!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_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 4.280328767365834e-01 4.280328767330586e-01 3.52485e-12 1.11622e-10 2 -2.782440375891200e-01 -2.782440375914871e-01 2.36716e-12 3.36564e-11 3 -2.427589046797544e-01 -2.427589046838607e-01 4.10627e-12 4.80772e-11 ----------------------------------------------------------------------------------------------------- 2 Ni 1 -8.945380340188884e-01 -8.945380340141850e-01 4.70346e-12 1.89476e-10 2 8.101560045347391e-01 8.101560044995791e-01 3.51600e-11 5.17277e-10 3 1.045849926620818e+00 1.045849926646941e+00 2.61233e-11 5.69140e-11 ----------------------------------------------------------------------------------------------------- 3 Ni 1 8.537894607145591e-01 8.537894607086534e-01 5.90572e-12 3.72754e-11 2 9.108791640041204e-01 9.108791640210715e-01 1.69511e-11 2.69672e-10 3 -7.459561105906443e-01 -7.459561106141560e-01 2.35117e-11 1.78879e-10 ----------------------------------------------------------------------------------------------------- 4 Ni 1 1.237798708062612e+00 1.237798708071469e+00 8.85692e-12 8.04015e-11 2 3.237916928563627e-01 3.237916928640728e-01 7.71011e-12 3.81918e-10 3 1.020636549337638e+00 1.020636549353884e+00 1.62461e-11 6.42573e-11 ----------------------------------------------------------------------------------------------------- 5 Ni 1 5.472543543146200e-01 5.472543543309886e-01 1.63686e-11 6.96853e-09 * 2 -3.646824746480146e-02 -3.646824750207459e-02 3.72731e-11 1.56060e-10 3 5.020282252234914e-01 5.020282252025802e-01 2.09113e-11 1.74060e-11 ----------------------------------------------------------------------------------------------------- 6 Ni 1 -7.277260560915425e-01 -7.277260561112275e-01 1.96850e-11 8.28632e-11 2 5.254050956244984e-01 5.254050956464585e-01 2.19601e-11 1.82207e-10 3 6.293922312975386e-01 6.293922313050763e-01 7.53764e-12 1.28781e-11 ----------------------------------------------------------------------------------------------------- 7 Ni 1 5.755781631746363e-01 5.755781630981562e-01 7.64800e-11 3.07279e-10 2 -3.415419410349350e+00 -3.415419410351931e+00 2.58060e-12 1.26816e-10 3 -4.141310042457676e+00 -4.141310042440418e+00 1.72582e-11 1.26256e-10 ----------------------------------------------------------------------------------------------------- 8 Ni 1 -2.302770906215878e+00 -2.302770906189868e+00 2.60103e-11 1.31803e-10 2 -2.085438814117923e+00 -2.085438814120866e+00 2.94298e-12 2.36753e-10 3 -1.083380028400895e+00 -1.083380028335392e+00 6.55027e-11 2.86890e-10 ----------------------------------------------------------------------------------------------------- 9 Ni 1 -1.896242239138805e-01 -1.896242239029095e-01 1.09709e-11 3.53349e-11 2 -1.930117541786761e+00 -1.930117541830042e+00 4.32805e-11 2.14298e-10 3 -2.326305877876811e+00 -2.326305877841653e+00 3.51581e-11 6.86574e-10 ----------------------------------------------------------------------------------------------------- 10 Ni 1 -1.511550624256461e+00 -1.511550624299571e+00 4.31104e-11 2.34817e-10 2 9.907434353336464e-01 9.907434353447913e-01 1.11449e-11 1.20453e-10 3 -1.699345186647437e+00 -1.699345186609285e+00 3.81528e-11 8.91134e-10 ----------------------------------------------------------------------------------------------------- 11 Ni 1 -1.014909288281546e+00 -1.014909288243873e+00 3.76739e-11 3.70248e-10 2 -1.556578901448131e+00 -1.556578901466465e+00 1.83338e-11 2.87183e-10 3 2.190061454599840e+00 2.190061454598120e+00 1.71996e-12 2.60206e-10 ----------------------------------------------------------------------------------------------------- 12 Ni 1 4.512112058011224e-01 4.512112057966454e-01 4.47703e-12 6.98989e-11 2 1.736567639909368e+00 1.736567639926223e+00 1.68550e-11 5.02266e-10 3 1.694858265167015e+00 1.694858265174674e+00 7.65987e-12 1.33176e-11 ----------------------------------------------------------------------------------------------------- 13 Ni 1 -2.474999677310322e+00 -2.474999677345062e+00 3.47398e-11 3.71585e-10 2 -3.293028711582906e+00 -3.293028711608358e+00 2.54525e-11 5.18388e-10 3 -4.692719167089805e+00 -4.692719167090073e+00 2.67342e-13 3.28130e-10 ----------------------------------------------------------------------------------------------------- 14 Ni 1 1.399709844018679e+00 1.399709843909102e+00 1.09576e-10 4.33983e-10 2 2.147799148310658e+00 2.147799148294309e+00 1.63487e-11 5.53940e-10 3 -8.893409192663698e-01 -8.893409192743036e-01 7.93376e-12 6.36987e-11 ----------------------------------------------------------------------------------------------------- 15 Ni 1 4.239730602372945e+00 4.239730602290818e+00 8.21272e-11 2.53315e-10 2 -1.612312898876705e+00 -1.612312898827462e+00 4.92428e-11 1.92701e-10 3 1.801700232006964e+00 1.801700231945208e+00 6.17557e-11 1.63157e-10 ----------------------------------------------------------------------------------------------------- 16 Ni 1 1.211779180619650e+00 1.211779180613462e+00 6.18861e-12 2.33627e-10 2 2.994416887489951e+00 2.994416887496612e+00 6.66045e-12 1.06734e-10 3 1.824782724573506e+00 1.824782724551436e+00 2.20701e-11 1.05245e-10 ----------------------------------------------------------------------------------------------------- 17 Ni 1 -1.481735581316239e+00 -1.481735581215874e+00 1.00365e-10 2.53054e-10 2 2.688543421177373e-01 2.688543420253767e-01 9.23606e-11 4.91998e-11 3 -5.997154327005894e-01 -5.997154327253075e-01 2.47181e-11 1.00228e-10 ----------------------------------------------------------------------------------------------------- 18 Ni 1 4.490262752886409e-01 4.490262752479722e-01 4.06687e-11 8.86005e-09 * 2 2.184895010390462e+00 2.184895010319040e+00 7.14220e-11 1.37972e-10 3 -1.579490783935639e+00 -1.579490783935071e+00 5.67768e-13 1.76789e-09 * ----------------------------------------------------------------------------------------------------- 19 Ni 1 1.465607819075948e+00 1.465607819090494e+00 1.45453e-11 6.23843e-11 2 -1.040682678389175e+00 -1.040682678395282e+00 6.10623e-12 8.04830e-10 3 1.651663478090029e+00 1.651663478124132e+00 3.41032e-11 2.37615e-10 ----------------------------------------------------------------------------------------------------- 20 Ni 1 2.930188062770290e-01 2.930188062721981e-01 4.83086e-12 1.77463e-10 2 6.104001046752859e-01 6.104001046868338e-01 1.15479e-11 1.14287e-10 3 -4.712963612397285e-01 -4.712963612194349e-01 2.02937e-11 5.43857e-11 ----------------------------------------------------------------------------------------------------- 21 Ni 1 -1.956201982490784e+00 -1.956201982379808e+00 1.10976e-10 2.84528e-10 2 1.455895920086931e-01 1.455895920233698e-01 1.46767e-11 6.37889e-09 * 3 8.949044710601552e-01 8.949044710249872e-01 3.51681e-11 4.12929e-10 ----------------------------------------------------------------------------------------------------- 22 Ni 1 5.333010050052989e-01 5.333010050252814e-01 1.99826e-11 1.60700e-10 2 3.672237983803994e+00 3.672237983816887e+00 1.28932e-11 8.19123e-11 3 3.919255206327094e+00 3.919255206324565e+00 2.52909e-12 3.54934e-10 ----------------------------------------------------------------------------------------------------- 23 Ni 1 5.353961637466113e-01 5.353961638269413e-01 8.03301e-11 9.86948e-11 2 -1.430183612834743e-01 -1.430183612596599e-01 2.38144e-11 7.14577e-11 3 -2.109345070041613e-01 -2.109345070037026e-01 4.58772e-13 7.66952e-10 ----------------------------------------------------------------------------------------------------- 24 Ni 1 -6.098919501839100e-01 -6.098919503548724e-01 1.70962e-10 5.87718e-10 2 9.537192037715307e-01 9.537192037588347e-01 1.26961e-11 2.70783e-10 3 -8.024843386659994e-01 -8.024843386739439e-01 7.94442e-12 1.99042e-10 ----------------------------------------------------------------------------------------------------- 25 Ni 1 -3.627087292171955e-01 -3.627087292368040e-01 1.96085e-11 1.69037e-10 2 -1.362245902184256e+00 -1.362245902169372e+00 1.48836e-11 1.98732e-09 * 3 3.902702788812192e-02 3.902702789062548e-02 2.50357e-12 5.97120e-11 ----------------------------------------------------------------------------------------------------- 26 Ni 1 -1.332009422395397e+00 -1.332009422389913e+00 5.48406e-12 1.23257e-08 * 2 9.934825220298096e-01 9.934825220376188e-01 7.80920e-12 1.00825e-10 3 -1.238105205862843e+00 -1.238105205854949e+00 7.89391e-12 1.37504e-09 * ----------------------------------------------------------------------------------------------------- 27 Ni 1 1.964564312231307e+00 1.964564312201256e+00 3.00504e-11 1.71706e-10 2 -4.706389970696477e+00 -4.706389970754214e+00 5.77369e-11 4.67767e-10 3 2.542328336926563e-01 2.542328337056567e-01 1.30004e-11 3.00741e-09 * ----------------------------------------------------------------------------------------------------- 28 Ni 1 -2.563228342546155e+00 -2.563228342521160e+00 2.49947e-11 1.77792e-10 2 2.603979029255498e+00 2.603979029244374e+00 1.11240e-11 4.31446e-11 3 -2.020190023021454e-01 -2.020190023260629e-01 2.39175e-11 1.21889e-10 ----------------------------------------------------------------------------------------------------- 29 Ni 1 -1.217893677299298e+00 -1.217893677288639e+00 1.06595e-11 8.54548e-10 2 -1.392987439996168e+00 -1.392987440079058e+00 8.28897e-11 1.29329e-08 * 3 1.460885371969691e+00 1.460885371997260e+00 2.75688e-11 1.10965e-10 ----------------------------------------------------------------------------------------------------- 30 Ni 1 5.621043352085575e-02 5.621043355867916e-02 3.78234e-11 3.04050e-10 2 1.082967059668339e+00 1.082967059682036e+00 1.36979e-11 1.88696e-10 3 9.294662072764065e-01 9.294662072629556e-01 1.34509e-11 1.80355e-10 ----------------------------------------------------------------------------------------------------- 31 Ni 1 1.124391364806108e+00 1.124391364804249e+00 1.85985e-12 2.79953e-10 2 -1.277258000784337e+00 -1.277258000784309e+00 2.81997e-14 2.97231e-10 3 5.596758415133651e-01 5.596758415182835e-01 4.91840e-12 3.28243e-10 ----------------------------------------------------------------------------------------------------- 32 Ni 1 1.273387919770291e+00 1.273387919774086e+00 3.79519e-12 1.27803e-10 2 1.174307000764893e+00 1.174307000758087e+00 6.80589e-12 2.80307e-09 * 3 5.067418220761699e-01 5.067418220968688e-01 2.06989e-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 6.609951180762934e-01 4.30778e-12 8.34307e-11 2 5.322517264735388e-01 5.322517264672533e-01 6.28553e-12 1.78361e-11 3 9.079650880001708e-01 9.079650880039144e-01 3.74356e-12 5.28149e-11 ----------------------------------------------------------------------------------------------------- 2 Ti 1 -1.054188795030433e+00 -1.054188795024610e+00 5.82334e-12 1.39711e-10 2 9.183280249974737e-01 9.183280249821973e-01 1.52763e-11 1.32862e-10 3 -1.073809860318412e+00 -1.073809860313726e+00 4.68625e-12 2.96669e-11 ----------------------------------------------------------------------------------------------------- 3 Ti 1 -1.440352340953070e+00 -1.440352340966543e+00 1.34730e-11 3.23237e-10 2 -9.842952138024768e-01 -9.842952137923542e-01 1.01226e-11 6.62332e-11 3 -5.855334671167900e-01 -5.855334671281510e-01 1.13610e-11 6.73058e-11 ----------------------------------------------------------------------------------------------------- 4 Ti 1 7.243352712369510e-01 7.243352712409407e-01 3.98970e-12 6.61493e-11 2 2.803625707895108e-01 2.803625708011341e-01 1.16233e-11 1.48140e-10 3 6.673816500384258e-01 6.673816500233326e-01 1.50931e-11 1.44310e-10 ----------------------------------------------------------------------------------------------------- 5 Ti 1 -2.419706202954396e-01 -2.419706203052417e-01 9.80202e-12 1.79775e-10 2 -5.108774825333964e-02 -5.108774823354539e-02 1.97942e-11 1.02094e-09 3 1.243111334704295e-01 1.243111334656199e-01 4.80960e-12 2.89419e-09 * ----------------------------------------------------------------------------------------------------- 6 Ti 1 1.465546956837913e-01 1.465546956794457e-01 4.34552e-12 1.39709e-11 2 -1.663321183751554e-01 -1.663321183513991e-01 2.37562e-11 8.92303e-11 3 9.823467695631849e-02 9.823467696870816e-02 1.23897e-11 2.02566e-10 ----------------------------------------------------------------------------------------------------- 7 Ti 1 -6.752819600344269e-01 -6.752819599951465e-01 3.92804e-11 1.98897e-10 2 -1.642860738285104e-02 -1.642860737841114e-02 4.43990e-12 1.26569e-10 3 1.826236228152541e-01 1.826236228051020e-01 1.01521e-11 3.76860e-10 ----------------------------------------------------------------------------------------------------- 8 Ti 1 1.692656588870760e+00 1.692656588880599e+00 9.83880e-12 1.25674e-10 2 2.137078558274299e+00 2.137078558222241e+00 5.20575e-11 2.00519e-10 3 1.237802424415408e+00 1.237802424429568e+00 1.41607e-11 3.57093e-10 ----------------------------------------------------------------------------------------------------- 9 Ti 1 -3.361416353494318e-01 -3.361416353503912e-01 9.59455e-13 5.52060e-11 2 -7.734689984058797e-01 -7.734689984077291e-01 1.84941e-12 3.56308e-11 3 -1.391023872445451e+00 -1.391023872433660e+00 1.17908e-11 1.29087e-10 ----------------------------------------------------------------------------------------------------- 10 Ti 1 -4.334541254984454e-01 -4.334541255054036e-01 6.95827e-12 6.08590e-10 2 1.917138790026021e+00 1.917138790018669e+00 7.35190e-12 4.44582e-11 3 -8.107674087363996e-01 -8.107674087537344e-01 1.73348e-11 1.51597e-10 ----------------------------------------------------------------------------------------------------- 11 Ti 1 1.872160660794091e+00 1.872160660817747e+00 2.36562e-11 6.90736e-12 2 -2.564797910581675e+00 -2.564797910655850e+00 7.41744e-11 2.75445e-10 3 2.172632698236789e+00 2.172632698243054e+00 6.26521e-12 5.62301e-11 ----------------------------------------------------------------------------------------------------- 12 Ti 1 -7.947570835549543e-01 -7.947570835379986e-01 1.69558e-11 1.63196e-09 2 1.146906679649930e+00 1.146906679647107e+00 2.82330e-12 9.68130e-10 3 1.328042548527027e+00 1.328042548526308e+00 7.19647e-13 1.37440e-10 ----------------------------------------------------------------------------------------------------- 13 Ti 1 1.066364259051039e+00 1.066364259071002e+00 1.99627e-11 1.31443e-10 2 -6.543023551065520e-01 -6.543023551358413e-01 2.92893e-11 9.01491e-10 3 1.434405991060535e-02 1.434405990828078e-02 2.32457e-12 1.21430e-10 ----------------------------------------------------------------------------------------------------- 14 Ti 1 -6.369188758316342e-01 -6.369188758184420e-01 1.31922e-11 6.49202e-11 2 -6.870687112914747e-01 -6.870687112796791e-01 1.17957e-11 8.91991e-11 3 2.213893719407330e-01 2.213893719299956e-01 1.07374e-11 1.71286e-09 ----------------------------------------------------------------------------------------------------- 15 Ti 1 2.967577642627320e-01 2.967577642635924e-01 8.60367e-13 3.45382e-07 * 2 -1.527804819573340e+00 -1.527804819522170e+00 5.11695e-11 2.17891e-10 3 4.812517547991456e-01 4.812517547551945e-01 4.39511e-11 7.59406e-10 ----------------------------------------------------------------------------------------------------- 16 Ti 1 -1.719015100691666e+00 -1.719015100710861e+00 1.91953e-11 4.47030e-10 2 5.795352666469569e-01 5.795352666579964e-01 1.10395e-11 8.86601e-10 3 -3.177405897694646e-01 -3.177405896859479e-01 8.35167e-11 9.35821e-11 ----------------------------------------------------------------------------------------------------- 17 Ti 1 -8.949290838076152e-02 -8.949290841193090e-02 3.11694e-11 5.39705e-11 2 -6.691504993188631e-01 -6.691504993288477e-01 9.98468e-12 2.70633e-10 3 6.507324510988802e-02 6.507324509329035e-02 1.65977e-11 6.64892e-11 ----------------------------------------------------------------------------------------------------- 18 Ti 1 7.786915375323221e-01 7.786915375007659e-01 3.15562e-11 1.36693e-09 2 7.948381640149914e-01 7.948381639924075e-01 2.25839e-11 6.33607e-11 3 -1.137221609323436e+00 -1.137221609366051e+00 4.26155e-11 1.29893e-10 ----------------------------------------------------------------------------------------------------- 19 Ti 1 -9.528200458795684e-01 -9.528200458877641e-01 8.19578e-12 7.92338e-11 2 3.695519224927615e-01 3.695519224937419e-01 9.80382e-13 6.37405e-11 3 1.023921250411325e+00 1.023921250411000e+00 3.25073e-13 2.62987e-10 ----------------------------------------------------------------------------------------------------- 20 Ti 1 -8.655750830349019e-01 -8.655750830341686e-01 7.33302e-13 2.11543e-09 * 2 -7.171769881944012e-01 -7.171769881946328e-01 2.31593e-13 5.84366e-10 3 4.161540636308677e-01 4.161540636397045e-01 8.83682e-12 7.61099e-10 ----------------------------------------------------------------------------------------------------- 21 Ti 1 9.489945488025592e-01 9.489945488334038e-01 3.08447e-11 2.81504e-10 2 -9.973296460125831e-01 -9.973296460122749e-01 3.08198e-13 8.27139e-10 3 5.229867946820246e-02 5.229867943849691e-02 2.97056e-11 7.95196e-10 ----------------------------------------------------------------------------------------------------- 22 Ti 1 1.181430568258568e+00 1.181430568303262e+00 4.46949e-11 2.19317e-09 * 2 1.966630728798052e+00 1.966630728800389e+00 2.33746e-12 1.65706e-10 3 4.870702160239756e-01 4.870702160227558e-01 1.21980e-12 3.15134e-10 ----------------------------------------------------------------------------------------------------- 23 Ti 1 -9.525982730624971e-01 -9.525982730850391e-01 2.25420e-11 4.64682e-10 2 8.583615436775737e-01 8.583615436465498e-01 3.10239e-11 1.12617e-09 3 -9.162132551427838e-01 -9.162132551605229e-01 1.77390e-11 2.65227e-10 ----------------------------------------------------------------------------------------------------- 24 Ti 1 -1.146702301575263e+00 -1.146702301550394e+00 2.48697e-11 1.57342e-10 2 -1.432530812091932e+00 -1.432530812095579e+00 3.64686e-12 2.20246e-10 3 -6.461208395343833e-01 -6.461208395254598e-01 8.92342e-12 1.78291e-10 ----------------------------------------------------------------------------------------------------- 25 Ti 1 -1.127470744200892e+00 -1.127470744215005e+00 1.41129e-11 3.74852e-09 * 2 -2.081506284343728e+00 -2.081506284316881e+00 2.68470e-11 9.46732e-11 3 -3.168347908691825e+00 -3.168347908701254e+00 9.42890e-12 1.86445e-09 ----------------------------------------------------------------------------------------------------- 26 Ti 1 2.621653520272723e+00 2.621653520258895e+00 1.38276e-11 4.73051e-10 2 1.556180400945928e-01 1.556180402025108e-01 1.07918e-10 1.55033e-10 3 -1.266017510389141e+00 -1.266017510314611e+00 7.45302e-11 6.99756e-09 * ----------------------------------------------------------------------------------------------------- 27 Ti 1 3.576481242692118e+00 3.576481242645642e+00 4.64762e-11 4.59415e-10 2 2.113018431411651e-02 2.113018431428489e-02 1.68383e-13 5.94735e-10 3 2.074080105199251e-01 2.074080105086457e-01 1.12794e-11 9.99975e-11 ----------------------------------------------------------------------------------------------------- 28 Ti 1 -1.758661638874706e+00 -1.758661638982328e+00 1.07622e-10 2.15433e-10 2 2.025507022660859e+00 2.025507022745600e+00 8.47415e-11 8.74023e-10 3 2.017927732994599e+00 2.017927732985759e+00 8.84004e-12 1.82131e-10 ----------------------------------------------------------------------------------------------------- 29 Ti 1 -1.041827171498267e+00 -1.041827171508574e+00 1.03071e-11 1.68430e-09 2 7.444821930403304e-01 7.444821929851811e-01 5.51492e-11 1.69013e-10 3 9.696186013931267e-01 9.696186014008283e-01 7.70162e-12 2.85463e-09 * ----------------------------------------------------------------------------------------------------- 30 Ti 1 4.150580388733511e-01 4.150580388937228e-01 2.03717e-11 2.14881e-10 2 4.886737253291984e-01 4.886737253224025e-01 6.79590e-12 8.49395e-11 3 -1.123870217234946e+00 -1.123870217297475e+00 6.25289e-11 2.00273e-10 ----------------------------------------------------------------------------------------------------- 31 Ti 1 5.672632116561380e-01 5.672632116553213e-01 8.16680e-13 1.26743e-10 2 -6.768553314390214e-01 -6.768553314229673e-01 1.60542e-11 1.57014e-10 3 9.606847413272510e-02 9.606847413549759e-02 2.77249e-12 1.65234e-10 ----------------------------------------------------------------------------------------------------- 32 Ti 1 -1.282168322312772e+00 -1.282168322332705e+00 1.99332e-11 5.34801e-09 * 2 -9.362590971069340e-01 -9.362590971413834e-01 3.44494e-11 6.77738e-11 3 -3.348527640919087e-01 -3.348527641079183e-01 1.60095e-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 = ----------------------- = 6.93480e-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 6.436752947661577e-01 1.03485e-11 1.49471e-09 2 5.958345186517418e-01 5.958345186952514e-01 4.35096e-11 1.51257e-10 3 3.826341038774572e-01 3.826341038823096e-01 4.85245e-12 1.07700e-10 ----------------------------------------------------------------------------------------------------- 2 Ni 1 -9.493715132937183e-01 -9.493715132991740e-01 5.45575e-12 2.11053e-09 2 2.624382926441520e-01 2.624382925881028e-01 5.60492e-11 2.05303e-10 3 -1.828756500156547e+00 -1.828756500143441e+00 1.31062e-11 1.21973e-10 ----------------------------------------------------------------------------------------------------- 3 Ni 1 -1.177531626229375e+00 -1.177531626205054e+00 2.43214e-11 2.58544e-10 2 -1.538268680803495e+00 -1.538268680784523e+00 1.89715e-11 4.43143e-10 3 9.971188577328678e-01 9.971188576685923e-01 6.42755e-11 4.72585e-10 ----------------------------------------------------------------------------------------------------- 4 Ni 1 -2.092793124958626e-02 -2.092793125547281e-02 5.88656e-12 2.63262e-10 2 4.101486844530978e-01 4.101486843952943e-01 5.78034e-11 4.83114e-10 3 -2.988430046309105e-01 -2.988430046941621e-01 6.32516e-11 4.04816e-10 ----------------------------------------------------------------------------------------------------- 5 Ti 1 -1.678055998908738e-01 -1.678055999020796e-01 1.12059e-11 2.20672e-09 2 -1.159772495488063e+00 -1.159772495487649e+00 4.13447e-13 6.89891e-10 3 -1.160909029602538e+00 -1.160909029597101e+00 5.43676e-12 2.43812e-11 ----------------------------------------------------------------------------------------------------- 6 Ni 1 -1.484272708086565e-01 -1.484272708140701e-01 5.41356e-12 3.23333e-10 2 3.511284314167453e-02 3.511284319326030e-02 5.15858e-11 1.31613e-10 3 -8.582802883183858e-01 -8.582802883296842e-01 1.12984e-11 2.78474e-10 ----------------------------------------------------------------------------------------------------- 7 Ni 1 -7.055603967406479e-01 -7.055603967556690e-01 1.50211e-11 1.20502e-10 2 2.348357002972788e-01 2.348357002983308e-01 1.05205e-12 3.04854e-10 3 7.053219662024897e-01 7.053219661875950e-01 1.48946e-11 1.53137e-10 ----------------------------------------------------------------------------------------------------- 8 Ti 1 2.582061504486206e+00 2.582061504485940e+00 2.65565e-13 5.95284e-11 2 -1.607378539648872e+00 -1.607378539641619e+00 7.25309e-12 2.83840e-09 * 3 1.497543541678192e+00 1.497543541679555e+00 1.36269e-12 1.61022e-10 ----------------------------------------------------------------------------------------------------- 9 Ti 1 -5.622599700346947e-01 -5.622599700119698e-01 2.27249e-11 1.32036e-10 2 -2.334187174949595e+00 -2.334187174920891e+00 2.87042e-11 5.85896e-11 3 -7.221494693202041e-01 -7.221494693104864e-01 9.71767e-12 1.05157e-10 ----------------------------------------------------------------------------------------------------- 10 Ni 1 9.682595519156072e-01 9.682595519191621e-01 3.55493e-12 2.77985e-10 2 -4.757697278190034e-02 -4.757697276297401e-02 1.89263e-11 4.93513e-09 * 3 8.225108671720751e-01 8.225108671457037e-01 2.63715e-11 1.69772e-09 ----------------------------------------------------------------------------------------------------- 11 Ni 1 -1.258962709411812e+00 -1.258962709443786e+00 3.19742e-11 1.35973e-10 2 2.141437496380900e+00 2.141437496255858e+00 1.25041e-10 1.30133e-10 3 1.281430511862311e+00 1.281430511870859e+00 8.54827e-12 2.85333e-10 ----------------------------------------------------------------------------------------------------- 12 Ni 1 1.505739816446260e-01 1.505739816405059e-01 4.12015e-12 2.63693e-09 * 2 8.181087213059143e-01 8.181087213045293e-01 1.38500e-12 7.37213e-10 3 7.334354709326699e-01 7.334354709401141e-01 7.44416e-12 1.13242e-09 ----------------------------------------------------------------------------------------------------- 13 Ni 1 -2.505643624419522e+00 -2.505643624392395e+00 2.71276e-11 2.32511e-10 2 5.583092400305693e-01 5.583092400779247e-01 4.73555e-11 4.11959e-10 3 -2.005217576044672e+00 -2.005217576043221e+00 1.45084e-12 3.17635e-11 ----------------------------------------------------------------------------------------------------- 14 Ti 1 2.683915791740853e-01 2.683915792077275e-01 3.36423e-11 2.72036e-10 2 1.496159832375425e-01 1.496159832070849e-01 3.04576e-11 1.23329e-10 3 -1.895569439782701e-01 -1.895569439776169e-01 6.53200e-13 2.45920e-09 ----------------------------------------------------------------------------------------------------- 15 Ni 1 1.854370507598553e+00 1.854370507605710e+00 7.15605e-12 3.76561e-11 2 1.144534135088059e+00 1.144534135082083e+00 5.97655e-12 1.19521e-10 3 3.104408048325977e+00 3.104408048343845e+00 1.78684e-11 7.41306e-10 ----------------------------------------------------------------------------------------------------- 16 Ni 1 -2.487963616387781e-01 -2.487963617104863e-01 7.17082e-11 7.22932e-11 2 -4.877093500008989e-01 -4.877093499636707e-01 3.72283e-11 2.34012e-10 3 8.427497870911652e-01 8.427497870842328e-01 6.93245e-12 7.22777e-12 ----------------------------------------------------------------------------------------------------- 17 Ni 1 3.912369066816147e-01 3.912369066859507e-01 4.33598e-12 1.07044e-09 2 5.385232161349267e-01 5.385232161376476e-01 2.72093e-12 1.92736e-10 3 -3.018169732328066e-01 -3.018169732322601e-01 5.46452e-13 9.45251e-11 ----------------------------------------------------------------------------------------------------- 18 Ti 1 4.998676539388389e-01 4.998676539190359e-01 1.98030e-11 9.86497e-10 2 1.688188705667766e+00 1.688188705634611e+00 3.31557e-11 1.75315e-10 3 -1.189275816097592e+00 -1.189275816003190e+00 9.44014e-11 2.50262e-10 ----------------------------------------------------------------------------------------------------- 19 Ti 1 -1.099310894993132e-01 -1.099310895216637e-01 2.23505e-11 7.27646e-11 2 -1.140094525197610e+00 -1.140094525203754e+00 6.14397e-12 3.27603e-10 3 1.544764138108742e+00 1.544764138145307e+00 3.65650e-11 3.78952e-10 ----------------------------------------------------------------------------------------------------- 20 Ti 1 -2.478355154730406e+00 -2.478355154721082e+00 9.32410e-12 3.84959e-10 2 -4.850491752096568e-01 -4.850491752380359e-01 2.83791e-11 2.62791e-10 3 3.826053036111253e-01 3.826053036094412e-01 1.68404e-12 1.17520e-09 ----------------------------------------------------------------------------------------------------- 21 Ni 1 1.036267869094522e+00 1.036267869171257e+00 7.67342e-11 3.12421e-10 2 8.314445051275525e-01 8.314445051185738e-01 8.97871e-12 3.11927e-10 3 -8.849107410442019e-01 -8.849107410206183e-01 2.35836e-11 3.77842e-10 ----------------------------------------------------------------------------------------------------- 22 Ti 1 7.320591942772950e-01 7.320591942679071e-01 9.38793e-12 6.55296e-10 2 -5.504646370872360e-01 -5.504646370907512e-01 3.51519e-12 1.21335e-09 3 -1.850566669339225e+00 -1.850566669315789e+00 2.34357e-11 2.38975e-10 ----------------------------------------------------------------------------------------------------- 23 Ni 1 -8.244998172993122e-01 -8.244998172891141e-01 1.01981e-11 2.11280e-09 2 -8.042615292744153e-01 -8.042615292606766e-01 1.37387e-11 5.68645e-10 3 4.035231098305684e-01 4.035231097276532e-01 1.02915e-10 3.15097e-10 ----------------------------------------------------------------------------------------------------- 24 Ni 1 6.569957663178301e-01 6.569957664662348e-01 1.48405e-10 4.35939e-10 2 7.497836281404964e-01 7.497836281147865e-01 2.57099e-11 2.72290e-10 3 -1.653042224270288e-01 -1.653042223552329e-01 7.17958e-11 1.34797e-10 ----------------------------------------------------------------------------------------------------- 25 Ni 1 1.667769703593731e-01 1.667769703524696e-01 6.90345e-12 2.59963e-09 * 2 -1.676808119344339e+00 -1.676808119324666e+00 1.96734e-11 1.36842e-10 3 -1.270868895973927e+00 -1.270868896002477e+00 2.85501e-11 6.37041e-09 * ----------------------------------------------------------------------------------------------------- 26 Ti 1 2.393317476017175e+00 2.393317475955879e+00 6.12959e-11 1.28442e-10 2 -2.306457395369310e-01 -2.306457394765508e-01 6.03801e-11 1.22221e-09 3 -1.692522157581586e+00 -1.692522157508424e+00 7.31621e-11 2.08491e-10 ----------------------------------------------------------------------------------------------------- 27 Ti 1 1.899486077971074e+00 1.899486077982370e+00 1.12952e-11 3.33499e-09 * 2 -4.273839560713222e-01 -4.273839559824113e-01 8.89109e-11 2.04150e-10 3 -1.649313321877594e-01 -1.649313321020995e-01 8.56600e-11 1.24988e-10 ----------------------------------------------------------------------------------------------------- 28 Ti 1 -6.072587886537330e-01 -6.072587889973508e-01 3.43618e-10 7.12888e-10 2 7.980484023915442e-02 7.980484026531111e-02 2.61567e-11 8.22545e-11 3 1.226776779550548e+00 1.226776779541405e+00 9.14291e-12 3.85849e-10 ----------------------------------------------------------------------------------------------------- 29 Ti 1 -2.289835694426861e+00 -2.289835694407472e+00 1.93898e-11 2.39262e-10 2 5.264523048455126e-01 5.264523049082735e-01 6.27609e-11 1.89027e-09 3 5.562934127704666e-01 5.562934127664090e-01 4.05764e-12 1.49073e-10 ----------------------------------------------------------------------------------------------------- 30 Ti 1 1.433218327172283e+00 1.433218327115945e+00 5.63383e-11 5.00570e-10 2 9.579068029117054e-01 9.579068029033884e-01 8.31701e-12 4.70888e-09 * 3 -2.770975924890522e+00 -2.770975924830177e+00 6.03455e-11 1.14729e-10 ----------------------------------------------------------------------------------------------------- 31 Ti 1 -4.559226769785342e-01 -4.559226769285930e-01 4.99412e-11 1.43880e-10 2 -6.391902764811409e-01 -6.391902764666242e-01 1.45167e-11 2.78646e-10 3 1.550361983512388e+00 1.550361983477057e+00 3.53304e-11 2.63346e-09 * ----------------------------------------------------------------------------------------------------- 32 Ti 1 -1.165468436119766e+00 -1.165468436105401e+00 1.43650e-11 2.52739e-10 2 1.406311553577431e+00 1.406311553589979e+00 1.25480e-11 2.16454e-11 3 1.323407662567134e+00 1.323407662571271e+00 4.13669e-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.