!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 = 3.5213918685913086 | (Configuration in file "config-Ni.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ni 1 4.280328767366016e-01 4.280328767258231e-01 1.07785e-11 1.90302e-11 2 -2.782440375890921e-01 -2.782440375837233e-01 5.36871e-12 2.69980e-11 3 -2.427589046797472e-01 -2.427589046826504e-01 2.90321e-12 4.38353e-10 ----------------------------------------------------------------------------------------------------- 2 Ni 1 -8.945380340188800e-01 -8.945380340354550e-01 1.65750e-11 1.36020e-10 2 8.101560045347640e-01 8.101560045426829e-01 7.91889e-12 3.52394e-10 3 1.045849926620834e+00 1.045849926636386e+00 1.55518e-11 1.05495e-09 ----------------------------------------------------------------------------------------------------- 3 Ni 1 8.537894607145765e-01 8.537894607341460e-01 1.95695e-11 2.65451e-10 2 9.108791640041347e-01 9.108791639973907e-01 6.74405e-12 1.93078e-10 3 -7.459561105906315e-01 -7.459561105667807e-01 2.38508e-11 6.23610e-10 ----------------------------------------------------------------------------------------------------- 4 Ni 1 1.237798708062607e+00 1.237798708071474e+00 8.86691e-12 7.97573e-11 2 3.237916928563325e-01 3.237916929094877e-01 5.31553e-11 1.99582e-10 3 1.020636549337618e+00 1.020636549326881e+00 1.07370e-11 8.22162e-11 ----------------------------------------------------------------------------------------------------- 5 Ni 1 5.472543543146531e-01 5.472543543553666e-01 4.07135e-11 6.95392e-09 * 2 -3.646824746480162e-02 -3.646824746879937e-02 3.99775e-12 3.61676e-10 3 5.020282252234607e-01 5.020282252021374e-01 2.13233e-11 2.30282e-12 ----------------------------------------------------------------------------------------------------- 6 Ni 1 -7.277260560915548e-01 -7.277260560961533e-01 4.59843e-12 7.20481e-11 2 5.254050956244856e-01 5.254050956018057e-01 2.26799e-11 1.42034e-10 3 6.293922312975200e-01 6.293922313102097e-01 1.26897e-11 4.45118e-11 ----------------------------------------------------------------------------------------------------- 7 Ni 1 5.755781631747003e-01 5.755781631959603e-01 2.12600e-11 1.91240e-10 2 -3.415419410349370e+00 -3.415419410359169e+00 9.79883e-12 6.29439e-11 3 -4.141310042457637e+00 -4.141310042467952e+00 1.03144e-11 1.08538e-10 ----------------------------------------------------------------------------------------------------- 8 Ni 1 -2.302770906216002e+00 -2.302770906205049e+00 1.09530e-11 2.49363e-10 2 -2.085438814118002e+00 -2.085438814112453e+00 5.54845e-12 3.24202e-10 3 -1.083380028400878e+00 -1.083380028384865e+00 1.60130e-11 9.52209e-11 ----------------------------------------------------------------------------------------------------- 9 Ni 1 -1.896242239139148e-01 -1.896242239251616e-01 1.12468e-11 1.18949e-10 2 -1.930117541786753e+00 -1.930117541793405e+00 6.65157e-12 6.26972e-11 3 -2.326305877876872e+00 -2.326305877858197e+00 1.86753e-11 3.13036e-10 ----------------------------------------------------------------------------------------------------- 10 Ni 1 -1.511550624256489e+00 -1.511550624306166e+00 4.96774e-11 1.27719e-10 2 9.907434353336334e-01 9.907434353392786e-01 5.64515e-12 9.82464e-10 3 -1.699345186647419e+00 -1.699345186650046e+00 2.62657e-12 2.91279e-10 ----------------------------------------------------------------------------------------------------- 11 Ni 1 -1.014909288281524e+00 -1.014909288354848e+00 7.33240e-11 2.29443e-10 2 -1.556578901448170e+00 -1.556578901462435e+00 1.42646e-11 2.83917e-10 3 2.190061454599847e+00 2.190061454593188e+00 6.65867e-12 2.86509e-10 ----------------------------------------------------------------------------------------------------- 12 Ni 1 4.512112058011193e-01 4.512112057458282e-01 5.52910e-11 1.12905e-10 2 1.736567639909413e+00 1.736567639885030e+00 2.43829e-11 1.00113e-10 3 1.694858265167019e+00 1.694858265170716e+00 3.69682e-12 1.11562e-10 ----------------------------------------------------------------------------------------------------- 13 Ni 1 -2.474999677310429e+00 -2.474999677281293e+00 2.91358e-11 1.18768e-09 2 -3.293028711583039e+00 -3.293028711684756e+00 1.01717e-10 1.26746e-09 * 3 -4.692719167089955e+00 -4.692719167057760e+00 3.21947e-11 2.58341e-10 ----------------------------------------------------------------------------------------------------- 14 Ni 1 1.399709844018758e+00 1.399709844017697e+00 1.06071e-12 3.76361e-10 2 2.147799148310737e+00 2.147799148189558e+00 1.21178e-10 2.84909e-10 3 -8.893409192664110e-01 -8.893409192685446e-01 2.13363e-12 2.76701e-10 ----------------------------------------------------------------------------------------------------- 15 Ni 1 4.239730602373040e+00 4.239730602416497e+00 4.34568e-11 2.60376e-10 2 -1.612312898876682e+00 -1.612312898939312e+00 6.26303e-11 2.98187e-10 3 1.801700232006973e+00 1.801700232029778e+00 2.28046e-11 8.01608e-11 ----------------------------------------------------------------------------------------------------- 16 Ni 1 1.211779180619629e+00 1.211779180628246e+00 8.61666e-12 2.00110e-10 2 2.994416887490068e+00 2.994416887495664e+00 5.59552e-12 1.24195e-10 3 1.824782724573592e+00 1.824782724551945e+00 2.16465e-11 7.44622e-10 ----------------------------------------------------------------------------------------------------- 17 Ni 1 -1.481735581316301e+00 -1.481735581321340e+00 5.03908e-12 5.86584e-10 2 2.688543421177306e-01 2.688543420418962e-01 7.58344e-11 1.57770e-10 3 -5.997154327005988e-01 -5.997154327507086e-01 5.01098e-11 1.62228e-10 ----------------------------------------------------------------------------------------------------- 18 Ni 1 4.490262752886333e-01 4.490262752745339e-01 1.40993e-11 8.90393e-09 * 2 2.184895010390425e+00 2.184895010420432e+00 3.00076e-11 1.22288e-10 3 -1.579490783935635e+00 -1.579490783918938e+00 1.66978e-11 1.75266e-09 * ----------------------------------------------------------------------------------------------------- 19 Ni 1 1.465607819076013e+00 1.465607819034090e+00 4.19231e-11 9.83791e-11 2 -1.040682678389202e+00 -1.040682678481640e+00 9.24383e-11 8.64704e-10 3 1.651663478090091e+00 1.651663478047755e+00 4.23361e-11 5.30135e-10 ----------------------------------------------------------------------------------------------------- 20 Ni 1 2.930188062770565e-01 2.930188062791751e-01 2.11864e-12 7.91163e-10 2 6.104001046753216e-01 6.104001046661898e-01 9.13181e-12 2.90832e-10 3 -4.712963612397715e-01 -4.712963612398058e-01 3.42504e-14 1.02438e-10 ----------------------------------------------------------------------------------------------------- 21 Ni 1 -1.956201982490796e+00 -1.956201982464881e+00 2.59148e-11 5.69306e-10 2 1.455895920087159e-01 1.455895920019725e-01 6.74338e-12 3.36921e-10 3 8.949044710601665e-01 8.949044710138382e-01 4.63283e-11 1.18588e-10 ----------------------------------------------------------------------------------------------------- 22 Ni 1 5.333010050053135e-01 5.333010049905540e-01 1.47595e-11 7.29995e-11 2 3.672237983803946e+00 3.672237983762843e+00 4.11031e-11 8.34266e-11 3 3.919255206327094e+00 3.919255206328079e+00 9.84546e-13 1.80355e-10 ----------------------------------------------------------------------------------------------------- 23 Ni 1 5.353961637465982e-01 5.353961637750152e-01 2.84170e-11 2.28954e-10 2 -1.430183612834765e-01 -1.430183612597576e-01 2.37189e-11 5.40195e-11 3 -2.109345070041751e-01 -2.109345070068110e-01 2.63589e-12 1.46078e-11 ----------------------------------------------------------------------------------------------------- 24 Ni 1 -6.098919501839387e-01 -6.098919501867210e-01 2.78233e-12 3.77809e-10 2 9.537192037714531e-01 9.537192038138742e-01 4.24211e-11 9.81000e-11 3 -8.024843386660111e-01 -8.024843386813507e-01 1.53396e-11 1.12375e-10 ----------------------------------------------------------------------------------------------------- 25 Ni 1 -3.627087292172492e-01 -3.627087292406988e-01 2.34496e-11 7.85541e-11 2 -1.362245902184346e+00 -1.362245902188310e+00 3.96350e-12 9.72484e-11 3 3.902702788806844e-02 3.902702788953336e-02 1.46492e-12 1.76877e-12 ----------------------------------------------------------------------------------------------------- 26 Ni 1 -1.332009422395317e+00 -1.332009422385154e+00 1.01623e-11 1.23957e-08 * 2 9.934825220298397e-01 9.934825220391481e-01 9.30844e-12 1.33167e-11 3 -1.238105205862909e+00 -1.238105205863162e+00 2.52909e-13 3.99862e-10 ----------------------------------------------------------------------------------------------------- 27 Ni 1 1.964564312231364e+00 1.964564312241293e+00 9.92895e-12 8.48001e-10 2 -4.706389970696528e+00 -4.706389970627615e+00 6.89129e-11 9.16566e-10 3 2.542328336927312e-01 2.542328336856904e-01 7.04081e-12 1.78205e-10 ----------------------------------------------------------------------------------------------------- 28 Ni 1 -2.563228342546263e+00 -2.563228342490832e+00 5.54312e-11 3.25497e-10 2 2.603979029255602e+00 2.603979029165687e+00 8.99147e-11 6.00108e-10 3 -2.020190023020728e-01 -2.020190023080487e-01 5.97594e-12 8.28356e-11 ----------------------------------------------------------------------------------------------------- 29 Ni 1 -1.217893677299357e+00 -1.217893677294540e+00 4.81704e-12 4.02525e-11 2 -1.392987439996168e+00 -1.392987439995737e+00 4.30767e-13 7.43816e-10 3 1.460885371969650e+00 1.460885372016191e+00 4.65408e-11 1.45639e-10 ----------------------------------------------------------------------------------------------------- 30 Ni 1 5.621043352090749e-02 5.621043351267645e-02 8.23104e-12 1.37606e-10 2 1.082967059668384e+00 1.082967059660060e+00 8.32467e-12 8.87521e-10 3 9.294662072764536e-01 9.294662072638102e-01 1.26433e-11 1.38110e-10 ----------------------------------------------------------------------------------------------------- 31 Ni 1 1.124391364806184e+00 1.124391364797204e+00 8.98015e-12 1.62594e-10 2 -1.277258000784337e+00 -1.277258000759007e+00 2.53297e-11 5.94642e-11 3 5.596758415133600e-01 5.596758415416246e-01 2.82646e-11 1.95755e-10 ----------------------------------------------------------------------------------------------------- 32 Ni 1 1.273387919770260e+00 1.273387919870660e+00 1.00400e-10 3.88658e-09 * 2 1.174307000764982e+00 1.174307000769857e+00 4.87477e-12 3.06035e-11 3 5.067418220762483e-01 5.067418220934623e-01 1.72140e-11 5.41991e-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 = 17, direction = 2: |F_model - F_numer| error = ----------------------- = 2.82065e-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 = 4.111299514770508 | (Configuration in file "config-Ti.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ti 1 6.609951180720237e-01 6.609951180627339e-01 9.28979e-12 2.52947e-11 2 5.322517264735829e-01 5.322517264641087e-01 9.47420e-12 2.78894e-10 3 9.079650880001917e-01 9.079650880025917e-01 2.39997e-12 2.39505e-10 ----------------------------------------------------------------------------------------------------- 2 Ti 1 -1.054188795030464e+00 -1.054188795027087e+00 3.37730e-12 2.15074e-10 2 9.183280249973954e-01 9.183280249458174e-01 5.15780e-11 4.22158e-10 3 -1.073809860318410e+00 -1.073809860308900e+00 9.50973e-12 4.02236e-11 ----------------------------------------------------------------------------------------------------- 3 Ti 1 -1.440352340953152e+00 -1.440352340966669e+00 1.35170e-11 3.12158e-10 2 -9.842952138024825e-01 -9.842952137944453e-01 8.03724e-12 1.52387e-10 3 -5.855334671167820e-01 -5.855334671192146e-01 2.43261e-12 1.41167e-10 ----------------------------------------------------------------------------------------------------- 4 Ti 1 7.243352712369334e-01 7.243352712865604e-01 4.96270e-11 2.17408e-10 2 2.803625707894773e-01 2.803625707804054e-01 9.07191e-12 6.82418e-11 3 6.673816500384160e-01 6.673816500491756e-01 1.07596e-11 1.54571e-10 ----------------------------------------------------------------------------------------------------- 5 Ti 1 -2.419706202954511e-01 -2.419706202706797e-01 2.47714e-11 1.94432e-10 2 -5.108774825331858e-02 -5.108774825280600e-02 5.12576e-13 6.22880e-10 3 1.243111334704299e-01 1.243111334743250e-01 3.89512e-12 1.78405e-10 ----------------------------------------------------------------------------------------------------- 6 Ti 1 1.465546956838980e-01 1.465546956840824e-01 1.84436e-13 1.42445e-10 2 -1.663321183751210e-01 -1.663321183835818e-01 8.46084e-12 8.41749e-11 3 9.823467695625747e-02 9.823467698320580e-02 2.69483e-11 1.83253e-10 ----------------------------------------------------------------------------------------------------- 7 Ti 1 -6.752819600343750e-01 -6.752819601261433e-01 9.17683e-11 1.75360e-10 2 -1.642860738291103e-02 -1.642860741280334e-02 2.98923e-11 8.58808e-10 3 1.826236228152349e-01 1.826236228395212e-01 2.42863e-11 2.89941e-10 ----------------------------------------------------------------------------------------------------- 8 Ti 1 1.692656588870496e+00 1.692656588859519e+00 1.09770e-11 2.90459e-09 * 2 2.137078558274236e+00 2.137078558213313e+00 6.09228e-11 2.83718e-10 3 1.237802424415632e+00 1.237802424429836e+00 1.42037e-11 2.40523e-10 ----------------------------------------------------------------------------------------------------- 9 Ti 1 -3.361416353494470e-01 -3.361416353253850e-01 2.40620e-11 2.06293e-11 2 -7.734689984057767e-01 -7.734689983783352e-01 2.74415e-11 1.93396e-09 * 3 -1.391023872445540e+00 -1.391023872438630e+00 6.91025e-12 2.20436e-07 * ----------------------------------------------------------------------------------------------------- 10 Ti 1 -4.334541254985639e-01 -4.334541255185180e-01 1.99541e-11 1.00423e-10 2 1.917138790026055e+00 1.917138789941108e+00 8.49467e-11 4.94444e-10 3 -8.107674087363005e-01 -8.107674087824226e-01 4.61221e-11 1.22809e-10 ----------------------------------------------------------------------------------------------------- 11 Ti 1 1.872160660794177e+00 1.872160660829828e+00 3.56510e-11 2.59365e-10 2 -2.564797910581772e+00 -2.564797910762613e+00 1.80841e-10 2.84090e-10 3 2.172632698236732e+00 2.172632698215468e+00 2.12639e-11 5.42272e-10 ----------------------------------------------------------------------------------------------------- 12 Ti 1 -7.947570835549403e-01 -7.947570835426192e-01 1.23211e-11 1.43091e-10 2 1.146906679650073e+00 1.146906679634577e+00 1.54956e-11 1.67320e-10 3 1.328042548527030e+00 1.328042548528428e+00 1.39799e-12 2.30252e-10 ----------------------------------------------------------------------------------------------------- 13 Ti 1 1.066364259051208e+00 1.066364258935860e+00 1.15348e-10 3.54136e-10 2 -6.543023551064622e-01 -6.543023550615654e-01 4.48968e-11 4.01201e-10 3 1.434405991060382e-02 1.434405992188614e-02 1.12823e-11 1.16491e-10 ----------------------------------------------------------------------------------------------------- 14 Ti 1 -6.369188758315780e-01 -6.369188758306285e-01 9.49574e-13 1.50058e-10 2 -6.870687112915274e-01 -6.870687112828935e-01 8.63387e-12 1.61528e-10 3 2.213893719407001e-01 2.213893719481028e-01 7.40269e-12 9.39874e-11 ----------------------------------------------------------------------------------------------------- 15 Ti 1 2.967577642628347e-01 2.967577642599927e-01 2.84200e-12 3.45411e-07 * 2 -1.527804819573361e+00 -1.527804819462940e+00 1.10421e-10 6.55612e-10 3 4.812517547989343e-01 4.812517546544293e-01 1.44505e-10 5.32330e-10 ----------------------------------------------------------------------------------------------------- 16 Ti 1 -1.719015100691884e+00 -1.719015100709257e+00 1.73732e-11 4.23407e-10 2 5.795352666469830e-01 5.795352666309782e-01 1.60048e-11 1.58039e-10 3 -3.177405897694435e-01 -3.177405895853899e-01 1.84054e-10 1.39271e-10 ----------------------------------------------------------------------------------------------------- 17 Ti 1 -8.949290838065717e-02 -8.949290840873536e-02 2.80782e-11 5.89039e-10 2 -6.691504993189216e-01 -6.691504993367540e-01 1.78324e-11 1.36484e-10 3 6.507324510990897e-02 6.507324509474532e-02 1.51636e-11 7.89328e-11 ----------------------------------------------------------------------------------------------------- 18 Ti 1 7.786915375323624e-01 7.786915374911643e-01 4.11982e-11 6.05370e-09 * 2 7.948381640149403e-01 7.948381640011667e-01 1.37736e-11 1.03922e-09 3 -1.137221609323496e+00 -1.137221609308537e+00 1.49589e-11 3.64828e-10 ----------------------------------------------------------------------------------------------------- 19 Ti 1 -9.528200458795489e-01 -9.528200458677449e-01 1.18040e-11 3.64733e-11 2 3.695519224927673e-01 3.695519224724196e-01 2.03477e-11 5.25917e-11 3 1.023921250411368e+00 1.023921250399474e+00 1.18940e-11 1.69955e-11 ----------------------------------------------------------------------------------------------------- 20 Ti 1 -8.655750830348943e-01 -8.655750830352326e-01 3.38285e-13 2.14535e-09 * 2 -7.171769881944231e-01 -7.171769881948822e-01 4.59077e-13 1.78108e-10 3 4.161540636308382e-01 4.161540636720468e-01 4.12086e-11 7.38443e-12 ----------------------------------------------------------------------------------------------------- 21 Ti 1 9.489945488027233e-01 9.489945487722168e-01 3.05065e-11 3.68703e-11 2 -9.973296460124613e-01 -9.973296459852713e-01 2.71900e-11 1.14513e-10 3 5.229867946821042e-02 5.229867965563685e-02 1.87426e-10 5.65204e-10 ----------------------------------------------------------------------------------------------------- 22 Ti 1 1.181430568258474e+00 1.181430568265666e+00 7.19180e-12 2.19959e-09 * 2 1.966630728797935e+00 1.966630728800675e+00 2.73981e-12 9.11756e-10 3 4.870702160239685e-01 4.870702160430942e-01 1.91257e-11 9.19333e-10 ----------------------------------------------------------------------------------------------------- 23 Ti 1 -9.525982730625264e-01 -9.525982730834496e-01 2.09232e-11 6.13501e-11 2 8.583615436775526e-01 8.583615436785237e-01 9.71112e-13 2.04553e-10 3 -9.162132551427645e-01 -9.162132551599090e-01 1.71445e-11 3.31735e-10 ----------------------------------------------------------------------------------------------------- 24 Ti 1 -1.146702301575339e+00 -1.146702301549379e+00 2.59597e-11 4.33108e-09 * 2 -1.432530812091938e+00 -1.432530812044624e+00 4.73148e-11 2.87073e-10 3 -6.461208395343350e-01 -6.461208395438418e-01 9.50684e-12 6.63237e-10 ----------------------------------------------------------------------------------------------------- 25 Ti 1 -1.127470744200832e+00 -1.127470744237711e+00 3.68798e-11 3.79265e-09 * 2 -2.081506284343709e+00 -2.081506284129885e+00 2.13825e-10 1.07146e-08 * 3 -3.168347908691667e+00 -3.168347908592979e+00 9.86873e-11 3.34202e-10 ----------------------------------------------------------------------------------------------------- 26 Ti 1 2.621653520272695e+00 2.621653520235035e+00 3.76597e-11 2.62093e-10 2 1.556180400946092e-01 1.556180401456097e-01 5.10005e-11 4.48456e-09 * 3 -1.266017510389267e+00 -1.266017510372248e+00 1.70184e-11 7.05526e-09 * ----------------------------------------------------------------------------------------------------- 27 Ti 1 3.576481242692092e+00 3.576481242570760e+00 1.21332e-10 2.10560e-10 2 2.113018431409178e-02 2.113018435449082e-02 4.03990e-11 4.50147e-10 3 2.074080105198624e-01 2.074080105708982e-01 5.10358e-11 3.83156e-10 ----------------------------------------------------------------------------------------------------- 28 Ti 1 -1.758661638874754e+00 -1.758661638956288e+00 8.15332e-11 1.76873e-10 2 2.025507022660860e+00 2.025507022668118e+00 7.25775e-12 2.47371e-10 3 2.017927732994592e+00 2.017927732991461e+00 3.13172e-12 1.80504e-09 ----------------------------------------------------------------------------------------------------- 29 Ti 1 -1.041827171498316e+00 -1.041827171518321e+00 2.00051e-11 1.70488e-09 2 7.444821930402667e-01 7.444821929952218e-01 4.50450e-11 4.18389e-10 3 9.696186013930600e-01 9.696186014006247e-01 7.56473e-12 5.25826e-11 ----------------------------------------------------------------------------------------------------- 30 Ti 1 4.150580388733510e-01 4.150580388375557e-01 3.57953e-11 3.21275e-10 2 4.886737253291816e-01 4.886737253311674e-01 1.98586e-12 3.01100e-11 3 -1.123870217234820e+00 -1.123870217156683e+00 7.81368e-11 6.36703e-09 * ----------------------------------------------------------------------------------------------------- 31 Ti 1 5.672632116561394e-01 5.672632116515406e-01 4.59877e-12 7.35410e-11 2 -6.768553314389035e-01 -6.768553314250750e-01 1.38285e-11 1.57024e-10 3 9.606847413269590e-02 9.606847412260965e-02 1.00863e-11 8.99903e-11 ----------------------------------------------------------------------------------------------------- 32 Ti 1 -1.282168322312686e+00 -1.282168322294360e+00 1.83262e-11 6.11289e-12 2 -9.362590971069175e-01 -9.362590971348761e-01 2.79586e-11 8.49288e-11 3 -3.348527640918391e-01 -3.348527640872806e-01 4.55846e-12 1.07139e-09 ----------------------------------------------------------------------------------------------------- * 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 = 21, direction = 3: |F_model - F_numer| error = ----------------------- = 3.58377e-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 = 3.8224251974519574 | (Configuration in file "config-NiTi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ti 1 6.436752947764834e-01 6.436752948008826e-01 2.43991e-11 1.66183e-10 2 5.958345186517092e-01 5.958345187187505e-01 6.70413e-11 7.13988e-11 3 3.826341038774113e-01 3.826341038957677e-01 1.83564e-11 9.13382e-11 ----------------------------------------------------------------------------------------------------- 2 Ni 1 -9.493715132937364e-01 -9.493715132991963e-01 5.45997e-12 2.12862e-09 * 2 2.624382926441546e-01 2.624382925799966e-01 6.41580e-11 4.89518e-10 3 -1.828756500156743e+00 -1.828756500143441e+00 1.33020e-11 1.21973e-10 ----------------------------------------------------------------------------------------------------- 3 Ni 1 -1.177531626229368e+00 -1.177531626207727e+00 2.16409e-11 2.41899e-10 2 -1.538268680803671e+00 -1.538268680782356e+00 2.13149e-11 1.09782e-10 3 9.971188577328700e-01 9.971188576033686e-01 1.29501e-10 2.94904e-10 ----------------------------------------------------------------------------------------------------- 4 Ni 1 -2.092793124969133e-02 -2.092793125633819e-02 6.64686e-12 2.65782e-10 2 4.101486844531172e-01 4.101486843936731e-01 5.94441e-11 3.54557e-10 3 -2.988430046308773e-01 -2.988430046732112e-01 4.23339e-11 1.07830e-10 ----------------------------------------------------------------------------------------------------- 5 Ti 1 -1.678055998909280e-01 -1.678055998738909e-01 1.70371e-11 1.09025e-10 2 -1.159772495488173e+00 -1.159772495487651e+00 5.21805e-13 6.92076e-10 3 -1.160909029602648e+00 -1.160909029607232e+00 4.58389e-12 8.30020e-11 ----------------------------------------------------------------------------------------------------- 6 Ni 1 -1.484272708086250e-01 -1.484272708140701e-01 5.44506e-12 3.23333e-10 2 3.511284314170965e-02 3.511284317011151e-02 2.84019e-11 1.40723e-09 3 -8.582802883184254e-01 -8.582802882832548e-01 3.51706e-11 2.29648e-10 ----------------------------------------------------------------------------------------------------- 7 Ni 1 -7.055603967406183e-01 -7.055603967717818e-01 3.11635e-11 4.36287e-10 2 2.348357002972428e-01 2.348357002723807e-01 2.48621e-11 5.27701e-10 3 7.053219662025622e-01 7.053219661875950e-01 1.49671e-11 1.53137e-10 ----------------------------------------------------------------------------------------------------- 8 Ti 1 2.582061504486322e+00 2.582061504488203e+00 1.88116e-12 2.39684e-10 2 -1.607378539648740e+00 -1.607378539641620e+00 7.12008e-12 2.83844e-09 * 3 1.497543541678247e+00 1.497543541611511e+00 6.67355e-11 6.59967e-10 ----------------------------------------------------------------------------------------------------- 9 Ti 1 -5.622599700346972e-01 -5.622599700248503e-01 9.84690e-12 5.58408e-10 2 -2.334187174949558e+00 -2.334187174907996e+00 4.15623e-11 1.38685e-10 3 -7.221494693202709e-01 -7.221494693033157e-01 1.69552e-11 8.58955e-11 ----------------------------------------------------------------------------------------------------- 10 Ni 1 9.682595519155662e-01 9.682595519345609e-01 1.89947e-11 6.29043e-11 2 -4.757697278191602e-02 -4.757697279376559e-02 1.18496e-11 1.80577e-10 3 8.225108671720350e-01 8.225108671611866e-01 1.08484e-11 1.72570e-09 ----------------------------------------------------------------------------------------------------- 11 Ni 1 -1.258962709411867e+00 -1.258962709409206e+00 2.66098e-12 1.14553e-10 2 2.141437496381074e+00 2.141437496359882e+00 2.11919e-11 4.36366e-10 3 1.281430511862382e+00 1.281430511825292e+00 3.70897e-11 2.28846e-09 * ----------------------------------------------------------------------------------------------------- 12 Ni 1 1.505739816445494e-01 1.505739816290993e-01 1.54500e-11 8.25879e-11 2 8.181087213059346e-01 8.181087213110755e-01 5.14089e-12 7.62187e-10 3 7.334354709326822e-01 7.334354709189252e-01 1.37570e-11 2.28423e-11 ----------------------------------------------------------------------------------------------------- 13 Ni 1 -2.505643624419488e+00 -2.505643624479789e+00 6.03007e-11 1.28307e-10 2 5.583092400305332e-01 5.583092400241466e-01 6.38656e-12 9.60332e-10 3 -2.005217576044723e+00 -2.005217576042872e+00 1.85096e-12 3.43492e-09 * ----------------------------------------------------------------------------------------------------- 14 Ti 1 2.683915791740996e-01 2.683915791679340e-01 6.16562e-12 2.98538e-10 2 1.496159832375845e-01 1.496159832462073e-01 8.62280e-12 2.14526e-10 3 -1.895569439783323e-01 -1.895569439603629e-01 1.79695e-11 1.25378e-10 ----------------------------------------------------------------------------------------------------- 15 Ni 1 1.854370507598547e+00 1.854370507602789e+00 4.24238e-12 3.72314e-09 * 2 1.144534135087967e+00 1.144534135065896e+00 2.20717e-11 4.81167e-09 * 3 3.104408048326068e+00 3.104408048322053e+00 4.01457e-12 3.10458e-10 ----------------------------------------------------------------------------------------------------- 16 Ni 1 -2.487963616387476e-01 -2.487963615600342e-01 7.87135e-11 2.08745e-10 2 -4.877093500008324e-01 -4.877093499974401e-01 3.39229e-12 6.71114e-11 3 8.427497870912137e-01 8.427497870842328e-01 6.98097e-12 7.22777e-12 ----------------------------------------------------------------------------------------------------- 17 Ni 1 3.912369066815883e-01 3.912369066761413e-01 5.44698e-12 8.49616e-10 2 5.385232161348671e-01 5.385232161380231e-01 3.15603e-12 1.78624e-10 3 -3.018169732328217e-01 -3.018169732161088e-01 1.67129e-11 5.38890e-11 ----------------------------------------------------------------------------------------------------- 18 Ti 1 4.998676539389024e-01 4.998676539027883e-01 3.61142e-11 1.14970e-10 2 1.688188705667742e+00 1.688188705660220e+00 7.52243e-12 2.70062e-10 3 -1.189275816097565e+00 -1.189275816107201e+00 9.63540e-12 2.29696e-10 ----------------------------------------------------------------------------------------------------- 19 Ti 1 -1.099310894992273e-01 -1.099310895187229e-01 1.94955e-11 1.26184e-10 2 -1.140094525197671e+00 -1.140094525168780e+00 2.88904e-11 5.95662e-10 3 1.544764138108704e+00 1.544764138095479e+00 1.32254e-11 1.70812e-10 ----------------------------------------------------------------------------------------------------- 20 Ti 1 -2.478355154730513e+00 -2.478355154712834e+00 1.76796e-11 3.68939e-10 2 -4.850491752096312e-01 -4.850491751665514e-01 4.30798e-11 1.11433e-10 3 3.826053036111952e-01 3.826053036216659e-01 1.04707e-11 1.28259e-09 ----------------------------------------------------------------------------------------------------- 21 Ni 1 1.036267869094531e+00 1.036267869106797e+00 1.22660e-11 3.54164e-10 2 8.314445051274627e-01 8.314445050864989e-01 4.09638e-11 2.60704e-10 3 -8.849107410441149e-01 -8.849107410131336e-01 3.09813e-11 4.02015e-10 ----------------------------------------------------------------------------------------------------- 22 Ti 1 7.320591942772776e-01 7.320591943186125e-01 4.13349e-11 1.61982e-10 2 -5.504646370873348e-01 -5.504646370565756e-01 3.07593e-11 2.11883e-10 3 -1.850566669339286e+00 -1.850566669449442e+00 1.10156e-10 7.17214e-09 * ----------------------------------------------------------------------------------------------------- 23 Ni 1 -8.244998172993291e-01 -8.244998173105235e-01 1.11944e-11 2.93359e-10 2 -8.042615292744263e-01 -8.042615292643680e-01 1.00583e-11 6.26891e-11 3 4.035231098305375e-01 4.035231098990548e-01 6.85172e-11 1.18173e-10 ----------------------------------------------------------------------------------------------------- 24 Ni 1 6.569957663177947e-01 6.569957664615336e-01 1.43739e-10 8.75126e-11 2 7.497836281405426e-01 7.497836281226447e-01 1.78979e-11 3.43262e-10 3 -1.653042224270375e-01 -1.653042224457563e-01 1.87188e-11 1.29347e-09 ----------------------------------------------------------------------------------------------------- 25 Ni 1 1.667769703593718e-01 1.667769703534520e-01 5.91979e-12 1.48195e-10 2 -1.676808119344221e+00 -1.676808119322655e+00 2.15661e-11 2.19810e-10 3 -1.270868895973869e+00 -1.270868896018906e+00 4.50375e-11 3.47055e-10 ----------------------------------------------------------------------------------------------------- 26 Ti 1 2.393317476017189e+00 2.393317475954277e+00 6.29123e-11 1.79417e-09 * 2 -2.306457395370807e-01 -2.306457394881480e-01 4.89327e-11 4.90248e-10 3 -1.692522157581531e+00 -1.692522157573658e+00 7.87348e-12 3.40169e-10 ----------------------------------------------------------------------------------------------------- 27 Ti 1 1.899486077971116e+00 1.899486077877226e+00 9.38893e-11 3.24584e-09 * 2 -4.273839560711379e-01 -4.273839558906928e-01 1.80445e-10 6.44255e-11 3 -1.649313321878040e-01 -1.649313321333962e-01 5.44078e-11 2.08246e-10 ----------------------------------------------------------------------------------------------------- 28 Ti 1 -6.072587886537150e-01 -6.072587887389750e-01 8.52600e-11 1.99735e-10 2 7.980484023907834e-02 7.980484024227778e-02 3.19944e-12 2.32012e-10 3 1.226776779550494e+00 1.226776779519793e+00 3.07010e-11 2.72075e-10 ----------------------------------------------------------------------------------------------------- 29 Ti 1 -2.289835694426773e+00 -2.289835694436733e+00 9.96003e-12 5.99149e-09 * 2 5.264523048455940e-01 5.264523048318082e-01 1.37859e-11 6.49120e-10 3 5.562934127705635e-01 5.562934127708912e-01 3.27627e-13 2.48604e-10 ----------------------------------------------------------------------------------------------------- 30 Ti 1 1.433218327172222e+00 1.433218327173205e+00 9.83436e-13 3.41708e-10 2 9.579068029116719e-01 9.579068029043056e-01 7.36622e-12 2.58032e-10 3 -2.770975924890372e+00 -2.770975924895233e+00 4.86100e-12 8.15370e-11 ----------------------------------------------------------------------------------------------------- 31 Ti 1 -4.559226769784593e-01 -4.559226769927193e-01 1.42600e-11 9.47228e-11 2 -6.391902764809977e-01 -6.391902764807019e-01 2.95763e-13 5.25485e-11 3 1.550361983512365e+00 1.550361983491030e+00 2.13340e-11 2.75384e-09 * ----------------------------------------------------------------------------------------------------- 32 Ti 1 -1.165468436119777e+00 -1.165468436203069e+00 8.32925e-11 5.35067e-10 2 1.406311553577404e+00 1.406311553567944e+00 9.46021e-12 5.36378e-10 3 1.323407662567092e+00 1.323407662571240e+00 4.14802e-12 4.57984e-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 = 6, direction = 2: |F_model - F_numer| error = ----------------------- = 8.08874e-10 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 3.58377e-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 3.58377e-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.