!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 : MEAM_LAMMPS_KangEunJun_2014_SiC__MO_477506997611_001 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 = 2.932835578918457 | (Configuration in file "config-C.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 C 1 5.625136755500876e-01 5.625136755804228e-01 3.03352e-11 2.70291e-10 2 1.789200363420250e+00 1.789200363393465e+00 2.67848e-11 2.42603e-10 3 -2.243144994418781e-01 -2.243144994405967e-01 1.28142e-12 1.00804e-10 ----------------------------------------------------------------------------------------------------- 2 C 1 2.052843745099271e+00 2.052843745137192e+00 3.79208e-11 1.11100e-10 2 -1.022443931488758e+00 -1.022443931452252e+00 3.65059e-11 4.76474e-11 3 -1.399039157400861e+00 -1.399039157383113e+00 1.77478e-11 6.44519e-10 ----------------------------------------------------------------------------------------------------- 3 C 1 2.559563788321413e+00 2.559563788341694e+00 2.02811e-11 1.42961e-10 2 -4.661878683588756e-01 -4.661878683717454e-01 1.28698e-11 1.01830e-10 3 5.539761845657329e-01 5.539761846133563e-01 4.76233e-11 8.17300e-11 ----------------------------------------------------------------------------------------------------- 4 C 1 -1.789421897262331e+00 -1.789421897266626e+00 4.29479e-12 1.45131e-10 2 -3.973978595274078e-01 -3.973978595256367e-01 1.77108e-12 2.20786e-10 3 4.348062198716346e-01 4.348062198936259e-01 2.19914e-11 5.67910e-10 ----------------------------------------------------------------------------------------------------- 5 C 1 -2.606195622685663e+00 -2.606195622793372e+00 1.07709e-10 1.55772e-10 2 2.762120981407799e-02 2.762120981586097e-02 1.78298e-12 1.35870e-10 3 -1.804937027402123e+00 -1.804937027405229e+00 3.10574e-12 1.20125e-10 ----------------------------------------------------------------------------------------------------- 6 C 1 1.482843347292091e+00 1.482843347301934e+00 9.84235e-12 6.86321e-10 2 -2.587650970313644e+00 -2.587650970257165e+00 5.64788e-11 1.24940e-11 3 -3.195337761028991e+00 -3.195337761051448e+00 2.24567e-11 1.32683e-10 ----------------------------------------------------------------------------------------------------- 7 C 1 -3.012685211760505e+00 -3.012685211750195e+00 1.03091e-11 7.69386e-10 2 1.655672100687561e+00 1.655672100668852e+00 1.87095e-11 1.48807e-10 3 5.225322259232376e+00 5.225322259191989e+00 4.03872e-11 2.06717e-10 ----------------------------------------------------------------------------------------------------- 8 C 1 -2.603090695264525e+00 -2.603090695087764e+00 1.76762e-10 1.80909e-11 2 -9.048333898301697e-02 -9.048333907431630e-02 9.12993e-11 4.95236e-10 3 3.943552749013881e+00 3.943552748906886e+00 1.06995e-10 4.10649e-10 ----------------------------------------------------------------------------------------------------- 9 C 1 -2.823629150582554e+00 -2.823629150566913e+00 1.56413e-11 6.50977e-10 2 -2.666278003166157e+00 -2.666278003154063e+00 1.20939e-11 2.71413e-10 3 -2.779925254237892e+00 -2.779925254233466e+00 4.42624e-12 1.79003e-10 ----------------------------------------------------------------------------------------------------- 10 C 1 4.105797615810650e-01 4.105797615591997e-01 2.18653e-11 5.45100e-09 * 2 6.460251620148290e+00 6.460251620191996e+00 4.37064e-11 1.46153e-08 * 3 -2.437145079926387e+00 -2.437145079940270e+00 1.38827e-11 7.54374e-09 * ----------------------------------------------------------------------------------------------------- 11 C 1 -2.375966457045526e+00 -2.375966457095791e+00 5.02651e-11 7.43921e-10 2 -7.661515530355443e+00 -7.661515530346194e+00 9.24860e-12 7.24412e-10 3 1.885584757073160e+00 1.885584757122625e+00 4.94653e-11 4.57982e-09 * ----------------------------------------------------------------------------------------------------- 12 C 1 -4.491273862617952e+00 -4.491273862634920e+00 1.69678e-11 1.44038e-10 2 2.962250375558404e+00 2.962250375572941e+00 1.45373e-11 1.32041e-10 3 2.282496690973273e+00 2.282496690969075e+00 4.19798e-12 4.64175e-11 ----------------------------------------------------------------------------------------------------- 13 C 1 6.936400697434575e-02 6.936400698312617e-02 8.78042e-12 3.73760e-10 2 3.089160828768666e+00 3.089160828744854e+00 2.38121e-11 7.16745e-10 3 -2.047963923581264e+00 -2.047963923606599e+00 2.53353e-11 2.65911e-10 ----------------------------------------------------------------------------------------------------- 14 C 1 5.445991587740969e+00 5.445991587752515e+00 1.15463e-11 2.42501e-10 2 2.947197750077344e+00 2.947197750070250e+00 7.09388e-12 8.48726e-11 3 -1.677839096459691e+00 -1.677839096515247e+00 5.55560e-11 1.62059e-10 ----------------------------------------------------------------------------------------------------- 15 C 1 1.038669651542699e+01 1.038669651544614e+01 1.91456e-11 2.25546e-09 * 2 -9.859542075893016e+00 -9.859542075866452e+00 2.65636e-11 3.42240e-10 3 -2.640334305798480e+00 -2.640334305849409e+00 5.09290e-11 7.23192e-10 ----------------------------------------------------------------------------------------------------- 16 C 1 -1.292494807989062e+01 -1.292494807986786e+01 2.27587e-11 5.29425e-10 2 7.702412742219553e+00 7.702412742166131e+00 5.34222e-11 2.14036e-10 3 3.430182905305310e-02 3.430182889812983e-02 1.54923e-10 5.59404e-10 ----------------------------------------------------------------------------------------------------- 17 C 1 -2.073150140801264e+00 -2.073150140818369e+00 1.71050e-11 3.47184e-10 2 -4.101210974418146e-01 -4.101210974957661e-01 5.39515e-11 2.79389e-10 3 -3.866385592066066e-01 -3.866385592135284e-01 6.92180e-12 1.14985e-09 ----------------------------------------------------------------------------------------------------- 18 C 1 1.453213597280440e+00 1.453213597283893e+00 3.45346e-12 3.68247e-10 2 3.765415000085902e+00 3.765415000030327e+00 5.55755e-11 4.18903e-10 3 4.963309480279348e-02 4.963309477586355e-02 2.69299e-11 4.43264e-10 ----------------------------------------------------------------------------------------------------- 19 C 1 -6.110941646035056e-01 -6.110941645789549e-01 2.45507e-11 2.31357e-10 2 -2.322006148029176e+00 -2.322006148063694e+00 3.45186e-11 2.04814e-10 3 2.024275063930026e+00 2.024275063908993e+00 2.10330e-11 2.05369e-10 ----------------------------------------------------------------------------------------------------- 20 C 1 -7.260830461352503e-02 -7.260830460021721e-02 1.33078e-11 1.02052e-08 * 2 6.128532721178694e-01 6.128532720589388e-01 5.89306e-11 3.19578e-10 3 -9.096666232208782e-02 -9.096666233871765e-02 1.66298e-11 3.37853e-10 ----------------------------------------------------------------------------------------------------- 21 C 1 -8.068774312847549e-01 -8.068774313546105e-01 6.98557e-11 1.89415e-10 2 -5.527310076916068e+00 -5.527310077031882e+00 1.15814e-10 5.79034e-10 3 -1.115999369354647e+00 -1.115999369334902e+00 1.97458e-11 5.52095e-10 ----------------------------------------------------------------------------------------------------- 22 C 1 1.038551277848069e+01 1.038551277840794e+01 7.27578e-11 4.06287e-10 2 2.396535505539251e+00 2.396535505503181e+00 3.60707e-11 3.53883e-10 3 1.816355073344160e+00 1.816355073313748e+00 3.04121e-11 2.94630e-10 ----------------------------------------------------------------------------------------------------- 23 C 1 -1.301440713695537e+00 -1.301440713617303e+00 7.82341e-11 4.74387e-10 2 1.063695473896342e+00 1.063695473918949e+00 2.26075e-11 6.83711e-10 3 -1.042870142922315e+00 -1.042870142897037e+00 2.52784e-11 4.98259e-10 ----------------------------------------------------------------------------------------------------- 24 C 1 -3.348375008379927e-01 -3.348375008044651e-01 3.35276e-11 1.24524e-10 2 4.537006913576151e-01 4.537006913595674e-01 1.95233e-12 5.45173e-10 3 -5.459572199296623e-01 -5.459572198812133e-01 4.84490e-11 9.34979e-11 ----------------------------------------------------------------------------------------------------- 25 C 1 -6.335788973029013e-01 -6.335788973069745e-01 4.07319e-12 1.20877e-10 2 6.718835498482621e-03 6.718835617075254e-03 1.18593e-10 7.30113e-09 * 3 -2.699845737711228e+00 -2.699845737740534e+00 2.93063e-11 3.25875e-10 ----------------------------------------------------------------------------------------------------- 26 C 1 1.358043011146041e+00 1.358043011174686e+00 2.86442e-11 2.90180e-09 * 2 2.360151892505056e+00 2.360151892500219e+00 4.83746e-12 1.49105e-10 3 -5.525655291109612e+00 -5.525655291070793e+00 3.88187e-11 1.08217e-10 ----------------------------------------------------------------------------------------------------- 27 C 1 -2.926925345968399e+00 -2.926925346020939e+00 5.25398e-11 3.32306e-10 2 -2.366101855428131e+00 -2.366101855396680e+00 3.14508e-11 1.42559e-10 3 5.079876516979344e+00 5.079876516937512e+00 4.18323e-11 4.27274e-09 * ----------------------------------------------------------------------------------------------------- 28 C 1 -1.749258381527720e+00 -1.749258381369309e+00 1.58411e-10 8.90611e-10 2 -1.543028349319887e+00 -1.543028349443204e+00 1.23318e-10 6.96304e-10 3 1.609033703317818e+00 1.609033703297817e+00 2.00007e-11 2.10960e-10 ----------------------------------------------------------------------------------------------------- 29 C 1 1.274832803408592e+00 1.274832803277873e+00 1.30719e-10 5.90296e-10 2 -1.357033775739795e+00 -1.357033775752400e+00 1.26055e-11 2.29592e-10 3 1.247717384369333e+00 1.247717384426879e+00 5.75460e-11 1.30128e-09 ----------------------------------------------------------------------------------------------------- 30 C 1 2.616076057114331e+00 2.616076057175000e+00 6.06697e-11 5.30157e-10 2 4.714293878533115e-01 4.714293877589181e-01 9.43933e-11 3.98113e-10 3 -1.123687044280452e+00 -1.123687044187051e+00 9.34008e-11 8.92597e-10 ----------------------------------------------------------------------------------------------------- 31 C 1 6.854702537929379e-01 6.854702537310894e-01 6.18485e-11 3.82534e-10 2 -8.467232892661448e-01 -8.467232893169185e-01 5.07737e-11 1.27119e-10 3 7.178963414398459e-01 7.178963414525138e-01 1.26679e-11 1.86708e-10 ----------------------------------------------------------------------------------------------------- 32 C 1 2.393436928536010e+00 2.393436928500895e+00 3.51150e-11 3.40551e-09 * 2 1.359557120679362e+00 1.359557120667872e+00 1.14899e-11 3.09473e-10 3 3.833628264147746e+00 3.833628264170581e+00 2.28355e-11 6.34350e-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 discontinuities. Maximum error obtained for particle = 16, direction = 3: |F_model - F_numer| error = ----------------------- = 4.51647e-09 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 = 3.9824066162109375 | (Configuration in file "config-Si.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Si 1 -8.356421362021372e-01 -8.356421361922519e-01 9.88531e-12 4.45525e-10 2 -1.731466483008505e+00 -1.731466483005299e+00 3.20544e-12 1.08560e-10 3 -1.072463734076987e+00 -1.072463734113795e+00 3.68081e-11 9.25482e-11 ----------------------------------------------------------------------------------------------------- 2 Si 1 1.606161543914344e+00 1.606161543940265e+00 2.59206e-11 1.07976e-10 2 2.459789949705544e+00 2.459789949734742e+00 2.91980e-11 5.69664e-11 3 -7.368772098108183e-01 -7.368772098122330e-01 1.41476e-12 2.31198e-10 ----------------------------------------------------------------------------------------------------- 3 Si 1 1.242678621459790e+00 1.242678621443267e+00 1.65228e-11 1.19005e-10 2 -1.350182384710251e+00 -1.350182384659077e+00 5.11748e-11 1.61893e-10 3 -1.827474238625565e+00 -1.827474238636191e+00 1.06259e-11 6.56558e-10 ----------------------------------------------------------------------------------------------------- 4 Si 1 -5.628384661550072e-01 -5.628384661574125e-01 2.40530e-12 6.24529e-10 2 1.104046399426262e+00 1.104046399416023e+00 1.02385e-11 1.21951e-09 3 2.294588182493511e+00 2.294588182445875e+00 4.76361e-11 2.79370e-10 ----------------------------------------------------------------------------------------------------- 5 Si 1 -1.726383314020539e-01 -1.726383314342947e-01 3.22407e-11 4.23332e-11 2 5.488222866309099e-01 5.488222865615083e-01 6.94016e-11 1.47604e-08 * 3 7.695187319595606e-01 7.695187319426765e-01 1.68840e-11 1.55307e-10 ----------------------------------------------------------------------------------------------------- 6 Si 1 -8.059157757816813e-01 -8.059157758358244e-01 5.41431e-11 5.64013e-11 2 3.953883561626358e-01 3.953883561609412e-01 1.69464e-12 1.05216e-11 3 1.113898234418485e+00 1.113898234396646e+00 2.18392e-11 6.71671e-10 ----------------------------------------------------------------------------------------------------- 7 Si 1 -4.657106900525940e-01 -4.657106900772817e-01 2.46877e-11 9.55885e-11 2 3.989208232877315e-01 3.989208232889728e-01 1.24134e-12 3.39248e-11 3 3.066162933278159e-01 3.066162933432114e-01 1.53955e-11 1.00086e-09 ----------------------------------------------------------------------------------------------------- 8 Si 1 -1.006363351895550e+00 -1.006363351924421e+00 2.88702e-11 2.24822e-09 * 2 1.397936958353271e+00 1.397936958287997e+00 6.52747e-11 3.02377e-10 3 8.783958694772167e-01 8.783958694953304e-01 1.81137e-11 1.07347e-09 ----------------------------------------------------------------------------------------------------- 9 Si 1 -1.378733380371046e-01 -1.378733380455370e-01 8.43242e-12 1.32078e-10 2 -1.089006625486706e+00 -1.089006625430855e+00 5.58511e-11 1.45278e-10 3 -1.131475302877663e+00 -1.131475302808027e+00 6.96361e-11 9.28544e-11 ----------------------------------------------------------------------------------------------------- 10 Si 1 2.192967092858812e+00 2.192967092836425e+00 2.23874e-11 3.73049e-10 2 1.223257987823083e+00 1.223257987861255e+00 3.81721e-11 3.03727e-10 3 -1.344142900816365e+00 -1.344142900802017e+00 1.43481e-11 5.88745e-10 ----------------------------------------------------------------------------------------------------- 11 Si 1 6.665972150052874e+00 6.665972149995927e+00 5.69473e-11 5.98313e-11 2 -1.993795059345197e+00 -1.993795059283673e+00 6.15239e-11 2.85373e-10 3 -2.532393580085577e-01 -2.532393579317322e-01 7.68255e-11 1.66732e-10 ----------------------------------------------------------------------------------------------------- 12 Si 1 -2.332777812713972e+00 -2.332777812771564e+00 5.75926e-11 3.65987e-11 2 3.238918157466148e+00 3.238918157452241e+00 1.39071e-11 5.13443e-11 3 1.750988226987677e+00 1.750988226995363e+00 7.68585e-12 4.02216e-10 ----------------------------------------------------------------------------------------------------- 13 Si 1 -9.979940213119280e-01 -9.979940213477922e-01 3.58642e-11 5.96181e-11 2 -5.825372757225742e-01 -5.825372757084626e-01 1.41116e-11 2.51243e-11 3 -4.839895419662402e-01 -4.839895419403979e-01 2.58423e-11 1.41596e-10 ----------------------------------------------------------------------------------------------------- 14 Si 1 -8.084957633205554e-01 -8.084957633214965e-01 9.41136e-13 9.28901e-12 2 -3.179452098265413e-01 -3.179452098397606e-01 1.32193e-11 2.93235e-10 3 4.619956795627168e-01 4.619956795554638e-01 7.25303e-12 1.02332e-10 ----------------------------------------------------------------------------------------------------- 15 Si 1 1.171027139188291e+00 1.171027139096646e+00 9.16451e-11 2.63964e-10 2 -2.922000418462623e+00 -2.922000418457361e+00 5.26157e-12 6.36875e-10 3 8.932064695374494e-01 8.932064694536512e-01 8.37982e-11 2.06083e-10 ----------------------------------------------------------------------------------------------------- 16 Si 1 -3.134413300542424e+00 -3.134413300582390e+00 3.99658e-11 5.33170e-10 2 2.141065757828235e+00 2.141065757833779e+00 5.54401e-12 2.73292e-10 3 -3.577712827051287e+00 -3.577712827019719e+00 3.15676e-11 8.41990e-10 ----------------------------------------------------------------------------------------------------- 17 Si 1 -2.126681585327253e+00 -2.126681585289373e+00 3.78795e-11 1.86407e-10 2 3.495359891405505e-01 3.495359891248508e-01 1.56997e-11 1.08664e-08 * 3 1.554094488519264e+00 1.554094488461683e+00 5.75817e-11 6.63736e-11 ----------------------------------------------------------------------------------------------------- 18 Si 1 -4.731502257935749e-01 -4.731502257640473e-01 2.95276e-11 2.27041e-10 2 2.534598018895661e-01 2.534598018908312e-01 1.26510e-12 5.74756e-10 3 -2.386107272256957e+00 -2.386107272235253e+00 2.17040e-11 3.18274e-10 ----------------------------------------------------------------------------------------------------- 19 Si 1 -8.885553577586518e-01 -8.885553577420801e-01 1.65717e-11 1.31961e-10 2 1.488429442968924e+00 1.488429442976824e+00 7.90035e-12 1.73139e-10 3 6.011294617538491e-01 6.011294617473493e-01 6.49980e-12 6.68146e-11 ----------------------------------------------------------------------------------------------------- 20 Si 1 8.675290263132422e-02 8.675290261668962e-02 1.46346e-11 2.16929e-09 * 2 3.747065019843586e-01 3.747065019740166e-01 1.03421e-11 1.24046e-10 3 -5.532238516455938e-01 -5.532238516425859e-01 3.00793e-12 2.59397e-10 ----------------------------------------------------------------------------------------------------- 21 Si 1 2.495871623798914e+00 2.495871623745852e+00 5.30611e-11 6.90816e-11 2 -1.080457447664275e+00 -1.080457447675361e+00 1.10862e-11 4.93412e-10 3 -3.319720079748822e-01 -3.319720079879764e-01 1.30942e-11 3.00607e-10 ----------------------------------------------------------------------------------------------------- 22 Si 1 1.082831995860179e+00 1.082831995900920e+00 4.07410e-11 3.65536e-11 2 2.989747688456894e+00 2.989747688423677e+00 3.32170e-11 2.41763e-10 3 -1.197059725627220e+00 -1.197059725632253e+00 5.03353e-12 4.38591e-10 ----------------------------------------------------------------------------------------------------- 23 Si 1 -2.384804875254596e-01 -2.384804875188173e-01 6.64233e-12 9.55306e-11 2 2.336318504454540e-01 2.336318504435592e-01 1.89482e-12 1.71339e-09 * 3 3.480399725776149e-01 3.480399725733038e-01 4.31111e-12 5.71833e-11 ----------------------------------------------------------------------------------------------------- 24 Si 1 4.089240708602015e-01 4.089240708485175e-01 1.16841e-11 3.75658e-10 2 1.022252906877637e+00 1.022252906867964e+00 9.67360e-12 4.08132e-10 3 1.381749668220663e+00 1.381749668235719e+00 1.50562e-11 2.55539e-10 ----------------------------------------------------------------------------------------------------- 25 Si 1 -2.968045310309978e+00 -2.968045310320703e+00 1.07248e-11 1.19190e-10 2 -3.073324016476094e+00 -3.073324016437201e+00 3.88929e-11 6.14126e-10 3 2.459394401502710e+00 2.459394401499228e+00 3.48210e-12 1.59716e-10 ----------------------------------------------------------------------------------------------------- 26 Si 1 1.438825843027277e+00 1.438825843130568e+00 1.03291e-10 3.16862e-08 * 2 6.476152111274360e-01 6.476152113657657e-01 2.38330e-10 1.30019e-10 3 -1.275584275575887e+00 -1.275584275638336e+00 6.24489e-11 1.54765e-10 ----------------------------------------------------------------------------------------------------- 27 Si 1 -7.799801702971920e-02 -7.799801704898110e-02 1.92619e-11 4.51532e-10 2 -1.680666856652740e+00 -1.680666856699331e+00 4.65907e-11 2.70588e-10 3 1.599762108057682e+00 1.599762108060518e+00 2.83640e-12 8.72067e-11 ----------------------------------------------------------------------------------------------------- 28 Si 1 3.750227087049542e-01 3.750227087340000e-01 2.90458e-11 1.98377e-10 2 -1.854912264092028e-01 -1.854912263944858e-01 1.47171e-11 3.50734e-10 3 4.034975721884720e-01 4.034975722532931e-01 6.48211e-11 3.75840e-10 ----------------------------------------------------------------------------------------------------- 29 Si 1 -3.995377682170843e+00 -3.995377681961551e+00 2.09292e-10 3.55413e-10 2 -4.678398349637322e+00 -4.678398349541842e+00 9.54801e-11 4.22011e-10 3 -2.764262806531265e+00 -2.764262806527214e+00 4.05098e-12 1.77723e-08 * ----------------------------------------------------------------------------------------------------- 30 Si 1 3.732242348118626e+00 3.732242348227969e+00 1.09343e-10 9.71015e-10 2 1.602861868462367e+00 1.602861868437814e+00 2.45528e-11 4.29332e-10 3 9.741555507417552e-01 9.741555508734434e-01 1.31688e-10 4.96422e-10 ----------------------------------------------------------------------------------------------------- 31 Si 1 5.209125018082503e-01 5.209125018033774e-01 4.87288e-12 4.19309e-11 2 -2.322820032868219e+00 -2.322820032823282e+00 4.49378e-11 3.40227e-09 * 3 3.316030706946336e-01 3.316030707070149e-01 1.23814e-11 8.11068e-11 ----------------------------------------------------------------------------------------------------- 32 Si 1 -9.912388889533510e-01 -9.912388889570518e-01 3.70082e-12 2.41604e-10 2 1.137703448233243e+00 1.137703448243522e+00 1.02784e-11 7.50267e-10 3 8.129510708242157e-01 8.129510708147925e-01 9.42324e-12 8.21651e-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 = 26, direction = 2: |F_model - F_numer| error = ----------------------- = 3.68011e-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 = 3.493736028012245 | (Configuration in file "config-CSi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 C 1 3.558748976042898e+00 3.558748976052746e+00 9.84812e-12 8.91075e-10 2 4.487475684913876e-01 4.487475684963577e-01 4.97002e-12 1.14599e-10 3 2.446909864823430e+00 2.446909864817477e+00 5.95390e-12 7.45022e-11 ----------------------------------------------------------------------------------------------------- 2 C 1 8.265106814541139e-01 8.265106814482109e-01 5.90294e-12 3.74445e-12 2 6.980119530313026e-01 6.980119530194480e-01 1.18546e-11 1.96808e-10 3 1.579908254412562e+00 1.579908254408680e+00 3.88223e-12 6.02498e-09 * ----------------------------------------------------------------------------------------------------- 3 Si 1 -3.550436598781483e+00 -3.550436598730929e+00 5.05533e-11 2.14530e-10 2 -2.391541422435298e+00 -2.391541422384736e+00 5.05618e-11 4.02140e-10 3 -1.128202874925568e+00 -1.128202874910860e+00 1.47087e-11 4.71216e-10 ----------------------------------------------------------------------------------------------------- 4 C 1 -7.084877409868816e-01 -7.084877409924487e-01 5.56710e-12 1.50126e-10 2 2.326277603104402e+00 2.326277603103172e+00 1.23057e-12 1.55266e-10 3 1.886326316063379e-01 1.886326316174130e-01 1.10751e-11 4.55716e-11 ----------------------------------------------------------------------------------------------------- 5 Si 1 1.504019219293848e+00 1.504019219309557e+00 1.57083e-11 3.52895e-10 2 -2.530241637870316e+00 -2.530241637835366e+00 3.49498e-11 8.06574e-10 3 -3.984844178823044e+00 -3.984844178817891e+00 5.15232e-12 1.54079e-10 ----------------------------------------------------------------------------------------------------- 6 C 1 2.099719158181237e+00 2.099719158132271e+00 4.89662e-11 1.77175e-10 2 -1.496303806434483e+00 -1.496303806463998e+00 2.95144e-11 4.74367e-10 3 -1.958447801709684e+00 -1.958447801735121e+00 2.54368e-11 6.95437e-10 ----------------------------------------------------------------------------------------------------- 7 Si 1 -5.395971482058162e+00 -5.395971482068121e+00 9.95914e-12 1.34206e-10 2 3.525048561330177e+00 3.525048561335156e+00 4.97913e-12 1.74683e-10 3 -4.507110698042427e-01 -4.507110698106713e-01 6.42858e-12 1.10397e-11 ----------------------------------------------------------------------------------------------------- 8 Si 1 -2.209472605928682e+00 -2.209472605857868e+00 7.08140e-11 6.65443e-10 2 -8.300467004656596e+00 -8.300467004683870e+00 2.72742e-11 1.28379e-09 3 4.113563061647482e+00 4.113563061668984e+00 2.15019e-11 7.12383e-10 ----------------------------------------------------------------------------------------------------- 9 Si 1 2.246565682912469e+00 2.246565682851281e+00 6.11879e-11 2.10044e-10 2 -1.616748652276711e+00 -1.616748652247958e+00 2.87528e-11 2.03357e-10 3 7.849780411604412e-01 7.849780411526159e-01 7.82530e-12 5.82340e-11 ----------------------------------------------------------------------------------------------------- 10 C 1 -1.183306842469949e-01 -1.183306842727387e-01 2.57438e-11 1.52631e-10 2 -1.628926497550355e+00 -1.628926497549097e+00 1.25810e-12 1.15967e-10 3 1.296046604442757e+00 1.296046604430895e+00 1.18616e-11 3.76882e-10 ----------------------------------------------------------------------------------------------------- 11 C 1 -1.545662106074738e+00 -1.545662106104813e+00 3.00744e-11 1.40376e-10 2 1.108101208045837e+00 1.108101208041379e+00 4.45799e-12 3.16549e-10 3 -3.545576322260220e+00 -3.545576322230572e+00 2.96487e-11 2.82252e-09 * ----------------------------------------------------------------------------------------------------- 12 Si 1 2.014385470510117e+00 2.014385470519393e+00 9.27569e-12 7.11626e-11 2 2.002815039609180e-01 2.002815039657209e-01 4.80288e-12 1.46810e-11 3 8.856593534574868e-01 8.856593534396269e-01 1.78599e-11 1.54146e-10 ----------------------------------------------------------------------------------------------------- 13 Si 1 -4.079191180874904e+00 -4.079191180865615e+00 9.28946e-12 2.64849e-10 2 3.885411749106185e+00 3.885411749154048e+00 4.78622e-11 6.80123e-09 * 3 -6.366677594726055e+00 -6.366677594690153e+00 3.59019e-11 1.22944e-10 ----------------------------------------------------------------------------------------------------- 14 C 1 -4.739428949067637e-01 -4.739428949336423e-01 2.68787e-11 1.29657e-09 2 -1.116956372547255e+00 -1.116956372555924e+00 8.66907e-12 6.10914e-11 3 5.143606948052321e-01 5.143606948026594e-01 2.57261e-12 5.68845e-11 ----------------------------------------------------------------------------------------------------- 15 Si 1 1.162860482416070e+01 1.162860482392491e+01 2.35788e-10 1.64574e-09 * 2 3.833783160554162e+00 3.833783160421937e+00 1.32225e-10 6.95489e-10 3 -9.165345551406964e-01 -9.165345551785752e-01 3.78788e-11 3.26997e-10 ----------------------------------------------------------------------------------------------------- 16 C 1 -9.870678516810325e-01 -9.870678516356071e-01 4.54254e-11 5.73485e-10 2 -1.047840090552873e+00 -1.047840090516892e+00 3.59810e-11 4.04929e-10 3 1.587106480545516e+00 1.587106480500770e+00 4.47458e-11 3.17315e-10 ----------------------------------------------------------------------------------------------------- 17 Si 1 -2.218954760530965e+00 -2.218954760528215e+00 2.74980e-12 2.27998e-10 2 -4.526377233411794e-01 -4.526377233367447e-01 4.43467e-12 2.78610e-09 * 3 7.602613968620350e-01 7.602613968457111e-01 1.63238e-11 1.28996e-10 ----------------------------------------------------------------------------------------------------- 18 C 1 -2.556610585691844e-02 -2.556610590565235e-02 4.87339e-11 2.40513e-10 2 -1.709263319280792e+00 -1.709263319258429e+00 2.23632e-11 2.02800e-10 3 7.733544070386986e-01 7.733544070232120e-01 1.54866e-11 3.87869e-10 ----------------------------------------------------------------------------------------------------- 19 Si 1 1.438545319201165e+00 1.438545319166607e+00 3.45572e-11 2.26611e-10 2 -3.286487703645300e+00 -3.286487703654278e+00 8.97860e-12 4.25571e-11 3 1.667395347662829e+00 1.667395347661854e+00 9.74776e-13 4.26886e-10 ----------------------------------------------------------------------------------------------------- 20 Si 1 -2.254006683172092e+00 -2.254006683202511e+00 3.04188e-11 2.98427e-10 2 2.835402973770789e-01 2.835402973028086e-01 7.42703e-11 4.48604e-10 3 -1.796169124032005e+00 -1.796169123996371e+00 3.56348e-11 1.20631e-10 ----------------------------------------------------------------------------------------------------- 21 C 1 1.870928486561590e-01 1.870928487209670e-01 6.48079e-11 2.44998e-10 2 4.902166926145915e-01 4.902166926161782e-01 1.58668e-12 8.94039e-11 3 -1.545357943137647e+00 -1.545357943163042e+00 2.53946e-11 1.46950e-10 ----------------------------------------------------------------------------------------------------- 22 C 1 8.682408991066309e-01 8.682408991342736e-01 2.76427e-11 2.08801e-10 2 1.661196953766447e+00 1.661196953708735e+00 5.77121e-11 1.97539e-10 3 3.120225550308962e+00 3.120225550269138e+00 3.98237e-11 2.27955e-09 * ----------------------------------------------------------------------------------------------------- 23 C 1 -2.218246635109890e+00 -2.218246635113028e+00 3.13749e-12 2.55308e-10 2 2.321491636595771e+00 2.321491636642050e+00 4.62790e-11 3.67470e-10 3 -1.470755549936390e+00 -1.470755549925070e+00 1.13207e-11 3.74791e-11 ----------------------------------------------------------------------------------------------------- 24 Si 1 1.731986593251234e-01 1.731986593194894e-01 5.63408e-12 1.75537e-11 2 -1.307513440941795e+00 -1.307513440884806e+00 5.69891e-11 6.76069e-10 3 2.253424064202669e-01 2.253424064177270e-01 2.53991e-12 4.81446e-10 ----------------------------------------------------------------------------------------------------- 25 C 1 -3.342630135102352e-01 -3.342630135492497e-01 3.90145e-11 4.52514e-11 2 2.690111896955050e-02 2.690111895755463e-02 1.19959e-11 8.25714e-10 3 1.252504569353829e+00 1.252504569375045e+00 2.12150e-11 6.27094e-10 ----------------------------------------------------------------------------------------------------- 26 C 1 1.907790645159340e-01 1.907790645120449e-01 3.88908e-12 7.71420e-11 2 -1.085280167767754e+00 -1.085280167738030e+00 2.97242e-11 1.82352e-10 3 -1.322751473573385e+00 -1.322751473578230e+00 4.84501e-12 1.57099e-10 ----------------------------------------------------------------------------------------------------- 27 C 1 2.333167134138836e-02 2.333167138843238e-02 4.70440e-11 6.05972e-10 2 8.446183465972985e-01 8.446183467249473e-01 1.27649e-10 1.86023e-10 3 1.661274118965066e+00 1.661274118911731e+00 5.33356e-11 1.19960e-09 ----------------------------------------------------------------------------------------------------- 28 C 1 2.007658235958290e+00 2.007658235930148e+00 2.81419e-11 8.50542e-11 2 -1.479707946064879e+00 -1.479707946054260e+00 1.06191e-11 2.26845e-10 3 -1.949487557814483e+00 -1.949487557718551e+00 9.59319e-11 1.22890e-10 ----------------------------------------------------------------------------------------------------- 29 Si 1 -3.341121476394142e+00 -3.341121476398195e+00 4.05276e-12 5.95448e-10 2 7.982397995303312e+00 7.982397995347183e+00 4.38716e-11 3.21645e-10 3 3.742237835537219e+00 3.742237835531654e+00 5.56488e-12 5.32484e-10 ----------------------------------------------------------------------------------------------------- 30 Si 1 -8.054512993423887e-01 -8.054512992894707e-01 5.29180e-11 7.76933e-11 2 -3.857995062967606e-02 -3.857995058069739e-02 4.89787e-11 1.82952e-10 3 -2.565825169244267e+00 -2.565825169196711e+00 4.75557e-11 1.79448e-10 ----------------------------------------------------------------------------------------------------- 31 Si 1 3.234344653362245e+00 3.234344653346927e+00 1.53184e-11 1.25668e-10 2 -3.152900117743618e+00 -3.152900117786789e+00 4.31712e-11 2.02334e-10 3 -3.378374362296440e-01 -3.378374362418267e-01 1.21826e-11 2.09068e-10 ----------------------------------------------------------------------------------------------------- 32 Si 1 -1.735572244566045e+00 -1.735572244578927e+00 1.28828e-11 4.47789e-10 2 3.005369504890459e+00 3.005369504905040e+00 1.45808e-11 3.20082e-11 3 2.739418032307183e+00 2.739418032267714e+00 3.94698e-11 3.15716e-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 discontinuities. Maximum error obtained for particle = 27, direction = 1: |F_model - F_numer| error = ----------------------- = 2.01632e-09 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 4.51647e-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 4.51647e-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.