!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_000 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 1.322101143217506e+00 9.72333e-13 1.18076e-10 2 6.629057345581258e-01 6.629057345552787e-01 2.84717e-12 1.01624e-09 * 3 1.216247307145428e+00 1.216247307152851e+00 7.42340e-12 7.58105e-12 ----------------------------------------------------------------------------------------------------- 2 N 1 -9.900835469155868e-01 -9.900835469138141e-01 1.77269e-12 2.36113e-11 2 -1.318875745418871e-01 -1.318875745426804e-01 7.93310e-13 8.92394e-11 3 -2.344545162949716e+00 -2.344545162953453e+00 3.73657e-12 8.39919e-11 ----------------------------------------------------------------------------------------------------- 3 N 1 -1.084720518657915e+00 -1.084720518683485e+00 2.55693e-11 5.99459e-10 2 -1.745616797286193e+00 -1.745616797288186e+00 1.99352e-12 5.78559e-12 3 6.902125327554298e-03 6.902125348843801e-03 2.12895e-11 8.97742e-11 ----------------------------------------------------------------------------------------------------- 4 N 1 -3.166468764818656e+00 -3.166468764802677e+00 1.59792e-11 1.20810e-10 2 -4.089433056053775e-01 -4.089433056020771e-01 3.30036e-12 3.39743e-11 3 -1.912014012149443e+00 -1.912014012139364e+00 1.00790e-11 1.32048e-10 ----------------------------------------------------------------------------------------------------- 5 N 1 3.542217240959095e-02 3.542217241693849e-02 7.34755e-12 3.79714e-11 2 -1.031137424512881e+00 -1.031137424515266e+00 2.38498e-12 6.70379e-11 3 -7.995731858471727e-01 -7.995731858410560e-01 6.11677e-12 3.38533e-11 ----------------------------------------------------------------------------------------------------- 6 N 1 1.442429581700747e+00 1.442429581696519e+00 4.22817e-12 1.54041e-10 2 -7.036357067059300e-01 -7.036357067182005e-01 1.22705e-11 7.07255e-11 3 -1.079025838493903e+00 -1.079025838496482e+00 2.57860e-12 2.66482e-11 ----------------------------------------------------------------------------------------------------- 7 N 1 -1.306256359618927e+00 -1.306256359645810e+00 2.68827e-11 2.61399e-10 2 1.921633741343022e+00 1.921633741342713e+00 3.08198e-13 3.89879e-11 3 8.546330883862268e-01 8.546330883917350e-01 5.50826e-12 9.10354e-11 ----------------------------------------------------------------------------------------------------- 8 N 1 7.502536097916433e-01 7.502536097981966e-01 6.55320e-12 3.08387e-10 2 -2.637885400933817e+00 -2.637885400953021e+00 1.92046e-11 2.33559e-10 3 3.267288223279078e+00 3.267288223308769e+00 2.96909e-11 1.58857e-10 ----------------------------------------------------------------------------------------------------- 9 N 1 3.161433993299055e-01 3.161433993285944e-01 1.31117e-12 5.66519e-12 2 1.472701709279039e+00 1.472701709310034e+00 3.09954e-11 2.38547e-10 3 5.412322514047607e-01 5.412322514043129e-01 4.47864e-13 6.45402e-11 ----------------------------------------------------------------------------------------------------- 10 N 1 2.544311514055783e-01 2.544311513839244e-01 2.16538e-11 3.10306e-10 2 3.098981230401047e+00 3.098981230400563e+00 4.83613e-13 1.90807e-11 3 -1.536532011850540e+00 -1.536532011844543e+00 5.99654e-12 6.33693e-12 ----------------------------------------------------------------------------------------------------- 11 N 1 -1.354958483502163e+00 -1.354958483492337e+00 9.82636e-12 5.07914e-11 2 -7.030421013395056e-01 -7.030421013136039e-01 2.59017e-11 1.17866e-10 3 -1.706430798208343e+00 -1.706430798216555e+00 8.21210e-12 1.24229e-10 ----------------------------------------------------------------------------------------------------- 12 N 1 -3.364245220615957e+00 -3.364245220614339e+00 1.61826e-12 4.66058e-11 2 1.426983796267353e+00 1.426983796278450e+00 1.10967e-11 2.37173e-11 3 6.445118569699065e-02 6.445118570269491e-02 5.70426e-12 4.49915e-10 ----------------------------------------------------------------------------------------------------- 13 N 1 4.764126365114974e+00 4.764126365129367e+00 1.43929e-11 5.75526e-10 2 2.458615483933751e+00 2.458615483924274e+00 9.47731e-12 1.22351e-10 3 -2.652114673114279e+00 -2.652114673115821e+00 1.54232e-12 5.39075e-11 ----------------------------------------------------------------------------------------------------- 14 N 1 7.183147896236700e-01 7.183147896235001e-01 1.69864e-13 4.63227e-11 2 9.746012506364480e-01 9.746012506345343e-01 1.91369e-12 2.03808e-11 3 -4.347149161575448e-01 -4.347149161580076e-01 4.62796e-13 1.32327e-11 ----------------------------------------------------------------------------------------------------- 15 N 1 4.859940849908828e-01 4.859940849929709e-01 2.08805e-12 4.97934e-11 2 -1.574812579656293e+00 -1.574812579659320e+00 3.02669e-12 7.67819e-11 3 2.190592173448536e-01 2.190592173705965e-01 2.57430e-11 5.03864e-11 ----------------------------------------------------------------------------------------------------- 16 N 1 -4.957576867821221e+00 -4.957576867818156e+00 3.06510e-12 2.38445e-10 2 -3.019153541742799e+00 -3.019153541757029e+00 1.42300e-11 2.80770e-09 * 3 -2.026511876747414e+00 -2.026511876753658e+00 6.24389e-12 3.99742e-09 * ----------------------------------------------------------------------------------------------------- 17 N 1 -9.881467589685062e-01 -9.881467589746340e-01 6.12776e-12 3.79106e-11 2 -7.185764448311681e-01 -7.185764448311499e-01 1.82077e-14 3.34255e-11 3 2.669000730079814e-01 2.669000730045169e-01 3.46445e-12 3.26119e-11 ----------------------------------------------------------------------------------------------------- 18 N 1 1.331754891298758e-01 1.331754891319928e-01 2.11697e-12 7.72364e-11 2 -1.721429616445088e+00 -1.721429616444105e+00 9.83214e-13 1.25019e-09 * 3 -8.943669784776942e-01 -8.943669784730197e-01 4.67448e-12 1.30138e-10 ----------------------------------------------------------------------------------------------------- 19 N 1 6.794965381703011e-01 6.794965381573089e-01 1.29922e-11 6.27304e-11 2 -5.136674806860075e-01 -5.136674807035986e-01 1.75910e-11 1.60293e-11 3 6.239299592849306e-01 6.239299592870595e-01 2.12896e-12 4.72293e-10 ----------------------------------------------------------------------------------------------------- 20 N 1 -1.265718003376652e+00 -1.265718003373232e+00 3.41993e-12 4.46347e-11 2 -2.814308871077738e-01 -2.814308871218834e-01 1.41095e-11 1.58590e-11 3 9.962666221206328e-01 9.962666221203226e-01 3.10196e-13 7.66820e-12 ----------------------------------------------------------------------------------------------------- 21 N 1 -4.959554562992275e-01 -4.959554562968642e-01 2.36328e-12 2.07327e-11 2 -2.563857245269726e+00 -2.563857245344327e+00 7.46008e-11 2.95995e-10 3 -1.850079136486043e-01 -1.850079136414093e-01 7.19499e-12 9.69557e-11 ----------------------------------------------------------------------------------------------------- 22 N 1 4.036999634286346e+00 4.036999634303312e+00 1.69660e-11 8.83833e-10 * 2 6.218776567097983e-01 6.218776567192869e-01 9.48852e-12 3.56665e-11 3 2.470062301257273e-01 2.470062301497404e-01 2.40131e-11 1.24541e-11 ----------------------------------------------------------------------------------------------------- 23 N 1 5.657869718141774e-01 5.657869718208552e-01 6.67788e-12 2.97891e-10 2 -4.757942988332161e-01 -4.757942988329806e-01 2.35534e-13 1.40722e-11 3 7.567986705459325e-01 7.567986705330493e-01 1.28833e-11 6.97693e-11 ----------------------------------------------------------------------------------------------------- 24 N 1 4.637778571162621e-01 4.637778570911591e-01 2.51030e-11 9.24816e-12 2 -1.510640975230302e-01 -1.510640975341334e-01 1.11033e-11 9.42648e-11 3 1.909224313521007e+00 1.909224313523985e+00 2.97806e-12 5.78306e-11 ----------------------------------------------------------------------------------------------------- 25 N 1 -1.382703486716934e+00 -1.382703486716478e+00 4.56080e-13 2.28505e-10 2 3.814188598262600e-01 3.814188598170435e-01 9.21652e-12 9.60091e-11 3 4.242050120338832e-01 4.242050120428413e-01 8.95806e-12 1.17727e-10 ----------------------------------------------------------------------------------------------------- 26 N 1 2.333864617457205e+00 2.333864617453688e+00 3.51674e-12 1.08136e-10 2 1.286183630882329e+00 1.286183630875596e+00 6.73261e-12 5.80997e-11 3 5.566047823294626e-01 5.566047823264375e-01 3.02514e-12 6.29518e-11 ----------------------------------------------------------------------------------------------------- 27 N 1 -1.619373285254367e-01 -1.619373285339324e-01 8.49562e-12 1.89882e-10 2 2.104367597729067e+00 2.104367597719665e+00 9.40137e-12 3.06470e-10 3 1.292731974887705e+00 1.292731974888246e+00 5.41345e-13 2.31563e-10 ----------------------------------------------------------------------------------------------------- 28 N 1 -1.175653470030422e+00 -1.175653470022682e+00 7.74070e-12 1.33104e-10 2 -1.100555433367986e+00 -1.100555433373330e+00 5.34373e-12 1.00944e-10 3 1.285525566932470e+00 1.285525566937864e+00 5.39391e-12 2.70816e-10 ----------------------------------------------------------------------------------------------------- 29 N 1 1.831699547229222e+00 1.831699547235008e+00 5.78648e-12 3.71618e-11 2 -1.227125711365095e-01 -1.227125711410875e-01 4.57795e-12 4.60635e-11 3 -6.363635214373182e-01 -6.363635214399651e-01 2.64688e-12 3.27986e-09 * ----------------------------------------------------------------------------------------------------- 30 N 1 1.593357849369039e+00 1.593357849379207e+00 1.01679e-11 7.41107e-11 2 1.529298244953744e+00 1.529298244936611e+00 1.71332e-11 2.63372e-10 3 -5.250727210677223e-01 -5.250727210631807e-01 4.54159e-12 2.75134e-10 ----------------------------------------------------------------------------------------------------- 31 N 1 -2.072386911967061e-01 -2.072386911898237e-01 6.88238e-12 6.07876e-11 2 -4.195316502745102e-01 -4.195316502647427e-01 9.76758e-12 5.35488e-11 3 3.407618324923504e-01 3.407618324916004e-01 7.50011e-13 5.58023e-11 ----------------------------------------------------------------------------------------------------- 32 N 1 1.742881549083598e-01 1.742881548754870e-01 3.28728e-11 7.87597e-11 2 2.085165221279714e+00 2.085165221280116e+00 4.01457e-13 1.18786e-10 3 1.862505174282720e+00 1.862505174302841e+00 2.01203e-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 3.455629189839681e-01 8.38052e-13 3.29796e-11 2 8.743558809082901e-02 8.743558805171728e-02 3.91117e-11 5.76997e-11 3 -1.506484180241523e-01 -1.506484180259673e-01 1.81496e-12 2.46919e-11 ----------------------------------------------------------------------------------------------------- 2 Ti 1 1.357962725977278e-01 1.357962725906391e-01 7.08877e-12 8.67437e-11 2 -8.103528466525300e-01 -8.103528466755653e-01 2.30352e-11 4.22076e-10 3 3.311303133976705e-01 3.311303133933638e-01 4.30667e-12 1.88556e-10 ----------------------------------------------------------------------------------------------------- 3 Ti 1 -1.559794209672646e-02 -1.559794213421720e-02 3.74907e-11 9.55070e-11 2 6.730642856594290e-01 6.730642856542367e-01 5.19229e-12 1.33546e-10 3 3.303767949205405e-01 3.303767949172178e-01 3.32273e-12 1.63005e-11 ----------------------------------------------------------------------------------------------------- 4 Ti 1 8.218299259872686e-01 8.218299260237668e-01 3.64982e-11 3.03411e-10 2 8.463657869850996e-03 8.463657854254585e-03 1.55964e-11 1.85698e-10 3 -2.294038302853515e-01 -2.294038302862158e-01 8.64281e-13 3.50298e-11 ----------------------------------------------------------------------------------------------------- 5 Ti 1 1.613715171557514e-01 1.613715171532368e-01 2.51466e-12 1.51008e-10 2 5.035016309531417e-01 5.035016309705198e-01 1.73781e-11 6.84797e-11 3 3.832001303326480e-01 3.832001303271024e-01 5.54556e-12 6.97198e-11 ----------------------------------------------------------------------------------------------------- 6 Ti 1 -3.521645043720372e-01 -3.521645043878550e-01 1.58178e-11 1.17827e-10 2 -1.068617643508797e-01 -1.068617643145799e-01 3.62998e-11 1.88077e-10 3 6.258955375171853e-01 6.258955375171836e-01 1.66533e-15 4.82903e-12 ----------------------------------------------------------------------------------------------------- 7 Ti 1 -5.884382542800943e-01 -5.884382542752511e-01 4.84324e-12 7.92425e-11 2 6.740433334244622e-01 6.740433334294700e-01 5.00777e-12 9.26412e-11 3 2.218150791189671e-02 2.218150789527508e-02 1.66216e-11 5.15879e-11 ----------------------------------------------------------------------------------------------------- 8 Ti 1 5.824606596551929e-01 5.824606596279255e-01 2.72674e-11 1.40378e-09 * 2 -5.395764707752918e-01 -5.395764707717131e-01 3.57869e-12 1.19062e-10 3 -7.013437581873281e-01 -7.013437581851677e-01 2.16038e-12 1.68970e-10 ----------------------------------------------------------------------------------------------------- 9 Ti 1 -4.671041090627950e-01 -4.671041090561448e-01 6.65024e-12 1.27379e-10 2 -1.341636820335422e-02 -1.341636818866750e-02 1.46867e-11 4.91746e-11 3 -5.164853509514771e-01 -5.164853509479165e-01 3.56060e-12 6.82201e-11 ----------------------------------------------------------------------------------------------------- 10 Ti 1 1.634354647298246e-01 1.634354646689919e-01 6.08327e-11 3.30167e-10 2 -3.625594920050687e-01 -3.625594920128348e-01 7.76607e-12 1.53987e-10 3 2.007877105292767e-01 2.007877105537640e-01 2.44873e-11 1.60421e-10 ----------------------------------------------------------------------------------------------------- 11 Ti 1 -2.686870195363852e-01 -2.686870195726779e-01 3.62926e-11 1.05446e-10 2 6.088791884589813e-01 6.088791884711505e-01 1.21693e-11 1.04526e-10 3 8.320520003230842e-01 8.320520002378093e-01 8.52749e-11 5.16153e-10 ----------------------------------------------------------------------------------------------------- 12 Ti 1 1.253925817583494e-01 1.253925817150552e-01 4.32942e-11 2.79565e-10 2 -1.390448637320160e-01 -1.390448637220064e-01 1.00096e-11 3.92265e-11 3 -6.998725692673005e-02 -6.998725691412359e-02 1.26065e-11 4.63451e-10 ----------------------------------------------------------------------------------------------------- 13 Ti 1 -1.518357943075422e+00 -1.518357943068300e+00 7.12141e-12 4.87618e-10 2 -1.016123999478388e+00 -1.016123999476511e+00 1.87650e-12 3.45095e-10 3 2.621350615211665e-01 2.621350614589469e-01 6.22196e-11 2.26917e-10 ----------------------------------------------------------------------------------------------------- 14 Ti 1 1.037800249467596e+00 1.037800249455752e+00 1.18443e-11 5.74856e-11 2 8.804893676029182e-01 8.804893675931972e-01 9.72100e-12 5.15754e-11 3 -6.882232234137292e-01 -6.882232234074382e-01 6.29097e-12 1.63495e-10 ----------------------------------------------------------------------------------------------------- 15 Ti 1 1.906139139686983e-01 1.906139139568149e-01 1.18835e-11 5.04922e-11 2 -1.311063637292532e+00 -1.311063637283431e+00 9.10183e-12 7.27425e-10 3 -2.462735875128732e-01 -2.462735875072880e-01 5.58517e-12 7.92109e-11 ----------------------------------------------------------------------------------------------------- 16 Ti 1 2.613918886617439e-03 2.613918910384991e-03 2.37676e-11 5.96992e-11 2 1.001499477570471e+00 1.001499477637739e+00 6.72677e-11 1.93500e-09 * 3 1.802344975406392e-01 1.802344975236961e-01 1.69432e-11 3.14266e-10 ----------------------------------------------------------------------------------------------------- 17 Ti 1 -3.337449304829202e-01 -3.337449304950407e-01 1.21205e-11 7.27920e-10 2 3.022659580361762e-01 3.022659580390643e-01 2.88802e-12 1.69900e-09 * 3 3.716202897251178e-01 3.716202897259344e-01 8.16569e-13 1.32919e-09 * ----------------------------------------------------------------------------------------------------- 18 Ti 1 1.397386462284766e-03 1.397386535266145e-03 7.29814e-11 1.27238e-10 2 -2.369306111141003e-01 -2.369306110985712e-01 1.55291e-11 4.13887e-11 3 -4.053820773511728e-01 -4.053820774354946e-01 8.43218e-11 1.59474e-10 ----------------------------------------------------------------------------------------------------- 19 Ti 1 3.749929087330671e-01 3.749929087469409e-01 1.38737e-11 1.24361e-10 2 -6.427914759935029e-01 -6.427914759879099e-01 5.59308e-12 9.58656e-05 * 3 -1.409683656602305e-01 -1.409683656560787e-01 4.15179e-12 8.88591e-11 ----------------------------------------------------------------------------------------------------- 20 Ti 1 -4.118349260338062e-01 -4.118349260768320e-01 4.30258e-11 5.69075e-10 2 5.801696061532949e-01 5.801696061235625e-01 2.97324e-11 1.52030e-10 3 -1.804969822659491e-01 -1.804969822425320e-01 2.34171e-11 5.14919e-10 ----------------------------------------------------------------------------------------------------- 21 Ti 1 5.805889096947218e-01 5.805889096838585e-01 1.08633e-11 1.05749e-10 2 7.146190294357151e-01 7.146190294503515e-01 1.46364e-11 1.03727e-10 3 -5.134700344244753e-01 -5.134700344396249e-01 1.51497e-11 6.83447e-11 ----------------------------------------------------------------------------------------------------- 22 Ti 1 -8.311008034521146e-01 -8.311008034081316e-01 4.39829e-11 8.32916e-10 2 -1.243708939193600e+00 -1.243708939200097e+00 6.49658e-12 2.89368e-10 3 9.173039986553923e-02 9.173039991634395e-02 5.08047e-11 2.59612e-10 ----------------------------------------------------------------------------------------------------- 23 Ti 1 1.490144331710582e-01 1.490144331718739e-01 8.15681e-13 1.09892e-10 2 4.572498242992692e-01 4.572498243100750e-01 1.08057e-11 1.76663e-10 3 -9.504454546441189e-02 -9.504454545447523e-02 9.93666e-12 1.76375e-10 ----------------------------------------------------------------------------------------------------- 24 Ti 1 9.278397022388733e-02 9.278397023892510e-02 1.50378e-11 8.45776e-11 2 2.181766076254024e-01 2.181766076021270e-01 2.32754e-11 6.13903e-11 3 -6.925309986319437e-01 -6.925309986505011e-01 1.85574e-11 5.11539e-11 ----------------------------------------------------------------------------------------------------- 25 Ti 1 8.994766231695067e-01 8.994766231861642e-01 1.66575e-11 1.36917e-10 2 6.400441548029910e-01 6.400441547961599e-01 6.83109e-12 2.44149e-10 3 6.954511272687393e-01 6.954511272703078e-01 1.56852e-12 1.83591e-10 ----------------------------------------------------------------------------------------------------- 26 Ti 1 2.300181344261331e-01 2.300181344232449e-01 2.88813e-12 2.12397e-10 2 -1.071913387777855e+00 -1.071913387802172e+00 2.43161e-11 1.53553e-10 3 7.303035207735562e-01 7.303035207732496e-01 3.06644e-13 2.26284e-10 ----------------------------------------------------------------------------------------------------- 27 Ti 1 -2.203496182609566e-01 -2.203496183936529e-01 1.32696e-10 3.27705e-10 2 -1.450907406846396e-01 -1.450907406976017e-01 1.29621e-11 8.28072e-11 3 -1.164583718766660e+00 -1.164583718775896e+00 9.23639e-12 8.03169e-11 ----------------------------------------------------------------------------------------------------- 28 Ti 1 2.958465435430436e-01 2.958465435655145e-01 2.24709e-11 1.89933e-10 2 -3.643250542949410e-01 -3.643250542603825e-01 3.45585e-11 3.51028e-10 3 -4.231424850179689e-01 -4.231424850198632e-01 1.89426e-12 1.18435e-10 ----------------------------------------------------------------------------------------------------- 29 Ti 1 -1.002462276727951e+00 -1.002462276689805e+00 3.81464e-11 1.07172e-10 2 -7.702043878184849e-01 -7.702043878223489e-01 3.86402e-12 8.63849e-11 3 4.445558041060840e-01 4.445558039819834e-01 1.24101e-10 4.18491e-10 ----------------------------------------------------------------------------------------------------- 30 Ti 1 3.467315848743968e-01 3.467315848363878e-01 3.80090e-11 2.12266e-10 2 8.420280884355873e-01 8.420280884396305e-01 4.04321e-12 8.60624e-11 3 4.188396538964719e-01 4.188396538782589e-01 1.82129e-11 9.21309e-11 ----------------------------------------------------------------------------------------------------- 31 Ti 1 -3.297447596478412e-01 -3.297447596475030e-01 3.38118e-13 1.78152e-09 * 2 1.012732024908925e-01 1.012732024862956e-01 4.59692e-12 3.62415e-10 3 -1.348447980566314e-01 -1.348447980466420e-01 9.98934e-12 1.37465e-10 ----------------------------------------------------------------------------------------------------- 32 Ti 1 -1.981408304592062e-01 -1.981408304452025e-01 1.40037e-11 7.70439e-11 2 4.807610384577733e-01 4.807610384451589e-01 1.26144e-11 2.20125e-10 3 4.323350813114694e-01 4.323350812627478e-01 4.87215e-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 2.705723875883163e-01 4.35141e-12 6.50391e-10 2 -5.776373418434505e-01 -5.776373418532984e-01 9.84790e-12 3.74790e-11 3 -6.210663502485075e-01 -6.210663502465343e-01 1.97320e-12 4.45383e-11 ----------------------------------------------------------------------------------------------------- 2 Ti 1 3.739726644572683e+00 3.739726644568784e+00 3.89910e-12 4.25054e-10 2 3.345635276554668e-03 3.345635280578948e-03 4.02428e-12 1.56387e-10 3 -3.037690075233395e-01 -3.037690075260798e-01 2.74031e-12 1.83978e-09 ----------------------------------------------------------------------------------------------------- 3 Ti 1 2.240209081790972e+00 2.240209081792517e+00 1.54499e-12 2.98331e-10 2 -1.559280853191728e+00 -1.559280853221797e+00 3.00693e-11 2.60867e-10 3 1.040845107072931e+00 1.040845107062607e+00 1.03235e-11 6.08503e-10 ----------------------------------------------------------------------------------------------------- 4 Ti 1 -1.846851434422295e+00 -1.846851434434805e+00 1.25107e-11 1.26640e-10 2 -2.052939821493398e+00 -2.052939821494483e+00 1.08491e-12 1.58145e-09 3 8.368880063170122e-01 8.368880062903098e-01 2.67024e-11 1.26735e-09 ----------------------------------------------------------------------------------------------------- 5 Ti 1 8.984198766026124e-01 8.984198766163995e-01 1.37872e-11 2.77325e-10 2 1.254042697527439e+00 1.254042697496161e+00 3.12776e-11 1.95104e-09 3 2.612142520264905e+00 2.612142520270003e+00 5.09859e-12 3.99941e-10 ----------------------------------------------------------------------------------------------------- 6 Ti 1 -2.416495905599791e+00 -2.416495905583183e+00 1.66080e-11 4.58157e-09 * 2 1.169902256825227e+00 1.169902256845701e+00 2.04745e-11 8.12008e-11 3 3.603374272606394e+00 3.603374272552164e+00 5.42291e-11 1.94166e-10 ----------------------------------------------------------------------------------------------------- 7 N 1 2.777429269130358e+00 2.777429269189359e+00 5.90004e-11 1.07669e-10 2 -3.056269714094903e+00 -3.056269714074006e+00 2.08971e-11 1.69896e-10 3 -1.053480440691913e+01 -1.053480440686354e+01 5.55893e-11 1.24439e-10 ----------------------------------------------------------------------------------------------------- 8 N 1 -1.612412462495600e+00 -1.612412462499848e+00 4.24727e-12 1.21731e-10 2 3.750471793912923e-01 3.750471793534939e-01 3.77984e-11 2.42545e-11 3 8.426957218158483e-01 8.426957218068818e-01 8.96649e-12 4.96752e-09 * ----------------------------------------------------------------------------------------------------- 9 Ti 1 1.370773816041004e+00 1.370773816005346e+00 3.56584e-11 2.56054e-10 2 3.206699798030684e+00 3.206699798046872e+00 1.61884e-11 1.12751e-10 3 6.582241276039411e-01 6.582241276078608e-01 3.91964e-12 1.45240e-10 ----------------------------------------------------------------------------------------------------- 10 N 1 -3.300858111533022e+00 -3.300858111455624e+00 7.73981e-11 2.98802e-10 2 -1.037048337936089e+00 -1.037048337941860e+00 5.77138e-12 1.64848e-11 3 -1.166483511639473e+00 -1.166483511635358e+00 4.11493e-12 7.88292e-11 ----------------------------------------------------------------------------------------------------- 11 Ti 1 2.270987114698642e+00 2.270987114700043e+00 1.40021e-12 1.64989e-09 2 5.074497687148138e+00 5.074497687275477e+00 1.27340e-10 5.54050e-09 * 3 -5.218597355079426e+00 -5.218597355149721e+00 7.02949e-11 5.04678e-10 ----------------------------------------------------------------------------------------------------- 12 N 1 1.054320039783375e+00 1.054320039787949e+00 4.57412e-12 1.41258e-10 2 -3.320313068324987e+00 -3.320313068267174e+00 5.78129e-11 1.82926e-10 3 1.610296788258471e+00 1.610296788293086e+00 3.46148e-11 3.39565e-10 ----------------------------------------------------------------------------------------------------- 13 N 1 -2.971069860427248e-01 -2.971069861193204e-01 7.65956e-11 5.15974e-10 2 -5.482876396234935e+00 -5.482876396269359e+00 3.44240e-11 2.92387e-10 3 -1.255351234670357e+00 -1.255351234669354e+00 1.00298e-12 1.16596e-09 ----------------------------------------------------------------------------------------------------- 14 N 1 6.762707970238502e-01 6.762707970167042e-01 7.14595e-12 3.07818e-10 2 1.407818049106876e-01 1.407818049449946e-01 3.43070e-11 2.55953e-10 3 2.009080685832539e+00 2.009080685846706e+00 1.41673e-11 2.47063e-10 ----------------------------------------------------------------------------------------------------- 15 Ti 1 -2.121895615639388e+00 -2.121895615628386e+00 1.10023e-11 2.14900e-10 2 1.459989164699080e+00 1.459989164715833e+00 1.67528e-11 1.27130e-08 * 3 -1.242517788344653e+00 -1.242517788320093e+00 2.45599e-11 3.18592e-11 ----------------------------------------------------------------------------------------------------- 16 N 1 -1.553927632190312e+00 -1.553927632165706e+00 2.46059e-11 5.90603e-11 2 -1.228070827142084e+00 -1.228070827124417e+00 1.76672e-11 3.70800e-09 * 3 3.399737097127390e+00 3.399737097144536e+00 1.71463e-11 3.98787e-10 ----------------------------------------------------------------------------------------------------- 17 N 1 1.379593661238147e+00 1.379593661258863e+00 2.07154e-11 1.04208e-10 2 1.113185963124229e+00 1.113185963126214e+00 1.98486e-12 4.51315e-11 3 -4.405784858269872e+00 -4.405784858272156e+00 2.28439e-12 1.21732e-10 ----------------------------------------------------------------------------------------------------- 18 Ti 1 6.765620863455295e-01 6.765620863295270e-01 1.60025e-11 3.78373e-11 2 -7.844466592525050e+00 -7.844466592619618e+00 9.45679e-11 5.91839e-10 3 5.639518344160217e+00 5.639518344183011e+00 2.27942e-11 8.28049e-11 ----------------------------------------------------------------------------------------------------- 19 N 1 2.355851423254449e-01 2.355851423205739e-01 4.87099e-12 9.36322e-11 2 -5.706033962657870e-01 -5.706033961923170e-01 7.34700e-11 1.03410e-11 3 -3.670824392187067e-01 -3.670824392262588e-01 7.55213e-12 2.16429e-11 ----------------------------------------------------------------------------------------------------- 20 N 1 1.602192724662239e+00 1.602192724636273e+00 2.59661e-11 1.54641e-10 2 5.217632907615806e+00 5.217632907627931e+00 1.21254e-11 2.88331e-09 * 3 -1.187958029555467e+00 -1.187958029533261e+00 2.22060e-11 1.22501e-10 ----------------------------------------------------------------------------------------------------- 21 N 1 -7.620752126161504e+00 -7.620752126158914e+00 2.58993e-12 1.67629e-10 2 2.407923480068333e-01 2.407923480258332e-01 1.89999e-11 4.01076e-10 3 -1.104784729249700e+00 -1.104784729206892e+00 4.28082e-11 1.16153e-10 ----------------------------------------------------------------------------------------------------- 22 N 1 1.524080806577185e+00 1.524080806561469e+00 1.57157e-11 1.67618e-10 2 3.350606014427419e+00 3.350606014404071e+00 2.33484e-11 1.94992e-10 3 -3.884521815087202e+00 -3.884521815064733e+00 2.24687e-11 1.39229e-09 ----------------------------------------------------------------------------------------------------- 23 N 1 2.037056631583464e+00 2.037056631578570e+00 4.89475e-12 2.11883e-09 2 5.387417009338886e-01 5.387417009107691e-01 2.31195e-11 1.03205e-09 3 1.803828514006690e+00 1.803828514013810e+00 7.12008e-12 1.34844e-09 ----------------------------------------------------------------------------------------------------- 24 N 1 -4.704274091189921e+00 -4.704274091189228e+00 6.92779e-13 3.63825e-11 2 2.721972870285477e+00 2.721972870307482e+00 2.20051e-11 1.49815e-09 3 1.516103229233655e+00 1.516103229237262e+00 3.60689e-12 4.55999e-09 * ----------------------------------------------------------------------------------------------------- 25 Ti 1 -2.377456221029214e+00 -2.377456220977137e+00 5.20775e-11 5.28083e-10 2 1.922750145788478e+00 1.922750145786899e+00 1.57918e-12 2.79092e-10 3 1.995183569501201e+00 1.995183569448671e+00 5.25306e-11 2.01358e-09 ----------------------------------------------------------------------------------------------------- 26 Ti 1 -7.794793226174197e-02 -7.794793226417020e-02 2.42822e-12 1.03857e-10 2 8.052660300298283e-01 8.052660300400433e-01 1.02149e-11 2.29159e-10 3 -2.748525560279788e+00 -2.748525560291053e+00 1.12648e-11 5.44672e-10 ----------------------------------------------------------------------------------------------------- 27 Ti 1 -2.743648674658310e+00 -2.743648674667808e+00 9.49862e-12 3.78176e-10 2 -2.682239683753816e+00 -2.682239683778786e+00 2.49702e-11 1.09341e-09 3 3.386887593405297e+00 3.386887593391100e+00 1.41971e-11 4.19022e-09 * ----------------------------------------------------------------------------------------------------- 28 Ti 1 -3.071803381086640e-01 -3.071803381791787e-01 7.05146e-11 2.29519e-10 2 5.729960160173064e-01 5.729960160444697e-01 2.71633e-11 6.43953e-11 3 8.788408251153016e-01 8.788408250929739e-01 2.23277e-11 2.64840e-10 ----------------------------------------------------------------------------------------------------- 29 Ti 1 8.065425702560018e+00 8.065425702522541e+00 3.74776e-11 1.71097e-10 2 -7.769104419161564e-02 -7.769104418913056e-02 2.48508e-12 2.09919e-10 3 1.396407901707192e+00 1.396407901737799e+00 3.06071e-11 6.48728e-10 ----------------------------------------------------------------------------------------------------- 30 N 1 7.433450151163539e-01 7.433450151284571e-01 1.21032e-11 4.79379e-11 2 -1.612740157498684e+00 -1.612740157468156e+00 3.05287e-11 7.99898e-10 3 3.799252182560522e-01 3.799252182605053e-01 4.45310e-12 1.28701e-10 ----------------------------------------------------------------------------------------------------- 31 N 1 -3.219226786851314e+00 -3.219226786850936e+00 3.78364e-13 1.80684e-10 2 2.071507287367081e+00 2.071507287415933e+00 4.88516e-11 3.79832e-10 3 5.754133185214620e-01 5.754133185444734e-01 2.30114e-11 1.14355e-09 ----------------------------------------------------------------------------------------------------- 32 Ti 1 2.637483520539254e+00 2.637483520556155e+00 1.69007e-11 3.50575e-10 2 -1.375802729089247e-01 -1.375802729252932e-01 1.63685e-11 2.60779e-09 * 3 -1.441457547208776e-01 -1.441457547291566e-01 8.27902e-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 = ----------------------- = 1.20284e-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.