749061e+00 2.731999226746620e+00 2.44160e-12 7.76863e-11 3 -2.899232832979876e+00 -2.899232832986897e+00 7.02105e-12 1.53437e-11 ----------------------------------------------------------------------------------------------------- 12 Si 1 7.087336623516650e+00 7.087336623521078e+00 4.42846e-12 3.67093e-11 2 -6.327038939233703e+00 -6.327038939248376e+00 1.46727e-11 5.94502e-11 3 -4.486303028589720e+00 -4.486303028587057e+00 2.66365e-12 7.03535e-11 ----------------------------------------------------------------------------------------------------- 13 Si 1 -7.897728093148417e+00 -7.897728093136975e+00 1.14415e-11 9.47065e-12 2 4.720610143740858e-01 4.720610143684624e-01 5.62345e-12 7.70584e-12 3 -3.424633101104135e+00 -3.424633101099387e+00 4.74865e-12 9.57412e-12 ----------------------------------------------------------------------------------------------------- 14 Si 1 -1.100575504364702e+00 -1.100575504363836e+00 8.65530e-13 5.91380e-10 * 2 -1.166142504014258e-01 -1.166142504014408e-01 1.49464e-14 7.18417e-12 3 1.177044965756959e+00 1.177044965754570e+00 2.38853e-12 5.20894e-12 ----------------------------------------------------------------------------------------------------- 15 Si 1 5.408514972671228e+00 5.408514972653518e+00 1.77103e-11 2.01674e-10 2 -2.919163684706197e+00 -2.919163684699162e+00 7.03526e-12 8.62843e-11 3 4.556462195280303e+00 4.556462195284039e+00 3.73568e-12 1.13802e-11 ----------------------------------------------------------------------------------------------------- 16 Si 1 -2.991247545011865e+00 -2.991247545006385e+00 5.47917e-12 5.31164e-10 * 2 3.082685736523944e+00 3.082685736520198e+00 3.74634e-12 7.33591e-12 3 3.292431975413331e-01 3.292431975384884e-01 2.84472e-12 1.62822e-10 ----------------------------------------------------------------------------------------------------- 17 Si 1 6.715821560734618e+00 6.715821560731690e+00 2.92832e-12 5.45235e-11 2 6.372852553876648e+00 6.372852553885700e+00 9.05231e-12 3.05675e-11 3 3.718307920572234e-01 3.718307920615224e-01 4.29901e-12 2.27250e-11 ----------------------------------------------------------------------------------------------------- 18 Si 1 -3.610347070168903e+00 -3.610347070165715e+00 3.18856e-12 7.60734e-11 2 -6.141735258066495e-01 -6.141735258153632e-01 8.71370e-12 6.39927e-11 3 1.010963483356908e+00 1.010963483356455e+00 4.52527e-13 1.38904e-09 * ----------------------------------------------------------------------------------------------------- 19 Si 1 -4.258449680064627e+00 -4.258449680066654e+00 2.02682e-12 2.98250e-11 2 -2.157374250535051e+00 -2.157374250539538e+00 4.48708e-12 1.08825e-10 3 -2.812043846040902e+00 -2.812043846047650e+00 6.74794e-12 1.05027e-10 ----------------------------------------------------------------------------------------------------- 20 Si 1 3.486193056104812e+00 3.486193056108216e+00 3.40394e-12 7.24483e-11 2 2.785849442523541e+00 2.785849442526091e+00 2.54952e-12 1.26912e-11 3 -5.687845584510582e+00 -5.687845584507843e+00 2.73914e-12 1.57940e-10 ----------------------------------------------------------------------------------------------------- 21 Si 1 1.347818524356851e+00 1.347818524353514e+00 3.33755e-12 3.02098e-11 2 2.490183843477706e+00 2.490183843484738e+00 7.03171e-12 2.74456e-11 3 1.932083839443195e+00 1.932083839437846e+00 5.34972e-12 6.35378e-11 ----------------------------------------------------------------------------------------------------- 22 Si 1 1.563371817459724e-01 1.563371817463671e-01 3.94740e-13 1.96154e-12 2 -6.574787662549018e+00 -6.574787662538300e+00 1.07176e-11 6.17808e-11 3 3.307339909610139e+00 3.307339909607379e+00 2.75957e-12 3.82303e-11 ----------------------------------------------------------------------------------------------------- 23 Si 1 -2.588390172335044e+00 -2.588390172336377e+00 1.33316e-12 2.50706e-11 2 5.427053792619445e+00 5.427053792619343e+00 1.02141e-13 3.02993e-11 3 -6.808057334750193e+00 -6.808057334723637e+00 2.65556e-11 4.53211e-11 ----------------------------------------------------------------------------------------------------- 24 Si 1 8.419500917244807e-01 8.419500917139420e-01 1.05387e-11 2.69117e-11 2 4.634218407549217e+00 4.634218407542256e+00 6.96154e-12 1.24882e-10 3 -2.354033241436913e+00 -2.354033241439577e+00 2.66409e-12 2.62488e-11 ----------------------------------------------------------------------------------------------------- 25 Si 1 4.505350506099204e+00 4.505350506095334e+00 3.86979e-12 1.23767e-10 2 -5.803948460371637e+00 -5.803948460364099e+00 7.53797e-12 3.68230e-11 3 -4.043420370547777e+00 -4.043420370549859e+00 2.08189e-12 2.38779e-10 ----------------------------------------------------------------------------------------------------- 26 Si 1 -3.629061818574677e+00 -3.629061818570484e+00 4.19265e-12 9.71840e-11 2 1.749303996418989e+00 1.749303996432044e+00 1.30558e-11 1.37278e-10 3 1.391800484262253e+00 1.391800484275234e+00 1.29809e-11 1.76421e-11 ----------------------------------------------------------------------------------------------------- 27 Si 1 -4.391848132897709e+00 -4.391848132907165e+00 9.45555e-12 2.67670e-11 2 -2.226603210225140e+00 -2.226603210223391e+00 1.74927e-12 1.22700e-10 3 -4.100677594806275e+00 -4.100677594797438e+00 8.83738e-12 1.81020e-11 ----------------------------------------------------------------------------------------------------- 28 Si 1 5.522070175995070e+00 5.522070175994148e+00 9.22817e-13 8.50253e-11 2 -3.989027505616666e+00 -3.989027505632261e+00 1.55951e-11 5.50870e-11 3 -1.731960298193560e+00 -1.731960298188732e+00 4.82836e-12 1.73452e-11 ----------------------------------------------------------------------------------------------------- 29 Si 1 3.235136459327017e+00 3.235136459341803e+00 1.47864e-11 2.72106e-10 2 -2.626983972775147e+00 -2.626983972785768e+00 1.06208e-11 1.42914e-10 3 2.507994264235485e-01 2.507994264261083e-01 2.55984e-12 1.21393e-10 ----------------------------------------------------------------------------------------------------- 30 Si 1 -8.101502813242311e-01 -8.101502813195151e-01 4.71601e-12 3.25029e-12 2 -2.096098428771310e+00 -2.096098428779162e+00 7.85194e-12 5.11777e-11 3 -1.165424914182873e+00 -1.165424914170809e+00 1.20639e-11 1.30365e-10 ----------------------------------------------------------------------------------------------------- 31 Si 1 -4.228757944919027e+00 -4.228757944911423e+00 7.60458e-12 4.58655e-12 2 -4.392869421563380e-01 -4.392869421497440e-01 6.59400e-12 9.93841e-11 3 -1.300545528140787e+00 -1.300545528140916e+00 1.28786e-13 5.88509e-11 ----------------------------------------------------------------------------------------------------- 32 Si 1 3.088895747153697e+00 3.088895747153775e+00 7.77156e-14 1.15598e-10 2 -1.511083419965476e+00 -1.511083419962091e+00 3.38507e-12 4.13101e-11 3 1.122504145268375e+00 1.122504145271574e+00 3.19944e-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 -4.429385738588945e+00 2.78462e-11 8.96359e-11 2 -3.610794773847990e+00 -3.610794773860976e+00 1.29861e-11 2.88878e-09 3 -3.534850893418047e+00 -3.534850893265015e+00 1.53032e-10 2.70847e-09 ----------------------------------------------------------------------------------------------------- 2 Si 1 -2.343184890787960e+00 -2.343184891045603e+00 2.57644e-10 6.64624e-09 2 7.347020885370153e+00 7.347020885356623e+00 1.35296e-11 9.22437e-10 3 -3.205648073679431e+00 -3.205648073743715e+00 6.42837e-11 3.23625e-09 ----------------------------------------------------------------------------------------------------- 3 Si 1 -2.289248685915231e+00 -2.289248685731808e+00 1.83423e-10 5.40134e-09 2 1.429379579193597e+00 1.429379578546597e+00 6.47000e-10 4.60402e-09 3 1.248292546578046e+01 1.248292546630744e+01 5.26979e-10 9.57844e-10 ----------------------------------------------------------------------------------------------------- 4 C 1 5.572216077641707e+00 5.572216077712068e+00 7.03606e-11 2.90868e-09 2 6.551580070924273e+00 6.551580070607542e+00 3.16732e-10 9.99219e-10 3 3.207655128866616e+00 3.207655128897157e+00 3.05409e-11 1.07518e-09 ----------------------------------------------------------------------------------------------------- 5 Si 1 5.550590904500809e+00 5.550590904499294e+00 1.51523e-12 1.17484e-09 2 -8.100148891899799e+00 -8.100148891607635e+00 2.92165e-10 5.58392e-09 3 -8.044341551412042e+00 -8.044341550990133e+00 4.21910e-10 7.16025e-10 ----------------------------------------------------------------------------------------------------- 6 C 1 -9.400482639569676e-01 -9.400482634388624e-01 5.18105e-10 2.92045e-09 2 1.264353795205283e+00 1.264353795114719e+00 9.05640e-11 6.48727e-09 3 3.521894996170722e+00 3.521894996087616e+00 8.31064e-11 3.36253e-09 ----------------------------------------------------------------------------------------------------- 7 C 1 3.495802677492472e-01 3.495802683672655e-01 6.18018e-10 2.54853e-09 2 -1.582437382141413e+00 -1.582437382037981e+00 1.03432e-10 2.22159e-09 3 -8.285676151554764e-01 -8.285676150940942e-01 6.13822e-11 2.45060e-09 ----------------------------------------------------------------------------------------------------- 8 Si 1 -7.526544979739126e-01 -7.526544980724817e-01 9.85692e-11 1.30540e-09 2 7.226391246751295e+00 7.226391247415257e+00 6.63961e-10 1.90544e-09 3 8.922252728946257e+00 8.922252729100535e+00 1.54278e-10 1.51953e-09 ----------------------------------------------------------------------------------------------------- 9 C 1 3.611767844274600e+00 3.611767844216750e+00 5.78502e-11 1.50432e-09 2 -2.697196766223743e+00 -2.697196766212726e+00 1.10179e-11 6.65827e-10 3 4.755921984215343e-01 4.755921985451817e-01 1.23647e-10 1.55921e-11 ----------------------------------------------------------------------------------------------------- 10 Si 1 3.733771169699545e-01 3.733771176805301e-01 7.10576e-10 3.28768e-09 2 -8.095772962422069e-01 -8.095772966794681e-01 4.37261e-10 3.79963e-08 * 3 -1.811633719408361e+00 -1.811633717994077e+00 1.41428e-09 1.07930e-09 ----------------------------------------------------------------------------------------------------- 11 C 1 -3.948028211313099e+00 -3.948028212869578e+00 1.55648e-09 1.66621e-09 2 -5.081940596684008e+00 -5.081940596074170e+00 6.09838e-10 4.87407e-09 3 9.330093682476676e-01 9.330093684779597e-01 2.30292e-10 4.33868e-09 ----------------------------------------------------------------------------------------------------- 12 Si 1 -9.623513340788594e-01 -9.623513342126332e-01 1.33774e-10 4.95930e-09 2 4.169059974635914e+00 4.169059974279761e+00 3.56153e-10 1.39395e-09 3 -6.168262659085827e+00 -6.168262658714391e+00 3.71436e-10 2.20265e-09 ----------------------------------------------------------------------------------------------------- 13 C 1 1.125118320640175e+00 1.125118320808774e+00 1.68599e-10 1.65088e-09 2 1.226470910201157e+00 1.226470908428986e+00 1.77217e-09 2.19951e-09 3 -3.775126573062368e+00 -3.775126571418668e+00 1.64370e-09 1.08634e-08 ----------------------------------------------------------------------------------------------------- 14 Si 1 -2.398893606218402e+00 -2.398893606026689e+00 1.91713e-10 7.57340e-10 2 -1.823607013279014e+00 -1.823607013309820e+00 3.08065e-11 2.01842e-09 3 -1.333632835098528e+00 -1.333632834793257e+00 3.05271e-10 1.56227e-09 ----------------------------------------------------------------------------------------------------- 15 Si 1 3.424633477508195e+00 3.424633477641816e+00 1.33621e-10 8.35399e-10 2 -3.311077883467980e+00 -3.311077883562658e+00 9.46780e-11 7.96341e-09 3 -5.865714993910704e+00 -5.865714994152096e+00 2.41393e-10 9.11860e-09 ----------------------------------------------------------------------------------------------------- 16 Si 1 -2.954605375528089e+00 -2.954605375289627e+00 2.38462e-10 5.89612e-09 2 8.914382886314359e+00 8.914382887549460e+00 1.23510e-09 2.95691e-09 3 2.054544108902513e+00 2.054544108811632e+00 9.08811e-11 2.06423e-09 ----------------------------------------------------------------------------------------------------- 17 C 1 3.558484338900397e+00 3.558484338752201e+00 1.48195e-10 5.85752e-10 2 -4.337428375585369e-01 -4.337428376824420e-01 1.23905e-10 2.99374e-10 3 -3.713087272682360e+00 -3.713087272570976e+00 1.11384e-10 5.84476e-10 ----------------------------------------------------------------------------------------------------- 18 C 1 -3.798207460969324e+00 -3.798207462217940e+00 1.24862e-09 1.12055e-08 2 -7.131160153705214e+00 -7.131160154496628e+00 7.91414e-10 3.72273e-08 * 3 5.042152898338379e+00 5.042152897832650e+00 5.05730e-10 3.97579e-09 ----------------------------------------------------------------------------------------------------- 19 C 1 7.398962524293021e-01 7.398962524249078e-01 4.39437e-12 6.50675e-11 2 4.573404652507292e+00 4.573404652499224e+00 8.06821e-12 8.85727e-11 3 -4.525613767339923e+00 -4.525613767342804e+00 2.88125e-12 1.39056e-10 ----------------------------------------------------------------------------------------------------- 20 C 1 -1.504780179516252e-01 -1.504780180366724e-01 8.50471e-11 9.88087e-09 2 -3.769764806285597e+00 -3.769764806132712e+00 1.52884e-10 7.02544e-09 3 -3.197191159961561e+00 -3.197191159395102e+00 5.66459e-10 1.32720e-08 ----------------------------------------------------------------------------------------------------- 21 C 1 2.206334902933893e+00 2.206334903290052e+00 3.56159e-10 2.74918e-08 * 2 1.680215414613905e+00 1.680215414279443e+00 3.34462e-10 3.73592e-09 3 -4.070934629638165e-01 -4.070934627924852e-01 1.71331e-10 9.86236e-09 ----------------------------------------------------------------------------------------------------- 22 Si 1 2.099060122236834e+00 2.099060121694200e+00 5.42634e-10 4.72275e-09 2 5.429342878299483e+00 5.429342879152511e+00 8.53028e-10 1.26206e-09 3 7.967028245203687e-01 7.967028253663497e-01 8.45981e-10 1.73229e-08 ----------------------------------------------------------------------------------------------------- 23 Si 1 -9.460036478894382e+00 -9.460036481377951e+00 2.48357e-09 6.02583e-09 2 -1.879480818161554e+00 -1.879480818488179e+00 3.26625e-10 1.28647e-09 3 -3.711974507136053e-01 -3.711974506247554e-01 8.88499e-11 2.33492e-09 ----------------------------------------------------------------------------------------------------- 24 C 1 6.846250374867995e+00 6.846250374644084e+00 2.23911e-10 2.71909e-08 * 2 7.099297447255389e+00 7.099297447028056e+00 2.27333e-10 1.13913e-08 3 -6.592321202615956e-02 -6.592321240340758e-02 3.77248e-10 7.24667e-09 ----------------------------------------------------------------------------------------------------- 25 Si 1 -8.946150052079522e+00 -8.946150047704545e+00 4.37498e-09 2.84343e-08 * 2 -7.891491122250726e+00 -7.891491128691216e+00 6.44049e-09 1.55082e-08 3 -5.115165795106035e+00 -5.115165795408680e+00 3.02644e-10 7.96891e-09 ----------------------------------------------------------------------------------------------------- 26 C 1 9.695199044282264e+00 9.695199044158350e+00 1.23913e-10 5.34390e-09 2 3.205306015619055e+00 3.205306015445680e+00 1.73375e-10 3.07906e-09 3 5.870848161560743e+00 5.870848161699310e+00 1.38567e-10 3.53450e-09 ----------------------------------------------------------------------------------------------------- 27 Si 1 1.452405054043679e+01 1.452405054050720e+01 7.04077e-11 9.27959e-09 2 -1.280848294973502e+00 -1.280848294836754e+00 1.36748e-10 1.52425e-09 3 8.885971369857304e+00 8.885971369609251e+00 2.48052e-10 2.16404e-09 ----------------------------------------------------------------------------------------------------- 28 Si 1 -2.304958113256527e-01 -2.304958112235626e-01 1.02090e-10 2.49751e-09 2 4.322720504222384e+00 4.322720504245346e+00 2.29621e-11 1.56600e-09 3 2.386064553674107e+00 2.386064553948887e+00 2.74780e-10 1.49577e-09 ----------------------------------------------------------------------------------------------------- 29 Si 1 1.451220730651389e+00 1.451220730529524e+00 1.21865e-10 2.58794e-08 * 2 -6.739729004625231e+00 -6.739729003387114e+00 1.23812e-09 2.33748e-09 3 6.490447800830826e+00 6.490447801067002e+00 2.36176e-10 2.33503e-09 ----------------------------------------------------------------------------------------------------- 30 C 1 -2.382484508127014e+00 -2.382484507886649e+00 2.40365e-10 1.43839e-09 2 -9.628356593143694e-02 -9.628356530605658e-02 6.25380e-10 1.61396e-09 3 -4.574594817130160e-01 -4.574594820332129e-01 3.20197e-10 1.90034e-09 ----------------------------------------------------------------------------------------------------- 31 C 1 -7.624097363674887e+00 -7.624097363444232e+00 2.30655e-10 6.73402e-09 2 -9.263893840800629e+00 -9.263893840240032e+00 5.60597e-10 1.35745e-09 3 -3.087422776374448e+00 -3.087422776387178e+00 1.27303e-11 3.37643e-09 ----------------------------------------------------------------------------------------------------- 32 C 1 -7.517430018667523e+00 -7.517430018769669e+00 1.02146e-10 1.15751e-09 2 1.064248786965067e+00 1.064248786970563e+00 5.49583e-12 4.10671e-10 3 -5.562128311005784e+00 -5.562128310982887e+00 2.28972e-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.