!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_KimLee_2008_TiN__MO_070542625990_001 Supported species : N Ti 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 = N | a0 = 8.375 | (Configuration in file "config-N.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 N 1 1.322101143216533e+00 1.322101143217507e+00 9.74110e-13 1.18075e-10 2 6.629057345581258e-01 6.629057345552783e-01 2.84750e-12 1.01624e-09 * 3 1.216247307145428e+00 1.216247307152852e+00 7.42406e-12 7.58038e-12 ----------------------------------------------------------------------------------------------------- 2 N 1 -9.900835469155868e-01 -9.900835469138147e-01 1.77203e-12 2.36113e-11 2 -1.318875745418871e-01 -1.318875745426805e-01 7.93393e-13 8.92396e-11 3 -2.344545162949716e+00 -2.344545162953454e+00 3.73745e-12 8.39928e-11 ----------------------------------------------------------------------------------------------------- 3 N 1 -1.084720518657915e+00 -1.084720518683484e+00 2.55687e-11 5.99459e-10 2 -1.745616797286193e+00 -1.745616797288187e+00 1.99463e-12 5.78582e-12 3 6.902125327554298e-03 6.902125348843806e-03 2.12895e-11 8.97742e-11 ----------------------------------------------------------------------------------------------------- 4 N 1 -3.166468764818656e+00 -3.166468764802680e+00 1.59766e-11 1.20812e-10 2 -4.089433056053775e-01 -4.089433056020774e-01 3.30008e-12 3.39741e-11 3 -1.912014012149443e+00 -1.912014012139365e+00 1.00777e-11 1.32048e-10 ----------------------------------------------------------------------------------------------------- 5 N 1 3.542217240959095e-02 3.542217241693852e-02 7.34757e-12 3.79714e-11 2 -1.031137424512881e+00 -1.031137424515267e+00 2.38587e-12 6.70382e-11 3 -7.995731858471727e-01 -7.995731858410563e-01 6.11644e-12 3.38530e-11 ----------------------------------------------------------------------------------------------------- 6 N 1 1.442429581700747e+00 1.442429581696520e+00 4.22706e-12 1.54040e-10 2 -7.036357067059300e-01 -7.036357067182011e-01 1.22711e-11 7.07261e-11 3 -1.079025838493903e+00 -1.079025838496482e+00 2.57883e-12 2.66474e-11 ----------------------------------------------------------------------------------------------------- 7 N 1 -1.306256359618927e+00 -1.306256359645811e+00 2.68836e-11 2.61398e-10 2 1.921633741343022e+00 1.921633741342715e+00 3.06866e-13 3.89879e-11 3 8.546330883862268e-01 8.546330883917358e-01 5.50904e-12 9.10354e-11 ----------------------------------------------------------------------------------------------------- 8 N 1 7.502536097916433e-01 7.502536097981972e-01 6.55387e-12 3.08387e-10 2 -2.637885400933817e+00 -2.637885400953023e+00 1.92064e-11 2.33561e-10 3 3.267288223279078e+00 3.267288223308772e+00 2.96940e-11 1.58858e-10 ----------------------------------------------------------------------------------------------------- 9 N 1 3.161433993299055e-01 3.161433993285945e-01 1.31106e-12 5.66541e-12 2 1.472701709279039e+00 1.472701709310035e+00 3.09963e-11 2.38547e-10 3 5.412322514047607e-01 5.412322514043132e-01 4.47531e-13 6.45410e-11 ----------------------------------------------------------------------------------------------------- 10 N 1 2.544311514055783e-01 2.544311513839246e-01 2.16537e-11 3.10306e-10 2 3.098981230401047e+00 3.098981230400565e+00 4.81837e-13 1.90803e-11 3 -1.536532011850540e+00 -1.536532011844544e+00 5.99587e-12 6.33782e-12 ----------------------------------------------------------------------------------------------------- 11 N 1 -1.354958483502163e+00 -1.354958483492337e+00 9.82570e-12 5.07911e-11 2 -7.030421013395056e-01 -7.030421013136043e-01 2.59013e-11 1.17866e-10 3 -1.706430798208343e+00 -1.706430798216557e+00 8.21343e-12 1.24229e-10 ----------------------------------------------------------------------------------------------------- 12 N 1 -3.364245220615957e+00 -3.364245220614345e+00 1.61293e-12 4.66089e-11 2 1.426983796267353e+00 1.426983796278451e+00 1.10971e-11 2.37184e-11 3 6.445118569699065e-02 6.445118570269495e-02 5.70430e-12 4.49915e-10 ----------------------------------------------------------------------------------------------------- 13 N 1 4.764126365114974e+00 4.764126365129364e+00 1.43903e-11 5.75525e-10 2 2.458615483933751e+00 2.458615483924275e+00 9.47598e-12 1.22347e-10 3 -2.652114673114279e+00 -2.652114673115821e+00 1.54232e-12 5.39067e-11 ----------------------------------------------------------------------------------------------------- 14 N 1 7.183147896236700e-01 7.183147896235006e-01 1.69420e-13 4.63228e-11 2 9.746012506364480e-01 9.746012506345351e-01 1.91291e-12 2.03814e-11 3 -4.347149161575448e-01 -4.347149161580078e-01 4.63074e-13 1.32327e-11 ----------------------------------------------------------------------------------------------------- 15 N 1 4.859940849908828e-01 4.859940849929712e-01 2.08839e-12 4.97934e-11 2 -1.574812579656293e+00 -1.574812579659320e+00 3.02758e-12 7.67817e-11 3 2.190592173448536e-01 2.190592173705967e-01 2.57431e-11 5.03864e-11 ----------------------------------------------------------------------------------------------------- 16 N 1 -4.957576867821221e+00 -4.957576867818158e+00 3.06244e-12 2.38449e-10 2 -3.019153541742799e+00 -3.019153541757028e+00 1.42286e-11 2.80770e-09 * 3 -2.026511876747414e+00 -2.026511876753657e+00 6.24256e-12 3.99742e-09 * ----------------------------------------------------------------------------------------------------- 17 N 1 -9.881467589685062e-01 -9.881467589746347e-01 6.12843e-12 3.79106e-11 2 -7.185764448311681e-01 -7.185764448311507e-01 1.74305e-14 3.34258e-11 3 2.669000730079814e-01 2.669000730045172e-01 3.46417e-12 3.26120e-11 ----------------------------------------------------------------------------------------------------- 18 N 1 1.331754891298758e-01 1.331754891319929e-01 2.11706e-12 7.72365e-11 2 -1.721429616445088e+00 -1.721429616444106e+00 9.82103e-13 1.25019e-09 * 3 -8.943669784776942e-01 -8.943669784730202e-01 4.67404e-12 1.30139e-10 ----------------------------------------------------------------------------------------------------- 19 N 1 6.794965381703011e-01 6.794965381573094e-01 1.29917e-11 6.27304e-11 2 -5.136674806860075e-01 -5.136674807035989e-01 1.75914e-11 1.60293e-11 3 6.239299592849306e-01 6.239299592870591e-01 2.12852e-12 4.72293e-10 ----------------------------------------------------------------------------------------------------- 20 N 1 -1.265718003376652e+00 -1.265718003373232e+00 3.41904e-12 4.46347e-11 2 -2.814308871077738e-01 -2.814308871218833e-01 1.41095e-11 1.58589e-11 3 9.962666221206328e-01 9.962666221203232e-01 3.09530e-13 7.66820e-12 ----------------------------------------------------------------------------------------------------- 21 N 1 -4.959554562992275e-01 -4.959554562968645e-01 2.36294e-12 2.07327e-11 2 -2.563857245269726e+00 -2.563857245344329e+00 7.46025e-11 2.95993e-10 3 -1.850079136486043e-01 -1.850079136414095e-01 7.19474e-12 9.69555e-11 ----------------------------------------------------------------------------------------------------- 22 N 1 4.036999634286346e+00 4.036999634303315e+00 1.69686e-11 8.83833e-10 * 2 6.218776567097983e-01 6.218776567192872e-01 9.48885e-12 3.56665e-11 3 2.470062301257273e-01 2.470062301497406e-01 2.40133e-11 1.24541e-11 ----------------------------------------------------------------------------------------------------- 23 N 1 5.657869718141774e-01 5.657869718208549e-01 6.67755e-12 2.97891e-10 2 -4.757942988332161e-01 -4.757942988329809e-01 2.35201e-13 1.40721e-11 3 7.567986705459325e-01 7.567986705330498e-01 1.28827e-11 6.97691e-11 ----------------------------------------------------------------------------------------------------- 24 N 1 4.637778571162621e-01 4.637778570911585e-01 2.51035e-11 9.24716e-12 2 -1.510640975230302e-01 -1.510640975341335e-01 1.11033e-11 9.42647e-11 3 1.909224313521007e+00 1.909224313523987e+00 2.97939e-12 5.78306e-11 ----------------------------------------------------------------------------------------------------- 25 N 1 -1.382703486716934e+00 -1.382703486716477e+00 4.56746e-13 2.28504e-10 2 3.814188598262600e-01 3.814188598170438e-01 9.21624e-12 9.60094e-11 3 4.242050120338832e-01 4.242050120428416e-01 8.95839e-12 1.17727e-10 ----------------------------------------------------------------------------------------------------- 26 N 1 2.333864617457205e+00 2.333864617453687e+00 3.51763e-12 1.08135e-10 2 1.286183630882329e+00 1.286183630875597e+00 6.73173e-12 5.80993e-11 3 5.566047823294626e-01 5.566047823264378e-01 3.02480e-12 6.29520e-11 ----------------------------------------------------------------------------------------------------- 27 N 1 -1.619373285254367e-01 -1.619373285339325e-01 8.49573e-12 1.89882e-10 2 2.104367597729067e+00 2.104367597719667e+00 9.40004e-12 3.06470e-10 3 1.292731974887705e+00 1.292731974888247e+00 5.42233e-13 2.31563e-10 ----------------------------------------------------------------------------------------------------- 28 N 1 -1.175653470030422e+00 -1.175653470022683e+00 7.73981e-12 1.33104e-10 2 -1.100555433367986e+00 -1.100555433373335e+00 5.34928e-12 1.00948e-10 3 1.285525566932470e+00 1.285525566937863e+00 5.39302e-12 2.70816e-10 ----------------------------------------------------------------------------------------------------- 29 N 1 1.831699547229222e+00 1.831699547235010e+00 5.78781e-12 3.71618e-11 2 -1.227125711365095e-01 -1.227125711410876e-01 4.57803e-12 4.60635e-11 3 -6.363635214373182e-01 -6.363635214399648e-01 2.64655e-12 3.27986e-09 * ----------------------------------------------------------------------------------------------------- 30 N 1 1.593357849369039e+00 1.593357849379208e+00 1.01685e-11 7.41103e-11 2 1.529298244953744e+00 1.529298244936610e+00 1.71343e-11 2.63372e-10 3 -5.250727210677223e-01 -5.250727210631808e-01 4.54148e-12 2.75133e-10 ----------------------------------------------------------------------------------------------------- 31 N 1 -2.072386911967061e-01 -2.072386911898238e-01 6.88233e-12 6.07877e-11 2 -4.195316502745102e-01 -4.195316502647433e-01 9.76697e-12 5.35491e-11 3 3.407618324923504e-01 3.407618324916006e-01 7.49845e-13 5.58023e-11 ----------------------------------------------------------------------------------------------------- 32 N 1 1.742881549083598e-01 1.742881548754870e-01 3.28728e-11 7.87597e-11 2 2.085165221279714e+00 2.085165221280118e+00 4.03233e-13 1.18788e-10 3 1.862505174282720e+00 1.862505174302840e+00 2.01195e-11 3.45693e-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 = 3, direction = 3: |F_model - F_numer| error = ----------------------- = 3.08449e-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 = Ti | a0 = 4.133002281188965 | (Configuration in file "config-Ti.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ti 1 3.455629189831300e-01 3.455629189839683e-01 8.38329e-13 3.29794e-11 2 8.743558809082901e-02 8.743558805171733e-02 3.91117e-11 5.76998e-11 3 -1.506484180241523e-01 -1.506484180259673e-01 1.81499e-12 2.46918e-11 ----------------------------------------------------------------------------------------------------- 2 Ti 1 1.357962725977278e-01 1.357962725906392e-01 7.08866e-12 8.67436e-11 2 -8.103528466525300e-01 -8.103528466755658e-01 2.30358e-11 4.22076e-10 3 3.311303133976705e-01 3.311303133933641e-01 4.30639e-12 1.88556e-10 ----------------------------------------------------------------------------------------------------- 3 Ti 1 -1.559794209672646e-02 -1.559794213421721e-02 3.74907e-11 9.55070e-11 2 6.730642856594290e-01 6.730642856542370e-01 5.19196e-12 1.33547e-10 3 3.303767949205405e-01 3.303767949172179e-01 3.32262e-12 1.63004e-11 ----------------------------------------------------------------------------------------------------- 4 Ti 1 8.218299259872686e-01 8.218299260237674e-01 3.64988e-11 3.03411e-10 2 8.463657869850996e-03 8.463657854254590e-03 1.55964e-11 1.85698e-10 3 -2.294038302853515e-01 -2.294038302862160e-01 8.64447e-13 3.50298e-11 ----------------------------------------------------------------------------------------------------- 5 Ti 1 1.613715171557514e-01 1.613715171532369e-01 2.51454e-12 1.51009e-10 2 5.035016309531417e-01 5.035016309705201e-01 1.73784e-11 6.84797e-11 3 3.832001303326480e-01 3.832001303271027e-01 5.54529e-12 6.97201e-11 ----------------------------------------------------------------------------------------------------- 6 Ti 1 -3.521645043720372e-01 -3.521645043878552e-01 1.58180e-11 1.17827e-10 2 -1.068617643508797e-01 -1.068617643145800e-01 3.62997e-11 1.88077e-10 3 6.258955375171853e-01 6.258955375171840e-01 1.33227e-15 4.82892e-12 ----------------------------------------------------------------------------------------------------- 7 Ti 1 -5.884382542800943e-01 -5.884382542752514e-01 4.84290e-12 7.92432e-11 2 6.740433334244622e-01 6.740433334294705e-01 5.00833e-12 9.26422e-11 3 2.218150791189671e-02 2.218150789527510e-02 1.66216e-11 5.15879e-11 ----------------------------------------------------------------------------------------------------- 8 Ti 1 5.824606596551929e-01 5.824606596279254e-01 2.72675e-11 1.40378e-09 * 2 -5.395764707752918e-01 -5.395764707717127e-01 3.57914e-12 1.19061e-10 3 -7.013437581873281e-01 -7.013437581851681e-01 2.15994e-12 1.68970e-10 ----------------------------------------------------------------------------------------------------- 9 Ti 1 -4.671041090627950e-01 -4.671041090561451e-01 6.64990e-12 1.27379e-10 2 -1.341636820335422e-02 -1.341636818866750e-02 1.46867e-11 4.91746e-11 3 -5.164853509514771e-01 -5.164853509479169e-01 3.56015e-12 6.82207e-11 ----------------------------------------------------------------------------------------------------- 10 Ti 1 1.634354647298246e-01 1.634354646689920e-01 6.08326e-11 3.30168e-10 2 -3.625594920050687e-01 -3.625594920128350e-01 7.76634e-12 1.53987e-10 3 2.007877105292767e-01 2.007877105537641e-01 2.44874e-11 1.60421e-10 ----------------------------------------------------------------------------------------------------- 11 Ti 1 -2.686870195363852e-01 -2.686870195726783e-01 3.62930e-11 1.05446e-10 2 6.088791884589813e-01 6.088791884711511e-01 1.21698e-11 1.04526e-10 3 8.320520003230842e-01 8.320520002378100e-01 8.52742e-11 5.16153e-10 ----------------------------------------------------------------------------------------------------- 12 Ti 1 1.253925817583494e-01 1.253925817150553e-01 4.32941e-11 2.79565e-10 2 -1.390448637320160e-01 -1.390448637220058e-01 1.00102e-11 3.92259e-11 3 -6.998725692673005e-02 -6.998725691412364e-02 1.26064e-11 4.63451e-10 ----------------------------------------------------------------------------------------------------- 13 Ti 1 -1.518357943075422e+00 -1.518357943068301e+00 7.12053e-12 4.87618e-10 2 -1.016123999478388e+00 -1.016123999476512e+00 1.87583e-12 3.45095e-10 3 2.621350615211665e-01 2.621350614589470e-01 6.22195e-11 2.26917e-10 ----------------------------------------------------------------------------------------------------- 14 Ti 1 1.037800249467596e+00 1.037800249455753e+00 1.18439e-11 5.74862e-11 2 8.804893676029182e-01 8.804893675931978e-01 9.72034e-12 5.15750e-11 3 -6.882232234137292e-01 -6.882232234074387e-01 6.29052e-12 1.63494e-10 ----------------------------------------------------------------------------------------------------- 15 Ti 1 1.906139139686983e-01 1.906139139568150e-01 1.18834e-11 5.04923e-11 2 -1.311063637292532e+00 -1.311063637283431e+00 9.10161e-12 7.27423e-10 3 -2.462735875128732e-01 -2.462735875072882e-01 5.58500e-12 7.92111e-11 ----------------------------------------------------------------------------------------------------- 16 Ti 1 2.613918886617439e-03 2.613918910384993e-03 2.37676e-11 5.96992e-11 2 1.001499477570471e+00 1.001499477637739e+00 6.72677e-11 1.93500e-09 * 3 1.802344975406392e-01 1.802344975236962e-01 1.69431e-11 3.14266e-10 ----------------------------------------------------------------------------------------------------- 17 Ti 1 -3.337449304829202e-01 -3.337449304950405e-01 1.21203e-11 7.27920e-10 2 3.022659580361762e-01 3.022659580390641e-01 2.88786e-12 1.69900e-09 * 3 3.716202897251178e-01 3.716202897259347e-01 8.16847e-13 1.32919e-09 * ----------------------------------------------------------------------------------------------------- 18 Ti 1 1.397386462284766e-03 1.397386535266146e-03 7.29814e-11 1.27238e-10 2 -2.369306111141003e-01 -2.369306110985714e-01 1.55289e-11 4.13887e-11 3 -4.053820773511728e-01 -4.053820774354954e-01 8.43227e-11 1.59474e-10 ----------------------------------------------------------------------------------------------------- 19 Ti 1 3.749929087330671e-01 3.749929087469411e-01 1.38740e-11 1.24362e-10 2 -6.427914759935029e-01 -6.427914759879095e-01 5.59341e-12 9.58656e-05 * 3 -1.409683656602305e-01 -1.409683656560788e-01 4.15168e-12 8.88589e-11 ----------------------------------------------------------------------------------------------------- 20 Ti 1 -4.118349260338062e-01 -4.118349260768324e-01 4.30262e-11 5.69075e-10 2 5.801696061532949e-01 5.801696061235628e-01 2.97321e-11 1.52030e-10 3 -1.804969822659491e-01 -1.804969822425321e-01 2.34170e-11 5.14919e-10 ----------------------------------------------------------------------------------------------------- 21 Ti 1 5.805889096947218e-01 5.805889096838588e-01 1.08630e-11 1.05749e-10 2 7.146190294357151e-01 7.146190294503532e-01 1.46381e-11 1.03728e-10 3 -5.134700344244753e-01 -5.134700344396252e-01 1.51500e-11 6.83447e-11 ----------------------------------------------------------------------------------------------------- 22 Ti 1 -8.311008034521146e-01 -8.311008034081322e-01 4.39824e-11 8.32916e-10 2 -1.243708939193600e+00 -1.243708939200096e+00 6.49569e-12 2.89368e-10 3 9.173039986553923e-02 9.173039991634400e-02 5.08048e-11 2.59612e-10 ----------------------------------------------------------------------------------------------------- 23 Ti 1 1.490144331710582e-01 1.490144331718739e-01 8.15764e-13 1.09892e-10 2 4.572498242992692e-01 4.572498243100755e-01 1.08062e-11 1.76663e-10 3 -9.504454546441189e-02 -9.504454545447530e-02 9.93659e-12 1.76375e-10 ----------------------------------------------------------------------------------------------------- 24 Ti 1 9.278397022388733e-02 9.278397023892515e-02 1.50378e-11 8.45777e-11 2 2.181766076254024e-01 2.181766076021271e-01 2.32753e-11 6.13902e-11 3 -6.925309986319437e-01 -6.925309986505014e-01 1.85577e-11 5.11539e-11 ----------------------------------------------------------------------------------------------------- 25 Ti 1 8.994766231695067e-01 8.994766231861647e-01 1.66580e-11 1.36917e-10 2 6.400441548029910e-01 6.400441547961603e-01 6.83076e-12 2.44148e-10 3 6.954511272687393e-01 6.954511272703082e-01 1.56897e-12 1.83590e-10 ----------------------------------------------------------------------------------------------------- 26 Ti 1 2.300181344261331e-01 2.300181344232451e-01 2.88797e-12 2.12397e-10 2 -1.071913387777855e+00 -1.071913387802172e+00 2.43170e-11 1.53553e-10 3 7.303035207735562e-01 7.303035207732501e-01 3.06088e-13 2.26284e-10 ----------------------------------------------------------------------------------------------------- 27 Ti 1 -2.203496182609566e-01 -2.203496183936530e-01 1.32696e-10 3.27705e-10 2 -1.450907406846396e-01 -1.450907406976018e-01 1.29622e-11 8.28072e-11 3 -1.164583718766660e+00 -1.164583718775898e+00 9.23794e-12 8.03166e-11 ----------------------------------------------------------------------------------------------------- 28 Ti 1 2.958465435430436e-01 2.958465435655148e-01 2.24711e-11 1.89933e-10 2 -3.643250542949410e-01 -3.643250542603828e-01 3.45582e-11 3.51028e-10 3 -4.231424850179689e-01 -4.231424850198634e-01 1.89448e-12 1.18435e-10 ----------------------------------------------------------------------------------------------------- 29 Ti 1 -1.002462276727951e+00 -1.002462276689805e+00 3.81457e-11 1.07172e-10 2 -7.702043878184849e-01 -7.702043878223495e-01 3.86458e-12 8.63853e-11 3 4.445558041060840e-01 4.445558039819837e-01 1.24100e-10 4.18491e-10 ----------------------------------------------------------------------------------------------------- 30 Ti 1 3.467315848743968e-01 3.467315848363881e-01 3.80088e-11 2.12266e-10 2 8.420280884355873e-01 8.420280884396316e-01 4.04432e-12 8.60618e-11 3 4.188396538964719e-01 4.188396538782592e-01 1.82127e-11 9.21309e-11 ----------------------------------------------------------------------------------------------------- 31 Ti 1 -3.297447596478412e-01 -3.297447596475029e-01 3.38229e-13 1.78152e-09 * 2 1.012732024908925e-01 1.012732024862955e-01 4.59698e-12 3.62415e-10 3 -1.348447980566314e-01 -1.348447980466421e-01 9.98923e-12 1.37465e-10 ----------------------------------------------------------------------------------------------------- 32 Ti 1 -1.981408304592062e-01 -1.981408304452026e-01 1.40035e-11 7.70440e-11 2 4.807610384577733e-01 4.807610384451593e-01 1.26140e-11 2.20125e-10 3 4.323350813114694e-01 4.323350812627481e-01 4.87213e-11 3.73494e-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 = 18, direction = 1: |F_model - F_numer| error = ----------------------- = 5.22271e-08 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 = N Ti | a0 = 3.7395357318303435 | (Configuration in file "config-NTi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ti 1 2.705723875926677e-01 2.705723875883161e-01 4.35157e-12 6.50391e-10 2 -5.776373418434505e-01 -5.776373418532986e-01 9.84812e-12 3.74797e-11 3 -6.210663502485075e-01 -6.210663502465344e-01 1.97309e-12 4.45388e-11 ----------------------------------------------------------------------------------------------------- 2 Ti 1 3.739726644572683e+00 3.739726644568787e+00 3.89644e-12 4.25053e-10 2 3.345635276554668e-03 3.345635280578950e-03 4.02428e-12 1.56387e-10 3 -3.037690075233395e-01 -3.037690075260797e-01 2.74014e-12 1.83978e-09 ----------------------------------------------------------------------------------------------------- 3 Ti 1 2.240209081790972e+00 2.240209081792515e+00 1.54277e-12 2.98337e-10 2 -1.559280853191728e+00 -1.559280853221799e+00 3.00711e-11 2.60869e-10 3 1.040845107072931e+00 1.040845107062608e+00 1.03229e-11 6.08503e-10 ----------------------------------------------------------------------------------------------------- 4 Ti 1 -1.846851434422295e+00 -1.846851434434807e+00 1.25120e-11 1.26640e-10 2 -2.052939821493398e+00 -2.052939821494484e+00 1.08624e-12 1.58145e-09 3 8.368880063170122e-01 8.368880062903095e-01 2.67028e-11 1.26735e-09 ----------------------------------------------------------------------------------------------------- 5 Ti 1 8.984198766026124e-01 8.984198766164001e-01 1.37877e-11 2.77325e-10 2 1.254042697527439e+00 1.254042697496160e+00 3.12783e-11 1.95104e-09 3 2.612142520264905e+00 2.612142520270005e+00 5.09992e-12 3.99940e-10 ----------------------------------------------------------------------------------------------------- 6 Ti 1 -2.416495905599791e+00 -2.416495905583182e+00 1.66089e-11 4.58157e-09 * 2 1.169902256825227e+00 1.169902256845703e+00 2.04758e-11 8.12013e-11 3 3.603374272606394e+00 3.603374272552167e+00 5.42268e-11 1.94165e-10 ----------------------------------------------------------------------------------------------------- 7 N 1 2.777429269130358e+00 2.777429269189357e+00 5.89990e-11 1.07665e-10 2 -3.056269714094903e+00 -3.056269714074007e+00 2.08953e-11 1.69895e-10 3 -1.053480440691913e+01 -1.053480440686351e+01 5.56213e-11 1.13099e-10 ----------------------------------------------------------------------------------------------------- 8 N 1 -1.612412462495600e+00 -1.612412462499849e+00 4.24838e-12 1.21730e-10 2 3.750471793912923e-01 3.750471793534941e-01 3.77982e-11 2.42545e-11 3 8.426957218158483e-01 8.426957218068813e-01 8.96694e-12 4.96752e-09 * ----------------------------------------------------------------------------------------------------- 9 Ti 1 1.370773816041004e+00 1.370773816005347e+00 3.56573e-11 2.56054e-10 2 3.206699798030684e+00 3.206699798046875e+00 1.61915e-11 1.12751e-10 3 6.582241276039411e-01 6.582241276078612e-01 3.92009e-12 1.45241e-10 ----------------------------------------------------------------------------------------------------- 10 N 1 -3.300858111533022e+00 -3.300858111455626e+00 7.73959e-11 2.98802e-10 2 -1.037048337936089e+00 -1.037048337941861e+00 5.77183e-12 1.64846e-11 3 -1.166483511639473e+00 -1.166483511635359e+00 4.11382e-12 7.88285e-11 ----------------------------------------------------------------------------------------------------- 11 Ti 1 2.270987114698642e+00 2.270987114700042e+00 1.39933e-12 1.64989e-09 2 5.074497687148138e+00 5.074497687275476e+00 1.27338e-10 5.54050e-09 * 3 -5.218597355079426e+00 -5.218597355149726e+00 7.02993e-11 5.04674e-10 ----------------------------------------------------------------------------------------------------- 12 N 1 1.054320039783375e+00 1.054320039787950e+00 4.57501e-12 1.41259e-10 2 -3.320313068324987e+00 -3.320313068267177e+00 5.78102e-11 1.82927e-10 3 1.610296788258471e+00 1.610296788293087e+00 3.46161e-11 3.39566e-10 ----------------------------------------------------------------------------------------------------- 13 N 1 -2.971069860427248e-01 -2.971069861193206e-01 7.65958e-11 5.15974e-10 2 -5.482876396234935e+00 -5.482876396269364e+00 3.44293e-11 2.92387e-10 3 -1.255351234670357e+00 -1.255351234669353e+00 1.00364e-12 1.16596e-09 ----------------------------------------------------------------------------------------------------- 14 N 1 6.762707970238502e-01 6.762707970167047e-01 7.14551e-12 3.07819e-10 2 1.407818049106876e-01 1.407818049449946e-01 3.43070e-11 2.55953e-10 3 2.009080685832539e+00 2.009080685846707e+00 1.41687e-11 2.47063e-10 ----------------------------------------------------------------------------------------------------- 15 Ti 1 -2.121895615639388e+00 -2.121895615628387e+00 1.10010e-11 2.14900e-10 2 1.459989164699080e+00 1.459989164715832e+00 1.67519e-11 1.27130e-08 * 3 -1.242517788344653e+00 -1.242517788320093e+00 2.45595e-11 3.18596e-11 ----------------------------------------------------------------------------------------------------- 16 N 1 -1.553927632190312e+00 -1.553927632165707e+00 2.46052e-11 5.90608e-11 2 -1.228070827142084e+00 -1.228070827124417e+00 1.76679e-11 3.70800e-09 * 3 3.399737097127390e+00 3.399737097144534e+00 1.71445e-11 3.98787e-10 ----------------------------------------------------------------------------------------------------- 17 N 1 1.379593661238147e+00 1.379593661258863e+00 2.07161e-11 1.04207e-10 2 1.113185963124229e+00 1.113185963126214e+00 1.98552e-12 4.51301e-11 3 -4.405784858269872e+00 -4.405784858272159e+00 2.28706e-12 1.21735e-10 ----------------------------------------------------------------------------------------------------- 18 Ti 1 6.765620863455295e-01 6.765620863295274e-01 1.60021e-11 3.78375e-11 2 -7.844466592525050e+00 -7.844466592619623e+00 9.45732e-11 5.91839e-10 3 5.639518344160217e+00 5.639518344183014e+00 2.27978e-11 8.28102e-11 ----------------------------------------------------------------------------------------------------- 19 N 1 2.355851423254449e-01 2.355851423205741e-01 4.87080e-12 9.36323e-11 2 -5.706033962657870e-01 -5.706033961923171e-01 7.34699e-11 1.03410e-11 3 -3.670824392187067e-01 -3.670824392262590e-01 7.55235e-12 2.16431e-11 ----------------------------------------------------------------------------------------------------- 20 N 1 1.602192724662239e+00 1.602192724636274e+00 2.59650e-11 1.54643e-10 2 5.217632907615806e+00 5.217632907627929e+00 1.21236e-11 2.88331e-09 * 3 -1.187958029555467e+00 -1.187958029533261e+00 2.22056e-11 1.22502e-10 ----------------------------------------------------------------------------------------------------- 21 N 1 -7.620752126161504e+00 -7.620752126158918e+00 2.58638e-12 1.67631e-10 2 2.407923480068333e-01 2.407923480258331e-01 1.89997e-11 4.01076e-10 3 -1.104784729249700e+00 -1.104784729206892e+00 4.28080e-11 1.16154e-10 ----------------------------------------------------------------------------------------------------- 22 N 1 1.524080806577185e+00 1.524080806561471e+00 1.57145e-11 1.67618e-10 2 3.350606014427419e+00 3.350606014404073e+00 2.33462e-11 1.94990e-10 3 -3.884521815087202e+00 -3.884521815064735e+00 2.24669e-11 1.39229e-09 ----------------------------------------------------------------------------------------------------- 23 N 1 2.037056631583464e+00 2.037056631578569e+00 4.89564e-12 2.11883e-09 2 5.387417009338886e-01 5.387417009107697e-01 2.31190e-11 1.03205e-09 3 1.803828514006690e+00 1.803828514013809e+00 7.11897e-12 1.34845e-09 ----------------------------------------------------------------------------------------------------- 24 N 1 -4.704274091189921e+00 -4.704274091189231e+00 6.90115e-13 3.63842e-11 2 2.721972870285477e+00 2.721972870307481e+00 2.20042e-11 1.49815e-09 3 1.516103229233655e+00 1.516103229237261e+00 3.60600e-12 4.55999e-09 * ----------------------------------------------------------------------------------------------------- 25 Ti 1 -2.377456221029214e+00 -2.377456220977137e+00 5.20770e-11 5.28087e-10 2 1.922750145788478e+00 1.922750145786898e+00 1.58007e-12 2.79092e-10 3 1.995183569501201e+00 1.995183569448670e+00 5.25318e-11 2.01358e-09 ----------------------------------------------------------------------------------------------------- 26 Ti 1 -7.794793226174197e-02 -7.794793226417024e-02 2.42827e-12 1.03857e-10 2 8.052660300298283e-01 8.052660300400436e-01 1.02153e-11 2.29159e-10 3 -2.748525560279788e+00 -2.748525560291055e+00 1.12665e-11 5.44668e-10 ----------------------------------------------------------------------------------------------------- 27 Ti 1 -2.743648674658310e+00 -2.743648674667810e+00 9.50040e-12 3.78176e-10 2 -2.682239683753816e+00 -2.682239683778789e+00 2.49729e-11 1.09341e-09 3 3.386887593405297e+00 3.386887593391098e+00 1.41989e-11 4.19022e-09 * ----------------------------------------------------------------------------------------------------- 28 Ti 1 -3.071803381086640e-01 -3.071803381791788e-01 7.05148e-11 2.29519e-10 2 5.729960160173064e-01 5.729960160444700e-01 2.71636e-11 6.43949e-11 3 8.788408251153016e-01 8.788408250929745e-01 2.23271e-11 2.64840e-10 ----------------------------------------------------------------------------------------------------- 29 Ti 1 8.065425702560018e+00 8.065425702522546e+00 3.74722e-11 1.71097e-10 2 -7.769104419161564e-02 -7.769104418913064e-02 2.48500e-12 2.09919e-10 3 1.396407901707192e+00 1.396407901737801e+00 3.06082e-11 6.48729e-10 ----------------------------------------------------------------------------------------------------- 30 N 1 7.433450151163539e-01 7.433450151284572e-01 1.21033e-11 4.79374e-11 2 -1.612740157498684e+00 -1.612740157468157e+00 3.05278e-11 7.99897e-10 3 3.799252182560522e-01 3.799252182605057e-01 4.45344e-12 1.28701e-10 ----------------------------------------------------------------------------------------------------- 31 N 1 -3.219226786851314e+00 -3.219226786850938e+00 3.76144e-13 1.80683e-10 2 2.071507287367081e+00 2.071507287415932e+00 4.88507e-11 3.79832e-10 3 5.754133185214620e-01 5.754133185444733e-01 2.30113e-11 1.14355e-09 ----------------------------------------------------------------------------------------------------- 32 Ti 1 2.637483520539254e+00 2.637483520556157e+00 1.69029e-11 3.50575e-10 2 -1.375802729089247e-01 -1.375802729252931e-01 1.63684e-11 2.60779e-09 * 3 -1.441457547208776e-01 -1.441457547291567e-01 8.27916e-12 1.49240e-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 = 2, direction = 2: |F_model - F_numer| error = ----------------------- = 1.20285e-09 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 5.22271e-08 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: B Comment: The letter grade B was assigned because the normalized error in the computation was 5.22271e-08 compared with a machine precision of 2.22045e-16. The letter grade was based on 'score=log10(error/eps)', with ranges A=[0, 7.5], B=(7.5, 10.0], C=(10.0, 12.5], D=(12.5, 15.0), F>15.0. 'A' is the best grade, and 'F' indicates failure.