!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_000 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 1.092309802999560e+00 1.86910e-11 1.57387e-10 2 1.319831845406630e+00 1.319831845371251e+00 3.53784e-11 2.86913e-10 3 1.328900843551863e+00 1.328900843553703e+00 1.84008e-12 4.16074e-11 ----------------------------------------------------------------------------------------------------- 2 C 1 1.492183003657831e-01 1.492183004268252e-01 6.10421e-11 3.04265e-10 2 1.026998871287893e-01 1.026998870957557e-01 3.30336e-11 1.63226e-10 3 -2.288644426060682e+00 -2.288644426029756e+00 3.09259e-11 4.48864e-10 ----------------------------------------------------------------------------------------------------- 3 C 1 -1.448196700771600e+00 -1.448196700755469e+00 1.61311e-11 4.80830e-10 2 -8.832314796931380e-01 -8.832314796440166e-01 4.91214e-11 1.29760e-10 3 1.658459070373087e-01 1.658459070335186e-01 3.79011e-12 6.75196e-09 * ----------------------------------------------------------------------------------------------------- 4 C 1 -3.628311895528528e+00 -3.628311895489185e+00 3.93432e-11 2.30564e-10 2 -4.591922040341706e-01 -4.591922039884682e-01 4.57024e-11 9.79615e-11 3 -1.207589794909647e+00 -1.207589794913511e+00 3.86424e-12 1.68193e-09 ----------------------------------------------------------------------------------------------------- 5 C 1 6.858701814828647e-01 6.858701814655963e-01 1.72684e-11 5.21551e-09 * 2 -5.153107337757361e-01 -5.153107337906410e-01 1.49049e-11 2.98697e-09 * 3 -2.258894181617966e+00 -2.258894181603334e+00 1.46323e-11 1.34192e-10 ----------------------------------------------------------------------------------------------------- 6 C 1 2.110833656452518e-01 2.110833656347575e-01 1.04943e-11 1.08346e-10 2 -1.117054731537882e+00 -1.117054731562423e+00 2.45413e-11 2.14581e-10 3 -4.880986281790642e-01 -4.880986281824094e-01 3.34516e-12 2.66460e-10 ----------------------------------------------------------------------------------------------------- 7 C 1 3.431912044599729e-01 3.431912044416418e-01 1.83311e-11 2.27232e-10 2 -2.569399759681310e+00 -2.569399759820184e+00 1.38874e-10 4.56987e-10 3 -7.952247948112268e-01 -7.952247947267580e-01 8.44688e-11 2.95031e-10 ----------------------------------------------------------------------------------------------------- 8 C 1 5.473821328082631e-02 5.473821327984944e-02 9.76878e-13 4.11137e-10 2 1.563464168237531e+00 1.563464168207171e+00 3.03593e-11 6.58409e-09 * 3 7.934801717528019e-01 7.934801717844651e-01 3.16631e-11 3.58603e-09 * ----------------------------------------------------------------------------------------------------- 9 C 1 -3.464296251829413e+00 -3.464296251812409e+00 1.70042e-11 1.64539e-10 2 -3.424179774438360e+00 -3.424179774506298e+00 6.79381e-11 4.08634e-09 * 3 5.112566877315827e-02 5.112566879851268e-02 2.53544e-11 1.12633e-09 ----------------------------------------------------------------------------------------------------- 10 C 1 -1.408664807263553e+00 -1.408664807241615e+00 2.19378e-11 6.03242e-09 * 2 7.681547641080305e+00 7.681547641087692e+00 7.38609e-12 3.10129e-10 3 -4.728738626883657e+00 -4.728738626816170e+00 6.74865e-11 4.05907e-10 ----------------------------------------------------------------------------------------------------- 11 C 1 -3.218321585503148e+00 -3.218321585512847e+00 9.69891e-12 4.28138e-10 2 -4.704251305214637e+00 -4.704251305202255e+00 1.23821e-11 1.47929e-09 3 -1.919712299717569e+00 -1.919712299647469e+00 7.00999e-11 4.96585e-10 ----------------------------------------------------------------------------------------------------- 12 C 1 -2.993055351985395e+00 -2.993055351978998e+00 6.39711e-12 6.82450e-11 2 1.325975386621440e+00 1.325975386641830e+00 2.03899e-11 5.36158e-11 3 9.093392470107302e-01 9.093392470067655e-01 3.96472e-12 1.17794e-10 ----------------------------------------------------------------------------------------------------- 13 C 1 4.590136052329797e+00 4.590136052379211e+00 4.94147e-11 9.23857e-11 2 -1.663281311194812e+00 -1.663281311198487e+00 3.67484e-12 6.12890e-09 * 3 -7.883992716583985e+00 -7.883992716638243e+00 5.42579e-11 2.81540e-10 ----------------------------------------------------------------------------------------------------- 14 C 1 1.546639137506575e+00 1.546639137487961e+00 1.86142e-11 3.90958e-11 2 1.382080087498057e-01 1.382080087545606e-01 4.75492e-12 5.50909e-11 3 -1.453227614319255e+00 -1.453227614355804e+00 3.65490e-11 1.69856e-09 ----------------------------------------------------------------------------------------------------- 15 C 1 8.683784956447388e+00 8.683784956459034e+00 1.16458e-11 1.96430e-11 2 -5.423129982879896e+00 -5.423129982923345e+00 4.34488e-11 1.58106e-10 3 -3.414020328086456e-01 -3.414020327749160e-01 3.37296e-11 2.01227e-11 ----------------------------------------------------------------------------------------------------- 16 C 1 -5.498095100814597e+00 -5.498095100716459e+00 9.81375e-11 1.64957e-10 2 1.051576875626454e+01 1.051576875639037e+01 1.25826e-10 5.36502e-10 3 6.363587109935056e+00 6.363587109936394e+00 1.33760e-12 2.83725e-09 * ----------------------------------------------------------------------------------------------------- 17 C 1 -2.888011769395275e+00 -2.888011769445520e+00 5.02456e-11 2.30433e-10 2 -3.584056127144209e+00 -3.584056127075596e+00 6.86136e-11 3.04114e-10 3 -1.094685429342641e+00 -1.094685429343689e+00 1.04827e-12 1.23886e-10 ----------------------------------------------------------------------------------------------------- 18 C 1 1.281709178602168e+00 1.281709178635524e+00 3.33553e-11 2.65091e-10 2 2.089589182527954e+00 2.089589182491759e+00 3.61946e-11 2.09119e-10 3 -1.760938938127330e+00 -1.760938938121222e+00 6.10800e-12 9.48794e-11 ----------------------------------------------------------------------------------------------------- 19 C 1 7.049561763120469e-01 7.049561764581472e-01 1.46100e-10 1.11533e-10 2 -2.849817383678894e+00 -2.849817383787306e+00 1.08412e-10 1.44814e-10 3 2.486429193571412e+00 2.486429193608128e+00 3.67160e-11 4.86549e-10 ----------------------------------------------------------------------------------------------------- 20 C 1 -2.087024528990674e+00 -2.087024529025628e+00 3.49543e-11 1.84662e-10 2 1.905507169858700e+00 1.905507169813222e+00 4.54781e-11 4.28747e-10 3 2.882481502802701e+00 2.882481502799059e+00 3.64198e-12 1.96583e-10 ----------------------------------------------------------------------------------------------------- 21 C 1 8.950418697317182e-01 8.950418696645540e-01 6.71642e-11 7.36200e-10 2 -4.380691667954360e+00 -4.380691668009225e+00 5.48654e-11 1.10028e-09 3 2.298247760613382e+00 2.298247760539093e+00 7.42886e-11 1.80707e-10 ----------------------------------------------------------------------------------------------------- 22 C 1 6.172679944024334e+00 6.172679944046707e+00 2.23732e-11 8.50138e-11 2 2.886466094621678e+00 2.886466094636857e+00 1.51781e-11 5.95101e-10 3 3.606962500981025e+00 3.606962501059743e+00 7.87175e-11 2.16217e-09 * ----------------------------------------------------------------------------------------------------- 23 C 1 -1.080359088745013e+00 -1.080359088734548e+00 1.04652e-11 5.54734e-10 2 4.007065666977156e-01 4.007065666945402e-01 3.17535e-12 1.97772e-10 3 -1.587128448527770e+00 -1.587128448498971e+00 2.87996e-11 1.38805e-10 ----------------------------------------------------------------------------------------------------- 24 C 1 2.741910355162985e-01 2.741910354649042e-01 5.13943e-11 1.01068e-10 2 5.072928420244481e-01 5.072928420899191e-01 6.54710e-11 4.23682e-10 3 6.379951497778881e-01 6.379951497652099e-01 1.26782e-11 3.18643e-10 ----------------------------------------------------------------------------------------------------- 25 C 1 1.450093812178269e-01 1.450093812140768e-01 3.75006e-12 4.76543e-10 2 -1.320626169395917e+00 -1.320626169425119e+00 2.92018e-11 6.04163e-09 * 3 -1.732980136309610e+00 -1.732980136316060e+00 6.44973e-12 5.89031e-11 ----------------------------------------------------------------------------------------------------- 26 C 1 1.970944259947623e+00 1.970944259924137e+00 2.34861e-11 9.53329e-11 2 2.387488445374495e+00 2.387488445373961e+00 5.33795e-13 1.19137e-10 3 -2.776032647115899e+00 -2.776032647228017e+00 1.12118e-10 7.41385e-10 ----------------------------------------------------------------------------------------------------- 27 C 1 -4.445179853430826e+00 -4.445179853442617e+00 1.17915e-11 9.11076e-11 2 7.159567039637784e-01 7.159567039950027e-01 3.12242e-11 4.72150e-10 3 2.367241153932202e+00 2.367241153888518e+00 4.36846e-11 2.56975e-10 ----------------------------------------------------------------------------------------------------- 28 C 1 -2.436705479245375e+00 -2.436705479196946e+00 4.84284e-11 3.03190e-10 2 2.496987873121324e-01 2.496987872825827e-01 2.95496e-11 1.00147e-08 * 3 4.099964378569751e+00 4.099964378571367e+00 1.61560e-12 1.35530e-10 ----------------------------------------------------------------------------------------------------- 29 C 1 9.263001257645251e-02 9.263001274314096e-02 1.66688e-10 3.64943e-10 2 -3.175489405882153e+00 -3.175489405944135e+00 6.19815e-11 2.20969e-10 3 3.241923858147287e-01 3.241923858854175e-01 7.06888e-11 2.20635e-10 ----------------------------------------------------------------------------------------------------- 30 C 1 3.282266703548638e+00 3.282266703534936e+00 1.37024e-11 2.95063e-10 2 -5.810755411889370e-01 -5.810755412010681e-01 1.21311e-11 8.74052e-10 3 -2.973366291119746e-01 -2.973366290961014e-01 1.58732e-11 6.99269e-10 ----------------------------------------------------------------------------------------------------- 31 C 1 2.882509911870786e-01 2.882509911688598e-01 1.82188e-11 7.76335e-11 2 9.345825145784814e-01 9.345825145222343e-01 5.62471e-11 1.50357e-10 3 -5.600674484472226e-01 -5.600674484617202e-01 1.44976e-11 2.32865e-09 * ----------------------------------------------------------------------------------------------------- 32 C 1 2.131571646339881e+00 2.131571646356843e+00 1.69620e-11 1.24025e-10 2 1.926003577245986e+00 1.926003577256951e+00 1.09650e-11 8.11158e-11 3 4.858901818750139e+00 4.858901818868162e+00 1.18023e-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 3.952916870664246e-01 3.44114e-12 2.62546e-10 2 5.851019501357041e-01 5.851019501394970e-01 3.79285e-12 4.74375e-10 3 5.343162802741456e-01 5.343162802794903e-01 5.34472e-12 1.75313e-10 ----------------------------------------------------------------------------------------------------- 2 Ti 1 -4.891589236656314e-01 -4.891589236727804e-01 7.14895e-12 6.57502e-11 2 4.891536633402360e-01 4.891536633367291e-01 3.50686e-12 7.99863e-11 3 7.619056338086078e-01 7.619056338069953e-01 1.61249e-12 2.72724e-10 ----------------------------------------------------------------------------------------------------- 3 Ti 1 -6.432324493611740e-01 -6.432324493744006e-01 1.32266e-11 9.05724e-11 2 6.150868889858914e-01 6.150868889942457e-01 8.35432e-12 6.46800e-11 3 1.601288597217320e-01 1.601288597407534e-01 1.90214e-11 1.14331e-10 ----------------------------------------------------------------------------------------------------- 4 Ti 1 8.119704517720784e-01 8.119704518091768e-01 3.70984e-11 1.11795e-10 2 5.096809948717682e-02 5.096809949746997e-02 1.02932e-11 6.40477e-12 3 -1.109214368864840e+00 -1.109214368862637e+00 2.20246e-12 7.63898e-11 ----------------------------------------------------------------------------------------------------- 5 Ti 1 -2.203519000006801e-01 -2.203519000000454e-01 6.34715e-13 1.78168e-10 2 4.965346983349432e-01 4.965346983341971e-01 7.46125e-13 1.38395e-10 3 2.557104627470483e-01 2.557104627501810e-01 3.13272e-12 8.19496e-11 ----------------------------------------------------------------------------------------------------- 6 Ti 1 1.418481322343794e-01 1.418481322591738e-01 2.47943e-11 7.02735e-10 2 1.401255227257719e-01 1.401255227054981e-01 2.02738e-11 1.01649e-10 3 3.661699228396878e-01 3.661699228030840e-01 3.66038e-11 2.83836e-11 ----------------------------------------------------------------------------------------------------- 7 Ti 1 -3.833435135309317e-01 -3.833435135360692e-01 5.13756e-12 3.16293e-10 2 5.212747754751468e-01 5.212747754565237e-01 1.86231e-11 4.37107e-11 3 3.549422676718712e-01 3.549422676436181e-01 2.82531e-11 1.21952e-10 ----------------------------------------------------------------------------------------------------- 8 Ti 1 1.770676743922203e+00 1.770676743908139e+00 1.40639e-11 1.83169e-10 2 -3.649178924161816e-01 -3.649178924203242e-01 4.14263e-12 6.41878e-10 3 -1.492208676581193e+00 -1.492208676561789e+00 1.94043e-11 6.92448e-11 ----------------------------------------------------------------------------------------------------- 9 Ti 1 6.133859691004522e-01 6.133859691058280e-01 5.37581e-12 1.43773e-10 2 -3.583353648032979e-01 -3.583353648070554e-01 3.75744e-12 1.39421e-09 * 3 5.392361646392592e-01 5.392361646389988e-01 2.60347e-13 7.47186e-11 ----------------------------------------------------------------------------------------------------- 10 Ti 1 5.031563954847819e-01 5.031563954891358e-01 4.35396e-12 4.95222e-11 2 -5.903740440398023e-01 -5.903740440321591e-01 7.64322e-12 1.62613e-09 * 3 1.160577768481769e-02 1.160577770617006e-02 2.13524e-11 3.10845e-09 * ----------------------------------------------------------------------------------------------------- 11 Ti 1 -3.888643495161364e-01 -3.888643495229721e-01 6.83575e-12 8.47826e-11 2 2.767946703047873e-01 2.767946703255858e-01 2.07985e-11 6.86277e-11 3 -1.521333377834875e+00 -1.521333377845067e+00 1.01923e-11 7.37597e-11 ----------------------------------------------------------------------------------------------------- 12 Ti 1 -3.199008041567555e-01 -3.199008041726114e-01 1.58558e-11 9.58752e-11 2 -4.836772085424978e-01 -4.836772085469745e-01 4.47670e-12 7.11219e-11 3 6.920349185741597e-01 6.920349185831458e-01 8.98615e-12 1.86828e-10 ----------------------------------------------------------------------------------------------------- 13 Ti 1 -1.648439403536129e+00 -1.648439403496935e+00 3.91935e-11 1.78403e-10 2 -5.844906034667270e-01 -5.844906034368696e-01 2.98573e-11 1.83112e-10 3 -6.591238209342214e-01 -6.591238209058741e-01 2.83473e-11 1.13103e-10 ----------------------------------------------------------------------------------------------------- 14 Ti 1 4.794432126556214e-01 4.794432126585791e-01 2.95769e-12 2.95770e-09 * 2 -2.163830269158781e-02 -2.163830269315294e-02 1.56512e-12 3.58146e-11 3 -4.410753949713462e-01 -4.410753949725625e-01 1.21630e-12 1.67904e-10 ----------------------------------------------------------------------------------------------------- 15 Ti 1 -6.631961259331611e-01 -6.631961259248415e-01 8.31968e-12 1.18918e-10 2 -5.616377268094894e-01 -5.616377268049189e-01 4.57057e-12 1.36203e-10 3 6.637924392235028e-02 6.637924395894390e-02 3.65936e-11 6.68713e-11 ----------------------------------------------------------------------------------------------------- 16 Ti 1 1.919441224943313e-01 1.919441225008068e-01 6.47543e-12 1.88360e-10 2 -5.420468653300065e-01 -5.420468653296497e-01 3.56715e-13 3.37738e-10 3 4.087813375414480e-01 4.087813375569764e-01 1.55284e-11 1.08292e-10 ----------------------------------------------------------------------------------------------------- 17 Ti 1 4.289479554860634e-01 4.289479554866163e-01 5.52891e-13 8.62734e-11 2 1.149831175848520e-01 1.149831175707769e-01 1.40750e-11 2.00514e-10 3 3.636191844368318e-01 3.636191844642435e-01 2.74116e-11 8.41421e-10 ----------------------------------------------------------------------------------------------------- 18 Ti 1 -2.284451198170410e+00 -2.284451198142112e+00 2.82978e-11 6.37805e-11 2 5.241591223045498e-01 5.241591223504932e-01 4.59435e-11 1.69258e-10 3 -2.103890391925179e-01 -2.103890391966498e-01 4.13189e-12 3.47821e-10 ----------------------------------------------------------------------------------------------------- 19 Ti 1 -1.531788895917519e+00 -1.531788895872737e+00 4.47824e-11 3.29551e-10 2 -1.022850610004173e+00 -1.022850609988399e+00 1.57743e-11 3.43715e-10 3 5.883914186972824e-01 5.883914186914614e-01 5.82101e-12 3.12024e-11 ----------------------------------------------------------------------------------------------------- 20 Ti 1 3.844652108551566e-01 3.844652108578061e-01 2.64955e-12 4.45135e-11 2 -3.202584513521621e-01 -3.202584513504543e-01 1.70780e-12 6.85925e-11 3 -2.471398631628105e-01 -2.471398631826998e-01 1.98892e-11 1.37710e-10 ----------------------------------------------------------------------------------------------------- 21 Ti 1 8.067307658064178e-01 8.067307657921815e-01 1.42363e-11 4.50044e-10 2 -6.714990251907560e-01 -6.714990252081384e-01 1.73824e-11 8.27229e-11 3 -7.389323775835758e-01 -7.389323775079312e-01 7.56446e-11 1.23027e-10 ----------------------------------------------------------------------------------------------------- 22 Ti 1 8.475081597611401e-01 8.475081597478509e-01 1.32893e-11 3.10834e-10 2 -1.861328015554936e-01 -1.861328015692514e-01 1.37578e-11 1.04053e-10 3 -1.427235237377535e+00 -1.427235237405185e+00 2.76497e-11 1.81049e-10 ----------------------------------------------------------------------------------------------------- 23 Ti 1 -3.304915503651321e-01 -3.304915503620623e-01 3.06982e-12 2.52359e-10 2 1.600197202293362e-01 1.600197202211622e-01 8.17404e-12 5.90072e-10 3 -2.833694333897871e-01 -2.833694334106532e-01 2.08661e-11 1.21446e-10 ----------------------------------------------------------------------------------------------------- 24 Ti 1 8.378780069448993e-01 8.378780069850601e-01 4.01608e-11 3.10146e-10 2 1.435621467467715e+00 1.435621467453246e+00 1.44691e-11 3.41383e-10 3 1.698633775996759e+00 1.698633776038414e+00 4.16553e-11 5.34679e-11 ----------------------------------------------------------------------------------------------------- 25 Ti 1 8.474987429008505e-01 8.474987429303557e-01 2.95052e-11 2.96899e-10 2 2.288004413729644e-01 2.288004413723146e-01 6.49869e-13 5.87924e-12 3 -3.770115575338218e-01 -3.770115575315431e-01 2.27868e-12 7.64687e-11 ----------------------------------------------------------------------------------------------------- 26 Ti 1 2.248820880256197e-02 2.248820883099933e-02 2.84374e-11 1.35269e-10 2 -6.884517453915586e-01 -6.884517453416347e-01 4.99240e-11 4.70382e-11 3 -5.710376670129693e-01 -5.710376670263144e-01 1.33451e-11 2.64981e-10 ----------------------------------------------------------------------------------------------------- 27 Ti 1 -6.597124380276992e-02 -6.597124382311206e-02 2.03421e-11 1.96223e-10 2 -1.054835112230541e+00 -1.054835112153054e+00 7.74869e-11 9.48368e-11 3 -6.523198494271477e-01 -6.523198494199961e-01 7.15161e-12 3.10685e-10 ----------------------------------------------------------------------------------------------------- 28 Ti 1 -6.659018210701433e-01 -6.659018210557961e-01 1.43472e-11 1.15455e-10 2 5.004181134677945e-01 5.004181134702040e-01 2.40952e-12 2.21500e-10 3 3.259156556666380e-01 3.259156556566442e-01 9.99378e-12 1.73326e-10 ----------------------------------------------------------------------------------------------------- 29 Ti 1 2.576440683632146e-01 2.576440683035215e-01 5.96931e-11 5.36754e-10 2 7.031211085899548e-01 7.031211086613302e-01 7.13754e-11 5.49935e-10 3 2.675697482365387e+00 2.675697482327777e+00 3.76104e-11 4.11170e-10 ----------------------------------------------------------------------------------------------------- 30 Ti 1 -2.199931283007387e-01 -2.199931283802417e-01 7.95029e-11 1.14966e-10 2 3.893613113743571e-02 3.893613113633352e-02 1.10219e-12 1.26010e-10 3 6.322950868103044e-01 6.322950867653744e-01 4.49301e-11 1.72402e-09 * ----------------------------------------------------------------------------------------------------- 31 Ti 1 -4.401937767906539e-01 -4.401937767902009e-01 4.52971e-13 1.56735e-10 2 5.529935081278111e-01 5.529935080722933e-01 5.55178e-11 2.97777e-10 3 -3.529681815571294e-01 -3.529681815002471e-01 5.68824e-11 2.92568e-10 ----------------------------------------------------------------------------------------------------- 32 Ti 1 9.544012504708306e-01 9.544012504187169e-01 5.21136e-11 1.21402e-10 2 1.705275475220464e-02 1.705275469968304e-02 5.25216e-11 3.19163e-10 3 -3.524046279745598e-01 -3.524046279616867e-01 1.28731e-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 3.714976300741566e-02 1.11095e-11 4.51199e-11 2 1.293161933434922e+00 1.293161933392098e+00 4.28249e-11 2.32411e-10 3 1.351054996424043e+00 1.351054996407728e+00 1.63152e-11 4.56635e-11 ----------------------------------------------------------------------------------------------------- 2 C 1 -1.949195189949214e+00 -1.949195189950423e+00 1.20859e-12 4.99789e-11 2 -8.192998737988718e-01 -8.192998738539244e-01 5.50526e-11 1.07695e-10 3 -4.240311780197148e-01 -4.240311779975700e-01 2.21449e-11 8.58956e-10 ----------------------------------------------------------------------------------------------------- 3 C 1 1.494455894388823e-01 1.494455894131366e-01 2.57457e-11 3.77783e-10 2 -8.343105088400335e-01 -8.343105088448877e-01 4.85412e-12 5.01210e-11 3 1.001526389893898e+00 1.001526389843282e+00 5.06164e-11 5.75049e-10 ----------------------------------------------------------------------------------------------------- 4 Ti 1 2.403250577316265e+00 2.403250577332312e+00 1.60467e-11 2.15961e-09 2 -3.110338341621519e+00 -3.110338341656955e+00 3.54361e-11 4.23716e-09 * 3 -1.297525584716195e+00 -1.297525584734943e+00 1.87477e-11 2.38773e-11 ----------------------------------------------------------------------------------------------------- 5 C 1 1.393266663875407e+00 1.393266663905653e+00 3.02460e-11 1.94867e-10 2 7.947778537010952e-01 7.947778537401277e-01 3.90324e-11 2.98909e-10 3 -4.207317592759373e-02 -4.207317593840683e-02 1.08131e-11 2.87656e-10 ----------------------------------------------------------------------------------------------------- 6 Ti 1 -2.035241985692072e+00 -2.035241985673494e+00 1.85776e-11 2.72396e-10 2 -8.018767337861832e-01 -8.018767337873233e-01 1.14009e-12 4.35026e-10 3 3.440799037402443e+00 3.440799037384660e+00 1.77827e-11 6.70637e-11 ----------------------------------------------------------------------------------------------------- 7 C 1 -1.472053416483687e+00 -1.472053416488511e+00 4.82370e-12 1.46195e-10 2 3.371074287043817e-01 3.371074287063316e-01 1.94994e-12 1.32408e-10 3 -3.394506257661207e-01 -3.394506257460054e-01 2.01154e-11 8.13330e-11 ----------------------------------------------------------------------------------------------------- 8 C 1 7.165850390325813e-01 7.165850390245223e-01 8.05900e-12 4.72882e-09 * 2 -2.084655106173106e+00 -2.084655106160250e+00 1.28564e-11 3.27789e-10 3 -1.046549661282566e+00 -1.046549661300208e+00 1.76426e-11 2.86011e-10 ----------------------------------------------------------------------------------------------------- 9 Ti 1 7.161846326664533e-01 7.161846326486917e-01 1.77616e-11 2.96808e-11 2 1.466377273270252e+00 1.466377273261497e+00 8.75522e-12 1.40016e-10 3 -5.107428325963168e-01 -5.107428325915661e-01 4.75076e-12 8.27689e-10 ----------------------------------------------------------------------------------------------------- 10 C 1 -1.067653500845338e+00 -1.067653500841741e+00 3.59690e-12 2.45441e-09 * 2 3.127547568945032e-01 3.127547568790474e-01 1.54558e-11 1.51407e-10 3 1.293795923597951e+00 1.293795923605761e+00 7.81020e-12 1.04903e-10 ----------------------------------------------------------------------------------------------------- 11 C 1 -3.006065520973876e+00 -3.006065520982539e+00 8.66285e-12 4.71612e-10 2 -1.009814688484811e+00 -1.009814688449463e+00 3.53479e-11 7.15730e-10 3 -1.930015002535439e+00 -1.930015002552297e+00 1.68576e-11 2.62834e-10 ----------------------------------------------------------------------------------------------------- 12 Ti 1 7.121310198544127e-01 7.121310198019943e-01 5.24184e-11 6.75351e-11 2 1.871791531041562e+00 1.871791531144499e+00 1.02937e-10 9.04424e-10 3 -2.544357021464263e+00 -2.544357021479406e+00 1.51426e-11 6.68095e-10 ----------------------------------------------------------------------------------------------------- 13 C 1 1.280045746931099e+00 1.280045746903676e+00 2.74230e-11 1.87157e-10 2 1.876129897269811e+00 1.876129897279191e+00 9.38005e-12 3.20721e-10 3 -1.574132057556738e+00 -1.574132057564840e+00 8.10174e-12 1.53715e-10 ----------------------------------------------------------------------------------------------------- 14 C 1 -1.537250584357119e+00 -1.537250584342441e+00 1.46780e-11 1.41138e-10 2 -4.478013570898425e-02 -4.478013571107946e-02 2.09521e-12 2.64261e-11 3 1.550325236855490e+00 1.550325236875299e+00 1.98090e-11 6.91307e-11 ----------------------------------------------------------------------------------------------------- 15 C 1 8.632875765593434e-01 8.632875765422841e-01 1.70594e-11 5.19771e-10 2 1.613243777213228e+00 1.613243777185578e+00 2.76503e-11 5.22533e-10 3 -6.156233141398632e-01 -6.156233141353195e-01 4.54370e-12 5.07646e-10 ----------------------------------------------------------------------------------------------------- 16 Ti 1 2.537592489986009e+00 2.537592489938114e+00 4.78950e-11 9.02589e-11 2 -1.902376991593863e+00 -1.902376991574298e+00 1.95646e-11 1.42969e-09 3 -6.144152301589526e+00 -6.144152301559288e+00 3.02380e-11 2.00608e-10 ----------------------------------------------------------------------------------------------------- 17 C 1 -1.363001197805364e+00 -1.363001197768651e+00 3.67131e-11 8.39164e-11 2 -1.906010847222082e-01 -1.906010847205118e-01 1.69637e-12 2.66309e-10 3 7.188007778063639e-01 7.188007778175789e-01 1.12150e-11 4.34934e-10 ----------------------------------------------------------------------------------------------------- 18 C 1 -2.646284592008805e+00 -2.646284591937177e+00 7.16280e-11 5.20141e-10 2 2.685102575037404e+00 2.685102575097797e+00 6.03939e-11 1.20305e-10 3 2.318346028834492e+00 2.318346028807946e+00 2.65459e-11 2.25593e-09 ----------------------------------------------------------------------------------------------------- 19 Ti 1 -1.573211713036229e+00 -1.573211713217776e+00 1.81547e-10 2.59726e-10 2 -1.448021959425811e+00 -1.448021959419834e+00 5.97744e-12 2.26166e-10 3 8.128933618180200e-01 8.128933618175128e-01 5.07150e-13 6.49277e-10 ----------------------------------------------------------------------------------------------------- 20 Ti 1 -1.017932110072423e+00 -1.017932110109312e+00 3.68887e-11 2.20069e-10 2 -7.568354080494527e-02 -7.568354083307813e-02 2.81329e-11 2.73073e-10 3 -1.039522998094151e+00 -1.039522998094831e+00 6.79901e-13 4.61288e-10 ----------------------------------------------------------------------------------------------------- 21 Ti 1 3.455801171478837e+00 3.455801171587895e+00 1.09058e-10 1.10019e-09 2 -2.538378544646601e+00 -2.538378544585297e+00 6.13047e-11 6.00283e-10 3 -7.024938281730606e+00 -7.024938281738491e+00 7.88525e-12 2.35283e-10 ----------------------------------------------------------------------------------------------------- 22 C 1 2.164865266892889e+00 2.164865266890903e+00 1.98552e-12 2.03178e-10 2 -4.871258924203944e-01 -4.871258923799846e-01 4.04098e-11 4.57870e-10 3 2.398342005798527e+00 2.398342005820529e+00 2.20024e-11 4.17785e-10 ----------------------------------------------------------------------------------------------------- 23 Ti 1 2.250190951291373e+00 2.250190951293377e+00 2.00462e-12 3.35864e-09 * 2 -9.869477246526398e-01 -9.869477246435662e-01 9.07363e-12 9.15142e-11 3 6.699141080915207e-01 6.699141080702691e-01 2.12517e-11 3.85778e-11 ----------------------------------------------------------------------------------------------------- 24 Ti 1 -1.846299600931542e+00 -1.846299601009191e+00 7.76488e-11 1.70181e-10 2 1.939141238216102e+00 1.939141238186806e+00 2.92963e-11 4.77858e-11 3 1.346723922182833e+00 1.346723922167944e+00 1.48885e-11 5.98614e-11 ----------------------------------------------------------------------------------------------------- 25 Ti 1 -2.061596908827949e+00 -2.061596908829473e+00 1.52456e-12 1.36844e-09 2 1.424513718413426e+00 1.424513718372667e+00 4.07590e-11 1.03884e-10 3 2.439626075874929e+00 2.439626075824440e+00 5.04894e-11 1.26066e-10 ----------------------------------------------------------------------------------------------------- 26 Ti 1 -3.390997684849125e+00 -3.390997684849729e+00 6.03961e-13 5.47689e-09 * 2 2.479829959137950e+00 2.479829959091718e+00 4.62319e-11 3.76983e-10 3 3.848353933749325e+00 3.848353933631703e+00 1.17622e-10 6.73886e-10 ----------------------------------------------------------------------------------------------------- 27 Ti 1 -1.177196896238194e+00 -1.177196896249414e+00 1.12204e-11 1.90767e-09 2 -1.855739649556756e+00 -1.855739649580523e+00 2.37672e-11 1.78811e-10 3 1.471330839835268e+00 1.471330839841781e+00 6.51257e-12 3.27601e-10 ----------------------------------------------------------------------------------------------------- 28 C 1 1.276705062656976e+00 1.276705062660007e+00 3.03135e-12 1.71746e-10 2 -1.392247747858364e+00 -1.392247747839085e+00 1.92797e-11 1.53610e-10 3 -1.654925241046236e+00 -1.654925241030446e+00 1.57900e-11 5.17562e-11 ----------------------------------------------------------------------------------------------------- 29 C 1 3.588488653026671e+00 3.588488653107817e+00 8.11458e-11 1.02286e-09 2 2.355546138891519e-01 2.355546139107377e-01 2.15858e-11 5.68159e-09 * 3 8.942289629464741e-01 8.942289629828543e-01 3.63801e-11 1.64543e-10 ----------------------------------------------------------------------------------------------------- 30 Ti 1 -5.017836002586991e-01 -5.017836003306168e-01 7.19177e-11 1.01367e-09 2 -1.228461629286462e+00 -1.228461629139675e+00 1.46786e-10 1.69917e-10 3 -2.319468303893850e-01 -2.319468303862501e-01 3.13494e-12 1.72010e-10 ----------------------------------------------------------------------------------------------------- 31 Ti 1 1.275397248444559e+00 1.275397248385645e+00 5.89144e-11 8.80254e-10 2 6.811091084237333e-01 6.811091084119814e-01 1.17519e-11 2.33868e-09 * 3 -9.666654275684784e-01 -9.666654275658831e-01 2.59526e-12 9.14237e-10 ----------------------------------------------------------------------------------------------------- 32 Ti 1 1.825377049881571e+00 1.825377050009646e+00 1.28075e-10 5.43477e-09 * 2 1.800064488734028e+00 1.800064488746015e+00 1.19871e-11 4.88748e-10 3 1.830589933311612e+00 1.830589933261116e+00 5.04963e-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 = ----------------------- = 3.71717e-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.