!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! VERIFICATION CHECK: vc-forces-numerical-derivative !!!!! !!!!! !!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Description: Comparison of the analytical forces obtained from the model with forces computed by numerical differentiation using Richardson extrapolation for a randomly distorted non-periodic structure based off the equilibrium face-centered cubic (fcc) structure. Separate configurations are tested for each species supported by the model, as well as one containing a random distribution of all species. Configurations used for testing are provided as auxiliary files. Author: Ellad Tadmor ----------------------------------------------------------------------------------------------------- Results for KIM Model : Tersoff_LAMMPS_Erhart_Juslin_Goy_Nordlund_Mueller_Albe_ZnO__MO_616776018688_000 Supported species : O Zn 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 = O | a0 = 3.41083049774 | (Configuration in file "config-O.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 O 1 7.293988884501881e-02 7.293988884611032e-02 1.09150e-12 1.02151e-11 2 2.198641904531065e-01 2.198641904525026e-01 6.03823e-13 4.64259e-12 3 8.994518617133568e-01 8.994518617136837e-01 3.26961e-13 2.73637e-12 ----------------------------------------------------------------------------------------------------- 2 O 1 7.395433497603027e-01 7.395433497606095e-01 3.06866e-13 9.31621e-12 2 1.045229094562193e-01 1.045229094534264e-01 2.79288e-12 1.61503e-11 3 -1.232855068896582e-01 -1.232855068907973e-01 1.13910e-12 3.05109e-12 ----------------------------------------------------------------------------------------------------- 3 O 1 -7.590257371181584e-01 -7.590257371172203e-01 9.38027e-13 1.45066e-11 2 3.267889869826648e-01 3.267889869811155e-01 1.54932e-12 2.50379e-11 3 1.009158422364013e-01 1.009158422381733e-01 1.77208e-12 6.03939e-12 ----------------------------------------------------------------------------------------------------- 4 O 1 -4.249473813603893e-01 -4.249473813644898e-01 4.10044e-12 2.37478e-11 2 -6.360215103044474e-01 -6.360215103020617e-01 2.38576e-12 1.32088e-11 3 -8.913896943287599e-01 -8.913896943307652e-01 2.00528e-12 1.45027e-11 ----------------------------------------------------------------------------------------------------- 5 O 1 -1.192060399378410e-01 -1.192060399384937e-01 6.52714e-13 1.02730e-11 2 5.030799978221504e-01 5.030799978211783e-01 9.72111e-13 3.27627e-12 3 -7.043524060731623e-01 -7.043524060731257e-01 3.66374e-14 2.07909e-11 ----------------------------------------------------------------------------------------------------- 6 O 1 -4.145374514626194e-01 -4.145374514615015e-01 1.11794e-12 3.15736e-12 2 -3.340043477586287e-01 -3.340043477586567e-01 2.80331e-14 6.98153e-12 3 -3.451545143232319e-01 -3.451545143235578e-01 3.25906e-13 1.77600e-11 ----------------------------------------------------------------------------------------------------- 7 O 1 2.578069416675899e-01 2.578069416686274e-01 1.03745e-12 4.76130e-12 2 -6.190547205229326e-01 -6.190547205275477e-01 4.61509e-12 1.32957e-11 3 4.654198515032887e-01 4.654198515039290e-01 6.40266e-13 6.05010e-12 ----------------------------------------------------------------------------------------------------- 8 O 1 5.696342215623382e-01 5.696342215690973e-01 6.75904e-12 5.54123e-12 2 -3.568559705711675e-01 -3.568559705560456e-01 1.51220e-11 9.08053e-11 * 3 -8.227616516292466e-02 -8.227616516520310e-02 2.27844e-12 3.66932e-11 ----------------------------------------------------------------------------------------------------- 9 O 1 3.833682319822721e-01 3.833682319824656e-01 1.93456e-13 3.70165e-12 2 6.237451097752860e-01 6.237451097744432e-01 8.42770e-13 2.75169e-11 3 5.838333637646771e-01 5.838333637642178e-01 4.59299e-13 6.98919e-12 ----------------------------------------------------------------------------------------------------- 10 O 1 -2.580383317133376e-01 -2.580383317136771e-01 3.39506e-13 2.11341e-10 * 2 -5.742956275616740e-02 -5.742956275554896e-02 6.18436e-13 7.05389e-12 3 -4.481573105836064e-01 -4.481573105843331e-01 7.26752e-13 7.86721e-12 ----------------------------------------------------------------------------------------------------- 11 O 1 -6.787855807613800e-01 -6.787855807603744e-01 1.00553e-12 1.20596e-10 * 2 1.146442835631397e-01 1.146442835635472e-01 4.07535e-13 2.48692e-11 3 -3.487619197821523e-01 -3.487619197830865e-01 9.34197e-13 8.87207e-12 ----------------------------------------------------------------------------------------------------- 12 O 1 -4.695780646475403e-02 -4.695780646489164e-02 1.37605e-13 3.59680e-12 2 -5.477659180324339e-01 -5.477659180315987e-01 8.35221e-13 1.98550e-11 3 6.986468315965166e-02 6.986468316135898e-02 1.70731e-12 8.81178e-12 ----------------------------------------------------------------------------------------------------- 13 O 1 4.900644180816720e-01 4.900644180786350e-01 3.03696e-12 3.19483e-11 2 7.511151616607824e-01 7.511151616633402e-01 2.55784e-12 2.22757e-11 3 -5.727314488501162e-01 -5.727314488514811e-01 1.36491e-12 8.94562e-12 ----------------------------------------------------------------------------------------------------- 14 O 1 -5.189363976044858e-01 -5.189363976045266e-01 4.07452e-14 1.55072e-11 2 -7.575091588235875e-01 -7.575091588232733e-01 3.14193e-13 3.66784e-12 3 3.835195254500625e-01 3.835195254499135e-01 1.48992e-13 4.26637e-12 ----------------------------------------------------------------------------------------------------- 15 O 1 2.828625733026429e-01 2.828625733015599e-01 1.08297e-12 1.94978e-11 2 9.836287833547648e-01 9.836287833550651e-01 3.00315e-13 3.71848e-11 3 -3.176950529814263e-01 -3.176950529852921e-01 3.86585e-12 2.42056e-11 ----------------------------------------------------------------------------------------------------- 16 O 1 -4.011206181864883e-01 -4.011206181834711e-01 3.01714e-12 9.05898e-12 2 -1.445499273874390e-02 -1.445499273913292e-02 3.89012e-13 5.63840e-12 3 -2.640121287478528e-01 -2.640121287495544e-01 1.70164e-12 4.85029e-12 ----------------------------------------------------------------------------------------------------- 17 O 1 4.329283501821873e-01 4.329283501827427e-01 5.55389e-13 5.51553e-12 2 1.052127105938645e-01 1.052127105936755e-01 1.88960e-13 8.99425e-12 3 5.875946735539859e-01 5.875946735549016e-01 9.15712e-13 6.39155e-13 ----------------------------------------------------------------------------------------------------- 18 O 1 -5.682824957222116e-01 -5.682824957250602e-01 2.84861e-12 2.77327e-11 2 -4.025850277553565e-01 -4.025850277499788e-01 5.37770e-12 3.80281e-11 3 4.352911783745353e-01 4.352911783728367e-01 1.69870e-12 1.88860e-12 ----------------------------------------------------------------------------------------------------- 19 O 1 -1.176218756583173e+00 -1.176218756584090e+00 9.17488e-13 4.86544e-12 2 1.793713510597591e-01 1.793713510572506e-01 2.50852e-12 2.42914e-12 3 -1.500079091963678e-02 -1.500079092021942e-02 5.82649e-13 9.77303e-12 ----------------------------------------------------------------------------------------------------- 20 O 1 6.326158713377245e-01 6.326158713366189e-01 1.10556e-12 4.49063e-12 2 -6.608361729949307e-01 -6.608361729955021e-01 5.71432e-13 6.78901e-12 3 -6.722363859645388e-01 -6.722363859658301e-01 1.29130e-12 3.10523e-11 ----------------------------------------------------------------------------------------------------- 21 O 1 1.155980377860298e+00 1.155980377858577e+00 1.72173e-12 5.14011e-12 2 -7.683543178044910e-02 -7.683543177729937e-02 3.14973e-12 2.55111e-11 3 5.922533719392629e-01 5.922533719386385e-01 6.24389e-13 1.67899e-11 ----------------------------------------------------------------------------------------------------- 22 O 1 4.381799652840797e-01 4.381799652844801e-01 4.00346e-13 2.11646e-11 2 -7.366060270921424e-01 -7.366060270841819e-01 7.96052e-12 1.31258e-11 3 3.544620582427062e-01 3.544620582428858e-01 1.79634e-13 3.13918e-11 ----------------------------------------------------------------------------------------------------- 23 O 1 -1.007278250497502e+00 -1.007278250498187e+00 6.84564e-13 1.02185e-11 2 3.628837166237329e-01 3.628837166270702e-01 3.33727e-12 6.90747e-12 3 -2.946515220972096e-01 -2.946515220973343e-01 1.24678e-13 1.53274e-11 ----------------------------------------------------------------------------------------------------- 24 O 1 1.083274200669900e+00 1.083274200671813e+00 1.91380e-12 3.38294e-11 2 -8.876819365878368e-01 -8.876819365896582e-01 1.82143e-12 3.22344e-11 3 4.182253304276728e-02 4.182253304174689e-02 1.02039e-12 3.45111e-12 ----------------------------------------------------------------------------------------------------- 25 O 1 -1.021682175538530e-01 -1.021682175536073e-01 2.45678e-13 1.19352e-11 2 6.944322877641502e-01 6.944322877656687e-01 1.51845e-12 2.27404e-11 3 -1.269385097003456e-01 -1.269385096973587e-01 2.98686e-12 7.11812e-11 ----------------------------------------------------------------------------------------------------- 26 O 1 -3.541795505017933e-01 -3.541795505004295e-01 1.36380e-12 1.41187e-10 * 2 7.025723555761566e-01 7.025723555671881e-01 8.96849e-12 1.07275e-10 * 3 -3.384372735815574e-01 -3.384372735828503e-01 1.29285e-12 1.50774e-11 ----------------------------------------------------------------------------------------------------- 27 O 1 -7.659318592231119e-01 -7.659318592224923e-01 6.19615e-13 1.13595e-10 * 2 -3.516155783479749e-01 -3.516155783502339e-01 2.25903e-12 1.06637e-10 * 3 9.438059919304795e-01 9.438059919293347e-01 1.14486e-12 8.92608e-12 ----------------------------------------------------------------------------------------------------- 28 O 1 -3.097440943007881e-02 -3.097440943074303e-02 6.64215e-13 9.50413e-12 2 -3.635103770755885e-02 -3.635103770791379e-02 3.54931e-13 3.26839e-12 3 -2.065077673878264e-01 -2.065077673872724e-01 5.54029e-13 4.14846e-12 ----------------------------------------------------------------------------------------------------- 29 O 1 -2.663144102843098e-01 -2.663144102842612e-01 4.85723e-14 6.99534e-11 2 5.763209569785754e-01 5.763209569792411e-01 6.65690e-13 4.35355e-11 3 -7.203640286828443e-01 -7.203640286930149e-01 1.01705e-11 8.47225e-11 ----------------------------------------------------------------------------------------------------- 30 O 1 6.773044128742491e-01 6.773044128744679e-01 2.18714e-13 3.07560e-11 2 -4.918623084608386e-01 -4.918623084592451e-01 1.59356e-12 1.75838e-11 3 -8.932928405225221e-03 -8.932928403135896e-03 2.08933e-12 4.21726e-12 ----------------------------------------------------------------------------------------------------- 31 O 1 7.235954005309625e-01 7.235954005318694e-01 9.06941e-13 7.26985e-12 2 1.117621269255230e+00 1.117621269255946e+00 7.16094e-13 4.40648e-11 3 8.658148662337402e-01 8.658148662348040e-01 1.06382e-12 1.17519e-11 ----------------------------------------------------------------------------------------------------- 32 O 1 -4.719490953574940e-02 -4.719490953427317e-02 1.47622e-12 2.43844e-11 2 -3.983343686843857e-01 -3.983343686826650e-01 1.72062e-12 4.82021e-11 3 1.568355533171614e-01 1.568355533199572e-01 2.79585e-12 8.41271e-12 ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as dicontinuities. Maximum error obtained for particle = 30, direction = 3: |F_model - F_numer| error = --------------------------------- = 2.33890e-10 max{(|F_model|+|F_numer|)/2, 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 = Zn | a0 = 3.81624603271 | (Configuration in file "config-Zn.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Zn 1 1.139036129237760e-01 1.139036129221271e-01 1.64888e-12 3.22317e-12 2 7.371993625698092e-01 7.371993625709372e-01 1.12799e-12 5.53546e-12 3 7.351822336562507e-01 7.351822336559611e-01 2.89546e-13 3.96072e-12 ----------------------------------------------------------------------------------------------------- 2 Zn 1 1.173760234653600e+00 1.173760234653695e+00 9.57012e-14 7.84817e-12 2 5.183697845663715e-01 5.183697845663190e-01 5.25135e-14 8.33367e-12 3 -6.654626147954364e-01 -6.654626147961852e-01 7.48734e-13 2.69644e-11 ----------------------------------------------------------------------------------------------------- 3 Zn 1 3.738895423722065e-01 3.738895423706587e-01 1.54771e-12 6.16951e-12 2 5.094512023985627e-02 5.094512023867884e-02 1.17743e-12 6.45795e-12 3 -1.419291205878337e-01 -1.419291205881881e-01 3.54439e-13 2.00198e-12 ----------------------------------------------------------------------------------------------------- 4 Zn 1 -1.225268345460995e+00 -1.225268345461629e+00 6.34603e-13 4.75486e-12 2 -2.427621142054693e-01 -2.427621142037300e-01 1.73928e-12 3.06198e-11 3 1.040916870965402e+00 1.040916870966122e+00 7.20757e-13 1.80717e-10 * ----------------------------------------------------------------------------------------------------- 5 Zn 1 6.423057334469023e-01 6.423057334463089e-01 5.93414e-13 1.07047e-11 2 4.015280830650650e-01 4.015280830653278e-01 2.62790e-13 4.67482e-12 3 6.277966685028784e-01 6.277966685026017e-01 2.76668e-13 5.31608e-12 ----------------------------------------------------------------------------------------------------- 6 Zn 1 -2.809251975498028e-01 -2.809251975492209e-01 5.81979e-13 4.53360e-12 2 3.313535729476035e-01 3.313535729459476e-01 1.65590e-12 6.04083e-12 3 6.616412897593438e-01 6.616412897588718e-01 4.71956e-13 6.71296e-12 ----------------------------------------------------------------------------------------------------- 7 Zn 1 -1.779267502350809e+00 -1.779267502352383e+00 1.57341e-12 1.03362e-12 2 1.251128188375814e+00 1.251128188375584e+00 2.30482e-13 4.82547e-12 3 -3.909873772408715e-01 -3.909873772409330e-01 6.15064e-14 2.08583e-12 ----------------------------------------------------------------------------------------------------- 8 Zn 1 1.252957079238955e+00 1.252957079227501e+00 1.14542e-11 1.45187e-10 * 2 -6.850601664604564e-01 -6.850601664617862e-01 1.32983e-12 2.07160e-11 3 -8.934938694185884e-01 -8.934938693763201e-01 4.22683e-11 1.77106e-10 * ----------------------------------------------------------------------------------------------------- 9 Zn 1 -1.079396381621258e+00 -1.079396381621746e+00 4.88054e-13 2.69273e-12 2 -2.950266650839190e+00 -2.950266650837226e+00 1.96376e-12 6.97842e-12 3 -1.318985813423157e+00 -1.318985813423295e+00 1.38334e-13 2.42384e-12 ----------------------------------------------------------------------------------------------------- 10 Zn 1 3.145636417514470e+00 3.145636417515135e+00 6.65246e-13 2.29194e-12 2 1.686700654105006e+00 1.686700654100602e+00 4.40314e-12 5.16320e-12 3 -1.136888589507116e+00 -1.136888589504935e+00 2.18092e-12 8.11418e-12 ----------------------------------------------------------------------------------------------------- 11 Zn 1 3.207238464536450e-01 3.207238464534871e-01 1.57985e-13 3.04471e-11 2 -2.091149929004811e-01 -2.091149928981296e-01 2.35148e-12 1.68949e-10 * 3 -3.718801669196129e+00 -3.718801669198895e+00 2.76579e-12 4.43383e-11 ----------------------------------------------------------------------------------------------------- 12 Zn 1 -1.862508299363288e+00 -1.862508299362637e+00 6.50813e-13 3.39062e-13 2 6.052010273416322e-01 6.052010273419755e-01 3.43281e-13 6.64346e-12 3 2.611486943713330e+00 2.611486943717692e+00 4.36184e-12 1.01972e-11 ----------------------------------------------------------------------------------------------------- 13 Zn 1 1.315883746300923e+00 1.315883746300855e+00 6.81677e-14 2.51288e-12 2 -1.379397772538936e-01 -1.379397772541134e-01 2.19852e-13 9.33154e-12 3 8.497994517617441e-01 8.497994517632294e-01 1.48526e-12 6.23568e-12 ----------------------------------------------------------------------------------------------------- 14 Zn 1 -1.776989440873893e+00 -1.776989440874614e+00 7.20979e-13 2.51799e-12 2 -1.480279257831330e+00 -1.480279257831463e+00 1.33449e-13 3.60467e-12 3 1.665363488558938e+00 1.665363488559978e+00 1.04028e-12 1.66345e-11 ----------------------------------------------------------------------------------------------------- 15 Zn 1 -7.020320237220783e-01 -7.020320237221782e-01 9.99201e-14 9.80926e-12 2 5.227046111549003e-01 5.227046111521959e-01 2.70439e-12 2.39444e-11 3 -6.416607138266656e-01 -6.416607138267900e-01 1.24456e-13 1.67173e-11 ----------------------------------------------------------------------------------------------------- 16 Zn 1 5.418702558847727e-01 5.418702558998824e-01 1.51097e-11 2.16488e-11 2 -8.603706467197650e-01 -8.603706467245197e-01 4.75464e-12 6.54155e-12 3 -9.149364289471348e-01 -9.149364289454067e-01 1.72806e-12 1.14837e-11 ----------------------------------------------------------------------------------------------------- 17 Zn 1 2.133131152557909e-01 2.133131152548368e-01 9.54015e-13 1.05618e-11 2 1.091543464276561e+00 1.091543464274784e+00 1.77658e-12 7.98885e-11 * 3 1.127768406360447e+00 1.127768406362139e+00 1.69220e-12 1.14413e-11 ----------------------------------------------------------------------------------------------------- 18 Zn 1 -1.630765086128267e+00 -1.630765086126194e+00 2.07390e-12 2.37685e-11 2 -4.235264247135787e+00 -4.235264247128589e+00 7.19869e-12 9.95826e-12 3 2.721999656604765e+00 2.721999656602970e+00 1.79456e-12 1.64593e-11 ----------------------------------------------------------------------------------------------------- 19 Zn 1 -1.309583853078714e+00 -1.309583853084629e+00 5.91505e-12 7.09566e-12 2 1.470480143825380e+00 1.470480143828046e+00 2.66609e-12 1.59843e-11 3 -5.712624883717450e-01 -5.712624883750602e-01 3.31524e-12 4.09262e-12 ----------------------------------------------------------------------------------------------------- 20 Zn 1 1.511291234649181e+00 1.511291234649078e+00 1.03473e-13 3.14704e-12 2 -8.036775328558735e-01 -8.036775328555219e-01 3.51608e-13 1.91154e-11 3 -1.651886032836800e+00 -1.651886032840122e+00 3.32134e-12 5.89018e-12 ----------------------------------------------------------------------------------------------------- 21 Zn 1 -3.820262001761534e-01 -3.820262001776706e-01 1.51723e-12 3.08209e-12 2 1.226833564376417e+00 1.226833564375508e+00 9.08384e-13 8.92508e-12 3 -1.975680027610734e+00 -1.975680027606926e+00 3.80829e-12 6.59739e-12 ----------------------------------------------------------------------------------------------------- 22 Zn 1 -3.537495991604131e-01 -3.537495991546281e-01 5.78498e-12 1.48567e-10 * 2 2.163880314753068e-01 2.163880314773018e-01 1.99502e-12 8.92631e-11 * 3 -2.138385949731052e+00 -2.138385949740825e+00 9.77352e-12 3.19762e-10 * ----------------------------------------------------------------------------------------------------- 23 Zn 1 1.024850093470150e+00 1.024850093470736e+00 5.85532e-13 7.51910e-12 2 -1.471445773142640e+00 -1.471445773143449e+00 8.08464e-13 1.07248e-12 3 1.968882531674065e+00 1.968882531674507e+00 4.42535e-13 7.89568e-12 ----------------------------------------------------------------------------------------------------- 24 Zn 1 1.360115391488069e+00 1.360115391489627e+00 1.55853e-12 3.41880e-11 2 -2.655473313324705e+00 -2.655473313331577e+00 6.87228e-12 1.37401e-11 3 1.009041928932352e+00 1.009041928932442e+00 8.99281e-14 6.77258e-12 ----------------------------------------------------------------------------------------------------- 25 Zn 1 -3.667830564832381e-01 -3.667830564829171e-01 3.21021e-13 5.40168e-12 2 -2.712047885148223e-01 -2.712047885103371e-01 4.48525e-12 2.11675e-12 3 1.655606920970147e+00 1.655606920967662e+00 2.48557e-12 5.54468e-12 ----------------------------------------------------------------------------------------------------- 26 Zn 1 3.413923870770226e-01 3.413923870750891e-01 1.93356e-12 1.14062e-11 2 1.963071871872973e+00 1.963071871871145e+00 1.82832e-12 1.71387e-11 3 2.493918747602579e+00 2.493918747603360e+00 7.80709e-13 3.42615e-12 ----------------------------------------------------------------------------------------------------- 27 Zn 1 -4.340934635923577e+00 -4.340934635921883e+00 1.69376e-12 1.20579e-11 2 2.869218649037911e+00 2.869218649040316e+00 2.40519e-12 1.21285e-11 3 7.441762965337152e-01 7.441762965342154e-01 5.00155e-13 3.12714e-11 ----------------------------------------------------------------------------------------------------- 28 Zn 1 1.426194865525365e+00 1.426194865525382e+00 1.70974e-14 9.01701e-12 2 -1.615525360752873e+00 -1.615525360749827e+00 3.04645e-12 5.98899e-12 3 -1.889900176805644e+00 -1.889900176805827e+00 1.83409e-13 1.70974e-11 ----------------------------------------------------------------------------------------------------- 29 Zn 1 1.559107160999061e+00 1.559107161005845e+00 6.78413e-12 1.06015e-11 2 1.362419114135148e+00 1.362419114134733e+00 4.15668e-13 2.33067e-11 3 -2.617615200123417e+00 -2.617615200123252e+00 1.64757e-13 3.49631e-12 ----------------------------------------------------------------------------------------------------- 30 Zn 1 -4.445289149333114e-01 -4.445289149329685e-01 3.42837e-13 1.84863e-12 2 3.796775208220099e-01 3.796775208232883e-01 1.27837e-12 4.16922e-12 3 2.792956139540338e-02 2.792956139718976e-02 1.78638e-12 8.45528e-12 ----------------------------------------------------------------------------------------------------- 31 Zn 1 1.188873508509060e+00 1.188873508509000e+00 6.08402e-14 3.10774e-12 2 7.204574092520168e-01 7.204574092518227e-01 1.94178e-13 2.22000e-12 3 1.112472793909159e+00 1.112472793909927e+00 7.67830e-13 1.11866e-12 ----------------------------------------------------------------------------------------------------- 32 Zn 1 2.869031106284852e-02 2.869031106101261e-02 1.83591e-12 1.68630e-11 2 2.131644484974965e-01 2.131644484995999e-01 2.10340e-12 1.40951e-11 3 -3.861077184781960e-01 -3.861077184830302e-01 4.83413e-12 6.59717e-12 ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as dicontinuities. Maximum error obtained for particle = 32, direction = 1: |F_model - F_numer| error = --------------------------------- = 6.39905e-11 max{(|F_model|+|F_numer|)/2, 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 = O Zn | a0 = 3.73283393558 | (Configuration in file "config-OZn.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 O 1 -1.241917538743772e+01 -1.241917538743497e+01 2.75513e-12 8.01847e-12 2 -5.888990959037375e+00 -5.888990959042147e+00 4.77129e-12 1.88001e-11 3 -1.006750305358956e+01 -1.006750305358655e+01 3.01625e-12 1.19069e-11 ----------------------------------------------------------------------------------------------------- 2 O 1 -1.936247683105809e+01 -1.936247683105646e+01 1.63425e-12 3.19567e-11 2 7.133725078039503e-01 7.133725078040764e-01 1.26010e-13 8.56287e-11 3 -1.636233488270100e+01 -1.636233488270354e+01 2.54374e-12 4.81712e-11 ----------------------------------------------------------------------------------------------------- 3 Zn 1 1.192407632115340e+01 1.192407632115227e+01 1.12443e-12 1.09090e-10 2 -1.734533236238816e+01 -1.734533236238465e+01 3.50653e-12 1.95968e-11 3 6.925324070648312e+00 6.925324070652315e+00 4.00302e-12 5.87708e-12 ----------------------------------------------------------------------------------------------------- 4 O 1 -7.460930444079168e+00 -7.460930444309046e+00 2.29878e-10 1.07842e-09 * 2 2.116332721006775e+00 2.116332716739412e+00 4.26736e-09 2.50254e-08 * 3 4.280415541786337e+00 4.280415529694860e+00 1.20915e-08 7.73640e-08 * ----------------------------------------------------------------------------------------------------- 5 Zn 1 2.138919740261859e+00 2.138919740199309e+00 6.25504e-11 3.64915e-10 * 2 -7.163322873155215e+00 -7.163322873137969e+00 1.72458e-11 1.60049e-10 3 -3.680782487844232e+00 -3.680782487844413e+00 1.80744e-13 2.48357e-11 ----------------------------------------------------------------------------------------------------- 6 Zn 1 5.242835312452396e+00 5.242835312450813e+00 1.58273e-12 8.81535e-11 2 3.865113785492759e-01 3.865113785273334e-01 2.19426e-11 8.73704e-11 3 -7.179406129912076e+00 -7.179406129910232e+00 1.84386e-12 9.99556e-12 ----------------------------------------------------------------------------------------------------- 7 O 1 1.503784852323617e+01 1.503784852323162e+01 4.54925e-12 4.69402e-11 2 -2.234260618470514e+01 -2.234260618470450e+01 6.46594e-13 7.18821e-11 3 3.611241971786548e+00 3.611241971782140e+00 4.40759e-12 3.95608e-11 ----------------------------------------------------------------------------------------------------- 8 Zn 1 -1.282426327908434e+00 -1.282426327906518e+00 1.91624e-12 3.19098e-11 2 6.090975243376968e+00 6.090975243374538e+00 2.43006e-12 4.01839e-11 3 1.403476463610009e+00 1.403476463620833e+00 1.08240e-11 3.79381e-11 ----------------------------------------------------------------------------------------------------- 9 Zn 1 -2.024027002566823e-01 -2.024027002558288e-01 8.53512e-13 9.68639e-12 2 2.644882203810110e+00 2.644882203810102e+00 7.54952e-15 1.56888e-11 3 -6.329069250334407e-01 -6.329069250281522e-01 5.28855e-12 5.71398e-12 ----------------------------------------------------------------------------------------------------- 10 O 1 -1.415473929949388e+01 -1.415473929947436e+01 1.95239e-11 3.12408e-11 2 1.285262692877534e+01 1.285262692877769e+01 2.35367e-12 8.83915e-12 3 -3.649607110883382e+00 -3.649607110884779e+00 1.39710e-12 1.07843e-10 ----------------------------------------------------------------------------------------------------- 11 O 1 -4.372511122720810e+00 -4.372511122724489e+00 3.67884e-12 6.04876e-11 2 -1.630086590945198e+00 -1.630086590946541e+00 1.34293e-12 1.20652e-11 3 -4.507713925421891e+00 -4.507713925423086e+00 1.19549e-12 5.77405e-11 ----------------------------------------------------------------------------------------------------- 12 Zn 1 -7.655431238435492e-02 -7.655431239089464e-02 6.53971e-12 4.68537e-11 2 1.539436027068840e-01 1.539436027111341e-01 4.25010e-12 2.00219e-11 3 -2.282881143066310e+00 -2.282881143058444e+00 7.86571e-12 4.98241e-11 ----------------------------------------------------------------------------------------------------- 13 O 1 1.288521401809915e+01 1.288521401809697e+01 2.18492e-12 1.30864e-11 2 9.090305582138646e+00 9.090305582178754e+00 4.01084e-11 6.95941e-11 3 -1.279817262823911e+01 -1.279817262823381e+01 5.30243e-12 4.44363e-10 * ----------------------------------------------------------------------------------------------------- 14 Zn 1 1.324072240143432e+00 1.324072240142641e+00 7.91811e-13 1.30427e-11 2 5.762808314726292e-01 5.762808314744685e-01 1.83931e-12 2.46105e-11 3 -7.804768165518924e-02 -7.804768165570275e-02 5.13506e-13 3.25771e-12 ----------------------------------------------------------------------------------------------------- 15 Zn 1 5.735837065015042e+00 5.735837065015024e+00 1.86517e-14 1.14405e-10 2 1.005843230069227e+01 1.005843230069460e+01 2.33413e-12 1.96524e-10 3 -5.461095854218272e+00 -5.461095854213119e+00 5.15321e-12 3.10685e-11 ----------------------------------------------------------------------------------------------------- 16 Zn 1 2.294298409753016e+00 2.294298409750813e+00 2.20268e-12 5.16431e-12 2 3.246044415040700e+00 3.246044415040166e+00 5.34239e-13 6.02629e-12 3 2.638331546699484e-01 2.638331546556176e-01 1.43308e-11 3.56812e-11 ----------------------------------------------------------------------------------------------------- 17 O 1 -1.868764021499870e+00 -1.868764021418659e+00 8.12101e-11 2.72918e-09 * 2 -3.275176991786334e+00 -3.275176992078933e+00 2.92599e-10 4.75783e-09 * 3 -3.705282927070235e+00 -3.705282923852995e+00 3.21724e-09 2.18376e-08 * ----------------------------------------------------------------------------------------------------- 18 O 1 -1.432933444489693e+01 -1.432933444489767e+01 7.38964e-13 1.85594e-11 2 -9.794958283896307e+00 -9.794958283892974e+00 3.33245e-12 4.44160e-11 3 -1.757936248815224e+00 -1.757936248817478e+00 2.25420e-12 4.18117e-11 ----------------------------------------------------------------------------------------------------- 19 O 1 1.451648333876124e-01 1.451648333581518e-01 2.94606e-11 2.60477e-11 2 9.326311831644702e-01 9.326311831684669e-01 3.99669e-12 3.13665e-11 3 -1.156314141972995e+00 -1.156314141972181e+00 8.13793e-13 1.35254e-11 ----------------------------------------------------------------------------------------------------- 20 Zn 1 -7.846551445719955e+00 -7.846551445721566e+00 1.61116e-12 6.17613e-11 2 -1.485967099295115e+00 -1.485967099279642e+00 1.54732e-11 2.00300e-11 3 5.148329282049982e+00 5.148329282051056e+00 1.07381e-12 7.21290e-12 ----------------------------------------------------------------------------------------------------- 21 O 1 -8.029891621168041e+00 -8.029891621169408e+00 1.36779e-12 3.46372e-11 2 -1.264489365023513e+01 -1.264489365023812e+01 2.99494e-12 5.23244e-11 3 -5.180875157210282e+00 -5.180875157218527e+00 8.24496e-12 3.81490e-11 ----------------------------------------------------------------------------------------------------- 22 O 1 1.763220307397473e+01 1.763220307398405e+01 9.32587e-12 1.22036e-10 2 -2.549844971692636e+00 -2.549844971687159e+00 5.47695e-12 4.19893e-10 * 3 1.049663473475011e+01 1.049663473471996e+01 3.01501e-11 2.52463e-10 ----------------------------------------------------------------------------------------------------- 23 Zn 1 1.217431235193473e+01 1.217431235193097e+01 3.75877e-12 2.42970e-11 2 -9.983240300506678e+00 -9.983240300506418e+00 2.59348e-13 2.18776e-11 3 1.056146536652070e+01 1.056146536652497e+01 4.27036e-12 1.68114e-11 ----------------------------------------------------------------------------------------------------- 24 O 1 -6.655919159286400e+00 -6.655919159269520e+00 1.68798e-11 1.30115e-04 * 2 -7.781257717287211e+00 -7.781257717284710e+00 2.50111e-12 8.10019e-11 3 2.170730642214848e+01 2.170730642214841e+01 7.10543e-14 1.00364e-11 ----------------------------------------------------------------------------------------------------- 25 Zn 1 -4.178696541188610e+00 -4.178696541197945e+00 9.33476e-12 6.25722e-12 2 2.133990686633192e+00 2.133990686631516e+00 1.67599e-12 1.05769e-11 3 -5.765237070806877e+00 -5.765237070817305e+00 1.04281e-11 3.79798e-10 * ----------------------------------------------------------------------------------------------------- 26 Zn 1 -3.846743758805235e+00 -3.846743758808391e+00 3.15614e-12 3.95945e-11 2 4.255160777754156e+00 4.255160777762070e+00 7.91367e-12 7.42686e-11 3 -5.540270332432645e+00 -5.540270332426596e+00 6.04850e-12 1.45572e-11 ----------------------------------------------------------------------------------------------------- 27 O 1 4.629294419937160e+00 4.629294419934501e+00 2.65832e-12 1.23483e-11 2 -4.599257526572453e+00 -4.599257526577544e+00 5.09104e-12 4.07701e-11 3 6.522755174599401e+00 6.522755174585072e+00 1.43290e-11 2.79785e-11 ----------------------------------------------------------------------------------------------------- 28 O 1 -4.854023945833452e+00 -4.854023945832098e+00 1.35447e-12 3.93984e-10 * 2 6.504165793536591e+00 6.504165793539715e+00 3.12461e-12 4.52696e-11 3 9.624439922054110e+00 9.624439922052423e+00 1.68754e-12 2.18403e-11 ----------------------------------------------------------------------------------------------------- 29 Zn 1 2.297086447462821e+00 2.297086447462010e+00 8.10907e-13 3.73852e-11 2 1.993659066410962e+01 1.993659066411701e+01 7.39320e-12 4.86935e-11 3 -9.623735077300044e+00 -9.623735077300541e+00 4.97380e-13 6.58922e-11 ----------------------------------------------------------------------------------------------------- 30 Zn 1 2.010269840470009e+00 2.010269840464769e+00 5.23981e-12 3.73324e-11 2 1.110317001509374e-01 1.110317001464144e-01 4.52298e-12 5.66100e-12 3 1.230665988045892e+00 1.230665988047524e+00 1.63181e-12 1.87057e-11 ----------------------------------------------------------------------------------------------------- 31 Zn 1 6.722454689126314e+00 6.722454689126507e+00 1.92735e-13 5.87619e-12 2 1.256100456648384e+01 1.256100456649292e+01 9.08429e-12 8.75655e-11 3 5.747092002179360e+00 5.747092002182973e+00 3.61311e-12 5.22551e-11 ----------------------------------------------------------------------------------------------------- 32 O 1 8.747254077329758e+00 8.747254077331137e+00 1.37845e-12 1.88756e-10 2 1.212065242429661e+01 1.212065242429839e+01 1.77991e-12 6.61622e-11 3 1.190712268332361e+01 1.190712268331975e+01 3.85825e-12 3.58433e-11 ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as dicontinuities. Maximum error obtained for particle = 19, direction = 1: |F_model - F_numer| error = --------------------------------- = 2.02946e-10 max{(|F_model|+|F_numer|)/2, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 2.33890e-10 Machine precision = 2.22045e-16 Grade: A Comment: The letter grade A was assigned because the normalized error in the computation was 2.33890e-10 compared with a machine precision of 2.22045e-16. The letter grade was based on 'score=log10(error/eps)', with ranges A=[0, 7.5], B=(7.5, 10.0], C=(10.0, 12.5], D=(12.5, 15.0), F>15.0. 'A' is the best grade, and 'F' indicates failure. 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.