!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! VERIFICATION CHECK: vc-forces-numerical-derivative !!!!! !!!!! !!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Description: Comparison of the analytical forces obtained from the model with forces computed by numerical differentiation using Richardson extrapolation for a randomly distorted non-periodic structure based off the equilibrium face-centered cubic (fcc) structure. Separate configurations are tested for each species supported by the model, as well as one containing a random distribution of all species. Configurations used for testing are provided as auxiliary files. Author: Ellad Tadmor ----------------------------------------------------------------------------------------------------- Results for KIM Model : MEAM_LAMMPS_KoGrabowskiNeugebauer_2015_NiTi__MO_663355627503_002 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 4.280328767365834e-01 4.280328767330589e-01 3.52451e-12 1.11622e-10 2 -2.782440375891200e-01 -2.782440375914874e-01 2.36744e-12 3.36561e-11 3 -2.427589046797544e-01 -2.427589046838609e-01 4.10649e-12 4.80772e-11 ----------------------------------------------------------------------------------------------------- 2 Ni 1 -8.945380340188884e-01 -8.945380340141859e-01 4.70257e-12 1.89476e-10 2 8.101560045347391e-01 8.101560044995798e-01 3.51593e-11 5.17276e-10 3 1.045849926620818e+00 1.045849926646942e+00 2.61242e-11 5.69158e-11 ----------------------------------------------------------------------------------------------------- 3 Ni 1 8.537894607145591e-01 8.537894607086541e-01 5.90494e-12 3.72756e-11 2 9.108791640041204e-01 9.108791640210722e-01 1.69518e-11 2.69671e-10 3 -7.459561105906443e-01 -7.459561106141586e-01 2.35143e-11 1.78877e-10 ----------------------------------------------------------------------------------------------------- 4 Ni 1 1.237798708062612e+00 1.237798708071471e+00 8.85825e-12 8.04028e-11 2 3.237916928563627e-01 3.237916928640731e-01 7.71039e-12 3.81918e-10 3 1.020636549337638e+00 1.020636549353885e+00 1.62472e-11 6.42570e-11 ----------------------------------------------------------------------------------------------------- 5 Ni 1 5.472543543146200e-01 5.472543543309882e-01 1.63682e-11 6.96853e-09 * 2 -3.646824746480146e-02 -3.646824750207461e-02 3.72732e-11 1.56060e-10 3 5.020282252234914e-01 5.020282252025805e-01 2.09109e-11 1.74064e-11 ----------------------------------------------------------------------------------------------------- 6 Ni 1 -7.277260560915425e-01 -7.277260561112282e-01 1.96857e-11 8.28634e-11 2 5.254050956244984e-01 5.254050956464590e-01 2.19605e-11 1.82208e-10 3 6.293922312975386e-01 6.293922313050775e-01 7.53886e-12 1.28774e-11 ----------------------------------------------------------------------------------------------------- 7 Ni 1 5.755781631746363e-01 5.755781630981569e-01 7.64794e-11 3.07279e-10 2 -3.415419410349350e+00 -3.415419410351933e+00 2.58282e-12 1.26817e-10 3 -4.141310042457676e+00 -4.141310042440430e+00 1.72466e-11 1.26250e-10 ----------------------------------------------------------------------------------------------------- 8 Ni 1 -2.302770906215878e+00 -2.302770906189871e+00 2.60068e-11 1.31805e-10 2 -2.085438814117923e+00 -2.085438814120868e+00 2.94431e-12 2.36754e-10 3 -1.083380028400895e+00 -1.083380028335393e+00 6.55018e-11 2.86890e-10 ----------------------------------------------------------------------------------------------------- 9 Ni 1 -1.896242239138805e-01 -1.896242239029097e-01 1.09708e-11 3.53349e-11 2 -1.930117541786761e+00 -1.930117541830043e+00 4.32820e-11 2.14299e-10 3 -2.326305877876811e+00 -2.326305877841655e+00 3.51563e-11 6.86573e-10 ----------------------------------------------------------------------------------------------------- 10 Ni 1 -1.511550624256461e+00 -1.511550624299573e+00 4.31122e-11 2.34820e-10 2 9.907434353336464e-01 9.907434353447921e-01 1.11458e-11 1.20452e-10 3 -1.699345186647437e+00 -1.699345186609286e+00 3.81517e-11 8.91134e-10 ----------------------------------------------------------------------------------------------------- 11 Ni 1 -1.014909288281546e+00 -1.014909288243873e+00 3.76732e-11 3.70248e-10 2 -1.556578901448131e+00 -1.556578901466467e+00 1.83351e-11 2.87183e-10 3 2.190061454599840e+00 2.190061454598121e+00 1.71863e-12 2.60204e-10 ----------------------------------------------------------------------------------------------------- 12 Ni 1 4.512112058011224e-01 4.512112057966456e-01 4.47675e-12 6.98987e-11 2 1.736567639909368e+00 1.736567639926225e+00 1.68563e-11 5.02265e-10 3 1.694858265167015e+00 1.694858265174676e+00 7.66143e-12 1.33167e-11 ----------------------------------------------------------------------------------------------------- 13 Ni 1 -2.474999677310322e+00 -2.474999677345069e+00 3.47469e-11 3.71590e-10 2 -3.293028711582906e+00 -3.293028711608361e+00 2.54556e-11 5.18388e-10 3 -4.692719167089805e+00 -4.692719167090077e+00 2.71783e-13 3.28120e-10 ----------------------------------------------------------------------------------------------------- 14 Ni 1 1.399709844018679e+00 1.399709843909104e+00 1.09575e-10 4.33983e-10 2 2.147799148310658e+00 2.147799148294311e+00 1.63469e-11 5.53941e-10 3 -8.893409192663698e-01 -8.893409192743043e-01 7.93443e-12 6.36982e-11 ----------------------------------------------------------------------------------------------------- 15 Ni 1 4.239730602372945e+00 4.239730602290821e+00 8.21236e-11 2.53315e-10 2 -1.612312898876705e+00 -1.612312898827465e+00 4.92406e-11 1.92701e-10 3 1.801700232006964e+00 1.801700231945211e+00 6.17526e-11 1.63156e-10 ----------------------------------------------------------------------------------------------------- 16 Ni 1 1.211779180619650e+00 1.211779180613463e+00 6.18749e-12 2.33629e-10 2 2.994416887489951e+00 2.994416887496614e+00 6.66311e-12 1.06735e-10 3 1.824782724573506e+00 1.824782724551438e+00 2.20686e-11 1.05245e-10 ----------------------------------------------------------------------------------------------------- 17 Ni 1 -1.481735581316239e+00 -1.481735581215877e+00 1.00362e-10 2.53053e-10 2 2.688543421177373e-01 2.688543420253768e-01 9.23605e-11 4.91996e-11 3 -5.997154327005894e-01 -5.997154327253080e-01 2.47187e-11 1.00228e-10 ----------------------------------------------------------------------------------------------------- 18 Ni 1 4.490262752886409e-01 4.490262752479720e-01 4.06690e-11 8.86005e-09 * 2 2.184895010390462e+00 2.184895010319041e+00 7.14211e-11 1.37973e-10 3 -1.579490783935639e+00 -1.579490783935070e+00 5.68656e-13 1.76789e-09 * ----------------------------------------------------------------------------------------------------- 19 Ni 1 1.465607819075948e+00 1.465607819090495e+00 1.45464e-11 6.23848e-11 2 -1.040682678389175e+00 -1.040682678395283e+00 6.10734e-12 8.04830e-10 3 1.651663478090029e+00 1.651663478124134e+00 3.41047e-11 2.37615e-10 ----------------------------------------------------------------------------------------------------- 20 Ni 1 2.930188062770290e-01 2.930188062721983e-01 4.83064e-12 1.77462e-10 2 6.104001046752859e-01 6.104001046868343e-01 1.15483e-11 1.14287e-10 3 -4.712963612397285e-01 -4.712963612194353e-01 2.02932e-11 5.43857e-11 ----------------------------------------------------------------------------------------------------- 21 Ni 1 -1.956201982490784e+00 -1.956201982379801e+00 1.10983e-10 2.84536e-10 2 1.455895920086931e-01 1.455895920233697e-01 1.46766e-11 6.37888e-09 * 3 8.949044710601552e-01 8.949044710249879e-01 3.51673e-11 4.12930e-10 ----------------------------------------------------------------------------------------------------- 22 Ni 1 5.333010050052989e-01 5.333010050252818e-01 1.99829e-11 1.60699e-10 2 3.672237983803994e+00 3.672237983816891e+00 1.28964e-11 8.19131e-11 3 3.919255206327094e+00 3.919255206324567e+00 2.52642e-12 3.54933e-10 ----------------------------------------------------------------------------------------------------- 23 Ni 1 5.353961637466113e-01 5.353961638269419e-01 8.03306e-11 9.86942e-11 2 -1.430183612834743e-01 -1.430183612596601e-01 2.38142e-11 7.14578e-11 3 -2.109345070041613e-01 -2.109345070037028e-01 4.58578e-13 7.66952e-10 ----------------------------------------------------------------------------------------------------- 24 Ni 1 -6.098919501839100e-01 -6.098919503548729e-01 1.70963e-10 5.87718e-10 2 9.537192037715307e-01 9.537192037588336e-01 1.26972e-11 2.70781e-10 3 -8.024843386659994e-01 -8.024843386739446e-01 7.94520e-12 1.99042e-10 ----------------------------------------------------------------------------------------------------- 25 Ni 1 -3.627087292171955e-01 -3.627087292368044e-01 1.96089e-11 1.69037e-10 2 -1.362245902184256e+00 -1.362245902169372e+00 1.48841e-11 1.98732e-09 * 3 3.902702788812192e-02 3.902702789062551e-02 2.50359e-12 5.97120e-11 ----------------------------------------------------------------------------------------------------- 26 Ni 1 -1.332009422395397e+00 -1.332009422389912e+00 5.48472e-12 1.23257e-08 * 2 9.934825220298096e-01 9.934825220376196e-01 7.80997e-12 1.00825e-10 3 -1.238105205862843e+00 -1.238105205854951e+00 7.89258e-12 1.37504e-09 * ----------------------------------------------------------------------------------------------------- 27 Ni 1 1.964564312231307e+00 1.964564312201258e+00 3.00486e-11 1.71704e-10 2 -4.706389970696477e+00 -4.706389970754218e+00 5.77414e-11 4.67767e-10 3 2.542328336926563e-01 2.542328337056566e-01 1.30003e-11 3.00741e-09 * ----------------------------------------------------------------------------------------------------- 28 Ni 1 -2.563228342546155e+00 -2.563228342521162e+00 2.49925e-11 1.77790e-10 2 2.603979029255498e+00 2.603979029244371e+00 1.11271e-11 4.31504e-11 3 -2.020190023021454e-01 -2.020190023260630e-01 2.39176e-11 1.21889e-10 ----------------------------------------------------------------------------------------------------- 29 Ni 1 -1.217893677299298e+00 -1.217893677288640e+00 1.06586e-11 8.54547e-10 2 -1.392987439996168e+00 -1.392987440079057e+00 8.28890e-11 1.29329e-08 * 3 1.460885371969691e+00 1.460885371997261e+00 2.75702e-11 1.10965e-10 ----------------------------------------------------------------------------------------------------- 30 Ni 1 5.621043352085575e-02 5.621043355867921e-02 3.78235e-11 3.04050e-10 2 1.082967059668339e+00 1.082967059682037e+00 1.36988e-11 1.88696e-10 3 9.294662072764065e-01 9.294662072629564e-01 1.34501e-11 1.80355e-10 ----------------------------------------------------------------------------------------------------- 31 Ni 1 1.124391364806108e+00 1.124391364804250e+00 1.85874e-12 2.79955e-10 2 -1.277258000784337e+00 -1.277258000784311e+00 2.62013e-14 2.97229e-10 3 5.596758415133651e-01 5.596758415182841e-01 4.91895e-12 3.28243e-10 ----------------------------------------------------------------------------------------------------- 32 Ni 1 1.273387919770291e+00 1.273387919774087e+00 3.79585e-12 1.27804e-10 2 1.174307000764893e+00 1.174307000758086e+00 6.80633e-12 2.80307e-09 * 3 5.067418220761699e-01 5.067418220968694e-01 2.06994e-11 1.11527e-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 = 5, direction = 2: |F_model - F_numer| error = ----------------------- = 1.02207e-09 max{|F_numer|, eps} Comparison of analytical forces obtained from the model, the force computed as a numerical derivative of the energy, the difference between them, and the uncertainty in the numerical estimate of the force. The computed equilibrium lattice constant for the crystal (a0) is given in the heading. MONOATOMIC STRUCTURE -- Species = Ti | a0 = 4.111299514770508 | (Configuration in file "config-Ti.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ti 1 6.609951180719856e-01 6.609951180762940e-01 4.30833e-12 8.34313e-11 2 5.322517264735388e-01 5.322517264672537e-01 6.28508e-12 1.78361e-11 3 9.079650880001708e-01 9.079650880039151e-01 3.74423e-12 5.28150e-11 ----------------------------------------------------------------------------------------------------- 2 Ti 1 -1.054188795030433e+00 -1.054188795024610e+00 5.82268e-12 1.39711e-10 2 9.183280249974737e-01 9.183280249821985e-01 1.52752e-11 1.32862e-10 3 -1.073809860318412e+00 -1.073809860313726e+00 4.68559e-12 2.96669e-11 ----------------------------------------------------------------------------------------------------- 3 Ti 1 -1.440352340953069e+00 -1.440352340966542e+00 1.34730e-11 3.23236e-10 2 -9.842952138024759e-01 -9.842952137923549e-01 1.01210e-11 6.62332e-11 3 -5.855334671167902e-01 -5.855334671281515e-01 1.13612e-11 6.73058e-11 ----------------------------------------------------------------------------------------------------- 4 Ti 1 7.243352712369510e-01 7.243352712409414e-01 3.99047e-12 6.61484e-11 2 2.803625707895108e-01 2.803625708011345e-01 1.16236e-11 1.48140e-10 3 6.673816500384258e-01 6.673816500233333e-01 1.50925e-11 1.44310e-10 ----------------------------------------------------------------------------------------------------- 5 Ti 1 -2.419706202954396e-01 -2.419706203052419e-01 9.80221e-12 1.79775e-10 2 -5.108774825333964e-02 -5.108774823354543e-02 1.97942e-11 1.02094e-09 3 1.243111334704295e-01 1.243111334656199e-01 4.80962e-12 2.89419e-09 * ----------------------------------------------------------------------------------------------------- 6 Ti 1 1.465546956837913e-01 1.465546956794458e-01 4.34544e-12 1.39709e-11 2 -1.663321183751554e-01 -1.663321183513992e-01 2.37561e-11 8.92304e-11 3 9.823467695631849e-02 9.823467696870820e-02 1.23897e-11 2.02566e-10 ----------------------------------------------------------------------------------------------------- 7 Ti 1 -6.752819600344269e-01 -6.752819599951471e-01 3.92798e-11 1.98897e-10 2 -1.642860738285104e-02 -1.642860737841116e-02 4.43988e-12 1.26569e-10 3 1.826236228152541e-01 1.826236228051022e-01 1.01519e-11 3.76860e-10 ----------------------------------------------------------------------------------------------------- 8 Ti 1 1.692656588870759e+00 1.692656588880600e+00 9.84057e-12 1.25674e-10 2 2.137078558274298e+00 2.137078558222243e+00 5.20544e-11 2.00517e-10 3 1.237802424415408e+00 1.237802424429569e+00 1.41618e-11 3.57093e-10 ----------------------------------------------------------------------------------------------------- 9 Ti 1 -3.361416353494318e-01 -3.361416353503914e-01 9.59677e-13 5.52060e-11 2 -7.734689984058797e-01 -7.734689984077286e-01 1.84897e-12 3.56298e-11 3 -1.391023872445451e+00 -1.391023872433662e+00 1.17895e-11 1.29086e-10 ----------------------------------------------------------------------------------------------------- 10 Ti 1 -4.334541254984454e-01 -4.334541255054041e-01 6.95871e-12 6.08590e-10 2 1.917138790026021e+00 1.917138790018670e+00 7.35034e-12 4.44575e-11 3 -8.107674087363996e-01 -8.107674087537350e-01 1.73354e-11 1.51597e-10 ----------------------------------------------------------------------------------------------------- 11 Ti 1 1.872160660794091e+00 1.872160660817749e+00 2.36580e-11 6.90759e-12 2 -2.564797910581675e+00 -2.564797910652962e+00 7.12865e-11 2.81656e-10 3 2.172632698236789e+00 2.172632698243057e+00 6.26788e-12 5.62297e-11 ----------------------------------------------------------------------------------------------------- 12 Ti 1 -7.947570835549543e-01 -7.947570835379980e-01 1.69563e-11 1.63196e-09 2 1.146906679649930e+00 1.146906679647107e+00 2.82374e-12 9.68130e-10 3 1.328042548527027e+00 1.328042548526308e+00 7.19425e-13 1.37439e-10 ----------------------------------------------------------------------------------------------------- 13 Ti 1 1.066364259051039e+00 1.066364259071003e+00 1.99636e-11 1.31444e-10 2 -6.543023551065520e-01 -6.543023551358419e-01 2.92899e-11 9.01490e-10 3 1.434405991060535e-02 1.434405990828079e-02 2.32456e-12 1.21430e-10 ----------------------------------------------------------------------------------------------------- 14 Ti 1 -6.369188758316342e-01 -6.369188758184428e-01 1.31914e-11 6.49205e-11 2 -6.870687112914747e-01 -6.870687112796795e-01 1.17952e-11 8.91995e-11 3 2.213893719407330e-01 2.213893719299955e-01 1.07375e-11 1.71286e-09 ----------------------------------------------------------------------------------------------------- 15 Ti 1 2.967577642627320e-01 2.967577642635923e-01 8.60256e-13 3.45382e-07 * 2 -1.527804819573340e+00 -1.527804819522172e+00 5.11680e-11 2.17892e-10 3 4.812517547991456e-01 4.812517547551949e-01 4.39507e-11 7.59406e-10 ----------------------------------------------------------------------------------------------------- 16 Ti 1 -1.719015100691666e+00 -1.719015100710863e+00 1.91969e-11 4.47031e-10 2 5.795352666469569e-01 5.795352666579969e-01 1.10401e-11 8.86601e-10 3 -3.177405897694646e-01 -3.177405896859483e-01 8.35164e-11 9.35819e-11 ----------------------------------------------------------------------------------------------------- 17 Ti 1 -8.949290838076152e-02 -8.949290841193096e-02 3.11694e-11 5.39705e-11 2 -6.691504993188631e-01 -6.691504993288484e-01 9.98535e-12 2.70633e-10 3 6.507324510988802e-02 6.507324509329039e-02 1.65976e-11 6.64892e-11 ----------------------------------------------------------------------------------------------------- 18 Ti 1 7.786915375323221e-01 7.786915375007667e-01 3.15554e-11 1.36693e-09 2 7.948381640149914e-01 7.948381639924115e-01 2.25799e-11 6.33571e-11 3 -1.137221609323436e+00 -1.137221609366052e+00 4.26164e-11 1.29894e-10 ----------------------------------------------------------------------------------------------------- 19 Ti 1 -9.528200458795684e-01 -9.528200458877650e-01 8.19667e-12 7.92338e-11 2 3.695519224927615e-01 3.695519224937422e-01 9.80660e-13 6.37403e-11 3 1.023921250411325e+00 1.023921250411001e+00 3.24407e-13 2.62987e-10 ----------------------------------------------------------------------------------------------------- 20 Ti 1 -8.655750830349028e-01 -8.655750830341682e-01 7.34635e-13 2.11543e-09 * 2 -7.171769881944021e-01 -7.171769881946333e-01 2.31148e-13 5.84365e-10 3 4.161540636308675e-01 4.161540636397048e-01 8.83726e-12 7.61099e-10 ----------------------------------------------------------------------------------------------------- 21 Ti 1 9.489945488025592e-01 9.489945488334046e-01 3.08454e-11 2.81504e-10 2 -9.973296460125831e-01 -9.973296460122756e-01 3.07532e-13 8.27139e-10 3 5.229867946820246e-02 5.229867943849695e-02 2.97055e-11 7.95196e-10 ----------------------------------------------------------------------------------------------------- 22 Ti 1 1.181430568258568e+00 1.181430568303262e+00 4.46947e-11 2.19317e-09 * 2 1.966630728798052e+00 1.966630728800393e+00 2.34124e-12 1.65704e-10 3 4.870702160239756e-01 4.870702160227562e-01 1.21941e-12 3.15134e-10 ----------------------------------------------------------------------------------------------------- 23 Ti 1 -9.525982730624971e-01 -9.525982730850400e-01 2.25429e-11 4.64682e-10 2 8.583615436775737e-01 8.583615436465505e-01 3.10232e-11 1.12617e-09 3 -9.162132551427838e-01 -9.162132551605238e-01 1.77399e-11 2.65227e-10 ----------------------------------------------------------------------------------------------------- 24 Ti 1 -1.146702301575263e+00 -1.146702301550394e+00 2.48690e-11 1.57343e-10 2 -1.432530812091932e+00 -1.432530812095581e+00 3.64908e-12 2.20245e-10 3 -6.461208395343833e-01 -6.461208395254604e-01 8.92286e-12 1.78290e-10 ----------------------------------------------------------------------------------------------------- 25 Ti 1 -1.127470744200892e+00 -1.127470744215004e+00 1.41125e-11 3.74852e-09 * 2 -2.081506284343728e+00 -2.081506284316883e+00 2.68447e-11 9.46723e-11 3 -3.168347908691825e+00 -3.168347908701256e+00 9.43157e-12 1.86445e-09 ----------------------------------------------------------------------------------------------------- 26 Ti 1 2.621653520272723e+00 2.621653520258898e+00 1.38249e-11 4.73048e-10 2 1.556180400945928e-01 1.556180402025109e-01 1.07918e-10 1.55033e-10 3 -1.266017510389141e+00 -1.266017510314610e+00 7.45308e-11 6.99756e-09 * ----------------------------------------------------------------------------------------------------- 27 Ti 1 3.576481242692119e+00 3.576481242645645e+00 4.64739e-11 4.59415e-10 2 2.113018431411740e-02 2.113018431428491e-02 1.67512e-13 5.94735e-10 3 2.074080105199253e-01 2.074080105086459e-01 1.12794e-11 9.99976e-11 ----------------------------------------------------------------------------------------------------- 28 Ti 1 -1.758661638874706e+00 -1.758661638982330e+00 1.07623e-10 2.15433e-10 2 2.025507022660859e+00 2.025507022745602e+00 8.47433e-11 8.74025e-10 3 2.017927732994599e+00 2.017927732985761e+00 8.83871e-12 1.82133e-10 ----------------------------------------------------------------------------------------------------- 29 Ti 1 -1.041827171498267e+00 -1.041827171508573e+00 1.03066e-11 1.68430e-09 2 7.444821930403304e-01 7.444821929851816e-01 5.51488e-11 1.69013e-10 3 9.696186013931267e-01 9.696186014008290e-01 7.70228e-12 2.85463e-09 * ----------------------------------------------------------------------------------------------------- 30 Ti 1 4.150580388733511e-01 4.150580388937232e-01 2.03721e-11 2.14881e-10 2 4.886737253291984e-01 4.886737253224028e-01 6.79556e-12 8.49397e-11 3 -1.123870217234946e+00 -1.123870217297475e+00 6.25295e-11 2.00274e-10 ----------------------------------------------------------------------------------------------------- 31 Ti 1 5.672632116561380e-01 5.672632116553218e-01 8.16236e-13 1.26744e-10 2 -6.768553314390214e-01 -6.768553314229677e-01 1.60537e-11 1.57015e-10 3 9.606847413272510e-02 9.606847413549767e-02 2.77257e-12 1.65234e-10 ----------------------------------------------------------------------------------------------------- 32 Ti 1 -1.282168322312772e+00 -1.282168322332704e+00 1.99323e-11 5.34801e-09 * 2 -9.362590971069340e-01 -9.362590971413843e-01 3.44503e-11 6.77740e-11 3 -3.348527640919087e-01 -3.348527641079185e-01 1.60098e-11 2.44788e-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 = 26, direction = 2: |F_model - F_numer| error = ----------------------- = 6.93481e-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. 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 6.436752947765062e-01 6.436752947661575e-01 1.03487e-11 1.49471e-09 2 5.958345186517418e-01 5.958345186952519e-01 4.35102e-11 1.51257e-10 3 3.826341038774572e-01 3.826341038823100e-01 4.85284e-12 1.07700e-10 ----------------------------------------------------------------------------------------------------- 2 Ni 1 -9.493715132937183e-01 -9.493715132991736e-01 5.45530e-12 2.11053e-09 2 2.624382926441520e-01 2.624382925881028e-01 5.60493e-11 2.05303e-10 3 -1.828756500156547e+00 -1.828756500143442e+00 1.31049e-11 1.21971e-10 ----------------------------------------------------------------------------------------------------- 3 Ni 1 -1.177531626229375e+00 -1.177531626205055e+00 2.43208e-11 2.58545e-10 2 -1.538268680803495e+00 -1.538268680784525e+00 1.89699e-11 4.43142e-10 3 9.971188577328678e-01 9.971188576685930e-01 6.42748e-11 4.72586e-10 ----------------------------------------------------------------------------------------------------- 4 Ni 1 -2.092793124958626e-02 -2.092793125547283e-02 5.88657e-12 2.63262e-10 2 4.101486844530978e-01 4.101486843952947e-01 5.78031e-11 4.83113e-10 3 -2.988430046309105e-01 -2.988430046941626e-01 6.32521e-11 4.04816e-10 ----------------------------------------------------------------------------------------------------- 5 Ti 1 -1.678055998908738e-01 -1.678055999020796e-01 1.12058e-11 2.20672e-09 2 -1.159772495488063e+00 -1.159772495487649e+00 4.13891e-13 6.89890e-10 3 -1.160909029602538e+00 -1.160909029597102e+00 5.43543e-12 2.43821e-11 ----------------------------------------------------------------------------------------------------- 6 Ni 1 -1.484272708086565e-01 -1.484272708140702e-01 5.41367e-12 3.23332e-10 2 3.511284314167453e-02 3.511284319326033e-02 5.15858e-11 1.31613e-10 3 -8.582802883183858e-01 -8.582802883296848e-01 1.12991e-11 2.78475e-10 ----------------------------------------------------------------------------------------------------- 7 Ni 1 -7.055603967406479e-01 -7.055603967556696e-01 1.50218e-11 1.20501e-10 2 2.348357002972788e-01 2.348357002983311e-01 1.05227e-12 3.04854e-10 3 7.053219662024897e-01 7.053219661875958e-01 1.48939e-11 1.53137e-10 ----------------------------------------------------------------------------------------------------- 8 Ti 1 2.582061504486206e+00 2.582061504485942e+00 2.63789e-13 5.95284e-11 2 -1.607378539648872e+00 -1.607378539641618e+00 7.25398e-12 2.83840e-09 * 3 1.497543541678192e+00 1.497543541679556e+00 1.36402e-12 1.61021e-10 ----------------------------------------------------------------------------------------------------- 9 Ti 1 -5.622599700346947e-01 -5.622599700119704e-01 2.27244e-11 1.32036e-10 2 -2.334187174949595e+00 -2.334187174920892e+00 2.87028e-11 5.85891e-11 3 -7.221494693202041e-01 -7.221494693104872e-01 9.71689e-12 1.05157e-10 ----------------------------------------------------------------------------------------------------- 10 Ni 1 9.682595519156072e-01 9.682595519191630e-01 3.55582e-12 2.77985e-10 2 -4.757697278190034e-02 -4.757697276297400e-02 1.89263e-11 4.93513e-09 * 3 8.225108671720751e-01 8.225108671457034e-01 2.63717e-11 1.69772e-09 ----------------------------------------------------------------------------------------------------- 11 Ni 1 -1.258962709411813e+00 -1.258962709443787e+00 3.19740e-11 1.35971e-10 2 2.141437496380900e+00 2.141437496255861e+00 1.25039e-10 1.30132e-10 3 1.281430511862310e+00 1.281430511870860e+00 8.55005e-12 2.85333e-10 ----------------------------------------------------------------------------------------------------- 12 Ni 1 1.505739816446260e-01 1.505739816405058e-01 4.12020e-12 2.63693e-09 * 2 8.181087213059143e-01 8.181087213045288e-01 1.38545e-12 7.37213e-10 3 7.334354709326699e-01 7.334354709401137e-01 7.44382e-12 1.13242e-09 ----------------------------------------------------------------------------------------------------- 13 Ni 1 -2.505643624419522e+00 -2.505643624392397e+00 2.71259e-11 2.32513e-10 2 5.583092400305693e-01 5.583092400779252e-01 4.73559e-11 4.11959e-10 3 -2.005217576044672e+00 -2.005217576043222e+00 1.44906e-12 3.17613e-11 ----------------------------------------------------------------------------------------------------- 14 Ti 1 2.683915791740853e-01 2.683915792077278e-01 3.36425e-11 2.72036e-10 2 1.496159832375425e-01 1.496159832070850e-01 3.04575e-11 1.23329e-10 3 -1.895569439782701e-01 -1.895569439776168e-01 6.53311e-13 2.45920e-09 ----------------------------------------------------------------------------------------------------- 15 Ni 1 1.854370507598569e+00 1.854370507605711e+00 7.14162e-12 3.76559e-11 2 1.144534135088056e+00 1.144534135082083e+00 5.97300e-12 1.19522e-10 3 3.104408048325959e+00 3.104408048343848e+00 1.78888e-11 7.41304e-10 ----------------------------------------------------------------------------------------------------- 16 Ni 1 -2.487963616387781e-01 -2.487963617104866e-01 7.17084e-11 7.22933e-11 2 -4.877093500008989e-01 -4.877093499636711e-01 3.72278e-11 2.34011e-10 3 8.427497870911652e-01 8.427497870842335e-01 6.93168e-12 7.22777e-12 ----------------------------------------------------------------------------------------------------- 17 Ni 1 3.912369066816123e-01 3.912369066859508e-01 4.33853e-12 1.07044e-09 2 5.385232161349245e-01 5.385232161376473e-01 2.72282e-12 1.92736e-10 3 -3.018169732328065e-01 -3.018169732322599e-01 5.46618e-13 9.45252e-11 ----------------------------------------------------------------------------------------------------- 18 Ti 1 4.998676539388414e-01 4.998676539190362e-01 1.98052e-11 9.86497e-10 2 1.688188705667769e+00 1.688188705634612e+00 3.31566e-11 1.75314e-10 3 -1.189275816097592e+00 -1.189275816003191e+00 9.44007e-11 2.50263e-10 ----------------------------------------------------------------------------------------------------- 19 Ti 1 -1.099310894993132e-01 -1.099310895216637e-01 2.23506e-11 7.27646e-11 2 -1.140094525197610e+00 -1.140094525203754e+00 6.14486e-12 3.27603e-10 3 1.544764138108742e+00 1.544764138145308e+00 3.65661e-11 3.78953e-10 ----------------------------------------------------------------------------------------------------- 20 Ti 1 -2.478355154730406e+00 -2.478355154721084e+00 9.32188e-12 3.84959e-10 2 -4.850491752096568e-01 -4.850491752380364e-01 2.83795e-11 2.62791e-10 3 3.826053036111253e-01 3.826053036094411e-01 1.68421e-12 1.17520e-09 ----------------------------------------------------------------------------------------------------- 21 Ni 1 1.036267869094522e+00 1.036267869171258e+00 7.67353e-11 3.12421e-10 2 8.314445051275525e-01 8.314445051185744e-01 8.97815e-12 3.11927e-10 3 -8.849107410442019e-01 -8.849107410206193e-01 2.35826e-11 3.77841e-10 ----------------------------------------------------------------------------------------------------- 22 Ti 1 7.320591942773146e-01 7.320591942679077e-01 9.40692e-12 6.55295e-10 2 -5.504646370872553e-01 -5.504646370907518e-01 3.49643e-12 1.21335e-09 3 -1.850566669339221e+00 -1.850566669315791e+00 2.34306e-11 2.38976e-10 ----------------------------------------------------------------------------------------------------- 23 Ni 1 -8.244998172993122e-01 -8.244998172891147e-01 1.01975e-11 2.11280e-09 2 -8.042615292744153e-01 -8.042615292606762e-01 1.37391e-11 5.68645e-10 3 4.035231098305684e-01 4.035231097276535e-01 1.02915e-10 3.15097e-10 ----------------------------------------------------------------------------------------------------- 24 Ni 1 6.569957663178301e-01 6.569957664662354e-01 1.48405e-10 4.35939e-10 2 7.497836281404964e-01 7.497836281147873e-01 2.57091e-11 2.72291e-10 3 -1.653042224270288e-01 -1.653042223552330e-01 7.17957e-11 1.34797e-10 ----------------------------------------------------------------------------------------------------- 25 Ni 1 1.667769703593731e-01 1.667769703524696e-01 6.90351e-12 2.59963e-09 * 2 -1.676808119344339e+00 -1.676808119324667e+00 1.96723e-11 1.36843e-10 3 -1.270868895973927e+00 -1.270868896002477e+00 2.85496e-11 6.37041e-09 * ----------------------------------------------------------------------------------------------------- 26 Ti 1 2.393317476017175e+00 2.393317475955893e+00 6.12821e-11 1.28430e-10 2 -2.306457395369310e-01 -2.306457394765511e-01 6.03799e-11 1.22221e-09 3 -1.692522157581586e+00 -1.692522157508426e+00 7.31604e-11 2.08492e-10 ----------------------------------------------------------------------------------------------------- 27 Ti 1 1.899486077971074e+00 1.899486077982369e+00 1.12943e-11 3.33499e-09 * 2 -4.273839560713222e-01 -4.273839559824116e-01 8.89106e-11 2.04151e-10 3 -1.649313321877594e-01 -1.649313321020996e-01 8.56598e-11 1.24988e-10 ----------------------------------------------------------------------------------------------------- 28 Ti 1 -6.072587886537330e-01 -6.072587889973505e-01 3.43618e-10 7.12888e-10 2 7.980484023915442e-02 7.980484026531118e-02 2.61568e-11 8.22544e-11 3 1.226776779550548e+00 1.226776779541406e+00 9.14180e-12 3.85847e-10 ----------------------------------------------------------------------------------------------------- 29 Ti 1 -2.289835694426896e+00 -2.289835694407473e+00 1.94227e-11 2.39263e-10 2 5.264523048455344e-01 5.264523049082739e-01 6.27395e-11 1.89027e-09 3 5.562934127704817e-01 5.562934127664095e-01 4.07219e-12 1.49073e-10 ----------------------------------------------------------------------------------------------------- 30 Ti 1 1.433218327172283e+00 1.433218327115946e+00 5.63372e-11 5.00571e-10 2 9.579068029117054e-01 9.579068029033879e-01 8.31746e-12 4.70888e-09 * 3 -2.770975924890522e+00 -2.770975924830187e+00 6.03353e-11 1.14720e-10 ----------------------------------------------------------------------------------------------------- 31 Ti 1 -4.559226769785342e-01 -4.559226769285934e-01 4.99408e-11 1.43880e-10 2 -6.391902764811409e-01 -6.391902764666247e-01 1.45162e-11 2.78647e-10 3 1.550361983512388e+00 1.550361983477057e+00 3.53311e-11 2.63346e-09 * ----------------------------------------------------------------------------------------------------- 32 Ti 1 -1.165468436119766e+00 -1.165468436105402e+00 1.43638e-11 2.52740e-10 2 1.406311553577431e+00 1.406311553589980e+00 1.25489e-11 2.16456e-11 3 1.323407662567134e+00 1.323407662571270e+00 4.13602e-12 2.25173e-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 = 6, direction = 2: |F_model - F_numer| error = ----------------------- = 1.46914e-09 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 1.46914e-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 1.46914e-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.