!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_002 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 1.86919e-11 1.57389e-10 2 1.319831845406630e+00 1.319831845371252e+00 3.53775e-11 2.86914e-10 3 1.328900843551863e+00 1.328900843553704e+00 1.84097e-12 4.16074e-11 ----------------------------------------------------------------------------------------------------- 2 C 1 1.492183003657831e-01 1.492183004268250e-01 6.10419e-11 3.04265e-10 2 1.026998871287893e-01 1.026998870957557e-01 3.30336e-11 1.63226e-10 3 -2.288644426060682e+00 -2.288644426029759e+00 3.09237e-11 4.48861e-10 ----------------------------------------------------------------------------------------------------- 3 C 1 -1.448196700771615e+00 -1.448196700755468e+00 1.61471e-11 4.80830e-10 2 -8.832314796931384e-01 -8.832314796440169e-01 4.91215e-11 1.29760e-10 3 1.658459070372974e-01 1.658459070335185e-01 3.77889e-12 6.75196e-09 * ----------------------------------------------------------------------------------------------------- 4 C 1 -3.628311895528528e+00 -3.628311895489188e+00 3.93396e-11 2.30563e-10 2 -4.591922040341706e-01 -4.591922039884686e-01 4.57021e-11 9.79615e-11 3 -1.207589794909647e+00 -1.207589794913512e+00 3.86513e-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 2.110833656347577e-01 1.04941e-11 1.08346e-10 2 -1.117054731537882e+00 -1.117054731562424e+00 2.45419e-11 2.14581e-10 3 -4.880986281790642e-01 -4.880986281824096e-01 3.34538e-12 2.66460e-10 ----------------------------------------------------------------------------------------------------- 7 C 1 3.431912044599729e-01 3.431912044416420e-01 1.83308e-11 2.27232e-10 2 -2.569399759681310e+00 -2.569399759820187e+00 1.38877e-10 4.56987e-10 3 -7.952247948112268e-01 -7.952247947267588e-01 8.44680e-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 -3.464296251812412e+00 1.70015e-11 1.64538e-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 -4.728738626816174e+00 6.74829e-11 4.05907e-10 ----------------------------------------------------------------------------------------------------- 11 C 1 -3.218321585503148e+00 -3.218321585512850e+00 9.70157e-12 4.28138e-10 2 -4.704251305214637e+00 -4.704251305202258e+00 1.23785e-11 1.47930e-09 3 -1.919712299717569e+00 -1.919712299647471e+00 7.00984e-11 4.96586e-10 ----------------------------------------------------------------------------------------------------- 12 C 1 -2.993055351985395e+00 -2.993055351978999e+00 6.39533e-12 6.82463e-11 2 1.325975386621440e+00 1.325975386641831e+00 2.03912e-11 5.36149e-11 3 9.093392470107302e-01 9.093392470067667e-01 3.96350e-12 1.17794e-10 ----------------------------------------------------------------------------------------------------- 13 C 1 4.590136052329797e+00 4.590136052379195e+00 4.93987e-11 9.23670e-11 2 -1.663281311194812e+00 -1.663281311198486e+00 3.67395e-12 6.12890e-09 * 3 -7.883992716583985e+00 -7.883992716638251e+00 5.42659e-11 2.81546e-10 ----------------------------------------------------------------------------------------------------- 14 C 1 1.546639137506575e+00 1.546639137487962e+00 1.86131e-11 3.90967e-11 2 1.382080087498057e-01 1.382080087545607e-01 4.75503e-12 5.50909e-11 3 -1.453227614319255e+00 -1.453227614355804e+00 3.65483e-11 1.69856e-09 ----------------------------------------------------------------------------------------------------- 15 C 1 8.683784956447388e+00 8.683784956459041e+00 1.16529e-11 1.96483e-11 2 -5.423129982879896e+00 -5.423129982923349e+00 4.34532e-11 1.58109e-10 3 -3.414020328086456e-01 -3.414020327749163e-01 3.37294e-11 2.01227e-11 ----------------------------------------------------------------------------------------------------- 16 C 1 -5.498095100814597e+00 -5.498095100716462e+00 9.81348e-11 1.64959e-10 2 1.051576875626454e+01 1.051576875639038e+01 1.25835e-10 5.36497e-10 3 6.363587109935056e+00 6.363587109936400e+00 1.34381e-12 2.83725e-09 * ----------------------------------------------------------------------------------------------------- 17 C 1 -2.888011769395275e+00 -2.888011769445523e+00 5.02478e-11 2.30434e-10 2 -3.584056127144209e+00 -3.584056127075599e+00 6.86100e-11 3.04113e-10 3 -1.094685429342641e+00 -1.094685429343691e+00 1.04938e-12 1.23886e-10 ----------------------------------------------------------------------------------------------------- 18 C 1 1.281709178602168e+00 1.281709178635525e+00 3.33569e-11 2.65090e-10 2 2.089589182527954e+00 2.089589182491761e+00 3.61937e-11 2.09119e-10 3 -1.760938938127330e+00 -1.760938938121224e+00 6.10623e-12 9.48792e-11 ----------------------------------------------------------------------------------------------------- 19 C 1 7.049561763120469e-01 7.049561764581479e-01 1.46101e-10 1.11532e-10 2 -2.849817383678894e+00 -2.849817383787307e+00 1.08413e-10 1.44813e-10 3 2.486429193571412e+00 2.486429193608130e+00 3.67173e-11 4.86548e-10 ----------------------------------------------------------------------------------------------------- 20 C 1 -2.087024528990674e+00 -2.087024529025630e+00 3.49556e-11 1.84663e-10 2 1.905507169858700e+00 1.905507169813224e+00 4.54763e-11 4.28747e-10 3 2.882481502802701e+00 2.882481502799062e+00 3.63931e-12 1.96582e-10 ----------------------------------------------------------------------------------------------------- 21 C 1 8.950418697317337e-01 8.950418696645549e-01 6.71788e-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 1.80707e-10 ----------------------------------------------------------------------------------------------------- 22 C 1 6.172679944024334e+00 6.172679944046712e+00 2.23785e-11 8.50164e-11 2 2.886466094621678e+00 2.886466094636861e+00 1.51825e-11 5.95104e-10 3 3.606962500981025e+00 3.606962501059746e+00 7.87206e-11 2.16217e-09 * ----------------------------------------------------------------------------------------------------- 23 C 1 -1.080359088745013e+00 -1.080359088734548e+00 1.04645e-11 5.54734e-10 2 4.007065666977156e-01 4.007065666945401e-01 3.17552e-12 1.97772e-10 3 -1.587128448527770e+00 -1.587128448498973e+00 2.87976e-11 1.38803e-10 ----------------------------------------------------------------------------------------------------- 24 C 1 2.741910355162985e-01 2.741910354649044e-01 5.13941e-11 1.01068e-10 2 5.072928420244481e-01 5.072928420899196e-01 6.54715e-11 4.23683e-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 6.45084e-12 5.89031e-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 -2.776032647228021e+00 1.12121e-10 7.41383e-10 ----------------------------------------------------------------------------------------------------- 27 C 1 -4.445179853430826e+00 -4.445179853442622e+00 1.17959e-11 9.11067e-11 2 7.159567039637784e-01 7.159567039950032e-01 3.12248e-11 4.72150e-10 3 2.367241153932202e+00 2.367241153888521e+00 4.36819e-11 2.56977e-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 4.099964378571372e+00 1.62004e-12 1.35532e-10 ----------------------------------------------------------------------------------------------------- 29 C 1 9.263001257645251e-02 9.263001274314102e-02 1.66689e-10 3.64943e-10 2 -3.175489405882153e+00 -3.175489405944137e+00 6.19838e-11 2.20970e-10 3 3.241923858147287e-01 3.241923858854179e-01 7.06892e-11 2.20635e-10 ----------------------------------------------------------------------------------------------------- 30 C 1 3.282266703548638e+00 3.282266703534938e+00 1.36997e-11 2.95060e-10 2 -5.810755411889370e-01 -5.810755412010684e-01 1.21314e-11 8.74052e-10 3 -2.973366291119746e-01 -2.973366290961016e-01 1.58729e-11 6.99269e-10 ----------------------------------------------------------------------------------------------------- 31 C 1 2.882509911870786e-01 2.882509911688598e-01 1.82188e-11 7.76337e-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 1.69647e-11 1.24024e-10 2 1.926003577245986e+00 1.926003577256952e+00 1.09668e-11 8.11158e-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 3.952916870664249e-01 3.44147e-12 2.62545e-10 2 5.851019501357041e-01 5.851019501394966e-01 3.79252e-12 4.74376e-10 3 5.343162802741456e-01 5.343162802794907e-01 5.34517e-12 1.75313e-10 ----------------------------------------------------------------------------------------------------- 2 Ti 1 -4.891589236656314e-01 -4.891589236727808e-01 7.14939e-12 6.57501e-11 2 4.891536633402360e-01 4.891536633367298e-01 3.50614e-12 7.99855e-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 9.05724e-11 2 6.150868889858914e-01 6.150868889942454e-01 8.35398e-12 6.46794e-11 3 1.601288597217320e-01 1.601288597407534e-01 1.90214e-11 1.14331e-10 ----------------------------------------------------------------------------------------------------- 4 Ti 1 8.119704517720784e-01 8.119704518091775e-01 3.70991e-11 1.11795e-10 2 5.096809948717682e-02 5.096809949747003e-02 1.02932e-11 6.40474e-12 3 -1.109214368864840e+00 -1.109214368862638e+00 2.20179e-12 7.63893e-11 ----------------------------------------------------------------------------------------------------- 5 Ti 1 -2.203519000006801e-01 -2.203519000000456e-01 6.34548e-13 1.78168e-10 2 4.965346983349432e-01 4.965346983341976e-01 7.45681e-13 1.38396e-10 3 2.557104627470483e-01 2.557104627501812e-01 3.13294e-12 8.19495e-11 ----------------------------------------------------------------------------------------------------- 6 Ti 1 1.418481322343794e-01 1.418481322591739e-01 2.47945e-11 7.02735e-10 2 1.401255227257719e-01 1.401255227054982e-01 2.02738e-11 1.01649e-10 3 3.661699228396878e-01 3.661699228030831e-01 3.66047e-11 2.83847e-11 ----------------------------------------------------------------------------------------------------- 7 Ti 1 -3.833435135309317e-01 -3.833435135360696e-01 5.13795e-12 3.16293e-10 2 5.212747754751468e-01 5.212747754565240e-01 1.86228e-11 4.37107e-11 3 3.549422676718712e-01 3.549422676436184e-01 2.82528e-11 1.21953e-10 ----------------------------------------------------------------------------------------------------- 8 Ti 1 1.770676743922203e+00 1.770676743908140e+00 1.40623e-11 1.83169e-10 2 -3.649178924161816e-01 -3.649178924203241e-01 4.14246e-12 6.41878e-10 3 -1.492208676581193e+00 -1.492208676561790e+00 1.94029e-11 6.92448e-11 ----------------------------------------------------------------------------------------------------- 9 Ti 1 6.133859691004522e-01 6.133859691058285e-01 5.37637e-12 1.43773e-10 2 -3.583353648032979e-01 -3.583353648070552e-01 3.75733e-12 1.39421e-09 * 3 5.392361646392592e-01 5.392361646389993e-01 2.59903e-13 7.47189e-11 ----------------------------------------------------------------------------------------------------- 10 Ti 1 5.031563954847819e-01 5.031563954891362e-01 4.35429e-12 4.95219e-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 -3.888643495229725e-01 6.83614e-12 8.47823e-11 2 2.767946703047873e-01 2.767946703255860e-01 2.07987e-11 6.86277e-11 3 -1.521333377834875e+00 -1.521333377845069e+00 1.01941e-11 7.37581e-11 ----------------------------------------------------------------------------------------------------- 12 Ti 1 -3.199008041567555e-01 -3.199008041726116e-01 1.58560e-11 9.58754e-11 2 -4.836772085424978e-01 -4.836772085469750e-01 4.47714e-12 7.11219e-11 3 6.920349185741597e-01 6.920349185831465e-01 8.98681e-12 1.86827e-10 ----------------------------------------------------------------------------------------------------- 13 Ti 1 -1.648439403536129e+00 -1.648439403496937e+00 3.91920e-11 1.78404e-10 2 -5.844906034667270e-01 -5.844906034368700e-01 2.98570e-11 1.83112e-10 3 -6.591238209342214e-01 -6.591238209058746e-01 2.83468e-11 1.13102e-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 -4.410753949725629e-01 1.21675e-12 1.67904e-10 ----------------------------------------------------------------------------------------------------- 15 Ti 1 -6.631961259331611e-01 -6.631961259248420e-01 8.31912e-12 1.18918e-10 2 -5.616377268094894e-01 -5.616377268049193e-01 4.57012e-12 1.36204e-10 3 6.637924392235028e-02 6.637924395894397e-02 3.65937e-11 6.68714e-11 ----------------------------------------------------------------------------------------------------- 16 Ti 1 1.919441224943313e-01 1.919441225008069e-01 6.47557e-12 1.88360e-10 2 -5.420468653300065e-01 -5.420468653296502e-01 3.56271e-13 3.37739e-10 3 4.087813375414480e-01 4.087813375569768e-01 1.55288e-11 1.08292e-10 ----------------------------------------------------------------------------------------------------- 17 Ti 1 4.289479554860634e-01 4.289479554866166e-01 5.53224e-13 8.62732e-11 2 1.149831175848520e-01 1.149831175707770e-01 1.40749e-11 2.00514e-10 3 3.636191844368318e-01 3.636191844642434e-01 2.74115e-11 8.41421e-10 ----------------------------------------------------------------------------------------------------- 18 Ti 1 -2.284451198170410e+00 -2.284451198142113e+00 2.82969e-11 6.37819e-11 2 5.241591223045498e-01 5.241591223504938e-01 4.59440e-11 1.69258e-10 3 -2.103890391925179e-01 -2.103890391966500e-01 4.13206e-12 3.47821e-10 ----------------------------------------------------------------------------------------------------- 19 Ti 1 -1.531788895917519e+00 -1.531788895872738e+00 4.47813e-11 3.29551e-10 2 -1.022850610004173e+00 -1.022850609988400e+00 1.57732e-11 3.43714e-10 3 5.883914186972824e-01 5.883914186914621e-01 5.82034e-12 3.12024e-11 ----------------------------------------------------------------------------------------------------- 20 Ti 1 3.844652108551566e-01 3.844652108578065e-01 2.64994e-12 4.45134e-11 2 -3.202584513521621e-01 -3.202584513504545e-01 1.70758e-12 6.85924e-11 3 -2.471398631628105e-01 -2.471398631827000e-01 1.98895e-11 1.37711e-10 ----------------------------------------------------------------------------------------------------- 21 Ti 1 8.067307658064178e-01 8.067307657921823e-01 1.42355e-11 4.50045e-10 2 -6.714990251907560e-01 -6.714990252081390e-01 1.73830e-11 8.27239e-11 3 -7.389323775835758e-01 -7.389323775079317e-01 7.56440e-11 1.23026e-10 ----------------------------------------------------------------------------------------------------- 22 Ti 1 8.475081597611401e-01 8.475081597478515e-01 1.32886e-11 3.10834e-10 2 -1.861328015554936e-01 -1.861328015692516e-01 1.37580e-11 1.04053e-10 3 -1.427235237377535e+00 -1.427235237405186e+00 2.76508e-11 1.81049e-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 -2.833694334106535e-01 2.08664e-11 1.21446e-10 ----------------------------------------------------------------------------------------------------- 24 Ti 1 8.378780069448993e-01 8.378780069850608e-01 4.01614e-11 3.10145e-10 2 1.435621467467715e+00 1.435621467453248e+00 1.44673e-11 3.41382e-10 3 1.698633775996759e+00 1.698633776038416e+00 4.16569e-11 5.34679e-11 ----------------------------------------------------------------------------------------------------- 25 Ti 1 8.474987429008505e-01 8.474987429303562e-01 2.95057e-11 2.96899e-10 2 2.288004413729644e-01 2.288004413723148e-01 6.49647e-13 5.87930e-12 3 -3.770115575338218e-01 -3.770115575315434e-01 2.27840e-12 7.64687e-11 ----------------------------------------------------------------------------------------------------- 26 Ti 1 2.248820880256197e-02 2.248820883099935e-02 2.84374e-11 1.35269e-10 2 -6.884517453915586e-01 -6.884517453416351e-01 4.99235e-11 4.70379e-11 3 -5.710376670129693e-01 -5.710376670263149e-01 1.33455e-11 2.64981e-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 9.48355e-11 3 -6.523198494271477e-01 -6.523198494199967e-01 7.15106e-12 3.10684e-10 ----------------------------------------------------------------------------------------------------- 28 Ti 1 -6.659018210701433e-01 -6.659018210557971e-01 1.43462e-11 1.15454e-10 2 5.004181134677945e-01 5.004181134702037e-01 2.40918e-12 2.21500e-10 3 3.259156556666380e-01 3.259156556566445e-01 9.99351e-12 1.73327e-10 ----------------------------------------------------------------------------------------------------- 29 Ti 1 2.576440683632146e-01 2.576440683035217e-01 5.96929e-11 5.36754e-10 2 7.031211085899548e-01 7.031211086613309e-01 7.13761e-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 1.14966e-10 2 3.893613113743571e-02 3.893613113633355e-02 1.10216e-12 1.26010e-10 3 6.322950868103044e-01 6.322950867653742e-01 4.49303e-11 1.72402e-09 * ----------------------------------------------------------------------------------------------------- 31 Ti 1 -4.401937767906539e-01 -4.401937767902013e-01 4.52582e-13 1.56735e-10 2 5.529935081278111e-01 5.529935080722939e-01 5.55173e-11 2.97777e-10 3 -3.529681815571294e-01 -3.529681815002475e-01 5.68819e-11 2.92568e-10 ----------------------------------------------------------------------------------------------------- 32 Ti 1 9.544012504708306e-01 9.544012504187178e-01 5.21128e-11 1.21402e-10 2 1.705275475220464e-02 1.705275469968305e-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 3.714976300741569e-02 1.11096e-11 4.51199e-11 2 1.293161933434922e+00 1.293161933392103e+00 4.28200e-11 2.32407e-10 3 1.351054996424043e+00 1.351054996407729e+00 1.63138e-11 4.56635e-11 ----------------------------------------------------------------------------------------------------- 2 C 1 -1.949195189949227e+00 -1.949195189950425e+00 1.19793e-12 4.99789e-11 2 -8.192998737988594e-01 -8.192998738539250e-01 5.50656e-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 5.01210e-11 3 1.001526389893898e+00 1.001526389843283e+00 5.06153e-11 5.75048e-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 3.02347e-11 1.94867e-10 2 7.947778537010828e-01 7.947778537401284e-01 3.90457e-11 2.98909e-10 3 -4.207317592759348e-02 -4.207317593840686e-02 1.08134e-11 2.87656e-10 ----------------------------------------------------------------------------------------------------- 6 Ti 1 -2.035241985692072e+00 -2.035241985673496e+00 1.85758e-11 2.72395e-10 2 -8.018767337861832e-01 -8.018767337873239e-01 1.14075e-12 4.35027e-10 3 3.440799037402443e+00 3.440799037384663e+00 1.77800e-11 6.70650e-11 ----------------------------------------------------------------------------------------------------- 7 C 1 -1.472053416483687e+00 -1.472053416488512e+00 4.82525e-12 1.46195e-10 2 3.371074287043817e-01 3.371074287063319e-01 1.95016e-12 1.32408e-10 3 -3.394506257661207e-01 -3.394506257460057e-01 2.01150e-11 8.13329e-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 3.27789e-10 3 -1.046549661282565e+00 -1.046549661300209e+00 1.76443e-11 2.86011e-10 ----------------------------------------------------------------------------------------------------- 9 Ti 1 7.161846326664533e-01 7.161846326486919e-01 1.77613e-11 2.96813e-11 2 1.466377273270252e+00 1.466377273261498e+00 8.75389e-12 1.40016e-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 3.127547568790477e-01 1.54555e-11 1.51407e-10 3 1.293795923597951e+00 1.293795923605763e+00 7.81131e-12 1.04904e-10 ----------------------------------------------------------------------------------------------------- 11 C 1 -3.006065520973873e+00 -3.006065520982541e+00 8.66729e-12 4.71612e-10 2 -1.009814688484811e+00 -1.009814688449465e+00 3.53468e-11 7.15729e-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 6.75349e-11 2 1.871791531041562e+00 1.871791531144501e+00 1.02938e-10 9.04425e-10 3 -2.544357021464263e+00 -2.544357021479405e+00 1.51417e-11 6.68094e-10 ----------------------------------------------------------------------------------------------------- 13 C 1 1.280045746931096e+00 1.280045746903677e+00 2.74192e-11 1.87158e-10 2 1.876129897269811e+00 1.876129897279192e+00 9.38138e-12 3.20721e-10 3 -1.574132057556737e+00 -1.574132057564842e+00 8.10507e-12 1.53715e-10 ----------------------------------------------------------------------------------------------------- 14 C 1 -1.537250584357119e+00 -1.537250584342442e+00 1.46767e-11 1.41137e-10 2 -4.478013570898425e-02 -4.478013571107942e-02 2.09518e-12 2.64260e-11 3 1.550325236855490e+00 1.550325236875300e+00 1.98106e-11 6.91309e-11 ----------------------------------------------------------------------------------------------------- 15 C 1 8.632875765593434e-01 8.632875765422847e-01 1.70587e-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 4.78924e-11 9.02562e-11 2 -1.902376991593863e+00 -1.902376991574300e+00 1.95628e-11 1.42969e-09 3 -6.144152301589526e+00 -6.144152301559292e+00 3.02336e-11 2.00609e-10 ----------------------------------------------------------------------------------------------------- 17 C 1 -1.363001197805364e+00 -1.363001197768652e+00 3.67117e-11 8.39164e-11 2 -1.906010847222082e-01 -1.906010847205120e-01 1.69617e-12 2.66308e-10 3 7.188007778063639e-01 7.188007777965872e-01 9.77662e-12 1.80871e-10 ----------------------------------------------------------------------------------------------------- 18 C 1 -2.646284592008805e+00 -2.646284591937182e+00 7.16223e-11 5.20138e-10 2 2.685102575037404e+00 2.685102575097799e+00 6.03948e-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 1.81549e-10 2.59728e-10 2 -1.448021959425811e+00 -1.448021959419835e+00 5.97589e-12 2.26168e-10 3 8.128933618180200e-01 8.128933618175136e-01 5.06373e-13 6.49277e-10 ----------------------------------------------------------------------------------------------------- 20 Ti 1 -1.017932110072423e+00 -1.017932110109312e+00 3.68896e-11 2.20069e-10 2 -7.568354080494527e-02 -7.568354083307820e-02 2.81329e-11 2.73073e-10 3 -1.039522998094151e+00 -1.039522998094832e+00 6.80345e-13 4.61287e-10 ----------------------------------------------------------------------------------------------------- 21 Ti 1 3.455801171478837e+00 3.455801171587898e+00 1.09061e-10 1.10018e-09 2 -2.538378544646601e+00 -2.538378544585299e+00 6.13025e-11 6.00281e-10 3 -7.024938281730606e+00 -7.024938281738497e+00 7.89147e-12 2.35279e-10 ----------------------------------------------------------------------------------------------------- 22 C 1 2.164865266892888e+00 2.164865266890906e+00 1.98197e-12 2.03178e-10 2 -4.871258924203944e-01 -4.871258923799849e-01 4.04096e-11 4.57870e-10 3 2.398342005798526e+00 2.398342005820531e+00 2.20055e-11 4.17785e-10 ----------------------------------------------------------------------------------------------------- 23 Ti 1 2.250190951291373e+00 2.250190951293376e+00 2.00329e-12 3.35864e-09 * 2 -9.869477246526398e-01 -9.869477246435673e-01 9.07252e-12 9.15142e-11 3 6.699141080915207e-01 6.699141080702699e-01 2.12509e-11 3.85779e-11 ----------------------------------------------------------------------------------------------------- 24 Ti 1 -1.846299600931542e+00 -1.846299601009193e+00 7.76508e-11 1.70181e-10 2 1.939141238216102e+00 1.939141238186807e+00 2.92950e-11 4.77849e-11 3 1.346723922182833e+00 1.346723922167945e+00 1.48874e-11 5.98614e-11 ----------------------------------------------------------------------------------------------------- 25 Ti 1 -2.061596908827949e+00 -2.061596908829475e+00 1.52589e-12 1.36844e-09 2 1.424513718413426e+00 1.424513718372668e+00 4.07578e-11 1.03884e-10 3 2.439626075874929e+00 2.439626075824441e+00 5.04881e-11 1.26066e-10 ----------------------------------------------------------------------------------------------------- 26 Ti 1 -3.390997684849125e+00 -3.390997684849728e+00 6.02185e-13 5.47689e-09 * 2 2.479829959137950e+00 2.479829959091723e+00 4.62266e-11 3.76980e-10 3 3.848353933749325e+00 3.848353933631703e+00 1.17622e-10 6.73882e-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 6.51434e-12 3.27601e-10 ----------------------------------------------------------------------------------------------------- 28 C 1 1.276705062656976e+00 1.276705062660008e+00 3.03224e-12 1.71745e-10 2 -1.392247747858364e+00 -1.392247747839086e+00 1.92779e-11 1.53611e-10 3 -1.654925241046236e+00 -1.654925241030447e+00 1.57889e-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 8.942289629828556e-01 3.63815e-11 1.64543e-10 ----------------------------------------------------------------------------------------------------- 30 Ti 1 -5.017836002586991e-01 -5.017836003306172e-01 7.19181e-11 1.01367e-09 2 -1.228461629286462e+00 -1.228461629139676e+00 1.46785e-10 1.69916e-10 3 -2.319468303893850e-01 -2.319468303862502e-01 3.13477e-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 -9.666654275658840e-01 2.59437e-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 1.830589933261118e+00 5.04947e-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.