!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_KimLee_2008_TiC__MO_134206624109_001 Supported species : C 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 = C | a0 = 3.379122734069824 | (Configuration in file "config-C.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 C 1 1.092309802980869e+00 1.092309802999561e+00 1.86917e-11 1.57389e-10 2 1.319831845406630e+00 1.319831845371252e+00 3.53775e-11 2.86914e-10 3 1.328900843551863e+00 1.328900843553704e+00 1.84119e-12 4.16085e-11 ----------------------------------------------------------------------------------------------------- 2 C 1 1.492183003657831e-01 1.492183004268248e-01 6.10418e-11 3.04265e-10 2 1.026998871287893e-01 1.026998870957557e-01 3.30336e-11 1.63226e-10 3 -2.288644426060682e+00 -2.288644426029758e+00 3.09242e-11 4.48864e-10 ----------------------------------------------------------------------------------------------------- 3 C 1 -1.448196700771615e+00 -1.448196700755468e+00 1.61471e-11 4.80830e-10 2 -8.832314796931384e-01 -8.832314796440167e-01 4.91217e-11 1.29760e-10 3 1.658459070372974e-01 1.658459070335185e-01 3.77889e-12 6.75196e-09 * ----------------------------------------------------------------------------------------------------- 4 C 1 -3.628311895528528e+00 -3.628311895489187e+00 3.93410e-11 2.30563e-10 2 -4.591922040341706e-01 -4.591922039884685e-01 4.57021e-11 9.79613e-11 3 -1.207589794909647e+00 -1.207589794913511e+00 3.86469e-12 1.68193e-09 ----------------------------------------------------------------------------------------------------- 5 C 1 6.858701814828647e-01 6.858701814655958e-01 1.72690e-11 5.21551e-09 * 2 -5.153107337757361e-01 -5.153107337906407e-01 1.49046e-11 2.98697e-09 * 3 -2.258894181617966e+00 -2.258894181603336e+00 1.46305e-11 1.34193e-10 ----------------------------------------------------------------------------------------------------- 6 C 1 2.110833656452518e-01 2.110833656347576e-01 1.04942e-11 1.08346e-10 2 -1.117054731537882e+00 -1.117054731562424e+00 2.45419e-11 2.14580e-10 3 -4.880986281790642e-01 -4.880986281824098e-01 3.34560e-12 2.66460e-10 ----------------------------------------------------------------------------------------------------- 7 C 1 3.431912044599729e-01 3.431912044416420e-01 1.83309e-11 2.27233e-10 2 -2.569399759681310e+00 -2.569399759820186e+00 1.38876e-10 4.56987e-10 3 -7.952247948112268e-01 -7.952247947267586e-01 8.44682e-11 2.95032e-10 ----------------------------------------------------------------------------------------------------- 8 C 1 5.473821328082631e-02 5.473821327984941e-02 9.76906e-13 4.11137e-10 2 1.563464168237531e+00 1.563464168207171e+00 3.03602e-11 6.58409e-09 * 3 7.934801717528019e-01 7.934801717844646e-01 3.16627e-11 3.58603e-09 * ----------------------------------------------------------------------------------------------------- 9 C 1 -3.464296251829413e+00 -3.464296251812411e+00 1.70020e-11 1.64539e-10 2 -3.424179774438360e+00 -3.424179774506297e+00 6.79372e-11 4.08634e-09 * 3 5.112566877315827e-02 5.112566879851265e-02 2.53544e-11 1.12633e-09 ----------------------------------------------------------------------------------------------------- 10 C 1 -1.408664807263553e+00 -1.408664807241615e+00 2.19380e-11 6.03242e-09 * 2 7.681547641080305e+00 7.681547641087697e+00 7.39142e-12 3.10129e-10 3 -4.728738626883657e+00 -4.728738626816172e+00 6.74847e-11 4.05907e-10 ----------------------------------------------------------------------------------------------------- 11 C 1 -3.218321585503148e+00 -3.218321585512849e+00 9.70068e-12 4.28138e-10 2 -4.704251305214637e+00 -4.704251305202257e+00 1.23794e-11 1.47929e-09 3 -1.919712299717569e+00 -1.919712299647470e+00 7.00986e-11 4.96585e-10 ----------------------------------------------------------------------------------------------------- 12 C 1 -2.993055351985395e+00 -2.993055351978998e+00 6.39622e-12 6.82472e-11 2 1.325975386621440e+00 1.325975386641830e+00 2.03908e-11 5.36144e-11 3 9.093392470107302e-01 9.093392470067667e-01 3.96350e-12 1.17794e-10 ----------------------------------------------------------------------------------------------------- 13 C 1 4.590136052329797e+00 4.590136052379194e+00 4.93969e-11 9.23670e-11 2 -1.663281311194812e+00 -1.663281311198486e+00 3.67395e-12 6.12890e-09 * 3 -7.883992716583985e+00 -7.883992716638248e+00 5.42633e-11 2.81540e-10 ----------------------------------------------------------------------------------------------------- 14 C 1 1.546639137506575e+00 1.546639137487962e+00 1.86129e-11 3.90956e-11 2 1.382080087498057e-01 1.382080087545607e-01 4.75497e-12 5.50909e-11 3 -1.453227614319255e+00 -1.453227614355804e+00 3.65483e-11 1.69856e-09 ----------------------------------------------------------------------------------------------------- 15 C 1 8.683784956447388e+00 8.683784956459037e+00 1.16493e-11 1.96483e-11 2 -5.423129982879896e+00 -5.423129982923348e+00 4.34524e-11 1.58106e-10 3 -3.414020328086456e-01 -3.414020327749163e-01 3.37294e-11 2.01226e-11 ----------------------------------------------------------------------------------------------------- 16 C 1 -5.498095100814597e+00 -5.498095100716463e+00 9.81339e-11 1.64956e-10 2 1.051576875626454e+01 1.051576875639038e+01 1.25834e-10 5.36502e-10 3 6.363587109935056e+00 6.363587109936399e+00 1.34204e-12 2.83725e-09 * ----------------------------------------------------------------------------------------------------- 17 C 1 -2.888011769395275e+00 -2.888011769445523e+00 5.02478e-11 2.30435e-10 2 -3.584056127144209e+00 -3.584056127075598e+00 6.86109e-11 3.04113e-10 3 -1.094685429342641e+00 -1.094685429343691e+00 1.04938e-12 1.23887e-10 ----------------------------------------------------------------------------------------------------- 18 C 1 1.281709178602168e+00 1.281709178635525e+00 3.33564e-11 2.65091e-10 2 2.089589182527954e+00 2.089589182491761e+00 3.61937e-11 2.09119e-10 3 -1.760938938127330e+00 -1.760938938121223e+00 6.10667e-12 9.48792e-11 ----------------------------------------------------------------------------------------------------- 19 C 1 7.049561763120469e-01 7.049561764581477e-01 1.46101e-10 1.11532e-10 2 -2.849817383678894e+00 -2.849817383787309e+00 1.08415e-10 1.44817e-10 3 2.486429193571412e+00 2.486429193608129e+00 3.67169e-11 4.86549e-10 ----------------------------------------------------------------------------------------------------- 20 C 1 -2.087024528990674e+00 -2.087024529025630e+00 3.49556e-11 1.84663e-10 2 1.905507169858700e+00 1.905507169813223e+00 4.54767e-11 4.28747e-10 3 2.882481502802701e+00 2.882481502799061e+00 3.64020e-12 1.96582e-10 ----------------------------------------------------------------------------------------------------- 21 C 1 8.950418697317337e-01 8.950418696645547e-01 6.71790e-11 7.36200e-10 2 -4.380691667954360e+00 -4.380691668003978e+00 4.96181e-11 1.03545e-09 3 2.298247760613393e+00 2.298247760539094e+00 7.42988e-11 1.80706e-10 ----------------------------------------------------------------------------------------------------- 22 C 1 6.172679944024334e+00 6.172679944046711e+00 2.23768e-11 8.50164e-11 2 2.886466094621678e+00 2.886466094636861e+00 1.51821e-11 5.95103e-10 3 3.606962500981025e+00 3.606962501059745e+00 7.87197e-11 2.16217e-09 * ----------------------------------------------------------------------------------------------------- 23 C 1 -1.080359088745013e+00 -1.080359088734548e+00 1.04647e-11 5.54735e-10 2 4.007065666977156e-01 4.007065666945401e-01 3.17552e-12 1.97772e-10 3 -1.587128448527770e+00 -1.587128448498972e+00 2.87981e-11 1.38803e-10 ----------------------------------------------------------------------------------------------------- 24 C 1 2.741910355162985e-01 2.741910354649044e-01 5.13941e-11 1.01068e-10 2 5.072928420244481e-01 5.072928420899194e-01 6.54713e-11 4.23682e-10 3 6.379951497778881e-01 6.379951497652097e-01 1.26784e-11 3.18643e-10 ----------------------------------------------------------------------------------------------------- 25 C 1 1.450093812178269e-01 1.450093812140767e-01 3.75011e-12 4.76543e-10 2 -1.320626169395917e+00 -1.320626169425118e+00 2.92009e-11 6.04163e-09 * 3 -1.732980136309610e+00 -1.732980136316061e+00 6.45106e-12 5.89038e-11 ----------------------------------------------------------------------------------------------------- 26 C 1 1.970944259947623e+00 1.970944259924138e+00 2.34845e-11 9.53340e-11 2 2.387488445374495e+00 2.387488445373963e+00 5.32019e-13 1.19137e-10 3 -2.776032647115899e+00 -2.776032647228020e+00 1.12121e-10 7.41385e-10 ----------------------------------------------------------------------------------------------------- 27 C 1 -4.445179853430826e+00 -4.445179853442618e+00 1.17923e-11 9.11085e-11 2 7.159567039637784e-01 7.159567039950032e-01 3.12248e-11 4.72149e-10 3 2.367241153932202e+00 2.367241153888520e+00 4.36824e-11 2.56974e-10 ----------------------------------------------------------------------------------------------------- 28 C 1 -2.436705479245375e+00 -2.436705479196949e+00 4.84262e-11 3.03188e-10 2 2.496987873121324e-01 2.496987872825826e-01 2.95498e-11 1.00147e-08 * 3 4.099964378569751e+00 4.099964378571370e+00 1.61826e-12 1.35532e-10 ----------------------------------------------------------------------------------------------------- 29 C 1 9.263001257645251e-02 9.263001274314099e-02 1.66688e-10 3.64943e-10 2 -3.175489405882153e+00 -3.175489405944136e+00 6.19829e-11 2.20970e-10 3 3.241923858147287e-01 3.241923858854178e-01 7.06891e-11 2.20635e-10 ----------------------------------------------------------------------------------------------------- 30 C 1 3.282266703548638e+00 3.282266703534938e+00 1.37002e-11 2.95064e-10 2 -5.810755411889370e-01 -5.810755412010684e-01 1.21314e-11 8.74052e-10 3 -2.973366291119746e-01 -2.973366290961016e-01 1.58730e-11 6.99270e-10 ----------------------------------------------------------------------------------------------------- 31 C 1 2.882509911870786e-01 2.882509911688595e-01 1.82191e-11 7.76339e-11 2 9.345825145784814e-01 9.345825145222350e-01 5.62465e-11 1.50357e-10 3 -5.600674484472226e-01 -5.600674484617199e-01 1.44973e-11 2.32865e-09 * ----------------------------------------------------------------------------------------------------- 32 C 1 2.131571646339881e+00 2.131571646356845e+00 1.69642e-11 1.24025e-10 2 1.926003577245986e+00 1.926003577256952e+00 1.09663e-11 8.11162e-11 3 4.858901818750139e+00 4.858901818868161e+00 1.18022e-10 6.51680e-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 = 29, direction = 1: |F_model - F_numer| error = ----------------------- = 1.79951e-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 = 4.133002281188965 | (Configuration in file "config-Ti.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ti 1 3.952916870629835e-01 3.952916870664248e-01 3.44136e-12 2.62545e-10 2 5.851019501357041e-01 5.851019501394966e-01 3.79252e-12 4.74376e-10 3 5.343162802741456e-01 5.343162802794906e-01 5.34506e-12 1.75313e-10 ----------------------------------------------------------------------------------------------------- 2 Ti 1 -4.891589236656314e-01 -4.891589236727807e-01 7.14928e-12 6.57502e-11 2 4.891536633402360e-01 4.891536633367294e-01 3.50658e-12 7.99861e-11 3 7.619056338086078e-01 7.619056338069947e-01 1.61304e-12 2.72724e-10 ----------------------------------------------------------------------------------------------------- 3 Ti 1 -6.432324493611740e-01 -6.432324493744010e-01 1.32271e-11 9.05722e-11 2 6.150868889858914e-01 6.150868889942459e-01 8.35454e-12 6.46802e-11 3 1.601288597217320e-01 1.601288597407533e-01 1.90213e-11 1.14331e-10 ----------------------------------------------------------------------------------------------------- 4 Ti 1 8.119704517720784e-01 8.119704518091774e-01 3.70990e-11 1.11795e-10 2 5.096809948717682e-02 5.096809949747000e-02 1.02932e-11 6.40476e-12 3 -1.109214368864840e+00 -1.109214368862638e+00 2.20224e-12 7.63893e-11 ----------------------------------------------------------------------------------------------------- 5 Ti 1 -2.203519000006801e-01 -2.203519000000455e-01 6.34576e-13 1.78168e-10 2 4.965346983349432e-01 4.965346983341976e-01 7.45681e-13 1.38396e-10 3 2.557104627470483e-01 2.557104627501812e-01 3.13288e-12 8.19496e-11 ----------------------------------------------------------------------------------------------------- 6 Ti 1 1.418481322343794e-01 1.418481322591739e-01 2.47945e-11 7.02735e-10 2 1.401255227257719e-01 1.401255227054981e-01 2.02738e-11 1.01649e-10 3 3.661699228396878e-01 3.661699228030830e-01 3.66048e-11 2.83847e-11 ----------------------------------------------------------------------------------------------------- 7 Ti 1 -3.833435135309317e-01 -3.833435135360695e-01 5.13783e-12 3.16293e-10 2 5.212747754751468e-01 5.212747754565242e-01 1.86225e-11 4.37105e-11 3 3.549422676718712e-01 3.549422676436184e-01 2.82528e-11 1.21952e-10 ----------------------------------------------------------------------------------------------------- 8 Ti 1 1.770676743922203e+00 1.770676743908140e+00 1.40625e-11 1.83170e-10 2 -3.649178924161816e-01 -3.649178924203241e-01 4.14246e-12 6.41878e-10 3 -1.492208676581193e+00 -1.492208676561790e+00 1.94034e-11 6.92444e-11 ----------------------------------------------------------------------------------------------------- 9 Ti 1 6.133859691004522e-01 6.133859691058284e-01 5.37625e-12 1.43772e-10 2 -3.583353648032979e-01 -3.583353648070552e-01 3.75733e-12 1.39421e-09 * 3 5.392361646392592e-01 5.392361646389990e-01 2.60125e-13 7.47189e-11 ----------------------------------------------------------------------------------------------------- 10 Ti 1 5.031563954847819e-01 5.031563954891362e-01 4.35429e-12 4.95222e-11 2 -5.903740440398023e-01 -5.903740440321589e-01 7.64344e-12 1.62613e-09 * 3 1.160577768481769e-02 1.160577770617005e-02 2.13524e-11 3.10845e-09 * ----------------------------------------------------------------------------------------------------- 11 Ti 1 -3.888643495161364e-01 -3.888643495229724e-01 6.83603e-12 8.47825e-11 2 2.767946703047873e-01 2.767946703255860e-01 2.07987e-11 6.86275e-11 3 -1.521333377834875e+00 -1.521333377845069e+00 1.01938e-11 7.37588e-11 ----------------------------------------------------------------------------------------------------- 12 Ti 1 -3.199008041567555e-01 -3.199008041726115e-01 1.58559e-11 9.58750e-11 2 -4.836772085424978e-01 -4.836772085469749e-01 4.47703e-12 7.11219e-11 3 6.920349185741597e-01 6.920349185831464e-01 8.98670e-12 1.86828e-10 ----------------------------------------------------------------------------------------------------- 13 Ti 1 -1.648439403536129e+00 -1.648439403496937e+00 3.91922e-11 1.78402e-10 2 -5.844906034667270e-01 -5.844906034368698e-01 2.98572e-11 1.83112e-10 3 -6.591238209342214e-01 -6.591238209058745e-01 2.83469e-11 1.13103e-10 ----------------------------------------------------------------------------------------------------- 14 Ti 1 4.794432126556214e-01 4.794432126585789e-01 2.95747e-12 2.95770e-09 * 2 -2.163830269158781e-02 -2.163830269315295e-02 1.56514e-12 3.58146e-11 3 -4.410753949713462e-01 -4.410753949725628e-01 1.21664e-12 1.67904e-10 ----------------------------------------------------------------------------------------------------- 15 Ti 1 -6.631961259331611e-01 -6.631961259248418e-01 8.31935e-12 1.18918e-10 2 -5.616377268094894e-01 -5.616377268049193e-01 4.57012e-12 1.36204e-10 3 6.637924392235028e-02 6.637924395894396e-02 3.65937e-11 6.68714e-11 ----------------------------------------------------------------------------------------------------- 16 Ti 1 1.919441224943313e-01 1.919441225008068e-01 6.47549e-12 1.88361e-10 2 -5.420468653300065e-01 -5.420468653296502e-01 3.56271e-13 3.37739e-10 3 4.087813375414480e-01 4.087813375569767e-01 1.55287e-11 1.08292e-10 ----------------------------------------------------------------------------------------------------- 17 Ti 1 4.289479554860634e-01 4.289479554866166e-01 5.53169e-13 8.62733e-11 2 1.149831175848520e-01 1.149831175707770e-01 1.40750e-11 2.00514e-10 3 3.636191844368318e-01 3.636191844642434e-01 2.74115e-11 8.41421e-10 ----------------------------------------------------------------------------------------------------- 18 Ti 1 -2.284451198170410e+00 -2.284451198142112e+00 2.82978e-11 6.37819e-11 2 5.241591223045498e-01 5.241591223504936e-01 4.59438e-11 1.69258e-10 3 -2.103890391925179e-01 -2.103890391966500e-01 4.13208e-12 3.47821e-10 ----------------------------------------------------------------------------------------------------- 19 Ti 1 -1.531788895917519e+00 -1.531788895872738e+00 4.47817e-11 3.29551e-10 2 -1.022850610004173e+00 -1.022850609988399e+00 1.57736e-11 3.43715e-10 3 5.883914186972824e-01 5.883914186914618e-01 5.82057e-12 3.12024e-11 ----------------------------------------------------------------------------------------------------- 20 Ti 1 3.844652108551566e-01 3.844652108578064e-01 2.64982e-12 4.45134e-11 2 -3.202584513521621e-01 -3.202584513504544e-01 1.70763e-12 6.85921e-11 3 -2.471398631628105e-01 -2.471398631826999e-01 1.98894e-11 1.37710e-10 ----------------------------------------------------------------------------------------------------- 21 Ti 1 8.067307658064178e-01 8.067307657921821e-01 1.42357e-11 4.50044e-10 2 -6.714990251907560e-01 -6.714990252081391e-01 1.73831e-11 8.27229e-11 3 -7.389323775835758e-01 -7.389323775079316e-01 7.56442e-11 1.23027e-10 ----------------------------------------------------------------------------------------------------- 22 Ti 1 8.475081597611401e-01 8.475081597478514e-01 1.32887e-11 3.10834e-10 2 -1.861328015554936e-01 -1.861328015692516e-01 1.37580e-11 1.04053e-10 3 -1.427235237377535e+00 -1.427235237405186e+00 2.76503e-11 1.81048e-10 ----------------------------------------------------------------------------------------------------- 23 Ti 1 -3.304915503651321e-01 -3.304915503620626e-01 3.06954e-12 2.52359e-10 2 1.600197202293362e-01 1.600197202211621e-01 8.17407e-12 5.90072e-10 3 -2.833694333897871e-01 -2.833694334106534e-01 2.08663e-11 1.21446e-10 ----------------------------------------------------------------------------------------------------- 24 Ti 1 8.378780069448993e-01 8.378780069850607e-01 4.01613e-11 3.10144e-10 2 1.435621467467715e+00 1.435621467453247e+00 1.44678e-11 3.41382e-10 3 1.698633775996759e+00 1.698633776038415e+00 4.16565e-11 5.34679e-11 ----------------------------------------------------------------------------------------------------- 25 Ti 1 8.474987429008505e-01 8.474987429303563e-01 2.95058e-11 2.96900e-10 2 2.288004413729644e-01 2.288004413723147e-01 6.49703e-13 5.87930e-12 3 -3.770115575338218e-01 -3.770115575315434e-01 2.27840e-12 7.64688e-11 ----------------------------------------------------------------------------------------------------- 26 Ti 1 2.248820880256197e-02 2.248820883099934e-02 2.84374e-11 1.35269e-10 2 -6.884517453915586e-01 -6.884517453416350e-01 4.99236e-11 4.70376e-11 3 -5.710376670129693e-01 -5.710376670263148e-01 1.33454e-11 2.64980e-10 ----------------------------------------------------------------------------------------------------- 27 Ti 1 -6.597124380276992e-02 -6.597124382311211e-02 2.03422e-11 1.96223e-10 2 -1.054835112230541e+00 -1.054835112153055e+00 7.74858e-11 9.48372e-11 3 -6.523198494271477e-01 -6.523198494199967e-01 7.15106e-12 3.10686e-10 ----------------------------------------------------------------------------------------------------- 28 Ti 1 -6.659018210701433e-01 -6.659018210557965e-01 1.43467e-11 1.15454e-10 2 5.004181134677945e-01 5.004181134702037e-01 2.40918e-12 2.21500e-10 3 3.259156556666380e-01 3.259156556566442e-01 9.99378e-12 1.73327e-10 ----------------------------------------------------------------------------------------------------- 29 Ti 1 2.576440683632146e-01 2.576440683035217e-01 5.96929e-11 5.36754e-10 2 7.031211085899548e-01 7.031211086613307e-01 7.13759e-11 5.49935e-10 3 2.675697482365387e+00 2.675697482327779e+00 3.76086e-11 4.11170e-10 ----------------------------------------------------------------------------------------------------- 30 Ti 1 -2.199931283007387e-01 -2.199931283802418e-01 7.95031e-11 1.14967e-10 2 3.893613113743571e-02 3.893613113633355e-02 1.10217e-12 1.26010e-10 3 6.322950868103044e-01 6.322950867653742e-01 4.49303e-11 1.72402e-09 * ----------------------------------------------------------------------------------------------------- 31 Ti 1 -4.401937767906539e-01 -4.401937767902012e-01 4.52693e-13 1.56734e-10 2 5.529935081278111e-01 5.529935080722937e-01 5.55174e-11 2.97776e-10 3 -3.529681815571294e-01 -3.529681815002474e-01 5.68821e-11 2.92568e-10 ----------------------------------------------------------------------------------------------------- 32 Ti 1 9.544012504708306e-01 9.544012504187176e-01 5.21130e-11 1.21402e-10 2 1.705275475220464e-02 1.705275469968304e-02 5.25216e-11 3.19163e-10 3 -3.524046279745598e-01 -3.524046279616865e-01 1.28733e-11 2.11403e-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 = 32, direction = 2: |F_model - F_numer| error = ----------------------- = 3.07995e-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 = C Ti | a0 = 3.603304827832835 | (Configuration in file "config-CTi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 C 1 3.714976299630614e-02 3.714976300741570e-02 1.11096e-11 4.51199e-11 2 1.293161933434922e+00 1.293161933392109e+00 4.28131e-11 2.32400e-10 3 1.351054996424043e+00 1.351054996407729e+00 1.63143e-11 4.56635e-11 ----------------------------------------------------------------------------------------------------- 2 C 1 -1.949195189949227e+00 -1.949195189950424e+00 1.19771e-12 4.99796e-11 2 -8.192998737988594e-01 -8.192998738539248e-01 5.50654e-11 1.07695e-10 3 -4.240311780197151e-01 -4.240311779975698e-01 2.21453e-11 8.58956e-10 ----------------------------------------------------------------------------------------------------- 3 C 1 1.494455894388820e-01 1.494455894131367e-01 2.57452e-11 3.77783e-10 2 -8.343105088400338e-01 -8.343105088448884e-01 4.85467e-12 5.01212e-11 3 1.001526389893898e+00 1.001526389843283e+00 5.06155e-11 5.75049e-10 ----------------------------------------------------------------------------------------------------- 4 Ti 1 2.403250577316265e+00 2.403250577332310e+00 1.60454e-11 2.15961e-09 2 -3.110338341621519e+00 -3.110338341656953e+00 3.54343e-11 4.23716e-09 * 3 -1.297525584716195e+00 -1.297525584734944e+00 1.87492e-11 2.38765e-11 ----------------------------------------------------------------------------------------------------- 5 C 1 1.393266663875420e+00 1.393266663905654e+00 3.02345e-11 1.94867e-10 2 7.947778537010828e-01 7.947778537401283e-01 3.90455e-11 2.98908e-10 3 -4.207317592759348e-02 -4.207317593840686e-02 1.08134e-11 2.87656e-10 ----------------------------------------------------------------------------------------------------- 6 Ti 1 -2.035241985692072e+00 -2.035241985673495e+00 1.85763e-11 2.72396e-10 2 -8.018767337861832e-01 -8.018767337873238e-01 1.14064e-12 4.35027e-10 3 3.440799037402443e+00 3.440799037384663e+00 1.77804e-11 6.70637e-11 ----------------------------------------------------------------------------------------------------- 7 C 1 -1.472053416483687e+00 -1.472053416488512e+00 4.82481e-12 1.46194e-10 2 3.371074287043817e-01 3.371074287063318e-01 1.95005e-12 1.32407e-10 3 -3.394506257661207e-01 -3.394506257460056e-01 2.01151e-11 8.13331e-11 ----------------------------------------------------------------------------------------------------- 8 C 1 7.165850390325826e-01 7.165850390245219e-01 8.06077e-12 4.72882e-09 * 2 -2.084655106173106e+00 -2.084655106160251e+00 1.28551e-11 3.27791e-10 3 -1.046549661282565e+00 -1.046549661300209e+00 1.76443e-11 2.86011e-10 ----------------------------------------------------------------------------------------------------- 9 Ti 1 7.161846326664533e-01 7.161846326486917e-01 1.77616e-11 2.96813e-11 2 1.466377273270252e+00 1.466377273261497e+00 8.75433e-12 1.40017e-10 3 -5.107428325963168e-01 -5.107428325915658e-01 4.75098e-12 8.27690e-10 ----------------------------------------------------------------------------------------------------- 10 C 1 -1.067653500845338e+00 -1.067653500841740e+00 3.59734e-12 2.45441e-09 * 2 3.127547568945032e-01 3.127547568790476e-01 1.54556e-11 1.51407e-10 3 1.293795923597951e+00 1.293795923605762e+00 7.81086e-12 1.04903e-10 ----------------------------------------------------------------------------------------------------- 11 C 1 -3.006065520973873e+00 -3.006065520982540e+00 8.66685e-12 4.71611e-10 2 -1.009814688484811e+00 -1.009814688449464e+00 3.53475e-11 7.15730e-10 3 -1.930015002535442e+00 -1.930015002552298e+00 1.68565e-11 2.62833e-10 ----------------------------------------------------------------------------------------------------- 12 Ti 1 7.121310198544127e-01 7.121310198019948e-01 5.24180e-11 6.75351e-11 2 1.871791531041562e+00 1.871791531144500e+00 1.02938e-10 9.04424e-10 3 -2.544357021464263e+00 -2.544357021479405e+00 1.51417e-11 6.68094e-10 ----------------------------------------------------------------------------------------------------- 13 C 1 1.280045746931096e+00 1.280045746903676e+00 2.74203e-11 1.87158e-10 2 1.876129897269811e+00 1.876129897279192e+00 9.38116e-12 3.20721e-10 3 -1.574132057556737e+00 -1.574132057564841e+00 8.10485e-12 1.53716e-10 ----------------------------------------------------------------------------------------------------- 14 C 1 -1.537250584357119e+00 -1.537250584342442e+00 1.46769e-11 1.41139e-10 2 -4.478013570898425e-02 -4.478013571107941e-02 2.09516e-12 2.64260e-11 3 1.550325236855490e+00 1.550325236875300e+00 1.98099e-11 6.91307e-11 ----------------------------------------------------------------------------------------------------- 15 C 1 8.632875765593434e-01 8.632875765422845e-01 1.70589e-11 5.19771e-10 2 1.613243777213228e+00 1.613243777185577e+00 2.76512e-11 5.22533e-10 3 -6.156233141398632e-01 -6.156233141353199e-01 4.54325e-12 5.07646e-10 ----------------------------------------------------------------------------------------------------- 16 Ti 1 2.537592489986009e+00 2.537592489938116e+00 4.78928e-11 9.02585e-11 2 -1.902376991593863e+00 -1.902376991574300e+00 1.95630e-11 1.42969e-09 3 -6.144152301589526e+00 -6.144152301559291e+00 3.02345e-11 2.00605e-10 ----------------------------------------------------------------------------------------------------- 17 C 1 -1.363001197805364e+00 -1.363001197768652e+00 3.67117e-11 8.39155e-11 2 -1.906010847222082e-01 -1.906010847205119e-01 1.69623e-12 2.66308e-10 3 7.188007778063639e-01 7.188007777965871e-01 9.77673e-12 1.80870e-10 ----------------------------------------------------------------------------------------------------- 18 C 1 -2.646284592008805e+00 -2.646284591937182e+00 7.16232e-11 5.20138e-10 2 2.685102575037404e+00 2.685102575097798e+00 6.03939e-11 1.20307e-10 3 2.318346028834493e+00 2.318346028807944e+00 2.65481e-11 2.25593e-09 ----------------------------------------------------------------------------------------------------- 19 Ti 1 -1.573211713036229e+00 -1.573211713217777e+00 1.81548e-10 2.59727e-10 2 -1.448021959425811e+00 -1.448021959419835e+00 5.97589e-12 2.26167e-10 3 8.128933618180200e-01 8.128933618175134e-01 5.06595e-13 6.49277e-10 ----------------------------------------------------------------------------------------------------- 20 Ti 1 -1.017932110072423e+00 -1.017932110109312e+00 3.68896e-11 2.20069e-10 2 -7.568354080494527e-02 -7.568354083307818e-02 2.81329e-11 2.73073e-10 3 -1.039522998094151e+00 -1.039522998094832e+00 6.80123e-13 4.61287e-10 ----------------------------------------------------------------------------------------------------- 21 Ti 1 3.455801171478837e+00 3.455801171587898e+00 1.09060e-10 1.10019e-09 2 -2.538378544646601e+00 -2.538378544585298e+00 6.13034e-11 6.00281e-10 3 -7.024938281730606e+00 -7.024938281738495e+00 7.88969e-12 2.35279e-10 ----------------------------------------------------------------------------------------------------- 22 C 1 2.164865266892888e+00 2.164865266890905e+00 1.98286e-12 2.03178e-10 2 -4.871258924203944e-01 -4.871258923799848e-01 4.04096e-11 4.57870e-10 3 2.398342005798526e+00 2.398342005820531e+00 2.20055e-11 4.17782e-10 ----------------------------------------------------------------------------------------------------- 23 Ti 1 2.250190951291373e+00 2.250190951293376e+00 2.00329e-12 3.35864e-09 * 2 -9.869477246526398e-01 -9.869477246435668e-01 9.07296e-12 9.15142e-11 3 6.699141080915207e-01 6.699141080702695e-01 2.12512e-11 3.85778e-11 ----------------------------------------------------------------------------------------------------- 24 Ti 1 -1.846299600931542e+00 -1.846299601009192e+00 7.76497e-11 1.70180e-10 2 1.939141238216102e+00 1.939141238186808e+00 2.92943e-11 4.77864e-11 3 1.346723922182833e+00 1.346723922167945e+00 1.48874e-11 5.98606e-11 ----------------------------------------------------------------------------------------------------- 25 Ti 1 -2.061596908827949e+00 -2.061596908829475e+00 1.52589e-12 1.36844e-09 2 1.424513718413426e+00 1.424513718372668e+00 4.07581e-11 1.03885e-10 3 2.439626075874929e+00 2.439626075824441e+00 5.04876e-11 1.26064e-10 ----------------------------------------------------------------------------------------------------- 26 Ti 1 -3.390997684849125e+00 -3.390997684849728e+00 6.02185e-13 5.47689e-09 * 2 2.479829959137950e+00 2.479829959091723e+00 4.62270e-11 3.76980e-10 3 3.848353933749325e+00 3.848353933631704e+00 1.17621e-10 6.73884e-10 ----------------------------------------------------------------------------------------------------- 27 Ti 1 -1.177196896238194e+00 -1.177196896249413e+00 1.12197e-11 1.90767e-09 2 -1.855739649556756e+00 -1.855739649580525e+00 2.37685e-11 1.78813e-10 3 1.471330839835268e+00 1.471330839841782e+00 6.51368e-12 3.27601e-10 ----------------------------------------------------------------------------------------------------- 28 C 1 1.276705062656976e+00 1.276705062660008e+00 3.03202e-12 1.71746e-10 2 -1.392247747858364e+00 -1.392247747839086e+00 1.92784e-11 1.53611e-10 3 -1.654925241046236e+00 -1.654925241030447e+00 1.57894e-11 5.17566e-11 ----------------------------------------------------------------------------------------------------- 29 C 1 3.588488653026671e+00 3.588488653107815e+00 8.11440e-11 1.02286e-09 2 2.355546138891519e-01 2.355546139107376e-01 2.15857e-11 5.68159e-09 * 3 8.942289629464741e-01 8.942289629828555e-01 3.63813e-11 1.64543e-10 ----------------------------------------------------------------------------------------------------- 30 Ti 1 -5.017836002586991e-01 -5.017836003306171e-01 7.19180e-11 1.01367e-09 2 -1.228461629286462e+00 -1.228461629139676e+00 1.46785e-10 1.69916e-10 3 -2.319468303893850e-01 -2.319468303862502e-01 3.13480e-12 1.72010e-10 ----------------------------------------------------------------------------------------------------- 31 Ti 1 1.275397248444559e+00 1.275397248385645e+00 5.89149e-11 8.80254e-10 2 6.811091084237333e-01 6.811091084119810e-01 1.17523e-11 2.33868e-09 * 3 -9.666654275684784e-01 -9.666654275658838e-01 2.59459e-12 9.14237e-10 ----------------------------------------------------------------------------------------------------- 32 Ti 1 1.825377049881571e+00 1.825377050009645e+00 1.28074e-10 5.43477e-09 * 2 1.800064488734028e+00 1.800064488746017e+00 1.19884e-11 4.88749e-10 3 1.830589933311612e+00 1.830589933261117e+00 5.04952e-11 1.87927e-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 = 20, direction = 2: |F_model - F_numer| error = ----------------------- = 3.71718e-10 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 3.07995e-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 3.07995e-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.