!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! VERIFICATION CHECK: vc-forces-numerical-derivative !!!!! !!!!! !!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Description: Comparison of the analytical forces obtained from the model with forces computed by numerical differentiation using Richardson extrapolation for a randomly distorted non-periodic structure based off the equilibrium face-centered cubic (fcc) structure. Separate configurations are tested for each species supported by the model, as well as one containing a random distribution of all species. Configurations used for testing are provided as auxiliary files. Author: Ellad Tadmor ----------------------------------------------------------------------------------------------------- Results for KIM Model : Sim_LAMMPS_EDIP_JiangMorganSzlufarska_2012_SiC__SM_435704953434_000 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 = 2.90533733368 | (Configuration in file "config-C.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 C 1 6.824787398707358e+00 6.824787398711799e+00 4.44089e-12 8.19425e-11 2 9.307021081520054e+00 9.307021081500190e+00 1.98632e-11 3.78684e-11 3 1.601035185503862e+01 1.601035185504079e+01 2.16716e-12 9.88010e-12 ----------------------------------------------------------------------------------------------------- 2 C 1 3.586395816621215e+00 3.586395816638868e+00 1.76534e-11 2.79348e-10 2 -6.074770752159491e+00 -6.074770752163887e+00 4.39559e-12 1.49565e-10 3 8.509463058309287e-01 8.509463058314249e-01 4.96270e-13 1.62038e-10 ----------------------------------------------------------------------------------------------------- 3 C 1 -5.742993049261121e+00 -5.742993049266849e+00 5.72786e-12 3.47065e-09 * 2 8.767499748318408e-01 8.767499748364154e-01 4.57456e-12 2.03518e-10 3 -1.032678854047938e+01 -1.032678854048148e+01 2.09610e-12 6.07127e-10 ----------------------------------------------------------------------------------------------------- 4 C 1 -5.599166632643054e-01 -5.599166632244283e-01 3.98771e-11 8.20948e-11 2 -1.086736017792040e+01 -1.086736017793797e+01 1.75646e-11 1.90903e-10 3 -8.823995807915962e+00 -8.823995807912951e+00 3.01092e-12 2.24913e-10 ----------------------------------------------------------------------------------------------------- 5 C 1 -1.298703149462234e+01 -1.298703149462621e+01 3.86358e-12 1.84171e-10 2 4.841448738920287e+00 4.841448738920737e+00 4.49418e-13 6.69393e-11 3 7.650592948640861e+00 7.650592948641923e+00 1.06226e-12 2.58034e-10 ----------------------------------------------------------------------------------------------------- 6 C 1 -1.039182469146698e+00 -1.039182469142488e+00 4.21019e-12 1.50401e-10 2 -5.092600654583555e+00 -5.092600654579944e+00 3.61133e-12 1.76801e-11 3 8.352725521195694e+00 8.352725521174534e+00 2.11600e-11 2.98090e-10 ----------------------------------------------------------------------------------------------------- 7 C 1 -3.694803911238724e+00 -3.694803911218078e+00 2.06466e-11 3.49039e-10 2 7.449526061008061e+00 7.449526061006734e+00 1.32694e-12 7.23128e-11 3 -4.085837294044652e+00 -4.085837294025927e+00 1.87255e-11 2.84907e-10 ----------------------------------------------------------------------------------------------------- 8 C 1 8.795673961509692e+00 8.795673961504638e+00 5.05374e-12 1.50102e-10 2 -8.384335398831828e+00 -8.384335398751348e+00 8.04796e-11 4.57865e-10 3 -8.933686562011101e-01 -8.933686561163156e-01 8.47945e-11 1.63477e-11 ----------------------------------------------------------------------------------------------------- 9 C 1 6.437679115965105e+00 6.437679115966045e+00 9.39693e-13 8.83063e-11 2 1.173184447399657e+01 1.173184447401733e+01 2.07621e-11 5.12639e-11 3 1.128900290733113e+01 1.128900290730443e+01 2.66951e-11 2.59325e-10 ----------------------------------------------------------------------------------------------------- 10 C 1 -7.726012414966158e+00 -7.726012414972363e+00 6.20481e-12 6.72209e-11 2 -7.007147564571268e+00 -7.007147564567613e+00 3.65485e-12 2.48788e-11 3 4.014199252396672e+00 4.014199252395271e+00 1.40066e-12 4.75850e-11 ----------------------------------------------------------------------------------------------------- 11 C 1 -1.559297046733326e+01 -1.559297046735676e+01 2.35048e-11 3.20846e-10 2 4.280813678138339e-01 4.280813678150568e-01 1.22297e-12 1.14654e-10 3 -9.925132512519507e+00 -9.925132512506856e+00 1.26512e-11 5.83649e-10 ----------------------------------------------------------------------------------------------------- 12 C 1 4.158803728093534e+00 4.158803728105782e+00 1.22480e-11 1.13562e-10 2 -9.055105409221659e+00 -9.055105409257834e+00 3.61755e-11 3.30909e-10 3 -5.149383246424113e+00 -5.149383246426376e+00 2.26219e-12 4.79803e-11 ----------------------------------------------------------------------------------------------------- 13 C 1 1.632691748251538e+00 1.632691748248493e+00 3.04512e-12 7.24818e-11 2 2.617989948519773e+00 2.617989948512297e+00 7.47624e-12 7.99214e-11 3 -1.002874538097931e+01 -1.002874538098612e+01 6.81233e-12 3.96820e-11 ----------------------------------------------------------------------------------------------------- 14 C 1 -4.565496008276316e+00 -4.565496008275724e+00 5.92415e-13 8.46736e-11 2 -8.023279030226011e+00 -8.023279030241639e+00 1.56284e-11 4.95657e-11 3 3.920618300704148e+00 3.920618300697684e+00 6.46372e-12 1.73630e-11 ----------------------------------------------------------------------------------------------------- 15 C 1 9.275119485234464e+00 9.275119485218545e+00 1.59197e-11 6.15987e-11 2 -9.457597411889574e-01 -9.457597411776179e-01 1.13396e-11 2.79544e-10 3 -6.995823281951989e+00 -6.995823281971913e+00 1.99245e-11 3.10272e-10 ----------------------------------------------------------------------------------------------------- 16 C 1 1.454549973550580e+00 1.454549973539282e+00 1.12979e-11 1.91403e-10 2 3.002769175518867e+00 3.002769175490783e+00 2.80838e-11 4.91540e-11 3 -1.317468989628765e+01 -1.317468989629527e+01 7.61524e-12 1.42252e-10 ----------------------------------------------------------------------------------------------------- 17 C 1 1.768007971685025e+01 1.768007971685219e+01 1.94333e-12 4.41212e-11 2 8.903414397527692e+00 8.903414397530240e+00 2.54730e-12 1.75966e-10 3 5.945616029033537e+00 5.945616029032059e+00 1.47793e-12 4.48622e-10 ----------------------------------------------------------------------------------------------------- 18 C 1 -7.094713336566147e+00 -7.094713336578767e+00 1.26201e-11 3.09095e-10 2 -5.255246873043789e+00 -5.255246873088643e+00 4.48539e-11 3.31518e-10 3 1.261838114027045e+01 1.261838114024787e+01 2.25757e-11 6.83649e-11 ----------------------------------------------------------------------------------------------------- 19 C 1 -7.874263743068904e+00 -7.874263743070258e+00 1.35358e-12 3.52935e-10 2 1.401029553888554e+01 1.401029553888235e+01 3.18856e-12 1.37129e-10 3 -5.562625736429918e+00 -5.562625736407726e+00 2.21920e-11 1.63848e-10 ----------------------------------------------------------------------------------------------------- 20 C 1 1.155384276434255e+01 1.155384276432629e+01 1.62590e-11 8.76810e-12 2 -1.207773094930554e+01 -1.207773094930390e+01 1.64668e-12 2.08297e-10 3 -1.420399610737711e+01 -1.420399610736247e+01 1.46425e-11 8.00036e-11 ----------------------------------------------------------------------------------------------------- 21 C 1 1.449720333831774e+01 1.449720333833709e+01 1.93516e-11 1.47335e-10 2 7.825533807658964e+00 7.825533807649527e+00 9.43690e-12 4.70307e-10 3 5.929212241248081e+00 5.929212241225026e+00 2.30544e-11 1.62149e-10 ----------------------------------------------------------------------------------------------------- 22 C 1 -5.511324960895770e+00 -5.511324960861214e+00 3.45564e-11 1.90993e-10 2 -8.433090084052766e+00 -8.433090084042600e+00 1.01661e-11 3.99734e-11 3 8.308344971301871e+00 8.308344971341787e+00 3.99165e-11 8.58620e-11 ----------------------------------------------------------------------------------------------------- 23 C 1 -7.845279628560452e+00 -7.845279628591921e+00 3.14690e-11 1.81424e-10 2 4.054441267538030e+00 4.054441267549264e+00 1.12346e-11 6.96339e-10 3 -1.701171268963164e+01 -1.701171268963024e+01 1.39977e-12 2.18634e-11 ----------------------------------------------------------------------------------------------------- 24 C 1 -6.103699024604666e+00 -6.103699024600608e+00 4.05809e-12 1.14195e-10 2 -7.439686927637242e+00 -7.439686927640178e+00 2.93632e-12 4.13642e-11 3 -7.002153237867539e+00 -7.002153237880040e+00 1.25011e-11 7.73106e-11 ----------------------------------------------------------------------------------------------------- 25 C 1 5.255938902105417e+00 5.255938902040842e+00 6.45759e-11 9.79066e-11 2 9.028947679715085e+00 9.028947679678138e+00 3.69464e-11 4.70944e-10 3 -3.128500245915875e-01 -3.128500245837362e-01 7.85128e-12 1.83779e-10 ----------------------------------------------------------------------------------------------------- 26 C 1 -1.173922168051173e+01 -1.173922168051297e+01 1.23279e-12 1.08487e-10 2 -7.141922851558548e-01 -7.141922851775400e-01 2.16852e-11 1.44159e-10 3 1.733170285681506e+01 1.733170285677741e+01 3.76552e-11 3.68569e-10 ----------------------------------------------------------------------------------------------------- 27 C 1 3.794790482865317e-01 3.794790482930472e-01 6.51557e-12 1.57126e-10 2 6.232936825598849e+00 6.232936825603342e+00 4.49241e-12 1.03549e-10 3 -5.097351301473191e+00 -5.097351301460369e+00 1.28217e-11 1.50383e-10 ----------------------------------------------------------------------------------------------------- 28 C 1 3.510488550139177e+00 3.510488550151803e+00 1.26263e-11 1.21017e-10 2 -3.787365138196318e+00 -3.787365138202269e+00 5.95124e-12 8.57185e-11 3 -4.820624951196918e+00 -4.820624951189554e+00 7.36389e-12 4.63265e-11 ----------------------------------------------------------------------------------------------------- 29 C 1 8.964482240452975e+00 8.964482240459290e+00 6.31495e-12 1.04317e-10 2 4.715790401448931e+00 4.715790401428577e+00 2.03544e-11 1.52400e-10 3 2.126472435354782e+01 2.126472435355094e+01 3.12284e-12 1.55147e-10 ----------------------------------------------------------------------------------------------------- 30 C 1 1.755457228200527e+00 1.755457228216186e+00 1.56593e-11 6.27425e-11 2 -3.345180311952764e+00 -3.345180311976124e+00 2.33604e-11 1.84474e-10 3 1.034791543319753e+01 1.034791543322120e+01 2.36700e-11 3.29065e-10 ----------------------------------------------------------------------------------------------------- 31 C 1 -7.401914221083959e+00 -7.401914221083818e+00 1.40332e-13 5.76605e-11 2 9.218449236017193e+00 9.218449236014125e+00 3.06777e-12 6.64908e-11 3 -5.755309172923145e+00 -5.755309172910905e+00 1.22400e-11 1.27496e-10 ----------------------------------------------------------------------------------------------------- 32 C 1 -2.838499432280885e-01 -2.838499432094331e-01 1.86555e-11 7.76687e-10 2 -7.742388678472129e+00 -7.742388678450327e+00 2.18021e-11 4.11209e-11 3 -4.663946278257677e+00 -4.663946278276432e+00 1.87557e-11 5.86067e-10 ----------------------------------------------------------------------------------------------------- * 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 = 8, direction = 3: |F_model - F_numer| error = ----------------------- = 9.49155e-11 max{|F_numer|, eps} Comparison of analytical forces obtained from the model, the force computed as a numerical derivative of the energy, the difference between them, and the uncertainty in the numerical estimate of the force. The computed equilibrium lattice constant for the crystal (a0) is given in the heading. MONOATOMIC STRUCTURE -- Species = Si | a0 = 3.93934345245 | (Configuration in file "config-Si.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Si 1 1.764101478364094e+00 1.764101478380429e+00 1.63354e-11 1.72543e-10 2 2.733589828380029e+00 2.733589828390033e+00 1.00040e-11 1.04268e-11 3 1.366496193482299e+00 1.366496193479915e+00 2.38409e-12 6.88318e-11 ----------------------------------------------------------------------------------------------------- 2 Si 1 -4.850660796852508e-01 -4.850660795944242e-01 9.08266e-11 8.30588e-11 2 -1.174996279001105e+00 -1.174996279015015e+00 1.39102e-11 4.81899e-11 3 -6.708822782863630e-01 -6.708822782674334e-01 1.89296e-11 4.40814e-11 ----------------------------------------------------------------------------------------------------- 3 Si 1 1.068112011406851e+01 1.068112011406825e+01 2.59348e-13 2.78849e-10 2 -1.653788383045472e-01 -1.653788382979170e-01 6.63014e-12 4.96528e-11 3 -2.709873553019798e+00 -2.709873553124402e+00 1.04604e-10 1.60420e-10 ----------------------------------------------------------------------------------------------------- 4 Si 1 -3.221039661588649e+00 -3.221039661591974e+00 3.32534e-12 1.18556e-10 2 8.234469992930835e-01 8.234469992864879e-01 6.59561e-12 3.71920e-11 3 -4.192856596170439e+00 -4.192856596160231e+00 1.02078e-11 5.03021e-10 ----------------------------------------------------------------------------------------------------- 5 Si 1 6.963299267631881e+00 6.963299267621192e+00 1.06892e-11 2.40803e-10 2 1.250637980447278e+01 1.250637980450657e+01 3.37899e-11 1.93424e-10 3 6.181880213896920e+00 6.181880213895936e+00 9.84102e-13 1.68089e-10 ----------------------------------------------------------------------------------------------------- 6 Si 1 -8.306693977411685e+00 -8.306693977413913e+00 2.22755e-12 1.42226e-09 * 2 -1.088841963423706e+01 -1.088841963423864e+01 1.58096e-12 2.12257e-10 3 5.622947785154607e+00 5.622947785202574e+00 4.79670e-11 2.48576e-10 ----------------------------------------------------------------------------------------------------- 7 Si 1 -8.361848451083398e+00 -8.361848451080734e+00 2.66454e-12 5.40368e-11 2 8.313611740019066e+00 8.313611739995885e+00 2.31815e-11 2.17870e-11 3 2.308672011512832e-01 2.308672011323531e-01 1.89302e-11 2.04057e-11 ----------------------------------------------------------------------------------------------------- 8 Si 1 -1.482900921103324e+00 -1.482900921127863e+00 2.45393e-11 7.78759e-11 2 -8.633578813542629e+00 -8.633578813576449e+00 3.38201e-11 3.50751e-10 3 -5.863127310967513e+00 -5.863127311078399e+00 1.10886e-10 4.32848e-10 ----------------------------------------------------------------------------------------------------- 9 Si 1 5.187851254133408e+00 5.187851254138002e+00 4.59366e-12 1.45892e-11 2 5.576895249124916e+00 5.576895249121812e+00 3.10330e-12 5.02176e-11 3 1.926447062644003e+00 1.926447062659048e+00 1.50442e-11 2.41356e-10 ----------------------------------------------------------------------------------------------------- 10 Si 1 -9.662257397040868e+00 -9.662257397020655e+00 2.02132e-11 9.04823e-11 2 -8.496478773264659e+00 -8.496478773256882e+00 7.77689e-12 8.53806e-11 3 6.848690658109895e+00 6.848690658108656e+00 1.23901e-12 8.33795e-11 ----------------------------------------------------------------------------------------------------- 11 Si 1 -2.248663934002414e+00 -2.248663934011236e+00 8.82228e-12 2.06941e-10 2 5.921819020183387e+00 5.921819020192972e+00 9.58522e-12 2.62560e-10 3 -7.086033082464319e+00 -7.086033082485629e+00 2.13101e-11 5.47231e-10 ----------------------------------------------------------------------------------------------------- 12 Si 1 7.742116924746019e+00 7.742116924744757e+00 1.26121e-12 7.37463e-11 2 -3.425154944664929e+00 -3.425154944665171e+00 2.41585e-13 6.56746e-11 3 -4.094169109531255e+00 -4.094169109530822e+00 4.33431e-13 3.79199e-11 ----------------------------------------------------------------------------------------------------- 13 Si 1 8.577817339506005e+00 8.577817339506398e+00 3.92575e-13 1.88651e-09 * 2 6.122652627230472e+00 6.122652627222652e+00 7.81952e-12 1.03037e-10 3 1.046822831494375e+01 1.046822831490802e+01 3.57279e-11 1.07253e-10 ----------------------------------------------------------------------------------------------------- 14 Si 1 -7.341384881092898e+00 -7.341384881094744e+00 1.84652e-12 4.73263e-10 2 -5.816186554411966e+00 -5.816186554400521e+00 1.14451e-11 3.17532e-10 3 1.043224101137530e+01 1.043224101138337e+01 8.06466e-12 1.64226e-09 * ----------------------------------------------------------------------------------------------------- 15 Si 1 -5.753805223439927e+00 -5.753805223402049e+00 3.78781e-11 6.15655e-10 2 -5.416774078550791e-01 -5.416774077915290e-01 6.35502e-11 7.43443e-11 3 -3.267786589867455e+00 -3.267786590027568e+00 1.60113e-10 7.11400e-10 ----------------------------------------------------------------------------------------------------- 16 Si 1 7.373552262156787e+00 7.373552262181289e+00 2.45022e-11 3.35721e-10 2 -7.906521515800659e+00 -7.906521515788313e+00 1.23457e-11 3.51061e-11 3 -6.451817430825492e+00 -6.451817430850852e+00 2.53602e-11 2.97475e-10 ----------------------------------------------------------------------------------------------------- 17 Si 1 2.723781407085686e-02 2.723781407499904e-02 4.14219e-12 9.13779e-11 2 1.627391870122595e-01 1.627391870137669e-01 1.50735e-12 1.06803e-10 3 1.595062740546837e+01 1.595062740547872e+01 1.03526e-11 1.55538e-11 ----------------------------------------------------------------------------------------------------- 18 Si 1 -2.529651304387861e-01 -2.529651304962823e-01 5.74962e-11 7.68096e-11 2 2.475144786997036e+00 2.475144787021663e+00 2.46274e-11 6.82023e-11 3 2.113910344725221e+00 2.113910344712459e+00 1.27622e-11 1.40333e-10 ----------------------------------------------------------------------------------------------------- 19 Si 1 -1.250141060960953e+01 -1.250141060962018e+01 1.06439e-11 3.28555e-11 2 8.573318369769233e+00 8.573318369762029e+00 7.20313e-12 1.04379e-10 3 -7.958992400908910e+00 -7.958992400911002e+00 2.09255e-12 2.39755e-11 ----------------------------------------------------------------------------------------------------- 20 Si 1 7.601804369089114e+00 7.601804369081498e+00 7.61613e-12 3.69304e-10 2 -1.181602093712264e+01 -1.181602093709693e+01 2.57181e-11 1.74893e-10 3 -4.516213059157340e+00 -4.516213059164745e+00 7.40474e-12 9.97709e-11 ----------------------------------------------------------------------------------------------------- 21 Si 1 5.231649295599563e+00 5.231649295628888e+00 2.93259e-11 4.82104e-10 2 -2.348915236662356e+00 -2.348915236703288e+00 4.09313e-11 2.89306e-10 3 -5.383757297071257e+00 -5.383757297075407e+00 4.14957e-12 8.90203e-11 ----------------------------------------------------------------------------------------------------- 22 Si 1 -8.053997867383757e+00 -8.053997867343421e+00 4.03357e-11 6.15513e-10 2 6.710469989638814e+00 6.710469989714284e+00 7.54694e-11 2.79801e-10 3 4.916456812313592e+00 4.916456812297205e+00 1.63869e-11 1.28873e-10 ----------------------------------------------------------------------------------------------------- 23 Si 1 -3.911468741730646e+00 -3.911468741757024e+00 2.63785e-11 2.27926e-10 2 5.864217103979088e+00 5.864217103975442e+00 3.64686e-12 7.89173e-11 3 -1.550258225453041e+00 -1.550258225492868e+00 3.98264e-11 2.74849e-11 ----------------------------------------------------------------------------------------------------- 24 Si 1 1.257656507198769e+01 1.257656507198552e+01 2.16538e-12 4.96225e-11 2 2.471376612526077e+00 2.471376612552517e+00 2.64397e-11 4.14528e-10 3 -6.999639667394524e+00 -6.999639667372263e+00 2.22613e-11 1.04615e-10 ----------------------------------------------------------------------------------------------------- 25 Si 1 -1.938038763580701e-01 -1.938038763464782e-01 1.15919e-11 1.54399e-10 2 5.609811937567324e+00 5.609811937600752e+00 3.34284e-11 5.86303e-10 3 5.928203171257689e+00 5.928203171269877e+00 1.21885e-11 1.94574e-10 ----------------------------------------------------------------------------------------------------- 26 Si 1 -8.305611892670370e+00 -8.305611892671138e+00 7.67386e-13 5.37401e-10 2 -6.107834453975278e+00 -6.107834453973958e+00 1.31983e-12 1.43303e-10 3 7.930119671300346e+00 7.930119671297171e+00 3.17524e-12 7.87476e-09 * ----------------------------------------------------------------------------------------------------- 27 Si 1 4.373843162488339e+00 4.373843162513200e+00 2.48610e-11 7.57741e-11 2 7.937476119216072e+00 7.937476119205479e+00 1.05933e-11 5.55902e-11 3 -4.731657838684419e+00 -4.731657838631323e+00 5.30962e-11 3.11255e-10 ----------------------------------------------------------------------------------------------------- 28 Si 1 9.524631630616645e+00 9.524631630613523e+00 3.12106e-12 3.24807e-10 2 -1.797863766385939e+00 -1.797863766376156e+00 9.78306e-12 1.22043e-10 3 -6.390138504903331e+00 -6.390138504910659e+00 7.32836e-12 9.54081e-11 ----------------------------------------------------------------------------------------------------- 29 Si 1 4.964609961170094e+00 4.964609961198644e+00 2.85496e-11 2.81724e-10 2 1.875270561668211e+00 1.875270561727786e+00 5.95755e-11 1.91447e-10 3 2.383975004903875e+00 2.383975004875963e+00 2.79115e-11 4.49426e-10 ----------------------------------------------------------------------------------------------------- 30 Si 1 -8.672282506436865e+00 -8.672282506452026e+00 1.51612e-11 8.86065e-11 2 -1.677726935606844e+00 -1.677726935600924e+00 5.91971e-12 7.81755e-11 3 3.620097730821363e+00 3.620097730832932e+00 1.15694e-11 7.11271e-11 ----------------------------------------------------------------------------------------------------- 31 Si 1 -7.923265658112487e+00 -7.923265658118471e+00 5.98455e-12 5.28080e-10 2 -5.349166538230878e+00 -5.349166538220157e+00 1.07212e-11 3.96971e-11 3 -5.252942132632704e+00 -5.252942132669362e+00 3.66578e-11 6.59033e-10 ----------------------------------------------------------------------------------------------------- 32 Si 1 4.088266863559927e+00 4.088266863534646e+00 2.52811e-11 2.14587e-10 2 -7.532299308011275e+00 -7.532299308013606e+00 2.33058e-12 2.16535e-10 3 -8.801043504210352e+00 -8.801043504200182e+00 1.01696e-11 9.30118e-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 = 18, direction = 1: |F_model - F_numer| error = ----------------------- = 2.27289e-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 = 3.24009708557 | (Configuration in file "config-CSi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Si 1 1.183950343333695e+01 1.183950343334205e+01 5.10170e-12 1.96181e-11 2 1.059840826942777e+01 1.059840826943291e+01 5.13545e-12 5.04325e-11 3 1.063352838576302e+01 1.063352838576228e+01 7.33635e-13 1.36032e-10 ----------------------------------------------------------------------------------------------------- 2 C 1 -7.027447997619142e+00 -7.027447997618937e+00 2.04281e-13 4.42748e-11 2 -1.911018231331374e-01 -1.911018231267513e-01 6.38609e-12 2.20806e-11 3 5.571602514745721e+00 5.571602514767307e+00 2.15863e-11 4.88036e-11 ----------------------------------------------------------------------------------------------------- 3 C 1 -3.653902329172576e+00 -3.653902329215155e+00 4.25793e-11 3.88773e-11 2 1.141339879282025e+00 1.141339879253971e+00 2.80547e-11 4.38029e-10 3 -7.410559022858472e+00 -7.410559022871059e+00 1.25873e-11 1.47251e-11 ----------------------------------------------------------------------------------------------------- 4 C 1 1.832683569912032e+00 1.832683569892878e+00 1.91538e-11 9.62832e-11 2 -2.664727113423496e+00 -2.664727113399485e+00 2.40106e-11 6.01217e-11 3 -6.573398823841241e+00 -6.573398823852999e+00 1.17586e-11 1.41135e-10 ----------------------------------------------------------------------------------------------------- 5 Si 1 -1.072466763776005e+01 -1.072466763776306e+01 3.00382e-12 1.33033e-10 2 2.166137454011456e+00 2.166137454008076e+00 3.37952e-12 3.96518e-11 3 -2.168306488059343e+00 -2.168306488062901e+00 3.55849e-12 7.44858e-11 ----------------------------------------------------------------------------------------------------- 6 C 1 3.457392231743272e+00 3.457392231748501e+00 5.22915e-12 2.96665e-11 2 -6.949736506306505e+00 -6.949736506289550e+00 1.69553e-11 1.63738e-10 3 6.757857583375219e-01 6.757857583052809e-01 3.22410e-11 3.17484e-10 ----------------------------------------------------------------------------------------------------- 7 Si 1 -6.395187680754999e-01 -6.395187680473925e-01 2.81074e-11 4.47614e-10 2 1.071540035547689e+00 1.071540035552863e+00 5.17320e-12 1.32532e-10 3 1.032626440622213e+01 1.032626440625677e+01 3.46407e-11 2.85425e-11 ----------------------------------------------------------------------------------------------------- 8 Si 1 -4.354478706263795e+00 -4.354478706268443e+00 4.64784e-12 2.22275e-10 2 -4.563689467438202e+00 -4.563689467438065e+00 1.36779e-13 2.09146e-10 3 -8.910761801128625e-01 -8.910761801057945e-01 7.06801e-12 5.07623e-11 ----------------------------------------------------------------------------------------------------- 9 C 1 8.201029614340243e+00 8.201029614342223e+00 1.98064e-12 4.30322e-11 2 -1.121517361713768e+01 -1.121517361713660e+01 1.07825e-12 4.15898e-11 3 -2.478132940990368e+00 -2.478132940995655e+00 5.28688e-12 3.71963e-10 ----------------------------------------------------------------------------------------------------- 10 C 1 -4.287562944552994e+00 -4.287562944564788e+00 1.17941e-11 2.03215e-11 2 4.495770528186660e+00 4.495770528183276e+00 3.38396e-12 7.50742e-11 3 -5.064715062580039e+00 -5.064715062579974e+00 6.48370e-14 1.24664e-10 ----------------------------------------------------------------------------------------------------- 11 Si 1 -5.527946696922631e+00 -5.527946696940210e+00 1.75797e-11 1.32585e-10 2 -4.761327561526891e+00 -4.761327561524294e+00 2.59703e-12 4.87461e-10 3 3.537358973099779e-01 3.537358973232660e-01 1.32881e-11 1.11157e-10 ----------------------------------------------------------------------------------------------------- 12 C 1 -4.129851724191008e+00 -4.129851724190475e+00 5.32907e-13 7.39995e-11 2 3.236924227294887e+00 3.236924227247271e+00 4.76157e-11 3.85844e-10 3 -3.550151133378039e+00 -3.550151133326438e+00 5.16009e-11 1.30421e-10 ----------------------------------------------------------------------------------------------------- 13 Si 1 -4.000637713459755e-01 -4.000637713488782e-01 2.90268e-12 3.41728e-11 2 -3.472207956428986e+00 -3.472207956428029e+00 9.56568e-13 1.24869e-10 3 -9.589162038457745e+00 -9.589162038456900e+00 8.45546e-13 3.77671e-11 ----------------------------------------------------------------------------------------------------- 14 C 1 7.479835500667520e-01 7.479835500931924e-01 2.64404e-11 2.48821e-10 2 1.159013474243811e+00 1.159013474258731e+00 1.49201e-11 1.67389e-10 3 -1.461403524118963e+00 -1.461403524124098e+00 5.13545e-12 6.06071e-12 ----------------------------------------------------------------------------------------------------- 15 Si 1 1.075379865400897e+01 1.075379865400690e+01 2.06768e-12 2.28191e-11 2 -2.783568204198417e-01 -2.783568204233480e-01 3.50636e-12 5.55760e-11 3 -3.414493546459592e+00 -3.414493546492415e+00 3.28226e-11 4.65481e-11 ----------------------------------------------------------------------------------------------------- 16 Si 1 5.896958603689106e-02 5.896958602716697e-02 9.72409e-12 9.17559e-11 2 1.043414226154964e+01 1.043414226154322e+01 6.42331e-12 4.61622e-11 3 -3.250153674854381e+00 -3.250153674848837e+00 5.54401e-12 9.32623e-11 ----------------------------------------------------------------------------------------------------- 17 C 1 -3.079575459729671e-01 -3.079575459914758e-01 1.85087e-11 1.40778e-11 2 1.702732736323954e+00 1.702732736327090e+00 3.13571e-12 5.43121e-13 3 1.664826993498921e+00 1.664826993501170e+00 2.24976e-12 1.21956e-11 ----------------------------------------------------------------------------------------------------- 18 Si 1 -1.010557021271828e+01 -1.010557021274563e+01 2.73506e-11 7.20883e-10 2 -5.132471883581728e+00 -5.132471883597144e+00 1.54152e-11 3.19493e-10 3 -4.976279242238311e-01 -4.976279242064690e-01 1.73622e-11 1.45044e-10 ----------------------------------------------------------------------------------------------------- 19 C 1 -5.730062747485624e+00 -5.730062747485704e+00 7.99361e-14 4.61213e-11 2 8.417803543687542e+00 8.417803543662833e+00 2.47091e-11 3.31912e-11 3 -3.198826171118751e+00 -3.198826171095824e+00 2.29270e-11 5.50050e-10 ----------------------------------------------------------------------------------------------------- 20 Si 1 6.185440809707623e+00 6.185440809669290e+00 3.83329e-11 4.02945e-10 2 -1.819428568904826e+00 -1.819428568888035e+00 1.67915e-11 2.57363e-10 3 -5.134926732823218e+00 -5.134926732809702e+00 1.35163e-11 5.70171e-10 ----------------------------------------------------------------------------------------------------- 21 C 1 -1.076695264530551e+00 -1.076695264532989e+00 2.43783e-12 3.35692e-10 2 -4.887006034170730e+00 -4.887006034166754e+00 3.97549e-12 1.98082e-11 3 -7.880762260141555e+00 -7.880762260084397e+00 5.71578e-11 8.71996e-11 ----------------------------------------------------------------------------------------------------- 22 C 1 9.915743487719034e+00 9.915743487722766e+00 3.73213e-12 1.73461e-11 2 -2.527147662517389e+00 -2.527147662508944e+00 8.44569e-12 1.89845e-10 3 -3.788626267055142e-01 -3.788626267001781e-01 5.33612e-12 2.06397e-10 ----------------------------------------------------------------------------------------------------- 23 Si 1 1.037841864244596e+01 1.037841864244333e+01 2.62901e-12 7.52589e-11 2 -3.085383822223776e+00 -3.085383822232457e+00 8.68061e-12 1.19975e-11 3 -8.435732784810027e+00 -8.435732784806191e+00 3.83515e-12 3.96824e-10 ----------------------------------------------------------------------------------------------------- 24 Si 1 -1.093947470779572e+01 -1.093947470776531e+01 3.04023e-11 3.91118e-11 2 3.096178785945674e+00 3.096178785894778e+00 5.08966e-11 1.26017e-10 3 1.329446603985427e+01 1.329446603986026e+01 5.98277e-12 4.33324e-10 ----------------------------------------------------------------------------------------------------- 25 C 1 2.926132679282262e+00 2.926132679289600e+00 7.33813e-12 1.05775e-10 2 -5.297530298196551e+00 -5.297530298133556e+00 6.29949e-11 2.56528e-10 3 7.882052162945188e+00 7.882052162971837e+00 2.66489e-11 3.29200e-10 ----------------------------------------------------------------------------------------------------- 26 Si 1 -6.139761939839204e+00 -6.139761939850381e+00 1.11768e-11 1.50287e-10 2 7.924185606007600e-01 7.924185605747983e-01 2.59617e-11 2.84626e-10 3 1.197278030189635e+01 1.197278030188521e+01 1.11342e-11 5.75172e-10 ----------------------------------------------------------------------------------------------------- 27 C 1 6.131270015657750e+00 6.131270015680685e+00 2.29354e-11 5.47904e-10 2 8.442435482302129e+00 8.442435482284585e+00 1.75433e-11 2.31784e-10 3 -2.480778051893830e+00 -2.480778051865133e+00 2.86975e-11 7.20939e-10 ----------------------------------------------------------------------------------------------------- 28 C 1 7.178264227958759e+00 7.178264227968509e+00 9.75042e-12 3.74989e-11 2 -3.820712146855888e+00 -3.820712146875943e+00 2.00555e-11 5.16569e-11 3 -4.897326097556219e+00 -4.897326097562071e+00 5.85221e-12 2.03035e-10 ----------------------------------------------------------------------------------------------------- 29 Si 1 -2.684231034555718e+00 -2.684231034574305e+00 1.85869e-11 4.89693e-11 2 3.085079036208369e-01 3.085079036105008e-01 1.03361e-11 3.81063e-11 3 1.409611810323108e+00 1.409611810334451e+00 1.13425e-11 1.35322e-10 ----------------------------------------------------------------------------------------------------- 30 C 1 4.737757655085574e+00 4.737757655089196e+00 3.62288e-12 4.03007e-10 2 5.466490777950673e+00 5.466490777954984e+00 4.31122e-12 1.49044e-10 3 5.525337630619492e+00 5.525337630626799e+00 7.30704e-12 4.89572e-10 ----------------------------------------------------------------------------------------------------- 31 Si 1 7.709857860225041e+00 7.709857860205890e+00 1.91509e-11 1.05775e-10 2 -1.267921146265609e+00 -1.267921146292005e+00 2.63962e-11 1.06908e-10 3 4.295707506888486e+00 4.295707506894192e+00 5.70566e-12 5.61871e-11 ----------------------------------------------------------------------------------------------------- 32 Si 1 -1.432505198872538e+01 -1.432505198871713e+01 8.24407e-12 2.38023e-10 2 -5.959214914442678e-01 -5.959214914436564e-01 6.11400e-13 1.05875e-10 3 5.150695676579804e+00 5.150695676570724e+00 9.08074e-12 6.54996e-11 ----------------------------------------------------------------------------------------------------- Maximum error obtained for particle = 16, direction = 1: |F_model - F_numer| error = ----------------------- = 1.64900e-10 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 2.27289e-10 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 2.27289e-10 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.