!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! VERIFICATION CHECK: vc-forces-numerical-derivative !!!!! !!!!! !!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Description: Comparison of the analytical forces obtained from the model with forces computed by numerical differentiation using Richardson extrapolation for a randomly distorted non-periodic structure based off the equilibrium face-centered cubic (fcc) structure. Separate configurations are tested for each species supported by the model, as well as one containing a random distribution of all species. Configurations used for testing are provided as auxiliary files. Author: Ellad Tadmor ----------------------------------------------------------------------------------------------------- Results for KIM Model : Sim_LAMMPS_MEAM_KoGrabowskiNeugebauer_2015_NiTi__SM_770142935022_000 Supported species : Ni 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 = Ni | a0 = 3.52139186859 | (Configuration in file "config-Ni.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ni 1 4.280328767366031e-01 4.280328767470775e-01 1.04743e-11 4.04359e-11 2 -2.782440375890849e-01 -2.782440375899430e-01 8.58147e-13 1.73841e-10 3 -2.427589046797390e-01 -2.427589046802051e-01 4.66044e-13 5.65675e-11 ----------------------------------------------------------------------------------------------------- 2 Ni 1 -8.945380340188868e-01 -8.945380340143620e-01 4.52471e-12 2.89169e-10 2 8.101560045347683e-01 8.101560045411746e-01 6.40632e-12 3.90527e-10 3 1.045849926620843e+00 1.045849926696307e+00 7.54639e-11 2.78892e-10 ----------------------------------------------------------------------------------------------------- 3 Ni 1 8.537894607146042e-01 8.537894607389720e-01 2.43678e-11 1.23507e-10 2 9.108791640041265e-01 9.108791640157381e-01 1.16116e-11 8.77487e-11 3 -7.459561105906666e-01 -7.459561105989759e-01 8.30935e-12 1.31818e-10 ----------------------------------------------------------------------------------------------------- 4 Ni 1 1.237798708062611e+00 1.237798708060474e+00 2.13674e-12 3.04804e-10 2 3.237916928563254e-01 3.237916927820811e-01 7.42442e-11 1.42332e-10 3 1.020636549337607e+00 1.020636549290276e+00 4.73301e-11 1.36136e-10 ----------------------------------------------------------------------------------------------------- 5 Ni 1 5.472543543146631e-01 5.472543543215288e-01 6.86573e-12 1.24140e-10 2 -3.646824746479177e-02 -3.646824746227492e-02 2.51685e-12 6.08414e-11 3 5.020282252234829e-01 5.020282252278050e-01 4.32210e-12 6.15172e-11 ----------------------------------------------------------------------------------------------------- 6 Ni 1 -7.277260560915613e-01 -7.277260561068108e-01 1.52496e-11 9.53848e-11 2 5.254050956244785e-01 5.254050956304482e-01 5.96978e-12 2.30840e-10 3 6.293922312975374e-01 6.293922312987050e-01 1.16762e-12 3.49868e-10 ----------------------------------------------------------------------------------------------------- 7 Ni 1 5.755781631746597e-01 5.755781632253933e-01 5.07336e-11 4.12436e-10 2 -3.415419410349356e+00 -3.415419410414162e+00 6.48064e-11 2.29595e-10 3 -4.141310042457690e+00 -4.141310042432108e+00 2.55813e-11 1.30390e-09 * ----------------------------------------------------------------------------------------------------- 8 Ni 1 -2.302770906215936e+00 -2.302770906117772e+00 9.81646e-11 2.42756e-10 2 -2.085438814118024e+00 -2.085438814218988e+00 1.00964e-10 2.30337e-10 3 -1.083380028400882e+00 -1.083380028365855e+00 3.50269e-11 4.92784e-11 ----------------------------------------------------------------------------------------------------- 9 Ni 1 -1.896242239138823e-01 -1.896242238962552e-01 1.76271e-11 3.90690e-11 2 -1.930117541786750e+00 -1.930117541781935e+00 4.81504e-12 2.21358e-10 3 -2.326305877876843e+00 -2.326305877881150e+00 4.30678e-12 4.00040e-11 ----------------------------------------------------------------------------------------------------- 10 Ni 1 -1.511550624256518e+00 -1.511550624253515e+00 3.00249e-12 5.42566e-10 2 9.907434353335944e-01 9.907434353247069e-01 8.88756e-12 1.21671e-09 * 3 -1.699345186647425e+00 -1.699345186650849e+00 3.42437e-12 1.57333e-10 ----------------------------------------------------------------------------------------------------- 11 Ni 1 -1.014909288281514e+00 -1.014909288238733e+00 4.27811e-11 9.13833e-10 2 -1.556578901448127e+00 -1.556578901423476e+00 2.46516e-11 3.28076e-10 3 2.190061454599780e+00 2.190061454623168e+00 2.33884e-11 2.29081e-10 ----------------------------------------------------------------------------------------------------- 12 Ni 1 4.512112058011262e-01 4.512112058125820e-01 1.14558e-11 2.89328e-10 2 1.736567639909392e+00 1.736567639918803e+00 9.41114e-12 7.42666e-09 * 3 1.694858265167039e+00 1.694858265195544e+00 2.85050e-11 2.84001e-10 ----------------------------------------------------------------------------------------------------- 13 Ni 1 -2.474999677310358e+00 -2.474999677315809e+00 5.45075e-12 1.06521e-09 2 -3.293028711582996e+00 -3.293028711527247e+00 5.57496e-11 2.53432e-10 3 -4.692719167089899e+00 -4.692719167122368e+00 3.24691e-11 6.19567e-11 ----------------------------------------------------------------------------------------------------- 14 Ni 1 1.399709844018694e+00 1.399709844027546e+00 8.85225e-12 2.02347e-10 2 2.147799148310658e+00 2.147799148324632e+00 1.39742e-11 2.23796e-10 3 -8.893409192663693e-01 -8.893409192663406e-01 2.86438e-14 1.24596e-11 ----------------------------------------------------------------------------------------------------- 15 Ni 1 4.239730602372984e+00 4.239730602408463e+00 3.54792e-11 7.42313e-11 2 -1.612312898876650e+00 -1.612312898869735e+00 6.91491e-12 5.49834e-11 3 1.801700232006915e+00 1.801700232019154e+00 1.22384e-11 3.60137e-10 ----------------------------------------------------------------------------------------------------- 16 Ni 1 1.211779180619658e+00 1.211779180635033e+00 1.53748e-11 3.39137e-10 2 2.994416887490026e+00 2.994416887528917e+00 3.88907e-11 2.17977e-10 3 1.824782724573648e+00 1.824782724489648e+00 8.40004e-11 7.73370e-11 ----------------------------------------------------------------------------------------------------- 17 Ni 1 -1.481735581316293e+00 -1.481735581316329e+00 3.59712e-14 1.59228e-09 * 2 2.688543421177451e-01 2.688543420967291e-01 2.10160e-11 4.68467e-11 3 -5.997154327005376e-01 -5.997154327008721e-01 3.34510e-13 4.30286e-09 * ----------------------------------------------------------------------------------------------------- 18 Ni 1 4.490262752885861e-01 4.490262752683872e-01 2.01989e-11 3.40554e-10 2 2.184895010390433e+00 2.184895010347391e+00 4.30420e-11 4.73956e-10 3 -1.579490783935601e+00 -1.579490783954045e+00 1.84439e-11 4.97649e-11 ----------------------------------------------------------------------------------------------------- 19 Ni 1 1.465607819075982e+00 1.465607819111562e+00 3.55798e-11 1.25620e-09 * 2 -1.040682678389187e+00 -1.040682678369000e+00 2.01874e-11 6.67291e-10 3 1.651663478090059e+00 1.651663478162017e+00 7.19578e-11 1.45082e-09 * ----------------------------------------------------------------------------------------------------- 20 Ni 1 2.930188062770843e-01 2.930188062902662e-01 1.31818e-11 3.22281e-10 2 6.104001046753096e-01 6.104001046621880e-01 1.31216e-11 4.09234e-10 3 -4.712963612398133e-01 -4.712963612748664e-01 3.50531e-11 5.23114e-11 ----------------------------------------------------------------------------------------------------- 21 Ni 1 -1.956201982490791e+00 -1.956201982514785e+00 2.39941e-11 1.48679e-09 * 2 1.455895920087056e-01 1.455895920386570e-01 2.99513e-11 3.34367e-10 3 8.949044710601838e-01 8.949044710810891e-01 2.09053e-11 1.82048e-10 ----------------------------------------------------------------------------------------------------- 22 Ni 1 5.333010050052988e-01 5.333010050234597e-01 1.81609e-11 4.28095e-10 2 3.672237983803984e+00 3.672237983808223e+00 4.23928e-12 5.06657e-11 3 3.919255206327100e+00 3.919255206313226e+00 1.38742e-11 7.96434e-11 ----------------------------------------------------------------------------------------------------- 23 Ni 1 5.353961637466016e-01 5.353961637270698e-01 1.95318e-11 4.27159e-10 2 -1.430183612834734e-01 -1.430183613581164e-01 7.46429e-11 7.31744e-11 3 -2.109345070041853e-01 -2.109345070042915e-01 1.06248e-13 1.86740e-10 ----------------------------------------------------------------------------------------------------- 24 Ni 1 -6.098919501839499e-01 -6.098919501963291e-01 1.23792e-11 1.70715e-10 2 9.537192037714636e-01 9.537192037088786e-01 6.25849e-11 4.77123e-10 3 -8.024843386660039e-01 -8.024843386478684e-01 1.81355e-11 8.84992e-11 ----------------------------------------------------------------------------------------------------- 25 Ni 1 -3.627087292172530e-01 -3.627087292244016e-01 7.14862e-12 4.77026e-10 2 -1.362245902184293e+00 -1.362245902185937e+00 1.64357e-12 6.44116e-11 3 3.902702788808406e-02 3.902702785012117e-02 3.79629e-11 1.69260e-10 ----------------------------------------------------------------------------------------------------- 26 Ni 1 -1.332009422395280e+00 -1.332009422397847e+00 2.56772e-12 2.09213e-10 2 9.934825220297924e-01 9.934825220452512e-01 1.54589e-11 3.03000e-11 3 -1.238105205862885e+00 -1.238105205899086e+00 3.62008e-11 8.81607e-10 ----------------------------------------------------------------------------------------------------- 27 Ni 1 1.964564312231397e+00 1.964564312207411e+00 2.39861e-11 2.64163e-09 * 2 -4.706389970696465e+00 -4.706389970668438e+00 2.80274e-11 6.64027e-09 * 3 2.542328336927027e-01 2.542328336567087e-01 3.59940e-11 5.47907e-11 ----------------------------------------------------------------------------------------------------- 28 Ni 1 -2.563228342546215e+00 -2.563228342472626e+00 7.35882e-11 1.04727e-10 2 2.603979029255556e+00 2.603979029281813e+00 2.62568e-11 2.99264e-10 3 -2.020190023021009e-01 -2.020190023125608e-01 1.04599e-11 2.35850e-10 ----------------------------------------------------------------------------------------------------- 29 Ni 1 -1.217893677299341e+00 -1.217893677333158e+00 3.38167e-11 3.52203e-10 2 -1.392987439996089e+00 -1.392987439999354e+00 3.26472e-12 1.16449e-10 3 1.460885371969695e+00 1.460885371979596e+00 9.90119e-12 2.83203e-10 ----------------------------------------------------------------------------------------------------- 30 Ni 1 5.621043352087879e-02 5.621043352679757e-02 5.91878e-12 3.07106e-10 2 1.082967059668348e+00 1.082967059662644e+00 5.70388e-12 2.52271e-10 3 9.294662072764537e-01 9.294662073247583e-01 4.83046e-11 1.20987e-10 ----------------------------------------------------------------------------------------------------- 31 Ni 1 1.124391364806129e+00 1.124391364803423e+00 2.70606e-12 3.14166e-10 2 -1.277258000784310e+00 -1.277258000807012e+00 2.27018e-11 3.52351e-10 3 5.596758415133206e-01 5.596758415947644e-01 8.14437e-11 1.15084e-10 ----------------------------------------------------------------------------------------------------- 32 Ni 1 1.273387919770218e+00 1.273387919790486e+00 2.02682e-11 1.02718e-10 2 1.174307000764892e+00 1.174307000749783e+00 1.51090e-11 1.01832e-11 3 5.067418220761893e-01 5.067418220804618e-01 4.27247e-12 3.31583e-10 ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as dicontinuities. Maximum error obtained for particle = 25, direction = 3: |F_model - F_numer| error = ----------------------- = 9.72733e-10 max{|F_numer|, eps} Comparison of analytical forces obtained from the model, the force computed as a numerical derivative of the energy, the difference between them, and the uncertainty in the numerical estimate of the force. The computed equilibrium lattice constant for the crystal (a0) is given in the heading. MONOATOMIC STRUCTURE -- Species = Ti | a0 = 4.11129951477 | (Configuration in file "config-Ti.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ti 1 6.609951180719951e-01 6.609951180694400e-01 2.55507e-12 8.67617e-12 2 5.322517264735594e-01 5.322517264745571e-01 9.97646e-13 9.36317e-11 3 9.079650880001784e-01 9.079650879875979e-01 1.25805e-11 1.31335e-10 ----------------------------------------------------------------------------------------------------- 2 Ti 1 -1.054188795030371e+00 -1.054188795007747e+00 2.26237e-11 2.82298e-10 2 9.183280249974256e-01 9.183280249723295e-01 2.50961e-11 8.48137e-10 3 -1.073809860318442e+00 -1.073809860334560e+00 1.61178e-11 1.22007e-11 ----------------------------------------------------------------------------------------------------- 3 Ti 1 -1.440352340953095e+00 -1.440352340967016e+00 1.39206e-11 2.96123e-11 2 -9.842952138024915e-01 -9.842952137957284e-01 6.76315e-12 6.61189e-11 3 -5.855334671167494e-01 -5.855334671180208e-01 1.27143e-12 3.98300e-11 ----------------------------------------------------------------------------------------------------- 4 Ti 1 7.243352712368971e-01 7.243352712392718e-01 2.37466e-12 7.59412e-10 2 2.803625707894501e-01 2.803625707816459e-01 7.80420e-12 1.41335e-10 3 6.673816500384577e-01 6.673816500533544e-01 1.48966e-11 3.03457e-12 ----------------------------------------------------------------------------------------------------- 5 Ti 1 -2.419706202954805e-01 -2.419706202991683e-01 3.68777e-12 2.02304e-10 2 -5.108774825333113e-02 -5.108774825587017e-02 2.53905e-12 1.17636e-10 3 1.243111334704124e-01 1.243111334641287e-01 6.28372e-12 4.24040e-11 ----------------------------------------------------------------------------------------------------- 6 Ti 1 1.465546956839072e-01 1.465546956653851e-01 1.85221e-11 8.36319e-11 2 -1.663321183751433e-01 -1.663321183356780e-01 3.94653e-11 1.30902e-09 * 3 9.823467695626246e-02 9.823467695603037e-02 2.32092e-13 1.71795e-08 * ----------------------------------------------------------------------------------------------------- 7 Ti 1 -6.752819600343426e-01 -6.752819600980253e-01 6.36827e-11 8.29251e-11 2 -1.642860738293873e-02 -1.642860740501098e-02 2.20722e-11 1.81918e-10 3 1.826236228152142e-01 1.826236228483415e-01 3.31272e-11 1.48953e-10 ----------------------------------------------------------------------------------------------------- 8 Ti 1 1.692656588870514e+00 1.692656588886713e+00 1.61993e-11 1.72292e-10 2 2.137078558274296e+00 2.137078558290368e+00 1.60720e-11 3.43300e-10 3 1.237802424415593e+00 1.237802424362519e+00 5.30742e-11 2.90835e-10 ----------------------------------------------------------------------------------------------------- 9 Ti 1 -3.361416353495216e-01 -3.361416353407064e-01 8.81523e-12 6.49589e-10 2 -7.734689984057266e-01 -7.734689983798663e-01 2.58603e-11 1.47341e-10 3 -1.391023872445574e+00 -1.391023872493995e+00 4.84217e-11 4.12895e-10 ----------------------------------------------------------------------------------------------------- 10 Ti 1 -4.334541254984970e-01 -4.334541254569887e-01 4.15083e-11 5.80577e-10 2 1.917138790025987e+00 1.917138790060017e+00 3.40303e-11 9.45755e-11 3 -8.107674087363175e-01 -8.107674088142799e-01 7.79624e-11 2.43917e-11 ----------------------------------------------------------------------------------------------------- 11 Ti 1 1.872160660794207e+00 1.872160660782419e+00 1.17879e-11 1.39992e-10 2 -2.564797910581742e+00 -2.564797910539898e+00 4.18443e-11 1.00731e-10 3 2.172632698236785e+00 2.172632698231150e+00 5.63549e-12 1.32693e-10 ----------------------------------------------------------------------------------------------------- 12 Ti 1 -7.947570835549289e-01 -7.947570835586565e-01 3.72757e-12 2.93047e-10 2 1.146906679650019e+00 1.146906679649283e+00 7.36300e-13 1.53191e-09 * 3 1.328042548527003e+00 1.328042548542027e+00 1.50244e-11 1.50370e-10 ----------------------------------------------------------------------------------------------------- 13 Ti 1 1.066364259051042e+00 1.066364259023576e+00 2.74656e-11 9.55271e-11 2 -6.543023551064171e-01 -6.543023551724670e-01 6.60499e-11 1.61544e-10 3 1.434405991057556e-02 1.434405990306479e-02 7.51078e-12 1.26588e-11 ----------------------------------------------------------------------------------------------------- 14 Ti 1 -6.369188758315532e-01 -6.369188758355943e-01 4.04110e-12 4.75702e-11 2 -6.870687112915349e-01 -6.870687113024831e-01 1.09482e-11 2.69442e-10 3 2.213893719407004e-01 2.213893719361251e-01 4.57537e-12 1.68167e-10 ----------------------------------------------------------------------------------------------------- 15 Ti 1 2.967577642628840e-01 2.967577642599727e-01 2.91128e-12 2.21441e-10 2 -1.527804819573364e+00 -1.527804819524587e+00 4.87770e-11 1.58825e-09 * 3 4.812517547989613e-01 4.812517547967286e-01 2.23266e-12 1.20205e-10 ----------------------------------------------------------------------------------------------------- 16 Ti 1 -1.719015100691897e+00 -1.719015100712829e+00 2.09321e-11 5.18302e-10 2 5.795352666470129e-01 5.795352666771402e-01 3.01272e-11 7.53612e-11 3 -3.177405897694269e-01 -3.177405897436725e-01 2.57544e-11 4.09111e-10 ----------------------------------------------------------------------------------------------------- 17 Ti 1 -8.949290838066647e-02 -8.949290835325918e-02 2.74073e-11 9.84393e-11 2 -6.691504993188989e-01 -6.691504993189588e-01 5.98410e-14 9.48462e-11 3 6.507324510991133e-02 6.507324511571889e-02 5.80756e-12 3.36129e-11 ----------------------------------------------------------------------------------------------------- 18 Ti 1 7.786915375322904e-01 7.786915375598877e-01 2.75974e-11 8.84823e-11 2 7.948381640149013e-01 7.948381640742198e-01 5.93186e-11 8.19135e-11 3 -1.137221609323485e+00 -1.137221609341514e+00 1.80296e-11 5.04754e-11 ----------------------------------------------------------------------------------------------------- 19 Ti 1 -9.528200458794979e-01 -9.528200459066249e-01 2.71271e-11 1.08301e-10 2 3.695519224927767e-01 3.695519224989354e-01 6.15863e-12 1.64917e-10 3 1.023921250411318e+00 1.023921250431689e+00 2.03708e-11 2.16372e-10 ----------------------------------------------------------------------------------------------------- 20 Ti 1 -8.655750830348695e-01 -8.655750830018772e-01 3.29923e-11 2.34685e-10 2 -7.171769881944182e-01 -7.171769881582880e-01 3.61302e-11 2.69118e-10 3 4.161540636308325e-01 4.161540636225256e-01 8.30691e-12 7.69025e-11 ----------------------------------------------------------------------------------------------------- 21 Ti 1 9.489945488025022e-01 9.489945488416960e-01 3.91938e-11 2.88268e-09 * 2 -9.973296460126011e-01 -9.973296460330157e-01 2.04146e-11 4.82316e-10 3 5.229867946826024e-02 5.229867917638353e-02 2.91877e-10 6.18509e-08 * ----------------------------------------------------------------------------------------------------- 22 Ti 1 1.181430568258585e+00 1.181430568254455e+00 4.13047e-12 7.43090e-11 2 1.966630728798072e+00 1.966630728798423e+00 3.50386e-13 1.52871e-10 3 4.870702160239921e-01 4.870702160818320e-01 5.78399e-11 7.44468e-10 ----------------------------------------------------------------------------------------------------- 23 Ti 1 -9.525982730625124e-01 -9.525982730699432e-01 7.43072e-12 1.65451e-10 2 8.583615436775404e-01 8.583615436960512e-01 1.85109e-11 3.90913e-10 3 -9.162132551427576e-01 -9.162132551344341e-01 8.32356e-12 2.23480e-10 ----------------------------------------------------------------------------------------------------- 24 Ti 1 -1.146702301575325e+00 -1.146702301556151e+00 1.91749e-11 1.83941e-10 2 -1.432530812091934e+00 -1.432530812090220e+00 1.71374e-12 5.24482e-10 3 -6.461208395343162e-01 -6.461208395638102e-01 2.94940e-11 6.30060e-10 ----------------------------------------------------------------------------------------------------- 25 Ti 1 -1.127470744200840e+00 -1.127470744173696e+00 2.71443e-11 2.06704e-10 2 -2.081506284343817e+00 -2.081506284293138e+00 5.06790e-11 8.40200e-10 3 -3.168347908691760e+00 -3.168347908574705e+00 1.17056e-10 3.36842e-10 ----------------------------------------------------------------------------------------------------- 26 Ti 1 2.621653520272732e+00 2.621653520290053e+00 1.73213e-11 1.78131e-10 2 1.556180400946404e-01 1.556180400848402e-01 9.80022e-12 6.10013e-10 3 -1.266017510389202e+00 -1.266017510403070e+00 1.38685e-11 2.27192e-10 ----------------------------------------------------------------------------------------------------- 27 Ti 1 3.576481242692077e+00 3.576481242665863e+00 2.62146e-11 2.22818e-10 2 2.113018431409742e-02 2.113018433052001e-02 1.64226e-11 8.63613e-10 3 2.074080105198655e-01 2.074080106429729e-01 1.23107e-10 3.02665e-10 ----------------------------------------------------------------------------------------------------- 28 Ti 1 -1.758661638874746e+00 -1.758661638871517e+00 3.22897e-12 2.30797e-10 2 2.025507022660932e+00 2.025507022684751e+00 2.38187e-11 1.30039e-10 3 2.017927732994652e+00 2.017927733038912e+00 4.42597e-11 9.12292e-11 ----------------------------------------------------------------------------------------------------- 29 Ti 1 -1.041827171498257e+00 -1.041827171501686e+00 3.42837e-12 8.78109e-11 2 7.444821930403012e-01 7.444821930401487e-01 1.52434e-13 2.04381e-10 3 9.696186013930475e-01 9.696186013175818e-01 7.54656e-11 4.57371e-10 ----------------------------------------------------------------------------------------------------- 30 Ti 1 4.150580388733758e-01 4.150580388940168e-01 2.06410e-11 5.38618e-11 2 4.886737253291722e-01 4.886737253153464e-01 1.38258e-11 1.05098e-10 3 -1.123870217234836e+00 -1.123870217236700e+00 1.86362e-12 1.32374e-09 * ----------------------------------------------------------------------------------------------------- 31 Ti 1 5.672632116561525e-01 5.672632116519499e-01 4.20253e-12 2.07507e-10 2 -6.768553314389206e-01 -6.768553313921317e-01 4.67889e-11 1.41685e-10 3 9.606847413268875e-02 9.606847413554262e-02 2.85387e-12 4.28153e-11 ----------------------------------------------------------------------------------------------------- 32 Ti 1 -1.282168322312761e+00 -1.282168322320048e+00 7.28662e-12 3.85521e-09 * 2 -9.362590971069048e-01 -9.362590971272013e-01 2.02965e-11 2.83695e-10 3 -3.348527640918470e-01 -3.348527640918305e-01 1.64868e-14 5.28798e-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 = 7, direction = 2: |F_model - F_numer| error = ----------------------- = 1.34353e-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. MIXED STRUCTURE -- Species = Ni Ti | a0 = 3.73952132403 | (Configuration in file "config-NiTi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ti 1 4.731004254711093e-01 4.731004254579427e-01 1.31666e-11 8.97866e-11 2 2.379908412489979e-01 2.379908412496864e-01 6.88533e-13 1.94106e-10 3 -1.982579750047950e-01 -1.982579750138236e-01 9.02858e-12 8.97114e-11 ----------------------------------------------------------------------------------------------------- 2 Ni 1 -1.429867838828202e+00 -1.429867838817803e+00 1.03988e-11 3.59209e-10 2 3.035597723443176e+00 3.035597723443495e+00 3.19300e-13 2.45278e-10 3 -2.757802085477368e+00 -2.757802085470053e+00 7.31548e-12 8.95057e-11 ----------------------------------------------------------------------------------------------------- 3 Ni 1 -5.422732430754135e-01 -5.422732431118380e-01 3.64245e-11 1.71349e-10 2 -2.951103829390901e+00 -2.951103829420480e+00 2.95795e-11 1.53642e-10 3 2.102380316850963e+00 2.102380316853077e+00 2.11386e-12 1.08124e-10 ----------------------------------------------------------------------------------------------------- 4 Ti 1 -1.543261044711121e-01 -1.543261044605847e-01 1.05274e-11 1.28736e-10 2 -2.445341650015181e+00 -2.445341650038817e+00 2.36358e-11 7.66209e-11 3 1.858746233869172e-01 1.858746233823931e-01 4.52408e-12 8.24035e-11 ----------------------------------------------------------------------------------------------------- 5 Ti 1 1.271309858994370e-01 1.271309858790331e-01 2.04039e-11 4.11056e-10 2 -8.067142705564367e-01 -8.067142705522832e-01 4.15357e-12 8.14080e-11 3 -5.832985901487516e-01 -5.832985901473620e-01 1.38967e-12 1.39013e-10 ----------------------------------------------------------------------------------------------------- 6 Ni 1 1.761920534308015e+00 1.761920534324300e+00 1.62845e-11 1.68269e-10 2 -1.713953944524890e+00 -1.713953944527944e+00 3.05378e-12 3.84133e-10 3 -1.866685406848440e+00 -1.866685406849642e+00 1.20171e-12 1.56366e-10 ----------------------------------------------------------------------------------------------------- 7 Ti 1 7.039820462870940e-01 7.039820462886555e-01 1.56142e-12 2.06405e-10 2 -2.999123426220878e-01 -2.999123426079823e-01 1.41056e-11 1.03879e-10 3 8.017512391679841e-01 8.017512391845896e-01 1.66055e-11 2.37660e-11 ----------------------------------------------------------------------------------------------------- 8 Ti 1 2.383433772231648e-02 2.383433771291049e-02 9.40600e-12 1.57721e-10 2 -2.912882354926415e+00 -2.912882354935604e+00 9.18954e-12 2.61076e-10 3 3.473622326180980e+00 3.473622326168416e+00 1.25642e-11 1.19833e-10 ----------------------------------------------------------------------------------------------------- 9 Ti 1 6.580271291324562e-01 6.580271291068649e-01 2.55913e-11 1.05838e-10 2 1.078323572612060e-01 1.078323572631459e-01 1.93981e-12 7.20944e-11 3 -4.706771686447643e-01 -4.706771686458289e-01 1.06454e-12 1.42048e-10 ----------------------------------------------------------------------------------------------------- 10 Ti 1 1.529107960750381e+00 1.529107960764707e+00 1.43263e-11 1.62656e-10 2 3.852451858406071e-01 3.852451858406660e-01 5.88973e-14 2.84802e-11 3 7.372272947236769e-02 7.372272946411325e-02 8.25444e-12 4.01808e-11 ----------------------------------------------------------------------------------------------------- 11 Ni 1 -1.665638014428416e+00 -1.665638014394087e+00 3.43290e-11 1.36942e-10 2 1.340202295614657e+00 1.340202295638156e+00 2.34988e-11 2.01230e-10 3 -6.065346640941592e-02 -6.065346646881550e-02 5.93996e-11 1.83487e-10 ----------------------------------------------------------------------------------------------------- 12 Ni 1 -6.508693776964946e-01 -6.508693777235144e-01 2.70198e-11 5.72573e-11 2 1.241815834747420e-01 1.241815834725960e-01 2.14606e-12 6.66524e-11 3 -7.307435014975795e-02 -7.307435015887628e-02 9.11833e-12 2.43276e-10 ----------------------------------------------------------------------------------------------------- 13 Ti 1 -1.721492794730927e+00 -1.721492794777407e+00 4.64799e-11 1.10360e-09 * 2 1.886587927979755e+00 1.886587927975881e+00 3.87401e-12 1.28920e-10 3 -2.504373009597176e+00 -2.504373009561498e+00 3.56781e-11 3.79873e-10 ----------------------------------------------------------------------------------------------------- 14 Ti 1 -8.435109892031903e-02 -8.435109889962032e-02 2.06987e-11 1.07387e-10 2 6.134491139612763e-01 6.134491139776284e-01 1.63520e-11 6.25489e-11 3 7.289963718502235e-01 7.289963718028343e-01 4.73892e-11 2.78512e-10 ----------------------------------------------------------------------------------------------------- 15 Ni 1 6.833029574295952e-01 6.833029574255898e-01 4.00546e-12 1.54458e-10 2 2.054449759029576e+00 2.054449759047666e+00 1.80909e-11 2.98569e-10 3 1.366780742791354e+00 1.366780742797070e+00 5.71654e-12 2.06013e-10 ----------------------------------------------------------------------------------------------------- 16 Ni 1 6.305775744463836e-01 6.305775744926601e-01 4.62764e-11 1.56802e-10 2 -1.197917710594849e+00 -1.197917710597413e+00 2.56417e-12 9.18059e-11 3 -9.371394101440812e-01 -9.371394101440624e-01 1.87628e-14 6.81047e-11 ----------------------------------------------------------------------------------------------------- 17 Ni 1 1.216669972466760e+00 1.216669972478634e+00 1.18736e-11 5.31426e-11 2 2.024846349533588e-02 2.024846349005672e-02 5.27916e-12 1.28677e-11 3 -3.654805037349912e-01 -3.654805037299926e-01 4.99867e-12 9.64473e-10 ----------------------------------------------------------------------------------------------------- 18 Ni 1 -1.633046959071784e+00 -1.633046959054723e+00 1.70608e-11 1.87192e-10 2 2.065945833036001e+00 2.065945833023652e+00 1.23488e-11 5.34093e-09 * 3 1.945002856169375e+00 1.945002856232386e+00 6.30107e-11 1.80116e-10 ----------------------------------------------------------------------------------------------------- 19 Ni 1 -4.992028688582318e-01 -4.992028688522428e-01 5.98904e-12 3.58000e-10 2 7.128964461360265e-01 7.128964461242603e-01 1.17663e-11 6.18405e-10 3 -3.905579468963932e-01 -3.905579468867241e-01 9.66910e-12 3.95354e-10 ----------------------------------------------------------------------------------------------------- 20 Ni 1 8.236223968409363e-01 8.236223968384289e-01 2.50744e-12 9.19561e-11 2 4.318049370166884e-01 4.318049370739192e-01 5.72308e-11 4.74130e-10 3 -6.424739198018361e-01 -6.424739197948012e-01 7.03493e-12 3.44535e-10 ----------------------------------------------------------------------------------------------------- 21 Ti 1 3.695766020279076e-03 3.695766026767990e-03 6.48891e-12 1.22781e-10 2 -4.711146276994674e-01 -4.711146277731412e-01 7.36737e-11 1.39549e-10 3 -1.996972071928446e-01 -1.996972071397630e-01 5.30817e-11 2.47102e-10 ----------------------------------------------------------------------------------------------------- 22 Ni 1 7.605704600859824e-01 7.605704600784322e-01 7.55018e-12 1.51246e-10 2 -1.188993578984936e+00 -1.188993578957508e+00 2.74276e-11 4.14972e-10 3 -1.042373297926888e+00 -1.042373297811079e+00 1.15810e-10 1.31426e-09 * ----------------------------------------------------------------------------------------------------- 23 Ti 1 -4.069170847900357e-01 -4.069170847921401e-01 2.10437e-12 7.16483e-11 2 9.778713511162747e-01 9.778713511062286e-01 1.00461e-11 1.01097e-09 3 -7.015000002310577e-01 -7.015000002394046e-01 8.34688e-12 2.64146e-10 ----------------------------------------------------------------------------------------------------- 24 Ni 1 -6.745642286763452e-01 -6.745642287644940e-01 8.81487e-11 1.67624e-10 2 -1.226208373942324e+00 -1.226208374122721e+00 1.80398e-10 3.97529e-10 3 1.036370991586293e+00 1.036370991636067e+00 4.97737e-11 1.05559e-09 ----------------------------------------------------------------------------------------------------- 25 Ti 1 -2.294653585832168e+00 -2.294653585774530e+00 5.76383e-11 3.32407e-10 2 -2.628448777289176e+00 -2.628448777266453e+00 2.27232e-11 1.70916e-10 3 -4.914743910865763e-01 -4.914743911007909e-01 1.42146e-11 3.01173e-10 ----------------------------------------------------------------------------------------------------- 26 Ti 1 2.141422733134397e+00 2.141422733167733e+00 3.33360e-11 2.70728e-10 2 3.271742967567007e+00 3.271742967462962e+00 1.04045e-10 1.25886e-10 3 -4.423253367277085e-01 -4.423253367209913e-01 6.71713e-12 4.03026e-10 ----------------------------------------------------------------------------------------------------- 27 Ni 1 1.387070236132603e+00 1.387070236164722e+00 3.21185e-11 3.21482e-09 * 2 -1.415666999280477e+00 -1.415666999359617e+00 7.91398e-11 8.47631e-11 3 1.140533044354630e+00 1.140533044325347e+00 2.92830e-11 2.93437e-09 * ----------------------------------------------------------------------------------------------------- 28 Ti 1 -6.947853750713048e-01 -6.947853750634557e-01 7.84905e-12 5.40101e-11 2 1.165651556458844e+00 1.165651556434591e+00 2.42528e-11 3.13753e-10 3 1.479827186257767e+00 1.479827186255691e+00 2.07612e-12 8.90701e-10 ----------------------------------------------------------------------------------------------------- 29 Ti 1 -1.366712881951643e+00 -1.366712882053758e+00 1.02115e-10 5.01075e-10 2 7.450139785501315e-01 7.450139786391079e-01 8.89764e-11 2.72651e-10 3 -1.055177892062817e+00 -1.055177892070952e+00 8.13549e-12 2.74611e-10 ----------------------------------------------------------------------------------------------------- 30 Ni 1 4.031687664805998e-01 4.031687665005570e-01 1.99571e-11 1.37697e-10 2 3.861120463678014e-01 3.861120463615149e-01 6.28647e-12 2.38601e-10 3 -8.709781702073579e-01 -8.709781701948680e-01 1.24899e-11 1.94302e-10 ----------------------------------------------------------------------------------------------------- 31 Ti 1 1.827183492122181e+00 1.827183492114274e+00 7.90701e-12 1.35296e-10 2 -8.842940461953552e-01 -8.842940462053915e-01 1.00363e-11 3.48154e-09 * 3 1.573431184984459e+00 1.573431184998407e+00 1.39484e-11 6.25784e-10 ----------------------------------------------------------------------------------------------------- 32 Ni 1 -1.335686318328128e+00 -1.335686318354375e+00 2.62466e-11 7.78035e-11 2 5.797281384243931e-01 5.797281384019232e-01 2.24699e-11 8.88460e-10 3 -2.542934847602921e-01 -2.542934848412199e-01 8.09278e-11 1.15566e-10 ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as dicontinuities. Maximum error obtained for particle = 21, direction = 1: |F_model - F_numer| error = ----------------------- = 1.75577e-09 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 1.75577e-09 Machine precision = 2.22045e-16 Note: Lower grades can reflect errors in the analytical forces, a lack of smoothness in the potential, or loss of precision in the numerical derivative computation. Grade: A Comment: The letter grade A was assigned because the normalized error in the computation was 1.75577e-09 compared with a machine precision of 2.22045e-16. The letter grade was based on 'score=log10(error/eps)', with ranges A=[0, 7.5], B=(7.5, 10.0], C=(10.0, 12.5], D=(12.5, 15.0), F>15.0. 'A' is the best grade, and 'F' indicates failure.